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  <metadata>
    <dcterms:identifier>ECHO:9TE6563P.xml</dcterms:identifier>
    <dcterms:creator identifier="GND:118645455">Apian, Petrus</dcterms:creator>
    <dcterms:title xml:lang="la">Instrvmentvm Sinvvm, sev primi mobilis</dcterms:title>
    <dcterms:alternative xml:lang="la">Instrumentum Sinuum, seu primi mobilis</dcterms:alternative>
    <dcterms:date xsi:type="dcterms:W3CDTF">1541</dcterms:date>
    <dcterms:language xsi:type="dcterms:ISO639-3">lat</dcterms:language>
    <dcterms:rights>CC-BY-SA</dcterms:rights>
    <dcterms:license xlink:href="http://creativecommons.org/licenses/by-sa/3.0/">CC-BY-SA</dcterms:license>
    <dcterms:rightsHolder xlink:href="http://www.mpiwg-berlin.mpg.de">Max Planck Institute for the History of Science, Library</dcterms:rightsHolder>
  </metadata>
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<pb file="0002" n="2"/>
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<div xml:id="echoid-div2" type="section" level="1" n="2">
<head xml:id="echoid-head1" xml:space="preserve">INSTRVMENTVM <lb/>SINVVM, SEV PRIMI MOBILIS, NV <lb/>PER A' PETRO APIANO INVENTVM, NVNC AVTEM <lb/>abeodem diligenter recognitum &amp; locupletatum. Cuius tractatione, cum <lb/>genuinus &amp; latiſsime patens Sinuum uſus clariſsime deprehenditur, tum uero <lb/>quicquid earundem Sinuum auxilio in rebus aſtronomicis ratiocinan-<lb/>do indagari poteſt, facilime ac celerrime conficitur.</head>
<p>
  <s xml:id="echoid-s1" xml:space="preserve">Adiectus eſt &amp; </s>
  <s xml:id="echoid-s2" xml:space="preserve">Quadrans Vniuerſalis ſeu Generalis, noua ſacie, in eundem <lb/>uſum fabreſactus. </s>
  <s xml:id="echoid-s3" xml:space="preserve">cuius uſu, quicquid ex tabulis Sinuum cõputãdo elici po <lb/>terat, ſine negotio, ſine´ numerorũ moleſtiore tractatiõe facilime ꝑſpicitur.</s>
  <s xml:id="echoid-s4" xml:space="preserve"/>
</p>
  <figure>
    <image file="0005-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0005-01"/>
  </figure>
<p>
  <s xml:id="echoid-s5" xml:space="preserve">Norimbergæ apud Iohan. </s>
  <s xml:id="echoid-s6" xml:space="preserve">Petreium, anno M. </s>
  <s xml:id="echoid-s7" xml:space="preserve">D. </s>
  <s xml:id="echoid-s8" xml:space="preserve">XLI.</s>
  <s xml:id="echoid-s9" xml:space="preserve"/>
</p>
<pb file="0006" n="6"/>
</div>
<div xml:id="echoid-div3" type="section" level="1" n="3">
<head xml:id="echoid-head2" xml:space="preserve">INSIGNIA DN. CHRISTHOPHORI</head>
<head xml:id="echoid-head3" xml:space="preserve">A STADION, EPISCOPI AVGVSTEN:</head>
  <figure>
    <image file="0006-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0006-01"/>
  </figure>
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<pb file="0007" n="7"/>
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<div xml:id="echoid-div4" type="section" level="1" n="4">
<head xml:id="echoid-head4" xml:space="preserve">AMPLISSIMO IN <lb/>CHRISTO PATRI AC DOMINO, <lb/>DOMINO CHRISTOPHORO A STADION, AVGV <lb/>guſtæ Vindelicorum Epiſcopo Reuerendiſsimo, Domino <lb/>&amp; Mœcenati ſuo Petrus Apianus S. D.</head>
<p>
  <s xml:id="echoid-s10" xml:space="preserve">MEMINIMVS adhuc, Ampliſsime Præſul, quanta <lb/>fuerint animi promptitudine noſtra, tuæ Celſitudini <lb/>ſuſcepta olim in honorem &amp; </s>
  <s xml:id="echoid-s11" xml:space="preserve">ornamentum familiæ Sta <lb/>dianæ conſcripta, in quibus <emph style="sc">Primi</emph> <emph style="sc">Mobilis</emph> commo <lb/>da ſub proſapiæ tuæ inſignibus æduntur. </s>
  <s xml:id="echoid-s12" xml:space="preserve">Eaipſa, lice <lb/>at citra iactantiam loqui, quamuis nihil deſiderent <lb/>quicquàm ad perfectionem ſui, numeris enim nihil <lb/>certius uſ extat, cum tamen altiora eadem ſint, quàm <lb/>ut â quouis accipi obuia poſsint, ob computi nimirum onus, quod unum <lb/>dum fugitur, neſcio quàm iniqué matheſi conſulitur, adactus ſum idem car-<lb/>men, alijs tamen fidibus recinere, ad id ſanè multo magis permotus, cum tan <lb/>tus emiſsi ſub nomine tuo, Ampliſs. </s>
  <s xml:id="echoid-s13" xml:space="preserve">Præſul, operis paſsim apud omnes Ma-<lb/>thematicos ſtudioſos cultus &amp; </s>
  <s xml:id="echoid-s14" xml:space="preserve">amor increbeſceret. </s>
  <s xml:id="echoid-s15" xml:space="preserve">Quadrantem igitur pri-<lb/>oribus adiecimus <emph style="sc">Primi</emph> <emph style="sc">Mobilis</emph> nuncupantes, eò quod nullus non pri-<lb/>mi mobilis uſus in eo depræhendatur, dicto uero citius quidlibet &amp; </s>
  <s xml:id="echoid-s16" xml:space="preserve">intra <lb/>calculos, ſola manus opera efficitur. </s>
  <s xml:id="echoid-s17" xml:space="preserve">Quod autem Tuæ Amplitudini eun-<lb/>dem dedicem, facit operis ſimilitudo, Cum enim antea ſub nomine Celſitu-<lb/>dinis Tuæ primum mobile tam fœliciter innotuerit, non potui non &amp; </s>
  <s xml:id="echoid-s18" xml:space="preserve">hanc <lb/>lucubrationis noſtræ partem, Tuæ Amplitudini offerre, quam iccirco ſpero <lb/>ſub tutela paſſuram ſua ædilibentius, quod &amp; </s>
  <s xml:id="echoid-s19" xml:space="preserve">in hoc creberrime ſeſelegat, <lb/>&amp; </s>
  <s xml:id="echoid-s20" xml:space="preserve">antea nobis ſinum ſuum non egre accedentibus obtulerit. </s>
  <s xml:id="echoid-s21" xml:space="preserve">Ne uero ſatis <lb/>fuit nobis hunc laborem Tuæ Reuerentiæ adſcribere tantum, niſi etiam ſin-<lb/>gula totius libri pronunciata per diem &amp; </s>
  <s xml:id="echoid-s22" xml:space="preserve">horam, nunquàm ſatis memoran-<lb/>dæ Sanctionis, ſiue intronizatiõis, ut uocant, tuæ illuſtraremus, &amp; </s>
  <s xml:id="echoid-s23" xml:space="preserve">hocideo <lb/>ut nemo non huius operis lector Celſitudinis tuæ frequenter meminiſſe co-<lb/>gatur unà mecum, quem ego perpetua memoria digniſsimum ſemper iudi-<lb/>caui. </s>
  <s xml:id="echoid-s24" xml:space="preserve">Atqui fortaſsis audiam opus non eſſe ſatis amplum ſeu folioſum, ſed <lb/>hic Anaxerxis Memoris appellati, meminiſſe tuam Celſitudinem uelim, <lb/>qui frigidam caua manu oblatam, non ſegnius hauſit, quàm ſi auro Lesbi-<lb/>um fuiſſet porrectum. </s>
  <s xml:id="echoid-s25" xml:space="preserve">Necnon Auguſti &amp; </s>
  <s xml:id="echoid-s26" xml:space="preserve">aliorum, quibus ſemper uolun <lb/>tas uidebatur pluris, quàm actus ipſe. </s>
  <s xml:id="echoid-s27" xml:space="preserve">Voluntatem enim non defuiſſe am-<lb/>pliora offerendi, Tua Celſitudo credat, ſed materiam. </s>
  <s xml:id="echoid-s28" xml:space="preserve">Ne uero deſpe-<lb/>ctui ſit, quia modicum eſt opellum. </s>
  <s xml:id="echoid-s29" xml:space="preserve">Ille enim non minus Homerum geſta <lb/>uit in nuce, ac ille, qui aureis literis eundem magnifice trãſcribi imperauit, &amp; </s>
  <s xml:id="echoid-s30" xml:space="preserve"><lb/>Maior in exiguo ſæpe extat pondere uirtus.</s>
  <s xml:id="echoid-s31" xml:space="preserve"/>
</p>
<pb file="0008" n="8"/>
<p>
  <s xml:id="echoid-s32" xml:space="preserve">utferè poeta inquit. </s>
  <s xml:id="echoid-s33" xml:space="preserve">Hoc enim in libro æque omnes <emph style="sc">Primi</emph> <emph style="sc">Mobilis</emph> con-<lb/>ſiderationes aſſequi licet, at in infinita magnitudine. </s>
  <s xml:id="echoid-s34" xml:space="preserve">Quid, quod in in-<lb/>numeris centonibus idem uix præſtari queat? </s>
  <s xml:id="echoid-s35" xml:space="preserve">Proinde reſtat, ut Tua Cel-<lb/>ſitudo recipiat animo, quo ſoluit antea, hoceſt, grato munus idem, copio-<lb/>ſius tamen redditum, aliquando auctiora eiuſdem generis receptura. </s>
  <s xml:id="echoid-s36" xml:space="preserve">Sic <lb/>igitur ualeat Reuerenda Paternitas Tua, Apianum´ clientem agnoſcat. <lb/></s>
  <s xml:id="echoid-s37" xml:space="preserve">Datum Ingolſtadij quinto Calendas Septembris, anno M. </s>
  <s xml:id="echoid-s38" xml:space="preserve">D. </s>
  <s xml:id="echoid-s39" xml:space="preserve">XL.</s>
</p>
<pb file="0009" n="9"/>
</div>
<div xml:id="echoid-div5" type="section" level="1" n="5">
<head xml:id="echoid-head5" xml:space="preserve">INDEX CENTVM PRONVNCIA-<lb/>torum, quæ hoclibello ſecundum genuinum &amp; <lb/>uniuerſalem uſum ſinuum declarantur.</head>
<head xml:id="echoid-head6" xml:space="preserve">PRONVNCIATVM I.</head>
<p>
  <s xml:id="echoid-s40" xml:space="preserve">1. </s>
  <s xml:id="echoid-s41" xml:space="preserve">Inſtrumentum hoc PRIMI MOBILIS componere, &amp; </s>
  <s xml:id="echoid-s42" xml:space="preserve">in genere uſum eius bre <lb/>uiter intelligere.</s>
  <s xml:id="echoid-s43" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s44" xml:space="preserve">Canones ſiue declaratio tabularum ſinuum.</s>
  <s xml:id="echoid-s45" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s46" xml:space="preserve">Appendix deuſu Quadrantis in eadem re.</s>
  <s xml:id="echoid-s47" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s48" xml:space="preserve">2. </s>
  <s xml:id="echoid-s49" xml:space="preserve">Sphæram octauam æquare cum nona &amp; </s>
  <s xml:id="echoid-s50" xml:space="preserve">decima, &amp; </s>
  <s xml:id="echoid-s51" xml:space="preserve">ſtellas fixas, ſimul ac planetarũ <lb/>auges per hoc uerificare.</s>
  <s xml:id="echoid-s52" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s53" xml:space="preserve">3. </s>
  <s xml:id="echoid-s54" xml:space="preserve">Latitudinem Lunæ ab eclyptica per ſinus colligere.</s>
  <s xml:id="echoid-s55" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s56" xml:space="preserve">4. </s>
  <s xml:id="echoid-s57" xml:space="preserve">Exipſa Lunæ latitudine, diſtantiam illius à capite uel cauda Draconis Lunæ (quã <lb/>in tabulis argumentum latitudinis Lunæ uocamus) cognoſcere.</s>
  <s xml:id="echoid-s58" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s59" xml:space="preserve">5. </s>
  <s xml:id="echoid-s60" xml:space="preserve">Cuiuſcun puncti imaginatione concepta in eclyptica, inuenire declinationem <lb/>ab æquinoctiali.</s>
  <s xml:id="echoid-s61" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s62" xml:space="preserve">6. </s>
  <s xml:id="echoid-s63" xml:space="preserve">Cognita Solis declinatione (quod &amp; </s>
  <s xml:id="echoid-s64" xml:space="preserve">in meridie &amp; </s>
  <s xml:id="echoid-s65" xml:space="preserve">oriente Sole facilime fieri po-<lb/>teſt) adhuc gradum illum zodiaci internoſcere, quem iſta declinatio tangit, at <lb/>unum cum eo punctum efficitur.</s>
  <s xml:id="echoid-s66" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s67" xml:space="preserve">7. </s>
  <s xml:id="echoid-s68" xml:space="preserve">Cuiuslibet arcus eclypticæ, qui principium ſuum ab æquinoctiali &amp; </s>
  <s xml:id="echoid-s69" xml:space="preserve">interſectione <lb/>cum eclyptica capit, aſcenſionem in ſphæra recta addiſcere.</s>
  <s xml:id="echoid-s70" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s71" xml:space="preserve">8. </s>
  <s xml:id="echoid-s72" xml:space="preserve">Habita iam aſcenſione recta æquinoctiali, arcum ipſius eclypticæ cum eo aſcenden <lb/>tem in ſphæra recta cognoſcere.</s>
  <s xml:id="echoid-s73" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s74" xml:space="preserve">9. </s>
  <s xml:id="echoid-s75" xml:space="preserve">Quum arcum aliquem eclypticæ cognoſcere cupis, cum quo æqualis arcus æqua-<lb/>toris aſcendit in ſphæra recta, iam´ principium ſiue terminus illius arcus tibi in-<lb/>notuit, alterum quo terminum ex artiſicioſa ſupputatione colligere.</s>
  <s xml:id="echoid-s76" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s77" xml:space="preserve">10. </s>
  <s xml:id="echoid-s78" xml:space="preserve">Punctum eclypticæ in qualibet quarta, qui terminat arcum illum, qui exceſsionem <lb/>habet ſuper aſcenſionem rectam, longe maximam, quam aliquis arcus eclypticæ <lb/>unquam habere poteſt, beneficio numerorum indagare.</s>
  <s xml:id="echoid-s79" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s80" xml:space="preserve">11. </s>
  <s xml:id="echoid-s81" xml:space="preserve">Si quis arcum eclypticæ &amp; </s>
  <s xml:id="echoid-s82" xml:space="preserve">aſcenſionem eius rectam utrun id in unam ſummam <lb/>redactũ tibi proponat, quemlibet arcũ eclypticæ &amp; </s>
  <s xml:id="echoid-s83" xml:space="preserve">æquatoris ſibi correſponden-<lb/>tis inde elicere.</s>
  <s xml:id="echoid-s84" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s85" xml:space="preserve">12. </s>
  <s xml:id="echoid-s86" xml:space="preserve">Cuiuslibet puncti eclypticæ uel etiam ſtellæ fixæ, cuius enim nota ſit declinatio, <lb/>amplitudinem ortiuam in quacun eleuatione poli perſcrutari.</s>
  <s xml:id="echoid-s87" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s88" xml:space="preserve">13. </s>
  <s xml:id="echoid-s89" xml:space="preserve">Cognita iam antea amplitudine, gradum inuenire zodiaci, qui amplitudinẽ iſtam <lb/>conſtituit.</s>
  <s xml:id="echoid-s90" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s91" xml:space="preserve">14. </s>
  <s xml:id="echoid-s92" xml:space="preserve">Altitudinem poli in ſingulos dies ex amplitudine ortiua uel occidua, Solis ſiue ſtel <lb/>larum, adpoſite inueſtigare.</s>
  <s xml:id="echoid-s93" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s94" xml:space="preserve">15. </s>
  <s xml:id="echoid-s95" xml:space="preserve">In qualibet regione differentiã inquirere aſcenſionalẽ, p quã longitudo dierũ &amp; </s>
  <s xml:id="echoid-s96" xml:space="preserve">no <lb/>ctiũ inuenitur, &amp; </s>
  <s xml:id="echoid-s97" xml:space="preserve">unde lõgitudo diurna per uniuerſum orbẽ facile cognoſci poteſt</s>
</p>
<p>
  <s xml:id="echoid-s98" xml:space="preserve">16. </s>
  <s xml:id="echoid-s99" xml:space="preserve">Longitudinem diurnam ſuper quodcun punctum eclypticæ alia quadam ratio-<lb/>ne addiſcere.</s>
  <s xml:id="echoid-s100" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s101" xml:space="preserve">17. </s>
  <s xml:id="echoid-s102" xml:space="preserve">Cognita regionis alicuius die longiſsima, aut alioqui propoſita, altitudinem poli, in <lb/>qua tanta eſt diei quantitas, ex ſphærica ſupputatione inuenire.</s>
  <s xml:id="echoid-s103" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s104" xml:space="preserve">18. </s>
  <s xml:id="echoid-s105" xml:space="preserve">Cuiuslibet arcus eclypticæ, qui incipiat in ſectione uernali, aſcenſionem obliquam <lb/>in quacun ſiue ciuitate ſiue regione ſupputare.</s>
  <s xml:id="echoid-s106" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s107" xml:space="preserve">19. </s>
  <s xml:id="echoid-s108" xml:space="preserve">Quod ſi forte aſcenſio obliqua iam antea fuerit cũ eleuatione poli cognita, adhuc ta <lb/>men gradũ eciypticæ ſimul tunc aſcendentẽ ſuper horizontẽ experiri &amp; </s>
  <s xml:id="echoid-s109" xml:space="preserve">indagare.</s>
  <s xml:id="echoid-s110" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s111" xml:space="preserve">20. </s>
  <s xml:id="echoid-s112" xml:space="preserve">Altitudinem Solis in circulo uerticali (dummodo ſit in ſigno aliquo ſeptentriona-<lb/>li) inueſtigare.</s>
  <s xml:id="echoid-s113" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s114" xml:space="preserve">21. </s>
  <s xml:id="echoid-s115" xml:space="preserve">Altitudinem ſeu eleuationẽ poli ex altitudine Solis in circulo uerticali inquirere.</s>
  <s xml:id="echoid-s116" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s117" xml:space="preserve">22. </s>
  <s xml:id="echoid-s118" xml:space="preserve">Gradum Solis &amp; </s>
  <s xml:id="echoid-s119" xml:space="preserve">quotidie &amp; </s>
  <s xml:id="echoid-s120" xml:space="preserve">expedite inuenire ex altitudine eiuſdem in circulo uer <lb/>ticali, ſi modo Sol fuerit in ſignis ſeptentrionalibus.</s>
  <s xml:id="echoid-s121" xml:space="preserve"/>
</p>
<pb file="0010" n="10" rhead="INDEX."/>
<p>
  <s xml:id="echoid-s122" xml:space="preserve">23. </s>
  <s xml:id="echoid-s123" xml:space="preserve">Cognita iam &amp; </s>
  <s xml:id="echoid-s124" xml:space="preserve">altitudine Solis in circulo uerticali, &amp; </s>
  <s xml:id="echoid-s125" xml:space="preserve">eleuatione poli, per utran <lb/>illam amplitudinem Solis ad eum diem, quo altitudinem Solis in circulo uertica-<lb/>li obſeruaſti, inuenire.</s>
  <s xml:id="echoid-s126" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s127" xml:space="preserve">24. </s>
  <s xml:id="echoid-s128" xml:space="preserve">Ex altitudine Solis in circulo uerticali, &amp; </s>
  <s xml:id="echoid-s129" xml:space="preserve">ex amplitudine Solis eiuſdẽ diei altitudi-<lb/>nẽ poli expedite inueſtigare, etiã ſi neſcias gradũ Solis ſimul &amp; </s>
  <s xml:id="echoid-s130" xml:space="preserve">declinationẽ illius</s>
</p>
<p>
  <s xml:id="echoid-s131" xml:space="preserve">25. </s>
  <s xml:id="echoid-s132" xml:space="preserve">Quocun tempore, ſiue qualibet hora, gradum eclypticæ, qui meridianum tangit, <lb/>ex ſphærica ſupputatione colligere.</s>
  <s xml:id="echoid-s133" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s134" xml:space="preserve">26. </s>
  <s xml:id="echoid-s135" xml:space="preserve">Quatuor illos angulos, quos eclyptica cauſſat cũ meridiano, ad unumquod pun-<lb/>ctum, quo eclyptica meridianum tangit, artificioſe cognoſcere.</s>
  <s xml:id="echoid-s136" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s137" xml:space="preserve">27. </s>
  <s xml:id="echoid-s138" xml:space="preserve">Eoſdem angulos quatuor, quos eclyptica facit cum meridiano, facilius inquirere.</s>
  <s xml:id="echoid-s139" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s140" xml:space="preserve">28. </s>
  <s xml:id="echoid-s141" xml:space="preserve">Angulos illos eclypticæ &amp; </s>
  <s xml:id="echoid-s142" xml:space="preserve">meridiani, adhuc tertia quadam ratione, à prioribus di-<lb/>uerſa, inueſtigare.</s>
  <s xml:id="echoid-s143" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s144" xml:space="preserve">29. </s>
  <s xml:id="echoid-s145" xml:space="preserve">Diſtantiam zenith à 90. </s>
  <s xml:id="echoid-s146" xml:space="preserve">gradu ab aſcendente, &amp; </s>
  <s xml:id="echoid-s147" xml:space="preserve">breuiſsime &amp; </s>
  <s xml:id="echoid-s148" xml:space="preserve">exactiſsime reperire</s>
</p>
<p>
  <s xml:id="echoid-s149" xml:space="preserve">30. </s>
  <s xml:id="echoid-s150" xml:space="preserve">Aſcendentem, hoc eſt, gradum eclypticæ, qui partiliter in horizonte conſtituitur, <lb/>quacun &amp; </s>
  <s xml:id="echoid-s151" xml:space="preserve">regione &amp; </s>
  <s xml:id="echoid-s152" xml:space="preserve">hora expedite cognoſcere.</s>
  <s xml:id="echoid-s153" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s154" xml:space="preserve">31. </s>
  <s xml:id="echoid-s155" xml:space="preserve">Angulum ab horizonte obliquo cum eclyptica cauſſatum, per expeditam ſupputa-<lb/>tionem cognoſcere.</s>
  <s xml:id="echoid-s156" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s157" xml:space="preserve">32. </s>
  <s xml:id="echoid-s158" xml:space="preserve">Quantitatem anguli ab horizonte et eclyptica cauſſati diuerſo modo inquirere, ha <lb/>bito tantum prius medij cœli gradu.</s>
  <s xml:id="echoid-s159" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s160" xml:space="preserve">33. </s>
  <s xml:id="echoid-s161" xml:space="preserve">Angulum occidentis, quem eclyptica cum horizonte efficit in parte occidua, prom <lb/>pte &amp; </s>
  <s xml:id="echoid-s162" xml:space="preserve">facile inueſtigare.</s>
  <s xml:id="echoid-s163" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s164" xml:space="preserve">34. </s>
  <s xml:id="echoid-s165" xml:space="preserve">Altitudinem Solis ſuper horizontem quotidie &amp; </s>
  <s xml:id="echoid-s166" xml:space="preserve">in ſingulas horas toto terrarum <lb/>orbe ex ſolerti quadam ſupputatione colligere.</s>
  <s xml:id="echoid-s167" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s168" xml:space="preserve">35. </s>
  <s xml:id="echoid-s169" xml:space="preserve">Eandem Solis altitudinem ſuper horizontem quacun hora, &amp; </s>
  <s xml:id="echoid-s170" xml:space="preserve">ubiuis gentium di <lb/>uerſa ratione indagare.</s>
  <s xml:id="echoid-s171" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s172" xml:space="preserve">36. </s>
  <s xml:id="echoid-s173" xml:space="preserve">Rurſus alio modo cognoſcere altitudinem Solis ſuper horizontem, omni die &amp; </s>
  <s xml:id="echoid-s174" xml:space="preserve">mo <lb/>mento per uniuerſum terrarum orbem.</s>
  <s xml:id="echoid-s175" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s176" xml:space="preserve">37. </s>
  <s xml:id="echoid-s177" xml:space="preserve">Adhuc diuerſa uia eandem Solis altitudinem ſupra horizontem in quacun eleua-<lb/>tione poli depræhendere.</s>
  <s xml:id="echoid-s178" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s179" xml:space="preserve">38. </s>
  <s xml:id="echoid-s180" xml:space="preserve">Etiamnum alia ratione altitudinem illam Solis ſupra horizontem ubiuis locorum <lb/>pulchre et expedite cognoſcere.</s>
  <s xml:id="echoid-s181" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s182" xml:space="preserve">39. </s>
  <s xml:id="echoid-s183" xml:space="preserve">Diſtantiam Solis ante meridiem per circulum magnum ab ipſo puncto interſecti-<lb/>onis æquatoris &amp; </s>
  <s xml:id="echoid-s184" xml:space="preserve">horizontis ſolerte inueſtigare.</s>
  <s xml:id="echoid-s185" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s186" xml:space="preserve">40. </s>
  <s xml:id="echoid-s187" xml:space="preserve">Angulum perquirere quem facitæquinoctialis cum circulo magno ducto per cor-<lb/>pus ſolare, &amp; </s>
  <s xml:id="echoid-s188" xml:space="preserve">ortum æquinoctialis iuxta punctum illud, ubi circulus iſte maior â <lb/>Sole ductus cum æquinoctiali horizontem attingit.</s>
  <s xml:id="echoid-s189" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s190" xml:space="preserve">41. </s>
  <s xml:id="echoid-s191" xml:space="preserve">Angulum etiam illum explorare, quem cum horizonte facit circulus magnus, du-<lb/>ctus à Sole ubicun ſito ad ortum æquinoctialem.</s>
  <s xml:id="echoid-s192" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s193" xml:space="preserve">42. </s>
  <s xml:id="echoid-s194" xml:space="preserve">Quãta ſit diſtãtia Solis aut ſtellæ â uero illo æꝗnoctiali ortu uel occaſu uerſus meri-<lb/>diem ſiue ſeptentrionem, aut uiciſsim à meridiano ad ortum uel occidentem, expe-<lb/>dite cognoſcere.</s>
  <s xml:id="echoid-s195" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s196" xml:space="preserve">43. </s>
  <s xml:id="echoid-s197" xml:space="preserve">Diſtantiam Solis horizontalem à circulo uerticali diuerſa ratione indagare, ſed e-<lb/>iuſmodi quæ ad omnes ſtellas fixas &amp; </s>
  <s xml:id="echoid-s198" xml:space="preserve">erroneas queat commode adhiberi.</s>
  <s xml:id="echoid-s199" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s200" xml:space="preserve">44. </s>
  <s xml:id="echoid-s201" xml:space="preserve">Altitudinem Solis ſupra horizontem omni momento, &amp; </s>
  <s xml:id="echoid-s202" xml:space="preserve">ubicun gentium adhuc <lb/>ſexta ratione inuenire.</s>
  <s xml:id="echoid-s203" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s204" xml:space="preserve">45. </s>
  <s xml:id="echoid-s205" xml:space="preserve">Diſtantiam Solis horizontalem à circulo uerticali alio modo perquirere.</s>
  <s xml:id="echoid-s206" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s207" xml:space="preserve">46. </s>
  <s xml:id="echoid-s208" xml:space="preserve">Angulum quem facit eclyptica cũ circulo altitudinis, quem Sol ſiue ſtella attingit <lb/>ad horam aliquam propoſitam expedite cognoſcere.</s>
  <s xml:id="echoid-s209" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s210" xml:space="preserve">47. </s>
  <s xml:id="echoid-s211" xml:space="preserve">Eundem hunc angulũ eclypticæ &amp; </s>
  <s xml:id="echoid-s212" xml:space="preserve">altitudinis circuli alio adhuc modo inueſtigare.</s>
  <s xml:id="echoid-s213" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s214" xml:space="preserve">48. </s>
  <s xml:id="echoid-s215" xml:space="preserve">Angulum eum ipſum quem duabus propoſitionibus oſtendimus adhuc alia ratio-<lb/>ne indicare.</s>
  <s xml:id="echoid-s216" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s217" xml:space="preserve">49. </s>
  <s xml:id="echoid-s218" xml:space="preserve">Angulum illum, de quo hactenus diſputatum eſt, etiamnum diuerſa uia inquirere.</s>
  <s xml:id="echoid-s219" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s220" xml:space="preserve">50. </s>
  <s xml:id="echoid-s221" xml:space="preserve">Cognito iã gradu aſcendentis, adhuc gradum eclypticæ ꝗ mediat cœlũ explorare.</s>
  <s xml:id="echoid-s222" xml:space="preserve"/>
</p>
<pb file="0011" n="11" rhead="INDEX."/>
<p>
  <s xml:id="echoid-s223" xml:space="preserve">51. </s>
  <s xml:id="echoid-s224" xml:space="preserve">Arcum circuli maioris, qui per utrun polum mundi &amp; </s>
  <s xml:id="echoid-s225" xml:space="preserve">corpus ſolare ducitur, at <lb/>alio nomine circulus horarius dicitur, quantus ille ſit à polo mundi arctico uſ ad <lb/>horizontem, per ſupputationem triangularem cognoſcere.</s>
  <s xml:id="echoid-s226" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s227" xml:space="preserve">52. </s>
  <s xml:id="echoid-s228" xml:space="preserve">Locum ſiue punctum horizontis, ubi linea horaria in plano horizontali, ſimiliter &amp; </s>
  <s xml:id="echoid-s229" xml:space="preserve"><lb/>circulus horarius in corpore ſphærico tangit horizontem, inuenire.</s>
  <s xml:id="echoid-s230" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s231" xml:space="preserve">53. </s>
  <s xml:id="echoid-s232" xml:space="preserve">Arcum illum horizontis inter meridianum &amp; </s>
  <s xml:id="echoid-s233" xml:space="preserve">circulum horarium comprehenſum <lb/>adhuc alia quadam ratione inueſtigare, iſtũ inquam, qui per locũ Solis ptenditur</s>
</p>
<p>
  <s xml:id="echoid-s234" xml:space="preserve">54. </s>
  <s xml:id="echoid-s235" xml:space="preserve">Arcum horizontis, quem arcus horarius inter ſeipſum &amp; </s>
  <s xml:id="echoid-s236" xml:space="preserve">meridianum includit, ad-<lb/>huc alia ea´ omnium facilima ratione perquirere.</s>
  <s xml:id="echoid-s237" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s238" xml:space="preserve">55. </s>
  <s xml:id="echoid-s239" xml:space="preserve">Arcum quo in circulo uerticali, inter circulum horarium &amp; </s>
  <s xml:id="echoid-s240" xml:space="preserve">meridianum interce-<lb/>ptum exacta &amp; </s>
  <s xml:id="echoid-s241" xml:space="preserve">diligenti ſupputatione indagare.</s>
  <s xml:id="echoid-s242" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s243" xml:space="preserve">56. </s>
  <s xml:id="echoid-s244" xml:space="preserve">Arcum circuli uerticalis, quem abſcindit circulus horarum, adhuc diuerſo modo <lb/>inueſtigare.</s>
  <s xml:id="echoid-s245" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s246" xml:space="preserve">57. </s>
  <s xml:id="echoid-s247" xml:space="preserve">Angulos horarios conficere ſuper quolibet plano, quæ quidem planæ ſuperficies à <lb/>ſuperficie plana horizontali inclinantur, &amp; </s>
  <s xml:id="echoid-s248" xml:space="preserve">tamen reſpectu ſuperficiei ipſius me-<lb/>ridiani ad angulos rectos ſunt compoſitæ.</s>
  <s xml:id="echoid-s249" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s250" xml:space="preserve">58. </s>
  <s xml:id="echoid-s251" xml:space="preserve">Cognito iam antea eclypticæ gradu, qui eſt in a ſcendente, ſimiliter &amp; </s>
  <s xml:id="echoid-s252" xml:space="preserve">habito gradu <lb/>æ quinoctialis coaſcendente, eleuationem poli inde elicere.</s>
  <s xml:id="echoid-s253" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s254" xml:space="preserve">59. </s>
  <s xml:id="echoid-s255" xml:space="preserve">Si quis ante nouerit duo puncta eclypticæ, &amp; </s>
  <s xml:id="echoid-s256" xml:space="preserve">arcum inter ea concluſum, ſimiliter <lb/>&amp; </s>
  <s xml:id="echoid-s257" xml:space="preserve">aſcenſionem obliquam (qui gradus ſunt æquatoris cum noto iſto loco eclypti <lb/>cæ in eadem regione coaſcendentes) inde quo eleuationem polarem eius regio <lb/>nis, in qua fit talis aſcenſio, colligere.</s>
  <s xml:id="echoid-s258" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s259" xml:space="preserve">60. </s>
  <s xml:id="echoid-s260" xml:space="preserve">Cognito antea &amp; </s>
  <s xml:id="echoid-s261" xml:space="preserve">gradu medĳ cœli, &amp; </s>
  <s xml:id="echoid-s262" xml:space="preserve">ſimul perſpecta amplitudine ortiua aſcẽden-<lb/>tis, altitudinem poli inde perquirere.</s>
  <s xml:id="echoid-s263" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s264" xml:space="preserve">61. </s>
  <s xml:id="echoid-s265" xml:space="preserve">Cognito iam gradu medĳ cœli, ſimiliter &amp; </s>
  <s xml:id="echoid-s266" xml:space="preserve">gradu aſcendentis, altitudinem poli in-<lb/>de cognoſcere.</s>
  <s xml:id="echoid-s267" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s268" xml:space="preserve">62. </s>
  <s xml:id="echoid-s269" xml:space="preserve">In quacun regione, perſpecta eleuatione poli, tempus quo punctum zodiaci ab <lb/>arcuper polos mundi &amp; </s>
  <s xml:id="echoid-s270" xml:space="preserve">arcum æquinoctialis ducto uſ ad circulum uerticalem <lb/>moueatur, dĳudicare.</s>
  <s xml:id="echoid-s271" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s272" xml:space="preserve">63. </s>
  <s xml:id="echoid-s273" xml:space="preserve">Intellecta iam altitudine poli, adhuc emetiri quanto tempore arcus aliquis eclypti-<lb/>cæ propoſitus à principio uſ in finem pertranſeat circulum uerticalem.</s>
  <s xml:id="echoid-s274" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s275" xml:space="preserve">64. </s>
  <s xml:id="echoid-s276" xml:space="preserve">Idem hoc tempus adhuc alio modo perquirere, at ea ueluti generalis eſt regula <lb/>ad totam eclypticam.</s>
  <s xml:id="echoid-s277" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s278" xml:space="preserve">65. </s>
  <s xml:id="echoid-s279" xml:space="preserve">Si in duabus regionibus altitudo poli ſit ignota, &amp; </s>
  <s xml:id="echoid-s280" xml:space="preserve">uno momento unus aſcendens <lb/>exiſtat, ſed ad meridianos eorum pertingat duplex eclypticæ pũctum etiam igno <lb/>tum, adhuc inſuper cognoſcere latitudines &amp; </s>
  <s xml:id="echoid-s281" xml:space="preserve">differentiam longitudinis earum.</s>
  <s xml:id="echoid-s282" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s283" xml:space="preserve">66. </s>
  <s xml:id="echoid-s284" xml:space="preserve">Ciuitatibus duabus eundem aſcendentem habentibus eadem hora &amp; </s>
  <s xml:id="echoid-s285" xml:space="preserve">momento, u-<lb/>triuſ etiam eleuationem poli perſpecta, differentiam longitudinum inter eas cõ <lb/>cluſum inuenire.</s>
  <s xml:id="echoid-s286" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s287" xml:space="preserve">67. </s>
  <s xml:id="echoid-s288" xml:space="preserve">Cognita duarum urbium latitudine, ſimiliter &amp; </s>
  <s xml:id="echoid-s289" xml:space="preserve">differentia ipſa lõgitudinis, an eun-<lb/>dem habeant uno momento aſcendentem uidere.</s>
  <s xml:id="echoid-s290" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s291" xml:space="preserve">68. </s>
  <s xml:id="echoid-s292" xml:space="preserve">Si quando duæ ciuitates, quarum cognitæ ſint latitudines &amp; </s>
  <s xml:id="echoid-s293" xml:space="preserve">longitudines, uel ſal-<lb/>tem differentia longitudinum, iam´ ex ſuperiori pronunciato inuentum ſit, eas <lb/>eodem momento quotidie ſemel aut bisunum habere aſcendentem, punctũ iam <lb/>iſtud eclypticæ in aſcendente expedite indagare.</s>
  <s xml:id="echoid-s294" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s295" xml:space="preserve">69. </s>
  <s xml:id="echoid-s296" xml:space="preserve">Quottidie ex altitudine &amp; </s>
  <s xml:id="echoid-s297" xml:space="preserve">Azimuth Solis eleuationem poli colligere.</s>
  <s xml:id="echoid-s298" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s299" xml:space="preserve">70. </s>
  <s xml:id="echoid-s300" xml:space="preserve">Si quando duorum locorum longitudines ſunt æquales, &amp; </s>
  <s xml:id="echoid-s301" xml:space="preserve">inſuper eorum latitudi-<lb/>nes notæ, at inæquales, diſtantiam inter ea ſecundum uiam directã inueſtigare.</s>
  <s xml:id="echoid-s302" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s303" xml:space="preserve">71. </s>
  <s xml:id="echoid-s304" xml:space="preserve">Quum loca duo uni ſubiecta ſunt meridiano, &amp; </s>
  <s xml:id="echoid-s305" xml:space="preserve">alterius tantum nota ſit latitudo &amp; </s>
  <s xml:id="echoid-s306" xml:space="preserve"><lb/>diſtantia ignota, inde latitudinem alterius elicere.</s>
  <s xml:id="echoid-s307" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s308" xml:space="preserve">72. </s>
  <s xml:id="echoid-s309" xml:space="preserve">Locis duobus æqualem poli altitudinem habentibus, quæ utra ſit nota, ſed ita, ut <lb/>diuerſis ſubiaceant meridianis, cognita etiam differentia longitudinis, adhuc eo-<lb/>rum inſuper diſtantiam cognoſcere.</s>
  <s xml:id="echoid-s310" xml:space="preserve"/>
</p>
<pb file="0012" n="12" rhead="INDEX."/>
<p>
  <s xml:id="echoid-s311" xml:space="preserve">73. </s>
  <s xml:id="echoid-s312" xml:space="preserve">Cognitis duorum locorum latitudine &amp; </s>
  <s xml:id="echoid-s313" xml:space="preserve">longitudine, diſtantiam inuenire.</s>
  <s xml:id="echoid-s314" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s315" xml:space="preserve">74. </s>
  <s xml:id="echoid-s316" xml:space="preserve">Duobus locis in gradibus longitudinis &amp; </s>
  <s xml:id="echoid-s317" xml:space="preserve">latitudinis cognitis, in quã mundi partẽ <lb/>alter ab altero declinet (angulũ hũc poſitionis alio nomine dicimus) inueſtigare.</s>
  <s xml:id="echoid-s318" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s319" xml:space="preserve">75. </s>
  <s xml:id="echoid-s320" xml:space="preserve">Propoſitis locis duobus, quorum alterius tantum latitudo ſimul &amp; </s>
  <s xml:id="echoid-s321" xml:space="preserve">longitudo ſit co <lb/>gnita, alterius autem utra ignota, angulus autem poſitionis ab altero conſtet <lb/>unà cum diſtantia ad alterum, inſuper eleuationem poli alterius loci, longitudi-<lb/>nem etiam ſiue diſtantiam longitudinis indagare.</s>
  <s xml:id="echoid-s322" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s323" xml:space="preserve">76. </s>
  <s xml:id="echoid-s324" xml:space="preserve">Cognita tantum unius loci propoſiti eleuatione polari ſimul et alterius, at hinc <lb/>etiam interca pedine habita inter utran, differentiam adhuc longitudinum &amp; </s>
  <s xml:id="echoid-s325" xml:space="preserve">an <lb/>gulum poſitionis ab altero ad alterum inuenire.</s>
  <s xml:id="echoid-s326" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s327" xml:space="preserve">77. </s>
  <s xml:id="echoid-s328" xml:space="preserve">Si trium locorum nota ſit intercapedo, duo etiam loca ex ĳs cognitas habeant ſuas <lb/>tum latitudines tum longitudines, adhuc tertĳ longitudinem &amp; </s>
  <s xml:id="echoid-s329" xml:space="preserve">latitudinem, an-<lb/>gulum´ poſitionis, inquirere.</s>
  <s xml:id="echoid-s330" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s331" xml:space="preserve">78. </s>
  <s xml:id="echoid-s332" xml:space="preserve">Arcum circuli uerticalis concluſum inter meridianum &amp; </s>
  <s xml:id="echoid-s333" xml:space="preserve">circulum poſitionis alicu <lb/>ius ſtellæ ſiue puncti in cœlo extra eclypticam, uel in ea conſiderare &amp; </s>
  <s xml:id="echoid-s334" xml:space="preserve">agnoſcere.</s>
  <s xml:id="echoid-s335" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s336" xml:space="preserve">79. </s>
  <s xml:id="echoid-s337" xml:space="preserve">Altitudinem poli arctici ſuper ſemicirculum poſitionis breuiſsime &amp; </s>
  <s xml:id="echoid-s338" xml:space="preserve">expeditiſsime <lb/>inueſtigare.</s>
  <s xml:id="echoid-s339" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s340" xml:space="preserve">80. </s>
  <s xml:id="echoid-s341" xml:space="preserve">Horam diurnam ex altitudine Solis ſuper horizontem in omni regione conĳcere.</s>
  <s xml:id="echoid-s342" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s343" xml:space="preserve">81. </s>
  <s xml:id="echoid-s344" xml:space="preserve">Altitudine poli Borealis ſuper ſemicirculum poſitionis cognita, etiam arcum æqua <lb/>toris inuenire, qui meridiano &amp; </s>
  <s xml:id="echoid-s345" xml:space="preserve">illo ſemicirculo poſitionis includitur.</s>
  <s xml:id="echoid-s346" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s347" xml:space="preserve">82. </s>
  <s xml:id="echoid-s348" xml:space="preserve">Quum iam altitudo poli ſuper ſemicirculum poſitionis cognita eſt, de hinc arcum <lb/>circuli uerticalis inter zenith &amp; </s>
  <s xml:id="echoid-s349" xml:space="preserve">iſtũ ſemicirculũ poſitionis cõcluſum inueſtigare.</s>
  <s xml:id="echoid-s350" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s351" xml:space="preserve">83. </s>
  <s xml:id="echoid-s352" xml:space="preserve">Si arcus æquatoris à meridiano ſumatur uſ ad ſemicirculum poſitionis, altitudi-<lb/>nem per hoc poliſuper ſemicirculum illum poſitionis perquirere.</s>
  <s xml:id="echoid-s353" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s354" xml:space="preserve">84. </s>
  <s xml:id="echoid-s355" xml:space="preserve">Altitudinem poli ſuper ſemicirculum poſitionis per arcum æquatoris inter eum &amp; </s>
  <s xml:id="echoid-s356" xml:space="preserve"><lb/>meridianum concluſum, diuerſa ratione colligere.</s>
  <s xml:id="echoid-s357" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s358" xml:space="preserve">85. </s>
  <s xml:id="echoid-s359" xml:space="preserve">Declinationem ſtellæ ab æquatore, ſi quam habet, cognoſcere.</s>
  <s xml:id="echoid-s360" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s361" xml:space="preserve">86. </s>
  <s xml:id="echoid-s362" xml:space="preserve">Declinationem ſtellæ alio &amp; </s>
  <s xml:id="echoid-s363" xml:space="preserve">iucundiore modo perquirere.</s>
  <s xml:id="echoid-s364" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s365" xml:space="preserve">87. </s>
  <s xml:id="echoid-s366" xml:space="preserve">Aſcenſionem rectam ſtellæ inuenire, puta gradum æquatoris, qui cum ſtella propo <lb/>ſita meridianum ſiue horizontem rectum attingit.</s>
  <s xml:id="echoid-s367" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s368" xml:space="preserve">88. </s>
  <s xml:id="echoid-s369" xml:space="preserve">Altitudinem poli ſupra horizontem quacun hora noctis, quum ſtellæ uidentur, <lb/>per totum annum ſine omni inſtrumento artificioſe dignoſcere.</s>
  <s xml:id="echoid-s370" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s371" xml:space="preserve">89. </s>
  <s xml:id="echoid-s372" xml:space="preserve">Punctum iſtud eclypticæ cum quo ſtella ſeu punctum quoduis cœli medium tan-<lb/>git, perſcrutari.</s>
  <s xml:id="echoid-s373" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s374" xml:space="preserve">90. </s>
  <s xml:id="echoid-s375" xml:space="preserve">Amplitudinem ortiuam &amp; </s>
  <s xml:id="echoid-s376" xml:space="preserve">occiduam ſtellarum fixarum &amp; </s>
  <s xml:id="echoid-s377" xml:space="preserve">erraticarum adinuenire.</s>
  <s xml:id="echoid-s378" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s379" xml:space="preserve">91. </s>
  <s xml:id="echoid-s380" xml:space="preserve">Aſcenſionẽ rectam ſtellarũ fixarũ &amp; </s>
  <s xml:id="echoid-s381" xml:space="preserve">erraticarum quàm expeditiſsime cognoſcere.</s>
  <s xml:id="echoid-s382" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s383" xml:space="preserve">92. </s>
  <s xml:id="echoid-s384" xml:space="preserve">Arcũ ſemidiurnũ ſtellæ &amp; </s>
  <s xml:id="echoid-s385" xml:space="preserve">eius etiam aſcenſionem obliquã in æquatore perſpicere.</s>
  <s xml:id="echoid-s386" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s387" xml:space="preserve">93. </s>
  <s xml:id="echoid-s388" xml:space="preserve">Cum quo gradu ſiue puncto eclypticæ quælibet ſtella fixa &amp; </s>
  <s xml:id="echoid-s389" xml:space="preserve">erratica, ſimiliter &amp; </s>
  <s xml:id="echoid-s390" xml:space="preserve">ali <lb/>ud quoduis punctum imaginarium Primi Mobilis ſuper horizontem obliquam <lb/>aſcendit, uel eum tangit, aut etiã in parte occidua demergitur, ſolerter indagare.</s>
  <s xml:id="echoid-s391" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s392" xml:space="preserve">94. </s>
  <s xml:id="echoid-s393" xml:space="preserve">Proiectionem radiorum per triangularem ſup putationem colligere.</s>
  <s xml:id="echoid-s394" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s395" xml:space="preserve">95. </s>
  <s xml:id="echoid-s396" xml:space="preserve">Interuallum apparitionis aut occultationis ſtellarum in arcu eclypticæ, ſubtiliter <lb/>explorare.</s>
  <s xml:id="echoid-s397" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s398" xml:space="preserve">96. </s>
  <s xml:id="echoid-s399" xml:space="preserve">Ex altitudine ſtellæ fixæ uel planetæ ſupra horizontem, etiã noctis horam elicere.</s>
  <s xml:id="echoid-s400" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s401" xml:space="preserve">97. </s>
  <s xml:id="echoid-s402" xml:space="preserve">Duarum ſtellarum fixarum uel errantium, diuerſas´ latitudinum denominationes <lb/>habentium, diſtantias ab inuicem colligere.</s>
  <s xml:id="echoid-s403" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s404" xml:space="preserve">98. </s>
  <s xml:id="echoid-s405" xml:space="preserve">Altitudinem ſtellæ ſupra horizontem exiſtentis, in omni regione omni´ hora ex-<lb/>acto calculo indagare.</s>
  <s xml:id="echoid-s406" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s407" xml:space="preserve">99. </s>
  <s xml:id="echoid-s408" xml:space="preserve">Diſtantiam ſtellæ horizontalem à circulo meridiano omnihora inueſtigare.</s>
  <s xml:id="echoid-s409" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s410" xml:space="preserve">100. </s>
  <s xml:id="echoid-s411" xml:space="preserve">Quocun anni tempore etiam in pauculis diebus per ſtellam incognitam &amp; </s>
  <s xml:id="echoid-s412" xml:space="preserve">ex-<lb/>ortum Solis, maximam Solis declinationem dignoſcere.</s>
  <s xml:id="echoid-s413" xml:space="preserve"/>
</p>
<pb file="0013" n="13"/>
</div>
<div xml:id="echoid-div6" type="section" level="1" n="6">
<head xml:id="echoid-head7" xml:space="preserve">PRONVNCIATA CEN-<lb/>TVM, CVM INTER PRETATIONIBVS, V-<lb/>TILITATIBVS, ET EXEMPLIS EORVNDEM APER-<lb/>tiſsimis, ſuper inſtrumento nouo Primi Mobilis, recens iam à Petro <lb/>Apiano cõpoſita &amp; conſcripta, magno futura uſui omnibus Aſtro <lb/>nomiæ ſtudioſis, fœliciter hic incipiunt.</head>
<head xml:id="echoid-head8" xml:space="preserve">PRONVNCIATVM PRIMVM.</head>
<p>
  <s xml:id="echoid-s414" xml:space="preserve">Inſtrumentum hoc <emph style="sc">Primi</emph> <emph style="sc">Mobilis</emph> componere, &amp; </s>
  <s xml:id="echoid-s415" xml:space="preserve">in genere uſum e-<lb/>ius breuiter intelligere.</s>
  <s xml:id="echoid-s416" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s417" xml:space="preserve">PRincipio cõpoſiturus inſtrumentũ, quo omne illud, q̊dcũ in uniuerſo pri <lb/>mo Mobili inquiri poteſt, inueniatur, Duc lineã rectam ea longitudine, q̃ <lb/>magnitudini ſiue quãtitati ꝓpoſiti inſtrumenti reſpondeat, Ad huius lineæ <lb/>finẽ ſeu extremitatẽ dextri lateris pone A, ex altera parte B. </s>
  <s xml:id="echoid-s418" xml:space="preserve">Deinde ex A <lb/>lineã erige perpendicularẽ, eadem longitudine plano´ æquali lineæ A B, <lb/>&amp; </s>
  <s xml:id="echoid-s419" xml:space="preserve">in altera extremitate q̃ eminet, ſcribe C. </s>
  <s xml:id="echoid-s420" xml:space="preserve">Mox circinũ altero illo pede fixo &amp; </s>
  <s xml:id="echoid-s421" xml:space="preserve">immoto <lb/>repone in A, mobilẽ aũt pedẽ educ extenſum in C uſ, &amp; </s>
  <s xml:id="echoid-s422" xml:space="preserve">ſic circulũ deſcribe à C uſ in <lb/>B, at hoc modo habebis ante te deſcriptum iamiam quadrantẽ, quartã. </s>
  <s xml:id="echoid-s423" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s424" xml:space="preserve">circuli totius <lb/>partẽ ex tribus illis literis A B C. </s>
  <s xml:id="echoid-s425" xml:space="preserve">Ad hæc circulũ iſtũ à B in C diuide in 90 partes æqua-<lb/>
<anchor type="note" xlink:label="note-0013-01a" xlink:href="note-0013-01"/>
les, id in hunc modũ. </s>
  <s xml:id="echoid-s426" xml:space="preserve">Primũ omniũ in tres partes æquales, deinde quãlibet earũ rurſus <lb/>in tres alias ꝑtes æquales, mox ſingulas illas adhuc partire in duas, &amp; </s>
  <s xml:id="echoid-s427" xml:space="preserve">has poſtremò in 5. <lb/></s>
  <s xml:id="echoid-s428" xml:space="preserve">at ſic circulũ habebis à B uſ in C diuiſum apte in 90. </s>
  <s xml:id="echoid-s429" xml:space="preserve">ꝑtes æquales, quas graduũ ap-<lb/>pellatione cõtinemus. </s>
  <s xml:id="echoid-s430" xml:space="preserve">Et hæc puncta graduũ occultè quidẽ deſcribi debent, ut facile de-<lb/>leri poſsint. </s>
  <s xml:id="echoid-s431" xml:space="preserve">Cæterũĳs ita peractis, porrò adhuc diuide lineã A B in duas ꝑ<unsure/>tes in pũcto <lb/>D, ſimiliter &amp; </s>
  <s xml:id="echoid-s432" xml:space="preserve">lineã A C in pũcto E, circinũ pone in D altero pede fixo, altero exten <lb/>ſo deſcribe circulũ ex A uſ in B, circinũ ita immotũ relinque, &amp; </s>
  <s xml:id="echoid-s433" xml:space="preserve">pedem alterũ colloca in <lb/>E, altero aũt ſimiliter duc ſemicirculũ ab Ã uſ in C, ita, ut duo illi interſectionẽ mutuã <lb/>habeant in pũcto F. </s>
  <s xml:id="echoid-s434" xml:space="preserve">At iſti iam ſemicirculi duo illi ſuntueri, qui ad diuiſionem ſinuum <lb/>&amp; </s>
  <s xml:id="echoid-s435" xml:space="preserve">neceſſario hic requirũtur &amp; </s>
  <s xml:id="echoid-s436" xml:space="preserve">adpoſite uſurpantur, q̊d hoc loco præmonuiſſe te oportu <lb/>it, nobis´ adeo conſultũ uiſum eſt, eo maxime ut deinceps ſcias ꝗd uelimus, quotieſcũ <lb/>de circulis ſinuũ diſſeremus. </s>
  <s xml:id="echoid-s437" xml:space="preserve">In pũcto aũt A filum adfigi oportet, quo uſui fit accommo <lb/>datior. </s>
  <s xml:id="echoid-s438" xml:space="preserve">Deinde punctis D E applica regulã, &amp; </s>
  <s xml:id="echoid-s439" xml:space="preserve">pinge aut trahe lineã occultam ex D in E <lb/>&amp; </s>
  <s xml:id="echoid-s440" xml:space="preserve">eam diuide p mediũ in puncto G, poſthac pone circinũ pede fixo, ſcilicet fixo in G, al-<lb/>tero extẽſo in B uel C deſcribe circulũ, &amp; </s>
  <s xml:id="echoid-s441" xml:space="preserve">ſic circulũ deſcribe à C uſ in B, ita tamẽ, ut ap <lb/>pareat circulus eminere aliquantulũ ultra B &amp; </s>
  <s xml:id="echoid-s442" xml:space="preserve">C. </s>
  <s xml:id="echoid-s443" xml:space="preserve">Iterũ expande circinũ, &amp; </s>
  <s xml:id="echoid-s444" xml:space="preserve">protrahe cir <lb/>culũ tantũ ſolummodo diſtantẽ à iam ducto circulo, ꝙ inter ipſos poſsint cadere ſingula <lb/>res graduũ diuiſiones. </s>
  <s xml:id="echoid-s445" xml:space="preserve">Rurſus iterũ comprime circinũ, &amp; </s>
  <s xml:id="echoid-s446" xml:space="preserve">depinge in eodẽ centro tertiũ <lb/>circulũ tantũ diſtantem à primo, ut inter ipſos poſsit ſcribi numerus graduũ diſtinctorũ <lb/>
<anchor type="figure" xlink:label="fig-0013-01a" xlink:href="fig-0013-01"/>
ꝑ 5 &amp; </s>
  <s xml:id="echoid-s447" xml:space="preserve">5. </s>
  <s xml:id="echoid-s448" xml:space="preserve">Hi circuli ſic rite deſcripti, cõſtituũt limbũ huius inſtru <lb/>mẽti. </s>
  <s xml:id="echoid-s449" xml:space="preserve">Demũ applica regulã cẽtro A &amp; </s>
  <s xml:id="echoid-s450" xml:space="preserve">fingulis diuiſionibus gra-<lb/>duũ in circulo B C occulto, &amp; </s>
  <s xml:id="echoid-s451" xml:space="preserve">ubi regula tangit iſtos circulos, <lb/>duc lineas minutas à primo citculo in <lb/>ſecũdũ, linea uero à 5. </s>
  <s xml:id="echoid-s452" xml:space="preserve">gradu ducenda <lb/>erit de ſecũdo circulo in tertiũ. </s>
  <s xml:id="echoid-s453" xml:space="preserve">Tandẽ <lb/>in ſpacio primi &amp; </s>
  <s xml:id="echoid-s454" xml:space="preserve">tertĳ, incipiẽdo à B <lb/>ſcribẽdo uerſus C in primo ſpacio 5. <lb/></s>
  <s xml:id="echoid-s455" xml:space="preserve">in ſecũdo 10, in tertio 15, &amp; </s>
  <s xml:id="echoid-s456" xml:space="preserve">ſic de alĳs <lb/>numeris ꝑ ꝗnariũ aſcẽdendo uſ ad <lb/>90. </s>
  <s xml:id="echoid-s457" xml:space="preserve">q̃ circa C ſedẽ ſibi uendicabunt. </s>
  <s xml:id="echoid-s458" xml:space="preserve"><lb/>Hactenus de compoſitiõe limbi Qua <lb/>drantis, cuius has ſume figuras.</s>
  <s xml:id="echoid-s459" xml:space="preserve"/>
</p>
<div xml:id="echoid-div6" type="float" level="2" n="1">
<note position="right" xlink:label="note-0013-01" xlink:href="note-0013-01a" xml:space="preserve"><emph style="it">Quomodo</emph> <lb/><emph style="it">Quadrans</emph> <lb/><emph style="it">in</emph> 90. <emph style="it">par-</emph> <lb/><emph style="it">tes diuidi</emph> <lb/><emph style="it">debeat.</emph></note>
  <figure xlink:label="fig-0013-01" xlink:href="fig-0013-01a">
    <image file="0013-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0013-01"/>
  </figure>
</div>
<pb file="0014" n="14" rhead="GENVINVS VS VS"/>
<p>
  <s xml:id="echoid-s460" xml:space="preserve">Ideo etiam potiſsimum hic mentionem fecimus duorum iſtorum ſemicirculorum, <lb/>quoniam iuxta utrũ illum ducendi tibi erunt adhuc duo circuli, &amp; </s>
  <s xml:id="echoid-s461" xml:space="preserve">illi quidem duo per <lb/>ſe nihil ſignificant, niſi ut inter eos graduum diuiſio ſimul et numeri conſignari poſsint, <lb/>ſicut in ultima figura manifeſte ſatis cernere potes. </s>
  <s xml:id="echoid-s462" xml:space="preserve">At in hunc modum apparet inde <lb/>imaginem relucere, ſimilima inſtrumento, quo lupis capiendis ſtrui ſolent inſidiæ. </s>
  <s xml:id="echoid-s463" xml:space="preserve">In <lb/>
<anchor type="note" xlink:label="note-0014-01a" xlink:href="note-0014-01"/>
ſuper lineam A B diuide in 100000. </s>
  <s xml:id="echoid-s464" xml:space="preserve">partes æquales, qui ſinus exiſtant totus ſiue perfe-<lb/>ctus, at diuiſionem hãc in partes 100000. </s>
  <s xml:id="echoid-s465" xml:space="preserve">eò magis tibi conſulo amplectendam, quòd <lb/>exempla omnia centum illarum propoſitionum per eiuſmodi ſinum perfectum ſuppu-<lb/>taui, id´ adeo feci libẽtius, quòd numerus ille ad hanc operationem mihi uidebatur om-<lb/>nium commodiſsimus.</s>
  <s xml:id="echoid-s466" xml:space="preserve"/>
</p>
<div xml:id="echoid-div7" type="float" level="2" n="2">
<note position="left" xlink:label="note-0014-01" xlink:href="note-0014-01a" xml:space="preserve"><emph style="it">Quare ſe-</emph> <lb/><emph style="it">midiameter</emph> <lb/>100000. <lb/><emph style="it">partes ha-</emph> <lb/><emph style="it">beat.</emph></note>
</div>
</div>
<div xml:id="echoid-div9" type="section" level="1" n="7">
<head xml:id="echoid-head9" xml:space="preserve">Sequitur ergo hic tabula, cuius iam <lb/>mentionem fecimus.</head>
<note position="right" xml:space="preserve"> <lb/>Puncta ſi \\ nusrecti. # g̃. # m̃. # Puncta ſi \\ nusrecti. # g̃. # m̃. # Puncta ſi \\ nus recti. # g̃. # m̃. # Puncta ſi \\ nus recti. # g̃. # m̃. <lb/>1 # 0 # 34 # 26 # 15 # 4 # 51 # 30 # 40 # 76 # 49 # 28 <lb/>2 # 1 # 9 # 27 # 15 # 40 # 52 # 31 # 20 # 77 # 50 # 21 <lb/>3 # 1 # 43 # 28 # 16 # 16 # 53 # 32 # 0 # 78 # 51 # 16 <lb/>4 # 2 # 18 # 29 # 16 # 51 # 54 # 32 # 41 # 79 # 52 # 11 <lb/>5 # 2 # 52 # 30 # 17 # 27 # 55 # 33 # 22 # 80 # 53 # 8 <lb/>6 # 3 # 26 # 31 # 18 # 4 # 56 # 34 # 3 # 81 # 54 # 6 <lb/>7 # 4 # 1 # 32 # 18 # 40 # 57 # 34 # 45 # 82 # 55 # 5 <lb/>8 # 4 # 35 # 33 # 19 # 16 # 58 # 35 # 27 # 83 # 56 # 6 <lb/>9 # 5 # 10 # 34 # 19 # 53 # 59 # 36 # 9 # 84 # 57 # 8 <lb/>10 # 5 # 44 # 35 # 20 # 29 # 60 # 36 # 52 # 85 # 58 # 13 <lb/>11 # 6 # 19 # 36 # 21 # 6 # 61 # 37 # 35 # 86 # 59 # 19 <lb/>12 # 6 # 54 # 37 # 21 # 43 # 62 # 38 # 19 # 87 # 60 # 28 <lb/>13 # 7 # 28 # 38 # 22 # 20 # 63 # 39 # 3 # 88 # 61 # 39 <lb/>14 # 8 # 3 # 39 # 22 # 57 # 64 # 39 # 48 # 89 # 62 # 52 <lb/>15 # 8 # 38 # 40 # 23 # 35 # 65 # 40 # 33 # 90 # 64 # 10 <lb/>16 # 9 # 12 # 41 # 24 # 12 # 66 # 41 # 18 # 91 # 65 # 30 <lb/>17 # 9 # 47 # 42 # 24 # 50 # 67 # 42 # 4 # 92 # 66 # 56 <lb/>18 # 10 # 22 # 43 # 25 # 28 # 68 # 42 # 51 # 93 # 68 # 26 <lb/>19 # 10 # 57 # 44 # 26 # 6 # 69 # 43 # 38 # 94 # 70 # 3 <lb/>20 # 11 # 32 # 45 # 26 # 45 # 70 # 44 # 26 # 95 # 71 # 48 <lb/>21 # 12 # 7 # 46 # 27 # 23 # 71 # 45 # 14 # 96 # 73 # 45 <lb/>22 # 12 # 43 # 47 # 28 # 2 # 72 # 46 # 3 # 97 # 75 # 56 <lb/>23 # 13 # 18 # 48 # 28 # 41 # 73 # 46 # 53 # 98 # 78 # 31 <lb/>24 # 13 # 53 # 49 # 29 # 21 # 74 # 47 # 42 # 99 # 81 # 54 <lb/>25 # 14 # 29 # 50 # 30 # 0 # 75 # 48 # 35 # 100 # 90 # 0 <lb/></note>
<pb file="0015" n="15" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
<p>
  <s xml:id="echoid-s467" xml:space="preserve">SEd ut nõnihil degenerali huius inſtrumẽti uſu dicamus, retulerit plurimũ, imò neceſ <lb/>ſariũ fuerit p̃mittere quædã, puta, ꝗd ſit Diameter, quid Chorda, quid etiã Sinus rect 9 <lb/>
<anchor type="note" xlink:label="note-0015-01a" xlink:href="note-0015-01"/>
&amp; </s>
  <s xml:id="echoid-s468" xml:space="preserve">quid ſituerſus. </s>
  <s xml:id="echoid-s469" xml:space="preserve">?</s>
  <s xml:id="echoid-s470" xml:space="preserve">?Diameter ſiue dimetiẽs circuli, eſt linea recta ꝑ eius umbilicum <lb/>trãſiens, illum´ in duo æqualia diuidens. </s>
  <s xml:id="echoid-s471" xml:space="preserve">?</s>
  <s xml:id="echoid-s472" xml:space="preserve">?Arcus eſt cuiuslibet circuli ſeu periferiæ <lb/>
<anchor type="note" xlink:label="note-0015-02a" xlink:href="note-0015-02"/>
portio. </s>
  <s xml:id="echoid-s473" xml:space="preserve">?</s>
  <s xml:id="echoid-s474" xml:space="preserve">?Chorda eſt linea recta ſecãs circulũ in duas portiones inæquales. </s>
  <s xml:id="echoid-s475" xml:space="preserve">?</s>
  <s xml:id="echoid-s476" xml:space="preserve">?Sinus <lb/>
<anchor type="note" xlink:label="note-0015-03a" xlink:href="note-0015-03"/>
eſt linea recta, diametro circuli lõgitudine uel potẽtia cõmenſurabilis. </s>
  <s xml:id="echoid-s477" xml:space="preserve">?</s>
  <s xml:id="echoid-s478" xml:space="preserve">?Sinus totus <lb/>
<anchor type="note" xlink:label="note-0015-04a" xlink:href="note-0015-04"/>
ſiue ꝑfectus eſt circuli ſemidiameter in aliquas ꝑtes diuiſa. </s>
  <s xml:id="echoid-s479" xml:space="preserve">?</s>
  <s xml:id="echoid-s480" xml:space="preserve">?Sinus diuiditur in Sinum <lb/>
<anchor type="note" xlink:label="note-0015-05a" xlink:href="note-0015-05"/>
rectũ ac uerſum. </s>
  <s xml:id="echoid-s481" xml:space="preserve">?</s>
  <s xml:id="echoid-s482" xml:space="preserve">?Sinus rectus ſubdiuidit̃ in primũ &amp; </s>
  <s xml:id="echoid-s483" xml:space="preserve">ſecũdũ. </s>
  <s xml:id="echoid-s484" xml:space="preserve">?</s>
  <s xml:id="echoid-s485" xml:space="preserve">?Sinus rectus pri-<lb/>mus eſt medietas chordæ arcus dupli ad arcũ, cuius eſt ſinus, ſiue dimidiũ chordæ reſpe-<lb/>ctu totius arcus. </s>
  <s xml:id="echoid-s486" xml:space="preserve">?</s>
  <s xml:id="echoid-s487" xml:space="preserve">?Sinus uerſus eſt portio diametri à ſinu recto ad periferiã cõprehen <lb/>
<anchor type="note" xlink:label="note-0015-06a" xlink:href="note-0015-06"/>
ſi, utpote ſagitta arcus. </s>
  <s xml:id="echoid-s488" xml:space="preserve">?</s>
  <s xml:id="echoid-s489" xml:space="preserve">?Sinus rectus ſecũdus eſt reſiduũ cuiuslibet arc9 ſubtracti ex <lb/>90. </s>
  <s xml:id="echoid-s490" xml:space="preserve">ſiue arcus ꝗ reſtat uſ ad cõplementũ quartæ circuli, is ſemper eſt æqualis ꝑti dime <lb/>tientis, quæ à cẽtro circuli ad ſinũ rectũ primũ terminatur. </s>
  <s xml:id="echoid-s491" xml:space="preserve">?</s>
  <s xml:id="echoid-s492" xml:space="preserve">?Sector circuli eſt figura <lb/>
<anchor type="note" xlink:label="note-0015-07a" xlink:href="note-0015-07"/>
q̃ continetur à duabus lineis recte à centro ad circumferentiã ductis, necnon ab arcu qui <lb/>
<anchor type="note" xlink:label="note-0015-08a" xlink:href="note-0015-08"/>
inter illos comprehẽditur. </s>
  <s xml:id="echoid-s493" xml:space="preserve">Verum hic quo teiſtud celare nolo, ꝙ inſtrumentũ hoc <lb/>oportet eſſe ſatis magnũ, omnino enim q̊ amplius fuerit, eò certius per illud operari pote <lb/>
<anchor type="note" xlink:label="note-0015-09a" xlink:href="note-0015-09"/>
ris. </s>
  <s xml:id="echoid-s494" xml:space="preserve">Quamuis ſi uoles, poteris q̊cũ alio numero ad hoc uti, alĳs tamẽ cõmodiores ſunt <lb/>numeri, qui unitatẽ habent cũ aliquot nullis 000 &amp;</s>
  <s xml:id="echoid-s495" xml:space="preserve">c. </s>
  <s xml:id="echoid-s496" xml:space="preserve">quales ſunt 10. </s>
  <s xml:id="echoid-s497" xml:space="preserve">100. </s>
  <s xml:id="echoid-s498" xml:space="preserve">1000. </s>
  <s xml:id="echoid-s499" xml:space="preserve">10000. <lb/></s>
  <s xml:id="echoid-s500" xml:space="preserve">100000 &amp;</s>
  <s xml:id="echoid-s501" xml:space="preserve">c. </s>
  <s xml:id="echoid-s502" xml:space="preserve">ſiquidẽ per iſtos operatio nõ paulo redditur facilior in multiplicando pari <lb/>ter &amp; </s>
  <s xml:id="echoid-s503" xml:space="preserve">diuidẽdo. </s>
  <s xml:id="echoid-s504" xml:space="preserve">Diuiſa igitur linea A B in hũc modũ, porrò circinũ altero pede repone <lb/>in A, alte℞ uero extẽde ad ſingula illa pũcta, extẽdens hoc pacto circinũ uſ ad ſemicir <lb/>culũ A F B, omnibus deinde illis in eũ circulũ ſinuũ redactis, numeros adſcribe incipien <lb/>do in B ꝑ F uſ ad A, ea´ dicentur puncta ſinus uerſi, quamobrẽ &amp; </s>
  <s xml:id="echoid-s505" xml:space="preserve">ſemicirculus ille cir <lb/>culus appellabitur ſinus uerſi. </s>
  <s xml:id="echoid-s506" xml:space="preserve">Deinceps adductis iam punctis iſtis à linea A B uſ in cir <lb/>
<anchor type="note" xlink:label="note-0015-10a" xlink:href="note-0015-10"/>
culũ A F B, remoueri omnino aut deleri debet linea A B. </s>
  <s xml:id="echoid-s507" xml:space="preserve">uniuerſa aũt operatio illa ſatis <lb/>patebit ex ſubiecta figura. </s>
  <s xml:id="echoid-s508" xml:space="preserve">?</s>
  <s xml:id="echoid-s509" xml:space="preserve">?Seꝗtur ita uſus huius ſemicirculi in hunc modum: </s>
  <s xml:id="echoid-s510" xml:space="preserve">Si <lb/>
<anchor type="figure" xlink:label="fig-0015-01a" xlink:href="fig-0015-01"/>
quando ſinũ uerſum ſcire cupis cuiuslibet arcus, filũ in centro A adfixũ <lb/>repone ſuper illũ gradum, &amp; </s>
  <s xml:id="echoid-s511" xml:space="preserve">ſtatim ubicun filum iſtud ſemicirculum <lb/>AFB attingit, ibi uidebis numerũ unà cũ punctis ſinus illius uerſi. </s>
  <s xml:id="echoid-s512" xml:space="preserve">Vi <lb/>ciſsim cum antea habes puncta ſinus uerſi, &amp; </s>
  <s xml:id="echoid-s513" xml:space="preserve">hinc deſideras arcum eius <lb/>cognoſcere, Age filum colloca ſuper illa puncta ſinus uerſi in ſemicir-<lb/>culo AFB, &amp; </s>
  <s xml:id="echoid-s514" xml:space="preserve">eo quo filum tanget circulũ AC, ſcilicet limbum exteri <lb/>orem, ibi noris eſſe arcũ illorũ punctorũ ſinus uerſi propoſiti. </s>
  <s xml:id="echoid-s515" xml:space="preserve">Quod <lb/>ſi &amp; </s>
  <s xml:id="echoid-s516" xml:space="preserve">alte℞ ſemicirculũ AFC cupis in pũcta ſinus recti diuidere, ſemper <lb/>tibi ꝓpone 10. </s>
  <s xml:id="echoid-s517" xml:space="preserve">aut 100 &amp;</s>
  <s xml:id="echoid-s518" xml:space="preserve">c. </s>
  <s xml:id="echoid-s519" xml:space="preserve">ſecũdũ q̊d plura puncta habes in ſinu per-<lb/>fecto, hoc eſt in tota ſemidiametro AB. </s>
  <s xml:id="echoid-s520" xml:space="preserve">Vt ſi iã lineã AB in 100000. <lb/></s>
  <s xml:id="echoid-s521" xml:space="preserve">partes habes diuiſam (nõ ꝙ totidẽ pũcta poſsis in ea conſignare, q̊rũ quodlibet ſignificet <lb/>unũ, ſed hoc ſatis eſt, ſi unũquod punctũ deſignet 100. </s>
  <s xml:id="echoid-s522" xml:space="preserve">aut 10. </s>
  <s xml:id="echoid-s523" xml:space="preserve">aut 5.) </s>
  <s xml:id="echoid-s524" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s525" xml:space="preserve">porrò ſinũ re-<lb/>ctum 100000. </s>
  <s xml:id="echoid-s526" xml:space="preserve">punctorũ uis in circulũ AFC conſcribere, &amp; </s>
  <s xml:id="echoid-s527" xml:space="preserve">cõprehendere in 100. </s>
  <s xml:id="echoid-s528" xml:space="preserve">pun-<lb/>ctis, ita, ꝙ unaquæ diuiſio cõprehendit 1000. </s>
  <s xml:id="echoid-s529" xml:space="preserve">tũc ſanè ſubtrahe 1000. </s>
  <s xml:id="echoid-s530" xml:space="preserve">à toto ſinu qui in <lb/>hoc exemplo eſſe debet 100000. </s>
  <s xml:id="echoid-s531" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s532" xml:space="preserve">remanebũt 99000. </s>
  <s xml:id="echoid-s533" xml:space="preserve">qui ſinus erit uerſus, cuius ſi arcũ <lb/>ex ſupra dictis quæras, inuenies 88. </s>
  <s xml:id="echoid-s534" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s535" xml:space="preserve">26. </s>
  <s xml:id="echoid-s536" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s537" xml:space="preserve">ea ſubtrahe à 90. </s>
  <s xml:id="echoid-s538" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s539" xml:space="preserve">reſidui erũt o. </s>
  <s xml:id="echoid-s540" xml:space="preserve">gr. </s>
  <s xml:id="echoid-s541" xml:space="preserve">34. </s>
  <s xml:id="echoid-s542" xml:space="preserve"><lb/>minut. </s>
  <s xml:id="echoid-s543" xml:space="preserve">Iam uero filũ repone ſuper o. </s>
  <s xml:id="echoid-s544" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s545" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s546" xml:space="preserve">34. </s>
  <s xml:id="echoid-s547" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s548" xml:space="preserve">numerãdo à Buerſus C, &amp; </s>
  <s xml:id="echoid-s549" xml:space="preserve">in eũ locũ <lb/>quo tanget circulũ AFC, adponito punctũ 1000. </s>
  <s xml:id="echoid-s550" xml:space="preserve">puncta ſinus recti deſignans ex illis <lb/>100000. </s>
  <s xml:id="echoid-s551" xml:space="preserve">pũctis. </s>
  <s xml:id="echoid-s552" xml:space="preserve">Quod ſi aũt ſinus totus ſiue perfectus fuerit 10000. </s>
  <s xml:id="echoid-s553" xml:space="preserve">tũc punctũ illud ſi-<lb/>gnificat 100. </s>
  <s xml:id="echoid-s554" xml:space="preserve">rurſus ſi ſit ſinus perfectus 1000. </s>
  <s xml:id="echoid-s555" xml:space="preserve">punctũ hoc deſignabit 10. </s>
  <s xml:id="echoid-s556" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s557" xml:space="preserve">ſi fuerit ſinus <lb/>perfectus 100. </s>
  <s xml:id="echoid-s558" xml:space="preserve">punctũ iſtud ſignabit unũ tantũ. </s>
  <s xml:id="echoid-s559" xml:space="preserve">At eo modo operaberis cum ſingulis <lb/>numeris prædictis, qñ locũ eius in ſemicirculo AFC quæris &amp; </s>
  <s xml:id="echoid-s560" xml:space="preserve">ſcire deſideras. </s>
  <s xml:id="echoid-s561" xml:space="preserve">Mihi au <lb/>tem conſultiſsimũ eſſe uidetur, ſi ſemicirculũ illũ diuidas in 100. </s>
  <s xml:id="echoid-s562" xml:space="preserve">partes, ſicut hic ſeꝗtur. </s>
  <s xml:id="echoid-s563" xml:space="preserve"><lb/>Principio ſemidiametrũ AB diuide in 100. </s>
  <s xml:id="echoid-s564" xml:space="preserve">partes æquales, adſcribe etiã numeros ſingu <lb/>larũ partiũ occulte ꝑ quinarios uel denarios retrorſum à B in A at ea pũcta erunt ſinus <lb/>uerſi, q̃ deinde, modo quo ſupra diximus, transfer cũ circino in ſemicirculũ AFB, adſcri <lb/>bendo numeros q̊ pari modo ſicut in ſemidiametro AB feciſti. </s>
  <s xml:id="echoid-s565" xml:space="preserve">Mox pũcta ſimul &amp; </s>
  <s xml:id="echoid-s566" xml:space="preserve">nu
<pb file="0016" n="16" rhead="GENVINVS VSVS"/>
meros in linea AB dele, quia amplius nulli erũt uſui. </s>
  <s xml:id="echoid-s567" xml:space="preserve">Totidem etiã puncta eſſe debebũt <lb/>ſinus recti, ea ſic inuenies. </s>
  <s xml:id="echoid-s568" xml:space="preserve">Propone tibi tabulã hic ſequentẽ, quæ in prima linea continet <lb/>100. </s>
  <s xml:id="echoid-s569" xml:space="preserve">uerſus unũquod repoliti ſunt gradus aliq̊t cũ minutis, id aũt quid ſit, hoc modo in <lb/>telliges. </s>
  <s xml:id="echoid-s570" xml:space="preserve">Quod ſi centeſimã partẽ cupis in ſemicirculũ A F C conſignare, filũ colloca ſu-<lb/>per 0. </s>
  <s xml:id="echoid-s571" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s572" xml:space="preserve">22. </s>
  <s xml:id="echoid-s573" xml:space="preserve">minut. </s>
  <s xml:id="echoid-s574" xml:space="preserve">iuxta literã B, &amp; </s>
  <s xml:id="echoid-s575" xml:space="preserve">ubicũ filum attinget ſemicirculũ A F C, ibi pri <lb/>mam partem ex centum repone. </s>
  <s xml:id="echoid-s576" xml:space="preserve">Rurſus ſi duo uis imponere in ſinu recto, filum age po-<lb/>
<anchor type="figure" xlink:label="fig-0016-01a" xlink:href="fig-0016-01"/>
nito ſuper 1. </s>
  <s xml:id="echoid-s577" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s578" xml:space="preserve">9. </s>
  <s xml:id="echoid-s579" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s580" xml:space="preserve">illud ubi tanget ſemicirculũ A F C, ibi conſigna <lb/>2000. </s>
  <s xml:id="echoid-s581" xml:space="preserve">Etin hũc modum operaretam diu, donec ſemicirculũ iſtum di-<lb/>uiſeris in centum partes, numeros quo adſcribe ab Auerſus C. </s>
  <s xml:id="echoid-s582" xml:space="preserve">Et ſic <lb/>totidem habebis pũcta ſinus recti quotuerſi ſeu perfecti. </s>
  <s xml:id="echoid-s583" xml:space="preserve">Hinc ſi adhuc <lb/>puncta ſinus uerſi in aliquot partes cupis ſubdiuidere, puto in 10. </s>
  <s xml:id="echoid-s584" xml:space="preserve">uel <lb/>100. </s>
  <s xml:id="echoid-s585" xml:space="preserve">ut hic, operæprecium fuerit te etiam puncta ſinus recti in tot par-<lb/>tes diſſecare. </s>
  <s xml:id="echoid-s586" xml:space="preserve">ne magnopere refert, ſi ea diuidas in tot partes æquales, <lb/>quamuis in ſe ſint inæquales. </s>
  <s xml:id="echoid-s587" xml:space="preserve">Quomodo autem in quibuſdã locis quan <lb/>dam diminutionem partium iſtarum facere debeas, ex ipſo aſpectu tu-<lb/>opte marte facile conijcies.</s>
  <s xml:id="echoid-s588" xml:space="preserve"/>
</p>
<div xml:id="echoid-div9" type="float" level="2" n="1">
<note position="right" xlink:label="note-0015-01" xlink:href="note-0015-01a" xml:space="preserve"><emph style="it">Diameter</emph> <lb/><emph style="it">quid.</emph></note>
<note position="right" xlink:label="note-0015-02" xlink:href="note-0015-02a" xml:space="preserve"><emph style="it">Arcus.</emph></note>
<note position="right" xlink:label="note-0015-03" xlink:href="note-0015-03a" xml:space="preserve"><emph style="it">Chorda.</emph></note>
<note position="right" xlink:label="note-0015-04" xlink:href="note-0015-04a" xml:space="preserve"><emph style="it">Sinus.</emph></note>
<note position="right" xlink:label="note-0015-05" xlink:href="note-0015-05a" xml:space="preserve"><emph style="it">Sinus totus</emph> <lb/><emph style="it">ſiue perfe-</emph> <lb/><emph style="it">ctus quid.</emph></note>
<note position="right" xlink:label="note-0015-06" xlink:href="note-0015-06a" xml:space="preserve"><emph style="it">Sinus rect<emph style="sub">9</emph></emph> <lb/><emph style="it">dupliater</emph> <lb/><emph style="it">diuiditur.</emph></note>
<note position="right" xlink:label="note-0015-07" xlink:href="note-0015-07a" xml:space="preserve"><emph style="it">Sinus uerſ<emph style="sub">9</emph></emph> <lb/><emph style="it">quid.</emph></note>
<note position="right" xlink:label="note-0015-08" xlink:href="note-0015-08a" xml:space="preserve"><emph style="it">Sinus rect<emph style="sub">9</emph></emph> <lb/><emph style="it">ſecundus.</emph></note>
<note position="right" xlink:label="note-0015-09" xlink:href="note-0015-09a" xml:space="preserve"><emph style="it">Sector cir-</emph> <lb/><emph style="it">culi.</emph></note>
<note position="right" xlink:label="note-0015-10" xlink:href="note-0015-10a" xml:space="preserve"><emph style="it">Vſus huius</emph> <lb/><emph style="it">ſemiarculi.</emph></note>
  <figure xlink:label="fig-0015-01" xlink:href="fig-0015-01a">
    <image file="0015-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0015-01"/>
  </figure>
  <figure xlink:label="fig-0016-01" xlink:href="fig-0016-01a">
    <image file="0016-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0016-01"/>
  </figure>
</div>
<p>
  <s xml:id="echoid-s589" xml:space="preserve">Faciem ita huius iam præparati inſtrumenti hic tibi propoſitã rectius intuere.</s>
  <s xml:id="echoid-s590" xml:space="preserve"/>
</p>
  <figure>
    <image file="0016-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0016-02"/>
  </figure>
<pb file="0017" n="17"/>
<note position="right" xml:space="preserve"> <lb/>########## Tabula Sinuum rectorum ſiue ſemichordarum, minutim extenſa. <lb/># 0 # 1 # 2 # 3 # 4 # 5 # 6 # 7 # 8 # 9 <lb/>m. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. <lb/>0 # 00 # 1745 # 3489 # 5233 # 6975 # 8715 # 10452 # 12186 # 13917 # 15643 <lb/>1 # 29 # 1774 # 3519 # 5262 # 7004 # 8744 # 10481 # 12215 # 13946 # 15672 <lb/>2 # 58 # 1803 # 3548 # 5291 # 7033 # 8773 # 10510 # 12244 # 13974 # 15700 <lb/>3 # 87 # 1832 # 3577 # 5320 # 7062 # 8802 # 10639 # 12273 # 14003 # 15729 <lb/>4 # 116 # 1861 # 3606 # 5349 # 7091 # 8831 # 10568 # 12302 # 14032 # 15758 <lb/>5 # 145 # 1890 # 3635 # 5378 # 7120 # 8860 # 10597 # 12331 # 14061 # 15787 <lb/>6 # 174 # 1919 # 3664 # 5407 # 7149 # 8889 # 10626 # 12360 # 14090 # 15815 <lb/>7 # 203 # 1948 # 3693 # 5436 # 7178 # 8918 # 10655 # 12389 # 14118 # 15844 <lb/>8 # 232 # 1977 # 3722 # 5465 # 7207 # 8947 # 10684 # 12417 # 14147 # 15873 <lb/>9 # 261 # 2007 # 3751 # 5495 # 7236 # 8976 # 10713 # 12446 # 14176 # 15991 <lb/>10 # 290 # 2036 # 3780 # 5524 # 7265 # 9005 # 10742 # 12475 # 14205 # 15930 <lb/>11 # 319 # 2065 # 3809 # 5553 # 7294 # 9034 # 10771 # 12504 # 14234 # 15959 <lb/>12 # 349 # 2094 # 3838 # 5582 # 7323 # 9063 # 10799 # 12533 # 14262 # 15988 <lb/>13 # 378 # 2123 # 3867 # 5611 # 7352 # 9092 # 10828 # 12562 # 14291 # 16016 <lb/>14 # 407 # 2152 # 3896 # 5649 # 7381 # 9121 # 10857 # 12591 # 14320 # 16045 <lb/>15 # 436 # 2181 # 3925 # 5669 # 7410 # 9150 # 10886 # 12619 # 14349 # 16074 <lb/>16 # 465 # 2210 # 3955 # 5698 # 7439 # 9179 # 10915 # 12648 # 14378 # 16102 <lb/>17 # 494 # 2239 # 3984 # 5727 # 7468 # 9208 # 10944 # 12677 # 14406 # 16131 <lb/>18 # 523 # 2268 # 4013 # 5756 # 7497 # 9237 # 10973 # 12706 # 14435 # 16160 <lb/>19 # 552 # 2297 # 4042 # 5785 # 7526 # 9266 # 11002 # 12735 # 14464 # 16189 <lb/>20 # 581 # 2326 # 4071 # 5814 # 7555 # 9294 # 11031 # 12764 # 14493 # 16217 <lb/>21 # 610 # 2355 # 4100 # 5843 # 7584 # 9323 # 11060 # 12793 # 14521 # 16246 <lb/>22 # 639 # 2385 # 4129 # 5872 # 7613 # 9352 # 11089 # 12821 # 14550 # 16275 <lb/>23 # 669 # 2414 # 4158 # 5901 # 7642 # 9381 # 11117 # 12850 # 14579 # 16303 <lb/>24 # 698 # 2443 # 4187 # 5930 # 7671 # 9410 # 11146 # 12879 # 14608 # 16332 <lb/>25 # 727 # 2472 # 4216 # 5959 # 7700 # 9439 # 11175 # 12908 # 14637 # 16361 <lb/>26 # 756 # 2501 # 4245 # 5988 # 7729 # 9468 # 11204 # 12937 # 14665 # 16379 <lb/>27 # 785 # 2530 # 4274 # 6017 # 7758 # 9497 # 11233 # 12966 # 14694 # 16418 <lb/>28 # 814 # 2559 # 4303 # 6046 # 7787 # 9526 # 11262 # 12994 # 14723 # 16447 <lb/>29 # 843 # 2588 # 4332 # 6075 # 7816 # 9555 # 11291 # 13023 # 14752 # 16476 <lb/>30 # 873 # 2617 # 4361 # 6104 # 7845 # 9584 # 11320 # 13052 # 14780 # 16504 <lb/>31 # 901 # 2646 # 4391 # 6133 # 7874 # 9613 # 11349 # 13081 # 14809 # 16533 <lb/>32 # 930 # 2675 # 4420 # 6162 # 7903 # 9642 # 11378 # 13110 # 14838 # 16562 <lb/>33 # 959 # 2704 # 4449 # 6191 # 7932 # 9671 # 11407 # 13139 # 14867 # 16590 <lb/>34 # 989 # 2734 # 4478 # 6220 # 7961 # 9700 # 11435 # 13167 # 14896 # 16619 <lb/>35 # 1018 # 2763 # 4507 # 6250 # 7990 # 9729 # 11464 # 13196 # 14924 # 16648 <lb/>36 # 1047 # 2792 # 4536 # 6279 # 8019 # 9758 # 11493 # 13225 # 14953 # 16676 <lb/>37 # 1076 # 2821 # 4565 # 6308 # 8048 # 9787 # 11522 # 13254 # 14982 # 16705 <lb/>38 # 1105 # 2850 # 4594 # 6337 # 8077 # 9816 # 11551 # 13283 # 15011 # 16734 <lb/>39 # 1134 # 2879 # 4622 # 6366 # 8106 # 9845 # 11580 # 13312 # 15039 # 16762 <lb/>40 # 1163 # 2908 # 4652 # 6395 # 8135 # 9874 # 11609 # 13340 # 15068 # 16791 <lb/>41 # 1192 # 2937 # 4681 # 6424 # 8164 # 9903 # 11638 # 13369 # 15097 # 16820 <lb/>42 # 1221 # 2966 # 4710 # 6453 # 8193 # 9931 # 11667 # 13398 # 15126 # 16848 <lb/>43 # 1250 # 2995 # 4739 # 6482 # 8222 # 9960 # 11695 # 13427 # 15154 # 16877 <lb/>44 # 1279 # 3024 # 4768 # 6511 # 8251 # 9989 # 11724 # 13456 # 15183 # 16906 <lb/>45 # 1308 # 3053 # 4797 # 6540 # 8280 # 10018 # 11753 # 13485 # 15212 # 16934 <lb/>46 # 1338 # 3082 # 4826 # 6569 # 8309 # 10047 # 11782 # 13513 # 15241 # 16963 <lb/>47 # 1367 # 3112 # 4855 # 6598 # 8338 # 10076 # 11811 # 13542 # 15269 # 16992 <lb/>48 # 1396 # 3141 # 4884 # 6627 # 8367 # 10105 # 11840 # 13571 # 15298 # 17020 <lb/>49 # 1425 # 3170 # 4914 # 6656 # 8396 # 10134 # 11869 # 13600 # 15327 # 17049 <lb/>50 # 1454 # 3199 # 4943 # 6685 # 8425 # 10163 # 11898 # 13629 # 15350 # 17078 <lb/>51 # 1483 # 3228 # 4972 # 6714 # 8454 # 10192 # 11927 # 13658 # 15384 # 17106 <lb/>52 # 1512 # 3257 # 5001 # 6743 # 8483 # 10221 # 11955 # 13686 # 15413 # 17135 <lb/>53 # 1541 # 3286 # 5030 # 6772 # 8512 # 10250 # 11984 # 13715 # 15442 # 17164 <lb/>54 # 1570 # 3315 # 5059 # 6801 # 8531 # 10279 # 12013 # 13744 # 15471 # 17192 <lb/>55 # 1599 # 3344 # 5088 # 6830 # 8570 # 10308 # 12042 # 13773 # 15499 # 17221 <lb/>56 # 1628 # 3373 # 5117 # 6859 # 8599 # 10337 # 12071 # 13802 # 15528 # 17259 <lb/>57 # 1657 # 3402 # 5146 # 6888 # 8628 # 10366 # 12100 # 13830 # 15557 # 17278 <lb/>58 # 1687 # 3431 # 5175 # 6917 # 8657 # 10394 # 12129 # 13859 # 15585 # 17307 <lb/>59 # 1716 # 3460 # 5204 # 6946 # 8686 # 10423 # 12158 # 13888 # 15614 # 17336 <lb/>60 # 1745 # 3489 # 5233 # 6975 # 8715 # 10452 # 12186 # 13917 # 15643 # 17364 <lb/></note>
<p>
  <s xml:id="echoid-s591" xml:space="preserve">Quandoquidem <lb/>alia alĳs placẽt, <lb/>&amp; </s>
  <s xml:id="echoid-s592" xml:space="preserve">in eodẽ diſcipli <lb/>næ genere alij ali <lb/>ter uerſantur pro <lb/>ſuo qſ arbitrio. <lb/></s>
  <s xml:id="echoid-s593" xml:space="preserve">Igitur quum ſint <lb/>multi, qui nume-<lb/>risetiã Arithme-<lb/>ticis plurimũ ob-<lb/>lectentur, ne pa <lb/>rum iuuentur. </s>
  <s xml:id="echoid-s594" xml:space="preserve">eſt <lb/>enim reuera ſtudi <lb/>um illud &amp; </s>
  <s xml:id="echoid-s595" xml:space="preserve">exerci <lb/>tium numerorum <lb/>longe utiliſsimũ. </s>
  <s xml:id="echoid-s596" xml:space="preserve"><lb/>libuit in gratiam <lb/>eorũ, quibꝰ nume <lb/>ri magis arrident <lb/>quàm inſtrumen-<lb/>ta, adponere hic <lb/>tabulas Sinuum, <lb/>quas ipſi ſupputa <lb/>uimus ad 100000 <lb/>pũcta, ne qua ꝑre <lb/>nõ ſatis ſtudioſo℞ <lb/>uideremur adiu-<lb/>uare profectum.</s>
  <s xml:id="echoid-s597" xml:space="preserve"/>
</p>
<pb file="0018" n="18"/>
<note position="right" xml:space="preserve"> <lb/>########## Tabula Sinuum rectorum ſiue ſemichordarum, minutim extenſa. <lb/># 10 # 11 # 12 # 13 # 14 # 15 # 16 # 17 # 18 # 19 <lb/>m. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. <lb/>0 # 17364 # 19080 # 20791 # 22495 # 24192 # 25881 # 27563 # 29237 # 30901 # 32556 <lb/>1 # 17393 # 19109 # 20819 # 22523 # 24220 # 25910 # 27591 # 29264 # 30929 # 32584 <lb/>2 # 17422 # 19138 # 20848 # 22551 # 24248 # 25938 # 27619 # 29292 # 30957 # 32611 <lb/>3 # 17450 # 19166 # 20876 # 22580 # 24276 # 25966 # 27647 # 29320 # 30984 # 32639 <lb/>4 # 17479 # 19195 # 20904 # 22608 # 24305 # 25994 # 27675 # 29348 # 31012 # 32666 <lb/>5 # 17508 # 19223 # 20933 # 22636 # 24333 # 26022 # 27703 # 29376 # 31939 # 32694 <lb/>6 # 17536 # 19252 # 20961 # 22665 # 24361 # 26050 # 27731 # 29404 # 31067 # 32721 <lb/>7 # 17565 # 19280 # 20990 # 22693 # 24389 # 26078 # 27759 # 29431 # 31095 # 32749 <lb/>8 # 17593 # 19309 # 21018 # 22721 # 24417 # 26106 # 27787 # 29459 # 31122 # 32776 <lb/>9 # 17622 # 19337 # 21047 # 22750 # 24446 # 26134 # 27815 # 29487 # 31150 # 32804 <lb/>10 # 17651 # 19366 # 21075 # 22778 # 24474 # 26162 # 27843 # 29515 # 31178 # 32831 <lb/>11 # 17679 # 19394 # 21104 # 22806 # 24504 # 26190 # 27871 # 29543 # 31205 # 32859 <lb/>12 # 17708 # 19423 # 21132 # 22835 # 24530 # 26218 # 27899 # 29570 # 31233 # 32886 <lb/>13 # 17737 # 19451 # 21160 # 22863 # 24558 # 26246 # 27927 # 29598 # 31261 # 32914 <lb/>14 # 17765 # 19480 # 21189 # 22891 # 24587 # 26275 # 27954 # 29626 # 31288 # 32941 <lb/>15 # 17794 # 19509 # 21217 # 22920 # 24615 # 26303 # 27982 # 29654 # 31316 # 32969 <lb/>16 # 17822 # 19537 # 21246 # 22948 # 24643 # 26331 # 28010 # 29681 # 31344 # 32996 <lb/>17 # 17851 # 19566 # 21274 # 22976 # 24671 # 26359 # 28038 # 29709 # 31371 # 33023 <lb/>18 # 17880 # 19594 # 21303 # 23004 # 24699 # 26387 # 28066 # 29737 # 31399 # 33051 <lb/>19 # 17908 # 19623 # 21331 # 23033 # 24728 # 26415 # 28094 # 29765 # 31426 # 33078 <lb/>20 # 17937 # 19651 # 21359 # 23061 # 24756 # 26443 # 28122 # 29793 # 31454 # 33106 <lb/>21 # 17966 # 19680 # 21388 # 23089 # 34784 # 26471 # 28150 # 29820 # 31482 # 33133 <lb/>22 # 17994 # 19708 # 21416 # 23118 # 24812 # 26499 # 28178 # 29848 # 31509 # 33161 <lb/>23 # 18023 # 19737 # 21445 # 23146 # 24840 # 26527 # 28206 # 29876 # 31537 # 33188 <lb/>24 # 18051 # 19765 # 21473 # 23174 # 24869 # 26555 # 28234 # 29904 # 31564 # 33216 <lb/>25 # 18080 # 19795 # 21501 # 23203 # 24897 # 26583 # 28262 # 29931 # 31592 # 33243 <lb/>26 # 18109 # 19822 # 21530 # 23231 # 24925 # 26611 # 28289 # 29959 # 31620 # 33270 <lb/>27 # 18137 # 19851 # 21558 # 23259 # 24953 # 26639 # 28317 # 29987 # 31647 # 13298 <lb/>28 # 18166 # 19879 # 21587 # 23287 # 24981 # 26667 # 28345 # 30015 # 31675 # 33325 <lb/>29 # 18194 # 19908 # 21615 # 23316 # 25009 # 26695 # 28373 # 30042 # 31702 # 33353 <lb/>30 # 18223 # 19936 # 21643 # 23344 # 25038 # 26723 # 28401 # 30070 # 31730 # 33380 <lb/>31 # 18252 # 19965 # 21672 # 23372 # 25066 # 26751 # 28429 # 30098 # 31758 # 33408 <lb/>32 # 18280 # 19993 # 21700 # 23401 # 25094 # 26779 # 28457 # 30126 # 31785 # 33435 <lb/>33 # 18309 # 20022 # 21729 # 23429 # 25122 # 26807 # 28485 # 30153 # 31813 # 33462 <lb/>34 # 18337 # 20050 # 21757 # 23457 # 25150 # 26835 # 28513 # 30181 # 31840 # 33490 <lb/>35 # 18366 # 20079 # 21785 # 23485 # 25178 # 26863 # 28540 # 30209 # 31868 # 33517 <lb/>36 # 18395 # 20107 # 21814 # 23514 # 25206 # 26891 # 28568 # 30236 # 31895 # 33545 <lb/>37 # 18423 # 20126 # 21842 # 23542 # 25235 # 26920 # 28596 # 30264 # 31923 # 33572 <lb/>38 # 18452 # 20164 # 21871 # 23570 # 25263 # 26948 # 28624 # 30292 # 31951 # 33599 <lb/>39 # 18480 # 20193 # 21899 # 23599 # 25291 # 26976 # 28652 # 30320 # 31978 # 33627 <lb/>40 # 18509 # 20221 # 21927 # 23627 # 25319 # 27004 # 28680 # 30347 # 32006 # 33654 <lb/>41 # 18538 # 20250 # 21956 # 23655 # 25347 # 27032 # 28708 # 30375 # 32033 # 33682 <lb/>42 # 18566 # 20278 # 21984 # 23683 # 25375 # 27060 # 28736 # 30403 # 32061 # 33709 <lb/>43 # 18595 # 20307 # 22013 # 23712 # 25403 # 27088 # 28763 # 30431 # 32088 # 33736 <lb/>44 # 18623 # 20335 # 22041 # 23740 # 25432 # 27116 # 28791 # 30458 # 32116 # 33763 <lb/>45 # 18652 # 20364 # 22069 # 23768 # 25460 # 27144 # 28819 # 30486 # 32143 # 33794 <lb/>46 # 18680 # 20392 # 22098 # 23796 # 25488 # 27172 # 28847 # 30514 # 32171 # 33819 <lb/>47 # 18709 # 20421 # 22126 # 23825 # 25516 # 27200 # 28875 # 30541 # 32199 # 33846 <lb/>48 # 18738 # 20449 # 22154 # 23853 # 25544 # 27228 # 28903 # 30569 # 32226 # 33873 <lb/>49 # 18766 # 20478 # 22183 # 23881 # 25572 # 27256 # 28931 # 30597 # 32254 # 33901 <lb/>50 # 18795 # 20506 # 22211 # 23999 # 25600 # 27284 # 28958 # 30624 # 32281 # 33928 <lb/>51 # 18823 # 20535 # 22239 # 23938 # 25628 # 27311 # 28986 # 30652 # 32309 # 33955 <lb/>52 # 18862 # 20563 # 22268 # 23966 # 25657 # 27339 # 29014 # 30680 # 32336 # 33983 <lb/>53 # 18880 # 20591 # 22296 # 23994 # 25685 # 27367 # 29042 # 30707 # 32364 # 34010 <lb/>54 # 18909 # 20620 # 22325 # 24022 # 25713 # 27395 # 29070 # 30735 # 32391 # 34037 <lb/>55 # 18958 # 20648 # 22353 # 24051 # 25741 # 27423 # 29098 # 30763 # 32419 # 34065 <lb/>56 # 18966 # 20677 # 22381 # 24079 # 25769 # 27451 # 29125 # 30791 # 32446 # 34092 <lb/>57 # 18995 # 20705 # 22410 # 24107 # 25797 # 27479 # 29153 # 30818 # 32474 # 34119 <lb/>58 # 19023 # 20734 # 22438 # 24135 # 25825 # 27507 # 29181 # 30846 # 32501 # 34147 <lb/>59 # 19052 # 20762 # 22466 # 24163 # 25853 # 27535 # 29209 # 30874 # 32529 # 34174 <lb/>60 # 19080 # 20791 # 22495 # 24192 # 25881 # 27563 # 29237 # 30901 # 32556 # 34102 <lb/></note>
<pb file="0019" n="19"/>
<note position="right" xml:space="preserve"> <lb/>########## Tabula Sinuum rectorum ſiue ſemichordarum, minutim extenſa. <lb/># 20 # 21 # 22 # 23 # 24 # 25 # 26 # 27 # 28 # 29 <lb/>m. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. <lb/>0 # 34202 # 35836 # 37460 # 39073 # 40673 # 42261 # 43837 # 45399 # 45947 # 48480 <lb/>1 # 34229 # 35863 # 37487 # 39099 # 40700 # 42288 # 43863 # 45424 # 46972 # 48506 <lb/>2 # 34256 # 35891 # 37514 # 39126 # 40736 # 42314 # 43889 # 45450 # 46998 # 48531 <lb/>3 # 34284 # 35918 # 37541 # 39153 # 40753 # 42340 # 43915 # 45476 # 47024 # 48557 <lb/>4 # 34311 # 35945 # 37568 # 39180 # 40779 # 42367 # 43941 # 45502 # 47049 # 48582 <lb/>5 # 34338 # 35972 # 37595 # 39206 # 40806 # 42393 # 43967 # 45528 # 47075 # 48608 <lb/>6 # 34365 # 35999 # 37622 # 39233 # 40833 # 42419 # 43993 # 45554 # 47101 # 48633 <lb/>7 # 34393 # 36026 # 37649 # 39260 # 40859 # 42446 # 44020 # 45580 # 47126 # 48658 <lb/>8 # 34420 # 36053 # 37676 # 39287 # 40886 # 42472 # 44046 # 45606 # 47152 # 48684 <lb/>9 # 34447 # 36081 # 37703 # 39313 # 40912 # 42498 # 44072 # 45632 # 47178 # 48709 <lb/>10 # 34475 # 36108 # 37730 # 39340 # 40939 # 42525 # 44098 # 45658 # 47203 # 48735 <lb/>11 # 34502 # 36135 # 37757 # 39367 # 40965 # 42551 # 44124 # 45683 # 47220 # 48760 <lb/>12 # 34529 # 36162 # 37784 # 39394 # 40992 # 42577 # 44150 # 45709 # 47255 # 48785 <lb/>13 # 34557 # 36189 # 37811 # 39420 # 41018 # 42604 # 44176 # 45735 # 47280 # 48811 <lb/>14 # 34584 # 36216 # 37837 # 39447 # 41045 # 42630 # 44202 # 45761 # 47306 # 48836 <lb/>15 # 34611 # 36243 # 37864 # 39474 # 41071 # 42656 # 44228 # 45787 # 47331 # 48862 <lb/>16 # 34639 # 36270 # 37891 # 39501 # 41098 # 42683 # 44254 # 45813 # 47357 # 48887 <lb/>17 # 34666 # 36298 # 37918 # 39527 # 41124 # 42709 # 44281 # 45839 # 47383 # 48912 <lb/>18 # 34693 # 36325 # 37945 # 39554 # 41151 # 42735 # 44207 # 45864 # 47408 # 48938 <lb/>19 # 34720 # 36352 # 37972 # 39581 # 41177 # 42762 # 44333 # 45890 # 47434 # 48963 <lb/>20 # 34748 # 36379 # 37999 # 39607 # 41204 # 42788 # 44359 # 45916 # 47460 # 48988 <lb/>21 # 34775 # 36406 # 38026 # 39634 # 41230 # 42814 # 44385 # 45942 # 47485 # 49014 <lb/>22 # 34802 # 36433 # 38053 # 39661 # 41257 # 42840 # 44411 # 45968 # 47511 # 49039 <lb/>23 # 34829 # 36460 # 38080 # 39688 # 41283 # 42867 # 44437 # 45994 # 47536 # 49065 <lb/>24 # 34857 # 36487 # 38107 # 39714 # 41310 # 42893 # 44463 # 46019 # 47562 # 49090 <lb/>25 # 34884 # 36514 # 38133 # 39741 # 41336 # 42919 # 44489 # 46045 # 47588 # 49115 <lb/>26 # 34911 # 36541 # 38160 # 39768 # 41363 # 42946 # 44515 # 46071 # 47613 # 49141 <lb/>27 # 34938 # 36568 # 38187 # 39794 # 41389 # 42972 # 44541 # 46097 # 47639 # 49166 <lb/>28 # 34966 # 36595 # 38212 # 49821 # 41416 # 42998 # 44567 # 46123 # 47664 # 49191 <lb/>29 # 34993 # 36623 # 38241 # 39848 # 41442 # 43024 # 44593 # 46149 # 47690 # 49217 <lb/>30 # 35020 # 36650 # 38268 # 39874 # 41469 # 43051 # 44619 # 46174 # 47715 # 49242 <lb/>31 # 35047 # 36677 # 38295 # 39901 # 41495 # 43077 # 44645 # 46200 # 47741 # 49267 <lb/>32 # 35075 # 36704 # 38322 # 39928 # 41522 # 43103 # 44671 # 46226 # 47767 # 49292 <lb/>33 # 35102 # 36731 # 38348 # 39954 # 41548 # 43129 # 44697 # 46252 # 47792 # 49318 <lb/>34 # 35129 # 36758 # 38375 # 39981 # 41575 # 43156 # 44723 # 46278 # 47818 # 49343 <lb/>35 # 35156 # 36785 # 38402 # 40008 # 41601 # 43182 # 44749 # 46303 # 47843 # 49368 <lb/>36 # 35184 # 36812 # 38429 # 40034 # 41628 # 43208 # 44775 # 46329 # 47860 # 49394 <lb/>37 # 35211 # 36839 # 38456 # 40061 # 41654 # 43234 # 44801 # 46355 # 47894 # 49419 <lb/>38 # 35238 # 36866 # 38483 # 40088 # 41680 # 43261 # 44827 # 46381 # 47920 # 49444 <lb/>39 # 35265 # 36893 # 38510 # 40114 # 41707 # 43287 # 44853 # 46406 # 47945 # 49470 <lb/>40 # 35293 # 36920 # 38536 # 40141 # 41733 # 43313 # 44879 # 46432 # 47971 # 49495 <lb/>41 # 35320 # 36947 # 38563 # 40168 # 41760 # 43339 # 44905 # 46458 # 47996 # 49520 <lb/>42 # 35347 # 36974 # 38590 # 40194 # 41786 # 43365 # 44931 # 46484 # 48022 # 49545 <lb/>43 # 35374 # 37001 # 38617 # 40221 # 41813 # 43392 # 44957 # 46509 # 48047 # 49571 <lb/>44 # 35401 # 37028 # 38644 # 40248 # 41839 # 43418 # 44983 # 46535 # 48073 # 49596 <lb/>45 # 35429 # 37055 # 38671 # 40274 # 41865 # 43444 # 45009 # 46561 # 48098 # 49621 <lb/>46 # 35456 # 37082 # 38697 # 40301 # 41892 # 43470 # 45035 # 46587 # 48124 # 49646 <lb/>47 # 35483 # 37109 # 38724 # 40327 # 41918 # 43496 # 45061 # 46612 # 48149 # 49672 <lb/>48 # 35510 # 37136 # 38751 # 40354 # 41945 # 43523 # 45087 # 46638 # 48175 # 49697 <lb/>49 # 35537 # 37163 # 38778 # 40381 # 41971 # 43549 # 45113 # 46664 # 48200 # 49722 <lb/>50 # 35565 # 37190 # 38805 # 40407 # 41998 # 43575 # 45139 # 46690 # 48226 # 49747 <lb/>51 # 35592 # 37217 # 38831 # 40434 # 42024 # 43601 # 45165 # 46715 # 48251 # 49773 <lb/>52 # 35619 # 37244 # 38858 # 40460 # 42050 # 43627 # 45191 # 46741 # 48277 # 49798 <lb/>53 # 35646 # 37271 # 38885 # 40487 # 42077 # 43654 # 45217 # 46767 # 48302 # 49823 <lb/>54 # 35673 # 37298 # 38912 # 40514 # 42103 # 43680 # 45243 # 46792 # 48328 # 49848 <lb/>55 # 35700 # 37325 # 38939 # 40540 # 42129 # 43706 # 45269 # 46818 # 48353 # 49873 <lb/>56 # 35728 # 37352 # 38965 # 40567 # 42156 # 43732 # 45295 # 46844 # 48379 # 49899 <lb/>57 # 35755 # 37379 # 38992 # 40593 # 42182 # 43758 # 45321 # 46870 # 48404 # 49924 <lb/>58 # 35782 # 37406 # 39019 # 40620 # 42209 # 43784 # 45347 # 46895 # 48430 # 49949 <lb/>59 # 35809 # 37433 # 39046 # 40647 # 42235 # 43810 # 45373 # 46921 # 48455 # 49974 <lb/>60 # 35836 # 37460 # 39073 # 40673 # 42261 # 43837 # 45399 # 46947 # 48480 # 50000 <lb/></note>
<pb file="0020" n="20"/>
<note position="right" xml:space="preserve"> <lb/>########## Tabula Sinuum rectorum ſiue ſemichordarum, minutim extenſa. <lb/># 30 # 31 # 32 # 33 # 34 # 35 # 36 # 37 # 38 # 39 <lb/>m. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. <lb/>0 # 50000 # 51503 # 52991 # 54463 # 55919 # 57357 # 58778 # 60181 # 61566 # 62932 <lb/>1 # 50025 # 51528 # 53016 # 54488 # 55943 # 57381 # 58802 # 60204 # 61589 # 62954 <lb/>2 # 50050 # 51553 # 53041 # 54512 # 55966 # 57405 # 58825 # 60227 # 61611 # 62977 <lb/>3 # 50075 # 51578 # 53065 # 64537 # 55991 # 57429 # 58849 # 60251 # 61634 # 62999 <lb/>4 # 50100 # 51603 # 53090 # 54561 # 56015 # 57452 # 58872 # 60274 # 61657 # 63022 <lb/>5 # 50125 # 51628 # 53115 # 54585 # 56039 # 57476 # 58896 # 60297 # 61680 # 63045 <lb/>6 # 50151 # 51653 # 53139 # 54610 # 56063 # 57500 # 58919 # 60320 # 61703 # 63067 <lb/>7 # 50176 # 51678 # 53164 # 54634 # 56087 # 57524 # 58943 # 60344 # 61726 # 63090 <lb/>8 # 50201 # 51703 # 53189 # 54658 # 56112 # 57548 # 58966 # 60367 # 61749 # 63112 <lb/>9 # 50226 # 51728 # 53213 # 54683 # 56136 # 57571 # 58990 # 60389 # 61772 # 63135 <lb/>10 # 50251 # 51752 # 53238 # 54707 # 56160 # 57595 # 59013 # 60413 # 61795 # 63157 <lb/>11 # 50276 # 51777 # 53263 # 54731 # 56184 # 57619 # 59037 # 60436 # 61817 # 63180 <lb/>12 # 50302 # 51802 # 53287 # 54756 # 56208 # 57643 # 59060 # 60459 # 61840 # 63202 <lb/>13 # 50327 # 51827 # 53312 # 54780 # 56232 # 57667 # 59084 # 60483 # 61863 # 63225 <lb/>14 # 50352 # 51852 # 53336 # 54804 # 56256 # 57690 # 59107 # 60506 # 61886 # 63248 <lb/>15 # 50377 # 51877 # 53361 # 54829 # 56280 # 57714 # 59130 # 60529 # 61909 # 63270 <lb/>16 # 50402 # 51902 # 53386 # 54853 # 56304 # 57738 # 59154 # 60552 # 61932 # 63293 <lb/>17 # 50427 # 51927 # 53410 # 54877 # 56328 # 57762 # 59177 # 60575 # 61955 # 63315 <lb/>18 # 50452 # 51951 # 53435 # 54902 # 56352 # 57785 # 59201 # 60598 # 61977 # 63338 <lb/>19 # 50477 # 51976 # 53459 # 54926 # 56376 # 57809 # 59224 # 60621 # 62000 # 63360 <lb/>20 # 50502 # 52001 # 53484 # 54950 # 56400 # 57833 # 59248 # 60645 # 62023 # 63383 <lb/>21 # 50528 # 52026 # 53508 # 54975 # 56424 # 57856 # 59271 # 60668 # 62046 # 63405 <lb/>22 # 50553 # 52051 # 53533 # 54999 # 56448 # 57880 # 59295 # 60691 # 62069 # 63428 <lb/>23 # 50578 # 52076 # 53558 # 55023 # 56472 # 57904 # 59318 # 60614 # 62091 # 63450 <lb/>24 # 50603 # 52100 # 53582 # 55048 # 56496 # 57928 # 59341 # 60737 # 62114 # 63473 <lb/>25 # 50628 # 52125 # 53607 # 55072 # 56520 # 57951 # 59365 # 60760 # 62137 # 63595 <lb/>26 # 50653 # 52150 # 53631 # 55096 # 56544 # 57975 # 59388 # 60783 # 62160 # 63518 <lb/>27 # 50678 # 52175 # 53656 # 55120 # 56568 # 57999 # 59412 # 60806 # 62183 # 63540 <lb/>28 # 50703 # 52200 # 53680 # 55145 # 56592 # 58022 # 59435 # 60829 # 62205 # 63562 <lb/>29 # 50728 # 52225 # 53705 # 55169 # 56616 # 58046 # 59458 # 60853 # 62228 # 63685 <lb/>30 # 50753 # 52249 # 53729 # 55193 # 56640 # 58070 # 59482 # 60876 # 62251 # 53607 <lb/>31 # 50778 # 52274 # 53754 # 55217 # 56664 # 58093 # 59505 # 60899 # 62274 # 63630 <lb/>32 # 50803 # 52299 # 53779 # 55242 # 56688 # 58117 # 59529 # 60922 # 62296 # 63652 <lb/>33 # 50829 # 52324 # 53803 # 55266 # 56712 # 58141 # 59552 # 60945 # 62319 # 63675 <lb/>34 # 50854 # 52349 # 53828 # 55290 # 56736 # 58164 # 59575 # 60968 # 62342 # 63697 <lb/>35 # 50879 # 52373 # 53852 # 55314 # 56760 # 58188 # 59599 # 60991 # 62365 # 63719 <lb/>36 # 50904 # 52398 # 53877 # 55339 # 56784 # 58212 # 59622 # 61014 # 62387 # 63742 <lb/>37 # 50929 # 52423 # 53901 # 55363 # 56808 # 58235 # 59645 # 61037 # 62410 # 63764 <lb/>38 # 50954 # 52448 # 53926 # 55387 # 56832 # 58259 # 59669 # 61060 # 62433 # 63787 <lb/>39 # 50979 # 52472 # 53950 # 55411 # 56856 # 58283 # 59692 # 61083 # 62456 # 63809 <lb/>40 # 51004 # 52497 # 53975 # 55436 # 56880 # 58306 # 59715 # 61106 # 62478 # 63832 <lb/>41 # 51029 # 52522 # 53999 # 55460 # 56904 # 58330 # 59739 # 61129 # 62501 # 63854 <lb/>42 # 51054 # 52547 # 54024 # 55484 # 56927 # 58354 # 59762 # 61152 # 62524 # 63876 <lb/>43 # 51079 # 52571 # 54048 # 55508 # 56951 # 58377 # 59785 # 61175 # 62546 # 63899 <lb/>44 # 51104 # 52596 # 54072 # 55532 # 56975 # 58401 # 59809 # 61198 # 62569 # 63921 <lb/>45 # 51129 # 52621 # 54097 # 55557 # 56999 # 58424 # 59832 # 61221 # 62592 # 63943 <lb/>46 # 51154 # 52646 # 54121 # 55581 # 57023 # 58448 # 59955 # 61244 # 62615 # 63966 <lb/>47 # 51179 # 52670 # 54146 # 55605 # 57047 # 58472 # 59979 # 61267 # 62637 # 63988 <lb/>48 # 51204 # 52695 # 54170 # 55629 # 57071 # 58495 # 59902 # 61290 # 62660 # 64010 <lb/>49 # 51229 # 52720 # 54195 # 55653 # 57095 # 58519 # 59925 # 61313 # 62683 # 64033 <lb/>50 # 51254 # 52745 # 54219 # 55677 # 57119 # 58542 # 59948 # 61336 # 62705 # 64055 <lb/>51 # 51279 # 52769 # 54244 # 55702 # 57142 # 58566 # 59972 # 61359 # 62728 # 64077 <lb/>52 # 51304 # 52794 # 54268 # 55726 # 57166 # 58590 # 59995 # 61382 # 62751 # 64100 <lb/>53 # 51329 # 52819 # 54293 # 55750 # 57190 # 58613 # 60018 # 61405 # 62773 # 64122 <lb/>54 # 51354 # 52843 # 54317 # 55774 # 57214 # 58637 # 60042 # 61428 # 62796 # 64144 <lb/>55 # 51379 # 52868 # 54341 # 55798 # 57238 # 58660 # 60065 # 61451 # 62818 # 64167 <lb/>56 # 51404 # 52893 # 54366 # 55822 # 57262 # 58684 # 60088 # 61474 # 62841 # 64189 <lb/>57 # 51428 # 52917 # 54390 # 55846 # 57286 # 58707 # 60111 # 61497 # 62864 # 64211 <lb/>58 # 51453 # 52942 # 54415 # 55871 # 57309 # 58731 # 60135 # 61520 # 62886 # 64234 <lb/>59 # 51478 # 52967 # 54439 # 55895 # 57333 # 58754 # 60158 # 61543 # 62909 # 64256 <lb/>60 # 51503 # 52991 # 54463 # 55919 # 57357 # 58778 # 60181 # 61566 # 62932 # 64278 <lb/></note>
<pb file="0021" n="21"/>
<note position="right" xml:space="preserve"> <lb/>########## Tabula Sinuum rectorum ſiue ſemichordarum, minutim extenſa. <lb/># 40 # 41 # 42 # 43 # 44 # 45 # 46 # 47 # 48 # 49 <lb/>m̃ # Sinus # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. <lb/>0 # 64278 # 65605 # 66913 # 68199 # 69465 # 70710 # 71933 # 73135 # 74314 # 75470 <lb/>1 # 64301 # 65627 # 66934 # 68221 # 69486 # 70731 # 71954 # 73155 # 74333 # 75490 <lb/>2 # 64323 # 65649 # 66956 # 68242 # 69507 # 70751 # 71974 # 73175 # 74353 # 75509 <lb/>3 # 64345 # 65671 # 66977 # 68263 # 69528 # 70772 # 71994 # 73194 # 74372 # 75528 <lb/>4 # 64367 # 65693 # 66999 # 68284 # 69549 # 70792 # 72014 # 73214 # 74392 # 75547 <lb/>5 # 64390 # 65715 # 67021 # 68306 # 69570 # 70813 # 72034 # 73234 # 74411 # 75566 <lb/>6 # 64412 # 65737 # 67042 # 68327 # 69591 # 70833 # 72055 # 73254 # 74431 # 75585 <lb/>7 # 64434 # 65759 # 67064 # 68348 # 69612 # 70854 # 72075 # 73274 # 74450 # 75604 <lb/>8 # 64456 # 65781 # 67085 # 68370 # 69633 # 70875 # 72095 # 73293 # 74470 # 75623 <lb/>9 # 64479 # 65803 # 67107 # 68391 # 69653 # 70895 # 72115 # 73313 # 74489 # 75642 <lb/>10 # 64501 # 65825 # 67128 # 68412 # 69674 # 70916 # 72135 # 73333 # 74508 # 75661 <lb/>11 # 64523 # 65847 # 67150 # 68433 # 69695 # 70936 # 72155 # 73352 # 74528 # 75680 <lb/>12 # 64545 # 65868 # 67172 # 68454 # 69716 # 70957 # 72175 # 73372 # 74547 # 75699 <lb/>13 # 64567 # 65890 # 67193 # 68475 # 69737 # 70977 # 72196 # 73392 # 74566 # 75718 <lb/>14 # 64590 # 65912 # 67215 # 68497 # 69758 # 70998 # 72216 # 73412 # 74586 # 75737 <lb/>15 # 64612 # 65934 # 67236 # 68518 # 69779 # 71018 # 72236 # 73432 # 74605 # 75756 <lb/>16 # 64634 # 65956 # 67258 # 68539 # 69799 # 71039 # 72256 # 73451 # 74625 # 75775 <lb/>17 # 64656 # 65978 # 67279 # 68560 # 69820 # 71059 # 72276 # 73471 # 74644 # 75794 <lb/>18 # 64678 # 66005 # 67301 # 68581 # 69841 # 71079 # 72296 # 73491 # 74663 # 75813 <lb/>19 # 64701 # 66022 # 67322 # 68603 # 69862 # 71100 # 72316 # 73511 # 74683 # 75832 <lb/>20 # 64723 # 66043 # 67344 # 68624 # 69883 # 71120 # 72336 # 73530 # 74702 # 75851 <lb/>21 # 64745 # 66065 # 67365 # 68645 # 69903 # 71141 # 72356 # 73550 # 74721 # 75870 <lb/>22 # 64767 # 66087 # 67387 # 68666 # 69924 # 71161 # 72377 # 73570 # 74741 # 75889 <lb/>23 # 64789 # 66199 # 67408 # 68687 # 69945 # 71181 # 72397 # 7379@ # 74760 # 75908 <lb/>24 # 64811 # 66131 # 67430 # 68708 # 69966 # 71202 # 72417 # 73609 # 74779 # 75925 <lb/>25 # 64834 # 66153 # 67451 # 68729 # 69987 # 71223 # 72437 # 73629 # 74799 # 75956 <lb/>26 # 64856 # 66174 # 67473 # 68751 # 70007 # 71243 # 72457 # 73649 # 74818 # 75964 <lb/>27 # 64878 # 66196 # 67494 # 68772 # 70028 # 71263 # 72477 # 73668 # 74837 # 75983 <lb/>28 # 64900 # 66218 # 67516 # 68793 # 70049 # 71284 # 72497 # 73688 # 74857 # 76002 <lb/>29 # 64922 # 66240 # 67537 # 68814 # 70070 # 71304 # 72517 # 73708 # 74876 # 76021 <lb/>30 # 64944 # 66262 # 67559 # 68835 # 70090 # 71325 # 72537 # 73727 # 74895 # 76040 <lb/>31 # 64966 # 66284 # 67580 # 68856 # 70111 # 71345 # 72557 # 73747 # 74914 # 76059 <lb/>32 # 64989 # 66305 # 67601 # 68877 # 70132 # 71365 # 72577 # 73767 # 74934 # 76078 <lb/>33 # 65011 # 66327 # 67623 # 68898 # 70153 # 71386 # 72597 # 73786 # 74953 # 76097 <lb/>34 # 65033 # 66349 # 67644 # 68919 # 70173 # 71406 # 72617 # 73806 # 74972 # 76116 <lb/>35 # 65055 # 66370 # 67666 # 68940 # 70194 # 71426 # 72637 # 73825 # 74991 # 76134 <lb/>36 # 65077 # 66392 # 67687 # 68961 # 70215 # 71447 # 72657 # 73845 # 75011 # 76153 <lb/>37 # 65099 # 66414 # 67709 # 68983 # 70236 # 71467 # 72677 # 73865 # 75030 # 76172 <lb/>38 # 65121 # 66436 # 67730 # 69004 # 70256 # 71487 # 72697 # 73884 # 75049 # 76191 <lb/>39 # 65143 # 66457 # 67751 # 69025 # 70277 # 71508 # 72717 # 73904 # 75068 # 76210 <lb/>40 # 65165 # 66479 # 67773 # 69046 # 70298 # 71528 # 72737 # 73923 # 75088 # 76229 <lb/>41 # 65187 # 66501 # 67794 # 69067 # 70318 # 71548 # 72757 # 73943 # 75107 # 76248 <lb/>42 # 65209 # 66523 # 67815 # 69088 # 70339 # 71569 # 72777 # 73963 # 75126 # 76266 <lb/>43 # 65231 # 66544 # 67837 # 69109 # 70360 # 71589 # 72797 # 73982 # 75145 # 76285 <lb/>44 # 65253 # 66566 # 67858 # 69130 # 70380 # 71609 # 72817 # 74002 # 75164 # 76304 <lb/>45 # 65275 # 66588 # 67880 # 69151 # 70401 # 71630 # 72837 # 74021 # 75183 # 76323 <lb/>46 # 65298 # 66609 # 67901 # 69172 # 70422 # 71650 # 72857 # 74041 # 75203 # 76342 <lb/>47 # 65320 # 66631 # 67922 # 69193 # 70442 # 71670 # 72876 # 74060 # 75222 # 76360 <lb/>48 # 65342 # 66653 # 67944 # 69214 # 70463 # 71691 # 72896 # 74080 # 75241 # 76379 <lb/>49 # 65364 # 66674 # 67964 # 69235 # 70484 # 71711 # 72916 # 74100 # 75260 # 76398 <lb/>50 # 65386 # 66696 # 67986 # 69256 # 70504 # 71731 # 72936 # 74119 # 75279 # 76417 <lb/>51 # 65408 # 66718 # 68008 # 69277 # 70525 # 71751 # 72956 # 74139 # 75299 # 76435 <lb/>52 # 65430 # 66739 # 68029 # 69298 # 70545 # 71772 # 72976 # 74158 # 75318 # 76454 <lb/>53 # 65452 # 66761 # 68050 # 69219 # 70566 # 71792 # 72996 # 74178 # 75337 # 76473 <lb/>54 # 65474 # 66783 # 68073 # 69349 # 70587 # 71812 # 73016 # 74197 # 75356 # 76492 <lb/>55 # 65496 # 66804 # 68094 # 69361 # 70607 # 71832 # 73036 # 74217 # 75375 # 76510 <lb/>56 # 65518 # 66826 # 68114 # 69382 # 70628 # 71853 # 73055 # 74236 # 75394 # 76529 <lb/>57 # 65540 # 66848 # 68135 # 69403 # 70648 # 71873 # 73075 # 74256 # 75413 # 76548 <lb/>58 # 65561 # 66869 # 68156 # 69423 # 70669 # 71893 # 73095 # 74275 # 75432 # 76567 <lb/>59 # 65583 # 66891 # 68178 # 69444 # 70790 # 71913 # 73115 # 74295 # 75451 # 76585 <lb/>60 # 65605 # 66913 # 68199 # 69465 # 70710 # 71933 # 73135 # 74314 # 75470 # 76604 <lb/></note>
<pb file="0022" n="22"/>
<note position="right" xml:space="preserve"> <lb/>########## Tabula Sinuum rectorum ſiue ſemichordarum, minutim extenſa. <lb/># 50 # 51 # 52 # 53 # 54 # 55 # 56 # 57 # 58 # 59 <lb/>m̃ # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. <lb/>0 # 76604 # 77714 # 78801 # 79863 # 80901 # 81915 # 82903 # 83867 # 84804 # 85716 <lb/>1 # 76623 # 77732 # 78818 # 79881 # 80918 # 81931 # 82920 # 83882 # 84820 # 85731 <lb/>2 # 76641 # 77751 # 78836 # 79898 # 80945 # 81948 # 82936 # 83898 # 84835 # 85746 <lb/>3 # 76660 # 77769 # 78854 # 79916 # 80952 # 81965 # 82952 # 83914 # 84851 # 85761 <lb/>4 # 76679 # 77787 # 78872 # 79933 # 80970 # 81981 # 82968 # 82930 # 84866 # 85776 <lb/>5 # 76697 # 77805 # 78890 # 79951 # 80987 # 81998 # 82985 # 83946 # 84881 # 85791 <lb/>6 # 76716 # 77824 # 78908 # 79968 # 81004 # 82015 # 83001 # 83961 # 84897 # 85806 <lb/>7 # 76735 # 77842 # 78926 # 79985 # 81021 # 82031 # 83017 # 83977 # 84912 # 85821 <lb/>8 # 76753 # 77860 # 73944 # 80003 # 81038 # 82048 # 83033 # 83993 # 84927 # 85836 <lb/>9 # 76772 # 77879 # 78961 # 80020 # 81055 # 82065 # 83049 # 84009 # 84943 # 85851 <lb/>10 # 76791 # 77897 # 78979 # 80038 # 81072 # 82081 # 83066 # 84025 # 84958 # 85866 <lb/>11 # 76809 # 77915 # 78997 # 80055 # 81089 # 82098 # 83082 # 84040 # 84973 # 85881 <lb/>12 # 76828 # 77933 # 79015 # 80073 # 81106 # 82114 # 83098 # 84056 # 84989 # 85896 <lb/>13 # 76846 # 77952 # 79033 # 80090 # 81123 # 82131 # 83115 # 84072 # 85004 # 85910 <lb/>14 # 76865 # 77970 # 79051 # 80107 # 81140 # 82148 # 83130 # 84088 # 85519 # 85925 <lb/>15 # 76884 # 77988 # 79068 # 80125 # 81157 # 82164 # 83146 # 84103 # 85035 # 85940 <lb/>16 # 76902 # 78006 # 79086 # 80142 # 81174 # 82181 # 83163 # 84119 # 85050 # 85955 <lb/>17 # 76921 # 78024 # 79104 # 80160 # 81191 # 82197 # 83179 # 84135 # 85065 # 85970 <lb/>18 # 76939 # 78043 # 79122 # 80177 # 81208 # 82214 # 83195 # 83151 # 85081 # 85985 <lb/>19 # 76958 # 78061 # 79140 # 80194 # 81225 # 82230 # 83211 # 83166 # 85096 # 86000 <lb/>20 # 76977 # 78079 # 79157 # 80212 # 81242 # 82247 # 83227 # 84182 # 85111 # 86014 <lb/>21 # 76995 # 78097 # 79175 # 80229 # 81259 # 82264 # 83243 # 84298 # 85126 # 86029 <lb/>22 # 77014 # 78115 # 79193 # 80247 # 81276 # 82280 # 83259 # 84213 # 85142 # 86044 <lb/>23 # 77032 # 78133 # 79211 # 80264 # 81293 # 82297 # 83276 # 84229 # 85157 # 86059 <lb/>24 # 77051 # 78152 # 79228 # 80281 # 81310 # 82313 # 83292 # 84245 # 85172 # 86074 <lb/>25 # 77069 # 78170 # 79246 # 80299 # 81327 # 82330 # 83208 # 84260 # 85187 # 86089 <lb/>26 # 77088 # 78188 # 79264 # 80316 # 81343 # 82346 # 83324 # 84276 # 85203 # 86103 <lb/>27 # 77106 # 78206 # 79282 # 80333 # 81360 # 82363 # 83340 # 84292 # 85218 # 86118 <lb/>28 # 77125 # 78224 # 79299 # 80351 # 81377 # 82379 # 83356 # 84370 # 85233 # 86133 <lb/>29 # 77143 # 78242 # 79317 # 80368 # 81394 # 82396 # 83372 # 84323 # 85248 # 86148 <lb/>30 # 77162 # 78260 # 79335 # 80385 # 81411 # 82412 # 83388 # 84339 # 85264 # 86162 <lb/>31 # 77180 # 78278 # 79353 # 80402 # 81428 # 82429 # 83404 # 84354 # 85279 # 86177 <lb/>32 # 77199 # 78297 # 79370 # 80420 # 81445 # 82445 # 83420 # 84370 # 85294 # 86192 <lb/>33 # 77217 # 78315 # 79388 # 80437 # 81462 # 82462 # 83436 # 84386 # 85309 # 86207 <lb/>34 # 77236 # 78333 # 79406 # 80454 # 81479 # 82478 # 83452 # 84401 # 85324 # 86221 <lb/>35 # 77254 # 78351 # 79423 # 80472 # 81495 # 82494 # 83468 # 84417 # 85439 # 86236 <lb/>36 # 77273 # 78369 # 79441 # 90489 # 81512 # 82511 # 83484 # 84432 # 85355 # 86251 <lb/>37 # 77291 # 78387 # 79459 # 80506 # 81529 # 82527 # 83500 # 84448 # 85370 # 86266 <lb/>38 # 77310 # 78405 # 79476 # 80523 # 81546 # 81544 # 83516 # 84463 # 85385 # 86280 <lb/>39 # 77328 # 78423 # 79494 # 80541 # 81563 # 82560 # 83532 # 84479 # 85400 # 86295 <lb/>40 # 77347 # 73441 # 79512 # 80558 # 81580 # 82577 # 83548 # 84495 # 85415 # 86310 <lb/>41 # 77365 # 78459 # 79529 # 80575 # 81596 # 82593 # 83564 # 84510 # 85430 # 86324 <lb/>42 # 77384 # 78477 # 79547 # 80592 # 81613 # 82609 # 83580 # 84526 # 85445 # 86339 <lb/>43 # 77302 # 78495 # 79564 # 80610 # 81630 # 82626 # 83596 # 84541 # 85460 # 86354 <lb/>44 # 77420 # 78513 # 79582 # 80627 # 81647 # 82642 # 83612 # 84557 # 85476 # 86368 <lb/>45 # 77439 # 78531 # 79600 # 80644 # 81664 # 82658 # 83628 # 84572 # 85491 # 86383 <lb/>46 # 77457 # 78549 # 79617 # 80661 # 81680 # 82675 # 83644 # 84588 # 85506 # 86398 <lb/>47 # 77476 # 78567 # 79635 # 80678 # 81697 # 82691 # 83660 # 84603 # 85521 # 86412 <lb/>48 # 77494 # 78585 # 79652 # 80696 # 81714 # 82708 # 83676 # 84619 # 85536 # 86427 <lb/>49 # 77512 # 78603 # 79670 # 80713 # 81731 # 82724 # 83692 # 84634 # 85551 # 86442 <lb/>50 # 77531 # 78621 # 79688 # 80730 # 81748 # 82740 # 83708 # 84650 # 85566 # 86456 <lb/>51 # 77549 # 78639 # 79705 # 80747 # 81764 # 82757 # 83724 # 84665 # 85581 # 86471 <lb/>52 # 77567 # 78657 # 79723 # 80764 # 81781 # 82773 # 83740 # 84681 # 85596 # 86485 <lb/>53 # 77586 # 78675 # 79740 # 80781 # 81798 # 82789 # 83755 # 84696 # 85611 # 86500 <lb/>54 # 77604 # 78693 # 79758 # 80798 # 81814 # 82806 # 83771 # 84712 # 85626 # 86515 <lb/>55 # 77622 # 78711 # 79775 # 80816 # 81831 # 82822 # 83787 # 84727 # 85641 # 86529 <lb/>56 # 77641 # 78729 # 79793 # 80833 # 81848 # 82838 # 83803 # 84743 # 85656 # 86544 <lb/>57 # 77659 # 78747 # 79811 # 80850 # 81865 # 82854 # 83819 # 84758 # 85671 # 86558 <lb/>58 # 77677 # 78756 # 79828 # 80867 # 81881 # 82871 # 83835 # 84773 # 85686 # 86573 <lb/>59 # 77696 # 78793 # 79846 # 80884 # 81898 # 82884 # 83851 # 84789 # 85701 # 86587 <lb/>60 # 77714 # 78801 # 79863 # 80901 # 81915 # 82903 # 83867 # 84804 # 85716 # 86602 <lb/></note>
<pb file="0023" n="23"/>
<note position="right" xml:space="preserve"> <lb/>########## Tabula Sinuum rectorum ſiue ſemichordarum, minutim extenſa <lb/># 60 # 61 # 62 # 63 # 64 # 65 # 66 # 67 # 68 # 69 <lb/>m̃. # Sinus # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. <lb/>0 # 86602 # 87461 # 88294 # 89100 # 89879 # 90630 # 91354 # 92050 # 92718 # 93358 <lb/>1 # 86617 # 87476 # 88308 # 89113 # 89892 # 90643 # 91366 # 92061 # 92729 # 93368 <lb/>2 # 86631 # 87490 # 88322 # 89127 # 89904 # 90655 # 91378 # 92073 # 92740 # 93378 <lb/>3 # 86646 # 87504 # 88335 # 89140 # 89917 # 90667 # 91390 # 92084 # 92751 # 93389 <lb/>4 # 86660 # 87518 # 88349 # 89153 # 89930 # 90679 # 91401 # 92095 # 92761 # 93399 <lb/>5 # 86675 # 87532 # 88362 # 89166 # 89943 # 90692 # 91413 # 92107 # 92772 # 93410 <lb/>6 # 86689 # 87546 # 88376 # 89179 # 89955 # 90704 # 91425 # 92118 # 92783 # 93420 <lb/>7 # 86704 # 87560 # 88390 # 89192 # 89968 # 90716 # 91437 # 92129 # 92794 # 93430 <lb/>8 # 86718 # 87574 # 88403 # 89206 # 89981 # 90728 # 91448 # 92141 # 92805 # 93441 <lb/>9 # 86733 # 87588 # 88417 # 89219 # 89993 # 90741 # 91460 # 92152 # 92816 # 93451 <lb/>10 # 86747 # 87602 # 88430 # 89232 # 90006 # 90753 # 91472 # 92163 # 92826 # 93461 <lb/>11 # 86762 # 87616 # 88444 # 89245 # 90019 # 90765 # 91484 # 92175 # 92837 # 93472 <lb/>12 # 86776 # 87630 # 88458 # 89258 # 90031 # 90777 # 91495 # 92186 # 92848 # 93482 <lb/>13 # 86791 # 87644 # 88471 # 89271 # 90044 # 90789 # 91507 # 92197 # 92859 # 93492 <lb/>14 # 86805 # 87658 # 88485 # 89284 # 90057 # 90802 # 91519 # 92208 # 92870 # 93503 <lb/>15 # 86819 # 87672 # 88498 # 89297 # 90069 # 90814 # 91531 # 92220 # 92880 # 93513 <lb/>16 # 86834 # 87686 # 88512 # 89310 # 90082 # 90826 # 91542 # 92231 # 92891 # 93523 <lb/>17 # 86848 # 87700 # 88525 # 89324 # 90095 # 90838 # 91554 # 92242 # 92902 # 93534 <lb/>18 # 86863 # 87714 # 88539 # 89337 # 90107 # 90850 # 91566 # 92253 # 92913 # 93544 <lb/>19 # 86877 # 87728 # 88552 # 89350 # 90120 # 90862 # 91577 # 92265 # 92924 # 93554 <lb/>20 # 86841 # 87742 # 88566 # 89363 # 90132 # 90875 # 91589 # 92276 # 92934 # 93564 <lb/>21 # 86906 # 87756 # 88579 # 89376 # 90145 # 90887 # 91601 # 92287 # 92945 # 93575 <lb/>22 # 86920 # 87770 # 88593 # 89389 # 90158 # 90899 # 91612 # 92298 # 92956 # 93585 <lb/>23 # 86935 # 87784 # 88606 # 89402 # 90170 # 90911 # 91624 # 92309 # 92966 # 93595 <lb/>24 # 86949 # 87798 # 88620 # 89415 # 90183 # 90923 # 91636 # 92321 # 92977 # 93605 <lb/>25 # 86963 # 87812 # 88633 # 89428 # 90195 # 90935 # 91647 # 92332 # 92988 # 93616 <lb/>26 # 86978 # 87826 # 88647 # 89441 # 90208 # 90947 # 91659 # 92343 # 92999 # 93626 <lb/>27 # 86992 # 87840 # 88660 # 89454 # 90220 # 90959 # 91671 # 92354 # 93009 # 93636 <lb/>28 # 87006 # 87853 # 88674 # 89467 # 90233 # 90971 # 91682 # 92365 # 93020 # 93646 <lb/>29 # 87021 # 87867 # 88687 # 89480 # 90246 # 90984 # 91694 # 92376 # 93031 # 93657 <lb/>30 # 87035 # 87881 # 88701 # 89493 # 90258 # 90996 # 91706 # 92387 # 93041 # 93667 <lb/>31 # 87049 # 87895 # 88714 # 89506 # 90271 # 91008 # 91717 # 92399 # 93052 # 93677 <lb/>32 # 87064 # 87909 # 88727 # 89519 # 90283 # 91020 # 91729 # 92410 # 93062 # 93687 <lb/>33 # 87078 # 87923 # 88741 # 89532 # 90296 # 91032 # 91740 # 92421 # 93073 # 93607 <lb/>34 # 87092 # 87937 # 88754 # 89545 # 90308 # 91044 # 91752 # 92432 # 93084 # 93707 <lb/>35 # 87107 # 87951 # 88768 # 89558 # 90321 # 91056 # 91763 # 92443 # 93094 # 93718 <lb/>36 # 87121 # 87964 # 88781 # 89571 # 90333 # 91068 # 91775 # 92454 # 93105 # 93728 <lb/>37 # 87135 # 87978 # 88794 # 89584 # 90346 # 91080 # 91787 # 92465 # 93116 # 93738 <lb/>38 # 87149 # 87992 # 88808 # 89597 # 90358 # 91092 # 91798 # 92476 # 93126 # 93748 <lb/>39 # 87164 # 88006 # 88821 # 89609 # 90370 # 91104 # 91810 # 92487 # 93137 # 93758 <lb/>40 # 87178 # 88020 # 88835 # 89622 # 90383 # 91116 # 91821 # 92498 # 93147 # 93768 <lb/>41 # 87192 # 88033 # 88848 # 89635 # 90395 # 91128 # 91833 # 92509 # 93158 # 93778 <lb/>42 # 87206 # 88047 # 88861 # 89648 # 90408 # 91140 # 91844 # 92520 # 93169 # 93788 <lb/>43 # 87221 # 88061 # 88875 # 89661 # 90420 # 91152 # 91856 # 92532 # 93179 # 93798 <lb/>44 # 87235 # 88075 # 88888 # 89674 # 90433 # 91164 # 91867 # 92543 # 93190 # 93809 <lb/>45 # 87249 # 88089 # 88901 # 89687 # 90445 # 91176 # 91879 # 92554 # 93200 # 93819 <lb/>46 # 87263 # 88102 # 88915 # 89700 # 90457 # 91188 # 91890 # 92565 # 93211 # 93829 <lb/>47 # 87278 # 88116 # 88928 # 89712 # 90470 # 91200 # 91902 # 92576 # 93221 # 93839 <lb/>48 # 87192 # 88130 # 88941 # 89725 # 90482 # 91212 # 91913 # 92587 # 93232 # 93849 <lb/>49 # 87306 # 88144 # 88954 # 89738 # 90495 # 91223 # 91924 # 92598 # 93242 # 93859 <lb/>50 # 87320 # 88157 # 88968 # 89751 # 90507 # 91235 # 91936 # 92609 # 93253 # 93869 <lb/>51 # 87334 # 88171 # 88981 # 89764 # 90519 # 91247 # 91947 # 92620 # 93263 # 93879 <lb/>52 # 87348 # 88185 # 88994 # 89777 # 90532 # 91259 # 91959 # 92630 # 93274 # 93889 <lb/>53 # 87363 # 88198 # 89008 # 89789 # 90544 # 91271 # 91970 # 92641 # 93284 # 93899 <lb/>54 # 87377 # 88212 # 89021 # 89802 # 90556 # 91283 # 91982 # 92652 # 93295 # 93909 <lb/>55 # 87391 # 88226 # 89034 # 89815 # 90569 # 91295 # 91993 # 93663 # 93305 # 93919 <lb/>56 # 87405 # 88240 # 89047 # 89828 # 90581 # 91307 # 92004 # 92674 # 93316 # 93929 <lb/>57 # 87419 # 88253 # 89060 # 89841 # 90593 # 91319 # 92016 # 92685 # 93326 # 93939 <lb/>58 # 87433 # 88267 # 89074 # 89853 # 90606 # 91330 # 92027 # 92696 # 93337 # 93949 <lb/>59 # 87447 # 88281 # 89087 # 89866 # 90618 # 91342 # 92039 # 92707 # 93347 # 93959 <lb/>60 # 87461 # 88294 # 89100 # 89879 # 90630 # 91354 # 92050 # 92718 # 93358 # 93969 <lb/></note>
<pb file="0024" n="24"/>
<note position="right" xml:space="preserve"> <lb/>########## Tabula Sinuum rectorum ſiue ſemichordarum, minutim extenſa. <lb/># 70 # 71 # 72 # 73 # 74 # 75 # 76 # 77 # 78 # 79 <lb/>m̃ # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. <lb/>0 # 93969 # 94551 # 95105 # 95630 # 96126 # 96592 # 97029 # 97437 # 97814 # 98162 <lb/>1 # 93979 # 94561 # 95114 # 95638 # 96134 # 96600 # 97036 # 97443 # 97820 # 98168 <lb/>2 # 93989 # 94570 # 95123 # 95647 # 96142 # 96607 # 97043 # 97450 # 97826 # 98173 <lb/>3 # 93999 # 94580 # 95132 # 95655 # 96150 # 96615 # 97050 # 97496 # 97832 # 98179 <lb/>4 # 94009 # 94589 # 95141 # 95664 # 96158 # 96622 # 97075 # 97463 # 97838 # 98184 <lb/>5 # 94018 # 94599 # 95150 # 95672 # 96166 # 96630 # 97064 # 97469 # 97844 # 98190 <lb/>6 # 94028 # 94608 # 95159 # 95681 # 96174 # 96637 # 97071 # 97476 # 97850 # 98195 <lb/>7 # 94038 # 94617 # 95168 # 95689 # 96182 # 96645 # 97078 # 97482 # 97856 # 98201 <lb/>8 # 94048 # 94627 # 95177 # 95698 # 96190 # 96652 # 97085 # 97489 # 97862 # 98206 <lb/>9 # 94058 # 94636 # 95186 # 95706 # 96198 # 96660 # 97092 # 97495 # 97868 # 98212 <lb/>10 # 94068 # 94646 # 95195 # 95715 # 96205 # 96667 # 97099 # 97502 # 97874 # 98217 <lb/>11 # 94078 # 94655 # 95204 # 95723 # 96213 # 96674 # 97106 # 97508 # 97880 # 98222 <lb/>12 # 94088 # 94664 # 95212 # 95731 # 96221 # 96682 # 97113 # 97514 # 97886 # 98228 <lb/>13 # 94097 # 94674 # 95221 # 95740 # 96229 # 96689 # 97120 # 97521 # 97892 # 98234 <lb/>14 # 94107 # 94683 # 95230 # 95748 # 96237 # 96697 # 97127 # 97527 # 97898 # 98239 <lb/>15 # 94117 # 94693 # 95239 # 95757 # 96245 # 96704 # 97134 # 97534 # 97904 # 98245 <lb/>16 # 94127 # 94702 # 95248 # 95765 # 96253 # 96711 # 97141 # 97540 # 97910 # 98250 <lb/>17 # 94137 # 94711 # 95257 # 95773 # 96261 # 96719 # 97148 # 97547 # 97916 # 98255 <lb/>18 # 94147 # 94721 # 95266 # 95782 # 96269 # 96726 # 97154 # 97553 # 97922 # 98261 <lb/>19 # 94156 # 94730 # 95274 # 95590 # 96277 # 96734 # 97161 # 97559 # 97928 # 98266 <lb/>20 # 94166 # 94739 # 95283 # 95798 # 96284 # 96741 # 97168 # 97566 # 97934 # 98272 <lb/>21 # 94176 # 94748 # 95292 # 95807 # 96292 # 96748 # 97175 # 97572 # 97939 # 98277 <lb/>22 # 94186 # 94758 # 95301 # 95815 # 96300 # 96756 # 97182 # 97578 # 97954 # 98282 <lb/>23 # 94195 # 94767 # 95310 # 95823 # 96308 # 96763 # 97189 # 97585 # 97951 # 98288 <lb/>24 # 94205 # 94776 # 95319 # 95832 # 96316 # 96770 # 97196 # 97591 # 97957 # 98293 <lb/>25 # 94215 # 94786 # 95327 # 95840 # 96324 # 96778 # 97202 # 97598 # 97963 # 98298 <lb/>26 # 94225 # 94795 # 95336 # 95848 # 96331 # 96785 # 97209 # 97604 # 97969 # 98304 <lb/>27 # 94234 # 94804 # 95345 # 95857 # 96339 # 96792 # 97216 # 97610 # 97975 # 98309 <lb/>28 # 94244 # 94813 # 95354 # 95865 # 96347 # 96800 # 97223 # 97616 # 97980 # 98314 <lb/>29 # 94254 # 94823 # 95362 # 95873 # 96355 # 96807 # 97230 # 97623 # 97986 # 98320 <lb/>30 # 94264 # 94832 # 95371 # 95881 # 96363 # 96814 # 97236 # 97629 # 97992 # 98325 <lb/>31 # 94273 # 94841 # 95380 # 95890 # 96370 # 96822 # 97243 # 97635 # 97998 # 98330 <lb/>32 # 94283 # 94850 # 95389 # 95898 # 96378 # 96829 # 97250 # 97642 # 98004 # 98336 <lb/>33 # 94293 # 94860 # 95397 # 95906 # 96386 # 96836 # 97257 # 97648 # 98009 # 98341 <lb/>34 # 94302 # 94869 # 95406 # 95914 # 96394 # 96843 # 97264 # 97654 # 98015 # 98346 <lb/>35 # 94312 # 94878 # 95415 # 95923 # 96401 # 96851 # 97270 # 97660 # 98021 # 98351 <lb/>36 # 94322 # 94887 # 95424 # 95931 # 96409 # 96858 # 97277 # 97667 # 98027 # 98357 <lb/>37 # 94331 # 94896 # 95432 # 95939 # 96417 # 96865 # 97284 # 97673 # 98032 # 98362 <lb/>38 # 94341 # 94905 # 95441 # 95947 # 96424 # 96872 # 97291 # 97679 # 98038 # 98367 <lb/>39 # 94351 # 94951 # 95450 # 95956 # 96432 # 96879 # 97297 # 97685 # 98044 # 98372 <lb/>40 # 94360 # 94924 # 95458 # 95964 # 96440 # 96887 # 97304 # 97692 # 98050 # 98378 <lb/>41 # 94370 # 94933 # 95467 # 95972 # 96448 # 96894 # 97311 # 97698 # 98055 # 98383 <lb/>42 # 94380 # 94942 # 95476 # 95980 # 96455 # 96901 # 97317 # 97704 # 98061 # 98388 <lb/>43 # 94389 # 94951 # 95484 # 95988 # 96463 # 96908 # 97324 # 97710 # 98067 # 98393 <lb/>44 # 94399 # 94960 # 95493 # 95996 # 96471 # 96915 # 97331 # 97716 # 98072 # 98398 <lb/>45 # 94408 # 94969 # 95501 # 96004 # 96478 # 96923 # 97337 # 97723 # 98078 # 98404 <lb/>46 # 94418 # 94979 # 95510 # 96013 # 96486 # 96930 # 97344 # 97729 # 98084 # 98409 <lb/>47 # 94428 # 94988 # 95519 # 96021 # 96494 # 96937 # 97351 # 97735 # 98089 # 98414 <lb/>48 # 94437 # 94997 # 95527 # 96029 # 96501 # 96944 # 97357 # 97741 # 98095 # 98419 <lb/>49 # 94447 # 95006 # 95536 # 96037 # 96509 # 96951 # 97364 # 97747 # 98101 # 98424 <lb/>50 # 94456 # 95015 # 95545 # 96045 # 96516 # 96958 # 97371 # 97753 # 98106 # 98429 <lb/>51 # 94366 # 95024 # 95553 # 96053 # 96524 # 96965 # 97377 # 97760 # 98112 # 98434 <lb/>52 # 94475 # 95033 # 95562 # 96061 # 96532 # 96973 # 97384 # 97766 # 98118 # 98440 <lb/>53 # 94485 # 95042 # 95570 # 96069 # 96539 # 96980 # 97390 # 97772 # 98123 # 98445 <lb/>54 # 94494 # 95051 # 95579 # 96077 # 96547 # 96987 # 97397 # 97778 # 98129 # 98450 <lb/>55 # 94504 # 95060 # 95587 # 96085 # 96554 # 96994 # 97404 # 97784 # 98134 # 98455 <lb/>56 # 94513 # 95069 # 95596 # 96094 # 96562 # 97001 # 97410 # 97790 # 98140 # 98460 <lb/>57 # 94523 # 95078 # 95604 # 96102 # 96569 # 97008 # 97417 # 97796 # 98146 # 98465 <lb/>58 # 94532 # 95087 # 95613 # 96110 # 96577 # 97015 # 97423 # 97802 # 98151 # 98470 <lb/>59 # 94542 # 95096 # 95621 # 96118 # 96585 # 97022 # 97430 # 97808 # 98157 # 98475 <lb/>60 # 94551 # 95105 # 95630 # 96126 # 96592 # 97029 # 97437 # 97814 # 98162 # 98480 <lb/></note>
<pb file="0025" n="25"/>
<note position="right" xml:space="preserve"> <lb/>########## Tabula Sinuum rectorum ſiue ſemichordarum, minutim extenſa. <lb/># 80 # 81 # 82 # 83 # 84 # 85 # 86 # 87 # 88 # 89 <lb/>m̃. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. # Sinus. <lb/>0 # 98480 # 98768 # 99026 # 99254 # 99452 # 99619 # 99756 # 99862 # 99939 # 99984 <lb/>1 # 98485 # 98773 # 99030 # 99258 # 99455 # 99622 # 99758 # 99864 # 99939 # 99985 <lb/>2 # 98490 # 98777 # 99034 # 99261 # 99458 # 99624 # 99760 # 99865 # 99940 # 99985 <lb/>3 # 98495 # 98782 # 99038 # 99265 # 99461 # 99627 # 99762 # 99867 # 99941 # 99985 <lb/>4 # 98500 # 98786 # 99042 # 99268 # 99464 # 99629 # 99764 # 99868 # 99942 # 99986 <lb/>5 # 98505 # 98791 # 99046 # 99272 # 99467 # 99632 # 99766 # 99870 # 99943 # 99987 <lb/>6 # 98510 # 98795 # 99050 # 99275 # 99470 # 99634 # 99768 # 99871 # 99944 # 99987 <lb/>7 # 98515 # 98800 # 99054 # 99279 # 99473 # 99637 # 99770 # 99873 # 99945 # 99988 <lb/>8 # 98520 # 98804 # 99058 # 99282 # 99476 # 99639 # 99772 # 99874 # 99945 # 99988 <lb/>9 # 98525 # 98809 # 99062 # 99285 # 99479 # 99641 # 99774 # 99876 # 99946 # 99988 <lb/>10 # 98530 # 98813 # 99066 # 99289 # 99482 # 99644 # 99776 # 99877 # 99947 # 99989 <lb/>11 # 98535 # 98818 # 99070 # 99293 # 99485 # 99646 # 99778 # 99878 # 99948 # 99989 <lb/>12 # 98540 # 98822 # 99074 # 99296 # 99488 # 99649 # 99780 # 99879 # 99949 # 99990 <lb/>13 # 98545 # 98827 # 99078 # 99300 # 99491 # 99651 # 99782 # 99880 # 99950 # 99990 <lb/>14 # 98550 # 98831 # 99082 # 99303 # 99493 # 99654 # 99783 # 99882 # 99951 # 99991 <lb/>15 # 98555 # 98836 # 99086 # 99306 # 99496 # 99656 # 99785 # 99883 # 99952 # 99991 <lb/>16 # 98560 # 98840 # 99090 # 99310 # 99499 # 99658 # 99787 # 99884 # 99953 # 99991 <lb/>17 # 98565 # 98844 # 99094 # 99313 # 99502 # 99661 # 99789 # 99886 # 99954 # 99992 <lb/>18 # 98570 # 98849 # 99098 # 99317 # 99505 # 99663 # 99791 # 99888 # 99955 # 99992 <lb/>19 # 98575 # 98853 # 99102 # 99520 # 99508 # 99666 # 99793 # 99890 # 99955 # 99992 <lb/>20 # 98580 # 98858 # 99106 # 99323 # 99511 # 99668 # 99795 # 99891 # 99956 # 99993 <lb/>21 # 98585 # 98862 # 99109 # 99327 # 99514 # 99670 # 99797 # 99893 # 99957 # 99993 <lb/>22 # 98589 # 98866 # 99113 # 99330 # 99517 # 99673 # 99799 # 99894 # 99958 # 99993 <lb/>23 # 98594 # 98871 # 99117 # 99333 # 99519 # 99675 # 99800 # 99895 # 99959 # 99994 <lb/>24 # 98599 # 98875 # 99121 # 99337 # 99522 # 99677 # 99802 # 99897 # 99960 # 99994 <lb/>25 # 98604 # 98879 # 99125 # 99340 # 99525 # 99680 # 99804 # 99898 # 99961 # 99994 <lb/>26 # 98@09 # 98884 # 99129 # 99343 # 99528 # 99682 # 99806 # 99899 # 99961 # 99995 <lb/>27 # 98614 # 98888 # 99133 # 99347 # 99531 # 99684 # 99808 # 99900 # 99962 # 99995 <lb/>28 # 98618 # 98892 # 99136 # 99350 # 99534 # 99687 # 99809 # 99902 # 99963 # 99995 <lb/>29 # 98623 # 98897 # 99140 # 99353 # 99536 # 99689 # 99811 # 99903 # 99964 # 99995 <lb/>30 # 98628 # 98901 # 99144 # 99357 # 99539 # 99691 # 99813 # 99904 # 99964 # 99996 <lb/>31 # 98633 # 98905 # 99148 # 99360 # 99542 # 99694 # 99815 # 99906 # 99965 # 99996 <lb/>32 # 98638 # 98910 # 99152 # 99363 # 99545 # 99696 # 99817 # 99907 # 99966 # 99996 <lb/>33 # 98642 # 98914 # 99155 # 99367 # 99547 # 99698 # 99818 # 99908 # 99967 # 99996 <lb/>34 # 98647 # 98918 # 99159 # 99370 # 99550 # 99700 # 99820 # 99909 # 99967 # 99997 <lb/>35 # 98652 # 98922 # 99163 # 99373 # 99553 # 99703 # 99822 # 99911 # 99968 # 99997 <lb/>36 # 98657 # 98927 # 99167 # 99376 # 99556 # 99705 # 99823 # 99912 # 99969 # 99997 <lb/>37 # 98661 # 98931 # 99170 # 99380 # 99558 # 99707 # 99825 # 99913 # 99970 # 99997 <lb/>38 # 98666 # 98935 # 99174 # 99383 # 99561 # 99709 # 99827 # 99914 # 99970 # 99997 <lb/>39 # 98671 # 98939 # 99178 # 99386 # 99564 # 99711 # 99829 # 99915 # 99971 # 99998 <lb/>40 # 98676 # 98944 # 99182 # 99389 # 99567 # 99714 # 99830 # 99917 # 99972 # 99998 <lb/>41 # 98680 # 98948 # 99185 # 99392 # 99569 # 99716 # 99832 # 99918 # 99972 # 99998 <lb/>42 # 98685 # 98952 # 99189 # 99396 # 99572 # 99718 # 99834 # 99919 # 99973 # 99998 <lb/>43 # 98690 # 98956 # 99193 # 99399 # 99575 # 99720 # 99835 # 99920 # 99974 # 99998 <lb/>44 # 98694 # 98960 # 99196 # 99402 # 99577 # 99722 # 99837 # 99921 # 99974 # 99998 <lb/>45 # 98699 # 98965 # 99200 # 99405 # 99580 # 99725 # 99839 # 99922 # 99975 # 99999 <lb/>46 # 98604 # 98969 # 99204 # 99408 # 99583 # 99727 # 99840 # 99924 # 99976 # 99999 <lb/>47 # 98608 # 98973 # 99207 # 99411 # 99585 # 99729 # 99842 # 99925 # 99976 # 99999 <lb/>48 # 98713 # 98977 # 99211 # 99415 # 99588 # 99731 # 99844 # 99926 # 99977 # 99999 <lb/>49 # 98718 # 98981 # 99215 # 99418 # 99591 # 99733 # 99845 # 99927 # 99978 # 99999 <lb/>50 # 98722 # 98985 # 99218 # 99421 # 99593 # 99735 # 99847 # 99928 # 99978 # 99999 <lb/>51 # 98727 # 98990 # 99222 # 99424 # 99396 # 99737 # 99848 # 99929 # 99979 # 99999 <lb/>52 # 98732 # 98994 # 99225 # 99427 # 99598 # 99739 # 99850 # 99937 # 99980 # 99999 <lb/>53 # 98736 # 98998 # 99229 # 99430 # 99601 # 99742 # 99852 # 99931 # 99981 # 99999 <lb/>54 # 98741 # 99002 # 99233 # 99433 # 99604 # 99744 # 99853 # 99932 # 99981 # 99999 <lb/>55 # 98745 # 99006 # 99236 # 99436 # 99606 # 99746 # 99855 # 99933 # 99982 # 99999 <lb/>56 # 98750 # 99010 # 99240 # 99439 # 99609 # 99748 # 99856 # 99934 # 99982 # 99999 <lb/>57 # 98755 # 99014 # 99244 # 99443 # 99611 # 99750 # 99858 # 99935 # 99983 # 99999 <lb/>58 # 98759 # 99018 # 99247 # 99446 # 99614 # 99752 # 99859 # 99937 # 99983 # 99999 <lb/>59 # 98764 # 99022 # 99251 # 99449 # 99616 # 99754 # 99861 # 99938 # 99984 # 100000 <lb/>60 # 98768 # 99025 # 99256 # 99452 # 99619 # 99756 # 99862 # 99939 # 99984 # 100000 <lb/></note>
<pb file="0026" n="26" rhead="GENVINVS VSVS"/>
</div>
<div xml:id="echoid-div11" type="section" level="1" n="8">
<head xml:id="echoid-head10" xml:space="preserve">Sequuntur nunc canones uſum ſiue ingreſſum iſtarum <lb/>tabularum lucidiſsime declarantes.</head>
<p>
  <s xml:id="echoid-s598" xml:space="preserve">QVando arcus propoſiti ſinum ex tabulis ſupputare deſideras, primo conſidera an <lb/>maior aut minor quadrãte exiſtat. </s>
  <s xml:id="echoid-s599" xml:space="preserve">fit interdum ut arcus quarta circuli parte ſit mi <lb/>
<anchor type="note" xlink:label="note-0026-01a" xlink:href="note-0026-01"/>
nor, aliquando maior, &amp; </s>
  <s xml:id="echoid-s600" xml:space="preserve">tamen ſemicirculo minor, hoc eſt gra. </s>
  <s xml:id="echoid-s601" xml:space="preserve">180. </s>
  <s xml:id="echoid-s602" xml:space="preserve">nonnunquam etiam <lb/>maior illo, &amp; </s>
  <s xml:id="echoid-s603" xml:space="preserve">adhuc minor gradibus 270. </s>
  <s xml:id="echoid-s604" xml:space="preserve">quæ tres quartæ ſunt circuli unius, quibus etiã <lb/>arcus dari poteſt maior, &amp; </s>
  <s xml:id="echoid-s605" xml:space="preserve">tamẽ toto circulo minor. </s>
  <s xml:id="echoid-s606" xml:space="preserve">Quicquid aũt ſit, facile huiuſmo <lb/>di arcus ſinum inuenire poteris in hunc modum. </s>
  <s xml:id="echoid-s607" xml:space="preserve">Si arcus 90. </s>
  <s xml:id="echoid-s608" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s609" xml:space="preserve">fuerit minor, tabulam <lb/>
<anchor type="note" xlink:label="note-0026-02a" xlink:href="note-0026-02"/>
præſcriptam ingredere, in eius capite quære gradus cum minutisiuxta lineam primam <lb/>manus ſiniſtræ deſcendẽdo, &amp; </s>
  <s xml:id="echoid-s610" xml:space="preserve">inuenies in angulo communi ſinũ arcus propoſiti. </s>
  <s xml:id="echoid-s611" xml:space="preserve">Sin <lb/>autẽ arcus gra. </s>
  <s xml:id="echoid-s612" xml:space="preserve">90. </s>
  <s xml:id="echoid-s613" xml:space="preserve">maior fuerit, &amp; </s>
  <s xml:id="echoid-s614" xml:space="preserve">tamen adhuc minor gradibus 180. </s>
  <s xml:id="echoid-s615" xml:space="preserve">ſubtrahe hinc 90. <lb/></s>
  <s xml:id="echoid-s616" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s617" xml:space="preserve">cum reſiduo tabulam ingreſſus, inuenies etiã ſinum arcus quem quærebas. </s>
  <s xml:id="echoid-s618" xml:space="preserve">Si porrò <lb/>arcus maior fuerit gradibus 180. </s>
  <s xml:id="echoid-s619" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s620" xml:space="preserve">tamen 270. </s>
  <s xml:id="echoid-s621" xml:space="preserve">minor, ſubtractis inde 180. </s>
  <s xml:id="echoid-s622" xml:space="preserve">ingredere <lb/>tabulam cũ reſiduo, &amp; </s>
  <s xml:id="echoid-s623" xml:space="preserve">inuenies quod optas. </s>
  <s xml:id="echoid-s624" xml:space="preserve">Similiter operare quum arcus maior eſt <lb/>gra. </s>
  <s xml:id="echoid-s625" xml:space="preserve">270. </s>
  <s xml:id="echoid-s626" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s627" xml:space="preserve">tamen minor 360. </s>
  <s xml:id="echoid-s628" xml:space="preserve">Quando &amp; </s>
  <s xml:id="echoid-s629" xml:space="preserve">hoc fit nõ raro, ut dati ſinus recti arcũ ſcire <lb/>cupias, tunc ita  ſinum illum quære in tabulis præſcriptis in area aliqua, ſi non præciſe <lb/>attamen quàm potes rectiſsime proximum illum accipiendo, qui nec magnus, nec nimi <lb/>um ſit paruus, &amp; </s>
  <s xml:id="echoid-s630" xml:space="preserve">tunc ab iſto digitum directe ad ſiniſtram educendo, inuenies in prima <lb/>linea numeros minutorum, &amp; </s>
  <s xml:id="echoid-s631" xml:space="preserve">ſi directe ſurſum ab eo ſinu tendas, inuenies in capite ta-<lb/>bulæ etiam gradus, quos ubi minutis coniunxeris, habebis arcũ quæſitum. </s>
  <s xml:id="echoid-s632" xml:space="preserve">Quid ſi au <lb/>tem tot fuerint ſinus ij, ut in tabula inuenire nequeant? </s>
  <s xml:id="echoid-s633" xml:space="preserve">tunc ſanè ſubtrahe ab eo ſinu <lb/>100000. </s>
  <s xml:id="echoid-s634" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s635" xml:space="preserve">cum reſiduo quære arcum ut ſupra. </s>
  <s xml:id="echoid-s636" xml:space="preserve">Quod ſi arcus propoſiti ſinũ uerſum <lb/>
<anchor type="note" xlink:label="note-0026-03a" xlink:href="note-0026-03"/>
inueſtigare uolueris, &amp; </s>
  <s xml:id="echoid-s637" xml:space="preserve">hic minor fuerit 90. </s>
  <s xml:id="echoid-s638" xml:space="preserve">cuius reſidui ſinum ſtatim rectum inquire, ip <lb/>ſum´ à ſinu toto ubi ſubtraxeris, remanebit ſinus uerſus quem quæſiſti. </s>
  <s xml:id="echoid-s639" xml:space="preserve">Sin aũt arcus 90 <lb/>maior fuerit, &amp; </s>
  <s xml:id="echoid-s640" xml:space="preserve">minor 180. </s>
  <s xml:id="echoid-s641" xml:space="preserve">ſubtrahe inde 90. </s>
  <s xml:id="echoid-s642" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s643" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s644" xml:space="preserve">cum reſiduo quære ſinũ rectũ, eũ ad-<lb/>de ad 100000. </s>
  <s xml:id="echoid-s645" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s646" xml:space="preserve">habebis ſinũ uerſum arcus ꝓpoſiti. </s>
  <s xml:id="echoid-s647" xml:space="preserve">Siuero habueris ſinũ uerſum, &amp; </s>
  <s xml:id="echoid-s648" xml:space="preserve">uis <lb/>
<anchor type="note" xlink:label="note-0026-04a" xlink:href="note-0026-04"/>
indagare arcum illius, conſidera ſi minor fuerit 100000. </s>
  <s xml:id="echoid-s649" xml:space="preserve">ſubtrahe eum â 100000. </s>
  <s xml:id="echoid-s650" xml:space="preserve">cũ eius <lb/>reſiduiſinu quærere arcũ illum, ſi ſubtraxeris à 90. </s>
  <s xml:id="echoid-s651" xml:space="preserve">remanebit arcus optatus. </s>
  <s xml:id="echoid-s652" xml:space="preserve">Sin uero <lb/>fuerit maior ſinu perſecto, inquiſiturus ſic quo arcum, ſubtrahe de ſinu uerſo 100000. <lb/></s>
  <s xml:id="echoid-s653" xml:space="preserve">eius reſidui quære arcum non ſecus ac ſi ſinus rectus eſſet. </s>
  <s xml:id="echoid-s654" xml:space="preserve">arcum illum adde ad grad. </s>
  <s xml:id="echoid-s655" xml:space="preserve">90. </s>
  <s xml:id="echoid-s656" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0026-05a" xlink:href="note-0026-05"/>
&amp; </s>
  <s xml:id="echoid-s657" xml:space="preserve">tunc habebis arcũ ſinus quẽ quærebas. </s>
  <s xml:id="echoid-s658" xml:space="preserve">Si uero arcus propoſiti chordam inuenire <lb/>uolueris, eodem modo operare, ut inquirendo ſinum, niſi quòd arcum illum medium tan <lb/>tum accipere debes, eius arcus inuentus &amp; </s>
  <s xml:id="echoid-s659" xml:space="preserve">duplicatus ſinus, chordam monſtrat quæſitã. <lb/></s>
  <s xml:id="echoid-s660" xml:space="preserve">ſiquidẽ cũ Sinus, quod principio cõmemorauimus, nihil aliud eſt quàm arcus dati chor <lb/>
<anchor type="note" xlink:label="note-0026-06a" xlink:href="note-0026-06"/>
da media. </s>
  <s xml:id="echoid-s661" xml:space="preserve">Chordæ uero propoſitæ arcũ inuenies facillime, modo chordam mediaris, <lb/>&amp; </s>
  <s xml:id="echoid-s662" xml:space="preserve">medij illius arcum quæſieris ex præmiſsis, arcum quo iſtum dehinc duplicaris, tunc <lb/>enim ſinum habebis quæſitum.</s>
  <s xml:id="echoid-s663" xml:space="preserve"/>
</p>
<div xml:id="echoid-div11" type="float" level="2" n="1">
<note position="left" xlink:label="note-0026-01" xlink:href="note-0026-01a" xml:space="preserve"><emph style="it">Cuiuslibet</emph> <lb/><emph style="it">arcus qud-</emph> <lb/><emph style="it">drãte mino</emph> <lb/><emph style="it">ris ſinũ ut</emph> <lb/><emph style="it">inuenias.</emph></note>
<note position="left" xlink:label="note-0026-02" xlink:href="note-0026-02a" xml:space="preserve"><emph style="it">Propoſiti</emph> <lb/><emph style="it">arcus qud-</emph> <lb/><emph style="it">drãte maio-</emph> <lb/><emph style="it">ris, nec non</emph> <lb/><emph style="it">ſemiãr culo</emph> <lb/><emph style="it">minoris</emph> <lb/><emph style="it">quõ ſinus</emph> <lb/><emph style="it">quærẽdg ſit</emph> <lb/><emph style="it">Vbi ſing nu</emph> <lb/><emph style="it">merũ ſupat</emph> <lb/><emph style="it">100000. ue</emph> <lb/><emph style="it">luti arcg eig</emph> <lb/><emph style="it">ſit inuenicn</emph> <lb/><emph style="it">dus.</emph></note>
<note position="left" xlink:label="note-0026-03" xlink:href="note-0026-03a" xml:space="preserve"><emph style="it">Vt inuenia</emph> <lb/><emph style="it">tur ſing uer</emph> <lb/><emph style="it">ſus ꝓ ppoſiti</emph> <lb/><emph style="it">arcus.</emph></note>
<note position="left" xlink:label="note-0026-04" xlink:href="note-0026-04a" xml:space="preserve"><emph style="it">Habito ſinu</emph> <lb/><emph style="it">uerſu quõ</emph> <lb/><emph style="it">arcus eiuſdê</emph> <lb/><emph style="it">agnoſ@tur.</emph></note>
<note position="left" xlink:label="note-0026-05" xlink:href="note-0026-05a" xml:space="preserve"><emph style="it">Chordã ꝓ-</emph> <lb/><emph style="it">poſiti arcus</emph> <lb/><emph style="it">ueluti de-</emph> <lb/><emph style="it">prehendas.</emph></note>
<note position="left" xlink:label="note-0026-06" xlink:href="note-0026-06a" xml:space="preserve"><emph style="it">Ad propo-</emph> <lb/><emph style="it">ſitam chor-</emph> <lb/><emph style="it">dam arcum</emph> <lb/><emph style="it">ut ſdas</emph>.</note>
</div>
  <figure>
    <image file="0026-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0026-01"/>
  </figure>
<pb file="0027" n="27" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
</div>
<div xml:id="echoid-div13" type="section" level="1" n="9">
<head xml:id="echoid-head11" xml:space="preserve">Appendix primi huius pronunciati.</head>
<p>
  <s xml:id="echoid-s664" xml:space="preserve">P Oſtquam abunde diſſertum eſt ſuper præparatione, qua quis ſupputando Primum <lb/>Mobile per ſinus aſſequatur, ſubinde non uanũ iudicauimus, ſi &amp; </s>
  <s xml:id="echoid-s665" xml:space="preserve">eoſdem Mobilis <lb/>primi uſus per inſtrumentum cõſequi tradamus, eo´ potiſſimum, quod maior ferè pars <lb/>huc incumbentium, ſphæricæ ſupputationis ignara indocta´ ſit, licet interim diffiteri <lb/>non audemus per calculos quæcun prædictorum commoda plura´ alia cõſummati-<lb/>us haberi poſſe longe quàm per inſtrumenta. </s>
  <s xml:id="echoid-s666" xml:space="preserve">Attamen ne pleri retroacti rationum <lb/>oneribus opus deſerant, idcirco inſtrumentum quo rem inuenire quàm promptiſsime <lb/>poſſunt adĳcere coacti ſumus. </s>
  <s xml:id="echoid-s667" xml:space="preserve">In eo enim non ſecus at per numeros omnia efficiun-<lb/>tur, qua muis non adeo exacte &amp; </s>
  <s xml:id="echoid-s668" xml:space="preserve">minutim uſ, niſi inſtrumentum quantitate præſter. <lb/></s>
  <s xml:id="echoid-s669" xml:space="preserve">quanto nan inſtrumentum eſt capacius tanto certius, &amp; </s>
  <s xml:id="echoid-s670" xml:space="preserve">computo uicinius reſpondet. </s>
  <s xml:id="echoid-s671" xml:space="preserve"><lb/>Compoſitionem igitur nunc trademus eiuſmodi, ut qualecun inſtrumentum libeat fa <lb/>
<anchor type="note" xlink:label="note-0027-01a" xlink:href="note-0027-01"/>
bricare (quale in poſterum uocabitur Primi mobilis Quadrans) non ægre liceat. </s>
  <s xml:id="echoid-s672" xml:space="preserve">Pri-<lb/>mum ergo ſemicirculus in ſuperficie plana, quæ, uel lignea, uel papyracea, uel metallica <lb/>ſit, fiat, cuius diametro KC inſcribantur, cẽtro litera A circuli KC mediũ quæratur, <lb/>&amp; </s>
  <s xml:id="echoid-s673" xml:space="preserve">cum B litera ſignetur, A &amp; </s>
  <s xml:id="echoid-s674" xml:space="preserve">B iungantur cũ linea recta, quæ diuidet ſemicirculi pla <lb/>num in quadrantes duos, quorŭ alter KB, alter BC uocabitur, ſingu!os in 90. </s>
  <s xml:id="echoid-s675" xml:space="preserve">partes <lb/>more aſtronomico ſectus. </s>
  <s xml:id="echoid-s676" xml:space="preserve">Puncta item uicina literis K &amp; </s>
  <s xml:id="echoid-s677" xml:space="preserve">C cõnectantur recta, quæ pa <lb/>rallela lineæ K C erit. </s>
  <s xml:id="echoid-s678" xml:space="preserve">Iam proxima ſequentia duo quadrantum puncta iunge linea re-<lb/>cta, item tertia, item quarta, donec omnia connexueris quadrantum amborum, ſicut <lb/>perpetuò in eadẽ diſtantia ſint à K &amp; </s>
  <s xml:id="echoid-s679" xml:space="preserve">C, quo ad in B uſ perueniatur. </s>
  <s xml:id="echoid-s680" xml:space="preserve">Sciendum tamẽ <lb/>lineas has in quadrãte A B C, dũtaxat ꝓduci ſic, ut manifeſtè ſint, oportere, in quadran <lb/>te A B K minime, ſed occultè, poſterior enim ille quadrans abĳciendus omnino erit, cũ <lb/>nihil uſui reliq̊ cõferat. </s>
  <s xml:id="echoid-s681" xml:space="preserve">Iam inchoando à C uerſus B limbi numera quin, ea´ ſigna <lb/>cum cyffra 5. </s>
  <s xml:id="echoid-s682" xml:space="preserve">Poſtea alia quin numera, &amp; </s>
  <s xml:id="echoid-s683" xml:space="preserve">ea cum 10. </s>
  <s xml:id="echoid-s684" xml:space="preserve">inſcribe, &amp; </s>
  <s xml:id="echoid-s685" xml:space="preserve">ſic conſequenter qua <lb/>drantem integrũ per quinarios, donec in 90. </s>
  <s xml:id="echoid-s686" xml:space="preserve">peruenias, inſigni, ſimiliter ab A uerſus B <lb/>fiat, &amp; </s>
  <s xml:id="echoid-s687" xml:space="preserve">quadrantem perfectum habebis, dempto quod filum adhuc unà cum margarica <lb/>centro A porrectum deſideretur, quod ſi addis, omnia habes, ueluti etiam prima illa ſe <lb/>quens docet figura.</s>
  <s xml:id="echoid-s688" xml:space="preserve"/>
</p>
<div xml:id="echoid-div13" type="float" level="2" n="1">
<note position="right" xlink:label="note-0027-01" xlink:href="note-0027-01a" xml:space="preserve"><emph style="it">Compoſitiò</emph> <lb/><emph style="it">Quaàrãtis</emph></note>
</div>
</div>
<div xml:id="echoid-div15" type="section" level="1" n="10">
<head xml:id="echoid-head12" xml:space="preserve">VSVS QVADRANTIS.</head>
<p>
  <s xml:id="echoid-s689" xml:space="preserve">Duplex uſus eſt inſtrumenti, quem aliàs ingreſſum appellaueris, ſcilicet Lateralis <lb/>&amp; </s>
  <s xml:id="echoid-s690" xml:space="preserve">Arealis. </s>
  <s xml:id="echoid-s691" xml:space="preserve">Lateralis eſt, quando duo numeri noti quæruntur, hic in diametro AB, il-<lb/>
<anchor type="note" xlink:label="note-0027-02a" xlink:href="note-0027-02"/>
le in limbo BC. </s>
  <s xml:id="echoid-s692" xml:space="preserve">Arealis, quando unus ſaltem &amp; </s>
  <s xml:id="echoid-s693" xml:space="preserve">is notus in area quadrantis requiritur <lb/>altero uero in diametro uel limbo. </s>
  <s xml:id="echoid-s694" xml:space="preserve">Lateralis uſus bifariam patet. </s>
  <s xml:id="echoid-s695" xml:space="preserve">Verum numeri duo <lb/>quibus latera ingredi paras diſsimiles eſſe debẽt, ueluti, hic maior, ille minor, uel contra, <lb/>nunquam uero pares. </s>
  <s xml:id="echoid-s696" xml:space="preserve">Primus introeundi modus ſic perficitur. </s>
  <s xml:id="echoid-s697" xml:space="preserve">Numerum minorem in <lb/>
<anchor type="note" xlink:label="note-0027-03a" xlink:href="note-0027-03"/>
dia metro AB accipis, cui filum cum margarita adducis, maiorempoſtea in limbo <lb/>BC requiris, filum´ per eundem extendis, ſic enim agenti unio numerum oſtendit quæ <lb/>
<anchor type="note" xlink:label="note-0027-04a" xlink:href="note-0027-04"/>
ſitum, Arealem ſcilicet in quadrantis area, Linea autem graduum cui margarita inci-<lb/>dit, numerum ſuum in diametro AB, nec non in limbo BC ſignatum obtinet, cuius rei <lb/>exemplum eſto. </s>
  <s xml:id="echoid-s698" xml:space="preserve">Vt ſi ponatur lateralis numerus minor 30. </s>
  <s xml:id="echoid-s699" xml:space="preserve">ſcilicet graduum, maior ue <lb/>ro 43. </s>
  <s xml:id="echoid-s700" xml:space="preserve">graduum &amp; </s>
  <s xml:id="echoid-s701" xml:space="preserve">10. </s>
  <s xml:id="echoid-s702" xml:space="preserve">minutorum. </s>
  <s xml:id="echoid-s703" xml:space="preserve">Minor uero 30. </s>
  <s xml:id="echoid-s704" xml:space="preserve">in diametro AB quæratur (id quod <lb/>eſt in figura per E literam expreſſum) filum´ ſuper inducatur margarita adiuncta, de <lb/>inde idem filum maiori numero, qui eſt graduũ 43. </s>
  <s xml:id="echoid-s705" xml:space="preserve">minut. </s>
  <s xml:id="echoid-s706" xml:space="preserve">10. </s>
  <s xml:id="echoid-s707" xml:space="preserve">admoueatur, &amp; </s>
  <s xml:id="echoid-s708" xml:space="preserve">hoc in lim <lb/>bo, tũ margarita cõperitur in area oſtendere gradũ 20. </s>
  <s xml:id="echoid-s709" xml:space="preserve">in puncto H, numerũ hactenus <lb/>ignotum. </s>
  <s xml:id="echoid-s710" xml:space="preserve">Nec ignorandum eſt, quod numeri Arealis non ſignentur tantum in area, ſed <lb/>etiã reperiam iuxta lineæ &amp; </s>
  <s xml:id="echoid-s711" xml:space="preserve">diametri AB arcus, itidem BC contactus. </s>
  <s xml:id="echoid-s712" xml:space="preserve">Inuertemus nũc <lb/>
<anchor type="note" xlink:label="note-0027-05a" xlink:href="note-0027-05"/>
exemplum hoc modo, quæ &amp; </s>
  <s xml:id="echoid-s713" xml:space="preserve">ſecunda lateraliter operandi uia eſt. </s>
  <s xml:id="echoid-s714" xml:space="preserve">Numerum maiorem <lb/>qui eſt graduũ 43. </s>
  <s xml:id="echoid-s715" xml:space="preserve">minut. </s>
  <s xml:id="echoid-s716" xml:space="preserve">10. </s>
  <s xml:id="echoid-s717" xml:space="preserve">in diametro AB ſumemus. </s>
  <s xml:id="echoid-s718" xml:space="preserve">quem locũ unione@ſignabimus <lb/>(id q̊d in tertia figura per literã D clarũ fit) iam ſi filum gradibus 30. </s>
  <s xml:id="echoid-s719" xml:space="preserve">qui numerus mi-<lb/>nor eſt, inferimus margaritam, non ſecus at antea gradum 20. </s>
  <s xml:id="echoid-s720" xml:space="preserve">demonſtrare in area cer
<pb file="0028" n="28" rhead="GENVINVS VSVS"/>
nemus in puncto I. </s>
  <s xml:id="echoid-s721" xml:space="preserve">Ita uia ſiue ingreſſu duplici idem nobis repertum eſt, lateraliter ta-<lb/>men, unde etiam illud patuit, quod citra diſcrimen lateraliter operanti numerus minor <lb/>accipi queat, tam in diametro AB, quàm in limbo BC, ubi ſi minor numerus è diame <lb/>
<anchor type="note" xlink:label="note-0028-01a" xlink:href="note-0028-01"/>
tro mutuatur, tum maior erat ex arcu ſumendus:</s>
  <s xml:id="echoid-s722" xml:space="preserve"><unsure/> maiore numero accepto è diametro, mi <lb/>nor in arcu BC legendus. </s>
  <s xml:id="echoid-s723" xml:space="preserve">Lateralis autẽ ideo uocatur, quia utri numeri in quadrã <lb/>tis lateribus inueſtigentur, non autẽ in area. </s>
  <s xml:id="echoid-s724" xml:space="preserve">Arealis uero ingreſſus eſtis, quando nu-<lb/>merus cognitus in area quadrantis ſumitur, qui idem generaliter quo &amp; </s>
  <s xml:id="echoid-s725" xml:space="preserve">perpetuo mi <lb/>nor eſſe debet, alius autem, hoc eſt, maior, ſiue in diametro ſiue in limbo pro agentis arbi <lb/>
<anchor type="note" xlink:label="note-0028-02a" xlink:href="note-0028-02"/>
trio. </s>
  <s xml:id="echoid-s726" xml:space="preserve">?</s>
  <s xml:id="echoid-s727" xml:space="preserve">? Exempli cauſſa: </s>
  <s xml:id="echoid-s728" xml:space="preserve">Numeri ſint duo, 30 gradus &amp; </s>
  <s xml:id="echoid-s729" xml:space="preserve">20, quibus cũ areatim ingredi ue <lb/>lis, 20 ergo numerus minor cum ſit, neceſſum eſt, ut in area requiratur, 30 uero ſi in <lb/>diametro AB (cuiuſmodi in figura quarta ſequenti per literam E docetur) capiuntur, <lb/>30 unione´ exprimuntur, &amp; </s>
  <s xml:id="echoid-s730" xml:space="preserve">filum denuo ab A uerſus C promouetur, donec unio 20 a-<lb/>reæ gradum, id eſt, 20 lineam à diametro AC diſsitam teneat, tum ſecari à filo gradus <lb/>43. </s>
  <s xml:id="echoid-s731" xml:space="preserve">minut. </s>
  <s xml:id="echoid-s732" xml:space="preserve">10. </s>
  <s xml:id="echoid-s733" xml:space="preserve">conſpiciuntur, id quod in quarta figura punctum F arguit, hic autem eſt <lb/>numerus lateralis alter, quem quærebas. </s>
  <s xml:id="echoid-s734" xml:space="preserve">Potes uiciſsim lateralem notum ueluti gradus <lb/>30 in limbo requirere (ſicuti figura quinta per G punctum inſinuat, filum´ eo dirigere, <lb/>quo directo ſi margaritam in 20 gradum areæ figis, iterum´ filum diametro AB in-<lb/>tendis, cernis ab unione ſimiliter gradus 43. </s>
  <s xml:id="echoid-s735" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s736" xml:space="preserve">10. </s>
  <s xml:id="echoid-s737" xml:space="preserve">in pũcto D, ut antea oſtẽdi. </s>
  <s xml:id="echoid-s738" xml:space="preserve">Is autem <lb/>lateralis ſecundus eſt, antea incognitus, ueluti habetur palam in figura quinta. </s>
  <s xml:id="echoid-s739" xml:space="preserve">Sed quæ <lb/>per ſecundam, tertiam, quartam &amp; </s>
  <s xml:id="echoid-s740" xml:space="preserve">quintam figuras docuimus, illa manifeſtius adhuc <lb/>per ſextam diſces.</s>
  <s xml:id="echoid-s741" xml:space="preserve"/>
</p>
<div xml:id="echoid-div15" type="float" level="2" n="1">
<note position="right" xlink:label="note-0027-02" xlink:href="note-0027-02a" xml:space="preserve"><emph style="it">Latcralis</emph> <lb/><emph style="it">ingreſſus</emph> <lb/><emph style="it">quid.</emph></note>
<note position="right" xlink:label="note-0027-03" xlink:href="note-0027-03a" xml:space="preserve"><emph style="it">Arealis in-</emph> <lb/><emph style="it">greſſus ꝗd.</emph></note>
<note position="right" xlink:label="note-0027-04" xlink:href="note-0027-04a" xml:space="preserve"><emph style="it">Prima uia</emph> <lb/><emph style="it">lateralis in</emph> <lb/><emph style="it">greſſus.</emph></note>
<note position="right" xlink:label="note-0027-05" xlink:href="note-0027-05a" xml:space="preserve"><emph style="it">Sccũda uia</emph> <lb/><emph style="it">lateralis in</emph> <lb/><emph style="it">greſſus.</emph></note>
<note position="left" xlink:label="note-0028-01" xlink:href="note-0028-01a" xml:space="preserve"><emph style="it">Latcralis</emph> <lb/><emph style="it">ingreſſus</emph> <lb/><emph style="it">cur ita nomi</emph> <lb/><emph style="it">natus.</emph></note>
<note position="left" xlink:label="note-0028-02" xlink:href="note-0028-02a" xml:space="preserve"><emph style="it">Arealis ꝗd</emph> <lb/><emph style="it">&amp; cur ita</emph> <lb/><emph style="it">nuncupatus</emph></note>
</div>
<pb file="0029" n="29"/>
  <figure>
    <image file="0029-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0029-01"/>
  </figure>
<pb file="0030" n="30" rhead="GENVINVS VSVS"/>
<p>
  <s xml:id="echoid-s742" xml:space="preserve">Hæcigitur ſufficiãt de ingreſsibus tradita. </s>
  <s xml:id="echoid-s743" xml:space="preserve">Reſtat ut generali quadam methodo doce <lb/>am, quomodo uſus centum ſubſcriptos per quadrantem quo hunc conſequi ualeas, cõ <lb/>fiat autem id duabus regulis, quarum prima eſt.</s>
  <s xml:id="echoid-s744" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div17" type="section" level="1" n="11">
<head xml:id="echoid-head13" xml:space="preserve">REGVLA PRIMA.</head>
<p>
  <s xml:id="echoid-s745" xml:space="preserve">Quotieſcun hoc in libro dicitur fieri oportere diuiſionem, hanc´ per ſinum inte-<lb/>grum ſiue perfectum, Toties putãdum eſt operationem eandem in qua drante exigi poſ <lb/>ſe per lateralem introitum.</s>
  <s xml:id="echoid-s746" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div18" type="section" level="1" n="12">
<head xml:id="echoid-head14" xml:space="preserve">REGVLA SECVNDA.</head>
<p>
  <s xml:id="echoid-s747" xml:space="preserve">Quoties multiplicationẽ fieri per ſinum integrum ſiue perfectũ contingit, toties o-<lb/>perandum eſt arealiter in quadrante, ueluti per totum opus in paginarum marginibus <lb/>paſsim indica mus, nunc arealem, nunc lateralem ingreſſum hortantes.</s>
  <s xml:id="echoid-s748" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div19" type="section" level="1" n="13">
<head xml:id="echoid-head15" xml:space="preserve">TALIS AD VSVM QVADRANS ADORNARI</head>
<head xml:id="echoid-head16" xml:space="preserve">debet quantuſcun ſit.</head>
  <figure>
    <image file="0030-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0030-01"/>
  </figure>
<pb file="0031" n="31" rhead="TABVLARVM SIVVM PER PET. APIAVM."/>
</div>
<div xml:id="echoid-div20" type="section" level="1" n="14">
<head xml:id="echoid-head17" xml:space="preserve">PRONVNCIATVM II.</head>
<p>
  <s xml:id="echoid-s749" xml:space="preserve">Sphæram octauam æquare cum nona &amp; </s>
  <s xml:id="echoid-s750" xml:space="preserve">decima, &amp; </s>
  <s xml:id="echoid-s751" xml:space="preserve">ſtellas fixas, ſimul ac <lb/>planetarum auges per hocuerificare.</s>
  <s xml:id="echoid-s752" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s753" xml:space="preserve">Ad æquandã octauã ſphæram cũ nona, operæpreciũ eſt principio ſcire, ꝙ initiũ octa <lb/>uæ ſphæræ incipit ꝓpe punctũ parui circuli, quẽ trepidationis ſeu titubatiõis dicimus, <lb/>
<anchor type="note" xlink:label="note-0031-01a" xlink:href="note-0031-01"/>
qui´ omniũ remotiſsime uergit ad ſeptẽtrionẽ, &amp; </s>
  <s xml:id="echoid-s754" xml:space="preserve">is ordinẽ motus ſuihabet uerſus ortũ <lb/>☉(sun) uſ in 90. </s>
  <s xml:id="echoid-s755" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s756" xml:space="preserve">ꝗ rurſus cadit ſup eclypticã, &amp; </s>
  <s xml:id="echoid-s757" xml:space="preserve">quũ medius motus 8. </s>
  <s xml:id="echoid-s758" xml:space="preserve">ſphæræ habuerit <lb/>90. </s>
  <s xml:id="echoid-s759" xml:space="preserve">(hoceſt, ut prædixi, quãdo primũ punctũ Arietis 8. </s>
  <s xml:id="echoid-s760" xml:space="preserve">ſphæræ directe ſteterit ſub ecly-<lb/>ptica nonæ) ibi nimi℞ fit &amp; </s>
  <s xml:id="echoid-s761" xml:space="preserve">eſt æquatio maxima, ea´ ex fundamẽto peritiſsimi doctiſsi <lb/>mi´ Aſtronomi Alfonſi Regis agno ſcitur eſſe nouẽ graduũ, at ideo æquatio illa ab <lb/>initio parui circuli uſ in 90. </s>
  <s xml:id="echoid-s762" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s763" xml:space="preserve">ſemꝑ accreſcit, hinc rurſus à 90. </s>
  <s xml:id="echoid-s764" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s765" xml:space="preserve">decreſcit, donec <lb/>trepidatio ꝑ<unsure/>ueniatad 180. </s>
  <s xml:id="echoid-s766" xml:space="preserve">parui circuli, ubi iterũ æquatio nulla eſt, ſicut in eius princi-<lb/>pio. </s>
  <s xml:id="echoid-s767" xml:space="preserve">Et inde à 180. </s>
  <s xml:id="echoid-s768" xml:space="preserve">gradibus rurſus augetur &amp; </s>
  <s xml:id="echoid-s769" xml:space="preserve">creſcit uſ ad gra. </s>
  <s xml:id="echoid-s770" xml:space="preserve">270. </s>
  <s xml:id="echoid-s771" xml:space="preserve">at hinc rurſus in <lb/>cipit ſe octaua ſphæra ad initiũ parui circuli ſupradictæ trepidatiõis declinare &amp; </s>
  <s xml:id="echoid-s772" xml:space="preserve">flectere <lb/>unde æquatio etiã ipſa eouſ decreſcit, dũ nulla omnino ſit reliqua, fit´ hoc ita in una <lb/>reuolutiõe (quæ ferè in ſeptẽ millibus annorũ cõficitur) bis, ut æquatio ſit nulla, in princi <lb/>pio parui circuli &amp; </s>
  <s xml:id="echoid-s773" xml:space="preserve">in 180. </s>
  <s xml:id="echoid-s774" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s775" xml:space="preserve">fimiliter &amp; </s>
  <s xml:id="echoid-s776" xml:space="preserve">in 90. </s>
  <s xml:id="echoid-s777" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s778" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s779" xml:space="preserve">280. </s>
  <s xml:id="echoid-s780" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s781" xml:space="preserve">omniũ maxime. </s>
  <s xml:id="echoid-s782" xml:space="preserve">Aequa <lb/>
<anchor type="note" xlink:label="note-0031-02a" xlink:href="note-0031-02"/>
tio prima uſ in 180. </s>
  <s xml:id="echoid-s783" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s784" xml:space="preserve">addẽda eſt medio motui nonæ ſphæræ, mot9 ille augiũ &amp; </s>
  <s xml:id="echoid-s785" xml:space="preserve">ſtel <lb/>larũ fixarũ in tabulis dici ſolet. </s>
  <s xml:id="echoid-s786" xml:space="preserve">Secũda aũt æquatio, ſi à 180. </s>
  <s xml:id="echoid-s787" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s788" xml:space="preserve">uſ in 270. </s>
  <s xml:id="echoid-s789" xml:space="preserve">ſubtrahitur <lb/>à medio motu augium &amp; </s>
  <s xml:id="echoid-s790" xml:space="preserve">ſtellarũ fixarũ, ꝓueniet &amp; </s>
  <s xml:id="echoid-s791" xml:space="preserve">remanebit uerus locus 8. </s>
  <s xml:id="echoid-s792" xml:space="preserve">ſphæræ in <lb/>nono orbe. </s>
  <s xml:id="echoid-s793" xml:space="preserve">Inuenturus ergo iam æquationẽ principio ex tabulis Aſtronomicis, quære <lb/>motũ octauæ ſphæræ, ꝗ cõiuſu &amp; </s>
  <s xml:id="echoid-s794" xml:space="preserve">cõſuetudine motus acceſſus &amp; </s>
  <s xml:id="echoid-s795" xml:space="preserve">receſſus appellat<unsure/>. </s>
  <s xml:id="echoid-s796" xml:space="preserve">mo-<lb/>tum illũ reſoluito primũ in gradus, dũmodo aliq̊t integra ſigna habuerit &amp; </s>
  <s xml:id="echoid-s797" xml:space="preserve">ſi minor ſit ̈ <lb/>90. </s>
  <s xml:id="echoid-s798" xml:space="preserve">ſubtrahito eũ â 90. </s>
  <s xml:id="echoid-s799" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s800" xml:space="preserve">erit operationi adcõmodus, ſin aũt maior ſit ̈ 90. </s>
  <s xml:id="echoid-s801" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s802" xml:space="preserve">tamen mi <lb/>
<anchor type="note" xlink:label="note-0031-03a" xlink:href="note-0031-03"/>
nor ̈ 180. </s>
  <s xml:id="echoid-s803" xml:space="preserve">ſubducito ipſum rurſus ab 180. </s>
  <s xml:id="echoid-s804" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s805" xml:space="preserve">remanebit numerus graduũ iuſte paratus <lb/>ad operandũ. </s>
  <s xml:id="echoid-s806" xml:space="preserve">Quod ſi tñ medius motus maior ſit ̈ 180. </s>
  <s xml:id="echoid-s807" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s808" xml:space="preserve">minor adhuc ̈ 270. </s>
  <s xml:id="echoid-s809" xml:space="preserve">ſubtra-<lb/>he tũc 180. </s>
  <s xml:id="echoid-s810" xml:space="preserve">â 270. </s>
  <s xml:id="echoid-s811" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s812" xml:space="preserve">hic quo reliquũ tibi manebit, q̊d ad hũc uſum cõducet. </s>
  <s xml:id="echoid-s813" xml:space="preserve">Simili mo-<lb/>do ſi excedat gradus 270. </s>
  <s xml:id="echoid-s814" xml:space="preserve">reĳciẽdo illos, &amp; </s>
  <s xml:id="echoid-s815" xml:space="preserve">tũc remanebit numerus ꝑ quẽ inuenit̃ æqua-<lb/>tio. </s>
  <s xml:id="echoid-s816" xml:space="preserve">Numero illo ſic inuẽto &amp; </s>
  <s xml:id="echoid-s817" xml:space="preserve">ad operationẽ cõpoſito, quære ſinũ illius rectũ, eũ multipli-<lb/>ca cũ ſinu recto 9. </s>
  <s xml:id="echoid-s818" xml:space="preserve">graduũ, ꝓductũ partire in ſinũ totũ, quotientis arcũ quære, mox ꝓpo-<lb/>
<anchor type="note" xlink:label="note-0031-04a" xlink:href="note-0031-04"/>
ne tibi ſinũ cõ plementi huius inuẽti, ſimiliter &amp; </s>
  <s xml:id="echoid-s819" xml:space="preserve">ſinũ cõplemẽti 9. </s>
  <s xml:id="echoid-s820" xml:space="preserve">graduũ(ſiquidem ſe-<lb/>midiameter circuli trepidatiõis ex ſuppoſitione eſt 9. </s>
  <s xml:id="echoid-s821" xml:space="preserve">graduũ.) </s>
  <s xml:id="echoid-s822" xml:space="preserve">Minorẽ ex ĳs duobus nu <lb/>merũ cũ toto ſeu perfecto ſinu multiplica, productũ diuide in ſinũ maiorẽ, numeri quoti <lb/>entis arcũ quære, eo ſubtra cto à 90. </s>
  <s xml:id="echoid-s823" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s824" xml:space="preserve">remanebit tibi æquatio 8. </s>
  <s xml:id="echoid-s825" xml:space="preserve">ſphæræ quæſita, &amp; </s>
  <s xml:id="echoid-s826" xml:space="preserve">il-<lb/>la quidem addi aut ſubtrahi debet à medio motu augiũ &amp; </s>
  <s xml:id="echoid-s827" xml:space="preserve">ſtellarũ fixarũ, ſecundũ quod <lb/>arguit medius mot9 acceſtus &amp; </s>
  <s xml:id="echoid-s828" xml:space="preserve">receſſus 8 ſphæræ, ꝗ ſi fuerit minor gradibus 180. </s>
  <s xml:id="echoid-s829" xml:space="preserve">æqua <lb/>
<anchor type="note" xlink:label="note-0031-05a" xlink:href="note-0031-05"/>
tio addẽda eſt, ſi maior, ſubtrahẽda. </s>
  <s xml:id="echoid-s830" xml:space="preserve">?</s>
  <s xml:id="echoid-s831" xml:space="preserve">? At obſcura hæc tibi forte uidẽtur, ꝓinde lucẽ ad <lb/>demus exemplo, q̊ deinceps ſemper ſumus uſuri, at proponimus hic diem 14. </s>
  <s xml:id="echoid-s832" xml:space="preserve">Maĳ, an-<lb/>ni 1517. </s>
  <s xml:id="echoid-s833" xml:space="preserve">id´ in honorẽ Reuerendiſsimi patris &amp; </s>
  <s xml:id="echoid-s834" xml:space="preserve">D. </s>
  <s xml:id="echoid-s835" xml:space="preserve">D. </s>
  <s xml:id="echoid-s836" xml:space="preserve">Chriſtophori à Stadio Epiſcopi <lb/>Auguſtẽſis, ꝗ eo die ad Epiſcopatũ intronizatus eſt. </s>
  <s xml:id="echoid-s837" xml:space="preserve">nolumus enim hic à cõi loquẽdi cõ <lb/>
<anchor type="note" xlink:label="note-0031-06a" xlink:href="note-0031-06"/>
ſuetudine diſcedere, eò maxime ꝙ nõ ſtyli elegantiã, ſed illuſtrãdæ aperiendæ´ rei ueri-<lb/>tatem ſectamur. </s>
  <s xml:id="echoid-s838" xml:space="preserve">Illo ipſo die inuenio mediũ motũ augiũ &amp; </s>
  <s xml:id="echoid-s839" xml:space="preserve">ſtellarũ fixarũ Signũ o. </s>
  <s xml:id="echoid-s840" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s841" xml:space="preserve">11. </s>
  <s xml:id="echoid-s842" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s843" xml:space="preserve">11. </s>
  <s xml:id="echoid-s844" xml:space="preserve">ſec. </s>
  <s xml:id="echoid-s845" xml:space="preserve">26. </s>
  <s xml:id="echoid-s846" xml:space="preserve">tert. </s>
  <s xml:id="echoid-s847" xml:space="preserve">21. </s>
  <s xml:id="echoid-s848" xml:space="preserve">Et mediũ motũ 8. </s>
  <s xml:id="echoid-s849" xml:space="preserve">ſphæræ 1. </s>
  <s xml:id="echoid-s850" xml:space="preserve">ſignũ, 17. </s>
  <s xml:id="echoid-s851" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s852" xml:space="preserve">11. </s>
  <s xml:id="echoid-s853" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s854" xml:space="preserve">38, ſec. </s>
  <s xml:id="echoid-s855" xml:space="preserve">28. </s>
  <s xml:id="echoid-s856" xml:space="preserve">ter. </s>
  <s xml:id="echoid-s857" xml:space="preserve"><lb/>Inuenire iam uolens æquationẽ, primũ oĩm reſoluere debes ſignũ in 60. </s>
  <s xml:id="echoid-s858" xml:space="preserve">gradus (quãdo <lb/>ſignũ illud phyſicum eſt, deinde addere gra. </s>
  <s xml:id="echoid-s859" xml:space="preserve">17. </s>
  <s xml:id="echoid-s860" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s861" xml:space="preserve">erũt gra. </s>
  <s xml:id="echoid-s862" xml:space="preserve">77. </s>
  <s xml:id="echoid-s863" xml:space="preserve">ĳs ſubtractis à 90. </s>
  <s xml:id="echoid-s864" xml:space="preserve">mane <lb/>bunt 12. </s>
  <s xml:id="echoid-s865" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s866" xml:space="preserve">48. </s>
  <s xml:id="echoid-s867" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s868" xml:space="preserve">ſinus horũ graduũ &amp; </s>
  <s xml:id="echoid-s869" xml:space="preserve">minutorũ eſt 22154. </s>
  <s xml:id="echoid-s870" xml:space="preserve">hunc ſinum ſi duxero in ſi <lb/>num 9. </s>
  <s xml:id="echoid-s871" xml:space="preserve">graduũ, ſcilicet 15643. </s>
  <s xml:id="echoid-s872" xml:space="preserve">reſultabunt inde 346555022. </s>
  <s xml:id="echoid-s873" xml:space="preserve">producto illo diuiſo in ſinũ <lb/>totum, qui eſt 100000. </s>
  <s xml:id="echoid-s874" xml:space="preserve">ex ea diuiſione prouenient. </s>
  <s xml:id="echoid-s875" xml:space="preserve">3466. </s>
  <s xml:id="echoid-s876" xml:space="preserve">arcus illius eſt 2. </s>
  <s xml:id="echoid-s877" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s878" xml:space="preserve">Poſtea ad <lb/>ſume cõplementũ eius, hoc eſt, reſiduũ ad 90. </s>
  <s xml:id="echoid-s879" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s880" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s881" xml:space="preserve">88. </s>
  <s xml:id="echoid-s882" xml:space="preserve">ſinus ip ſius erit 99939. </s>
  <s xml:id="echoid-s883" xml:space="preserve">hinc adhuc <lb/>propone ſinũ cõplementi 9. </s>
  <s xml:id="echoid-s884" xml:space="preserve">graduum. </s>
  <s xml:id="echoid-s885" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s886" xml:space="preserve">81. </s>
  <s xml:id="echoid-s887" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s888" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s889" xml:space="preserve">erit 98768. </s>
  <s xml:id="echoid-s890" xml:space="preserve">ex ĳs duobus ſinum adſu-<lb/>me minorem, eũ ducin ſinum perfectũ, ꝓductũ diuide in maiorẽ, qui eſt 99939. </s>
  <s xml:id="echoid-s891" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s892" xml:space="preserve">proue <lb/>nient in quotiente 98828. </s>
  <s xml:id="echoid-s893" xml:space="preserve">arcus illius erit 81. </s>
  <s xml:id="echoid-s894" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s895" xml:space="preserve">13. </s>
  <s xml:id="echoid-s896" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s897" xml:space="preserve">Complementum eius 8. </s>
  <s xml:id="echoid-s898" xml:space="preserve">gra.</s>
  <s xml:id="echoid-s899" xml:space="preserve">
<pb file="0032" n="32" rhead="GENVINVS VSVS"/>
42. </s>
  <s xml:id="echoid-s900" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s901" xml:space="preserve">æquatio nimirũ illa optata, ea addenda eſt (qñ medius motus acceſſus &amp; </s>
  <s xml:id="echoid-s902" xml:space="preserve">receſſus <lb/>8. </s>
  <s xml:id="echoid-s903" xml:space="preserve">ſphæræ minor eſt in quadrãte ad motũ mediũ augiũ &amp; </s>
  <s xml:id="echoid-s904" xml:space="preserve">ſtellarũ fixarũ, in hoc, ut ꝓue-<lb/>
<anchor type="note" xlink:label="note-0032-01a" xlink:href="note-0032-01"/>
niat uerus motus nonæ &amp; </s>
  <s xml:id="echoid-s905" xml:space="preserve">octauæ ſphæræ ſimul, hoc eſt, quantũ auges planetarũ, &amp; </s>
  <s xml:id="echoid-s906" xml:space="preserve">ſtel-<lb/>læ fixæ iam inde â Chriſto nato ſint ꝓmotæ, puta o. </s>
  <s xml:id="echoid-s907" xml:space="preserve">Sig. </s>
  <s xml:id="echoid-s908" xml:space="preserve">19. </s>
  <s xml:id="echoid-s909" xml:space="preserve">gr. </s>
  <s xml:id="echoid-s910" xml:space="preserve">55. </s>
  <s xml:id="echoid-s911" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s912" xml:space="preserve">Et dicitur ea aux <lb/>communis Epiſcopi Auguſtenſis. </s>
  <s xml:id="echoid-s913" xml:space="preserve">A Chriſto autem uſ ad Alfonſum motus 9. </s>
  <s xml:id="echoid-s914" xml:space="preserve">ſphæræ <lb/>eſt o. </s>
  <s xml:id="echoid-s915" xml:space="preserve">Sig. </s>
  <s xml:id="echoid-s916" xml:space="preserve">9. </s>
  <s xml:id="echoid-s917" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s918" xml:space="preserve">11. </s>
  <s xml:id="echoid-s919" xml:space="preserve">mi 38, ſec. </s>
  <s xml:id="echoid-s920" xml:space="preserve">Motus 8. </s>
  <s xml:id="echoid-s921" xml:space="preserve">ſphæræ 1. </s>
  <s xml:id="echoid-s922" xml:space="preserve">Sig. </s>
  <s xml:id="echoid-s923" xml:space="preserve">4. </s>
  <s xml:id="echoid-s924" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s925" xml:space="preserve">21. </s>
  <s xml:id="echoid-s926" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s927" xml:space="preserve">30. </s>
  <s xml:id="echoid-s928" xml:space="preserve">ſec. </s>
  <s xml:id="echoid-s929" xml:space="preserve">Aequatio 8. <lb/></s>
  <s xml:id="echoid-s930" xml:space="preserve">
<anchor type="note" xlink:label="note-0032-02a" xlink:href="note-0032-02"/>
ſphæræ 8. </s>
  <s xml:id="echoid-s931" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s932" xml:space="preserve">6. </s>
  <s xml:id="echoid-s933" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s934" xml:space="preserve">24. </s>
  <s xml:id="echoid-s935" xml:space="preserve">ſec. </s>
  <s xml:id="echoid-s936" xml:space="preserve">Aequationem hanc ſi addidero ad motũ 9. </s>
  <s xml:id="echoid-s937" xml:space="preserve">ſphæræ, prodibit <lb/>inde 9. </s>
  <s xml:id="echoid-s938" xml:space="preserve">Sig. </s>
  <s xml:id="echoid-s939" xml:space="preserve">17. </s>
  <s xml:id="echoid-s940" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s941" xml:space="preserve">18. </s>
  <s xml:id="echoid-s942" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s943" xml:space="preserve">2. </s>
  <s xml:id="echoid-s944" xml:space="preserve">ſec. </s>
  <s xml:id="echoid-s945" xml:space="preserve">aux cõmunis Alfonſi, eam ſi rurſus ſubtraxero ab auge <lb/>Auguſtenſis Epiſcopi, manebunt 2. </s>
  <s xml:id="echoid-s946" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s947" xml:space="preserve">37. </s>
  <s xml:id="echoid-s948" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s949" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s950" xml:space="preserve">tantũ quidem auges omniũ planeta℞ <lb/>&amp; </s>
  <s xml:id="echoid-s951" xml:space="preserve">ſtellæ fixæ promotæ ſunt à tempore Alfonſi uſ in diem intronizationis Reueren-<lb/>
<anchor type="note" xlink:label="note-0032-03a" xlink:href="note-0032-03"/>
diſsimi Epiſcopi Auguſtenſis. </s>
  <s xml:id="echoid-s952" xml:space="preserve">lta  ubi gradus illos &amp; </s>
  <s xml:id="echoid-s953" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s954" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s955" xml:space="preserve">ſec. </s>
  <s xml:id="echoid-s956" xml:space="preserve">addidero ad auges Al-<lb/>fonſi, ſimul´ ad longitudines ſtellarũ Alfonſi, rectificatas eas habuero ad ipſum diem in <lb/>tronizationis. </s>
  <s xml:id="echoid-s957" xml:space="preserve">Latitudines autem non mutamus adhuc ſectãtes ueſtigia Hyparchi, Pto <lb/>lemæi Peluſiani, &amp; </s>
  <s xml:id="echoid-s958" xml:space="preserve">Alfonſi Regis, Et ſi aũt hic eo modo ſtellas uerificare docemus, quaſi <lb/>circul 9 paruus in motu titubatiõis eſſet 9. </s>
  <s xml:id="echoid-s959" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s960" xml:space="preserve">tñ nedũ apud me cõſtat recte ſentire eos, <lb/>ne adeo cõſentire ipſis, ꝗ dicũt Ae ꝗ noctia ex hoc paruo circulo, iam noſtris tempori <lb/>bus ad 25. </s>
  <s xml:id="echoid-s961" xml:space="preserve">gradũ κ cõuerti, certa enim ego obſeruatione depræhendi, quòd umbra gno <lb/>monis in quacun  ſuperficie plana, ſiue recta, ſiue ia cente, ſiue inclinata in latus, illo tem <lb/>pore lineam rectam non deſcribit, qualis tamen eſſe debet cuiuslibet umbræ Sole per-<lb/>tranſeunte circulum maiorem hoc eſt æquinoctialem. </s>
  <s xml:id="echoid-s962" xml:space="preserve">ſed ego obſeruaui etiam tunc quã <lb/>
<anchor type="note" xlink:label="note-0032-04a" xlink:href="note-0032-04"/>
libet umbram deſcribere arcum. </s>
  <s xml:id="echoid-s963" xml:space="preserve">Id hoc loco commemorare uiſum eſt eo tantum, ut non-<lb/>nulli melius ſuper ſententia ſua deliberent, &amp; </s>
  <s xml:id="echoid-s964" xml:space="preserve">æquinoctium, quod maxime pertinet ad <lb/>uerificationem Kalendarĳ Romani, rectius demonſtrent.</s>
  <s xml:id="echoid-s965" xml:space="preserve"/>
</p>
<div xml:id="echoid-div20" type="float" level="2" n="1">
<note position="right" xlink:label="note-0031-01" xlink:href="note-0031-01a" xml:space="preserve"><emph style="it">Quẽ in lo-</emph> <lb/><emph style="it">cũ nonæ</emph> <lb/><emph style="it">ſphæræ prĩ</emph> <lb/><emph style="it">apiũ trepi-</emph> <lb/><emph style="it">dationis re</emph> <lb/><emph style="it">ferri debent</emph></note>
<note position="right" xlink:label="note-0031-02" xlink:href="note-0031-02a" xml:space="preserve"><emph style="it">Quandoœ</emph> <lb/><emph style="it">quatio octa</emph> <lb/><emph style="it">uœ ſbhæræ</emph> <lb/><emph style="it">ſit addenda</emph> <lb/><emph style="it">aut ſubtra-</emph> <lb/><emph style="it">benda à mc</emph> <lb/><emph style="it">dio motu.</emph></note>
<note position="right" xlink:label="note-0031-03" xlink:href="note-0031-03a" xml:space="preserve"><emph style="it">Illud perfi-</emph> <lb/><emph style="it">acs in qua-</emph> <lb/><emph style="it">drante ſi la</emph> <lb/><emph style="it">ter aliter in</emph> <lb/><emph style="it">grediaris.</emph></note>
<note position="right" xlink:label="note-0031-04" xlink:href="note-0031-04a" xml:space="preserve"><emph style="it">Per arealẽ</emph> <lb/><emph style="it">ingreſſum</emph> <lb/><emph style="it">in quadrãte</emph> <lb/><emph style="it">ſimile aſſe</emph> <lb/><emph style="it">queris.</emph></note>
<note position="right" xlink:label="note-0031-05" xlink:href="note-0031-05a" xml:space="preserve">EXEM <lb/>PLVM</note>
<note position="right" xlink:label="note-0031-06" xlink:href="note-0031-06a" xml:space="preserve"><emph style="it">Quo anno</emph> <lb/><emph style="it">&amp; die R@-</emph> <lb/><emph style="it">uerẽdißim9</emph> <lb/><emph style="it">Dñs D.</emph> <lb/><emph style="it">Chriſtopho</emph> <lb/><emph style="it">rus epiſoo<unsure/>-</emph> <lb/><emph style="it">pus Augu-</emph> <lb/><emph style="it">ſtenſis &amp; c.</emph> <lb/><emph style="it">introniza-</emph> <lb/><emph style="it">ius ſit, ad</emph> <lb/><emph style="it">qd’ tpis mo</emph> <lb/><emph style="it">mẽtũ oẽs il</emph> <lb/><emph style="it">læ propoſi</emph> <lb/><emph style="it">tiões dire-</emph> <lb/><emph style="it">ctœ ſunt.</emph></note>
<note position="left" xlink:label="note-0032-01" xlink:href="note-0032-01a" xml:space="preserve"><emph style="it">Aux cõis E</emph> <lb/><emph style="it">piſcopi Au</emph> <lb/><emph style="it">guſteñ.</emph></note>
<note position="left" xlink:label="note-0032-02" xlink:href="note-0032-02a" xml:space="preserve"><emph style="it">Aux cõis</emph> <lb/><emph style="it">Rcgis Al-</emph> <lb/><emph style="it">fonſi.</emph></note>
<note position="left" xlink:label="note-0032-03" xlink:href="note-0032-03a" xml:space="preserve"><emph style="it">Per quot e</emph> <lb/><emph style="it">clypticæ ꝑ-</emph> <lb/><emph style="it">tes ſtellæ fi-</emph> <lb/><emph style="it">xæ et plane</emph> <lb/><emph style="it">tarũ auges</emph> <lb/><emph style="it">ꝓmouerint</emph> <lb/><emph style="it">à tꝑe Alfon</emph> <lb/><emph style="it">ſi uſq; ad in</emph> <lb/><emph style="it">tronizatio</emph> <lb/><emph style="it">nis boram.</emph></note>
<note position="left" xlink:label="note-0032-04" xlink:href="note-0032-04a" xml:space="preserve"><emph style="it">Aeꝗnoctĳ</emph> <lb/><emph style="it">uarictatem</emph> <lb/><emph style="it">in Aſtrono</emph> <lb/><emph style="it">mico noſtro</emph> <lb/><emph style="it">requires</emph> <lb/><emph style="it">melius.</emph></note>
</div>
</div>
<div xml:id="echoid-div22" type="section" level="1" n="15">
<head xml:id="echoid-head18" xml:space="preserve">PRONVNCIATVM III.</head>
<head xml:id="echoid-head19" xml:space="preserve">Latitudinem Lunæ ab eclyptica per ſinus colligere.</head>
<p>
  <s xml:id="echoid-s966" xml:space="preserve">Priuſquam hic latitudinem doceam inuenire, operæprecium eſt te uerum curſum Lu <lb/>næ &amp; </s>
  <s xml:id="echoid-s967" xml:space="preserve">Capitis draconis Lunæ ex Ephemeridibus cognoſcere, uel aliàs ex tabulis in hoc <lb/>paratis. </s>
  <s xml:id="echoid-s968" xml:space="preserve">nam quotieſcũ deinceps de planetis aliquid dicetur, &amp; </s>
  <s xml:id="echoid-s969" xml:space="preserve">de motu eorundem uer <lb/>ſus decimam ſphæram ſupputando, ſemper antea præſciendus erit uerus curſus ſecun-<lb/>dum longitudinem &amp; </s>
  <s xml:id="echoid-s970" xml:space="preserve">latitudincm. </s>
  <s xml:id="echoid-s971" xml:space="preserve">ſemel ita  præmonitum hoc uolo, ne deinde hocſæ <lb/>pius te habeat ſollicitũ. </s>
  <s xml:id="echoid-s972" xml:space="preserve">Latitudinem Lunæ inuenturus, principio inquire quantum di-<lb/>
<anchor type="note" xlink:label="note-0032-05a" xlink:href="note-0032-05"/>
ſtet ipſa Luna à Capite Draconis uel Cauda, cuicun tandem fuerit propior, ſiue an-<lb/>trorſum ſiue retrorſum, eius diſtantiæ ſinum rectũ quære, quem deinde cum ſinu 5. </s>
  <s xml:id="echoid-s973" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s974" xml:space="preserve">hoc eſt 8715. </s>
  <s xml:id="echoid-s975" xml:space="preserve">multiplicabis, ſiquidem maxima Lunæ latitudo ab eclyptica 5. </s>
  <s xml:id="echoid-s976" xml:space="preserve">graduum eſ <lb/>ſe cognoſcitur, productum inde diuide in ſinum totum, &amp; </s>
  <s xml:id="echoid-s977" xml:space="preserve">arcus quotientis rectiſsime ti-<lb/>bi mõſtrabit ueram latitudinem Lunæ ab eclyptica. </s>
  <s xml:id="echoid-s978" xml:space="preserve">?</s>
  <s xml:id="echoid-s979" xml:space="preserve">? Sit autem hoc tibi exemplum, <lb/>
<anchor type="note" xlink:label="note-0032-06a" xlink:href="note-0032-06"/>
hora intronizationis Reuerendiſs. </s>
  <s xml:id="echoid-s980" xml:space="preserve">patris Epiſcopi Auguſtenſis erat Luna in 23. </s>
  <s xml:id="echoid-s981" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s982" xml:space="preserve">32 <lb/>mi. </s>
  <s xml:id="echoid-s983" xml:space="preserve">♉. </s>
  <s xml:id="echoid-s984" xml:space="preserve">Caput autem Draconis Lunæ in 9. </s>
  <s xml:id="echoid-s985" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s986" xml:space="preserve">12. </s>
  <s xml:id="echoid-s987" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s988" xml:space="preserve">♋. </s>
  <s xml:id="echoid-s989" xml:space="preserve">lam uero Luna ſita eſt à capi-<lb/>te Draconis 45. </s>
  <s xml:id="echoid-s990" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s991" xml:space="preserve">40. </s>
  <s xml:id="echoid-s992" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s993" xml:space="preserve">Sinum illius 71528. </s>
  <s xml:id="echoid-s994" xml:space="preserve">ducin ſinum 5. </s>
  <s xml:id="echoid-s995" xml:space="preserve">graduũ, puta 8715. </s>
  <s xml:id="echoid-s996" xml:space="preserve">pro <lb/>ductum diuide in ſinum perfectum, &amp; </s>
  <s xml:id="echoid-s997" xml:space="preserve">prouenient in quotiente 6234. </s>
  <s xml:id="echoid-s998" xml:space="preserve">arcus illius erit lati <lb/>tudo Lunæ quæſita, ea´ eſt 3. </s>
  <s xml:id="echoid-s999" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1000" xml:space="preserve">35. </s>
  <s xml:id="echoid-s1001" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1002" xml:space="preserve">meridionalis. </s>
  <s xml:id="echoid-s1003" xml:space="preserve">Nã quò ſe Luna inclinet, uel ad <lb/>
<anchor type="note" xlink:label="note-0032-07a" xlink:href="note-0032-07"/>
Auſtrum, uel in Boream inde cognoſces, quia ſi diſtantia Lunæ â capite draconis ſecun-<lb/>dum ordinem ſignorum, uel à Cauda contra ordinem ſignorum numeretur, conſtat Lu-<lb/>nam eſſe in latitudine ſeptentrionali. </s>
  <s xml:id="echoid-s1004" xml:space="preserve">ſin autem diſtantia talis Lunæ à Capite contra or-<lb/>dinem ſignorum, uel à Cauda ſecundum ſeriem illorum numerabitur, argumentum cer-<lb/>tum eſt Lunam eſſe in latitudine meridionali.</s>
  <s xml:id="echoid-s1005" xml:space="preserve"/>
</p>
<div xml:id="echoid-div22" type="float" level="2" n="1">
<note position="left" xlink:label="note-0032-05" xlink:href="note-0032-05a" xml:space="preserve"><emph style="it">Illud inueni</emph> <lb/><emph style="it">es ſi latera</emph> <lb/><emph style="it">liter ingre-</emph> <lb/><emph style="it">diaris.</emph></note>
<note position="left" xlink:label="note-0032-06" xlink:href="note-0032-06a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
<note position="left" xlink:label="note-0032-07" xlink:href="note-0032-07a" xml:space="preserve"><emph style="it">Latitudo</emph> <lb/><emph style="it">☽ hora in</emph> <lb/><emph style="it">tronizatio</emph> <lb/><emph style="it">nis.</emph></note>
</div>
</div>
<div xml:id="echoid-div24" type="section" level="1" n="16">
<head xml:id="echoid-head20" xml:space="preserve">PRONVNCIATVM IIII.</head>
<p>
  <s xml:id="echoid-s1006" xml:space="preserve">Exipſa Lunæ latitudine, diſtantiam illius à capite uel cauda Draconis Lu <lb/>næ (quam in tabulis argumentum latitudinis Lunæ uocamus) cognoſcere.</s>
  <s xml:id="echoid-s1007" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1008" xml:space="preserve">Pronunciatũ hoc planè inuerſum eſt à ſuꝑiori, ꝓinde habitu iã latitudine Lunæ, quũ <lb/>ex ea argumẽtũ latitudinis Lunæ inuenire cupis, hoc eſt diſtantiã eius à Capite uel Cau <lb/>da Draconis, age ſinũ ipſum latitudinis Lunæ ducito in totũ ſinũ rectũ, productũ deinde
<pb file="0033" n="33" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
diuide in ſinũ latitudinis Lunæ maioris, puta 5. </s>
  <s xml:id="echoid-s1009" xml:space="preserve">graduũ, &amp; </s>
  <s xml:id="echoid-s1010" xml:space="preserve">ſic quotiẽtis arcus cõmonſtra <lb/>bit tibi diſtantiã optatã. </s>
  <s xml:id="echoid-s1011" xml:space="preserve">?</s>
  <s xml:id="echoid-s1012" xml:space="preserve">? V is &amp; </s>
  <s xml:id="echoid-s1013" xml:space="preserve">huius rei exemplum @ Ecce, ſi latitudo Lunæ fuerit 3. <lb/></s>
  <s xml:id="echoid-s1014" xml:space="preserve">
<anchor type="note" xlink:label="note-0033-01a" xlink:href="note-0033-01"/>
gra. </s>
  <s xml:id="echoid-s1015" xml:space="preserve">3. </s>
  <s xml:id="echoid-s1016" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1017" xml:space="preserve">talis autem erat ipſa hora intronizationis Epiſcopi, tunc ſinũ ipſius 6234. </s>
  <s xml:id="echoid-s1018" xml:space="preserve">duc <lb/>in totũ ſinũ, &amp; </s>
  <s xml:id="echoid-s1019" xml:space="preserve">hinc diuide ꝓductũ in ſinũ 5. </s>
  <s xml:id="echoid-s1020" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1021" xml:space="preserve">8715. </s>
  <s xml:id="echoid-s1022" xml:space="preserve">ꝓueniet in q̊tiente 71531. </s>
  <s xml:id="echoid-s1023" xml:space="preserve">is ipſe <lb/>ꝓducet 45. </s>
  <s xml:id="echoid-s1024" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1025" xml:space="preserve">40. </s>
  <s xml:id="echoid-s1026" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1027" xml:space="preserve">diſtantiã ſcilicet Lunæ â nodo capitis uel caudæ Draconis Lunæ.</s>
  <s xml:id="echoid-s1028" xml:space="preserve"/>
</p>
<div xml:id="echoid-div24" type="float" level="2" n="1">
<note position="right" xlink:label="note-0033-01" xlink:href="note-0033-01a" xml:space="preserve"><emph style="it">EXEM-</emph> <lb/><emph style="it">PLVM</emph> <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div26" type="section" level="1" n="17">
<head xml:id="echoid-head21" xml:space="preserve">PRONVNCIATVM V.</head>
<p>
  <s xml:id="echoid-s1029" xml:space="preserve">Cuiuſcun puncti imaginatione concepta in eclyptica, inuenire declina <lb/>tionem ab æquinoctiali.</s>
  <s xml:id="echoid-s1030" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1031" xml:space="preserve">Propoſitio hæc quũ frequẽtiſsimũ habeat uſum in uniuerſa ſupputatiõe a ſtronomica, <lb/>maxime uero in cõpoſitiõe aliq̊t inſtrumentorũ, ſupputarunt Aſtronomi quandã gene-<lb/>ralem tabulã de gradu in gradũ, unde citra magnũ laborẽ quotidie colligi poteſt declina <lb/>tio Solis. </s>
  <s xml:id="echoid-s1032" xml:space="preserve">Non multũ diſsimili inſtituto noſtro, &amp; </s>
  <s xml:id="echoid-s1033" xml:space="preserve">nos quo tabulã cõfecimus in Meteo-<lb/>roſcopum numerorũ, ubi etiã minuta totius eclypticæ omnia cõtinentur. </s>
  <s xml:id="echoid-s1034" xml:space="preserve">Eiuſmodi de-<lb/>clinationẽ, imò &amp; </s>
  <s xml:id="echoid-s1035" xml:space="preserve">ipſius tabulæ cõpoſitionẽ uti pſe poſsis cõficere, en rem totã paucis ti <lb/>bi cõmonſtrabo. </s>
  <s xml:id="echoid-s1036" xml:space="preserve">Si punctũ habes in eclyptica, cuius declinationẽ ab æquinoctiali ſcire <lb/>deſideras, principio cõſidera, ubi tandem interſectioni æquatoriæ, hoc eſt, primo puncto <lb/>♈ &amp; </s>
  <s xml:id="echoid-s1037" xml:space="preserve">♎ punctũ illud exiſtat propinquius, nam ea diſtantia ad hanc operationem requi-<lb/>ritur, ſinum illius ſi multiplicaris, cũ ſinu maximo declinationis Solis, &amp; </s>
  <s xml:id="echoid-s1038" xml:space="preserve">productũ diuiſe <lb/>ris in ſinũ totũ, iam ſtatim ipſe arcus quotientis oſtendet ueluti digito declinationem illi <lb/>us pũcti in eclyptica. </s>
  <s xml:id="echoid-s1039" xml:space="preserve">?</s>
  <s xml:id="echoid-s1040" xml:space="preserve">? Sed ne hic quo deſideres exemplũ illuſtrandæ rei adcommo <lb/>dum, age conuerte mihi animũ cogitationem´ tuam ad horam intronizationis, eo tem-<lb/>
<anchor type="note" xlink:label="note-0033-02a" xlink:href="note-0033-02"/>
pore ☉(sun) fuit in 2. </s>
  <s xml:id="echoid-s1041" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1042" xml:space="preserve">26. </s>
  <s xml:id="echoid-s1043" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1044" xml:space="preserve">II, hoc ipſum iã punctũ ſtationis uel loci ſolaris uideamus <lb/>ab æquatore diſtantiam. </s>
  <s xml:id="echoid-s1045" xml:space="preserve">Ecce principio nobis occurrit, quia ☉(sun) Arieti tunc fuit proxi-<lb/>mus, ideo´ diſtantiã colligemus à principio ♈, q̃eſt 62. </s>
  <s xml:id="echoid-s1046" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1047" xml:space="preserve">26. </s>
  <s xml:id="echoid-s1048" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1049" xml:space="preserve">eius arcus ſinus erit <lb/>88647. </s>
  <s xml:id="echoid-s1050" xml:space="preserve">hunc ita ducemus in ſinũ maximæ declinationis eclypticæ, quæ nunc temꝑe <lb/>
<anchor type="note" xlink:label="note-0033-03a" xlink:href="note-0033-03"/>
noſtro agnoſcitur eſſe 23. </s>
  <s xml:id="echoid-s1051" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1052" xml:space="preserve">30. </s>
  <s xml:id="echoid-s1053" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1054" xml:space="preserve">ſinus eius eſt 39874. </s>
  <s xml:id="echoid-s1055" xml:space="preserve">ꝓductũ diuidemus in ſinũ to-<lb/>tum, &amp; </s>
  <s xml:id="echoid-s1056" xml:space="preserve">proueniet in quotiente 35347. </s>
  <s xml:id="echoid-s1057" xml:space="preserve">illius arcus 20. </s>
  <s xml:id="echoid-s1058" xml:space="preserve">gradus. </s>
  <s xml:id="echoid-s1059" xml:space="preserve">42. </s>
  <s xml:id="echoid-s1060" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1061" xml:space="preserve">arguit declinationẽ <lb/>☉(sun) quæſitã ipſa hora intronizationis. </s>
  <s xml:id="echoid-s1062" xml:space="preserve">Sed quia maxima illa declinatio Solis aliquot an-<lb/>norum ſpacio nonnihil uariatur, operæpreciũ eſt, ut ipſam interdũ Aſtronomi obſeruẽt <lb/>diligẽtius ex integro, cõſtat enim illi uniuerſam inniti ſupputationem aſtronomicam.</s>
  <s xml:id="echoid-s1063" xml:space="preserve"/>
</p>
<div xml:id="echoid-div26" type="float" level="2" n="1">
<note position="right" xlink:label="note-0033-02" xlink:href="note-0033-02a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
<note position="right" xlink:label="note-0033-03" xlink:href="note-0033-03a" xml:space="preserve"><emph style="it">Locus ☉(sun)</emph> <lb/><emph style="it">bora intro</emph> <lb/><emph style="it">nizationis</emph> <lb/><emph style="it">gra. 2. mi-</emph> <lb/><emph style="it">nut. 26. II.</emph></note>
</div>
</div>
<div xml:id="echoid-div28" type="section" level="1" n="18">
<head xml:id="echoid-head22" xml:space="preserve">PRONVNCIATVM VI.</head>
<p>
  <s xml:id="echoid-s1064" xml:space="preserve">Cognita Solis declinatione (quod &amp; </s>
  <s xml:id="echoid-s1065" xml:space="preserve">in meridie &amp; </s>
  <s xml:id="echoid-s1066" xml:space="preserve">orien te Sole facilime <lb/>fieri poteſt) adhuc gradum illum zodiaci internoſcere, quem iſta declinatio <lb/>tangit, at unum eum eo punctum efficitur.</s>
  <s xml:id="echoid-s1067" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1068" xml:space="preserve">Superiori, ꝓnunciato docuimus inuentionẽ declinationis ex diſtantia puncti illius â <lb/>principio ♈ uel ♎, nũc uerſa, ꝓpoſitione docebimus ex ipſa declinatiõe inuenire diſtanti <lb/>am pũcti illius à principio ♈ uel ♎. </s>
  <s xml:id="echoid-s1069" xml:space="preserve">Vnde porrò collectu facile eſt, cuinã pũcto eclypti-<lb/>cæ declinatio illa reſpondeat. </s>
  <s xml:id="echoid-s1070" xml:space="preserve">Primũ omnium cõſtat, ꝙ æquinoctialis &amp; </s>
  <s xml:id="echoid-s1071" xml:space="preserve">eclyptica more <lb/>maximorũ circulorũ per mediũ in duas ꝑtes æquales diuidũtur, ita ut quælibet pars me <lb/>dia eclypticæ æqualẽ habeat declinationẽ ab æquatore. </s>
  <s xml:id="echoid-s1072" xml:space="preserve">hinc liquet ſemꝑeſſe 4. </s>
  <s xml:id="echoid-s1073" xml:space="preserve">pũcta in <lb/>eclyptica, q̃ æqualẽ habent declinationẽ, ut ſi ꝓponã 10. </s>
  <s xml:id="echoid-s1074" xml:space="preserve">gradũ ♈, eius declinatione ha-<lb/>bita ſimul habeo declinationẽ 20. </s>
  <s xml:id="echoid-s1075" xml:space="preserve">gradus κ, ꝗa 20. </s>
  <s xml:id="echoid-s1076" xml:space="preserve">gradus κ, 10 gradibus diſtat à prin-<lb/>cipio ♈, ſimili modo intelliges etiã de 10 gradu ♎ &amp; </s>
  <s xml:id="echoid-s1077" xml:space="preserve">20. </s>
  <s xml:id="echoid-s1078" xml:space="preserve">♍, q̊niã uter 10. </s>
  <s xml:id="echoid-s1079" xml:space="preserve">gradibus diſ-<lb/>ſitus eſt abinterſectione æquinoctialis &amp; </s>
  <s xml:id="echoid-s1080" xml:space="preserve">eclypticæ. </s>
  <s xml:id="echoid-s1081" xml:space="preserve">Ecce iam puncta 4. </s>
  <s xml:id="echoid-s1082" xml:space="preserve">habes in eclypti <lb/>
<anchor type="note" xlink:label="note-0033-04a" xlink:href="note-0033-04"/>
ca, quæ ſingula unã &amp; </s>
  <s xml:id="echoid-s1083" xml:space="preserve">æqualẽ habent ab æquatore declinationẽ, tantũ primus punctus <lb/>♋ &amp; </s>
  <s xml:id="echoid-s1084" xml:space="preserve">primus etiã ♑ maximam habent declinationem, ne plura ſunt quàm duo hæc <lb/>puncta, quæ æqualem habent declinationem, aliàs ſemper 4. </s>
  <s xml:id="echoid-s1085" xml:space="preserve">puncta unam &amp; </s>
  <s xml:id="echoid-s1086" xml:space="preserve">æqualẽ de <lb/>clinationem obtinent, Vt autẽ pronũciati huius operationẽ expeditius &amp; </s>
  <s xml:id="echoid-s1087" xml:space="preserve">certius confici <lb/>as, duc ſinũ ꝓpoſitæ huius declinationis in ſinũ totum ſiue ꝑfectũ, ꝓductũ diuide in ſinũ <lb/>maximæ declinationis, &amp; </s>
  <s xml:id="echoid-s1088" xml:space="preserve">arcus quotientis monſtrabit tibi diſtantiam dati puncti ecly-
<pb file="0034" n="34" rhead="GENVINVS VSVS"/>
pticæ ab una &amp; </s>
  <s xml:id="echoid-s1089" xml:space="preserve">proxima interſectione eclypticæ &amp; </s>
  <s xml:id="echoid-s1090" xml:space="preserve">æꝗnoctialis ?</s>
  <s xml:id="echoid-s1091" xml:space="preserve">? Exẽplores tibi fiet <lb/>apertior&amp; </s>
  <s xml:id="echoid-s1092" xml:space="preserve">dilucidior. </s>
  <s xml:id="echoid-s1093" xml:space="preserve">Sit ꝓpoſita tibi declinatio gradus, in q̊ ☉(sun) fuit ea hora qua intro-<lb/>nizatus eſt Reuerendiſs. </s>
  <s xml:id="echoid-s1094" xml:space="preserve">pater Epiſcopus Auguſtenſis, ſicut in priori propoſitione com-<lb/>
<anchor type="note" xlink:label="note-0034-01a" xlink:href="note-0034-01"/>
memorauimus, gradus autem Solis non conſtet, ſed hoc tantum, quòd declinatio ſit 20. <lb/></s>
  <s xml:id="echoid-s1095" xml:space="preserve">graduum, 42. </s>
  <s xml:id="echoid-s1096" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1097" xml:space="preserve">Iam ad inueniendum gradum Solis eo ipſo die &amp; </s>
  <s xml:id="echoid-s1098" xml:space="preserve">hora intronizatio-<lb/>nis, multiplica ſinũ huius declinationis 35347. </s>
  <s xml:id="echoid-s1099" xml:space="preserve">cũ toto ſinu, &amp; </s>
  <s xml:id="echoid-s1100" xml:space="preserve">prouenient 3534700000 <lb/>idipſum ſi diuidas in ſinum maximæ declinationis 39874, emanabũt in quotiente 88647 <lb/>eius ſinus arcus 62. </s>
  <s xml:id="echoid-s1101" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1102" xml:space="preserve">26. </s>
  <s xml:id="echoid-s1103" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1104" xml:space="preserve">diſtantia illa iuſta eſt quam quærebas. </s>
  <s xml:id="echoid-s1105" xml:space="preserve">Et quia introniza <lb/>tio huiuſmodi facta in Maio, diſtantia hæc à principio ♈ numerari debet, &amp; </s>
  <s xml:id="echoid-s1106" xml:space="preserve">cadet ſuꝑ <lb/>2. </s>
  <s xml:id="echoid-s1107" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1108" xml:space="preserve">26. </s>
  <s xml:id="echoid-s1109" xml:space="preserve">mi II, at hoc erat quod intendebatur.</s>
  <s xml:id="echoid-s1110" xml:space="preserve"/>
</p>
<div xml:id="echoid-div28" type="float" level="2" n="1">
<note position="right" xlink:label="note-0033-04" xlink:href="note-0033-04a" xml:space="preserve"><emph style="it">Per arealẽ</emph> <lb/><emph style="it">introitũ in</emph> <lb/><emph style="it">quadrante</emph> <lb/><emph style="it">idem aſſe-</emph> <lb/><emph style="it">queris.</emph></note>
<note position="left" xlink:label="note-0034-01" xlink:href="note-0034-01a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div30" type="section" level="1" n="19">
<head xml:id="echoid-head23" xml:space="preserve">PRONVNCIATVM VII.</head>
<p>
  <s xml:id="echoid-s1111" xml:space="preserve">Cuiuslibet arcus eclypticæ, quiprincipium ſuum ab æquinoctiali &amp; </s>
  <s xml:id="echoid-s1112" xml:space="preserve">in-<lb/>terſectione cum eclyptica capit, a cenſionem in ſphæra recta addiſcere.</s>
  <s xml:id="echoid-s1113" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1114" xml:space="preserve">Per hanc aſcenſionẽ rectã intelligi debet arcus æꝗnoctialis interceptus inter ipſum <lb/>eclypticæ &amp; </s>
  <s xml:id="echoid-s1115" xml:space="preserve">æꝗnoctialis interſectionẽ, ſimul at circulũ illũ maiorem, qui à polo mundi <lb/>per punctũ iſtum eclypticæ ꝓpoſitũ (cuius aſcenſionẽ ſcire deſideras) uſ ad æquinocti <lb/>alem ad angulos rectos ſphærales eſt ductus. </s>
  <s xml:id="echoid-s1116" xml:space="preserve">Et quũ zodiacus in 4. </s>
  <s xml:id="echoid-s1117" xml:space="preserve">quadrantes per 4. </s>
  <s xml:id="echoid-s1118" xml:space="preserve">ſi-<lb/>gna cardinalia ♈ ♋ ♎ &amp; </s>
  <s xml:id="echoid-s1119" xml:space="preserve">♑, per quæ etiã circuli maiores 4. </s>
  <s xml:id="echoid-s1120" xml:space="preserve">ex polis mũdi protẽſi ſunt, <lb/>diuidatur, æquinoctialis etiã in 4. </s>
  <s xml:id="echoid-s1121" xml:space="preserve">quadrantes, partiendus eſt, nõ quidẽ per ſigna, ſed pri-<lb/>ma quarta à principio æquinoctialis uſ in 90. </s>
  <s xml:id="echoid-s1122" xml:space="preserve">gradus, reſpõdet primo gradu ♋ ſupra <lb/>horizontẽ ſphæræ rectæ, &amp; </s>
  <s xml:id="echoid-s1123" xml:space="preserve">180. </s>
  <s xml:id="echoid-s1124" xml:space="preserve">gradus æquinoctialis, hoc eſt media pars æquinoctialis <lb/>reſpõdet etiã mediæ eclypticæ, primus enim gradus ♎ (quæ interſectio eſt æquinoctia-<lb/>lis cũ eclyptica) eſt gradus 180. </s>
  <s xml:id="echoid-s1125" xml:space="preserve">â primo gradu ♈. </s>
  <s xml:id="echoid-s1126" xml:space="preserve">Et quia utrun principiũ æꝗnoctialis <lb/>&amp; </s>
  <s xml:id="echoid-s1127" xml:space="preserve">eclypticæ apud primũ minutũ ♈ initiũ habet, etiã inde numerari debẽt quartæ &amp; </s>
  <s xml:id="echoid-s1128" xml:space="preserve">me <lb/>diæ partes circulorũ. </s>
  <s xml:id="echoid-s1129" xml:space="preserve">Quum´ cõſtet 4. </s>
  <s xml:id="echoid-s1130" xml:space="preserve">quartas æquinoctialis cũ 4. </s>
  <s xml:id="echoid-s1131" xml:space="preserve">quartis eclypticæ, ſin <lb/>gulas cũ adia centibus ſibi, æqualiter aſcẽdere in ſphæra recta, &amp; </s>
  <s xml:id="echoid-s1132" xml:space="preserve">tamẽ inter principiũ et <lb/>finẽ cuiuslibet quartæ nullus alioquin gradus, ne punctũ æquali numero cũ adiacẽte <lb/>quarta in aſcenſione cõuenit, neceſſariũ eſt cõſcenſionẽ iſtã per ſupputationẽ ſphæricã <lb/>internoſcere, id´ ꝑ hãc regulã. </s>
  <s xml:id="echoid-s1133" xml:space="preserve">Si arcus eclypticæ minor fuerit ̈ 90. </s>
  <s xml:id="echoid-s1134" xml:space="preserve">erit ille planè ac-<lb/>commodus inueniendæ huic aſcenſioni, at is primus modus eſto. </s>
  <s xml:id="echoid-s1135" xml:space="preserve">Sin aũt maior fuerit <lb/>̈ 90. </s>
  <s xml:id="echoid-s1136" xml:space="preserve">ſubtrahito eum ab 180. </s>
  <s xml:id="echoid-s1137" xml:space="preserve">ipſo nimi℞ ſemicirculo, &amp; </s>
  <s xml:id="echoid-s1138" xml:space="preserve">ꝗcquid reliquũ manſerit, id aptũ <lb/>erit cognoſcẽdæ aſcẽſioni rectæ, &amp; </s>
  <s xml:id="echoid-s1139" xml:space="preserve">hæc altera ſit ratio inueniendæ aſcenſionis. </s>
  <s xml:id="echoid-s1140" xml:space="preserve">Sicut au <lb/>tem ex media parte eclypticæ duos modos oſtendimus, ita reliquã partẽ nedũ â princi-<lb/>pio ♎ uſ ad finẽ κ identidẽ diuides in duas uias ſeu rationes inueniendi aſcenſionem. <lb/></s>
  <s xml:id="echoid-s1141" xml:space="preserve">Quod ſi numerũ cõueniẽtẽ ex primo modo iã inuentũ habes, hoc eſt, ſi arcus eclypticæ <lb/>minor fuerit ̈ 90. </s>
  <s xml:id="echoid-s1142" xml:space="preserve">tũc ſubtrahe eũ à 90. </s>
  <s xml:id="echoid-s1143" xml:space="preserve">reſiduũ uo cabit̃ cõplementũ ipſius, tũc etiã com <lb/>plementũ aſſume declinationis, ultimi pũcti ꝓpoſiti arcus eclypticæ, &amp; </s>
  <s xml:id="echoid-s1144" xml:space="preserve">ſinũ minimi cõ-<lb/>plemẽti duc in totũ ſinũ, ꝓductũ diuide in ſinũ cõplementi maioris, hinc ſubtracto arcu <lb/>q̊tiẽtis à 90. </s>
  <s xml:id="echoid-s1145" xml:space="preserve">manebit aſcenſio recta arcus ꝓpoſiti. </s>
  <s xml:id="echoid-s1146" xml:space="preserve">Quod ſi aũt nume℞ cõuenientẽ altero <lb/>modo inueniſti, iã nõ opus habebis ultima ſubtractiõe â 90. </s>
  <s xml:id="echoid-s1147" xml:space="preserve">ſed tũc addes inſuper gradus <lb/>
<anchor type="note" xlink:label="note-0034-02a" xlink:href="note-0034-02"/>
90. </s>
  <s xml:id="echoid-s1148" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1149" xml:space="preserve">ſic q̊ habebis arcũ æꝗnoctialis cũ ꝓpoſito arcu coaſcendentem in ſphæra recta. <lb/></s>
  <s xml:id="echoid-s1150" xml:space="preserve">Cæterũ ſi tibi ꝓponas arcũ zodiaci â principio ♎ cõputando uſ ad finẽ κ, ubicun il <lb/>le deſierit, inter hoc ſpacium, aſcenſionem eius quære eo planè modo q̊ iam edoctus es, <lb/>niſi ꝙ ad extremũ addes gradus 180. </s>
  <s xml:id="echoid-s1151" xml:space="preserve">Primus em̃ gradus ♎ habet gradus 180. </s>
  <s xml:id="echoid-s1152" xml:space="preserve">æꝗnoctia <lb/>lis in ſua aſcẽſione, ſicut antea docuimus. </s>
  <s xml:id="echoid-s1153" xml:space="preserve">?</s>
  <s xml:id="echoid-s1154" xml:space="preserve">? lam uero exemplis rem demonſtremus ad <lb/>
<anchor type="note" xlink:label="note-0034-03a" xlink:href="note-0034-03"/>
oculũ. </s>
  <s xml:id="echoid-s1155" xml:space="preserve">Adſumo ecce 2. </s>
  <s xml:id="echoid-s1156" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1157" xml:space="preserve">62. </s>
  <s xml:id="echoid-s1158" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1159" xml:space="preserve">II, in q̊ ☉(sun) fuit tꝑe &amp; </s>
  <s xml:id="echoid-s1160" xml:space="preserve">hora intronizationis, nunc ſinu <lb/>merauero arcũ à principio ♈, inueniã uti 62. </s>
  <s xml:id="echoid-s1161" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1162" xml:space="preserve">26. </s>
  <s xml:id="echoid-s1163" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1164" xml:space="preserve">cõplemẽtũ eius eſt 27. </s>
  <s xml:id="echoid-s1165" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1166" xml:space="preserve">34 <lb/>mi. </s>
  <s xml:id="echoid-s1167" xml:space="preserve">ſinus aũt cõplementi 46278. </s>
  <s xml:id="echoid-s1168" xml:space="preserve">declinationẽ puncti terminantis, arcũ iam inueni ꝓpo <lb/>ſitione 5. </s>
  <s xml:id="echoid-s1169" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1170" xml:space="preserve">20. </s>
  <s xml:id="echoid-s1171" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1172" xml:space="preserve">42. </s>
  <s xml:id="echoid-s1173" xml:space="preserve">cõplementũ declinatiõis eſt 69. </s>
  <s xml:id="echoid-s1174" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1175" xml:space="preserve">18. </s>
  <s xml:id="echoid-s1176" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1177" xml:space="preserve">ſinus uero cõplemen <lb/>ti iſtius 93544. </s>
  <s xml:id="echoid-s1178" xml:space="preserve">Iam ita duco ſinum minorem 46278. </s>
  <s xml:id="echoid-s1179" xml:space="preserve">in totũ ſinum, &amp; </s>
  <s xml:id="echoid-s1180" xml:space="preserve">productum diui <lb/>do in ſinum maiorem, ſcilicet 93544. </s>
  <s xml:id="echoid-s1181" xml:space="preserve">at in quotiente prouenient 49471. </s>
  <s xml:id="echoid-s1182" xml:space="preserve">arcus erit 29. <lb/></s>
  <s xml:id="echoid-s1183" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1184" xml:space="preserve">39. </s>
  <s xml:id="echoid-s1185" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1186" xml:space="preserve">eum ſi ſubtraxero à 90. </s>
  <s xml:id="echoid-s1187" xml:space="preserve">remanebit aſcenſio recta quæſita 60. </s>
  <s xml:id="echoid-s1188" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1189" xml:space="preserve">29. </s>
  <s xml:id="echoid-s1190" xml:space="preserve">minut.</s>
  <s xml:id="echoid-s1191" xml:space="preserve"/>
</p>
<div xml:id="echoid-div30" type="float" level="2" n="1">
<note position="left" xlink:label="note-0034-02" xlink:href="note-0034-02a" xml:space="preserve"><emph style="it">Operatio</emph> <lb/><emph style="it">arealis.</emph></note>
<note position="left" xlink:label="note-0034-03" xlink:href="note-0034-03a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
</div>
<pb file="0035" n="35" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
</div>
<div xml:id="echoid-div32" type="section" level="1" n="20">
<head xml:id="echoid-head24" xml:space="preserve">PRONVNCIATVM VIII.</head>
<p>
  <s xml:id="echoid-s1192" xml:space="preserve">Habita iam aſcenſione recta in æquinoctiali, arcum ipſius eclypticæ cum <lb/>eo aſcendentem in ſphæra recta cognoſcere.</s>
  <s xml:id="echoid-s1193" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1194" xml:space="preserve">Pronunciatũ hoc quo inuertit quod ſuperior docuerat, at ideo qñ multũ cõueniũt <lb/>ambæ illæ, diutius hic nõ immorabimur oſtendẽdo, quõ aſcenſio recta debeat intelligi, <lb/>ſed prætermiſsis amba gibus &amp; </s>
  <s xml:id="echoid-s1195" xml:space="preserve">inuolutis uerbis, ad ipſam ſtatim operationẽ uenia mus. <lb/></s>
  <s xml:id="echoid-s1196" xml:space="preserve">Vbi iam noris, qualis declinatio eclypticæ fit penes arcũ æquinoctialis, ex ſuperiori ꝓ-<lb/>poſitiõe aſcenſionẽ eclypticæ cũ æquino ctiali facile inuenies hoc modo. </s>
  <s xml:id="echoid-s1197" xml:space="preserve">Si multiplices <lb/>
<anchor type="note" xlink:label="note-0035-01a" xlink:href="note-0035-01"/>
ſinum declinatiõis cũ toto ſinu, &amp; </s>
  <s xml:id="echoid-s1198" xml:space="preserve">ꝓductũ diuidas cum ſinu maximæ declinatiõis ☉(sun), ar <lb/>cus quotientis mõſtrabit tibi arcũ eclypticæ, qui cũ arcu æquatoris aſcẽdit in ſphæra re <lb/>cta. </s>
  <s xml:id="echoid-s1199" xml:space="preserve">Habe eius rei hoc tibi exemplũ. </s>
  <s xml:id="echoid-s1200" xml:space="preserve">Sit arcus æquatoris à principio æquinoctialis 60. <lb/></s>
  <s xml:id="echoid-s1201" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1202" xml:space="preserve">21. </s>
  <s xml:id="echoid-s1203" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1204" xml:space="preserve">declinatio aũt eclypticæ in eoloco 20. </s>
  <s xml:id="echoid-s1205" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1206" xml:space="preserve">42. </s>
  <s xml:id="echoid-s1207" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1208" xml:space="preserve">ſinus eius 35347. </s>
  <s xml:id="echoid-s1209" xml:space="preserve">ſinũ hũc <lb/>ubi duxeris in totũ ſinũ ꝓductũ inde diuiſeris in ſinũ rectũ maximæ declinatiõis ☉(sun), puta <lb/>39874. </s>
  <s xml:id="echoid-s1210" xml:space="preserve">ꝓuenient in quotiẽte 88647. </s>
  <s xml:id="echoid-s1211" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s1212" xml:space="preserve">ĳ gradus ſunt 62. </s>
  <s xml:id="echoid-s1213" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1214" xml:space="preserve">26. </s>
  <s xml:id="echoid-s1215" xml:space="preserve">hoc ipſum ſi numerem à <lb/>
<anchor type="note" xlink:label="note-0035-02a" xlink:href="note-0035-02"/>
principio ♈, deſinet numerus in 2. </s>
  <s xml:id="echoid-s1216" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1217" xml:space="preserve">26. </s>
  <s xml:id="echoid-s1218" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1219" xml:space="preserve">II. </s>
  <s xml:id="echoid-s1220" xml:space="preserve">ubi Sol fuit hora intronizationis. </s>
  <s xml:id="echoid-s1221" xml:space="preserve">Etſi <lb/>aũt modus ille non ſit uerus ac ſolidus, quũ uſurpari nequeat in arcu æquatoris, ſed ad de <lb/>clinationẽ tantũ, nolui tamẽ, &amp; </s>
  <s xml:id="echoid-s1222" xml:space="preserve">hũc ipſum te latere, ne ꝗd haberes ambiguum in ĳs quæ <lb/>obiter tibi circa hãc rem poſſent offerri &amp; </s>
  <s xml:id="echoid-s1223" xml:space="preserve">incidere. </s>
  <s xml:id="echoid-s1224" xml:space="preserve">Alia etea quidẽ aptiſsima operatio <lb/>hæc eſt, propoſitum habes arcũ æquatoris, iam´ cupis inuenire arcum ſuum coaſcẽden <lb/>tem in eclyptica, multiplica principio ſinum cõplementi arcus æquinoctialis propoſiti, <lb/>ſi ſaltem ſit quadrante minor, cũ ſinu maximæ declinationis, ꝓductũ inde diuide per ſinũ <lb/>
<anchor type="note" xlink:label="note-0035-03a" xlink:href="note-0035-03"/>
totũ &amp; </s>
  <s xml:id="echoid-s1225" xml:space="preserve">ſubtracto quotientis arcu à 90. </s>
  <s xml:id="echoid-s1226" xml:space="preserve">ſinũ reſidui tibi ꝓpone, ſimul´ ſinũ arcus propoſi <lb/>ti æquatoris, uter eorũ fuerit minor, multiplicandus erit cũ toto ſinu, ꝓductum´ diui-<lb/>dendum in ſinũ maiorem, &amp; </s>
  <s xml:id="echoid-s1227" xml:space="preserve">tunc arcus quotientis monſtrabit tibi arcũ eclypticæ, qui cũ <lb/>arcu æquatoris propoſito aſcendit in ſphæra recta. </s>
  <s xml:id="echoid-s1228" xml:space="preserve">lam autẽ fixo hic pede priuſ̈ ulteri-<lb/>us in regula progrediamur, lubet exemplo rem apertius declarare, quando adhuc opera <lb/>tio in recenti memoria hæret. </s>
  <s xml:id="echoid-s1229" xml:space="preserve">?</s>
  <s xml:id="echoid-s1230" xml:space="preserve">? Eſto ut hora intronizationis Solis in aſcenſione recta <lb/>
<anchor type="note" xlink:label="note-0035-04a" xlink:href="note-0035-04"/>
contigerit 60. </s>
  <s xml:id="echoid-s1231" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1232" xml:space="preserve">21. </s>
  <s xml:id="echoid-s1233" xml:space="preserve">mi ego aũt cupiã ſcire gradũ Solis in eclyptica, eum facile cogno <lb/>ſcam ſi quæſiero arcũ eclypticæ, qui cũ arcu æquatoris aſcẽdit in ſphæra recta: </s>
  <s xml:id="echoid-s1234" xml:space="preserve">ita quũ <lb/>duco ſinũ cõplementi arcus propoſiti æquatoris. </s>
  <s xml:id="echoid-s1235" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s1236" xml:space="preserve">29. </s>
  <s xml:id="echoid-s1237" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1238" xml:space="preserve">39. </s>
  <s xml:id="echoid-s1239" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1240" xml:space="preserve">49471. </s>
  <s xml:id="echoid-s1241" xml:space="preserve">in ſinũ maxi-<lb/>mæ declinatiõis Solis, puta 39874. </s>
  <s xml:id="echoid-s1242" xml:space="preserve">productũ diuido cũ ſinu toto, prodibunt in quotiẽte <lb/>19726. </s>
  <s xml:id="echoid-s1243" xml:space="preserve">arcus eius eſt 11. </s>
  <s xml:id="echoid-s1244" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1245" xml:space="preserve">23. </s>
  <s xml:id="echoid-s1246" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1247" xml:space="preserve">Cõplementũ uero 78. </s>
  <s xml:id="echoid-s1248" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1249" xml:space="preserve">37. </s>
  <s xml:id="echoid-s1250" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1251" xml:space="preserve">habet in ſinu pro-<lb/>poſiti arcus æquatoris 86906. </s>
  <s xml:id="echoid-s1252" xml:space="preserve">ſinum illum (quãdo minimus eſt) multiplico cũ toto, pro-<lb/>ductum diuido in maiorem, &amp; </s>
  <s xml:id="echoid-s1253" xml:space="preserve">prouenient in quotiente 88647. </s>
  <s xml:id="echoid-s1254" xml:space="preserve">arcus eius eſt 62. </s>
  <s xml:id="echoid-s1255" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1256" xml:space="preserve">26 <lb/>mi. </s>
  <s xml:id="echoid-s1257" xml:space="preserve">at is eſt arcus eclypticæ ſimul aſcendens cum arcu æquatoris propoſito in ſphæ-<lb/>ra recta, tunc ſi reĳciam 60. </s>
  <s xml:id="echoid-s1258" xml:space="preserve">hoc eſt 2 ſigna remanebunt 2. </s>
  <s xml:id="echoid-s1259" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1260" xml:space="preserve">26. </s>
  <s xml:id="echoid-s1261" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1262" xml:space="preserve">II. </s>
  <s xml:id="echoid-s1263" xml:space="preserve">Quod ſi autem <lb/>arcus propoſitus æquatoris maior ſit ̈ 90. </s>
  <s xml:id="echoid-s1264" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1265" xml:space="preserve">tamẽ minor ̈ 180. </s>
  <s xml:id="echoid-s1266" xml:space="preserve">ſubduc eum à ſemicir <lb/>culo, &amp; </s>
  <s xml:id="echoid-s1267" xml:space="preserve">deinde cum reſiduo operare modo prædicto. </s>
  <s xml:id="echoid-s1268" xml:space="preserve">atqui numerus poſtremo inuentus <lb/>uerus nõ eſt, niſi eũ à ſemicirculo ſubtrahes, tunc tandem manebit arcus quælitus, quem <lb/>ſemper numerabis à principio ♈. </s>
  <s xml:id="echoid-s1269" xml:space="preserve">Quid uero ſi arcus propoſitus æquatoris fuerit ſemi-<lb/>circulo maior @ tunc ſane ſubtrahe ſemicir culum gra. </s>
  <s xml:id="echoid-s1270" xml:space="preserve">180. </s>
  <s xml:id="echoid-s1271" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1272" xml:space="preserve">cum eo, quod reliquũ ma-<lb/>net, operare ſicut edoctus es antea. </s>
  <s xml:id="echoid-s1273" xml:space="preserve">At extremũ quũ omnia iam perfeceris, adhuc adde <lb/>180. </s>
  <s xml:id="echoid-s1274" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1275" xml:space="preserve">ſic demum habebis arcum eclypticæ, quem tam operoſe hactenus inquirebas.</s>
  <s xml:id="echoid-s1276" xml:space="preserve"/>
</p>
<div xml:id="echoid-div32" type="float" level="2" n="1">
<note position="right" xlink:label="note-0035-01" xlink:href="note-0035-01a" xml:space="preserve"><emph style="it">Primũ in-</emph> <lb/><emph style="it">uenies m-</emph> <lb/><emph style="it">greſſu late</emph> <lb/><emph style="it">rali, ſecũdũ</emph> <lb/><emph style="it">uero per a-</emph> <lb/><emph style="it">realem.</emph></note>
<note position="right" xlink:label="note-0035-02" xlink:href="note-0035-02a" xml:space="preserve"><emph style="it">Hoc areali</emph> <lb/><emph style="it">introitu</emph> <lb/><emph style="it">quœrenti</emph> <lb/><emph style="it">apparet.</emph></note>
<note position="right" xlink:label="note-0035-03" xlink:href="note-0035-03a" xml:space="preserve"><emph style="it">Hoc reſp♉-</emph> <lb/><emph style="it">det laterali</emph> <lb/><emph style="it">ingreſſu.</emph></note>
<note position="right" xlink:label="note-0035-04" xlink:href="note-0035-04a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div34" type="section" level="1" n="21">
<head xml:id="echoid-head25" xml:space="preserve">PRONVNCIATVM IX.</head>
<p>
  <s xml:id="echoid-s1277" xml:space="preserve">Quum arcum aliquẽ eclypticæ cognoſcere cupis, cum quo æqualis arcus <lb/>æquatoris aſcẽdit in ſphæra recta, iam´ principiũ ſiue terminus illius arcus <lb/>tibi innotuit, alterum quo terminũ ex artificioſa ſupputatione colligere.</s>
  <s xml:id="echoid-s1278" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1279" xml:space="preserve">Arcũ hic eclypticæ intellige inter duo ſigna cardinalia intercluſum, ut inter ♈ &amp; </s>
  <s xml:id="echoid-s1280" xml:space="preserve">pri <lb/>mũ mi. </s>
  <s xml:id="echoid-s1281" xml:space="preserve">♋, inter primũ pũctũ ♋ &amp; </s>
  <s xml:id="echoid-s1282" xml:space="preserve">primũ mi. </s>
  <s xml:id="echoid-s1283" xml:space="preserve">♎, ſimiliter inter ♎ &amp; </s>
  <s xml:id="echoid-s1284" xml:space="preserve">♑ &amp; </s>
  <s xml:id="echoid-s1285" xml:space="preserve">♑ &amp; </s>
  <s xml:id="echoid-s1286" xml:space="preserve">♈, tbi ſa <lb/>nè talis erit operatio. </s>
  <s xml:id="echoid-s1287" xml:space="preserve">Eius termini ſiue principĳ tandẽ ſiue finis tibi cogniti quære de <lb/>clinationẽ per ꝓpoſitionẽ 5. </s>
  <s xml:id="echoid-s1288" xml:space="preserve">declinationis illius ſinũ cõplementi tibi propone, ſimul´ ſi-
<pb file="0036" n="36" rhead="GENVINVS VSVS"/>
num cõplementi maximæ declinationis Solis, &amp; </s>
  <s xml:id="echoid-s1289" xml:space="preserve">hunc quidẽ duc in ſinum totum, produ <lb/>ctum diuide in ſinũ complementi declinationis ꝓpoſiti arcus, arcus quotiẽtis ex 90. </s>
  <s xml:id="echoid-s1290" xml:space="preserve">ſub <lb/>latus relinquit declinationẽ alterius pũcti finalis. </s>
  <s xml:id="echoid-s1291" xml:space="preserve">Poſt hæc per 6. </s>
  <s xml:id="echoid-s1292" xml:space="preserve">ꝓnunciatũ quære pun-<lb/>
<anchor type="note" xlink:label="note-0036-01a" xlink:href="note-0036-01"/>
ctum eclypticæ, q̊d declinationi illi reſpõdeat. </s>
  <s xml:id="echoid-s1293" xml:space="preserve">?</s>
  <s xml:id="echoid-s1294" xml:space="preserve">?Exemplũ ſit hoc tibi: </s>
  <s xml:id="echoid-s1295" xml:space="preserve">Propone ecce <lb/>mihi 2. </s>
  <s xml:id="echoid-s1296" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1297" xml:space="preserve">26. </s>
  <s xml:id="echoid-s1298" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1299" xml:space="preserve">II, ubi ☉(sun) fuit hora intronizatiõis, declinationẽ ip ſius iã inueni ꝓpoſi <lb/>
<anchor type="note" xlink:label="note-0036-02a" xlink:href="note-0036-02"/>
tione 5. </s>
  <s xml:id="echoid-s1300" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1301" xml:space="preserve">20. </s>
  <s xml:id="echoid-s1302" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1303" xml:space="preserve">42. </s>
  <s xml:id="echoid-s1304" xml:space="preserve">cõplementũ ipſius eſt 69. </s>
  <s xml:id="echoid-s1305" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1306" xml:space="preserve">18. </s>
  <s xml:id="echoid-s1307" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1308" xml:space="preserve">Sinus aũt 93544. </s>
  <s xml:id="echoid-s1309" xml:space="preserve">iã multipli <lb/>co ſinũ cõplementi maximæ declinationis 91706. </s>
  <s xml:id="echoid-s1310" xml:space="preserve">cũ toto ſinu ꝓductũ diuido in ſinũ cõ-<lb/>plemẽti dati arcus, &amp; </s>
  <s xml:id="echoid-s1311" xml:space="preserve">prouenient in quotiẽte 98035. </s>
  <s xml:id="echoid-s1312" xml:space="preserve">arcus ipſius eſt 78. </s>
  <s xml:id="echoid-s1313" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1314" xml:space="preserve">38. </s>
  <s xml:id="echoid-s1315" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1316" xml:space="preserve">quæ <lb/>ſi ſubduxero à 90. </s>
  <s xml:id="echoid-s1317" xml:space="preserve">manebunt 11. </s>
  <s xml:id="echoid-s1318" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1319" xml:space="preserve">22. </s>
  <s xml:id="echoid-s1320" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1321" xml:space="preserve">ea´ erit declinatio illius gradus eclypticæ <lb/>at hinc uſ in 2. </s>
  <s xml:id="echoid-s1322" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1323" xml:space="preserve">26. </s>
  <s xml:id="echoid-s1324" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1325" xml:space="preserve">II æquatio in æquatore adæquatur. </s>
  <s xml:id="echoid-s1326" xml:space="preserve">lam porrò p. </s>
  <s xml:id="echoid-s1327" xml:space="preserve">6. </s>
  <s xml:id="echoid-s1328" xml:space="preserve">ꝓpoſi <lb/>tionem quæro gradũ eclypticæ cõuenientẽ cũ hac ipſa declinatione 11. </s>
  <s xml:id="echoid-s1329" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1330" xml:space="preserve">22. </s>
  <s xml:id="echoid-s1331" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1332" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1333" xml:space="preserve">in <lb/>uenio 29. </s>
  <s xml:id="echoid-s1334" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1335" xml:space="preserve">37. </s>
  <s xml:id="echoid-s1336" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1337" xml:space="preserve">♈. </s>
  <s xml:id="echoid-s1338" xml:space="preserve">At inter hæc duo loca eclypticæ comperio rurſus 32. </s>
  <s xml:id="echoid-s1339" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1340" xml:space="preserve">49. <lb/></s>
  <s xml:id="echoid-s1341" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1342" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1343" xml:space="preserve">tot ſanè gradus at minuta æquinoctialis aſcendunt cum eo in ſphæra recta.</s>
  <s xml:id="echoid-s1344" xml:space="preserve"/>
</p>
<div xml:id="echoid-div34" type="float" level="2" n="1">
<note position="left" xlink:label="note-0036-01" xlink:href="note-0036-01a" xml:space="preserve"><emph style="it">Illud area-</emph> <lb/><emph style="it">tim aſſeque</emph> <lb/><emph style="it">ris.</emph></note>
<note position="left" xlink:label="note-0036-02" xlink:href="note-0036-02a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div36" type="section" level="1" n="22">
<head xml:id="echoid-head26" xml:space="preserve">PRONVNCIATVM X.</head>
<p>
  <s xml:id="echoid-s1345" xml:space="preserve">Punctum eclypticæ in qualibet quarta, qui terminat arcum illum qui ex-<lb/>ceſsionem habet ſuper aſcenſionem rectam, longe maximam, quam aliquis <lb/>arcus eclypticæ unquam habere poteſt, beneficio numerorum indagare.</s>
  <s xml:id="echoid-s1346" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1347" xml:space="preserve">Quòd ſi hoc ipſum eclypticæ punctũ, &amp; </s>
  <s xml:id="echoid-s1348" xml:space="preserve">inde arcũ eclypticæ ſcire deſideras, propone <lb/>ſinum cõplementi maximæ declinationis, qui eſt 91706. </s>
  <s xml:id="echoid-s1349" xml:space="preserve">eum duc in totum ſinum, ex il <lb/>lo quod inde prouenit, quære radicem quadratam, quæ in tali declinatione erit 95763. <lb/></s>
  <s xml:id="echoid-s1350" xml:space="preserve">huius radicis arcum inquire ſicut in quocun alio ſinu recto, &amp; </s>
  <s xml:id="echoid-s1351" xml:space="preserve">producit 73. </s>
  <s xml:id="echoid-s1352" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1353" xml:space="preserve">16. </s>
  <s xml:id="echoid-s1354" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1355" xml:space="preserve"><lb/>complementum ip ſius ſcilicet 16. </s>
  <s xml:id="echoid-s1356" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1357" xml:space="preserve">44. </s>
  <s xml:id="echoid-s1358" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1359" xml:space="preserve">arguunt declinationem ab æ quinoctialie-<lb/>ius puncti eclypticæ. </s>
  <s xml:id="echoid-s1360" xml:space="preserve">Iam porro per pronuncia tum 6. </s>
  <s xml:id="echoid-s1361" xml:space="preserve">arcum eclypticæ, qui huic declina <lb/>tioni reſpõdeat, &amp; </s>
  <s xml:id="echoid-s1362" xml:space="preserve">inuenies 46. </s>
  <s xml:id="echoid-s1363" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1364" xml:space="preserve">14. </s>
  <s xml:id="echoid-s1365" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1366" xml:space="preserve">à princípio ♈ numerando. </s>
  <s xml:id="echoid-s1367" xml:space="preserve">Arcus ille deſinit <lb/>in 16. </s>
  <s xml:id="echoid-s1368" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1369" xml:space="preserve">14. </s>
  <s xml:id="echoid-s1370" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1371" xml:space="preserve">♉, &amp; </s>
  <s xml:id="echoid-s1372" xml:space="preserve">hoc ipſum ſanè punctum eſt quod hactenus quæſiui, ſi adhuc a-<lb/>ſcenſionem eius per 7. </s>
  <s xml:id="echoid-s1373" xml:space="preserve">pronunciatũ quæras, inuenies 43. </s>
  <s xml:id="echoid-s1374" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1375" xml:space="preserve">34. </s>
  <s xml:id="echoid-s1376" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1377" xml:space="preserve">utrum arcum ſi <lb/>in unam ſummã redigas, conficient tibi 90. </s>
  <s xml:id="echoid-s1378" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1379" xml:space="preserve">Exceſſus arcus eclypticæ ſuper aſcenſio-<lb/>nem rectam erit 2. </s>
  <s xml:id="echoid-s1380" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1381" xml:space="preserve">28. </s>
  <s xml:id="echoid-s1382" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1383" xml:space="preserve">At hoc retulerit plurimũ ſcire in ſequenti pronunciato, <lb/>quamobrẽ hic tanquã cõmodiore loco &amp; </s>
  <s xml:id="echoid-s1384" xml:space="preserve">ordine decentiſsimo tibi uoluimus ſignificare.</s>
  <s xml:id="echoid-s1385" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div37" type="section" level="1" n="23">
<head xml:id="echoid-head27" xml:space="preserve">PRONVNCIATVM XI.</head>
<p>
  <s xml:id="echoid-s1386" xml:space="preserve">Si quis arcum eclypticæ &amp; </s>
  <s xml:id="echoid-s1387" xml:space="preserve">aſcenſionem eius rectam utrun id in unam <lb/>ſummam redactum tibi proponat, quemlibet arcum eclypticæ &amp; </s>
  <s xml:id="echoid-s1388" xml:space="preserve">æ quatoris <lb/>ſibi correſpondentis inde elicere.</s>
  <s xml:id="echoid-s1389" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1390" xml:space="preserve">Quum aliquis tibi proponit arcum, ex arcu eclypticæ &amp; </s>
  <s xml:id="echoid-s1391" xml:space="preserve">aſcenſione ſua cõpoſitum, &amp; </s>
  <s xml:id="echoid-s1392" xml:space="preserve"><lb/>tu iam quẽlibet ſingillare ſcire cupis, maximã tibi ꝓpone differentiã ex proximo ꝓnun-<lb/>ciato, quã aliquis arcus eclypticæ &amp; </s>
  <s xml:id="echoid-s1393" xml:space="preserve">aſcenſio eius haberi poteſt, eã ex ſupputatione inue <lb/>nies 2. </s>
  <s xml:id="echoid-s1394" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1395" xml:space="preserve">28. </s>
  <s xml:id="echoid-s1396" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1397" xml:space="preserve">ſinũ ipſius 4303. </s>
  <s xml:id="echoid-s1398" xml:space="preserve">multiplica cum ſinu arcus ꝓpoſiti, productũ in totũ <lb/>diuide ſinum, &amp; </s>
  <s xml:id="echoid-s1399" xml:space="preserve">arcus quotientis oſtendet differentiam illã qua arcus eclypticæ a ſcenſio <lb/>
<anchor type="note" xlink:label="note-0036-03a" xlink:href="note-0036-03"/>
nem ſuam excedit. </s>
  <s xml:id="echoid-s1400" xml:space="preserve">Subtracta hac differentia ab arcu ꝓpoſito, &amp; </s>
  <s xml:id="echoid-s1401" xml:space="preserve">reſiduo mediato, mediũ <lb/>illud monſtrat aſcenſionem rectã, differentiã hinc adde ad reliquam partem mediã, &amp; </s>
  <s xml:id="echoid-s1402" xml:space="preserve">ha <lb/>bebis arcũ eclypticæ quæſitũ. </s>
  <s xml:id="echoid-s1403" xml:space="preserve">?</s>
  <s xml:id="echoid-s1404" xml:space="preserve">?Sed ne hic quo deſideres exemplũ, en hoc breuiter <lb/>tibi: </s>
  <s xml:id="echoid-s1405" xml:space="preserve">Sit arcus propoſitus 36. </s>
  <s xml:id="echoid-s1406" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1407" xml:space="preserve">30. </s>
  <s xml:id="echoid-s1408" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1409" xml:space="preserve">ſinus eius rectus 59482. </s>
  <s xml:id="echoid-s1410" xml:space="preserve">eum multiplica cum ſi-<lb/>
<anchor type="note" xlink:label="note-0036-04a" xlink:href="note-0036-04"/>
nu 2. </s>
  <s xml:id="echoid-s1411" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1412" xml:space="preserve">28. </s>
  <s xml:id="echoid-s1413" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1414" xml:space="preserve">ſcilicet 4303. </s>
  <s xml:id="echoid-s1415" xml:space="preserve">productũ diuide in totum ſinum, quotiens erit 2576. </s>
  <s xml:id="echoid-s1416" xml:space="preserve">arcus <lb/>iſtius eſt differentia quæſita. </s>
  <s xml:id="echoid-s1417" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s1418" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1419" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1420" xml:space="preserve">29. </s>
  <s xml:id="echoid-s1421" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1422" xml:space="preserve">differentiã hanc ſi ſubduco ab arcu propo-<lb/>ſito, remanebunt gra. </s>
  <s xml:id="echoid-s1423" xml:space="preserve">35. </s>
  <s xml:id="echoid-s1424" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1425" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1426" xml:space="preserve">Mediũ illius eſt 17. </s>
  <s xml:id="echoid-s1427" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1428" xml:space="preserve">31. </s>
  <s xml:id="echoid-s1429" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1430" xml:space="preserve">ferè, tantus eſt arcus æqua <lb/>toris. </s>
  <s xml:id="echoid-s1431" xml:space="preserve">Iam addo differentiam iſtam ad illud medium, &amp; </s>
  <s xml:id="echoid-s1432" xml:space="preserve">prouenient inde 19. </s>
  <s xml:id="echoid-s1433" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1434" xml:space="preserve">arcus il <lb/>e eclypticæ, quem hoc modo habeo inuentum ſimul cum aſcenſione ſua.</s>
  <s xml:id="echoid-s1435" xml:space="preserve"/>
</p>
<div xml:id="echoid-div37" type="float" level="2" n="1">
<note position="left" xlink:label="note-0036-03" xlink:href="note-0036-03a" xml:space="preserve"><emph style="it">Lateralis</emph> <lb/><emph style="it">operatio.</emph></note>
<note position="left" xlink:label="note-0036-04" xlink:href="note-0036-04a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div39" type="section" level="1" n="24">
<head xml:id="echoid-head28" xml:space="preserve">PRONVNCIATVM XII.</head>
<p>
  <s xml:id="echoid-s1436" xml:space="preserve">Cuiuslibet puncti eclyticæ uel etiam ſtellæ fixæ, cuius enim nota ſit decli-
<pb file="0037" n="37" rhead="TABVLARVM SINVVM."/>
natio, amplitudinem ortiuam in quacun eleuatione poli perſcrutari.</s>
  <s xml:id="echoid-s1437" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1438" xml:space="preserve">Quandoquidẽ quid ſibi uelit hoc loco Amplitudinis uocabulum, nõ ita omnibus ma-<lb/>ximè huius diſciplinæ tyronibus cõſtat, conſultũ uidetur ſuper eo nonnihil hic diſſerere. <lb/></s>
  <s xml:id="echoid-s1439" xml:space="preserve">
<anchor type="note" xlink:label="note-0037-01a" xlink:href="note-0037-01"/>
Amplitudo ortus, eſt arcus horizontis inter ortum æquatoris &amp; </s>
  <s xml:id="echoid-s1440" xml:space="preserve">punctum, ubi Sol ſiue <lb/>ſtella oritur, interceptus. </s>
  <s xml:id="echoid-s1441" xml:space="preserve">Amplitudo occaſus, eſt arcus inter occaſum æquatoris &amp; </s>
  <s xml:id="echoid-s1442" xml:space="preserve">pun <lb/>
<anchor type="note" xlink:label="note-0037-02a" xlink:href="note-0037-02"/>
ctum horizontis, ubi occidit Sol ſiue ſtella. </s>
  <s xml:id="echoid-s1443" xml:space="preserve">Ortus aũt æ quinoctialis, eſt pũctus horizon <lb/>tis in quo Sol oritur in primo minuto ♈ &amp; </s>
  <s xml:id="echoid-s1444" xml:space="preserve">♎, ſimili modo imaginaberis etiã occaſum <lb/>æquatoris, eo loco ubi Sol occidit in primo puncto ♈ uel ♎. </s>
  <s xml:id="echoid-s1445" xml:space="preserve">Ortus hic æquinoctialis, ali <lb/>
<anchor type="note" xlink:label="note-0037-03a" xlink:href="note-0037-03"/>
âs etiam uerus ortus dici ſolet, ad eum religioſa &amp; </s>
  <s xml:id="echoid-s1446" xml:space="preserve">ſancta cõſuetudine iam inde à priſcis <lb/>eccleſiæ proceribus deducta, extrui ſolent omnia templa. </s>
  <s xml:id="echoid-s1447" xml:space="preserve">Ortum illũ quacun hora in-<lb/>uenire potes per compaſſum uiatorium, quoniã hora 6. </s>
  <s xml:id="echoid-s1448" xml:space="preserve">occaſum hunc &amp; </s>
  <s xml:id="echoid-s1449" xml:space="preserve">ortum, duodeci <lb/>ma aũt meridiem &amp; </s>
  <s xml:id="echoid-s1450" xml:space="preserve">ſeptentrionẽ repræſentant. </s>
  <s xml:id="echoid-s1451" xml:space="preserve">Quicquid iam ab ortu uero ſiue æquino <lb/>ctiali numeratur uerſus meridiem in horizõte per gra. </s>
  <s xml:id="echoid-s1452" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1453" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1454" xml:space="preserve">uſ ad punctũ ortus ☉(sun) uel <lb/>ſtellæ, amplitudo dicitur ortus meridionalis, ſi aũt ortus hic fiat uerſus ſeptẽtrionẽ, arcus <lb/>ille horizontis amplitudo dicetur ortus ſeptentrionalis: </s>
  <s xml:id="echoid-s1455" xml:space="preserve">idem´ planè iudiciũ eſt de occa <lb/>ſu. </s>
  <s xml:id="echoid-s1456" xml:space="preserve">Operationẽ porrò conſicies in hunc modũ: </s>
  <s xml:id="echoid-s1457" xml:space="preserve">Propone tibi ſinũ cõplementi altitudi-<lb/>nis poli tuæ regionis, &amp; </s>
  <s xml:id="echoid-s1458" xml:space="preserve">ſinum declinationis Solis uel ſtellæ, ſinũ minorẽ duc in totũ illũ, <lb/>ꝓductũ diuide in maiorẽ, &amp; </s>
  <s xml:id="echoid-s1459" xml:space="preserve">arcus quotientis oſtendet amplitudinẽ ortus meridionalem, <lb/>ſi ta men punctus datus ab æquatore uerſus meridiẽ declinet, qui ſi uergat ad ſeptentrio-<lb/>nem, amplitudo ea dicetur ſeptentrionalis. </s>
  <s xml:id="echoid-s1460" xml:space="preserve">?</s>
  <s xml:id="echoid-s1461" xml:space="preserve">? Exempliloco, pono Solem ut antea in <lb/>
<anchor type="note" xlink:label="note-0037-04a" xlink:href="note-0037-04"/>
2. </s>
  <s xml:id="echoid-s1462" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1463" xml:space="preserve">26. </s>
  <s xml:id="echoid-s1464" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1465" xml:space="preserve">II. </s>
  <s xml:id="echoid-s1466" xml:space="preserve">declinationẽ huius inueni ex 5. </s>
  <s xml:id="echoid-s1467" xml:space="preserve">pronũciato 20. </s>
  <s xml:id="echoid-s1468" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1469" xml:space="preserve">42. </s>
  <s xml:id="echoid-s1470" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1471" xml:space="preserve">Intronizatio <lb/>aũt facta ſit in 48. </s>
  <s xml:id="echoid-s1472" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1473" xml:space="preserve">eleuatiõis polaris, iam ſinũ declinatio nis ex ꝓnunciato 5. </s>
  <s xml:id="echoid-s1474" xml:space="preserve">inuentũ <lb/>35347. </s>
  <s xml:id="echoid-s1475" xml:space="preserve">duco in ſinũ totũ, ꝓductũ diuido in ſinũ cõplemẽti altitudinis poli, ſcilicet 66913. <lb/></s>
  <s xml:id="echoid-s1476" xml:space="preserve">quotiens erit 52825. </s>
  <s xml:id="echoid-s1477" xml:space="preserve">arcus uero 31. </s>
  <s xml:id="echoid-s1478" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1479" xml:space="preserve">53. </s>
  <s xml:id="echoid-s1480" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1481" xml:space="preserve">amplitudo nimirum illa quæſita.</s>
  <s xml:id="echoid-s1482" xml:space="preserve"/>
</p>
<div xml:id="echoid-div39" type="float" level="2" n="1">
<note position="right" xlink:label="note-0037-01" xlink:href="note-0037-01a" xml:space="preserve"><emph style="it">Amplitudo</emph> <lb/><emph style="it">ortus quid.</emph></note>
<note position="right" xlink:label="note-0037-02" xlink:href="note-0037-02a" xml:space="preserve"><emph style="it">Amplitudo</emph> <lb/><emph style="it">occaſus.</emph></note>
<note position="right" xlink:label="note-0037-03" xlink:href="note-0037-03a" xml:space="preserve"><emph style="it">Ortus æꝗ-</emph> <lb/><emph style="it">noctialis et</emph> <lb/><emph style="it">uerus idem</emph></note>
<note position="right" xlink:label="note-0037-04" xlink:href="note-0037-04a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſoo<unsure/>pi</emph>.</note>
</div>
</div>
<div xml:id="echoid-div41" type="section" level="1" n="25">
<head xml:id="echoid-head29" xml:space="preserve">PRONVNCIATVM XIII.</head>
<p>
  <s xml:id="echoid-s1483" xml:space="preserve">Cognita iam antea amplitudine, gradum inuenire zodiaci, qui amplitudi <lb/>nem iſtam conſtituit.</s>
  <s xml:id="echoid-s1484" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1485" xml:space="preserve">Occurrit hic aliquid mihi, quod te celare neuti̈ poſſum, qm̃ in ſphæra recta quilibet <lb/>gradus zodiaci maiorem in horizõte amplitudinẽ nõ admittit, ̈ ſit declinatio ipſius. </s>
  <s xml:id="echoid-s1486" xml:space="preserve">Si <lb/>quidẽ declinatio in ſphæra recta alicuius gradus eclypticæ, etiã amplitudo eſt illius gra <lb/>dus, nec aliqua alia indiget ſupputatiõe noua. </s>
  <s xml:id="echoid-s1487" xml:space="preserve">Sciendũ eſt inſuper, ꝙ nulla amplitudo fit <lb/>minor ̈ ſit illius gradus declinatio. </s>
  <s xml:id="echoid-s1488" xml:space="preserve">maior tamẽ fieri poteſt, ꝗa quo magis adcreſcit ele-<lb/>uatio poli, eò plus accedit &amp; </s>
  <s xml:id="echoid-s1489" xml:space="preserve">amplitudini: </s>
  <s xml:id="echoid-s1490" xml:space="preserve">tamdiu etiam creſcit amplitudo ab æquinoctia <lb/>li uerſus utroſ polos, donec gradus ille ſiue in eclyptica, ſiue ſtella fuerit fixa, horizõtẽ <lb/>
<anchor type="note" xlink:label="note-0037-05a" xlink:href="note-0037-05"/>
amplius nõ attingit, tũc em̃ ſtella iſta uel ☉(sun) amplius nõ exoritur, ſed ſupra horizontem <lb/>ſemper manet. </s>
  <s xml:id="echoid-s1491" xml:space="preserve">Quum´ declinatio Solis ſiue ſtellæ tãta efficitur, quantũ eſt cõplemen <lb/>tum altitudinis poli, tũc Sol ſiue ſtella horizontẽ in parte ſeptentrionali in pũcto attin-<lb/>git, nec amplius ſub horizontẽ uenit: </s>
  <s xml:id="echoid-s1492" xml:space="preserve">ſed ſi declinatio ſit maior cõplemẽto altitudinis po <lb/>li, tunc ſtella aut Sol horizontẽ penitus nõ attingit. </s>
  <s xml:id="echoid-s1493" xml:space="preserve">Conſtat etiã, ꝙ declinatio ſepten <lb/>trionalis æque magnã facit amplitudinem at illa meridionalis. </s>
  <s xml:id="echoid-s1494" xml:space="preserve">Qñ igitur ☉(sun) eſt in ♋, <lb/>tantã facit amplitudinẽ, quantã quũ eſt in ♑, in ♉ q̊  ut in ♏ &amp; </s>
  <s xml:id="echoid-s1495" xml:space="preserve">c. </s>
  <s xml:id="echoid-s1496" xml:space="preserve">Pronunciati huius <lb/>operationẽ experiri uolẽs, multiplica ſinũ cõplementi altitudinis poli cum ſinu amplitu <lb/>dinis ortiuæ, productũ diuide in ſinũ perfectũ, &amp; </s>
  <s xml:id="echoid-s1497" xml:space="preserve">arcus quotientis tibi monſtrabit declina <lb/>tionem puncti illius, quod amplitudinẽ hãc fecit. </s>
  <s xml:id="echoid-s1498" xml:space="preserve">ꝓnunciatũ aũt. </s>
  <s xml:id="echoid-s1499" xml:space="preserve">6. </s>
  <s xml:id="echoid-s1500" xml:space="preserve">inuenire te docuit ex <lb/>declinatione gradũ eclypticæ ſibi reſpondentẽ. </s>
  <s xml:id="echoid-s1501" xml:space="preserve">?</s>
  <s xml:id="echoid-s1502" xml:space="preserve">? Sed iã exemplo rẽ hanc plenius ex <lb/>
<anchor type="note" xlink:label="note-0037-06a" xlink:href="note-0037-06"/>
plicemus, quãdo ꝓnunciatũ hoc cõtrariũ habet ſuperioris, exemplũ quo illius inuerte-<lb/>mus tantũ hoc modo. </s>
  <s xml:id="echoid-s1503" xml:space="preserve">Amplitudinẽ habeo 31. </s>
  <s xml:id="echoid-s1504" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1505" xml:space="preserve">33. </s>
  <s xml:id="echoid-s1506" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1507" xml:space="preserve">ſinus eius eſt 52825. </s>
  <s xml:id="echoid-s1508" xml:space="preserve">facta autẽ <lb/>ſit intronizatio in eleuatiõe polari 48. </s>
  <s xml:id="echoid-s1509" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1510" xml:space="preserve">ſinus complementi altitudinis poli ſit 66913. <lb/></s>
  <s xml:id="echoid-s1511" xml:space="preserve">iam multiplica unum numerũ ſinuũ cũ reliquo, productũ diuide in totũ ſinum, &amp; </s>
  <s xml:id="echoid-s1512" xml:space="preserve">inueni-<lb/>es in quotiente 35347. </s>
  <s xml:id="echoid-s1513" xml:space="preserve">arcus illius 20. </s>
  <s xml:id="echoid-s1514" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1515" xml:space="preserve">42. </s>
  <s xml:id="echoid-s1516" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1517" xml:space="preserve">mõſtrat tibi declinationẽ Solis quæſitã. </s>
  <s xml:id="echoid-s1518" xml:space="preserve"><lb/>Inuenturus a dhuc porrò gradũ Solis, cõperies illũ per 6. </s>
  <s xml:id="echoid-s1519" xml:space="preserve">ꝓnunciatũ gra. </s>
  <s xml:id="echoid-s1520" xml:space="preserve">2. </s>
  <s xml:id="echoid-s1521" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1522" xml:space="preserve">26. </s>
  <s xml:id="echoid-s1523" xml:space="preserve">II ſic
<pb file="0038" n="38" rhead="GENVINVS VSVS"/>
igitur habes gradũ Solis ex amplitudine ortiua collectũ. </s>
  <s xml:id="echoid-s1524" xml:space="preserve">Et ſimili planè modo intelliges <lb/>omnia de occaſu, ſiquidem amplitudo una alteri reſpondet ſaltem unius ꝓpoſiti gradus.</s>
  <s xml:id="echoid-s1525" xml:space="preserve"/>
</p>
<div xml:id="echoid-div41" type="float" level="2" n="1">
<note position="right" xlink:label="note-0037-05" xlink:href="note-0037-05a" xml:space="preserve"><emph style="it">Amplitudo</emph> <lb/><emph style="it">Solis ſiue</emph> <lb/><emph style="it">ſtellæ ſemꝑ</emph> <lb/><emph style="it">maior aut</emph> <lb/><emph style="it">æqualis ect</emph> <lb/><emph style="it">declinatiõe</emph> <lb/><emph style="it">nunquam</emph> <lb/><emph style="it">minor.</emph></note>
<note position="right" xlink:label="note-0037-06" xlink:href="note-0037-06a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div43" type="section" level="1" n="26">
<head xml:id="echoid-head30" xml:space="preserve">PRONVNCIATVM XIIII.</head>
<p>
  <s xml:id="echoid-s1526" xml:space="preserve">Altitudinem poli in ſingulos dies examplitudine ortiua uel occidua, So-<lb/>lis ſiue ſtellarum, adpoſite inueſtigare.</s>
  <s xml:id="echoid-s1527" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1528" xml:space="preserve">Vno hoc pronunciato tres ſimul uelut uno faſce cõſtrinximus, 12. </s>
  <s xml:id="echoid-s1529" xml:space="preserve">13. </s>
  <s xml:id="echoid-s1530" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1531" xml:space="preserve">14. </s>
  <s xml:id="echoid-s1532" xml:space="preserve">tria enim <lb/>illa expendenda fuerunt, declinatio, amplitudo, &amp; </s>
  <s xml:id="echoid-s1533" xml:space="preserve">altitudo poli, ex ijs: </s>
  <s xml:id="echoid-s1534" xml:space="preserve">quia priora duo <lb/>
<anchor type="note" xlink:label="note-0038-01a" xlink:href="note-0038-01"/>
iam antea docuimus, reliquum eſt, ut etiã hoc tertium expediamus. </s>
  <s xml:id="echoid-s1535" xml:space="preserve">Si forte altitudinem <lb/>poli ex amplitudine ſiue declinatione cognoſcere cupis, propone tibi ſinum amplitudi-<lb/>nis ſimul cum ſinu declinationis, minorem duc in ſinum totum, productum diuide in ma <lb/>iorem, arcus quotientis oſtendet complementum altitudinis poli, id ſi ſubtrahas à 90. </s>
  <s xml:id="echoid-s1536" xml:space="preserve">re <lb/>
<anchor type="note" xlink:label="note-0038-02a" xlink:href="note-0038-02"/>
manebit altitudo poli quam quæſiuiſti. </s>
  <s xml:id="echoid-s1537" xml:space="preserve">?</s>
  <s xml:id="echoid-s1538" xml:space="preserve">? Vis &amp; </s>
  <s xml:id="echoid-s1539" xml:space="preserve">hic exemplum tibi dari@ Enipſo in-<lb/>tronizationis die Sol fuit in 2. </s>
  <s xml:id="echoid-s1540" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1541" xml:space="preserve">26. </s>
  <s xml:id="echoid-s1542" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1543" xml:space="preserve">II. </s>
  <s xml:id="echoid-s1544" xml:space="preserve">ex 5. </s>
  <s xml:id="echoid-s1545" xml:space="preserve">ergo pronunciato inueni declinatio <lb/>nem 20. </s>
  <s xml:id="echoid-s1546" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1547" xml:space="preserve">42. </s>
  <s xml:id="echoid-s1548" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1549" xml:space="preserve">ſinus eius eſt 35347. </s>
  <s xml:id="echoid-s1550" xml:space="preserve">Amplitudinem autem ortiuam Solis in die in-<lb/>tronizationis inueni 31. </s>
  <s xml:id="echoid-s1551" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1552" xml:space="preserve">53. </s>
  <s xml:id="echoid-s1553" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1554" xml:space="preserve">iam paro elicere inde altitudinem poli. </s>
  <s xml:id="echoid-s1555" xml:space="preserve">Sinus igitur <lb/>amplitudinis eſt 52825. </s>
  <s xml:id="echoid-s1556" xml:space="preserve">iam duco minorem iſtam 3534. </s>
  <s xml:id="echoid-s1557" xml:space="preserve">à toto ſinu, productum diuido <lb/>in 52825. </s>
  <s xml:id="echoid-s1558" xml:space="preserve">tanquam numerum maiorem, quotientis erit 66913. </s>
  <s xml:id="echoid-s1559" xml:space="preserve">arcus illius 42. </s>
  <s xml:id="echoid-s1560" xml:space="preserve">eum ubi <lb/>ſubtraxeris à 90. </s>
  <s xml:id="echoid-s1561" xml:space="preserve">remanebunt gradus 8. </s>
  <s xml:id="echoid-s1562" xml:space="preserve">ipſa eleuatio polaris optata.</s>
  <s xml:id="echoid-s1563" xml:space="preserve"/>
</p>
<div xml:id="echoid-div43" type="float" level="2" n="1">
<note position="left" xlink:label="note-0038-01" xlink:href="note-0038-01a" xml:space="preserve"><emph style="it">Per aream</emph> <lb/><emph style="it">quadr antis</emph> <lb/><emph style="it">ſimile perſi</emph> <lb/><emph style="it">acs.</emph></note>
<note position="left" xlink:label="note-0038-02" xlink:href="note-0038-02a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div45" type="section" level="1" n="27">
<head xml:id="echoid-head31" xml:space="preserve">PRONVNCIATVM XV.</head>
<p>
  <s xml:id="echoid-s1564" xml:space="preserve">In qualibet regione differentiam inquirere aſcenſionalem, per quam lon-<lb/>gitudo dierum &amp; </s>
  <s xml:id="echoid-s1565" xml:space="preserve">noctium inuenitur, &amp; </s>
  <s xml:id="echoid-s1566" xml:space="preserve">unde longitudo diurna per uniuer-<lb/>ſum orbem facile cognoſci poteſt.</s>
  <s xml:id="echoid-s1567" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1568" xml:space="preserve">Differentia aſcenſionalis arcus eſt æquatoris, per quem longitudo diurna agnoſci-<lb/>
<anchor type="note" xlink:label="note-0038-03a" xlink:href="note-0038-03"/>
tur, is autem ſic intelligitur. </s>
  <s xml:id="echoid-s1569" xml:space="preserve">Quum ab ortu æquinoctiali uſ  ad meridianũ 90. </s>
  <s xml:id="echoid-s1570" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1571" xml:space="preserve">ſem-<lb/>per interſint, deinde in ſingulas horas gradus 15. </s>
  <s xml:id="echoid-s1572" xml:space="preserve">emergũt ſuper horizontem, 90. </s>
  <s xml:id="echoid-s1573" xml:space="preserve">illi gra <lb/>dus præciſe horas 6. </s>
  <s xml:id="echoid-s1574" xml:space="preserve">cõficiũt, quo dies medius horis 6. </s>
  <s xml:id="echoid-s1575" xml:space="preserve">uel longior eſt uel breuior, idip <lb/>ſum uocamus differentiam aſcenſionalem, eam inuenire cupiens, propone tibi ſinus utri <lb/>uſ complementi, declinationis &amp; </s>
  <s xml:id="echoid-s1576" xml:space="preserve">amplitudinis, minorem duc in finum totum, produ-<lb/>ctum diuide in ſinum maiorem, arcu quotientis dehinc ſubtracto à 90. </s>
  <s xml:id="echoid-s1577" xml:space="preserve">remanebit diffe-<lb/>
<anchor type="note" xlink:label="note-0038-04a" xlink:href="note-0038-04"/>
rentia aſcenſionalis: </s>
  <s xml:id="echoid-s1578" xml:space="preserve">quod ſi declinatio fuerit meridionalis, ſubtrahe differentiam illam <lb/>aſcenſionalem à 90. </s>
  <s xml:id="echoid-s1579" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1580" xml:space="preserve">remanebit arcus ſemidiurnus: </s>
  <s xml:id="echoid-s1581" xml:space="preserve">ſin autem declinatio ſit ſeptentrio-<lb/>nalis, illam rurſus adde ad 90. </s>
  <s xml:id="echoid-s1582" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1583" xml:space="preserve">iterum habebis arcum ſemidiurnum. </s>
  <s xml:id="echoid-s1584" xml:space="preserve">Tantundem eſt, ſi <lb/>arcum quotientis ſubtrahas à ſemicirculo, nam &amp; </s>
  <s xml:id="echoid-s1585" xml:space="preserve">tunc manebit arcus ſemidiurnus, illo <lb/>duplicato, habes arcum diurnum, quem ſi rurſus ſubtrahas à toto circulo, arcus relinque-<lb/>tur nocturnus. </s>
  <s xml:id="echoid-s1586" xml:space="preserve">ſemper tamen hic intellige 15. </s>
  <s xml:id="echoid-s1587" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1588" xml:space="preserve">pro unica hora. </s>
  <s xml:id="echoid-s1589" xml:space="preserve">?</s>
  <s xml:id="echoid-s1590" xml:space="preserve">? Sit &amp; </s>
  <s xml:id="echoid-s1591" xml:space="preserve">hic exem-<lb/>
<anchor type="note" xlink:label="note-0038-05a" xlink:href="note-0038-05"/>
plum tibi huiuſmodi: </s>
  <s xml:id="echoid-s1592" xml:space="preserve">Inuenturus longitudinem diei intronizationis, iam antea habeo <lb/>perfectam declinationem Solis ex pronunciato 5. </s>
  <s xml:id="echoid-s1593" xml:space="preserve">quoniam ille in 2. </s>
  <s xml:id="echoid-s1594" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1595" xml:space="preserve">26. </s>
  <s xml:id="echoid-s1596" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1597" xml:space="preserve">fuit II. </s>
  <s xml:id="echoid-s1598" xml:space="preserve">ea <lb/>declinatio eſt 20. </s>
  <s xml:id="echoid-s1599" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1600" xml:space="preserve">42. </s>
  <s xml:id="echoid-s1601" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1602" xml:space="preserve">ex 12. </s>
  <s xml:id="echoid-s1603" xml:space="preserve">pronunciato quo inuentam habeo amplitudinem <lb/>ad eundem ipſum gradum Solis, puta 31. </s>
  <s xml:id="echoid-s1604" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1605" xml:space="preserve">53. </s>
  <s xml:id="echoid-s1606" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1607" xml:space="preserve">Nunc iam colligo complementa, <lb/>alterum eſt 58. </s>
  <s xml:id="echoid-s1608" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1609" xml:space="preserve">7. </s>
  <s xml:id="echoid-s1610" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1611" xml:space="preserve">ſinus eius 849 12. </s>
  <s xml:id="echoid-s1612" xml:space="preserve">alterum porrò complementum eſt 69. </s>
  <s xml:id="echoid-s1613" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1614" xml:space="preserve">18. <lb/></s>
  <s xml:id="echoid-s1615" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1616" xml:space="preserve">arcus ipſius 93544. </s>
  <s xml:id="echoid-s1617" xml:space="preserve">ſinum minorem multiplica cum toto ſinu, productum diuide in <lb/>maximum, &amp; </s>
  <s xml:id="echoid-s1618" xml:space="preserve">quotiens erit 90772, arcus eius eſt 65. </s>
  <s xml:id="echoid-s1619" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1620" xml:space="preserve">12. </s>
  <s xml:id="echoid-s1621" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1622" xml:space="preserve">Arcũ illum ſi ſubtrahas à <lb/>90. </s>
  <s xml:id="echoid-s1623" xml:space="preserve">remanebit differentia aſcenſionalis 24. </s>
  <s xml:id="echoid-s1624" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1625" xml:space="preserve">49. </s>
  <s xml:id="echoid-s1626" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1627" xml:space="preserve">differentiam hanc adde, &amp; </s>
  <s xml:id="echoid-s1628" xml:space="preserve">habe-<lb/>bis arcum ſemidiurnum 114. </s>
  <s xml:id="echoid-s1629" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1630" xml:space="preserve">49. </s>
  <s xml:id="echoid-s1631" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1632" xml:space="preserve">Vel ſubtrahe 65. </s>
  <s xml:id="echoid-s1633" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1634" xml:space="preserve">11. </s>
  <s xml:id="echoid-s1635" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1636" xml:space="preserve">de ſemicirculo, &amp; </s>
  <s xml:id="echoid-s1637" xml:space="preserve"><lb/>rurſus manebit arcus ſemidiurnus, eũ ſi reſoluas in horas, habebis horas 7. </s>
  <s xml:id="echoid-s1638" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1639" xml:space="preserve">48. </s>
  <s xml:id="echoid-s1640" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1641" xml:space="preserve">Sin <lb/>autem duplaris numerum, habebis arcũ diurnum 15. </s>
  <s xml:id="echoid-s1642" xml:space="preserve">horas 36. </s>
  <s xml:id="echoid-s1643" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1644" xml:space="preserve">Ad extremum ſi ſub-<lb/>trahas arcum diurnum à 24. </s>
  <s xml:id="echoid-s1645" xml:space="preserve">horis, reliquæ tibi manebunt horæ 8. </s>
  <s xml:id="echoid-s1646" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1647" xml:space="preserve">24. </s>
  <s xml:id="echoid-s1648" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1649" xml:space="preserve">tempus ſcili-<lb/>cet nocturnum. </s>
  <s xml:id="echoid-s1650" xml:space="preserve">At hoc modo cuiuslibet puncti uel ſtellæ fixæ potes arcum inuenire <lb/>diurnum, hoc eſt, quot horis &amp; </s>
  <s xml:id="echoid-s1651" xml:space="preserve">minutis maneat ſuper horizontem, ſiue interdiu tandem <lb/>ſiue noctu id fiat. </s>
  <s xml:id="echoid-s1652" xml:space="preserve">Quod autem ad puncta eclypticæ tantum pertinet, ſequenti pronun <lb/>ciato explicabimus.</s>
  <s xml:id="echoid-s1653" xml:space="preserve"/>
</p>
<div xml:id="echoid-div45" type="float" level="2" n="1">
<note position="left" xlink:label="note-0038-03" xlink:href="note-0038-03a" xml:space="preserve"><emph style="it">Differentia</emph> <lb/><emph style="it">aſcẽſionalis</emph> <lb/><emph style="it">quid ſit.</emph></note>
<note position="left" xlink:label="note-0038-04" xlink:href="note-0038-04a" xml:space="preserve"><emph style="it">Simile per</emph> <lb/><emph style="it">introitum</emph> <lb/><emph style="it">arealem</emph> <lb/><emph style="it">quærenti</emph> <lb/><emph style="it">apparet.</emph></note>
<note position="left" xlink:label="note-0038-05" xlink:href="note-0038-05a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſoo<unsure/>pi.</emph></note>
</div>
<pb file="0039" n="39" rhead="TABVLARVM SINVVM."/>
</div>
<div xml:id="echoid-div47" type="section" level="1" n="28">
<head xml:id="echoid-head32" xml:space="preserve">PRONVNCIATVM XVI.</head>
<p>
  <s xml:id="echoid-s1654" xml:space="preserve">Longitudinem diurnam ſuper quodcun punctum eclypticæ alia qua-<lb/>dam ratione addiſcere.</s>
  <s xml:id="echoid-s1655" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1656" xml:space="preserve">Quod ſi lõitudinẽ diurnã diuerſo modo cupis cognoſcere, quære principio ex 12. </s>
  <s xml:id="echoid-s1657" xml:space="preserve">ꝓ <lb/>nunciato amplitudinẽ ☉(sun), quãdo ille eſt in primo minuto ♑, deinde ex ſuperiori pronun <lb/>
<anchor type="note" xlink:label="note-0039-01a" xlink:href="note-0039-01"/>
ciato inquire differentiã aſcẽſionalẽ, ex ſeptimo aũt aſcẽſionem rectã gradus Solis, ad eũ <lb/>diem cuius quantita tẽ ſcire deſideras, mox multiplica ſinũ rectũ eius aſcenſionis rectæ cũ <lb/>ſinu differentiæ aſcenſionalis principij ♑, productũ partire in totũ ſinũ, arcus quotien-<lb/>tis tibi cõmonſtrabit uerã differentiã aſcenſionalẽ, eam addes ad gra. </s>
  <s xml:id="echoid-s1658" xml:space="preserve">90. </s>
  <s xml:id="echoid-s1659" xml:space="preserve">in ſignis ſepten <lb/>trionalibus, ſubtrahes aũt in meridionalibus, &amp; </s>
  <s xml:id="echoid-s1660" xml:space="preserve">remanebit arcus ſemidiurnus. </s>
  <s xml:id="echoid-s1661" xml:space="preserve">?</s>
  <s xml:id="echoid-s1662" xml:space="preserve">? Ex-<lb/>
<anchor type="note" xlink:label="note-0039-02a" xlink:href="note-0039-02"/>
emplũ ſuꝑ ea re illuſtranda accipe huiuſmodi, ſicut in ſuperiori ꝓnunciato diem introni <lb/>zationis propoſuim us, ita eundem etiam hic ſeruabimus, at eius quantitatẽ inquiſitu <lb/>rus, primum omniũ eleuationem poli aſſumo 48. </s>
  <s xml:id="echoid-s1663" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1664" xml:space="preserve">complementũ eius eſt 42. </s>
  <s xml:id="echoid-s1665" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1666" xml:space="preserve">Iam <lb/>uero per pronũciatũ 12. </s>
  <s xml:id="echoid-s1667" xml:space="preserve">inuenio amplitudinẽ ☉(sun), qñ ille eſt in primo minuto ♑ 36. </s>
  <s xml:id="echoid-s1668" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s1669" xml:space="preserve">35. </s>
  <s xml:id="echoid-s1670" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1671" xml:space="preserve">ſinũ cõplemẽti illius amplitudinis 80299. </s>
  <s xml:id="echoid-s1672" xml:space="preserve">duco in ſinũ totũ, ꝓductũ in ſinũ cõple-<lb/>menti maximæ declinatiõis Solis diuide, &amp; </s>
  <s xml:id="echoid-s1673" xml:space="preserve">ꝓueniũt in quotiente 87561. </s>
  <s xml:id="echoid-s1674" xml:space="preserve">arcus porro eſt <lb/>61. </s>
  <s xml:id="echoid-s1675" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1676" xml:space="preserve">7. </s>
  <s xml:id="echoid-s1677" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1678" xml:space="preserve">id quũ ſubtraho à 90. </s>
  <s xml:id="echoid-s1679" xml:space="preserve">remanent 28. </s>
  <s xml:id="echoid-s1680" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1681" xml:space="preserve">53. </s>
  <s xml:id="echoid-s1682" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1683" xml:space="preserve">differentia aſcẽſionalis oĩm <lb/>maxima, eam ſi addo ad 90. </s>
  <s xml:id="echoid-s1684" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1685" xml:space="preserve">ꝓdit inde mihi tempus ſemidiurnũ lõgiſ simæ diei, ſi aũt <lb/>ſubtraho à 90. </s>
  <s xml:id="echoid-s1686" xml:space="preserve">reliquũ, manet tẽpus ſemidiurnũ breuiſsimæ diei totius anni. </s>
  <s xml:id="echoid-s1687" xml:space="preserve">Poſtea quæ <lb/>ro aſcenſionẽ rectã (ꝑ 7. </s>
  <s xml:id="echoid-s1688" xml:space="preserve">ꝓnunciatũ) gradus eclypticæ in q̊ Sol fuit die intronzationis, <lb/>&amp; </s>
  <s xml:id="echoid-s1689" xml:space="preserve">ibi inuenio 60. </s>
  <s xml:id="echoid-s1690" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1691" xml:space="preserve">21. </s>
  <s xml:id="echoid-s1692" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1693" xml:space="preserve">iã ſinũ illius aſcenſiõis rectæ 86906. </s>
  <s xml:id="echoid-s1694" xml:space="preserve">duco in ſinũ differẽtiæ <lb/>aſcenſionalis 28. </s>
  <s xml:id="echoid-s1695" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1696" xml:space="preserve">53. </s>
  <s xml:id="echoid-s1697" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1698" xml:space="preserve">ſcilicet 48302. </s>
  <s xml:id="echoid-s1699" xml:space="preserve">ꝓductũ diuido in ſinũ ꝑfectũ, et ꝓueniũt in q̊ <lb/>tiente 41977. </s>
  <s xml:id="echoid-s1700" xml:space="preserve">arcus erit 24. </s>
  <s xml:id="echoid-s1701" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1702" xml:space="preserve">49. </s>
  <s xml:id="echoid-s1703" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1704" xml:space="preserve">quæ differentia uera eſt aſcenſionalis, quam ex <lb/>proximo pronunciato non paulò diuerſo adinueni, illam ſi addas ad gra. </s>
  <s xml:id="echoid-s1705" xml:space="preserve">90. </s>
  <s xml:id="echoid-s1706" xml:space="preserve">(ſi quidẽ ☉(sun) <lb/>in ſigno eſt ſeptentrionali) ꝓueniet hinc arcus ſemidiurnus 114. </s>
  <s xml:id="echoid-s1707" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1708" xml:space="preserve">42. </s>
  <s xml:id="echoid-s1709" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1710" xml:space="preserve">ꝗbus horæ 7 <lb/>conficiuntur &amp; </s>
  <s xml:id="echoid-s1711" xml:space="preserve">48. </s>
  <s xml:id="echoid-s1712" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1713" xml:space="preserve">productũ diuerſæ huius operationis, conſimile tamen ſuperiori.</s>
  <s xml:id="echoid-s1714" xml:space="preserve"/>
</p>
<div xml:id="echoid-div47" type="float" level="2" n="1">
<note position="right" xlink:label="note-0039-01" xlink:href="note-0039-01a" xml:space="preserve"><emph style="it">Illud repe-</emph> <lb/><emph style="it">rics ſi qua-</emph> <lb/><emph style="it">drantem la</emph> <lb/><emph style="it">teraliter in</emph> <lb/><emph style="it">grediaris.</emph></note>
<note position="right" xlink:label="note-0039-02" xlink:href="note-0039-02a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſoo<unsure/>pi</emph>.</note>
</div>
</div>
<div xml:id="echoid-div49" type="section" level="1" n="29">
<head xml:id="echoid-head33" xml:space="preserve">PRONVNCIATVM XVII.</head>
<p>
  <s xml:id="echoid-s1715" xml:space="preserve">Cognita regionis alicuius die longiſsima, aut alioqui propoſita, altitudi-<lb/>nem poli, in qua tanta eſt diei quantitas, ex ſphærica ſupputatione inuenire.</s>
  <s xml:id="echoid-s1716" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1717" xml:space="preserve">Non tantũ ꝑ diem lõgiſsimũ, ſed &amp; </s>
  <s xml:id="echoid-s1718" xml:space="preserve">breuiſsimũ oꝑari hoc potes, at in hoc tibi ꝓpone <lb/>diẽ lõ giſsimũ, eũ diuide in duas ꝑtes, qua℞ q̃libet dicet̃ tẽpus ſemidiurnũ, inde ſubtrahe <lb/>horas 6. </s>
  <s xml:id="echoid-s1719" xml:space="preserve">q̊d inde remanet, diciſolet differẽtia aſcẽſionalis maxima, eã cõuerte in gradus, <lb/>ita, ut ſemꝑ 15. </s>
  <s xml:id="echoid-s1720" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1721" xml:space="preserve">reſpõdeãt horæ, &amp; </s>
  <s xml:id="echoid-s1722" xml:space="preserve">uni minuto tꝑis 15. </s>
  <s xml:id="echoid-s1723" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1724" xml:space="preserve">gradus. </s>
  <s xml:id="echoid-s1725" xml:space="preserve">Differentiã illam <lb/>aſcenſionalẽ iã in gradus &amp; </s>
  <s xml:id="echoid-s1726" xml:space="preserve">minuta graduũ cõuerſam, diuides in duas partes æquales, <lb/>
<anchor type="note" xlink:label="note-0039-03a" xlink:href="note-0039-03"/>
ea℞ alterutra ſufficiet tibi ad hãc oꝑationẽ. </s>
  <s xml:id="echoid-s1727" xml:space="preserve">Accipe deinde &amp; </s>
  <s xml:id="echoid-s1728" xml:space="preserve">ſinũ cõplementi, eũ multi-<lb/>plica cũ ſinu cõplementi maximæ declinatiõis Solis. </s>
  <s xml:id="echoid-s1729" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s1730" xml:space="preserve">66. </s>
  <s xml:id="echoid-s1731" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1732" xml:space="preserve">30. </s>
  <s xml:id="echoid-s1733" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1734" xml:space="preserve">ꝓductũ diuide in ſi <lb/>nũ totũ, &amp; </s>
  <s xml:id="echoid-s1735" xml:space="preserve">arcus ille q̊tiẽtis ex 90. </s>
  <s xml:id="echoid-s1736" xml:space="preserve">relinquet tibi amplitudinẽ ortiuã principij ♋ uel ♑ in <lb/>regiõe ꝓpoſita, eius amplitudinis ſinũ tibi ꝓpone ſimul cũ ſinu maximæ declinatiõis So <lb/>
<anchor type="note" xlink:label="note-0039-04a" xlink:href="note-0039-04"/>
lis, minorem duc in ſinũ totũ, ꝓductũ diuide in maiorẽ, arcus illius q̊tientis mõſtrabit al-<lb/>titudinẽ æquatoris, q̃ à 90. </s>
  <s xml:id="echoid-s1737" xml:space="preserve">ſublata, relin ꝗt altitudinẽ poli q̃ſitã. </s>
  <s xml:id="echoid-s1738" xml:space="preserve">Eodẽ modo potes q̊cũ <lb/>tꝑe anni cognoſcere eleuationẽ poli, ſi tm̃ tibi ꝓponas ꝗ̃ntitatẽ diei et declinationẽ gra-<lb/>dus eclypticæ, quẽ ꝑmeat Sol illo die. </s>
  <s xml:id="echoid-s1739" xml:space="preserve">?</s>
  <s xml:id="echoid-s1740" xml:space="preserve">? Habe in hoc tibi ſimilitudinẽ huiuſmodi. </s>
  <s xml:id="echoid-s1741" xml:space="preserve">Au <lb/>
<anchor type="note" xlink:label="note-0039-05a" xlink:href="note-0039-05"/>
guſtæ, ubi talis intronizatio facta eſt, dies lõgiſsima horas habet 15. </s>
  <s xml:id="echoid-s1742" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1743" xml:space="preserve">50. </s>
  <s xml:id="echoid-s1744" xml:space="preserve">ſi uelim iã in-<lb/>de eleuationẽ poli eius loci colligere, à lõgitudine diurna, adimo horas 12. </s>
  <s xml:id="echoid-s1745" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1746" xml:space="preserve">remanẽt ho <lb/>ræ 3. </s>
  <s xml:id="echoid-s1747" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1748" xml:space="preserve">50. </s>
  <s xml:id="echoid-s1749" xml:space="preserve">ea ſi mediaro, habebo horã 1. </s>
  <s xml:id="echoid-s1750" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1751" xml:space="preserve">55. </s>
  <s xml:id="echoid-s1752" xml:space="preserve">Vel etiã diuido lõgitudinẽ diurnã totã in <lb/>duas ꝑtes, qua℞ q̃libet habebit horas 7. </s>
  <s xml:id="echoid-s1753" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1754" xml:space="preserve">55. </s>
  <s xml:id="echoid-s1755" xml:space="preserve">inde ſi ſubtraxero 6. </s>
  <s xml:id="echoid-s1756" xml:space="preserve">horas, remanet hora <lb/>unica cũ 55. </s>
  <s xml:id="echoid-s1757" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1758" xml:space="preserve">ſicut prius. </s>
  <s xml:id="echoid-s1759" xml:space="preserve">Horas illas poſtea redigo in gradus, &amp; </s>
  <s xml:id="echoid-s1760" xml:space="preserve">erunt 28. </s>
  <s xml:id="echoid-s1761" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1762" xml:space="preserve">53. </s>
  <s xml:id="echoid-s1763" xml:space="preserve">min. <lb/></s>
  <s xml:id="echoid-s1764" xml:space="preserve">eos ſubtrahe tu deinde de quadrãte, manebit cõplementũ eius 61. </s>
  <s xml:id="echoid-s1765" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1766" xml:space="preserve">7. </s>
  <s xml:id="echoid-s1767" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1768" xml:space="preserve">Sinũ illius <lb/>87561 multiplica cũ ſinu cõplemẽti maxĩæ declinatiõis 91706 ꝓductũ diuide ĩ totũ ſinũ <lb/>&amp; </s>
  <s xml:id="echoid-s1769" xml:space="preserve">ĩ q̊tiẽte habebis 80299. </s>
  <s xml:id="echoid-s1770" xml:space="preserve">cui9 arc9 ẽ 53 gr. </s>
  <s xml:id="echoid-s1771" xml:space="preserve">25. </s>
  <s xml:id="echoid-s1772" xml:space="preserve">m̃. </s>
  <s xml:id="echoid-s1773" xml:space="preserve">cõplemẽtũ eius 36 g. </s>
  <s xml:id="echoid-s1774" xml:space="preserve">35 m̃. </s>
  <s xml:id="echoid-s1775" xml:space="preserve">q̃ ☉(sun) ampli <lb/>plitudo maxĩa eſt in ea regiõe, ſinũ illius amplitudinis 59599. </s>
  <s xml:id="echoid-s1776" xml:space="preserve">adſume ꝓ diuiſore, qñꝗdẽ
<pb file="0040" n="40" rhead="GENVINVS VSVS"/>
maior eſt ſinu maximæ declinationis Solis 39874. </s>
  <s xml:id="echoid-s1777" xml:space="preserve">tunc aũt ipſum maximæ decli-<lb/>nationis Solis multiplica cum toto ſinu, productũ diuide in diuiſorem, &amp; </s>
  <s xml:id="echoid-s1778" xml:space="preserve">prouenſent in <lb/>quotiente 66904. </s>
  <s xml:id="echoid-s1779" xml:space="preserve">arcus iſtius erit 42. </s>
  <s xml:id="echoid-s1780" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1781" xml:space="preserve">quæ altitudo eſt æquatoris, eam ſi ſubtrahas <lb/>à 90. </s>
  <s xml:id="echoid-s1782" xml:space="preserve">remanebunt 48. </s>
  <s xml:id="echoid-s1783" xml:space="preserve">gradus, eleuatio ſcilicet polaris quam tantopere inquirebas.</s>
  <s xml:id="echoid-s1784" xml:space="preserve"/>
</p>
<div xml:id="echoid-div49" type="float" level="2" n="1">
<note position="right" xlink:label="note-0039-03" xlink:href="note-0039-03a" xml:space="preserve"><emph style="it">Oſtẽdit hoc</emph> <lb/><emph style="it">ingreſſum</emph> <lb/><emph style="it">lateralem.</emph></note>
<note position="right" xlink:label="note-0039-04" xlink:href="note-0039-04a" xml:space="preserve"><emph style="it">Hoc area-</emph> <lb/><emph style="it">tim aſſeque</emph> <lb/><emph style="it">ris.</emph></note>
<note position="right" xlink:label="note-0039-05" xlink:href="note-0039-05a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div51" type="section" level="1" n="30">
<head xml:id="echoid-head34" xml:space="preserve">PRONVNCIATVM XVIII.</head>
<p>
  <s xml:id="echoid-s1785" xml:space="preserve">Cuiuslibet arcus eclypticæ, qui incipiat in ſectione uernali, aſcenſionem <lb/>obliquam in quacun ſiue ciuitate ſiue regione ſupputare.</s>
  <s xml:id="echoid-s1786" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1787" xml:space="preserve">Iam ſupra edoctus es pronunciato 15. </s>
  <s xml:id="echoid-s1788" xml:space="preserve">cognoſcere differentiã aſcenſionalem, ea res ti <lb/>bi hic plurimũ erit uſui. </s>
  <s xml:id="echoid-s1789" xml:space="preserve">Cæterum in pronunciato 7. </s>
  <s xml:id="echoid-s1790" xml:space="preserve">didiciſti inuentionem aſcenſionis re <lb/>ctæ. </s>
  <s xml:id="echoid-s1791" xml:space="preserve">Iam igitur ſi punctũ, ſuper quo differentia aſcenfionalis eſt quæſtia, declinationem <lb/>habet ſeptentrionalem, tũc tu differentiã illam ſubtrahe ab aſcenſiõe recta pũcti dati, ſin <lb/>aũt declinatio fuerit meridionalis, operæpreciũ erit te addere differentiã iſtã ad aſcenſio <lb/>
<anchor type="note" xlink:label="note-0040-01a" xlink:href="note-0040-01"/>
nem rectã, &amp; </s>
  <s xml:id="echoid-s1792" xml:space="preserve">tũc ſanè reliqua tibi manebit aſcenſio illius pũcti obliqua. </s>
  <s xml:id="echoid-s1793" xml:space="preserve">?</s>
  <s xml:id="echoid-s1794" xml:space="preserve">? Nunc ſi uis <lb/>cape eius rei tibi exemplũ huiuſmodi: </s>
  <s xml:id="echoid-s1795" xml:space="preserve">Sol in ipſo die intronizationis ornatiſsimi Præſu <lb/>lis Auguſtenſis fuit in 2. </s>
  <s xml:id="echoid-s1796" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1797" xml:space="preserve">26. </s>
  <s xml:id="echoid-s1798" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1799" xml:space="preserve">II, quapropter &amp; </s>
  <s xml:id="echoid-s1800" xml:space="preserve">declinationem oportet habeat <lb/>ſeptentrionalem, porrò ex 7. </s>
  <s xml:id="echoid-s1801" xml:space="preserve">pronunciato inuentã habeo aſcenſionem eius rectã 60. </s>
  <s xml:id="echoid-s1802" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s1803" xml:space="preserve">21. </s>
  <s xml:id="echoid-s1804" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1805" xml:space="preserve">Ex pronũciato autem 15. </s>
  <s xml:id="echoid-s1806" xml:space="preserve">inueni ſuper eundem gradum Solis differentiam aſcen <lb/>ſionalem 24. </s>
  <s xml:id="echoid-s1807" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1808" xml:space="preserve">49. </s>
  <s xml:id="echoid-s1809" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1810" xml:space="preserve">Nunc ita ſibi differentiam illam aſcenſionalem ſubtrahã à 60. </s>
  <s xml:id="echoid-s1811" xml:space="preserve"><lb/>gra. </s>
  <s xml:id="echoid-s1812" xml:space="preserve">21. </s>
  <s xml:id="echoid-s1813" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1814" xml:space="preserve">ſiquidem declinatio ibi eſt ſeptentrionalis, remanent 35. </s>
  <s xml:id="echoid-s1815" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1816" xml:space="preserve">32. </s>
  <s xml:id="echoid-s1817" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1818" xml:space="preserve">æquato-<lb/>ris, &amp; </s>
  <s xml:id="echoid-s1819" xml:space="preserve">exurgunt in horizonte exortiuo cum gradu Solis, quod ipſum erat optatum.</s>
  <s xml:id="echoid-s1820" xml:space="preserve"/>
</p>
<div xml:id="echoid-div51" type="float" level="2" n="1">
<note position="left" xlink:label="note-0040-01" xlink:href="note-0040-01a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div53" type="section" level="1" n="31">
<head xml:id="echoid-head35" xml:space="preserve">PRONVNCIATVM XIX.</head>
<p>
  <s xml:id="echoid-s1821" xml:space="preserve">Quod ſi forte aſcenſio obliqua iam antea fuerit cum eleuatione poli cogni <lb/>ta, adhuc tamen gradum eclypticæ ſimul tunc aſcendentem ſuper horizon-<lb/>tem experiri &amp; </s>
  <s xml:id="echoid-s1822" xml:space="preserve">indagare.</s>
  <s xml:id="echoid-s1823" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1824" xml:space="preserve">Hic principio admonendus es, ut ſemper aſcenſionem incipias cõputare à proxima in <lb/>terſectione æquino ctialis &amp; </s>
  <s xml:id="echoid-s1825" xml:space="preserve">eclypticæ, ſiquidem ab utra  illa interſectiõe incipit aſcen-<lb/>ſio, operationem hãc ita ꝓponemus breuiſsime, nã in ſe admodũ operoſa eſt &amp; </s>
  <s xml:id="echoid-s1826" xml:space="preserve">ꝓlixa. </s>
  <s xml:id="echoid-s1827" xml:space="preserve">Ha <lb/>bita iam aſcenſione obliqua, imaginare eam ſic quaſi eſſet aſcenſio recta, eius aſcenſionis <lb/>quære ex pronunciato 8. </s>
  <s xml:id="echoid-s1828" xml:space="preserve">arcũ eclypticæ, qui cũ illo arcu æquatoris in ſphæra recta aſcen <lb/>dit ſuper horizõtem, inuento illo, porrò cõquire per ꝓpoſitionem 5, declinationem eius <lb/>ab æquatore. </s>
  <s xml:id="echoid-s1829" xml:space="preserve">Mox arcus illius æquatoris, quem tibi per modũ aſcenſionis rectæ, propo-<lb/>
<anchor type="note" xlink:label="note-0040-02a" xlink:href="note-0040-02"/>
ſuiſti ſinũ, duc in totũ illum ſinũ, productũ inde diuide cũ ſinu arcus eclypticæ, qui ſimul <lb/>aſcendit, arcũ quotientis ſubtrahe à ſemicirculo, ſi tamen arcus eclypticæ deſinat &amp; </s>
  <s xml:id="echoid-s1830" xml:space="preserve">finia <lb/>tur in ſemicirculo aſcendente, hoc eſt inter principiũ ♑ ſecundũ ordinem ſigno℞ uſ ad <lb/>principiũ ♋. </s>
  <s xml:id="echoid-s1831" xml:space="preserve">ſin aũt finis arcus eclypticæ fuerit inter principiũ ♋ &amp; </s>
  <s xml:id="echoid-s1832" xml:space="preserve">♑. </s>
  <s xml:id="echoid-s1833" xml:space="preserve">relinques ita ar <lb/>cum illũ quotientis, q̊d aũt iſto primo modo uel altero tibi per operationem prouenit, id <lb/>inuentum primũ dicetur. </s>
  <s xml:id="echoid-s1834" xml:space="preserve">Deinde multiplica ſinũ altitudinis poli cũ ſinu declinationis ꝓ <lb/>poſiti arcus eclypticæ, &amp; </s>
  <s xml:id="echoid-s1835" xml:space="preserve">productũ diuide in ſinũ totũ, at is arcus quotientis uocabitur <lb/>
<anchor type="note" xlink:label="note-0040-03a" xlink:href="note-0040-03"/>
inuentum ſecundũ. </s>
  <s xml:id="echoid-s1836" xml:space="preserve">Præterea propone tibi ſinũ cõplementi huius ſecundi inuenti, &amp; </s>
  <s xml:id="echoid-s1837" xml:space="preserve">ſi-<lb/>mul etiã ſinũ cõplemẽti altitudinis poli, ſinũ ex ijs minorem duc in integrũ ſiue perfectũ, <lb/>productũ diuide in maiorem, &amp; </s>
  <s xml:id="echoid-s1838" xml:space="preserve">arcus quotientis appellabitur inuentũ tertiũ. </s>
  <s xml:id="echoid-s1839" xml:space="preserve">hoc ipſum <lb/>
<anchor type="note" xlink:label="note-0040-04a" xlink:href="note-0040-04"/>
ſi ſubtrahas ab inuento primo, &amp; </s>
  <s xml:id="echoid-s1840" xml:space="preserve">finũ reſidui ducas in ſinũ cõplementi ſecũdi inuenti, at <lb/>diuidas in totũ, deinde arcũ quotientis ſubtra has à 90. </s>
  <s xml:id="echoid-s1841" xml:space="preserve">ſinũ quo reſidui tibi ꝓponas cũ <lb/>
<anchor type="note" xlink:label="note-0040-05a" xlink:href="note-0040-05"/>
ſinu ſecundi inuenti, minorem ex ijs ducas in ſinũ totũ, productũ in maiorem diuidas: </s>
  <s xml:id="echoid-s1842" xml:space="preserve">tũc <lb/>tandem arcus quotientis tibi monſtrabit optatũ, dummodo addideris eũ ad arcũ eclypti <lb/>
<anchor type="note" xlink:label="note-0040-06a" xlink:href="note-0040-06"/>
cæ, qui propoſitæ aſcenſioni in ſphæra recta reſpõdet, arcu etiã eclypticæ deſinẽte in me <lb/>dietate aſcenſionali, ſi inter ♑ &amp; </s>
  <s xml:id="echoid-s1843" xml:space="preserve">♋, uel ſubtraxeris, ſi finiatur ille in medietate zodiaci, <lb/>deſcendente à principio nimirũ ♋ uſ ad principiũ ♑, ſecundũ ordinem ſigno℞ nume-<lb/>rando: </s>
  <s xml:id="echoid-s1844" xml:space="preserve">ſic iam habebis arcũ eclypticæ quæſitum. </s>
  <s xml:id="echoid-s1845" xml:space="preserve">?</s>
  <s xml:id="echoid-s1846" xml:space="preserve">? Adſume quo in hãcrem exem-<lb/>
<anchor type="note" xlink:label="note-0040-07a" xlink:href="note-0040-07"/>
plum tibi huiuſcemodi, niſi forte moleſtũ eſt, nõ erit aũt ſi pleniorem intelligentiã habe-<lb/>re deſideras. </s>
  <s xml:id="echoid-s1847" xml:space="preserve">Propoſito ipſo intronizationis die, ecce aſcenſio recta æ quatoris à principio
<pb file="0041" n="41" rhead="TABVLARVM SINVVM."/>
♈eſt 35. </s>
  <s xml:id="echoid-s1848" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1849" xml:space="preserve">32. </s>
  <s xml:id="echoid-s1850" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1851" xml:space="preserve">iam ſi cupiam &amp; </s>
  <s xml:id="echoid-s1852" xml:space="preserve">arcum eclypticæ ſibi reſpondentem inuenire in <lb/>ſphæra o bliqua, at adeo eleuato ibi polo ad 48. </s>
  <s xml:id="echoid-s1853" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1854" xml:space="preserve">ubi talis etiam intronizatio facta <lb/>eſt. </s>
  <s xml:id="echoid-s1855" xml:space="preserve">Principio quæro per 8. </s>
  <s xml:id="echoid-s1856" xml:space="preserve">propoſitionem arcum eclypticæ in ſphæra recta cum arcu æ-<lb/>quatoris aſcendentem, in hunc modum: </s>
  <s xml:id="echoid-s1857" xml:space="preserve">Duco ſinum complementi huius aſcenſionis re-<lb/>ctæ, ſcilicet 35. </s>
  <s xml:id="echoid-s1858" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1859" xml:space="preserve">32. </s>
  <s xml:id="echoid-s1860" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1861" xml:space="preserve">qui gradus ſunt 54. </s>
  <s xml:id="echoid-s1862" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1863" xml:space="preserve">minut. </s>
  <s xml:id="echoid-s1864" xml:space="preserve">28. </s>
  <s xml:id="echoid-s1865" xml:space="preserve">ſinus autem 81377. </s>
  <s xml:id="echoid-s1866" xml:space="preserve">in ſinũ <lb/>
<anchor type="note" xlink:label="note-0041-01a" xlink:href="note-0041-01"/>
maximæ declinationis Solis 39874. </s>
  <s xml:id="echoid-s1867" xml:space="preserve">diuido, deinde quotientem in totum ſinum, qui erit <lb/>32448. </s>
  <s xml:id="echoid-s1868" xml:space="preserve">arcus illius 18. </s>
  <s xml:id="echoid-s1869" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1870" xml:space="preserve">56. </s>
  <s xml:id="echoid-s1871" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1872" xml:space="preserve">hoc ſanè ſubtraho à 90. </s>
  <s xml:id="echoid-s1873" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1874" xml:space="preserve">remanent adhuc 71. </s>
  <s xml:id="echoid-s1875" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1876" xml:space="preserve">4. <lb/></s>
  <s xml:id="echoid-s1877" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1878" xml:space="preserve">ſinum iſtius ſi mihi proponam ſimul cum ſinu aſcenſionis rectæ, ſcilicet 58117. </s>
  <s xml:id="echoid-s1879" xml:space="preserve">mino <lb/>rem quo ducam in ſinum totũ, productum uero diuidam in maiorem, proueniet inde <lb/>
<anchor type="note" xlink:label="note-0041-02a" xlink:href="note-0041-02"/>
61441. </s>
  <s xml:id="echoid-s1880" xml:space="preserve">arcus eius erit 37. </s>
  <s xml:id="echoid-s1881" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1882" xml:space="preserve">55. </s>
  <s xml:id="echoid-s1883" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1884" xml:space="preserve">qui etiam arcus eſt eclypticæ à<unsure/> principio ♈, reſpon <lb/>dens arcui æquatoris in ſphæra recta in aſcenſu. </s>
  <s xml:id="echoid-s1885" xml:space="preserve">Ad hæc amplius inquiro per 5. </s>
  <s xml:id="echoid-s1886" xml:space="preserve">pronun-<lb/>ciatum iſtius arcus eclypticæ declinationem ab æquatore, &amp; </s>
  <s xml:id="echoid-s1887" xml:space="preserve">quia arcus ille 37. </s>
  <s xml:id="echoid-s1888" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1889" xml:space="preserve">55. <lb/></s>
  <s xml:id="echoid-s1890" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1891" xml:space="preserve">directe pertingit ad 7. </s>
  <s xml:id="echoid-s1892" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1893" xml:space="preserve">55. </s>
  <s xml:id="echoid-s1894" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1895" xml:space="preserve">♉. </s>
  <s xml:id="echoid-s1896" xml:space="preserve">quæro iam adhuc ipſum gradum &amp; </s>
  <s xml:id="echoid-s1897" xml:space="preserve">minutũ ♉ <lb/>declinationem hoc modo. </s>
  <s xml:id="echoid-s1898" xml:space="preserve">Duco ſinum arcus 37. </s>
  <s xml:id="echoid-s1899" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1900" xml:space="preserve">55. </s>
  <s xml:id="echoid-s1901" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1902" xml:space="preserve">in ſinũ maximæ declinatiõis <lb/>Solis, ſcilicet 39874. </s>
  <s xml:id="echoid-s1903" xml:space="preserve">productũ diuido in ſinum totum, &amp; </s>
  <s xml:id="echoid-s1904" xml:space="preserve">prodibit 24499. </s>
  <s xml:id="echoid-s1905" xml:space="preserve">arcus illius eſt <lb/>
<anchor type="note" xlink:label="note-0041-03a" xlink:href="note-0041-03"/>
14. </s>
  <s xml:id="echoid-s1906" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1907" xml:space="preserve">11. </s>
  <s xml:id="echoid-s1908" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1909" xml:space="preserve">declinatio nimi℞ arcus eclypticæ quæſita. </s>
  <s xml:id="echoid-s1910" xml:space="preserve">Poſtea adhuc ſinũ arcus aſcenſi <lb/>onis rectæ æquatoris 58117. </s>
  <s xml:id="echoid-s1911" xml:space="preserve">duxi in ſinũ totũ, productũ diuiſi per ſinũ arcus eclypticæ ei <lb/>
<anchor type="note" xlink:label="note-0041-04a" xlink:href="note-0041-04"/>
in aſcenſione recta reſpondentẽ, &amp; </s>
  <s xml:id="echoid-s1912" xml:space="preserve">prouenit in quotiente 94589. </s>
  <s xml:id="echoid-s1913" xml:space="preserve">arcus ipſius eſt 71. </s>
  <s xml:id="echoid-s1914" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s1915" xml:space="preserve">4. </s>
  <s xml:id="echoid-s1916" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1917" xml:space="preserve">qui quia finitur in medietate eclypticæ aſcendente, ſubtraxi iam 71. </s>
  <s xml:id="echoid-s1918" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1919" xml:space="preserve">4. </s>
  <s xml:id="echoid-s1920" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1921" xml:space="preserve">à ſe-<lb/>
<anchor type="note" xlink:label="note-0041-05a" xlink:href="note-0041-05"/>
micirculo, &amp; </s>
  <s xml:id="echoid-s1922" xml:space="preserve">remanſerunt gra. </s>
  <s xml:id="echoid-s1923" xml:space="preserve">108. </s>
  <s xml:id="echoid-s1924" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1925" xml:space="preserve">56. </s>
  <s xml:id="echoid-s1926" xml:space="preserve">at hoc inuentũ dico primũ. </s>
  <s xml:id="echoid-s1927" xml:space="preserve">Deinde ſinum <lb/>altitudinis poli 48. </s>
  <s xml:id="echoid-s1928" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1929" xml:space="preserve">74314. </s>
  <s xml:id="echoid-s1930" xml:space="preserve">duxi in ſinũ declinationis extremitatis arcus eclypticæ, ſci <lb/>licet 14. </s>
  <s xml:id="echoid-s1931" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1932" xml:space="preserve">11. </s>
  <s xml:id="echoid-s1933" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1934" xml:space="preserve">24499. </s>
  <s xml:id="echoid-s1935" xml:space="preserve">ꝓductũ diuiſi in ſinũ totum, &amp; </s>
  <s xml:id="echoid-s1936" xml:space="preserve">quotiens eſt 18206. </s>
  <s xml:id="echoid-s1937" xml:space="preserve">arcus aũt <lb/>
<anchor type="note" xlink:label="note-0041-06a" xlink:href="note-0041-06"/>
illius 10. </s>
  <s xml:id="echoid-s1938" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1939" xml:space="preserve">29. </s>
  <s xml:id="echoid-s1940" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1941" xml:space="preserve">inuentum illud ſecũdũ. </s>
  <s xml:id="echoid-s1942" xml:space="preserve">Inſuper etiã ſinũ cõplementi altitudinis poli <lb/>66913. </s>
  <s xml:id="echoid-s1943" xml:space="preserve">tan̈ minorem in ſinũ totũ duxi, diuiſi eundẽ in ſinũ cõplementi ſecundi inuenti, <lb/>ſcilicet 79. </s>
  <s xml:id="echoid-s1944" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1945" xml:space="preserve">31. </s>
  <s xml:id="echoid-s1946" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1947" xml:space="preserve">98330. </s>
  <s xml:id="echoid-s1948" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1949" xml:space="preserve">prouenit in quotiente 68049. </s>
  <s xml:id="echoid-s1950" xml:space="preserve">arcus eius 42. </s>
  <s xml:id="echoid-s1951" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1952" xml:space="preserve">53. </s>
  <s xml:id="echoid-s1953" xml:space="preserve">min. <lb/></s>
  <s xml:id="echoid-s1954" xml:space="preserve">adpellabitur inuentũ tertiũ, hoc deinde ipſum à primo inuento ſubtraxi, hoc eſt 42. </s>
  <s xml:id="echoid-s1955" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1956" xml:space="preserve"><lb/>53. </s>
  <s xml:id="echoid-s1957" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1958" xml:space="preserve">à 180. </s>
  <s xml:id="echoid-s1959" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1960" xml:space="preserve">56. </s>
  <s xml:id="echoid-s1961" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1962" xml:space="preserve">reſiduũ eſt 66. </s>
  <s xml:id="echoid-s1963" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1964" xml:space="preserve">3. </s>
  <s xml:id="echoid-s1965" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1966" xml:space="preserve">quo℞ ſinũ 91390. </s>
  <s xml:id="echoid-s1967" xml:space="preserve">duxi in ſinũ cõplemẽ <lb/>
<anchor type="note" xlink:label="note-0041-07a" xlink:href="note-0041-07"/>
tiſecũdi inuẽti 79. </s>
  <s xml:id="echoid-s1968" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1969" xml:space="preserve">31. </s>
  <s xml:id="echoid-s1970" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1971" xml:space="preserve">hoc eſt 98330. </s>
  <s xml:id="echoid-s1972" xml:space="preserve">ꝓductũ diuiſi in ſinũ totũ, &amp; </s>
  <s xml:id="echoid-s1973" xml:space="preserve">prodijt in quo <lb/>tienti 89864. </s>
  <s xml:id="echoid-s1974" xml:space="preserve">arcus illorum ſinuũ eſt 63. </s>
  <s xml:id="echoid-s1975" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1976" xml:space="preserve">59. </s>
  <s xml:id="echoid-s1977" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1978" xml:space="preserve">quibus ſubtractis à 90. </s>
  <s xml:id="echoid-s1979" xml:space="preserve">remanent 26. <lb/></s>
  <s xml:id="echoid-s1980" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1981" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1982" xml:space="preserve">Poſtremò ꝓpono ſinũ iſtorum 26. </s>
  <s xml:id="echoid-s1983" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1984" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1985" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1986" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1987" xml:space="preserve">ſcilicet 43863. </s>
  <s xml:id="echoid-s1988" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1989" xml:space="preserve">ſinum ſecundi in-<lb/>uenti 18206. </s>
  <s xml:id="echoid-s1990" xml:space="preserve">hunc tan̈ minorem duco in totum, productum diuido in 43863. </s>
  <s xml:id="echoid-s1991" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1992" xml:space="preserve">prode <lb/>
<anchor type="note" xlink:label="note-0041-08a" xlink:href="note-0041-08"/>
unt in quotiente 41506. </s>
  <s xml:id="echoid-s1993" xml:space="preserve">arcum illius, puta 24. </s>
  <s xml:id="echoid-s1994" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1995" xml:space="preserve">31. </s>
  <s xml:id="echoid-s1996" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s1997" xml:space="preserve">ſi iuxta regulã ſiue præſcriptũ <lb/>operationis, propter medietatem eclypticæ aſcendentem addidero ad arcũ eclypticæ 37. <lb/></s>
  <s xml:id="echoid-s1998" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s1999" xml:space="preserve">55. </s>
  <s xml:id="echoid-s2000" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2001" xml:space="preserve">prouenient uti 62. </s>
  <s xml:id="echoid-s2002" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2003" xml:space="preserve">26. </s>
  <s xml:id="echoid-s2004" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2005" xml:space="preserve">eclypticæ, quæ cũ illa aſcenſione ſiue arcu æ-<lb/>
<anchor type="note" xlink:label="note-0041-09a" xlink:href="note-0041-09"/>
quatoris 35. </s>
  <s xml:id="echoid-s2006" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2007" xml:space="preserve">32. </s>
  <s xml:id="echoid-s2008" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2009" xml:space="preserve">in eleuatione poli 48. </s>
  <s xml:id="echoid-s2010" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2011" xml:space="preserve">aſcendũt, ſiue horizontem attingunt <lb/>planè in 2. </s>
  <s xml:id="echoid-s2012" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2013" xml:space="preserve">26. </s>
  <s xml:id="echoid-s2014" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2015" xml:space="preserve">II, ubi tunc Solerat in ipſo die intronizationis ornatiſsimi Præ-<lb/>
<anchor type="note" xlink:label="note-0041-10a" xlink:href="note-0041-10"/>
ſulis Auguſtani. </s>
  <s xml:id="echoid-s2016" xml:space="preserve">Ecce quàm operoſa &amp; </s>
  <s xml:id="echoid-s2017" xml:space="preserve">prolixa operatione hacidẽ illud adinueni, cuius <lb/>contrarium ſuperior propoſitio facili &amp; </s>
  <s xml:id="echoid-s2018" xml:space="preserve">compendiaria uia monſtrauit, quamuis in <lb/>reliquis tribus quartis zodia ci à ♋ uſ ad ♎, &amp; </s>
  <s xml:id="echoid-s2019" xml:space="preserve">inde à ♎ ad ♑, at à ♑ ad ♈, aliquan-<lb/>do alia operatio eſt, attamen mihi conſultum uiſum eſt, illas nullis peculiaribus exem-<lb/>plis indicare: </s>
  <s xml:id="echoid-s2020" xml:space="preserve">quiſquis em̃ operationem hanc cũ exemplo adiuncto recte intellexrit, is <lb/>etiam in reliquis illis nõ aberrabit, ſedubi facile ſe extricabit, nos igitur aliò iam prope <lb/>rabimus, animum &amp; </s>
  <s xml:id="echoid-s2021" xml:space="preserve">cogitationem eleuaturi ad altitudinem Solis ſuper horizontem.</s>
  <s xml:id="echoid-s2022" xml:space="preserve"/>
</p>
<div xml:id="echoid-div53" type="float" level="2" n="1">
<note position="left" xlink:label="note-0040-02" xlink:href="note-0040-02a" xml:space="preserve"><emph style="it">per aream</emph> <lb/><emph style="it">aſſequcris.</emph></note>
<note position="left" xlink:label="note-0040-03" xlink:href="note-0040-03a" xml:space="preserve"><emph style="it">per latera.</emph></note>
<note position="left" xlink:label="note-0040-04" xlink:href="note-0040-04a" xml:space="preserve"><emph style="it">Per aream</emph></note>
<note position="left" xlink:label="note-0040-05" xlink:href="note-0040-05a" xml:space="preserve"><emph style="it">per latera.</emph></note>
<note position="left" xlink:label="note-0040-06" xlink:href="note-0040-06a" xml:space="preserve"><emph style="it">Per aream</emph></note>
<note position="left" xlink:label="note-0040-07" xlink:href="note-0040-07a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſoo<unsure/>pi.</emph></note>
<note position="right" xlink:label="note-0041-01" xlink:href="note-0041-01a" xml:space="preserve"><emph style="it">Illud deprc</emph> <lb/><emph style="it">henditur la</emph> <lb/><emph style="it">terali in-</emph> <lb/><emph style="it">greſſu.</emph></note>
<note position="right" xlink:label="note-0041-02" xlink:href="note-0041-02a" xml:space="preserve"><emph style="it">Areali in-</emph> <lb/><emph style="it">greſſu idẽ</emph> <lb/><emph style="it">cõſequeris.</emph></note>
<note position="right" xlink:label="note-0041-03" xlink:href="note-0041-03a" xml:space="preserve"><emph style="it">Lateralis.</emph></note>
<note position="right" xlink:label="note-0041-04" xlink:href="note-0041-04a" xml:space="preserve"><emph style="it">Arealis.</emph></note>
<note position="right" xlink:label="note-0041-05" xlink:href="note-0041-05a" xml:space="preserve"><emph style="it">Inucntunt</emph> <lb/><emph style="it">primum.</emph></note>
<note position="right" xlink:label="note-0041-06" xlink:href="note-0041-06a" xml:space="preserve"><emph style="it">Lateralis</emph> <lb/><emph style="it">ingreſſus</emph> <lb/><emph style="it">oſtendet in-</emph> <lb/><emph style="it">uentum ſe-</emph> <lb/><emph style="it">cundum.</emph></note>
<note position="right" xlink:label="note-0041-07" xlink:href="note-0041-07a" xml:space="preserve"><emph style="it">Arealis</emph> <lb/><emph style="it">operatio.</emph> <lb/><emph style="it">Inuentum</emph> <lb/><emph style="it">tertium.</emph></note>
<note position="right" xlink:label="note-0041-08" xlink:href="note-0041-08a" xml:space="preserve"><emph style="it">Lateralis</emph> <lb/><emph style="it">introitus.</emph></note>
<note position="right" xlink:label="note-0041-09" xlink:href="note-0041-09a" xml:space="preserve"><emph style="it">Arealis in-</emph> <lb/><emph style="it">greſſus.</emph></note>
<note position="right" xlink:label="note-0041-10" xlink:href="note-0041-10a" xml:space="preserve"><emph style="it">Locus So-</emph> <lb/><emph style="it">lis die intro</emph> <lb/><emph style="it">nizationis</emph> <lb/><emph style="it">præſulis</emph> <lb/><emph style="it">Auguſtani.</emph></note>
</div>
</div>
<div xml:id="echoid-div55" type="section" level="1" n="32">
<head xml:id="echoid-head36" xml:space="preserve">PRONVNCIATVM XX.</head>
<p>
  <s xml:id="echoid-s2023" xml:space="preserve">Altitudinem Solis in circulo uerticali (dummodo ſit in ſigno aliquo ſe-<lb/>ptentrionali) inueſtigare.</s>
  <s xml:id="echoid-s2024" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2025" xml:space="preserve">Iam ſupra pronunciato 12. </s>
  <s xml:id="echoid-s2026" xml:space="preserve">edoctus es, quidnã ſit ortus æquinoctialis, quamobrẽ ſuꝑ-<lb/>uacuũ ſuerit idẽ hic denuo cõmemorare, tm̃ ne ignores, quid hic nomine circuli uertica-<lb/>lis intelligamus, illũ tibi breuiter deſcribemus. </s>
  <s xml:id="echoid-s2027" xml:space="preserve">Vertex igit̃ ſiue pũctus uerticalis, eſt pun <lb/>
<anchor type="note" xlink:label="note-0041-11a" xlink:href="note-0041-11"/>
ctus cœli capiti tuo directe imminens, ſi modo tu ſtes erectus, monſtrat punctũ illũ tibi <lb/>filũ ſuſpenſum, ex quo plumbimaſſa, aut aliud quiddã graue dependeat, quẽ igitur ſuperi <lb/>or ſili pars in cœlo locum demonſtrat, ibi ſcias eſſe punctum uerticalem, Arabeszenith
<pb file="0042" n="42" rhead="GENVINVS VSVS"/>
uocare conſueuerunt, ab eo puncto ſi protrahas cir culum ab ipſo occaſu æquinoctialis <lb/>uſ ad ortum æ quinoctialem, circulus ille dicetur uerticalis, ad quem Sol peruenire non <lb/>
<anchor type="note" xlink:label="note-0042-01a" xlink:href="note-0042-01"/>
poteſt, niſi fuerit in aliquo ſignorũ ſeptentrionalium, ubi ſi extiterit, &amp; </s>
  <s xml:id="echoid-s2028" xml:space="preserve">tu iam ſcire cupi-<lb/>as altitudinem ipſius in circulo uerticali, propone tibi ſinum rectum altitudinis poli, &amp; </s>
  <s xml:id="echoid-s2029" xml:space="preserve"><lb/>ſinum rectum declinationis Solis, minorem duc in ſinum perfectum, productũ diuide in <lb/>maiorem, &amp; </s>
  <s xml:id="echoid-s2030" xml:space="preserve">tũc arcus quotientis cõmonſtrabit tibi altitudinem Solis quæſitã. </s>
  <s xml:id="echoid-s2031" xml:space="preserve">?</s>
  <s xml:id="echoid-s2032" xml:space="preserve">? Ex-<lb/>emplo rem planius intelliges, eo loco ubi intronizatio ornatiſsimi præſulis facta eſt, po <lb/>
<anchor type="note" xlink:label="note-0042-02a" xlink:href="note-0042-02"/>
lus eleuatus eſt ad 48. </s>
  <s xml:id="echoid-s2033" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2034" xml:space="preserve">Sol aũt in ipſo die intronizationis fuit in 2. </s>
  <s xml:id="echoid-s2035" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2036" xml:space="preserve">26. </s>
  <s xml:id="echoid-s2037" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2038" xml:space="preserve">II, de-<lb/>clinatio ergo Solis eſt 20. </s>
  <s xml:id="echoid-s2039" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2040" xml:space="preserve">42. </s>
  <s xml:id="echoid-s2041" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2042" xml:space="preserve">ſinus declinationis 35347. </s>
  <s xml:id="echoid-s2043" xml:space="preserve">ſinus uero altitudinis po <lb/>li 74314. </s>
  <s xml:id="echoid-s2044" xml:space="preserve">ſi ita 35347. </s>
  <s xml:id="echoid-s2045" xml:space="preserve">ducas in ſinum totum ſiue perfectũ, &amp; </s>
  <s xml:id="echoid-s2046" xml:space="preserve">diuidas in 74314. </s>
  <s xml:id="echoid-s2047" xml:space="preserve">proue-<lb/>nient 47564. </s>
  <s xml:id="echoid-s2048" xml:space="preserve">arcus illius ſinus 28. </s>
  <s xml:id="echoid-s2049" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2050" xml:space="preserve">24. </s>
  <s xml:id="echoid-s2051" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2052" xml:space="preserve">altitudo ſcilicet Solis in circulo uerticali.</s>
  <s xml:id="echoid-s2053" xml:space="preserve"/>
</p>
<div xml:id="echoid-div55" type="float" level="2" n="1">
<note position="right" xlink:label="note-0041-11" xlink:href="note-0041-11a" xml:space="preserve"><emph style="it">Vertex ſiue</emph> <lb/><emph style="it">zenith ꝗd.</emph></note>
<note position="left" xlink:label="note-0042-01" xlink:href="note-0042-01a" xml:space="preserve"><emph style="it">per arcalẽ</emph> <lb/><emph style="it">introitum</emph> <lb/><emph style="it">ſimile inue</emph> <lb/><emph style="it">nies.</emph></note>
<note position="left" xlink:label="note-0042-02" xlink:href="note-0042-02a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div57" type="section" level="1" n="33">
<head xml:id="echoid-head37" xml:space="preserve">PRONVNCIATVM XXI.</head>
<p>
  <s xml:id="echoid-s2054" xml:space="preserve">Altitudinem ſeu eleuationem poli ex altitudine Solis in circulo uerticali <lb/>inquirere.</s>
  <s xml:id="echoid-s2055" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2056" xml:space="preserve">Pronunciatũ hoc planê inuerſo modo ꝓpoſitũ eſt cũ ſuperiori, ſi ergo altitudinem po <lb/>
<anchor type="note" xlink:label="note-0042-03a" xlink:href="note-0042-03"/>
li ſic q̊ ſcire deſideras rurſus utrũ tibi ſinũ ꝓpone, puta ſinũ altitudinis Solis in circu <lb/>lo uerticali &amp; </s>
  <s xml:id="echoid-s2057" xml:space="preserve">declinationis, minorem duc in ſinũ totũ, ꝓductũ deinde in maiorem diui-<lb/>
<anchor type="note" xlink:label="note-0042-04a" xlink:href="note-0042-04"/>
de, &amp; </s>
  <s xml:id="echoid-s2058" xml:space="preserve">arcus ſinus q̊tientis exhibebit tibi altitudinem poli tuæ regiõis. </s>
  <s xml:id="echoid-s2059" xml:space="preserve">?</s>
  <s xml:id="echoid-s2060" xml:space="preserve">? Accipe &amp; </s>
  <s xml:id="echoid-s2061" xml:space="preserve">hu <lb/>iusrei exemplũ, Eſto ut ſit mihi eleuatio poli incognita, eo autem die quo intronizatus <lb/>eſt ampliſs. </s>
  <s xml:id="echoid-s2062" xml:space="preserve">ille pater Epiſcopus Auguſtanus, altitudinem Solis inuentã iã &amp; </s>
  <s xml:id="echoid-s2063" xml:space="preserve">obſerua tã <lb/>habeo in circulo uerticali ad 28. </s>
  <s xml:id="echoid-s2064" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2065" xml:space="preserve">24. </s>
  <s xml:id="echoid-s2066" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2067" xml:space="preserve">ſinũ igitur declinationis, puta minorẽ 35347 <lb/>duco in ſinum totũ, productũ diuido in ſinum altitudinis, ſcilicet 47564. </s>
  <s xml:id="echoid-s2068" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2069" xml:space="preserve">proueniunt in <lb/>quotiente 74312. </s>
  <s xml:id="echoid-s2070" xml:space="preserve">arcus illius eſt 48. </s>
  <s xml:id="echoid-s2071" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2072" xml:space="preserve">eleuatio poli inquiſita ad locũ intronizatiõis.</s>
  <s xml:id="echoid-s2073" xml:space="preserve"/>
</p>
<div xml:id="echoid-div57" type="float" level="2" n="1">
<note position="left" xlink:label="note-0042-03" xlink:href="note-0042-03a" xml:space="preserve"><emph style="it">Areatim.</emph></note>
<note position="left" xlink:label="note-0042-04" xlink:href="note-0042-04a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div59" type="section" level="1" n="34">
<head xml:id="echoid-head38" xml:space="preserve">PRONVNCIATVM XXII.</head>
<p>
  <s xml:id="echoid-s2074" xml:space="preserve">Gradum Solis &amp; </s>
  <s xml:id="echoid-s2075" xml:space="preserve">quotidie &amp; </s>
  <s xml:id="echoid-s2076" xml:space="preserve">expedite inuenire ex altitudine eiuſdem in <lb/>circulo uerticali, ſi modo Sol ſuerit in ſignis ſeptentrionalibus.</s>
  <s xml:id="echoid-s2077" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2078" xml:space="preserve">Iam antea ꝓnũciato 20. </s>
  <s xml:id="echoid-s2079" xml:space="preserve">admonitus es, Solem nũ̈ attingere cir culũ uerticalem, niſi <lb/>in aliq̊ ſigno℞ ſeptentrionaliũ fuerit. </s>
  <s xml:id="echoid-s2080" xml:space="preserve">actũ ita egeris, ſi à fefto Michaelis ꝑ totã hyemẽ <lb/>uſ ad ferias D. </s>
  <s xml:id="echoid-s2081" xml:space="preserve">Gregorij in quadrageſima gradum Solis ex altitudine ipſius in circulo <lb/>uerticali inuenire labores, ꝗa tunc ipſum attingere nõ poteſt. </s>
  <s xml:id="echoid-s2082" xml:space="preserve">Verum in æſtate quando <lb/>
<anchor type="note" xlink:label="note-0042-05a" xlink:href="note-0042-05"/>
eũ tangit, &amp; </s>
  <s xml:id="echoid-s2083" xml:space="preserve">inde gradũ Solis ſcire cupis, duc ſinũ altitudinis Solis in cir culo uerticali, in <lb/>ſinũ altitudinis poli, &amp; </s>
  <s xml:id="echoid-s2084" xml:space="preserve">diuide ꝓductũ in ſinũ totũ, mox quære arcũ q̊tientis, is tibi mon-<lb/>ſtrabit declinationẽ Solis abæ ꝗnoctiali, deinde adhuc quære ꝑ pronunciatũ 6. </s>
  <s xml:id="echoid-s2085" xml:space="preserve">gradum <lb/>eclypticæ huic de clinatiõi reſpõi reſpõdentem, &amp; </s>
  <s xml:id="echoid-s2086" xml:space="preserve">is ſanè eſt gradus Solis quæſitus. </s>
  <s xml:id="echoid-s2087" xml:space="preserve">?</s>
  <s xml:id="echoid-s2088" xml:space="preserve">? Exem <lb/>
<anchor type="note" xlink:label="note-0042-06a" xlink:href="note-0042-06"/>
plo res erit apertior: </s>
  <s xml:id="echoid-s2089" xml:space="preserve">Eſto, in die intronizatiõis fuerit Sol in circulo uerticali 28. </s>
  <s xml:id="echoid-s2090" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2091" xml:space="preserve">24. <lb/></s>
  <s xml:id="echoid-s2092" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2093" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2094" xml:space="preserve">ibidẽ ubi illa facta eſt, ſit altitudo poli 48. </s>
  <s xml:id="echoid-s2095" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2096" xml:space="preserve">Iam nũc ſinũ altitudinis poli 74314. </s>
  <s xml:id="echoid-s2097" xml:space="preserve"><lb/>duco in ſinũ altitudinis Solis in circulo uerticali 47564. </s>
  <s xml:id="echoid-s2098" xml:space="preserve">ꝓductũ diuido in ſinũ totum, &amp; </s>
  <s xml:id="echoid-s2099" xml:space="preserve"><lb/>in quotiente prodibunt 35347. </s>
  <s xml:id="echoid-s2100" xml:space="preserve">arcus illius eſt declinatio Solis quæſita 20. </s>
  <s xml:id="echoid-s2101" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2102" xml:space="preserve">42. </s>
  <s xml:id="echoid-s2103" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2104" xml:space="preserve"><lb/>Nũc inuenies tandem ex ꝓnunciato 6. </s>
  <s xml:id="echoid-s2105" xml:space="preserve">Solem eſſe in 2. </s>
  <s xml:id="echoid-s2106" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2107" xml:space="preserve">26. </s>
  <s xml:id="echoid-s2108" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2109" xml:space="preserve">II q̊d erat in ꝗrendũ.</s>
  <s xml:id="echoid-s2110" xml:space="preserve"/>
</p>
<div xml:id="echoid-div59" type="float" level="2" n="1">
<note position="left" xlink:label="note-0042-05" xlink:href="note-0042-05a" xml:space="preserve"><emph style="it">Lateraliter</emph></note>
<note position="left" xlink:label="note-0042-06" xlink:href="note-0042-06a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div61" type="section" level="1" n="35">
<head xml:id="echoid-head39" xml:space="preserve">PRONVNCIATVM XXIII.</head>
<p>
  <s xml:id="echoid-s2111" xml:space="preserve">Cognita iam &amp; </s>
  <s xml:id="echoid-s2112" xml:space="preserve">altitudine Solis in circulo uerticali, &amp; </s>
  <s xml:id="echoid-s2113" xml:space="preserve">eleuatione poli, per <lb/>utran illam amplitudinem Solis ad eum diem, quo altitudinem Solis in <lb/>circulo uerticali obſeruaſti, inuenire.</s>
  <s xml:id="echoid-s2114" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2115" xml:space="preserve">Iam ſupra ꝓnunciato 12. </s>
  <s xml:id="echoid-s2116" xml:space="preserve">docuimus inuentionẽ amplitudinis Solis ortiuæ ex eleuatio <lb/>ne poli &amp; </s>
  <s xml:id="echoid-s2117" xml:space="preserve">declinatione Solis, nunc aũt eandem illã docebimus te colligere ex altitudine <lb/>
<anchor type="note" xlink:label="note-0042-07a" xlink:href="note-0042-07"/>
Solis in circulo uerticali &amp; </s>
  <s xml:id="echoid-s2118" xml:space="preserve">eleuatiõe poli, Principio duc ſinũ altitudinis uerticalis in ſinũ <lb/>totũ, productũ diuide in ſinum complementi altitudinis poli, quotientem in ſe multipli-<lb/>ca quadrate, ſimiliter quo quadrate in ſe ducito ſinũ altitudinis Solis uerticalẽ, ꝗ̃dratũ <lb/>illud ſubtrahe à priori numero quadrato, ex reſiduo quære radicem quadratã, radicis eius
<pb file="0043" n="43" rhead="TABVLARVM SINVVM."/>
arcus eſt ipſe arcus horizontis inter punctũ Solis aſcendentis &amp; </s>
  <s xml:id="echoid-s2119" xml:space="preserve">ortum æ quinoctialem. <lb/></s>
  <s xml:id="echoid-s2120" xml:space="preserve">?</s>
  <s xml:id="echoid-s2121" xml:space="preserve">? Exemplum ſit hoc tibi, in die intronizationis eſto, ut obſeruarit quis altitudinem So-<lb/>
<anchor type="note" xlink:label="note-0043-01a" xlink:href="note-0043-01"/>
lis in circulo uerticali, ea fuit 28. </s>
  <s xml:id="echoid-s2122" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2123" xml:space="preserve">24. </s>
  <s xml:id="echoid-s2124" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2125" xml:space="preserve">ſinum illius 47564. </s>
  <s xml:id="echoid-s2126" xml:space="preserve">duxerit in ſinum totum, <lb/>productum diuiſerit in ſinum complementi altitudinis poli 66913. </s>
  <s xml:id="echoid-s2127" xml:space="preserve">in quotiente proue-<lb/>nerũt 71083. </s>
  <s xml:id="echoid-s2128" xml:space="preserve">ex eo quadrato, hoc eſt in ſe ducto, ꝓdijt numer<emph style="sub">9</emph> ille q̃dratus 5052792889 <lb/>deinde ſimili modo quadrato etiam ſinum altitudinis uerticalis, prouenit 2262334096. <lb/></s>
  <s xml:id="echoid-s2129" xml:space="preserve">eo ſubtracto à ſuperiori, remanſit 2790458793. </s>
  <s xml:id="echoid-s2130" xml:space="preserve">radix illius numeri quadrata eſt 52825. </s>
  <s xml:id="echoid-s2131" xml:space="preserve"><lb/>arcus eius 31. </s>
  <s xml:id="echoid-s2132" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2133" xml:space="preserve">53. </s>
  <s xml:id="echoid-s2134" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2135" xml:space="preserve">amplitudo illa Solis ad diem intronizationis, quam pronuncia-<lb/>to 12. </s>
  <s xml:id="echoid-s2136" xml:space="preserve">diuerſo modo docuimus inuenire.</s>
  <s xml:id="echoid-s2137" xml:space="preserve"/>
</p>
<div xml:id="echoid-div61" type="float" level="2" n="1">
<note position="left" xlink:label="note-0042-07" xlink:href="note-0042-07a" xml:space="preserve"><emph style="it">Illud habe-</emph> <lb/><emph style="it">bis per in-</emph> <lb/><emph style="it">troitum</emph> <lb/><emph style="it">arealem.</emph></note>
<note position="right" xlink:label="note-0043-01" xlink:href="note-0043-01a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div63" type="section" level="1" n="36">
<head xml:id="echoid-head40" xml:space="preserve">PRONVNCIATVM XXIIII.</head>
<p>
  <s xml:id="echoid-s2138" xml:space="preserve">Ex altitudine Solis in circulo uerticali, &amp; </s>
  <s xml:id="echoid-s2139" xml:space="preserve">ex amplitudine Solis eiuſdem di <lb/>ei altitudinem poli expedite inueſtigare, etiam ſi neſcias gradum Solis ſimul <lb/>&amp; </s>
  <s xml:id="echoid-s2140" xml:space="preserve">declinationem illius.</s>
  <s xml:id="echoid-s2141" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2142" xml:space="preserve">Per hoc q̊d iam docebimus. </s>
  <s xml:id="echoid-s2143" xml:space="preserve">poteſt ꝗs quotidie tota æſtate mane altitudinem poli ob-<lb/>ſeruare, nõ cognito gradu &amp; </s>
  <s xml:id="echoid-s2144" xml:space="preserve">declinatione Solis, ſi modo ꝑ inſtrumentũ aliq̊d amplitudi <lb/>nem Solis ortiuã &amp; </s>
  <s xml:id="echoid-s2145" xml:space="preserve">occiduã obſeruarit (quicꝗd em̃ hic de amplitudine ortiua dicimus ſi-<lb/>mul &amp; </s>
  <s xml:id="echoid-s2146" xml:space="preserve">de altitudine uerticali, idẽ etiã de amplitudine occidua &amp; </s>
  <s xml:id="echoid-s2147" xml:space="preserve">altitudine Solis in circu <lb/>lo uerticali occiduo intelligi debet) parit’ &amp; </s>
  <s xml:id="echoid-s2148" xml:space="preserve">altitudinẽ Solis in circulo uerticali exiſten-<lb/>tis, ſtatim duc ſinũ amplitudinis in ſe ꝗ̃drate, deinde etiã ſinũ altitudinis uerticalis, utrũ <lb/>hũc nume℞ quadratũ in unã ſummã cõponito, ex ea rurſus quære radicem quadratã, &amp; </s>
  <s xml:id="echoid-s2149" xml:space="preserve">il <lb/>
<anchor type="note" xlink:label="note-0043-02a" xlink:href="note-0043-02"/>
lam propone in regulã philoſopho℞ primo loco, ſecũdo ſinũ altitudinis Solis in circulo <lb/>uerticali, tertio ſinũ totũ. </s>
  <s xml:id="echoid-s2150" xml:space="preserve">Et iuxta regulã numerũ ultimũ duc in mediũ, ꝓductũ in primũ <lb/>diuide, &amp; </s>
  <s xml:id="echoid-s2151" xml:space="preserve">arcus q̊tientis ex quadra circuli ſubtractus, oſtendet tibi altitudinem poli quæ-<lb/>
<anchor type="note" xlink:label="note-0043-03a" xlink:href="note-0043-03"/>
ſitam. </s>
  <s xml:id="echoid-s2152" xml:space="preserve">?</s>
  <s xml:id="echoid-s2153" xml:space="preserve">?Sed obſcurius paulò hoc tibiuidetur, en exemplo ſit dilucidius. </s>
  <s xml:id="echoid-s2154" xml:space="preserve">Altitudo So <lb/>lis in circulo uerticali in die intronizationis fuit 28. </s>
  <s xml:id="echoid-s2155" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2156" xml:space="preserve">24. </s>
  <s xml:id="echoid-s2157" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2158" xml:space="preserve">ſinus eius 47564. </s>
  <s xml:id="echoid-s2159" xml:space="preserve">amplitu <lb/>do q̊ ortiua ꝑ in ſtrumentũ inuenta eſt 31. </s>
  <s xml:id="echoid-s2160" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2161" xml:space="preserve">53. </s>
  <s xml:id="echoid-s2162" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2163" xml:space="preserve">ſinus ipſius 52825. </s>
  <s xml:id="echoid-s2164" xml:space="preserve">quadratũ illi-<lb/>us 2790458793. </s>
  <s xml:id="echoid-s2165" xml:space="preserve">quadratũ aũt ſinus altitudinis 2262334096. </s>
  <s xml:id="echoid-s2166" xml:space="preserve">utrun quadratũ hoc con <lb/>iunctũ in una ſumma, facit 5052792889. </s>
  <s xml:id="echoid-s2167" xml:space="preserve">radix eius quadrata eſt 71083. </s>
  <s xml:id="echoid-s2168" xml:space="preserve">Si ergo in regu-<lb/>lam proportionũ cõpoſuero hoc modo 71083. </s>
  <s xml:id="echoid-s2169" xml:space="preserve">dant mihi 47564. </s>
  <s xml:id="echoid-s2170" xml:space="preserve">Quid ita ex toto pro <lb/>ueniet ſinu@ Inueniam uti ex operatione regulæ huius 66913. </s>
  <s xml:id="echoid-s2171" xml:space="preserve">Arcus eius 42. </s>
  <s xml:id="echoid-s2172" xml:space="preserve">ex circuli <lb/>quadra ſubtra ctus, reliquã faciet altitudinem poli 48. </s>
  <s xml:id="echoid-s2173" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2174" xml:space="preserve">quæſitã ad locũ obſeruationis.</s>
  <s xml:id="echoid-s2175" xml:space="preserve"/>
</p>
<div xml:id="echoid-div63" type="float" level="2" n="1">
<note position="right" xlink:label="note-0043-02" xlink:href="note-0043-02a" xml:space="preserve"><emph style="it">Lateraliter</emph> <lb/><emph style="it">idem inue-</emph> <lb/><emph style="it">nies.</emph></note>
<note position="right" xlink:label="note-0043-03" xlink:href="note-0043-03a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div65" type="section" level="1" n="37">
<head xml:id="echoid-head41" xml:space="preserve">PRONVNCIATVM XXV.</head>
<p>
  <s xml:id="echoid-s2176" xml:space="preserve">Quocun tempore, ſiue qualibet hora, gradum eclypticæ, quimeridia, <lb/>num tangit, ex ſphærica ſupputatione colligere.</s>
  <s xml:id="echoid-s2177" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2178" xml:space="preserve">Si quando mediũ cœli in eclyptica noſſe cupis, uel ante uel poſt meridiem: </s>
  <s xml:id="echoid-s2179" xml:space="preserve">ꝓpone tibi <lb/>diſtantiã Solis à meridie, &amp; </s>
  <s xml:id="echoid-s2180" xml:space="preserve">reſolue eã in gradus, deinde adſume etiã aſcenſionem rectam <lb/>gradus Solis ꝑ pronunciatũ 7. </s>
  <s xml:id="echoid-s2181" xml:space="preserve">Quòd ſi tempus operationis huius fuerit antemeridianũ, <lb/>tũc ſubtrahe gradus diſtãtiæ à meridiano: </s>
  <s xml:id="echoid-s2182" xml:space="preserve">ſin aũt pomeridianũ fuerit, addenda tibi erit di <lb/>ſtantia horaria in gradus cõuerſa ad aſcenſionem rectã gradus Solis. </s>
  <s xml:id="echoid-s2183" xml:space="preserve">Ex additiõe uel ſub <lb/>tractione huiuſmodi quicquid prouenerituel reliquũ manſerit, aſcenſio recta dicet̃ me-<lb/>dij cœli. </s>
  <s xml:id="echoid-s2184" xml:space="preserve">Hinc ſi adhuc ſcire deſideras gradũ eclypticæ eo ipſo momento tangentem me-<lb/>ridianũ, is ſanè eſt, qui cum eo in ſphæra recta aſcendit, quære eũ ex pronunciato 8. <lb/></s>
  <s xml:id="echoid-s2185" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2186" xml:space="preserve">habebis punctum eclypticæ, qui mediat cœlum tempore propoſito. </s>
  <s xml:id="echoid-s2187" xml:space="preserve">?</s>
  <s xml:id="echoid-s2188" xml:space="preserve">?Et ſit eius rei <lb/>
<anchor type="note" xlink:label="note-0043-04a" xlink:href="note-0043-04"/>
exemplum tale. </s>
  <s xml:id="echoid-s2189" xml:space="preserve">Scire for ſitan cupio ad ipſam horã intronizationis, quid tunc mediũ cœ <lb/>li habuerit, quando intronizatio facta eſt hora 9. </s>
  <s xml:id="echoid-s2190" xml:space="preserve">ante meridiem: </s>
  <s xml:id="echoid-s2191" xml:space="preserve">diſtantia uti horaria <lb/>eſt 3. </s>
  <s xml:id="echoid-s2192" xml:space="preserve">graduũ, quoniã à 9. </s>
  <s xml:id="echoid-s2193" xml:space="preserve">uſad 12. </s>
  <s xml:id="echoid-s2194" xml:space="preserve">horæ tres ſunt: </s>
  <s xml:id="echoid-s2195" xml:space="preserve">in reſolutione ergo ſemper 15. </s>
  <s xml:id="echoid-s2196" xml:space="preserve">gradus <lb/>pro hora cõnumerando, faciũt horæ tres gradus 45. </s>
  <s xml:id="echoid-s2197" xml:space="preserve">eos ſubtraho ab aſcenſione gradus <lb/>Solis, quem ſupra in pronũciato 7. </s>
  <s xml:id="echoid-s2198" xml:space="preserve">inueni: </s>
  <s xml:id="echoid-s2199" xml:space="preserve">ſiquidem tũc Sol ſuit in 2. </s>
  <s xml:id="echoid-s2200" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2201" xml:space="preserve">26. </s>
  <s xml:id="echoid-s2202" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2203" xml:space="preserve">II. </s>
  <s xml:id="echoid-s2204" xml:space="preserve">aſcen <lb/>ſio eius eſt 60. </s>
  <s xml:id="echoid-s2205" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2206" xml:space="preserve">21. </s>
  <s xml:id="echoid-s2207" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2208" xml:space="preserve">unde ſubtraho 45. </s>
  <s xml:id="echoid-s2209" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2210" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2211" xml:space="preserve">remanent 6. </s>
  <s xml:id="echoid-s2212" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2213" xml:space="preserve">21. </s>
  <s xml:id="echoid-s2214" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2215" xml:space="preserve">æquatoris, <lb/>quæ tangunt medium cœli ipſa hora intronizationis. </s>
  <s xml:id="echoid-s2216" xml:space="preserve">Si igitur iuxta pronuhciatum 8.</s>
  <s xml:id="echoid-s2217" xml:space="preserve">
<pb file="0044" n="44" rhead="GENVINVS VSVS"/>
cupio inquirere gradum eclypticæ, qui cum eo aſcẽdit in ſphæra recta, propono mihi 15 <lb/>gra. </s>
  <s xml:id="echoid-s2218" xml:space="preserve">21. </s>
  <s xml:id="echoid-s2219" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2220" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2221" xml:space="preserve">quæro cõ plementũ ipſius, ſcilicet 74. </s>
  <s xml:id="echoid-s2222" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2223" xml:space="preserve">39. </s>
  <s xml:id="echoid-s2224" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2225" xml:space="preserve">ſinum eius 96432. </s>
  <s xml:id="echoid-s2226" xml:space="preserve">duco <lb/>in ſinum maximæ declinationis Solis, ſcilicet 29874. </s>
  <s xml:id="echoid-s2227" xml:space="preserve">productum diuido in ſinum perfe-<lb/>ctum, &amp; </s>
  <s xml:id="echoid-s2228" xml:space="preserve">proueniũt in quotiente 38451. </s>
  <s xml:id="echoid-s2229" xml:space="preserve">arcus eius eſt 22. </s>
  <s xml:id="echoid-s2230" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2231" xml:space="preserve">37. </s>
  <s xml:id="echoid-s2232" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2233" xml:space="preserve">Si iam adſumo com <lb/>plementũ ip ſius 67. </s>
  <s xml:id="echoid-s2234" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2235" xml:space="preserve">23. </s>
  <s xml:id="echoid-s2236" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2237" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2238" xml:space="preserve">propono itidem mihi ſinum ipſius 92309. </s>
  <s xml:id="echoid-s2239" xml:space="preserve">ſimiliter eti-<lb/>
<anchor type="note" xlink:label="note-0044-01a" xlink:href="note-0044-01"/>
am ſinũ 15. </s>
  <s xml:id="echoid-s2240" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2241" xml:space="preserve">21. </s>
  <s xml:id="echoid-s2242" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2243" xml:space="preserve">ſcilicet 26471. </s>
  <s xml:id="echoid-s2244" xml:space="preserve">utrũ eorũ tan̈ minorem duxero in ſinum totum, <lb/>&amp; </s>
  <s xml:id="echoid-s2245" xml:space="preserve">per maiorem 92309. </s>
  <s xml:id="echoid-s2246" xml:space="preserve">diuiſero, proueniũt in quotiente 28676. </s>
  <s xml:id="echoid-s2247" xml:space="preserve">arcus eius eſt 16. </s>
  <s xml:id="echoid-s2248" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2249" xml:space="preserve">40 <lb/>mi. </s>
  <s xml:id="echoid-s2250" xml:space="preserve">qui arcus eſt eclypticæ, numeratus à proxima interſectione eclypticæ &amp; </s>
  <s xml:id="echoid-s2251" xml:space="preserve">æquidialis, <lb/>
<anchor type="note" xlink:label="note-0044-02a" xlink:href="note-0044-02"/>
eſt´ ille gradus 16. </s>
  <s xml:id="echoid-s2252" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2253" xml:space="preserve">40. </s>
  <s xml:id="echoid-s2254" xml:space="preserve">♈. </s>
  <s xml:id="echoid-s2255" xml:space="preserve">at ipſa intronizationis hora ſuit in medio cœli.</s>
  <s xml:id="echoid-s2256" xml:space="preserve"/>
</p>
<div xml:id="echoid-div65" type="float" level="2" n="1">
<note position="right" xlink:label="note-0043-04" xlink:href="note-0043-04a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſoo<unsure/>pi.</emph></note>
<note position="left" xlink:label="note-0044-01" xlink:href="note-0044-01a" xml:space="preserve"><emph style="it">Operatio</emph> <lb/><emph style="it">lateralis.</emph></note>
<note position="left" xlink:label="note-0044-02" xlink:href="note-0044-02a" xml:space="preserve"><emph style="it">Operatio</emph> <lb/><emph style="it">arcalis.</emph></note>
</div>
</div>
<div xml:id="echoid-div67" type="section" level="1" n="38">
<head xml:id="echoid-head42" xml:space="preserve">PRONVNCIATVM XXVI.</head>
<p>
  <s xml:id="echoid-s2257" xml:space="preserve">Quatuor illos angulos, quos eclyptica cauſſat cum meridiano, ad unum-<lb/>quod punctum, quo eclyptica meridianum tangit, artificioſe cognoſcere.</s>
  <s xml:id="echoid-s2258" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2259" xml:space="preserve">Operæprecium hic principio fuerit præſcire te, quod hic ex 4 iſtis angulis unicũ tantũ <lb/>te inuenire docebimus, quo cognito reliqui tres per ſe patent ex ſubtractione, ne plu-<lb/>res uno hic te indagare neceſſe eſt. </s>
  <s xml:id="echoid-s2260" xml:space="preserve">Deinde ſcias per hãc operationẽ in prima quarta Zo <lb/>diaci à principio ♈, uſ ad finem II, inueniri angulum Borealem orientalem, in ſecun-<lb/>da à principio ♋ ad ſinẽ ♍ angulũ orientalẽ meridionalẽ, in tertia uero quarta à prinei-<lb/>pio ♎ ad finem ♐ angulũ meridionalẽ orientalẽ, &amp; </s>
  <s xml:id="echoid-s2261" xml:space="preserve">in ultima quarta etiam includi an-<lb/>gulũ Borealẽ orientalẽ. </s>
  <s xml:id="echoid-s2262" xml:space="preserve">Operatio ita iſta ſic cõficietur, ꝓpone tibi illã zodiaci quar <lb/>tam, in qua punctũ eclypticæ inuenitur, &amp; </s>
  <s xml:id="echoid-s2263" xml:space="preserve">quære gradũ æquinoctialis, qui cum illo in <lb/>ſphæra recta tangit horizontẽ iuxta ꝓnunciatũ 7. </s>
  <s xml:id="echoid-s2264" xml:space="preserve">deinde diſtantiã accipe puncti illius <lb/>à proxima interſectione æquinoctialis, &amp; </s>
  <s xml:id="echoid-s2265" xml:space="preserve">propone tibi ſinum ſui cõplemẽti, eũ duc in ſi-<lb/>num maximæ de clinationis, ꝓductũ diuide in ſinũ totũ, &amp; </s>
  <s xml:id="echoid-s2266" xml:space="preserve">quotientis arcus ex quadra cir <lb/>
<anchor type="note" xlink:label="note-0044-03a" xlink:href="note-0044-03"/>
culi relinquet angulũ tibi quæſitũ. </s>
  <s xml:id="echoid-s2267" xml:space="preserve">Ex quo ſi cæteros etiam angulos ſcire cupis, tunc ſub <lb/>trahe angulũ inuẽtũ ex gradibus ſemicirculi, &amp; </s>
  <s xml:id="echoid-s2268" xml:space="preserve">in reſiduo manebit angulus eius collatera <lb/>lis, qui iuxta illum eſt in medietate cœli oriẽtalis. </s>
  <s xml:id="echoid-s2269" xml:space="preserve">Hinc ſi quãtitatẽ anguli Borealis occi-<lb/>dentalis cupis habere, adſume tibi quantitatẽ anguli orientalis meridionalis. </s>
  <s xml:id="echoid-s2270" xml:space="preserve">qm̃ anguli <lb/>
<anchor type="note" xlink:label="note-0044-04a" xlink:href="note-0044-04"/>
contra ſe poſiti ſemꝑ ſunt æquales. </s>
  <s xml:id="echoid-s2271" xml:space="preserve">?</s>
  <s xml:id="echoid-s2272" xml:space="preserve">? Exemplũ hoc tibi rẽ planius oſtẽder, ſi uelim ad <lb/>diẽ intronizatiõis ſcire quantitatẽ 4. </s>
  <s xml:id="echoid-s2273" xml:space="preserve">illo℞ angulo℞ meridiani &amp; </s>
  <s xml:id="echoid-s2274" xml:space="preserve">eclypticæ planẽ in ipſo <lb/>meridie, qũ gradus 2. </s>
  <s xml:id="echoid-s2275" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2276" xml:space="preserve">26. </s>
  <s xml:id="echoid-s2277" xml:space="preserve">II, ubi tunc ☉(sun) erat, tetigit meridianũ. </s>
  <s xml:id="echoid-s2278" xml:space="preserve">Primũ oĩm quæro ꝑ <lb/>ꝓnunc. </s>
  <s xml:id="echoid-s2279" xml:space="preserve">7. </s>
  <s xml:id="echoid-s2280" xml:space="preserve">aſcenſionẽ rectã gradus ☉(sun), quæ eſt 60. </s>
  <s xml:id="echoid-s2281" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2282" xml:space="preserve">21. </s>
  <s xml:id="echoid-s2283" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2284" xml:space="preserve">tantũ abeſt etiã à proxima <lb/>interſectiõe, cõplementũ illius eſt 29. </s>
  <s xml:id="echoid-s2285" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2286" xml:space="preserve">39. </s>
  <s xml:id="echoid-s2287" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2288" xml:space="preserve">lam ſi ſinũ eius 49470. </s>
  <s xml:id="echoid-s2289" xml:space="preserve">ducã in ſinũ ma <lb/>ximæ declinationis 39874. </s>
  <s xml:id="echoid-s2290" xml:space="preserve">productum diuidam in ſinum totum, tuncin quotiente proue <lb/>nient 19726. </s>
  <s xml:id="echoid-s2291" xml:space="preserve">arcus eius eſt 11. </s>
  <s xml:id="echoid-s2292" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2293" xml:space="preserve">37. </s>
  <s xml:id="echoid-s2294" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2295" xml:space="preserve">qui &amp; </s>
  <s xml:id="echoid-s2296" xml:space="preserve">angulus eſt. </s>
  <s xml:id="echoid-s2297" xml:space="preserve">Gradus autem illos &amp; </s>
  <s xml:id="echoid-s2298" xml:space="preserve">minu <lb/>ta ſi ſubtraxero à 90. </s>
  <s xml:id="echoid-s2299" xml:space="preserve">tunc remanebunt 78. </s>
  <s xml:id="echoid-s2300" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2301" xml:space="preserve">37. </s>
  <s xml:id="echoid-s2302" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2303" xml:space="preserve">angulus ſcilicet Borealis orienta-<lb/>lis quæſitus: </s>
  <s xml:id="echoid-s2304" xml:space="preserve">hunc tibi ſubtraho à 180. </s>
  <s xml:id="echoid-s2305" xml:space="preserve">ipſo nimirum ſemicirculo, rem anent 101. </s>
  <s xml:id="echoid-s2306" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2307" xml:space="preserve">23. <lb/></s>
  <s xml:id="echoid-s2308" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2309" xml:space="preserve">quantitas illa anguli Auſtralis orientalis, &amp; </s>
  <s xml:id="echoid-s2310" xml:space="preserve">tantus etiam erit angulus occidentalis <lb/>Borealis, ſimiliter illi primo, ſcilicet 78. </s>
  <s xml:id="echoid-s2311" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2312" xml:space="preserve">37. </s>
  <s xml:id="echoid-s2313" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2314" xml:space="preserve">æqualis eſt angulus occidentalis me <lb/>ridionalis. </s>
  <s xml:id="echoid-s2315" xml:space="preserve">Et hoc modo ſatis mea quidem ſententia uidentur anguli iſti excuſsi.</s>
  <s xml:id="echoid-s2316" xml:space="preserve"/>
</p>
<div xml:id="echoid-div67" type="float" level="2" n="1">
<note position="left" xlink:label="note-0044-03" xlink:href="note-0044-03a" xml:space="preserve"><emph style="it">Lateralis</emph> <lb/><emph style="it">ingreſſus.</emph></note>
<note position="left" xlink:label="note-0044-04" xlink:href="note-0044-04a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div69" type="section" level="1" n="39">
<head xml:id="echoid-head43" xml:space="preserve">PRONVNCIATVM XXVII.</head>
<p>
  <s xml:id="echoid-s2317" xml:space="preserve">Eoſdẽ angulos quatuor, q̊s eclyptica facit cũ meridiano, facilius inquirere.</s>
  <s xml:id="echoid-s2318" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2319" xml:space="preserve">Qđ ſi angulos illos diuerſo modo cupis inuenire, grauat<emph style="sub">9</emph> forſitã nimiũ ꝓlixaiſta ſuꝑi <lb/>oriet oꝑoſa oꝑatiõe, ꝓpones pricipio tibi ſinũ diſtãtiæ arcus pũcti eclypticæ q̃ntũ diſtet <lb/>
<anchor type="note" xlink:label="note-0044-05a" xlink:href="note-0044-05"/>
ille à ꝓxĩa interſectiõe eclypticæ &amp; </s>
  <s xml:id="echoid-s2320" xml:space="preserve">meridiani, ſinũ illi9 rectũ tibi ꝓpone, ſimilit &amp; </s>
  <s xml:id="echoid-s2321" xml:space="preserve">ſinũ re <lb/>ctũ ipſius aſcẽſiõis rectæ, quã ex 7. </s>
  <s xml:id="echoid-s2322" xml:space="preserve">ꝓnũciato inueniſti, &amp; </s>
  <s xml:id="echoid-s2323" xml:space="preserve">deide ſinũ minorẽ duc in ſinũ to-<lb/>tũ ꝓductũ diuide in maiorẽ, et arcus q̊tiẽtis oſtẽdet angulũ q̃ſitũ, Borealẽ oriẽtalẽ in q̃r-<lb/>ta prima, in ſcd’a aũt quarta zodiaci mõſtrat angulũ orientalẽ meridionalẽ, in tertia an <lb/>gulũ orientalẽ meridionalẽ, quarta ſimilit’ ut prĩa oſtendit angulũ Borealẽ oriẽtalẽ. </s>
  <s xml:id="echoid-s2324" xml:space="preserve">Reli <lb/>
<anchor type="note" xlink:label="note-0044-06a" xlink:href="note-0044-06"/>
q̊s tres angulos ita inuenies, ut præcedẽti ꝓnunciato edoctus es. </s>
  <s xml:id="echoid-s2325" xml:space="preserve">?</s>
  <s xml:id="echoid-s2326" xml:space="preserve">?Exemplũ hic tibi <lb/>dabimus huiuſmodi. </s>
  <s xml:id="echoid-s2327" xml:space="preserve">in ipſo die intronizationis gradus ☉(sun), ut antea diximus, fuit 2. </s>
  <s xml:id="echoid-s2328" xml:space="preserve">gra.</s>
  <s xml:id="echoid-s2329" xml:space="preserve">
<pb file="0045" n="45" rhead="TABVLARVM SINVVM."/>
26. </s>
  <s xml:id="echoid-s2330" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2331" xml:space="preserve">II, diſtantia ab ♈, quæ interſectio proxima eſt, fuit 62. </s>
  <s xml:id="echoid-s2332" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2333" xml:space="preserve">26. </s>
  <s xml:id="echoid-s2334" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2335" xml:space="preserve">ſinus illius <lb/>88647. </s>
  <s xml:id="echoid-s2336" xml:space="preserve">hunc ſepone in locum aliquem peculiarem, deinde propone tibi ſinum aſcenſio-<lb/>nis eius rectæ, quam ex pronunciato 7. </s>
  <s xml:id="echoid-s2337" xml:space="preserve">inueniſti 60. </s>
  <s xml:id="echoid-s2338" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2339" xml:space="preserve">51. </s>
  <s xml:id="echoid-s2340" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2341" xml:space="preserve">86906. </s>
  <s xml:id="echoid-s2342" xml:space="preserve">ſinum illum pu-<lb/>ta minorem duc in illum totum, productum diuide in maiorem, &amp; </s>
  <s xml:id="echoid-s2343" xml:space="preserve">prouenient in quotien <lb/>te 98036. </s>
  <s xml:id="echoid-s2344" xml:space="preserve">arcus illius erit 78. </s>
  <s xml:id="echoid-s2345" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2346" xml:space="preserve">37. </s>
  <s xml:id="echoid-s2347" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2348" xml:space="preserve">quæ etiam quantitas eſt anguli primi, ſcilicet ſe <lb/>ptentrionalis orientalis, complementum eius de ſemicirculo eſt 101. </s>
  <s xml:id="echoid-s2349" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2350" xml:space="preserve">23. </s>
  <s xml:id="echoid-s2351" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2352" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2353" xml:space="preserve">is an-<lb/>gulus eſt orientalis meridionalis, at in hunc modum uides iam te faciliori uia inueniſſe <lb/>idem, quod ſuperior propoſitio longa &amp; </s>
  <s xml:id="echoid-s2354" xml:space="preserve">operoſa operatione docuit.</s>
  <s xml:id="echoid-s2355" xml:space="preserve"/>
</p>
<div xml:id="echoid-div69" type="float" level="2" n="1">
<note position="left" xlink:label="note-0044-05" xlink:href="note-0044-05a" xml:space="preserve"><emph style="it">Illud habc-</emph> <lb/><emph style="it">tur in qua-</emph> <lb/><emph style="it">drante are</emph> <lb/><emph style="it">atim.</emph></note>
<note position="left" xlink:label="note-0044-06" xlink:href="note-0044-06a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div71" type="section" level="1" n="40">
<head xml:id="echoid-head44" xml:space="preserve">PRONVNCIATVM XXVIII.</head>
<p>
  <s xml:id="echoid-s2356" xml:space="preserve">Angulos illos eclypticæ &amp; </s>
  <s xml:id="echoid-s2357" xml:space="preserve">meridiani, adhuc tertia quadam ratione, à prio <lb/>ribus diuerſa, inue ſtigare.</s>
  <s xml:id="echoid-s2358" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2359" xml:space="preserve">Propone hic principio tibi ſinũ cõplementi maximæ declinatiõis ☉(sun), &amp; </s>
  <s xml:id="echoid-s2360" xml:space="preserve">ſinum cõple <lb/>
<anchor type="note" xlink:label="note-0045-01a" xlink:href="note-0045-01"/>
menti declinatiõis pũcti propoſiti, minorẽ ex ijs duc in ſinũ ꝑfectũ, ꝓductũ diuide in ma <lb/>iorem, &amp; </s>
  <s xml:id="echoid-s2361" xml:space="preserve">arcus quotientis oſtendet tibi angulũ quæſitũ iuxta ea quæ docuimus pronun-<lb/>ciato 26. </s>
  <s xml:id="echoid-s2362" xml:space="preserve">de 4. </s>
  <s xml:id="echoid-s2363" xml:space="preserve">quartis. </s>
  <s xml:id="echoid-s2364" xml:space="preserve">Vbi adhuc tñ admonendus es mihi, ꝙ primũ punctũ ♋, &amp; </s>
  <s xml:id="echoid-s2365" xml:space="preserve">ſimili-<lb/>ter primũ punctũ ♑ nõ alios niſi rectos faciunt angulos, principiũ autẽ ?</s>
  <s xml:id="echoid-s2366" xml:space="preserve">? in angulo Bo <lb/>reali orientali, angulũ habet æqualẽ cõplemento maximæ declinationis. </s>
  <s xml:id="echoid-s2367" xml:space="preserve">Conſimilẽ q̊ <lb/>
<anchor type="note" xlink:label="note-0045-02a" xlink:href="note-0045-02"/>
quantitatẽ ſeruat principiũ ♎ in angulo Auſtrali orientali. </s>
  <s xml:id="echoid-s2368" xml:space="preserve">?</s>
  <s xml:id="echoid-s2369" xml:space="preserve">? Sed hic forſitan exem <lb/>plum adhuc deſideras? </s>
  <s xml:id="echoid-s2370" xml:space="preserve">en habe. </s>
  <s xml:id="echoid-s2371" xml:space="preserve">Scire cupio quantus quiſ ſit angulus, quẽ eclyptica iu-<lb/>xta gradũ ☉(sun), in q̊ ſaltẽ ipſe fuit in die intronizationis, facit cũ meridiano. </s>
  <s xml:id="echoid-s2372" xml:space="preserve">Gradus ita <lb/>Solis fuit 2. </s>
  <s xml:id="echoid-s2373" xml:space="preserve">II. </s>
  <s xml:id="echoid-s2374" xml:space="preserve">26 mi. </s>
  <s xml:id="echoid-s2375" xml:space="preserve">declinationẽ ipſius inueni ꝑ 5. </s>
  <s xml:id="echoid-s2376" xml:space="preserve">ꝓnunc. </s>
  <s xml:id="echoid-s2377" xml:space="preserve">20. </s>
  <s xml:id="echoid-s2378" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2379" xml:space="preserve">42. </s>
  <s xml:id="echoid-s2380" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2381" xml:space="preserve">cõplemẽtum <lb/>eius eſt 69. </s>
  <s xml:id="echoid-s2382" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2383" xml:space="preserve">18. </s>
  <s xml:id="echoid-s2384" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2385" xml:space="preserve">Propono deinde mihi etiã cõplemẽtũ maxiæ declinatiõis ☉(sun), ſinus <lb/>prioris cõplementi eſt 93544. </s>
  <s xml:id="echoid-s2386" xml:space="preserve">alterius aũt 91706. </s>
  <s xml:id="echoid-s2387" xml:space="preserve">iã minorem duco in totũ, &amp; </s>
  <s xml:id="echoid-s2388" xml:space="preserve">productũ <lb/>diuido in maiorem, at in q̊tiente ꝓueniũt 98035. </s>
  <s xml:id="echoid-s2389" xml:space="preserve">arcus eius eſt 78. </s>
  <s xml:id="echoid-s2390" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2391" xml:space="preserve">37. </s>
  <s xml:id="echoid-s2392" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2393" xml:space="preserve">Borealis <lb/>&amp; </s>
  <s xml:id="echoid-s2394" xml:space="preserve">orientalis. </s>
  <s xml:id="echoid-s2395" xml:space="preserve">Ecce quomodo hac triplici ratione inueniangulũ iſtum æqualis ſemper <lb/>quantitatis, reliquos angulos tres ipſe facile colligere poteris, ſed aliud adhuc exemplũ <lb/>dabimus hic tibi ad mediũ cœli, q̊d &amp; </s>
  <s xml:id="echoid-s2396" xml:space="preserve">cõtingit ſub ipſam horã intronizationis, nam ne <lb/>ceſſe fuerit etiã deinceps hoc exemplũ cognoſcere. </s>
  <s xml:id="echoid-s2397" xml:space="preserve">Ex 25. </s>
  <s xml:id="echoid-s2398" xml:space="preserve">pronunciato inueni in medio <lb/>cœli ſtetiſſe 16. </s>
  <s xml:id="echoid-s2399" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2400" xml:space="preserve">40. </s>
  <s xml:id="echoid-s2401" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2402" xml:space="preserve">♈, duco igitur ſinũ cõplementi maximæ declinationis 91706 <lb/>in ſinum perfectum, &amp; </s>
  <s xml:id="echoid-s2403" xml:space="preserve">diuido in ſinum rectum ſecundum declinationis gradus medij cœ <lb/>li, ſcilicet 99343. </s>
  <s xml:id="echoid-s2404" xml:space="preserve">at in ipſo quotiente inueni 92312. </s>
  <s xml:id="echoid-s2405" xml:space="preserve">arcus eius eſt 67. </s>
  <s xml:id="echoid-s2406" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2407" xml:space="preserve">23. </s>
  <s xml:id="echoid-s2408" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2409" xml:space="preserve">qui &amp; </s>
  <s xml:id="echoid-s2410" xml:space="preserve"><lb/>angulus eſt eclypticæ &amp; </s>
  <s xml:id="echoid-s2411" xml:space="preserve">meridiani in parte Boreali orientali.</s>
  <s xml:id="echoid-s2412" xml:space="preserve"/>
</p>
<div xml:id="echoid-div71" type="float" level="2" n="1">
<note position="right" xlink:label="note-0045-01" xlink:href="note-0045-01a" xml:space="preserve"><emph style="it">Per arealẽ</emph> <lb/><emph style="it">ingreſſum</emph> <lb/><emph style="it">idem aſſe-</emph> <lb/><emph style="it">queris.</emph></note>
<note position="right" xlink:label="note-0045-02" xlink:href="note-0045-02a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſcopi.</emph></note>
</div>
</div>
<div xml:id="echoid-div73" type="section" level="1" n="41">
<head xml:id="echoid-head45" xml:space="preserve">PRONVNCIATVM XXIX.</head>
<p>
  <s xml:id="echoid-s2413" xml:space="preserve">Diſtantiam zenich à 90. </s>
  <s xml:id="echoid-s2414" xml:space="preserve">gradu ab aſcendẽte, &amp; </s>
  <s xml:id="echoid-s2415" xml:space="preserve">breuiſsime &amp; </s>
  <s xml:id="echoid-s2416" xml:space="preserve">exactiſsime <lb/>reperire.</s>
  <s xml:id="echoid-s2417" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2418" xml:space="preserve">Quandoquidem diſtantia hæc deinceps quo ad multa cõducet, ideo &amp; </s>
  <s xml:id="echoid-s2419" xml:space="preserve">eam hic pau <lb/>
<anchor type="note" xlink:label="note-0045-03a" xlink:href="note-0045-03"/>
eis docebimus inuenire, ubi iã angulũ meridiani &amp; </s>
  <s xml:id="echoid-s2420" xml:space="preserve">eclypticæ ex aliqua triũ illarũ propoſi <lb/>tionũ, ex 25. </s>
  <s xml:id="echoid-s2421" xml:space="preserve">26. </s>
  <s xml:id="echoid-s2422" xml:space="preserve">aut 27. </s>
  <s xml:id="echoid-s2423" xml:space="preserve">cognitã habes (angulũ inquã minorem uerſus ortũ) &amp; </s>
  <s xml:id="echoid-s2424" xml:space="preserve">eius angu <lb/>li ſinũ ducis in ſinũ cõplementi altitudinis meridianæ, productũ uero diuidis in totũ, ar-<lb/>
<anchor type="note" xlink:label="note-0045-04a" xlink:href="note-0045-04"/>
cus uti q̊tientis iſtius erit diſtãtia zenith à 90. </s>
  <s xml:id="echoid-s2425" xml:space="preserve">gradu ab aſcendẽte. </s>
  <s xml:id="echoid-s2426" xml:space="preserve">?</s>
  <s xml:id="echoid-s2427" xml:space="preserve">? Id ut magis in-<lb/>telligas, exemplũ cape huiuſmodi. </s>
  <s xml:id="echoid-s2428" xml:space="preserve">Eſto utinuenerim mediũ cœli ad ipſam horã introni-<lb/>zationis ex ꝓnunciato 28. </s>
  <s xml:id="echoid-s2429" xml:space="preserve">16. </s>
  <s xml:id="echoid-s2430" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2431" xml:space="preserve">40. </s>
  <s xml:id="echoid-s2432" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2433" xml:space="preserve">♈, ſimiliter &amp; </s>
  <s xml:id="echoid-s2434" xml:space="preserve">angulũ meridiani at eclypti-<lb/>cæ per ꝓnunciatũ 26. </s>
  <s xml:id="echoid-s2435" xml:space="preserve">uel 27. </s>
  <s xml:id="echoid-s2436" xml:space="preserve">uel 28. </s>
  <s xml:id="echoid-s2437" xml:space="preserve">repererim 67 gra. </s>
  <s xml:id="echoid-s2438" xml:space="preserve">23. </s>
  <s xml:id="echoid-s2439" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2440" xml:space="preserve">ſinũ eius 92309. </s>
  <s xml:id="echoid-s2441" xml:space="preserve">duxi dein-<lb/>de in ſinum cõplementi altitudinis meridianæ, ſcilicet 66174. </s>
  <s xml:id="echoid-s2442" xml:space="preserve">productum diuiſi in ſinum <lb/>perfectũ, quotiens uti erit 61084. </s>
  <s xml:id="echoid-s2443" xml:space="preserve">arcus eius 37. </s>
  <s xml:id="echoid-s2444" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2445" xml:space="preserve">39. </s>
  <s xml:id="echoid-s2446" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2447" xml:space="preserve">diſtãtia nimi℞ illa quæſita.</s>
  <s xml:id="echoid-s2448" xml:space="preserve"/>
</p>
<div xml:id="echoid-div73" type="float" level="2" n="1">
<note position="right" xlink:label="note-0045-03" xlink:href="note-0045-03a" xml:space="preserve"><emph style="it">Lateralis</emph> <lb/><emph style="it">ingreſſus.</emph></note>
<note position="right" xlink:label="note-0045-04" xlink:href="note-0045-04a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div75" type="section" level="1" n="42">
<head xml:id="echoid-head46" xml:space="preserve">PRONVNCIATVM XXX.</head>
<p>
  <s xml:id="echoid-s2449" xml:space="preserve">Aſcendentem, hoc eſt gradum eclypticæ, qui partiliter in horizonte con-<lb/>ſtituitur, quacun &amp; </s>
  <s xml:id="echoid-s2450" xml:space="preserve">regione &amp; </s>
  <s xml:id="echoid-s2451" xml:space="preserve">hora expedite cognoſcere.</s>
  <s xml:id="echoid-s2452" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2453" xml:space="preserve">Principio quære diſtantiã nonageſimiab abſcendente gradus à medio cœli in hũc mo <lb/>dum: </s>
  <s xml:id="echoid-s2454" xml:space="preserve">Multiplica ſinum diſtãtiæ gradus medij cœli à proxima interſectione æquatoris &amp;</s>
  <s xml:id="echoid-s2455" xml:space="preserve">
<pb file="0046" n="46" rhead="GENVINVS VSVS"/>
eclypticæ cũ ſinu maximæ declinatiõis ☉(sun), ꝓductũ inde diuide in totũ, ſinũ, &amp; </s>
  <s xml:id="echoid-s2456" xml:space="preserve">proueniet <lb/>
<anchor type="note" xlink:label="note-0046-01a" xlink:href="note-0046-01"/>
declinatio medij cœli ab æquatore, quod etiã didiciſtiiam ſupra quærere in pronunciato <lb/>5. </s>
  <s xml:id="echoid-s2457" xml:space="preserve">Deinde fac inuenias per pronunc. </s>
  <s xml:id="echoid-s2458" xml:space="preserve">27. </s>
  <s xml:id="echoid-s2459" xml:space="preserve">angulũ eclypticæ &amp; </s>
  <s xml:id="echoid-s2460" xml:space="preserve">meridiani in parte orientis, <lb/>angulũ inquã illum, qui recto minor eſt, eũ inuenies, ſi ſinũ ſecundũ maximæ declinatio-<lb/>nis tibi proponas, &amp; </s>
  <s xml:id="echoid-s2461" xml:space="preserve">ſinum cõplementi declinationis medij cœli minorẽ duxeris in ſinũ <lb/>
<anchor type="note" xlink:label="note-0046-02a" xlink:href="note-0046-02"/>
totum, productũ in maiorẽ diuiſeris, tũc ſanè arcus quotientis erit quantitas eius angu-<lb/>li. </s>
  <s xml:id="echoid-s2462" xml:space="preserve">Porrò ſi ſinũ diſtantiæ zenith à gradu medij cœli ducas in ſinũ anguli iam inuenti, ꝓ-<lb/>ductũ in ſinum totũ diuide, arcus quotientis oſtendet diſtantiã zenith à 90. </s>
  <s xml:id="echoid-s2463" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2464" xml:space="preserve">ab aſcen-<lb/>dente, qui arcus ſemper ad angulos rectos ſphærales ſup circulũ ma iorem ductũ ex polis <lb/>zodiaci per zenith capitis cadit. </s>
  <s xml:id="echoid-s2465" xml:space="preserve">Ad hæc quære quantũ 90. </s>
  <s xml:id="echoid-s2466" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2467" xml:space="preserve">ab aſcendẽte diſtet à me <lb/>dio cœli, &amp; </s>
  <s xml:id="echoid-s2468" xml:space="preserve">quidẽ ꝓpone tibi ſinũ cõplementi arcus diſtantiæ zenith à 90. </s>
  <s xml:id="echoid-s2469" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2470" xml:space="preserve">ab aſcen-<lb/>dente, &amp; </s>
  <s xml:id="echoid-s2471" xml:space="preserve">ſinũ cõplementi diſtantiæ zenith à medio cœli, minorẽ duc in ſinũ totũ, produ <lb/>
<anchor type="note" xlink:label="note-0046-03a" xlink:href="note-0046-03"/>
ctum diuide in maiorẽ, &amp; </s>
  <s xml:id="echoid-s2472" xml:space="preserve">arcus quotiẽtis mõſtrabit arcũ eclypticæ à medio cœli uſ ad <lb/>
<anchor type="note" xlink:label="note-0046-04a" xlink:href="note-0046-04"/>
gradũ eclypticæ, qui occidit in parte occidentis: </s>
  <s xml:id="echoid-s2473" xml:space="preserve">ſin aũt ſubtraxeris illũ arcũ à 90. </s>
  <s xml:id="echoid-s2474" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2475" xml:space="preserve">tũc <lb/>manebit arcus ille diſtantiæ 90. </s>
  <s xml:id="echoid-s2476" xml:space="preserve">gradus ab aſcendente à ſupremo cœli. </s>
  <s xml:id="echoid-s2477" xml:space="preserve">Etſi acceperis gra <lb/>dum oppoſitũ occidentis, habebis gradũ illum ꝗ oritur in oriente ſuper horizõtem. </s>
  <s xml:id="echoid-s2478" xml:space="preserve">Sin <lb/>uero punctũ medĳ cœli fuerit in medietate eclypticæ deſcendenti, tũc adde arcũ quotien <lb/>tis ad medium cczli, &amp; </s>
  <s xml:id="echoid-s2479" xml:space="preserve">proueniet gradus aſcendentis, cuius contrariũ eſt gradus eclypti-<lb/>cæ occidens in parte occidentis. </s>
  <s xml:id="echoid-s2480" xml:space="preserve">Sed ſi arcũ quotientis ſubtrahas à 90. </s>
  <s xml:id="echoid-s2481" xml:space="preserve">reſiduũ etiã ſubtra <lb/>has à gradu medij cœli, tunc manet gradus 90. </s>
  <s xml:id="echoid-s2482" xml:space="preserve">ab aſcendẽte &amp; </s>
  <s xml:id="echoid-s2483" xml:space="preserve">occidente, ꝗſemper ſupre <lb/>mus ſiue altiſsimus exiſtit eclypticæ gradus ſupra horizontẽ, nõ ille (ut imperiti putãt) <lb/>
<anchor type="note" xlink:label="note-0046-05a" xlink:href="note-0046-05"/>
qui tangit mediũ cœli ?</s>
  <s xml:id="echoid-s2484" xml:space="preserve">? At in ea re operæ preciũ adhuc fuerit exemplũ proponere, q̊ <lb/>facilius intelligas. </s>
  <s xml:id="echoid-s2485" xml:space="preserve">Proximo pronunciato inueni iã mediũ cœli ad horã intr onizationis, <lb/>gradus ille fuit 15. </s>
  <s xml:id="echoid-s2486" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2487" xml:space="preserve">40. </s>
  <s xml:id="echoid-s2488" xml:space="preserve">♈, ſinũ quo diſtãtiæ illius à principio ♈, ſcilicet 28680. </s>
  <s xml:id="echoid-s2489" xml:space="preserve">du-<lb/>xi in ſinũ maximæ declinatiõis, ꝓductũ diuiſi in ſinũ totũ, &amp; </s>
  <s xml:id="echoid-s2490" xml:space="preserve">in q̊tiẽte ecce iam inuenio <lb/>11435, arcus eius 6, gra, 34. </s>
  <s xml:id="echoid-s2491" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2492" xml:space="preserve">declinatio eſt medĳ cœli, deinde quæro angulũ eclypticæ <lb/>&amp; </s>
  <s xml:id="echoid-s2493" xml:space="preserve">meridiani, multiplicando ſinũ cõplementi maximæ declinatiõis ☉(sun) 91706. </s>
  <s xml:id="echoid-s2494" xml:space="preserve">cũ toto ſi-<lb/>nu, &amp; </s>
  <s xml:id="echoid-s2495" xml:space="preserve">diuidendo ꝓductũ in ſinũ cõplementi declinationis medij cœli 99343. </s>
  <s xml:id="echoid-s2496" xml:space="preserve">in quotiente <lb/>iã inuenio 92312. </s>
  <s xml:id="echoid-s2497" xml:space="preserve">arcus eius 67. </s>
  <s xml:id="echoid-s2498" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2499" xml:space="preserve">23. </s>
  <s xml:id="echoid-s2500" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2501" xml:space="preserve">angulus ille eſt cauſatus ab eclyptica &amp; </s>
  <s xml:id="echoid-s2502" xml:space="preserve">meri <lb/>diano orientalis Borealis. </s>
  <s xml:id="echoid-s2503" xml:space="preserve">Adhuc aũt multiplico quotientẽ iſtũ rurſus cũ ſinu diſtantiæ <lb/>zenith à puncto medĳ cœli, ſcilicet 66 174. </s>
  <s xml:id="echoid-s2504" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2505" xml:space="preserve">diuido productũ in ſinũ perfectum, in quo-<lb/>tiente inuenio 6 1084. </s>
  <s xml:id="echoid-s2506" xml:space="preserve">arcus quotientis illius eſt 37. </s>
  <s xml:id="echoid-s2507" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2508" xml:space="preserve">39. </s>
  <s xml:id="echoid-s2509" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2510" xml:space="preserve">quæ &amp; </s>
  <s xml:id="echoid-s2511" xml:space="preserve">diſtãtia eſt zenith <lb/>à 90. </s>
  <s xml:id="echoid-s2512" xml:space="preserve">gradu, qui cõputatur ab aſcendente. </s>
  <s xml:id="echoid-s2513" xml:space="preserve">Si deinceps ſinũ cõplementi illius 79 175. </s>
  <s xml:id="echoid-s2514" xml:space="preserve">adſer <lb/>uem in locũ diuiſoris, &amp; </s>
  <s xml:id="echoid-s2515" xml:space="preserve">ſinũ altitudinis medĳ cœli, ꝓ &amp; </s>
  <s xml:id="echoid-s2516" xml:space="preserve">ſinus eſt cõplementi diſtantiæ ze <lb/>nith à medio cœlo, ducã in ſinũ totũ, &amp; </s>
  <s xml:id="echoid-s2517" xml:space="preserve">productũ diuidã in ipſum diuiſorem, inueniam u-<lb/>ti in quotiente 94691. </s>
  <s xml:id="echoid-s2518" xml:space="preserve">arcus eius eſt 71. </s>
  <s xml:id="echoid-s2519" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2520" xml:space="preserve">15. </s>
  <s xml:id="echoid-s2521" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2522" xml:space="preserve">Iam ſi tantũ quo accipias contra <lb/>ſignorũ ordinem à puncto medij cœli, finietur arcus in 5. </s>
  <s xml:id="echoid-s2523" xml:space="preserve">gradu. </s>
  <s xml:id="echoid-s2524" xml:space="preserve">25. </s>
  <s xml:id="echoid-s2525" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2526" xml:space="preserve">♒, qui gradus eſt <lb/>occidens in parte occidentis ipſo tempore iutronizationis, 5. </s>
  <s xml:id="echoid-s2527" xml:space="preserve">etiam gra. </s>
  <s xml:id="echoid-s2528" xml:space="preserve">25. </s>
  <s xml:id="echoid-s2529" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2530" xml:space="preserve">♌, eſt a-<lb/>ſcendens quem quærebam. </s>
  <s xml:id="echoid-s2531" xml:space="preserve">Si autem ſubtrahas 71. </s>
  <s xml:id="echoid-s2532" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2533" xml:space="preserve">15. </s>
  <s xml:id="echoid-s2534" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2535" xml:space="preserve">à 90. </s>
  <s xml:id="echoid-s2536" xml:space="preserve">remanebunt tibi 18. <lb/></s>
  <s xml:id="echoid-s2537" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2538" xml:space="preserve">45. </s>
  <s xml:id="echoid-s2539" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2540" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2541" xml:space="preserve">tantum quidem diſtat gradus ille 90. </s>
  <s xml:id="echoid-s2542" xml:space="preserve">ab aſcendente à medio cœli uerſus or-<lb/>tum, ſi autem addas medium cœli, puta 16. </s>
  <s xml:id="echoid-s2543" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2544" xml:space="preserve">40. </s>
  <s xml:id="echoid-s2545" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2546" xml:space="preserve">ad 18. </s>
  <s xml:id="echoid-s2547" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2548" xml:space="preserve">45. </s>
  <s xml:id="echoid-s2549" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2550" xml:space="preserve">tunc attingit <lb/>planè 5. </s>
  <s xml:id="echoid-s2551" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2552" xml:space="preserve">25. </s>
  <s xml:id="echoid-s2553" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2554" xml:space="preserve">♉, qui &amp; </s>
  <s xml:id="echoid-s2555" xml:space="preserve">gradus eſt nonageſimus ab aſcendente.</s>
  <s xml:id="echoid-s2556" xml:space="preserve"/>
</p>
<div xml:id="echoid-div75" type="float" level="2" n="1">
<note position="left" xlink:label="note-0046-01" xlink:href="note-0046-01a" xml:space="preserve"><emph style="it">Lateraliter</emph> <lb/><emph style="it">illud ex</emph> <lb/><emph style="it">quadrante</emph> <lb/><emph style="it">inuenitur.</emph></note>
<note position="left" xlink:label="note-0046-02" xlink:href="note-0046-02a" xml:space="preserve"><emph style="it">Arealiter</emph></note>
<note position="left" xlink:label="note-0046-03" xlink:href="note-0046-03a" xml:space="preserve"><emph style="it">Arealiter</emph></note>
<note position="left" xlink:label="note-0046-04" xlink:href="note-0046-04a" xml:space="preserve"><emph style="it">Nonageſi-</emph> <lb/><emph style="it">mus ab a-</emph> <lb/><emph style="it">ſcẽdẽte gra</emph> <lb/><emph style="it">dus altißi-</emph> <lb/><emph style="it">ma eclypti</emph> <lb/><emph style="it">cœ pars eſt</emph> <lb/><emph style="it">ſupra hori</emph> <lb/><emph style="it">zontem.</emph></note>
<note position="left" xlink:label="note-0046-05" xlink:href="note-0046-05a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſcopi.</emph></note>
</div>
</div>
<div xml:id="echoid-div77" type="section" level="1" n="43">
<head xml:id="echoid-head47" xml:space="preserve">PRONVNCIATVM XXXI.</head>
<p>
  <s xml:id="echoid-s2557" xml:space="preserve">Angulum ab horizonte obliquo cum eclyptica cauſſatum, per expeditam <lb/>ſupputationem cognoſcere.</s>
  <s xml:id="echoid-s2558" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2559" xml:space="preserve">Inuento iam gradu aſcendente ex 30. </s>
  <s xml:id="echoid-s2560" xml:space="preserve">ꝓnunc. </s>
  <s xml:id="echoid-s2561" xml:space="preserve">quære deinceps per aliquã ex tribus illis <lb/>pronunc. </s>
  <s xml:id="echoid-s2562" xml:space="preserve">26. </s>
  <s xml:id="echoid-s2563" xml:space="preserve">27. </s>
  <s xml:id="echoid-s2564" xml:space="preserve">aut 28. </s>
  <s xml:id="echoid-s2565" xml:space="preserve">angulũ quẽ effecit eclyptica præciſe in gradu aſcendentis cũ me <lb/>ridiano uerſus orientẽ. </s>
  <s xml:id="echoid-s2566" xml:space="preserve">Porrô aũt ubi ſcire cupis etiam illũ angulũ, quem facit eclyptica <lb/>in ipſo puncto aſcendentis cum horizonte, tunc tibi propone ſinum cõplementi declina <lb/>
<anchor type="note" xlink:label="note-0046-06a" xlink:href="note-0046-06"/>
tionis illius gradus eclypticæ, ſimiliter &amp; </s>
  <s xml:id="echoid-s2567" xml:space="preserve">ſinũ eleuationis poli, minorẽ ex ijs duc in ſinũ <lb/>totũ, productũ diuide in ſinũ maiorẽ, &amp; </s>
  <s xml:id="echoid-s2568" xml:space="preserve">arcũ quotientis dico angulũ cõmunem, id'´ eo <lb/>maxime, qñ ſi punctũ illud eclypticæ aſcendens, uel penes quod angulum horizontis &amp;</s>
  <s xml:id="echoid-s2569" xml:space="preserve">
<pb file="0047" n="47" rhead="TABVLARVM SINVVM."/>
eclypticæ noſſe deſideras, fuerit in ſigno aliquo deſcendente, tunc addes angulum cõmu <lb/>nem ad angulum, quem facit idem illud punctum in medio cœli cum eclyptica &amp; </s>
  <s xml:id="echoid-s2570" xml:space="preserve">me <lb/>ridiano, ſumma ea à ſemicirculo ſubtracta, remanebit tibi angulus cauſſatus ab eclypti-<lb/>ca iuxta punctum propoſitum cum horizonte. </s>
  <s xml:id="echoid-s2571" xml:space="preserve">Si aũt punctum illud eclypticæ ſit in ſemi <lb/>circulo eclypticæ aſcendente, tũc ſubtrahe angulum cõmunem ab angulo meridian, &amp; </s>
  <s xml:id="echoid-s2572" xml:space="preserve"><lb/>remanebit angulus eclypticæ &amp; </s>
  <s xml:id="echoid-s2573" xml:space="preserve">horizontis iuxta propoſitũ punctũ eclypticæ. </s>
  <s xml:id="echoid-s2574" xml:space="preserve">?</s>
  <s xml:id="echoid-s2575" xml:space="preserve">? Ex-<lb/>
<anchor type="note" xlink:label="note-0047-01a" xlink:href="note-0047-01"/>
emplum ſit hoc tibi, ex 30. </s>
  <s xml:id="echoid-s2576" xml:space="preserve">propoſitione iam inueni in ipſa hora &amp; </s>
  <s xml:id="echoid-s2577" xml:space="preserve">minuto intronizatio <lb/>nis fuiſſe in aſcendente 5. </s>
  <s xml:id="echoid-s2578" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2579" xml:space="preserve">25. </s>
  <s xml:id="echoid-s2580" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2581" xml:space="preserve">♌, declinatio huius eſt 18. </s>
  <s xml:id="echoid-s2582" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2583" xml:space="preserve">58. </s>
  <s xml:id="echoid-s2584" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2585" xml:space="preserve">cõplementũ <lb/>aũt 71. </s>
  <s xml:id="echoid-s2586" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2587" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2588" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2589" xml:space="preserve">ſinum huius cõplementi propono deinceps 94570. </s>
  <s xml:id="echoid-s2590" xml:space="preserve">ſimul &amp; </s>
  <s xml:id="echoid-s2591" xml:space="preserve">ſinũ cõple-<lb/>menti maximæ declinationis 91706. </s>
  <s xml:id="echoid-s2592" xml:space="preserve">tunc puta minorem duco in ſinũ ꝑfectum, &amp; </s>
  <s xml:id="echoid-s2593" xml:space="preserve">ꝓdu-<lb/>
<anchor type="note" xlink:label="note-0047-02a" xlink:href="note-0047-02"/>
ctum diuido in 94570: </s>
  <s xml:id="echoid-s2594" xml:space="preserve">in quotiente uideo mihi ꝓueniſſe 96971. </s>
  <s xml:id="echoid-s2595" xml:space="preserve">arcus huius quotientis <lb/>75. </s>
  <s xml:id="echoid-s2596" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2597" xml:space="preserve">52. </s>
  <s xml:id="echoid-s2598" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2599" xml:space="preserve">oſtendit quãtitatẽ anguli quem facit eclyptica cũ meridiano iuxta 5. </s>
  <s xml:id="echoid-s2600" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s2601" xml:space="preserve">25. </s>
  <s xml:id="echoid-s2602" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2603" xml:space="preserve">♌. </s>
  <s xml:id="echoid-s2604" xml:space="preserve">Deinceps adhuc multiplico ſinũ eleuationis poli 48. </s>
  <s xml:id="echoid-s2605" xml:space="preserve">graduum, ſcilicet 74314. </s>
  <s xml:id="echoid-s2606" xml:space="preserve"><lb/>(ſiquidem is eſt minor) in ſinũ totũ, &amp; </s>
  <s xml:id="echoid-s2607" xml:space="preserve">diuido ꝓductũ cũ ſinu cõplemẽti declinatiõis pun <lb/>
<anchor type="note" xlink:label="note-0047-03a" xlink:href="note-0047-03"/>
cti, ꝓpoſiti 94578. </s>
  <s xml:id="echoid-s2608" xml:space="preserve">quotiens erit 79581 arcus uero 51. </s>
  <s xml:id="echoid-s2609" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2610" xml:space="preserve">48. </s>
  <s xml:id="echoid-s2611" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2612" xml:space="preserve">ꝗ uocatur angulus cõ-<lb/>munis, &amp; </s>
  <s xml:id="echoid-s2613" xml:space="preserve">quia ♌ eſt inter principiũ ♋ &amp; </s>
  <s xml:id="echoid-s2614" xml:space="preserve">♑, quæ ſigna ſunt deſcendentia, angulũ illum <lb/>cõmunem addo ad angulũ medij cœli 75. </s>
  <s xml:id="echoid-s2615" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2616" xml:space="preserve">52. </s>
  <s xml:id="echoid-s2617" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2618" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2619" xml:space="preserve">prouenient 127. </s>
  <s xml:id="echoid-s2620" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2621" xml:space="preserve">40. </s>
  <s xml:id="echoid-s2622" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2623" xml:space="preserve">qui-<lb/>bus à ſemicirculo ſubtractis, remanent 52. </s>
  <s xml:id="echoid-s2624" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2625" xml:space="preserve">20. </s>
  <s xml:id="echoid-s2626" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2627" xml:space="preserve">qui angulus eſt horizontis &amp; </s>
  <s xml:id="echoid-s2628" xml:space="preserve">ecly-<lb/>pticæ, quando 5. </s>
  <s xml:id="echoid-s2629" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2630" xml:space="preserve">25. </s>
  <s xml:id="echoid-s2631" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2632" xml:space="preserve">♌ partiliter, ut ſic liceat loqui, in horizõte cõſiſtunt 48. </s>
  <s xml:id="echoid-s2633" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s2634" xml:space="preserve">Accedat adhuc aliud exemplũ, ne quid prætermittamus q̊d ad intelligentiã huius rei fa-<lb/>cere uideatur, ſi forte punctũ eclypticæ in horizonte conſtitutum fuerit in ſemicirculo e-<lb/>clypticæ aſcendente, hoc eſt à principio ♑ ad finem II, ego´ cupiam habere angulum <lb/>eclypticæ &amp; </s>
  <s xml:id="echoid-s2635" xml:space="preserve">horizontis, quem gradus Solis, ſcilicet 2. </s>
  <s xml:id="echoid-s2636" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2637" xml:space="preserve">26. </s>
  <s xml:id="echoid-s2638" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2639" xml:space="preserve">II in die intronizationis <lb/>ſub ipſum Solis ortũ effecit (&amp; </s>
  <s xml:id="echoid-s2640" xml:space="preserve">eſto ut Sol eo die proprio ſuo motu ſteterit in eclyptica) <lb/>ibi principio per 26. </s>
  <s xml:id="echoid-s2641" xml:space="preserve">27. </s>
  <s xml:id="echoid-s2642" xml:space="preserve">aut 28. </s>
  <s xml:id="echoid-s2643" xml:space="preserve">propoſitiones inueni angulum eclypticæ &amp; </s>
  <s xml:id="echoid-s2644" xml:space="preserve">meridiani, ꝗ <lb/>fuit iuxta gradum Solis, illum inquam inueni 78. </s>
  <s xml:id="echoid-s2645" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2646" xml:space="preserve">37. </s>
  <s xml:id="echoid-s2647" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2648" xml:space="preserve">Deinde ſinũ altitudinis po-<lb/>li 48. </s>
  <s xml:id="echoid-s2649" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2650" xml:space="preserve">ſcilicet 743 14. </s>
  <s xml:id="echoid-s2651" xml:space="preserve">tan̈ minorẽ duco in ſinũ totum, productũ diuido in ſinũ com-<lb/>
<anchor type="note" xlink:label="note-0047-04a" xlink:href="note-0047-04"/>
plementi declinationis Solis, ſcilicet 93544. </s>
  <s xml:id="echoid-s2652" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2653" xml:space="preserve">quotiens erit 79335. </s>
  <s xml:id="echoid-s2654" xml:space="preserve">arcus eius 52. </s>
  <s xml:id="echoid-s2655" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s2656" xml:space="preserve">30. </s>
  <s xml:id="echoid-s2657" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2658" xml:space="preserve">angulus ille communis, quem mox ſubtraho ab angulo medij cœli, &amp; </s>
  <s xml:id="echoid-s2659" xml:space="preserve">remane-<lb/>bunt pro angulo orientis eclypticæ &amp; </s>
  <s xml:id="echoid-s2660" xml:space="preserve">horizontis iuxta gradum Solis 26. </s>
  <s xml:id="echoid-s2661" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2662" xml:space="preserve">7. </s>
  <s xml:id="echoid-s2663" xml:space="preserve">mi.</s>
  <s xml:id="echoid-s2664" xml:space="preserve"/>
</p>
<div xml:id="echoid-div77" type="float" level="2" n="1">
<note position="left" xlink:label="note-0046-06" xlink:href="note-0046-06a" xml:space="preserve"><emph style="it">Arealis in-</emph> <lb/><emph style="it">greſſus.</emph></note>
<note position="right" xlink:label="note-0047-01" xlink:href="note-0047-01a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoopi.</emph></note>
<note position="right" xlink:label="note-0047-02" xlink:href="note-0047-02a" xml:space="preserve"><emph style="it">Arealis in-</emph> <lb/><emph style="it">greſſus.</emph></note>
<note position="right" xlink:label="note-0047-03" xlink:href="note-0047-03a" xml:space="preserve"><emph style="it">Arcalis in-</emph> <lb/><emph style="it">greſſus.</emph></note>
<note position="right" xlink:label="note-0047-04" xlink:href="note-0047-04a" xml:space="preserve"><emph style="it">Arealis.</emph></note>
</div>
</div>
<div xml:id="echoid-div79" type="section" level="1" n="44">
<head xml:id="echoid-head48" xml:space="preserve">PRONVNCIATVM XXXII.</head>
<p>
  <s xml:id="echoid-s2665" xml:space="preserve">Quantitatem anguli ab horizonte &amp; </s>
  <s xml:id="echoid-s2666" xml:space="preserve">eclyptica cauſſati diuerſo modo in <lb/>quirere, habito tantum prius medij cœli gradu.</s>
  <s xml:id="echoid-s2667" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2668" xml:space="preserve">Quum primũ habueris medij cœli gradũ, ſtatim quære per aliquã propoſitionum 26. <lb/></s>
  <s xml:id="echoid-s2669" xml:space="preserve">27. </s>
  <s xml:id="echoid-s2670" xml:space="preserve">uel 28. </s>
  <s xml:id="echoid-s2671" xml:space="preserve">angulũ quem facit eclyptica cum meridiano, deinde duc ſinũ anguli illius in ſi <lb/>
<anchor type="note" xlink:label="note-0047-05a" xlink:href="note-0047-05"/>
num diſtantiæ zenith à gradu medij cœli, productũ diuide in totum, &amp; </s>
  <s xml:id="echoid-s2672" xml:space="preserve">cõplementũ arcus <lb/>quotientis erit angulus eclypticæ &amp; </s>
  <s xml:id="echoid-s2673" xml:space="preserve">horizontis, qualiſcun tandem fuerit in aſcenden-<lb/>te gradus. </s>
  <s xml:id="echoid-s2674" xml:space="preserve">?</s>
  <s xml:id="echoid-s2675" xml:space="preserve">? Id adeo tali confirmabimus exemplo. </s>
  <s xml:id="echoid-s2676" xml:space="preserve">ꝓpono ecce mihi gradũ medij cœli <lb/>
<anchor type="note" xlink:label="note-0047-06a" xlink:href="note-0047-06"/>
15. </s>
  <s xml:id="echoid-s2677" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2678" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2679" xml:space="preserve">40. </s>
  <s xml:id="echoid-s2680" xml:space="preserve">♈, quẽ iam ſupra pronunciato 26. </s>
  <s xml:id="echoid-s2681" xml:space="preserve">ad horã intronizationis inueni in medio <lb/>cœli, &amp; </s>
  <s xml:id="echoid-s2682" xml:space="preserve">per tres illas propoſitiones per 26. </s>
  <s xml:id="echoid-s2683" xml:space="preserve">27. </s>
  <s xml:id="echoid-s2684" xml:space="preserve">ſiue 28. </s>
  <s xml:id="echoid-s2685" xml:space="preserve">reperi etiam angulum meridiani <lb/>&amp; </s>
  <s xml:id="echoid-s2686" xml:space="preserve">eclypticæ ad idem illud momentum 67. </s>
  <s xml:id="echoid-s2687" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2688" xml:space="preserve">23. </s>
  <s xml:id="echoid-s2689" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2690" xml:space="preserve">ſinus ipſius eſt 92309. </s>
  <s xml:id="echoid-s2691" xml:space="preserve">eum ſi du-<lb/>cam in ſinum diſtantiæ zenith à medio cœli, quæ eſt 41. </s>
  <s xml:id="echoid-s2692" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2693" xml:space="preserve">26. </s>
  <s xml:id="echoid-s2694" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2695" xml:space="preserve">ſcilicet 66 174. </s>
  <s xml:id="echoid-s2696" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2697" xml:space="preserve">di-<lb/>uidam productum in ſinum perfectum, inueniam in quotiente 61084. </s>
  <s xml:id="echoid-s2698" xml:space="preserve">complementum <lb/>eius arcus oſtendit quantitatem anguli quem facit eclyptica cum horizonte in parte ori <lb/>entis &amp; </s>
  <s xml:id="echoid-s2699" xml:space="preserve">occidentis, ſunt´ gradus 25. </s>
  <s xml:id="echoid-s2700" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2701" xml:space="preserve">21. </s>
  <s xml:id="echoid-s2702" xml:space="preserve">in quibus quærendis laboratum eſt.</s>
  <s xml:id="echoid-s2703" xml:space="preserve"/>
</p>
<div xml:id="echoid-div79" type="float" level="2" n="1">
<note position="right" xlink:label="note-0047-05" xlink:href="note-0047-05a" xml:space="preserve"><emph style="it">Lateraliter</emph> <lb/><emph style="it">hoc aſſe-</emph> <lb/><emph style="it">queris.</emph></note>
<note position="right" xlink:label="note-0047-06" xlink:href="note-0047-06a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div81" type="section" level="1" n="45">
<head xml:id="echoid-head49" xml:space="preserve">PRONVNCIATVM XXXIII.</head>
<p>
  <s xml:id="echoid-s2704" xml:space="preserve">Angulum occidentis, quem eclyptica cum horizonte efficit in parte occi-<lb/>dua, prompte &amp; </s>
  <s xml:id="echoid-s2705" xml:space="preserve">facile inueſtigare.</s>
  <s xml:id="echoid-s2706" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2707" xml:space="preserve">Operæpreciũ nõ eſt hoc ꝓnunciatũ multis explicare, quũ ſuperiori 31. </s>
  <s xml:id="echoid-s2708" xml:space="preserve">planê ſimilis <lb/>fit, niſi q̊d hic addẽdũ eſt, ubi illic ſubtractũ, &amp; </s>
  <s xml:id="echoid-s2709" xml:space="preserve">uiciſsim ſubtrahẽdũ, ubi additũ eſt illic, qñ <lb/>
<anchor type="note" xlink:label="note-0047-07a" xlink:href="note-0047-07"/>
angulũ horizõtis et eclypticæ quærebas, ſicuti ſequens monſtrabit exemplũ. </s>
  <s xml:id="echoid-s2710" xml:space="preserve">?</s>
  <s xml:id="echoid-s2711" xml:space="preserve">? Cupio <lb/>ſcire angulũ quẽ facit eclyptica in 5. </s>
  <s xml:id="echoid-s2712" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2713" xml:space="preserve">25. </s>
  <s xml:id="echoid-s2714" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2715" xml:space="preserve">♌, cum horizonte occiduo, ex 31. </s>
  <s xml:id="echoid-s2716" xml:space="preserve">igitur
<pb file="0048" n="48" rhead="GENVINVS VSVS"/>
pronunciato iam inueni angulum, quem iuxta prædictũ gradum eclyptica cũ meridia-<lb/>no efficit, is autem eſt 75. </s>
  <s xml:id="echoid-s2717" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2718" xml:space="preserve">52. </s>
  <s xml:id="echoid-s2719" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2720" xml:space="preserve">Angulũ deinceps cõmunem ſic quæro, ſinũ eleuatio <lb/>nis poli 48. </s>
  <s xml:id="echoid-s2721" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2722" xml:space="preserve">ſcilicet 743 14. </s>
  <s xml:id="echoid-s2723" xml:space="preserve">quia minor eſt, duco in totũ, ꝓductũ diuido in ſinũ cõple <lb/>
<anchor type="note" xlink:label="note-0048-01a" xlink:href="note-0048-01"/>
menti declinationis 5. </s>
  <s xml:id="echoid-s2724" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2725" xml:space="preserve">25. </s>
  <s xml:id="echoid-s2726" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2727" xml:space="preserve">♌ qui eſt 94570. </s>
  <s xml:id="echoid-s2728" xml:space="preserve">in quotiente inueni 78581. </s>
  <s xml:id="echoid-s2729" xml:space="preserve">arcus eius <lb/>eſt 31. </s>
  <s xml:id="echoid-s2730" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2731" xml:space="preserve">48. </s>
  <s xml:id="echoid-s2732" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2733" xml:space="preserve">angulus ille communis, per quem inuenire poſſum angulũ orientalem <lb/>&amp; </s>
  <s xml:id="echoid-s2734" xml:space="preserve">occidentalem. </s>
  <s xml:id="echoid-s2735" xml:space="preserve">At quũ ♌ ſit ex ſignis deſcendentibus, angulũ hunc cõmunem ſub-<lb/>traho ab angulo meridiani &amp; </s>
  <s xml:id="echoid-s2736" xml:space="preserve">eclypticæ. </s>
  <s xml:id="echoid-s2737" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s2738" xml:space="preserve">75. </s>
  <s xml:id="echoid-s2739" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2740" xml:space="preserve">52. </s>
  <s xml:id="echoid-s2741" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2742" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2743" xml:space="preserve">remanent 24. </s>
  <s xml:id="echoid-s2744" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2745" xml:space="preserve">4. </s>
  <s xml:id="echoid-s2746" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2747" xml:space="preserve">an-<lb/>gulus ſcilicet eclypticæ &amp; </s>
  <s xml:id="echoid-s2748" xml:space="preserve">horizontis occidẽtalis. </s>
  <s xml:id="echoid-s2749" xml:space="preserve">?</s>
  <s xml:id="echoid-s2750" xml:space="preserve">? Vis adhuc aliud exemplũ, id´ de <lb/>
<anchor type="note" xlink:label="note-0048-02a" xlink:href="note-0048-02"/>
ſumptum ex medietate ſignorũ aſcendentiũ? </s>
  <s xml:id="echoid-s2751" xml:space="preserve">Ecce ꝓpono mibi 2. </s>
  <s xml:id="echoid-s2752" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2753" xml:space="preserve">26. </s>
  <s xml:id="echoid-s2754" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2755" xml:space="preserve">II, ubi ☉(sun) <lb/>fuit ipſo die intronizationis, iam autem inquirere cupio quantitatẽ anguli, quẽ facit ecly <lb/>ptica iuxta gradum illum cũ horizonte occidentali, per 26. </s>
  <s xml:id="echoid-s2756" xml:space="preserve">pronunc. </s>
  <s xml:id="echoid-s2757" xml:space="preserve">inueni angulũ eius <lb/>cum meridiano, qui erat 78. </s>
  <s xml:id="echoid-s2758" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2759" xml:space="preserve">37. </s>
  <s xml:id="echoid-s2760" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2761" xml:space="preserve">Nunc ergo ta ntũ quæro angulũ cõmunẽ, &amp; </s>
  <s xml:id="echoid-s2762" xml:space="preserve">hic <lb/>quidẽ adſumo ſinum altitudinis poli 48. </s>
  <s xml:id="echoid-s2763" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2764" xml:space="preserve">ſcilicet 74114. </s>
  <s xml:id="echoid-s2765" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2766" xml:space="preserve">ſinũ complementi declina <lb/>tionis gradus Solis, ſcilicet 93544. </s>
  <s xml:id="echoid-s2767" xml:space="preserve">ſinum altitudinis poli duco in ſinũ totũ, &amp; </s>
  <s xml:id="echoid-s2768" xml:space="preserve">ꝓductum <lb/>diuido in ſinũ alterũ, tunc quotiens producet 79442. </s>
  <s xml:id="echoid-s2769" xml:space="preserve">arcus eius eſt 52. </s>
  <s xml:id="echoid-s2770" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2771" xml:space="preserve">36. </s>
  <s xml:id="echoid-s2772" xml:space="preserve">min. </s>
  <s xml:id="echoid-s2773" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2774" xml:space="preserve">is ſa <lb/>
<anchor type="note" xlink:label="note-0048-03a" xlink:href="note-0048-03"/>
nè angulus eſt communis, quem ſi addam ad angulum meridiani &amp; </s>
  <s xml:id="echoid-s2775" xml:space="preserve">eclypticæ, inueniã <lb/>tunc 131. </s>
  <s xml:id="echoid-s2776" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2777" xml:space="preserve">13. </s>
  <s xml:id="echoid-s2778" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2779" xml:space="preserve">qui angulus eſt ſeptentrionalis eclypticæ &amp; </s>
  <s xml:id="echoid-s2780" xml:space="preserve">horizontis occidui, gra <lb/>dibus illis à ſemicirculo ſubtractis, remanent 48. </s>
  <s xml:id="echoid-s2781" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2782" xml:space="preserve">47. </s>
  <s xml:id="echoid-s2783" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2784" xml:space="preserve">angulus nimirũ eclypticæ <lb/>&amp; </s>
  <s xml:id="echoid-s2785" xml:space="preserve">horizontis occidui meridionalis, quem adeo anxie pequiſiuimus.</s>
  <s xml:id="echoid-s2786" xml:space="preserve"/>
</p>
<div xml:id="echoid-div81" type="float" level="2" n="1">
<note position="right" xlink:label="note-0047-07" xlink:href="note-0047-07a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
<note position="left" xlink:label="note-0048-01" xlink:href="note-0048-01a" xml:space="preserve"><emph style="it">Lateralis</emph> <lb/><emph style="it">ingreſſus</emph> <lb/><emph style="it">ſimile de-</emph> <lb/><emph style="it">prchendet.</emph></note>
<note position="left" xlink:label="note-0048-02" xlink:href="note-0048-02a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
<note position="left" xlink:label="note-0048-03" xlink:href="note-0048-03a" xml:space="preserve"><emph style="it">Arealis in-</emph> <lb/><emph style="it">greſſus.</emph></note>
</div>
</div>
<div xml:id="echoid-div83" type="section" level="1" n="46">
<head xml:id="echoid-head50" xml:space="preserve">PRONVNCIATVM XXXIIII.</head>
<p>
  <s xml:id="echoid-s2787" xml:space="preserve">Altitudinem Solis ſuper horizontem quotidie &amp; </s>
  <s xml:id="echoid-s2788" xml:space="preserve">in ſingulas horas toto <lb/>terrarum orbe ex ſolerti quadam ſupputatione colligere.</s>
  <s xml:id="echoid-s2789" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2790" xml:space="preserve">Hic principio præſcire operæpreciũ eſt ipſam Solis declinationẽ, eã ſubtrahe â 90. </s>
  <s xml:id="echoid-s2791" xml:space="preserve">re-<lb/>ſidui quære ſinũ rectũ, deinde etiã ſinũ rectũ differentiæ aſcenſionalis ex pronunciato 15. <lb/></s>
  <s xml:id="echoid-s2792" xml:space="preserve">habito ſinu differentiæ, colloca eum in regulã philoſophorũ, ſiue, ut alĳ loquũtur, de Trl, <lb/>in hunc modum, ultimo loco, primo aũt ſinũ totũ, &amp; </s>
  <s xml:id="echoid-s2793" xml:space="preserve">in medio ſinũ cõplementi declinatio <lb/>nis, ſi ergo ſecundũ operationẽ regulæ quotientẽ addas ad ſinũ cõplementi declinatiõis, <lb/>habebis tunc ſinũ huius operationis. </s>
  <s xml:id="echoid-s2794" xml:space="preserve">Mox ꝓpone etiã horã uel ante uel pomeridianã ad <lb/>quamcũ cupis ſcire Solis altitudinẽ, horã illã aut horas (ſi modo plures fuerint) redige <lb/>in gradus, quo℞ ſemꝑ 15. </s>
  <s xml:id="echoid-s2795" xml:space="preserve">ꝓ hora cõnumeres, gradus eos horarũ ſubduc à 90. </s>
  <s xml:id="echoid-s2796" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2797" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2798" xml:space="preserve">reſi-<lb/>dui ſinũ quære rectũ, ipſum´ ſubtrahe à ſinu toto, reſiduũ uocabit̃ ſinus uerſus horarũ, <lb/>eũ ſinũ uerſum cõpone in regulã ꝓportionũ tertio loco, primo aũt ſinũ totũ, &amp; </s>
  <s xml:id="echoid-s2799" xml:space="preserve">in medio <lb/>ſinũ cõplemẽti declinationis Solis, operatiõe illa ad præſcriptũ regulæ perfecta, ſubtra-<lb/>he q̊tientẽ à ſinu huius operatiõis toto, &amp; </s>
  <s xml:id="echoid-s2800" xml:space="preserve">reſiduũ rurſus cõpone in poſtremũ regulæ, pri-<lb/>mo aũt ſinũ totũ, &amp; </s>
  <s xml:id="echoid-s2801" xml:space="preserve">in medio ſinũ cõplementi altitudinis poli, quicquid ex hac operatio <lb/>ne prouenerit, ſinus eſt altitudinis Solis ad horã ꝓpoſitã. </s>
  <s xml:id="echoid-s2802" xml:space="preserve">Vnum hoc admonendus es mi <lb/>hi, ꝙ operatio talis, ſicut à nobis deſcripta hactenus eſt, ueritatem quidẽ obtinet, ſed Sole <lb/>exiſtente in ſignis ſeptẽtrionalibus, qui ſi forſitan in meridionalibus fuerit, tũc ſubtrahen <lb/>dus à ſinu cõplementi declinatiõis, eſt ſinus differentiæ aſcenſionalis, cõuerſus iam per re <lb/>gulã ꝓportionũ, &amp; </s>
  <s xml:id="echoid-s2803" xml:space="preserve">ſic reliquus tibi manebit ſinus ꝑfectus huius oꝑationis. </s>
  <s xml:id="echoid-s2804" xml:space="preserve">?</s>
  <s xml:id="echoid-s2805" xml:space="preserve">? Quam ut <lb/>
<anchor type="note" xlink:label="note-0048-04a" xlink:href="note-0048-04"/>
intelligas cõmodius, en exemplũ tibi ꝓponimus huiuſmodi. </s>
  <s xml:id="echoid-s2806" xml:space="preserve">Cupio forte ſcire altitudinẽ <lb/>☉(sun) ad ipſam horã intronizationis, q̊ fuit Sol, ſicuti ſæpe diximus, in 2. </s>
  <s xml:id="echoid-s2807" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2808" xml:space="preserve">26. </s>
  <s xml:id="echoid-s2809" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2810" xml:space="preserve">II, decli <lb/>nationẽ eius inueni ꝓnunciato 5. </s>
  <s xml:id="echoid-s2811" xml:space="preserve">20. </s>
  <s xml:id="echoid-s2812" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2813" xml:space="preserve">18. </s>
  <s xml:id="echoid-s2814" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2815" xml:space="preserve">quibus ſubtractis à 90. </s>
  <s xml:id="echoid-s2816" xml:space="preserve">remanẽt 69. </s>
  <s xml:id="echoid-s2817" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s2818" xml:space="preserve">18. </s>
  <s xml:id="echoid-s2819" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2820" xml:space="preserve">ſinus illius 93544. </s>
  <s xml:id="echoid-s2821" xml:space="preserve">eſt, qui numerus in hac ſupputatione, ꝗa frequẽtiſsime uſurpa <lb/>tur, ideo etiã creditur eſſe oĩm ꝑfectiſsimus. </s>
  <s xml:id="echoid-s2822" xml:space="preserve">Deinde per 15. </s>
  <s xml:id="echoid-s2823" xml:space="preserve">ꝓnunciatũ adinueni differen <lb/>tiã aſcenſionalẽ 24. </s>
  <s xml:id="echoid-s2824" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2825" xml:space="preserve">49. </s>
  <s xml:id="echoid-s2826" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2827" xml:space="preserve">ſinũ quo eius 41971. </s>
  <s xml:id="echoid-s2828" xml:space="preserve">cõuerto, ita, ut uter fiat æqualis <lb/>ſinui cõplementi declinationis, quia locũ gerũt totius cuiuſdã ſinus. </s>
  <s xml:id="echoid-s2829" xml:space="preserve">Pono ergo 100000. </s>
  <s xml:id="echoid-s2830" xml:space="preserve"><lb/>in primũ locum, deinde ſinum cõplementi declinationis Solis, ſcilicet 93544. </s>
  <s xml:id="echoid-s2831" xml:space="preserve">poſtremò <lb/>ſinum huius differentiæ 41971. </s>
  <s xml:id="echoid-s2832" xml:space="preserve">hinc operor multiplicando &amp; </s>
  <s xml:id="echoid-s2833" xml:space="preserve">diuidendo iuxta regulam <lb/>ꝓportionũ, &amp; </s>
  <s xml:id="echoid-s2834" xml:space="preserve">inuenio in q̊tiente 39261. </s>
  <s xml:id="echoid-s2835" xml:space="preserve">ea addo(quando quidẽ ſignũ ☉(sun) eſt in medieta-<lb/>te ſeptẽtrionali) ad ſinũ cõplemẽti declinatiõis Solis, &amp; </s>
  <s xml:id="echoid-s2836" xml:space="preserve">ꝓueniet talis ſumma 132805. </s>
  <s xml:id="echoid-s2837" xml:space="preserve">ſi-<lb/>nus. </s>
  <s xml:id="echoid-s2838" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s2839" xml:space="preserve">perfectus huius operationis. </s>
  <s xml:id="echoid-s2840" xml:space="preserve">Adhuc deinceps ex 3. </s>
  <s xml:id="echoid-s2841" xml:space="preserve">horis feci gradus 45. </s>
  <s xml:id="echoid-s2842" xml:space="preserve">eas ſub-
<pb file="0049" n="49" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
traho à 90. </s>
  <s xml:id="echoid-s2843" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2844" xml:space="preserve">reliqui ſunt gradus 45. </s>
  <s xml:id="echoid-s2845" xml:space="preserve">ſinus eſt 70710. </s>
  <s xml:id="echoid-s2846" xml:space="preserve">quo ſubtracto à ſinu toto, manent <lb/>29290. </s>
  <s xml:id="echoid-s2847" xml:space="preserve">ſinus ille uerſus trium horarum, quos etiam conuertere oportet, ſicut in differẽtia <lb/>aſcenſionali factum eſt, ſic enim regula cõſtituenda eſt proportionũ, 100000 dant 93544 <lb/>quid igitur proueniet ex 29290? </s>
  <s xml:id="echoid-s2848" xml:space="preserve">iuxta operationem inuenio 27399. </s>
  <s xml:id="echoid-s2849" xml:space="preserve">ea ſubtraho à ſinu to <lb/>to huius operationis, &amp; </s>
  <s xml:id="echoid-s2850" xml:space="preserve">remanent 105406. </s>
  <s xml:id="echoid-s2851" xml:space="preserve">At ſic rurſus propo@o regulam, 100000. <lb/></s>
  <s xml:id="echoid-s2852" xml:space="preserve">dant 66913. </s>
  <s xml:id="echoid-s2853" xml:space="preserve">(qui ſinus eſt complementi altitudinis poli) quid da@unt 105406? </s>
  <s xml:id="echoid-s2854" xml:space="preserve">inde aũt <lb/>per multiplicationem &amp; </s>
  <s xml:id="echoid-s2855" xml:space="preserve">diuiſionem reſultant in quotiente 70530. </s>
  <s xml:id="echoid-s2856" xml:space="preserve">arcus illius 44. </s>
  <s xml:id="echoid-s2857" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2858" xml:space="preserve"><lb/>52. </s>
  <s xml:id="echoid-s2859" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2860" xml:space="preserve">quibus manifeſta fit altitudo Solis tantopere quæſita.</s>
  <s xml:id="echoid-s2861" xml:space="preserve"/>
</p>
<div xml:id="echoid-div83" type="float" level="2" n="1">
<note position="left" xlink:label="note-0048-04" xlink:href="note-0048-04a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div85" type="section" level="1" n="47">
<head xml:id="echoid-head51" xml:space="preserve">PRONVNCIATVM XXXV.</head>
<p>
  <s xml:id="echoid-s2862" xml:space="preserve">Eandem Solis altitudinem ſuper horizõtem quacun hora, &amp; </s>
  <s xml:id="echoid-s2863" xml:space="preserve">ubiuis gen <lb/>tium diuerſaratione indagare.</s>
  <s xml:id="echoid-s2864" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2865" xml:space="preserve">Vbi iã ex 31. </s>
  <s xml:id="echoid-s2866" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2867" xml:space="preserve">32. </s>
  <s xml:id="echoid-s2868" xml:space="preserve">pronunc. </s>
  <s xml:id="echoid-s2869" xml:space="preserve">angulũ didiciſti aſcẽdentis, deinde &amp; </s>
  <s xml:id="echoid-s2870" xml:space="preserve">aſcendentis gradũ <lb/>
<anchor type="note" xlink:label="note-0049-01a" xlink:href="note-0049-01"/>
ex pronunc. </s>
  <s xml:id="echoid-s2871" xml:space="preserve">30, mox à gradu Solis numera uſ ad gradũ aſcendentis, ſinũ eius duc in ſi-<lb/>num anguli eclypticæ &amp; </s>
  <s xml:id="echoid-s2872" xml:space="preserve">horizontis, ꝓductũ diuide in ſinũ totũ, hinc ſi quæras quotiẽtis <lb/>arcũ, is ipſe arguit altitudinẽ Solis quã quærebas. </s>
  <s xml:id="echoid-s2873" xml:space="preserve">Atqui etiã hoc tibi obſeruandum eſt, ꝙ <lb/>ſemper duæ horæ, altera ante, altera poſt meridiem æ qualẽ habent altitudinẽ, puta ante <lb/>&amp; </s>
  <s xml:id="echoid-s2874" xml:space="preserve">poſt meridiẽ æqualiter cõputãdo, ſic em̃ 11. </s>
  <s xml:id="echoid-s2875" xml:space="preserve">ante meridiẽ &amp; </s>
  <s xml:id="echoid-s2876" xml:space="preserve">prima pomeridiana eandẽ <lb/>habent altitudinẽ, ſimiliter &amp; </s>
  <s xml:id="echoid-s2877" xml:space="preserve">10. </s>
  <s xml:id="echoid-s2878" xml:space="preserve">ante &amp; </s>
  <s xml:id="echoid-s2879" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2880" xml:space="preserve">poſt meridiẽ &amp;</s>
  <s xml:id="echoid-s2881" xml:space="preserve">c. </s>
  <s xml:id="echoid-s2882" xml:space="preserve">Inuenta igitur altitudine una <lb/>quacũ tandem, ſiue ante ſiue poſt meridiem, alterã amplius quærere neceſſe nõ eſt. <lb/></s>
  <s xml:id="echoid-s2883" xml:space="preserve">?</s>
  <s xml:id="echoid-s2884" xml:space="preserve">? Vis &amp; </s>
  <s xml:id="echoid-s2885" xml:space="preserve">hic exemplũ dari tibi, ne fruſtra laboraſſe uideamur? </s>
  <s xml:id="echoid-s2886" xml:space="preserve">Ecce ex propoſitione 30. </s>
  <s xml:id="echoid-s2887" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0049-02a" xlink:href="note-0049-02"/>
inueni ſub ipſam horã intronizationis 5. </s>
  <s xml:id="echoid-s2888" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2889" xml:space="preserve">25. </s>
  <s xml:id="echoid-s2890" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2891" xml:space="preserve">♌ fuiſſe in aſcendente, deinde ꝑ 31. <lb/></s>
  <s xml:id="echoid-s2892" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2893" xml:space="preserve">32. </s>
  <s xml:id="echoid-s2894" xml:space="preserve">propoſitiones inueni etiã angulũ eclypticæ &amp; </s>
  <s xml:id="echoid-s2895" xml:space="preserve">horizontis 52. </s>
  <s xml:id="echoid-s2896" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2897" xml:space="preserve">21. </s>
  <s xml:id="echoid-s2898" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2899" xml:space="preserve">Nũc por-<lb/>rò accipienda mihi eſt diſtantia gradus Solis à gradu aſcendẽtis, ea´ eſt 62. </s>
  <s xml:id="echoid-s2900" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2901" xml:space="preserve">59. </s>
  <s xml:id="echoid-s2902" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2903" xml:space="preserve"><lb/>Contingit etiam interdum, ꝙ diſtantia Solis ab aſcendente maior ſit 90. </s>
  <s xml:id="echoid-s2904" xml:space="preserve">gradibus, &amp; </s>
  <s xml:id="echoid-s2905" xml:space="preserve">tũc <lb/>ſanè diſtantia illa ſubtrahenda tibi eſt à ſemicirculo, &amp; </s>
  <s xml:id="echoid-s2906" xml:space="preserve">remanebit arcus uerus huius ope <lb/>rationis. </s>
  <s xml:id="echoid-s2907" xml:space="preserve">Iam propono mihi ſinũ anguli 52. </s>
  <s xml:id="echoid-s2908" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2909" xml:space="preserve">21. </s>
  <s xml:id="echoid-s2910" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2911" xml:space="preserve">ſcilicet 79175. </s>
  <s xml:id="echoid-s2912" xml:space="preserve">eũ duco in ſinũ ar-<lb/>cus à gradu Solis ad gradũ aſcendentis, qui fuit 62. </s>
  <s xml:id="echoid-s2913" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2914" xml:space="preserve">59. </s>
  <s xml:id="echoid-s2915" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2916" xml:space="preserve">89087. </s>
  <s xml:id="echoid-s2917" xml:space="preserve">ſi ergo unũ in alte <lb/>rũ duxero, productũ in ſinũ totũ diuiſero, prouenient in quotiente 70534. </s>
  <s xml:id="echoid-s2918" xml:space="preserve">arcus eius eſt <lb/>44. </s>
  <s xml:id="echoid-s2919" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2920" xml:space="preserve">52. </s>
  <s xml:id="echoid-s2921" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2922" xml:space="preserve">altitudo nimirũ Solis ad horam, imò &amp; </s>
  <s xml:id="echoid-s2923" xml:space="preserve">minutum ipſius intronizationis.</s>
  <s xml:id="echoid-s2924" xml:space="preserve"/>
</p>
<div xml:id="echoid-div85" type="float" level="2" n="1">
<note position="right" xlink:label="note-0049-01" xlink:href="note-0049-01a" xml:space="preserve"><emph style="it">Lateraliter</emph> <lb/><emph style="it">in quadran</emph> <lb/><emph style="it">te hoc perſi</emph> <lb/><emph style="it">aes.</emph></note>
<note position="right" xlink:label="note-0049-02" xlink:href="note-0049-02a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div87" type="section" level="1" n="48">
<head xml:id="echoid-head52" xml:space="preserve">PRONVNCIATVM XXXVI.</head>
<p>
  <s xml:id="echoid-s2925" xml:space="preserve">Rurſus alio modo cognoſcere altitudinem Solis ſuper horizontem, omni <lb/>die &amp; </s>
  <s xml:id="echoid-s2926" xml:space="preserve">momento per uniuerſum terrarum orbem.</s>
  <s xml:id="echoid-s2927" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2928" xml:space="preserve">Operæpreciũ hic principio fuerit noſſe cõplemẽtũ altitudinis poli &amp; </s>
  <s xml:id="echoid-s2929" xml:space="preserve">declinatiõem So <lb/>lis, deinde q̊ diſtantiã Solis à meridiano, hoc eſt diſtantiã horariã, puta q̊t horis ante uel <lb/>
<anchor type="note" xlink:label="note-0049-03a" xlink:href="note-0049-03"/>
poſt meridiẽ altitudo illa Solis debeat ſupputari. </s>
  <s xml:id="echoid-s2930" xml:space="preserve">Primũ ita oĩm duc ſinũ cõplemẽti de <lb/>clinatiõis Solis in ſinũ diſtãtiæ ante uel poſt meridiẽ, ꝓductũ diuide in ſinũ totũ, &amp; </s>
  <s xml:id="echoid-s2931" xml:space="preserve">quo-<lb/>tientẽ ſepone ſeorſim, qm̃ is eſt ſinus arcus diſtãtiæ Solis ab ortu æquatoris, quotiẽti op-<lb/>
<anchor type="note" xlink:label="note-0049-04a" xlink:href="note-0049-04"/>
pone ſinũ declinationis minorẽ, &amp; </s>
  <s xml:id="echoid-s2932" xml:space="preserve">duc in ſinũ totũ, ꝓductũ in maiorẽ diuide, &amp; </s>
  <s xml:id="echoid-s2933" xml:space="preserve">arcũ quo <lb/>tientis adde ad cõplementũ altitudinis poli, Sole exiſtente in ſigno aliquo ſeptentrionali <lb/>uel ſubtrahe ab eo ubi Sol fuerit in aliquo ſignorũ meridionaliũ, quicꝗd ex hac ſiue addi-<lb/>tione ſiue ſubtractione ꝓuenerit, uel reliquũ manſerit, dicet̃ angulus operationis, ꝗ ſi fue-<lb/>erit quadrãs circuli, iã ipſe ꝑ ſe oſtẽdit altitudinẽ Solis quæſitã, quã antea altitudinẽ Solis <lb/>uerticalẽ diximus. </s>
  <s xml:id="echoid-s2934" xml:space="preserve">Qđ ſi autẽ angulus operatiõis maior fuerit ̈ 90. </s>
  <s xml:id="echoid-s2935" xml:space="preserve">ſubtrahe eũ à ſemicir <lb/>culo, &amp; </s>
  <s xml:id="echoid-s2936" xml:space="preserve">tunc tandẽ remanebit angulus uerus operatiõis, ſinũ anguli huius duc in ſinũ pri <lb/>
<anchor type="note" xlink:label="note-0049-05a" xlink:href="note-0049-05"/>
mi q̊tientis, ꝓductũ diuide cum ſinu toto, &amp; </s>
  <s xml:id="echoid-s2937" xml:space="preserve">arcus quotientis mõſtrabit altitudinem Solis <lb/>quã quærebas, ſed exemplo adiuncto melius operationẽ hanc intelliges. </s>
  <s xml:id="echoid-s2938" xml:space="preserve">?</s>
  <s xml:id="echoid-s2939" xml:space="preserve">? Iterũ hic <lb/>
<anchor type="note" xlink:label="note-0049-06a" xlink:href="note-0049-06"/>
mihi ꝓpono horã intronizationis ampliſsimi patris &amp; </s>
  <s xml:id="echoid-s2940" xml:space="preserve">ornatiſsimi Præſulis Auguſtẽſis <lb/>quæ fuit hora 9. </s>
  <s xml:id="echoid-s2941" xml:space="preserve">ante meridiẽ, eius diſtãtia à meridie eſt 3. </s>
  <s xml:id="echoid-s2942" xml:space="preserve">horarũ, ꝗ ſunt gradus 45. </s>
  <s xml:id="echoid-s2943" xml:space="preserve">ſemꝑ <lb/>em̃ in una hora oriunt̃ 15. </s>
  <s xml:id="echoid-s2944" xml:space="preserve">gradus æquino ctialis ſuꝑ horizontẽ ab ortu uerſus occaſum, ſi <lb/>nus illius eſt 70710. </s>
  <s xml:id="echoid-s2945" xml:space="preserve">declinatio Solis 20. </s>
  <s xml:id="echoid-s2946" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2947" xml:space="preserve">42. </s>
  <s xml:id="echoid-s2948" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2949" xml:space="preserve">cõplementũ eius 69. </s>
  <s xml:id="echoid-s2950" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2951" xml:space="preserve">18. </s>
  <s xml:id="echoid-s2952" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2953" xml:space="preserve">ſinus <lb/>uero 93544. </s>
  <s xml:id="echoid-s2954" xml:space="preserve">ſinũ iſto℞ ſi duxero in alterũ, productũ autem diuiſero in ſinum totum, pro-
<pb file="0050" n="50" rhead="GENVINVS VSVS"/>
uenient in quotiente 66145. </s>
  <s xml:id="echoid-s2955" xml:space="preserve">arcus eius eſt 41. </s>
  <s xml:id="echoid-s2956" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2957" xml:space="preserve">25. </s>
  <s xml:id="echoid-s2958" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2959" xml:space="preserve">eum ſubtraho à 90. </s>
  <s xml:id="echoid-s2960" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2961" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2962" xml:space="preserve">re-<lb/>manent 48. </s>
  <s xml:id="echoid-s2963" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2964" xml:space="preserve">35. </s>
  <s xml:id="echoid-s2965" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2966" xml:space="preserve">quæ diſtantia eſt Solis ab ortu æquatoris, eam repono in locum <lb/>ſingularem, &amp; </s>
  <s xml:id="echoid-s2967" xml:space="preserve">ſimul etiam ſinum illius diſtantiæ, ſcilicet 74991. </s>
  <s xml:id="echoid-s2968" xml:space="preserve">deinde quo ſinum decli <lb/>nationis Solis, qui quia minor eſt, duco eum in ſinum totum, productum diuido in maio-<lb/>rem, &amp; </s>
  <s xml:id="echoid-s2969" xml:space="preserve">prodeunt in quotiente 47135. </s>
  <s xml:id="echoid-s2970" xml:space="preserve">arcus quotientis illius eſt 28. </s>
  <s xml:id="echoid-s2971" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2972" xml:space="preserve">8. </s>
  <s xml:id="echoid-s2973" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2974" xml:space="preserve">Et quia ☉(sun) <lb/>eſt in ſigno ſeptentrionali, addo eum ad complementum altitudinis poli, ſcilicet 42. </s>
  <s xml:id="echoid-s2975" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s2976" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2977" xml:space="preserve">proueniunt 70. </s>
  <s xml:id="echoid-s2978" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2979" xml:space="preserve">8. </s>
  <s xml:id="echoid-s2980" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2981" xml:space="preserve">angulus ille operationis, cuius anguli ſinum ſcilicet 94048. </s>
  <s xml:id="echoid-s2982" xml:space="preserve"><lb/>ſi ducam in ſinum diſtantiæ Solis ab ortu æquinoctialis, ſcilicet 74991. </s>
  <s xml:id="echoid-s2983" xml:space="preserve">productum diui-<lb/>dam in ſinum totum, prodibunt in quotiente 70528. </s>
  <s xml:id="echoid-s2984" xml:space="preserve">arcus eius eſt 44. </s>
  <s xml:id="echoid-s2985" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s2986" xml:space="preserve">52. </s>
  <s xml:id="echoid-s2987" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s2988" xml:space="preserve">altitu-<lb/>do Solis quæſita, &amp; </s>
  <s xml:id="echoid-s2989" xml:space="preserve">hanc iam tertia ratione æqualiter inuenta.</s>
  <s xml:id="echoid-s2990" xml:space="preserve"/>
</p>
<div xml:id="echoid-div87" type="float" level="2" n="1">
<note position="right" xlink:label="note-0049-03" xlink:href="note-0049-03a" xml:space="preserve"><emph style="it">Lateralis</emph> <lb/><emph style="it">introitus.</emph></note>
<note position="right" xlink:label="note-0049-04" xlink:href="note-0049-04a" xml:space="preserve"><emph style="it">Arealis.</emph></note>
<note position="right" xlink:label="note-0049-05" xlink:href="note-0049-05a" xml:space="preserve"><emph style="it">Lateralis.</emph></note>
<note position="right" xlink:label="note-0049-06" xlink:href="note-0049-06a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div89" type="section" level="1" n="49">
<head xml:id="echoid-head53" xml:space="preserve">PRONVNCIATVM XXXVII.</head>
<p>
  <s xml:id="echoid-s2991" xml:space="preserve">Adhuc diuerſa uia eandem Solis altitudinem ſupra horizontem in qua-<lb/>cun eleuatione poli depræhendere.</s>
  <s xml:id="echoid-s2992" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2993" xml:space="preserve">Hic propones primo tibi diſtantiam medĳ cœli ab ortu uel occaſu, utrolibet tandem <lb/>
<anchor type="note" xlink:label="note-0050-01a" xlink:href="note-0050-01"/>
propius acceſſerit, deinde &amp; </s>
  <s xml:id="echoid-s2994" xml:space="preserve">altitudinem meridianam, hoc eſt ̈ ſublimis ſit gradus ille ab <lb/>horizonte, qui attingit medium cœli, minorem ex ĳs duces in ſinum totum, productum <lb/>diuides in maiorem, &amp; </s>
  <s xml:id="echoid-s2995" xml:space="preserve">quotientem rurſus duces in ſinum diſtantiæ Solis ab aſcendente <lb/>&amp; </s>
  <s xml:id="echoid-s2996" xml:space="preserve">arcus quotientis monſtrabit tibi altitudinem Solis optatam. </s>
  <s xml:id="echoid-s2997" xml:space="preserve">Quod ſi autem principi-<lb/>
<anchor type="note" xlink:label="note-0050-02a" xlink:href="note-0050-02"/>
um ♋ uel ♑ obtinuerit medium cœli, propones tibi utrũ ſuum altitudinis meridianæ <lb/>&amp; </s>
  <s xml:id="echoid-s2998" xml:space="preserve">diſtãtiæ Solis ab oriente uel occidente, minorem duces in ſinum totum, productum <lb/>diuides in maiorem, tunc arcus quotientis oſtendet altitudinem quæſitam. </s>
  <s xml:id="echoid-s2999" xml:space="preserve">Sciendum eti-<lb/>am eſt, quod primus quotiens deſignat angulum, quem facit horizon cum eclyptica in <lb/>
<anchor type="note" xlink:label="note-0050-03a" xlink:href="note-0050-03"/>
eo ipſo momento. </s>
  <s xml:id="echoid-s3000" xml:space="preserve">?</s>
  <s xml:id="echoid-s3001" xml:space="preserve">? Exemplum hic quo accipe tale, ſi cupiam rurſus ſcire altitudi-<lb/>nem Solis ad horam intronizationis 9. </s>
  <s xml:id="echoid-s3002" xml:space="preserve">ante meridiem, quo tempore eſto, ut Sol fuerit in <lb/>2. </s>
  <s xml:id="echoid-s3003" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3004" xml:space="preserve">26. </s>
  <s xml:id="echoid-s3005" xml:space="preserve">mi II, altitudo meridiana eſt 48. </s>
  <s xml:id="echoid-s3006" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3007" xml:space="preserve">34. </s>
  <s xml:id="echoid-s3008" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3009" xml:space="preserve">ſinus eius 74972. </s>
  <s xml:id="echoid-s3010" xml:space="preserve">eũ duco in ſinum <lb/>totũ, ꝓductum diuido in ſinum diſtantiæ grad. </s>
  <s xml:id="echoid-s3011" xml:space="preserve">medĳ cœli ab occaſu, medium aũt cœli, <lb/>ut antea diximus, eſt 16. </s>
  <s xml:id="echoid-s3012" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3013" xml:space="preserve">40. </s>
  <s xml:id="echoid-s3014" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3015" xml:space="preserve">♈, &amp; </s>
  <s xml:id="echoid-s3016" xml:space="preserve">quia mediũ illud cœli propinquius eſt occiden <lb/>ti ̈ ortui, diſtãtia eius eſt 71. </s>
  <s xml:id="echoid-s3017" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3018" xml:space="preserve">15. </s>
  <s xml:id="echoid-s3019" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3020" xml:space="preserve">ſinus uero 94693. </s>
  <s xml:id="echoid-s3021" xml:space="preserve">ſi in eum diuidam productũ, <lb/>prouenient in quotiente 79182. </s>
  <s xml:id="echoid-s3022" xml:space="preserve">angulus ſcilicet horizontis orientalis &amp; </s>
  <s xml:id="echoid-s3023" xml:space="preserve">eclypticæ, quo-<lb/>tientem iſtum duco rurſus in ſinũ diſtantiæ gradus Solis ab aſcendente, quæ eſt 62. </s>
  <s xml:id="echoid-s3024" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s3025" xml:space="preserve">59. </s>
  <s xml:id="echoid-s3026" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3027" xml:space="preserve">ſinus eius eſt 89087. </s>
  <s xml:id="echoid-s3028" xml:space="preserve">productum diuido in ſinum totum, &amp; </s>
  <s xml:id="echoid-s3029" xml:space="preserve">in quotiente proueni-<lb/>unt 70540. </s>
  <s xml:id="echoid-s3030" xml:space="preserve">arcus eius eſt 44. </s>
  <s xml:id="echoid-s3031" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3032" xml:space="preserve">22. </s>
  <s xml:id="echoid-s3033" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3034" xml:space="preserve">altitudo eadem quam ſuperius inueneram.</s>
  <s xml:id="echoid-s3035" xml:space="preserve"/>
</p>
<div xml:id="echoid-div89" type="float" level="2" n="1">
<note position="left" xlink:label="note-0050-01" xlink:href="note-0050-01a" xml:space="preserve"><emph style="it">Areatim</emph> <lb/><emph style="it">quærenti</emph> <lb/><emph style="it">apparet.</emph></note>
<note position="left" xlink:label="note-0050-02" xlink:href="note-0050-02a" xml:space="preserve"><emph style="it">Areatim</emph> <lb/><emph style="it">quoq; illud</emph> <lb/><emph style="it">perfiaes.</emph></note>
<note position="left" xlink:label="note-0050-03" xlink:href="note-0050-03a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſcopi.</emph></note>
</div>
</div>
<div xml:id="echoid-div91" type="section" level="1" n="50">
<head xml:id="echoid-head54" xml:space="preserve">PRONVNCIATVM XXXVIII.</head>
<p>
  <s xml:id="echoid-s3036" xml:space="preserve">Etiamnum alia ratione altitudinem illam Solis ſupra horizontem ubiuis <lb/>locorum pulchre &amp; </s>
  <s xml:id="echoid-s3037" xml:space="preserve">expedite cognoſcere.</s>
  <s xml:id="echoid-s3038" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3039" xml:space="preserve">Modus hic etſi ſuperioribus aliquãto prolixior eſt, attamen cum ipſa longitudine ſi-<lb/>mul multã ſecũ iucunditatẽ affert, ſic aũt habet. </s>
  <s xml:id="echoid-s3040" xml:space="preserve">Sol hic oibus conſpicuus, uel à meridiano <lb/>diſtat præciſe gradibus 90. </s>
  <s xml:id="echoid-s3041" xml:space="preserve">at ea ſemꝑ hora 6. </s>
  <s xml:id="echoid-s3042" xml:space="preserve">eſt, uel amplius 90. </s>
  <s xml:id="echoid-s3043" xml:space="preserve">gradibus, ut ſi ante 6. <lb/></s>
  <s xml:id="echoid-s3044" xml:space="preserve">horã, uel ad 4. </s>
  <s xml:id="echoid-s3045" xml:space="preserve">uel 5. </s>
  <s xml:id="echoid-s3046" xml:space="preserve">cupias ſcire altitudinẽ, uel deni nõ tantũ diſtat à meridiano, ut per-<lb/>tingat uſ in 90. </s>
  <s xml:id="echoid-s3047" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3048" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3049" xml:space="preserve">tales ſunt reliquæ horæ oẽs à 6. </s>
  <s xml:id="echoid-s3050" xml:space="preserve">uſ in 12. </s>
  <s xml:id="echoid-s3051" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3052" xml:space="preserve">ſimiliter à 12. </s>
  <s xml:id="echoid-s3053" xml:space="preserve">uſ in <lb/>6. </s>
  <s xml:id="echoid-s3054" xml:space="preserve">pomeridianã. </s>
  <s xml:id="echoid-s3055" xml:space="preserve">Si ergo præciſe ad horã 6. </s>
  <s xml:id="echoid-s3056" xml:space="preserve">cupis ſcire altitudinẽ ante uel poſt meridiem, <lb/>quia horæ 6. </s>
  <s xml:id="echoid-s3057" xml:space="preserve">faciunt gra. </s>
  <s xml:id="echoid-s3058" xml:space="preserve">90. </s>
  <s xml:id="echoid-s3059" xml:space="preserve">debes etiã huc referre horas ab ortu &amp; </s>
  <s xml:id="echoid-s3060" xml:space="preserve">occaſu, quoniam ea-<lb/>
<anchor type="note" xlink:label="note-0050-04a" xlink:href="note-0050-04"/>
rum unaquæ poteſt 90. </s>
  <s xml:id="echoid-s3061" xml:space="preserve">gradibus à meridie diſtare, tunc ita ſi altitudinem ſcire cupis, <lb/>duc ſinũ eleuationis poli in ſinũ declinationis ☉(sun), &amp; </s>
  <s xml:id="echoid-s3062" xml:space="preserve">diuide productũ in ſinũ totũ, arcus q̊-<lb/>tientis mõſtrabit altitudinẽ ☉(sun) ad eã horam. </s>
  <s xml:id="echoid-s3063" xml:space="preserve">?</s>
  <s xml:id="echoid-s3064" xml:space="preserve">? Vis exemplũ? </s>
  <s xml:id="echoid-s3065" xml:space="preserve">en tibi dabimus huiuſmo <lb/>di. </s>
  <s xml:id="echoid-s3066" xml:space="preserve">Cupio ſcire altitudinem Solis ſupra horizontẽ in die intronizationis ante meridiem, <lb/>
<anchor type="note" xlink:label="note-0050-05a" xlink:href="note-0050-05"/>
qñ declinatio ☉(sun) fuit 20. </s>
  <s xml:id="echoid-s3067" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3068" xml:space="preserve">42. </s>
  <s xml:id="echoid-s3069" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3070" xml:space="preserve">ſinũ eius 35342. </s>
  <s xml:id="echoid-s3071" xml:space="preserve">duco in ſinũ 48. </s>
  <s xml:id="echoid-s3072" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3073" xml:space="preserve">eleuationis poli <lb/>74314. </s>
  <s xml:id="echoid-s3074" xml:space="preserve">productũ diuido in ſinũ totũ, &amp; </s>
  <s xml:id="echoid-s3075" xml:space="preserve">quotiens erit 26267. </s>
  <s xml:id="echoid-s3076" xml:space="preserve">arcus 15. </s>
  <s xml:id="echoid-s3077" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3078" xml:space="preserve">14. </s>
  <s xml:id="echoid-s3079" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3080" xml:space="preserve">altitu-<lb/>dinem deſignat quæſitã horæ 6. </s>
  <s xml:id="echoid-s3081" xml:space="preserve">ante &amp; </s>
  <s xml:id="echoid-s3082" xml:space="preserve">poſt meridiem. </s>
  <s xml:id="echoid-s3083" xml:space="preserve">Porrò ſi diſtantia Solis à meridia-<lb/>no quadrante fuerit minor, tunc ducito ſinũ huius diſtantiæ in ſinum cõplementialtitudi <lb/>nis poli, &amp; </s>
  <s xml:id="echoid-s3084" xml:space="preserve">hinc diuide per ſinũ totũ, arcus quotientis ex quadra circuli demptus, relinquet <lb/>
<anchor type="note" xlink:label="note-0050-06a" xlink:href="note-0050-06"/>
inuentum primum. </s>
  <s xml:id="echoid-s3085" xml:space="preserve">Mox eius inuenti tibi propone ſinũ, ſimiliter &amp; </s>
  <s xml:id="echoid-s3086" xml:space="preserve">ſinum altitudinis po
<pb file="0051" n="51" rhead="TABVLARVM SINVVM."/>
li, minorem duc in totum, ꝓductũ diuide in maiorem, &amp; </s>
  <s xml:id="echoid-s3087" xml:space="preserve">arcũ quotientis ſubtrahe à 90, <lb/>
<anchor type="note" xlink:label="note-0051-01a" xlink:href="note-0051-01"/>
ad reſiduũ adde declinationẽ ☉(sun), ſi Borealis fuerit, uel ſubtrahe, ſi extiterit meridionalis, <lb/>reſiduũ uel ꝓductũ illud, ſi quadrante minus fuerit, oſtendet inuentũ ſecundũ: </s>
  <s xml:id="echoid-s3088" xml:space="preserve">ſin maius, <lb/>
<anchor type="note" xlink:label="note-0051-02a" xlink:href="note-0051-02"/>
ſubtrahendũ erit à 90. </s>
  <s xml:id="echoid-s3089" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3090" xml:space="preserve">reliquũ q̊d manſerit, dicetur inuentũ ſecundũ. </s>
  <s xml:id="echoid-s3091" xml:space="preserve">Vtrun illud in-<lb/>uentum propone tibi, &amp; </s>
  <s xml:id="echoid-s3092" xml:space="preserve">alterius ſinũ itidem duc in ſinũ alterius, productũ diuide in ſinũ <lb/>
<anchor type="note" xlink:label="note-0051-03a" xlink:href="note-0051-03"/>
totũ, &amp; </s>
  <s xml:id="echoid-s3093" xml:space="preserve">arcus quotientis dabit altitudinẽ Solis optatã. </s>
  <s xml:id="echoid-s3094" xml:space="preserve">?</s>
  <s xml:id="echoid-s3095" xml:space="preserve">? Exemplũ, rurſus adſumo il-<lb/>
<anchor type="note" xlink:label="note-0051-04a" xlink:href="note-0051-04"/>
lud per q̊d operationem hãc ſemꝑ hactenus abſolui, id´ eo maxime, ut uideas tam diuer <lb/>ſas uias in eundem ſemper tendere finẽ. </s>
  <s xml:id="echoid-s3096" xml:space="preserve">Eſto ergo, ut Sol fuerit in 2. </s>
  <s xml:id="echoid-s3097" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3098" xml:space="preserve">26. </s>
  <s xml:id="echoid-s3099" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3100" xml:space="preserve">II, ego <lb/>uero iam ſcire cupio altitudinẽ Solis ſupra horizontẽ hora 9. </s>
  <s xml:id="echoid-s3101" xml:space="preserve">ante meridiẽ, qñ introniza <lb/>tio facta eſt, diſtãtia ꝗdem eſt 45. </s>
  <s xml:id="echoid-s3102" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3103" xml:space="preserve">ſinus eius 70710. </s>
  <s xml:id="echoid-s3104" xml:space="preserve">ſinus aũt cõplementi altitudinis <lb/>poli 42. </s>
  <s xml:id="echoid-s3105" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3106" xml:space="preserve">eſt 66913. </s>
  <s xml:id="echoid-s3107" xml:space="preserve">iã ſi alte℞ in alterum ducã, ꝓductũ in totũ diuidã, prouenient in q̊ <lb/>
<anchor type="note" xlink:label="note-0051-05a" xlink:href="note-0051-05"/>
tiente 473 14. </s>
  <s xml:id="echoid-s3108" xml:space="preserve">arcus eius eſt 28. </s>
  <s xml:id="echoid-s3109" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3110" xml:space="preserve">14. </s>
  <s xml:id="echoid-s3111" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3112" xml:space="preserve">quo ſubtracto à quadrãte, remanent 61. </s>
  <s xml:id="echoid-s3113" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s3114" xml:space="preserve">46. </s>
  <s xml:id="echoid-s3115" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3116" xml:space="preserve">at id uocamus inuentũ primũ. </s>
  <s xml:id="echoid-s3117" xml:space="preserve">Deinde ſinũ eius propono ſcilicet 88102. </s>
  <s xml:id="echoid-s3118" xml:space="preserve">cum ſi <lb/>
<anchor type="note" xlink:label="note-0051-06a" xlink:href="note-0051-06"/>
nu altitudinis poli 48. </s>
  <s xml:id="echoid-s3119" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3120" xml:space="preserve">743 14. </s>
  <s xml:id="echoid-s3121" xml:space="preserve">eum duco in totũ, ꝓductũ diuido in primũ illud inuen <lb/>ti primi, &amp; </s>
  <s xml:id="echoid-s3122" xml:space="preserve">in quotiente ꝓuenient 84349. </s>
  <s xml:id="echoid-s3123" xml:space="preserve">arcus eſt 57. </s>
  <s xml:id="echoid-s3124" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3125" xml:space="preserve">31 mi. </s>
  <s xml:id="echoid-s3126" xml:space="preserve">Cõplementũ uero 32. <lb/></s>
  <s xml:id="echoid-s3127" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3128" xml:space="preserve">29. </s>
  <s xml:id="echoid-s3129" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3130" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3131" xml:space="preserve">quia Sol eſt ſeptentrionalis, addo declinationẽ ipſius, &amp; </s>
  <s xml:id="echoid-s3132" xml:space="preserve">ſimul 20. </s>
  <s xml:id="echoid-s3133" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3134" xml:space="preserve">42. </s>
  <s xml:id="echoid-s3135" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0051-07a" xlink:href="note-0051-07"/>
mi. </s>
  <s xml:id="echoid-s3136" xml:space="preserve">unde prouenient 53. </s>
  <s xml:id="echoid-s3137" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3138" xml:space="preserve">11. </s>
  <s xml:id="echoid-s3139" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3140" xml:space="preserve">inuentũ illud ſecundũ, cuius ſinus eſt 80055. </s>
  <s xml:id="echoid-s3141" xml:space="preserve">Ad ex-<lb/>tremum quũ iam ſinum alterius inuenti duxeris in alterũ, productũ quo in ſinũ totum <lb/>diuiſeris, prouenient in quotiente 70530. </s>
  <s xml:id="echoid-s3142" xml:space="preserve">arcus eius eſt 44 gra. </s>
  <s xml:id="echoid-s3143" xml:space="preserve">52. </s>
  <s xml:id="echoid-s3144" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3145" xml:space="preserve">quæ &amp; </s>
  <s xml:id="echoid-s3146" xml:space="preserve">altitudo eſt <lb/>Solis ad ipſum momentũ intronizationis, quã nunc quinta ratione adinueni. </s>
  <s xml:id="echoid-s3147" xml:space="preserve">Si aũt di-<lb/>ſtantia Solis data hora maior fuerit ̈ 90, tunc ſubtrahe eam à ſemicirculo, &amp; </s>
  <s xml:id="echoid-s3148" xml:space="preserve">reſidui ſi-<lb/>
<anchor type="note" xlink:label="note-0051-08a" xlink:href="note-0051-08"/>
num duc in ſinum cõplementi altitudinis poli, &amp; </s>
  <s xml:id="echoid-s3149" xml:space="preserve">diuide in totũ, arcũ quotientis ſubtrahe <lb/>ex quadrante, reſiduũ dicetur inuentũ primũ. </s>
  <s xml:id="echoid-s3150" xml:space="preserve">Primihuius inuenti ſinũ tibi propone, &amp; </s>
  <s xml:id="echoid-s3151" xml:space="preserve"><lb/>ſinũ altitudinis poli, minorẽ duc in ſinũ totũ, productũ diuide in maiorẽ, de arcu quotien-<lb/>
<anchor type="note" xlink:label="note-0051-09a" xlink:href="note-0051-09"/>
tis ſubtrahe complementũ declinationis, &amp; </s>
  <s xml:id="echoid-s3152" xml:space="preserve">reliquũ manebit inuentũ ſecundum. </s>
  <s xml:id="echoid-s3153" xml:space="preserve">Deinde <lb/>ſi ſinum primi ducas in ſinum inuenti ſecundi, &amp; </s>
  <s xml:id="echoid-s3154" xml:space="preserve">in totũ diuidas, arcus quotientis mon-<lb/>ſtrabit altitudinem quæſitã. </s>
  <s xml:id="echoid-s3155" xml:space="preserve">?</s>
  <s xml:id="echoid-s3156" xml:space="preserve">? Accipe &amp; </s>
  <s xml:id="echoid-s3157" xml:space="preserve">hic exemplũ tibi. </s>
  <s xml:id="echoid-s3158" xml:space="preserve">Volo ſcire altitudinẽ Solis <lb/>
<anchor type="note" xlink:label="note-0051-10a" xlink:href="note-0051-10"/>
ſupra horizontem adhorã quintã ante meridianã ipſo die intronizationis, ideo´ gradũ <lb/>&amp; </s>
  <s xml:id="echoid-s3159" xml:space="preserve">minutũ Solis relinquo ita, ut fuerunt antea. </s>
  <s xml:id="echoid-s3160" xml:space="preserve">diſtãtia Solis à meridiano eſt 105. </s>
  <s xml:id="echoid-s3161" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3162" xml:space="preserve">dũ <lb/>
<anchor type="note" xlink:label="note-0051-11a" xlink:href="note-0051-11"/>
ſubtraho à ſemicirculo &amp; </s>
  <s xml:id="echoid-s3163" xml:space="preserve">manent 75. </s>
  <s xml:id="echoid-s3164" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3165" xml:space="preserve">in reſiduo, quo℞ ſinus eſt 96592. </s>
  <s xml:id="echoid-s3166" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3167" xml:space="preserve">hunc duco <lb/>in ſinũ cõplementi altitudinis poli, ſcilicet 66913. </s>
  <s xml:id="echoid-s3168" xml:space="preserve">producto diuiſo per ſinũ totũ, proueni-<lb/>ent in quotiente 64632. </s>
  <s xml:id="echoid-s3169" xml:space="preserve">arcus erit 40. </s>
  <s xml:id="echoid-s3170" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3171" xml:space="preserve">16. </s>
  <s xml:id="echoid-s3172" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3173" xml:space="preserve">quẽ ſi ſubtraho à quadrante, reliqui ma-<lb/>
<anchor type="note" xlink:label="note-0051-12a" xlink:href="note-0051-12"/>
nent 49. </s>
  <s xml:id="echoid-s3174" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3175" xml:space="preserve">cum 44. </s>
  <s xml:id="echoid-s3176" xml:space="preserve">minutis, inuentum puta primũ, cuius ſinũ mihi deinceps propono, <lb/>ſimiliter &amp; </s>
  <s xml:id="echoid-s3177" xml:space="preserve">ſinum altitudinis poli 74314. </s>
  <s xml:id="echoid-s3178" xml:space="preserve">eum tanquam minorẽ duco in ſinũ totũ, &amp; </s>
  <s xml:id="echoid-s3179" xml:space="preserve">in ſi <lb/>
<anchor type="note" xlink:label="note-0051-13a" xlink:href="note-0051-13"/>
num primi inuenti diuido, unde ꝓdeunt in quotiente 97272. </s>
  <s xml:id="echoid-s3180" xml:space="preserve">arcus illius quotientis eſt <lb/>76. </s>
  <s xml:id="echoid-s3181" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3182" xml:space="preserve">35. </s>
  <s xml:id="echoid-s3183" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3184" xml:space="preserve">hinc ſnbtraho complementũ declinationis Solis, ſcilicet 69. </s>
  <s xml:id="echoid-s3185" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3186" xml:space="preserve">18. </s>
  <s xml:id="echoid-s3187" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3188" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3189" xml:space="preserve"><lb/>manent in reſiduo gra. </s>
  <s xml:id="echoid-s3190" xml:space="preserve">7. </s>
  <s xml:id="echoid-s3191" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3192" xml:space="preserve">17. </s>
  <s xml:id="echoid-s3193" xml:space="preserve">inuentũ ſecũdũ. </s>
  <s xml:id="echoid-s3194" xml:space="preserve">Iam ita utriuſ inuenti ſinus ſcilicet <lb/>
<anchor type="note" xlink:label="note-0051-14a" xlink:href="note-0051-14"/>
76398. </s>
  <s xml:id="echoid-s3195" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3196" xml:space="preserve">12677. </s>
  <s xml:id="echoid-s3197" xml:space="preserve">inter ſe multiplico, &amp; </s>
  <s xml:id="echoid-s3198" xml:space="preserve">quotientẽ in totum diuido, at hinc ꝓuenient in <lb/>quotiẽte 9685. </s>
  <s xml:id="echoid-s3199" xml:space="preserve">arcus eſt 5. </s>
  <s xml:id="echoid-s3200" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3201" xml:space="preserve">33. </s>
  <s xml:id="echoid-s3202" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3203" xml:space="preserve">altitudo nimi℞ Solis quæſita ad horã 5. </s>
  <s xml:id="echoid-s3204" xml:space="preserve">antemeri-<lb/>dianã in ipſo die intronizationis. </s>
  <s xml:id="echoid-s3205" xml:space="preserve">Fit aliquãdo ut inuentũ ſecundũ præciſe ſit 90. </s>
  <s xml:id="echoid-s3206" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3207" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3208" xml:space="preserve"><lb/>tũc inuentũ illud ꝑ ſe erit altitudo Solis quæſita, ne ulla ulteriori indiget ſupputatiõe. <lb/></s>
  <s xml:id="echoid-s3209" xml:space="preserve">Inſuper &amp; </s>
  <s xml:id="echoid-s3210" xml:space="preserve">hoc ſcitu neceſſariũ eſt, ꝙ quũ ☉(sun) eſt in principio ♈ uel ♎, tunc multiplicare <lb/>
<anchor type="note" xlink:label="note-0051-15a" xlink:href="note-0051-15"/>
debes ſinus utriuſ cõplemẽti, diſtãtiæ ſcilicet Solis à meridie &amp; </s>
  <s xml:id="echoid-s3211" xml:space="preserve">altitudinis poli, produ-<lb/>ctum uero diuides in ſinũ totum, &amp; </s>
  <s xml:id="echoid-s3212" xml:space="preserve">ſic arcus quotiẽtis ſtatim tibi mõſtrabit altitudinem <lb/>Solis quã quærebas. </s>
  <s xml:id="echoid-s3213" xml:space="preserve">Præterea quæcun hic te ꝑ Solem docuimus inuenire, puta arcum <lb/>diurnum, altitudinẽ ab horizõte, &amp; </s>
  <s xml:id="echoid-s3214" xml:space="preserve">id genus ſimilia plura, intelliges etiam de ſtellis, ita <lb/>ꝙ quæ de eclyptica tradidimus, in reliquorũ etiã ſyderum motibus uſum ſuum retineãt.</s>
  <s xml:id="echoid-s3215" xml:space="preserve"/>
</p>
<div xml:id="echoid-div91" type="float" level="2" n="1">
<note position="left" xlink:label="note-0050-04" xlink:href="note-0050-04a" xml:space="preserve"><emph style="it">Lateralis</emph> <lb/><emph style="it">ingreſſus</emph> <lb/><emph style="it">hæc docet.</emph></note>
<note position="left" xlink:label="note-0050-05" xlink:href="note-0050-05a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
<note position="left" xlink:label="note-0050-06" xlink:href="note-0050-06a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">primum-</emph></note>
<note position="right" xlink:label="note-0051-01" xlink:href="note-0051-01a" xml:space="preserve"><emph style="it">Areatim.</emph></note>
<note position="right" xlink:label="note-0051-02" xlink:href="note-0051-02a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">ſecundum.</emph></note>
<note position="right" xlink:label="note-0051-03" xlink:href="note-0051-03a" xml:space="preserve"><emph style="it">Lateraliter</emph></note>
<note position="right" xlink:label="note-0051-04" xlink:href="note-0051-04a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
<note position="right" xlink:label="note-0051-05" xlink:href="note-0051-05a" xml:space="preserve"><emph style="it">Lateraliter</emph> <lb/><emph style="it">idem inue-</emph> <lb/><emph style="it">nies.</emph></note>
<note position="right" xlink:label="note-0051-06" xlink:href="note-0051-06a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">primum.</emph></note>
<note position="right" xlink:label="note-0051-07" xlink:href="note-0051-07a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">ſecundum.</emph></note>
<note position="right" xlink:label="note-0051-08" xlink:href="note-0051-08a" xml:space="preserve"><emph style="it">Lateralis</emph> <lb/><emph style="it">ingreſſus</emph></note>
<note position="right" xlink:label="note-0051-09" xlink:href="note-0051-09a" xml:space="preserve"><emph style="it">Lateralis</emph> <lb/><emph style="it">ingreſſus.</emph></note>
<note position="right" xlink:label="note-0051-10" xlink:href="note-0051-10a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
<note position="right" xlink:label="note-0051-11" xlink:href="note-0051-11a" xml:space="preserve"><emph style="it">Lateralis</emph> <lb/><emph style="it">introitus.</emph></note>
<note position="right" xlink:label="note-0051-12" xlink:href="note-0051-12a" xml:space="preserve"><emph style="it">Inucntum</emph> <lb/><emph style="it">primum.</emph></note>
<note position="right" xlink:label="note-0051-13" xlink:href="note-0051-13a" xml:space="preserve"><emph style="it">Lateralis</emph> <lb/><emph style="it">ingreſſus</emph>.</note>
<note position="right" xlink:label="note-0051-14" xlink:href="note-0051-14a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">ſecundum</emph>.</note>
<note position="right" xlink:label="note-0051-15" xlink:href="note-0051-15a" xml:space="preserve"><emph style="it">Lateraliter</emph> <lb/><emph style="it">ſimile per</emph> <lb/><emph style="it">quadrantë</emph> <lb/><emph style="it">reperies.</emph></note>
</div>
</div>
<div xml:id="echoid-div93" type="section" level="1" n="51">
<head xml:id="echoid-head55" xml:space="preserve">PRONVNCIATVM XXXIX.</head>
<p>
  <s xml:id="echoid-s3216" xml:space="preserve">Diſtantiam Solis ante meridiem per circulum magnum ab ipſo puncto <lb/>interſectionis æ quatoris &amp; </s>
  <s xml:id="echoid-s3217" xml:space="preserve">horizontis ſolerte inueſtigare.</s>
  <s xml:id="echoid-s3218" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3219" xml:space="preserve">Si quãdo arcum illũ ex ſphærica ratione inuenire cupis, primũ multiplica ſinum cõple <lb/>menti declinationis Solis cum ſinu diſtantiæ Solis à meridiano (qñ diſtantia illa in æqui
<pb file="0052" n="52" rhead="GENVINVS VSVS"/>
noctiali circulo numerari ſolet) productum diuide in ſinum totum, &amp; </s>
  <s xml:id="echoid-s3220" xml:space="preserve">arcus quotientis <lb/>eſt diſtantia Solis ab ortu æquinoctialis, putain circulo maiori, qui per corpus ſolare du <lb/>citur &amp; </s>
  <s xml:id="echoid-s3221" xml:space="preserve">punctum horizontis, ubi æquinoctialis oritur. </s>
  <s xml:id="echoid-s3222" xml:space="preserve">Sin autem diſtantia Solis horaria <lb/>à meridie maior eſt 90. </s>
  <s xml:id="echoid-s3223" xml:space="preserve">gradibus, tũc ſubtrahe in de 90. </s>
  <s xml:id="echoid-s3224" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3225" xml:space="preserve">cũ reſiduo operare, ſicut antea <lb/>cum uera diſtantia feciſti. </s>
  <s xml:id="echoid-s3226" xml:space="preserve">Contingit interdum quòd diſtantra Solis à meridiano directe <lb/>eſt 90. </s>
  <s xml:id="echoid-s3227" xml:space="preserve">graduum, ſicut in communibus horis ſemꝑ fit hora 6. </s>
  <s xml:id="echoid-s3228" xml:space="preserve">ante &amp; </s>
  <s xml:id="echoid-s3229" xml:space="preserve">poſt meridiem, tunc <lb/>neceſſe non eſt diſtantiam Solis ab ortu æquatoris quærere, quoniam ipſa per ſe declina <lb/>tio Solis eſt diſtantia illa. </s>
  <s xml:id="echoid-s3230" xml:space="preserve">?</s>
  <s xml:id="echoid-s3231" xml:space="preserve">? At huius primæ &amp; </s>
  <s xml:id="echoid-s3232" xml:space="preserve">communis regulæ ſit hoc tibi exem-<lb/>
<anchor type="note" xlink:label="note-0052-01a" xlink:href="note-0052-01"/>
plum: </s>
  <s xml:id="echoid-s3233" xml:space="preserve">In ipſo die intronizationis fuit Sol in 2. </s>
  <s xml:id="echoid-s3234" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3235" xml:space="preserve">26. </s>
  <s xml:id="echoid-s3236" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3237" xml:space="preserve">II, declinatio eius ab æ quato-<lb/>re eſt 20. </s>
  <s xml:id="echoid-s3238" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3239" xml:space="preserve">42. </s>
  <s xml:id="echoid-s3240" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3241" xml:space="preserve">declinationis huius cõplementũ 69. </s>
  <s xml:id="echoid-s3242" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3243" xml:space="preserve">18. </s>
  <s xml:id="echoid-s3244" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3245" xml:space="preserve">ſinus huius comple <lb/>menti eſt 93544. </s>
  <s xml:id="echoid-s3246" xml:space="preserve">diſtantia Solis à meridie 3. </s>
  <s xml:id="echoid-s3247" xml:space="preserve">horarum tempore intronizationis, ea confi-<lb/>cit gradus 45. </s>
  <s xml:id="echoid-s3248" xml:space="preserve">ſinum illius 70710. </s>
  <s xml:id="echoid-s3249" xml:space="preserve">ducin ſinum complementi declinationis, productũ di-<lb/>
<anchor type="note" xlink:label="note-0052-02a" xlink:href="note-0052-02"/>
uide in ſinum totum, &amp; </s>
  <s xml:id="echoid-s3250" xml:space="preserve">prouenient in quotiente 66145. </s>
  <s xml:id="echoid-s3251" xml:space="preserve">arcus eius eſt 41. </s>
  <s xml:id="echoid-s3252" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3253" xml:space="preserve">24. </s>
  <s xml:id="echoid-s3254" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3255" xml:space="preserve">cõ-<lb/>plementum uero 48. </s>
  <s xml:id="echoid-s3256" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3257" xml:space="preserve">36. </s>
  <s xml:id="echoid-s3258" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3259" xml:space="preserve">hoc ipſum ſcilicet quod hactenus quærebamus.</s>
  <s xml:id="echoid-s3260" xml:space="preserve"/>
</p>
<div xml:id="echoid-div93" type="float" level="2" n="1">
<note position="left" xlink:label="note-0052-01" xlink:href="note-0052-01a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſcopi.</emph></note>
<note position="left" xlink:label="note-0052-02" xlink:href="note-0052-02a" xml:space="preserve"><emph style="it">Lateraliter</emph> <lb/><emph style="it">quærenti</emph> <lb/><emph style="it">patet.</emph></note>
</div>
</div>
<div xml:id="echoid-div95" type="section" level="1" n="52">
<head xml:id="echoid-head56" xml:space="preserve">PRONVNCIATVM XL.</head>
<p>
  <s xml:id="echoid-s3261" xml:space="preserve">Angulum perquirere quem facit æquinoctialis cũ circulo magno ducto <lb/>per corpus ſolare, &amp; </s>
  <s xml:id="echoid-s3262" xml:space="preserve">ortum æ quinoctialis iuxta punctum illud, ubi circulus <lb/>iſte maior à Sole ductus cum æ quinoctiali horizontem attingit.</s>
  <s xml:id="echoid-s3263" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3264" xml:space="preserve">Quod ſi &amp; </s>
  <s xml:id="echoid-s3265" xml:space="preserve">hunc angulum ſcire cupis, ago propone tibi ſinum diſtantiæ Solis ab ortu <lb/>æquinoctialis ſup putando in circulo magno per corpus ſolare, &amp; </s>
  <s xml:id="echoid-s3266" xml:space="preserve">ortum illum deducto, <lb/>
<anchor type="note" xlink:label="note-0052-03a" xlink:href="note-0052-03"/>
eius inuentionem didiciſti iam ſupra in pronunc. </s>
  <s xml:id="echoid-s3267" xml:space="preserve">39. </s>
  <s xml:id="echoid-s3268" xml:space="preserve">deinde aſſume ſinum declinationis <lb/>Solis, quem inuenies ex 3. </s>
  <s xml:id="echoid-s3269" xml:space="preserve">pronunc. </s>
  <s xml:id="echoid-s3270" xml:space="preserve">minorem ſinum duc in totum, productum diuide in <lb/>maiorem, &amp; </s>
  <s xml:id="echoid-s3271" xml:space="preserve">quotiens ſtatim oſtendet in arcu ſuo angulũ hunc quæſitum, ſicut hic uides <lb/>in exemplo ſubiecto. </s>
  <s xml:id="echoid-s3272" xml:space="preserve">?</s>
  <s xml:id="echoid-s3273" xml:space="preserve">? Diſtantia Solis in ſuo circulo magno ab ortu æquatoris ipſa <lb/>
<anchor type="note" xlink:label="note-0052-04a" xlink:href="note-0052-04"/>
hora intronizationis habet 48. </s>
  <s xml:id="echoid-s3274" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3275" xml:space="preserve">36. </s>
  <s xml:id="echoid-s3276" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3277" xml:space="preserve">uti ſuperior propoſitio monſtrat, ſinus eius eſt <lb/>74991. </s>
  <s xml:id="echoid-s3278" xml:space="preserve">ſinusitem declinationis 35347. </s>
  <s xml:id="echoid-s3279" xml:space="preserve">quo hactenus uſus ſum ſemper, hunc tan̈ mino <lb/>rem ſi duxero in ſinum totum, &amp; </s>
  <s xml:id="echoid-s3280" xml:space="preserve">productum in maiorem, puta 74991. </s>
  <s xml:id="echoid-s3281" xml:space="preserve">diuiſero, prodi-<lb/>bunt in quotiente 47155. </s>
  <s xml:id="echoid-s3282" xml:space="preserve">arcus eius eſt 20. </s>
  <s xml:id="echoid-s3283" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3284" xml:space="preserve">8. </s>
  <s xml:id="echoid-s3285" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3286" xml:space="preserve">angulus ille optatus.</s>
  <s xml:id="echoid-s3287" xml:space="preserve"/>
</p>
<div xml:id="echoid-div95" type="float" level="2" n="1">
<note position="left" xlink:label="note-0052-03" xlink:href="note-0052-03a" xml:space="preserve"><emph style="it">Areatim il</emph> <lb/><emph style="it">lud ex qua-</emph> <lb/><emph style="it">drãte diſæs</emph></note>
<note position="left" xlink:label="note-0052-04" xlink:href="note-0052-04a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div97" type="section" level="1" n="53">
<head xml:id="echoid-head57" xml:space="preserve">PRONVNCIATVM XLI.</head>
<p>
  <s xml:id="echoid-s3288" xml:space="preserve">Angulum etiam illum explorare, quem cum horizonte facit circulus ma-<lb/>gnus, ductus à Sole ubicun ſito ad ortum æquinoctialem.</s>
  <s xml:id="echoid-s3289" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3290" xml:space="preserve">Hic principio mihi fac cogites, circulum illũ magnum à Sole ad ortũ æquinoctialis <lb/>ductũ in horizõte, Sole exiſtente in ſignis meridionalibus ſemper facere angulũ recto <lb/>minorẽ, in ſignis a ũt ſeptentrionalibus Sole exiſtẽte in circulo uerticali facere cũ horizõ <lb/>te angulũ rectũ, ̈primũ deinde Sol altior eſt ̈fuerat in circulo uerticali, ſtatim etiã effi <lb/>cit cũ horizonte angulũ recto minorem, Et ſi ex ſuperiori pronunc. </s>
  <s xml:id="echoid-s3291" xml:space="preserve">iam inueniſti angu-<lb/>lum, quem facit æquinoctialis cũ circulo magno ex Sole perortum æquinoctialis tranſe <lb/>unte, ſi tunc Sol fuerit in ſigno Auſtrali, ſubtrahe angulum illũ à cõplemẽto altitudinis <lb/>poli, &amp; </s>
  <s xml:id="echoid-s3292" xml:space="preserve">remanebit angulus quẽ facit circulus magnus Solis cum horizonte in puncto ubi <lb/>æquinoctialis ſecat horizontẽ. </s>
  <s xml:id="echoid-s3293" xml:space="preserve">Sed ſi Sol eſt in ſigno aliquo Boreali, tunc adde angulum <lb/>inuentũ ad cõplementũ altitudinis poli, &amp; </s>
  <s xml:id="echoid-s3294" xml:space="preserve">rurſus emerget angulus quæſitus. </s>
  <s xml:id="echoid-s3295" xml:space="preserve">Atqui Sole <lb/>cũ altitudine ſua ſupra horizontẽ nõ attingente circulũ uerticalem, hoc eſt, quũ in ſigno <lb/>aliq̊ ſeptentrionali fuerit, &amp; </s>
  <s xml:id="echoid-s3296" xml:space="preserve">diſtãtia Solis horaria à meridiano 90. </s>
  <s xml:id="echoid-s3297" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3298" xml:space="preserve">nõ excedit, tũc ſa-<lb/>nè addes angulũ, quẽ ex ſuperiori ꝓpoſitiõe inueniſtiad cõplementũ altitudinis poli, &amp; </s>
  <s xml:id="echoid-s3299" xml:space="preserve"><lb/>q̊d inde prouenit, à ſemicirculo ſubtrahe, ſic´ manebit angulus huius circuli &amp; </s>
  <s xml:id="echoid-s3300" xml:space="preserve">horizon <lb/>tis uerſus ſeptẽtrionẽ. </s>
  <s xml:id="echoid-s3301" xml:space="preserve">Sin autẽ diſtãtia Solis horaria à meridie maior fuerit ̈ 90. </s>
  <s xml:id="echoid-s3302" xml:space="preserve">tũc ſub <lb/>trahes ab angulo illo altitudinẽ poli, ꝗ ſemꝑ eſt maior eleuatione poli, &amp; </s>
  <s xml:id="echoid-s3303" xml:space="preserve">remanebitue-<lb/>rus angulus inter horizontẽ et circulũ datũ, à Sole ductũ per ortũ æquatoris, quẽ uoleba <lb/>mus ſcire. </s>
  <s xml:id="echoid-s3304" xml:space="preserve">?</s>
  <s xml:id="echoid-s3305" xml:space="preserve">? Et hic quo exemplũ tibi dabimus huiuſcemodi. </s>
  <s xml:id="echoid-s3306" xml:space="preserve">In hora intronizatiõis <lb/>
<anchor type="note" xlink:label="note-0052-05a" xlink:href="note-0052-05"/>
fuit angulus æquinoctialis cũ circulo magno per corpus ſolare ducto, quem præceden-<lb/>ti enunciato adinueni 28. </s>
  <s xml:id="echoid-s3307" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3308" xml:space="preserve">8. </s>
  <s xml:id="echoid-s3309" xml:space="preserve">minut, quibus addo complementum altitudinis poli,
<pb file="0053" n="53" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
ſcilicet 42. </s>
  <s xml:id="echoid-s3310" xml:space="preserve">gradus. </s>
  <s xml:id="echoid-s3311" xml:space="preserve">unde proueniunt 70. </s>
  <s xml:id="echoid-s3312" xml:space="preserve">gradus, 8. </s>
  <s xml:id="echoid-s3313" xml:space="preserve">minuta, angulus ille quæſitus.</s>
  <s xml:id="echoid-s3314" xml:space="preserve"/>
</p>
<div xml:id="echoid-div97" type="float" level="2" n="1">
<note position="left" xlink:label="note-0052-05" xlink:href="note-0052-05a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſcopi.</emph></note>
</div>
</div>
<div xml:id="echoid-div99" type="section" level="1" n="54">
<head xml:id="echoid-head58" xml:space="preserve">PRONVNCIATVM XLII.</head>
<p>
  <s xml:id="echoid-s3315" xml:space="preserve">Quanta ſit diſtantio Solis aut ſtellæ à uero illo æquinoctiali ortu uel oc-<lb/>caſu uerſus meridiem ſiue ſeptentrionem, aut uiciſsim à meridiano ad ortũ <lb/>uel occidentem, expedite cognoſcere.</s>
  <s xml:id="echoid-s3316" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3317" xml:space="preserve">Iam antea quũ de amplitudine &amp; </s>
  <s xml:id="echoid-s3318" xml:space="preserve">altitudine ☉(sun) in circulo uerticali ageretur d ctũ etiã <lb/>eſt quid ſit ortus uel occaſus æquinoctialis. </s>
  <s xml:id="echoid-s3319" xml:space="preserve">Circulus q̊ ille maior à Zenith per æquino <lb/>ctialia iſta puncta ortus &amp; </s>
  <s xml:id="echoid-s3320" xml:space="preserve">occaſus eductus, uocatur circulus uerticalis, unde ferè ſolet di <lb/>ſtantia hæc Solis &amp; </s>
  <s xml:id="echoid-s3321" xml:space="preserve">ſtellarũ cõnumerari, ̈uis idẽ eſt, quũ diſtãtia à meridiano ſupputat̃ <lb/>uerſus ortũ uel occaſum. </s>
  <s xml:id="echoid-s3322" xml:space="preserve">Sciendum etiã eſt in uniuerſum, ꝙ quilibet circulus maior ex <lb/>zenith capitis ꝑ locũ Solis aut ſtellæ ubicun cõſiſtentis uſ ad horizontẽ eductus, cir <lb/>culus uerticalis uocatur. </s>
  <s xml:id="echoid-s3323" xml:space="preserve">Vbietiã circulus ille horizontẽ attingit, &amp; </s>
  <s xml:id="echoid-s3324" xml:space="preserve">tu diſtantiã graduũ <lb/>ab ortu æquatoris, uel à circulo uerticali uero numeras uſ ad huc, ea diſtãtia dicit̃ diſtan <lb/>tia Solis horizõtalis ab ortu. </s>
  <s xml:id="echoid-s3325" xml:space="preserve">Sed ſi gradus horizontis à meridie uſ ad illũ circulũ alti-<lb/>tudinis, qui etiã uerticalis dici poteſt, ſupputas, uocabitur hæc diſtãtia Solis horizõtalis <lb/>meridionalis uerſus ortũ. </s>
  <s xml:id="echoid-s3326" xml:space="preserve">Et diſtantia quidẽ hæc à pleriſ ferè oĩbus Aſtronomis lingua <lb/>&amp; </s>
  <s xml:id="echoid-s3327" xml:space="preserve">idiomate Arabũ Azimuth dici ſolet, quæ uocula, neſcio an cõmodius à Latinis niſi <lb/>
<anchor type="note" xlink:label="note-0053-01a" xlink:href="note-0053-01"/>
Quorſum, à Germanis @ohinaus, uerti poteſt? </s>
  <s xml:id="echoid-s3328" xml:space="preserve">Quũ ita diſtantiã illã ſcire deſideras <lb/>in motu Solis, primũ quære angulũ quẽ facit eclyptica cũ horizonte orientaliad illã illã ho <lb/>
<anchor type="note" xlink:label="note-0053-02a" xlink:href="note-0053-02"/>
ram, id´ ꝑpronunc. </s>
  <s xml:id="echoid-s3329" xml:space="preserve">31. </s>
  <s xml:id="echoid-s3330" xml:space="preserve">ſimiliter &amp; </s>
  <s xml:id="echoid-s3331" xml:space="preserve">gradũ eclypticæ, qui aſcendit ſuper horizontẽ ex 30. <lb/></s>
  <s xml:id="echoid-s3332" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3333" xml:space="preserve">altitudinẽ Solis ſupra horizontẽ ꝑ 34. </s>
  <s xml:id="echoid-s3334" xml:space="preserve">35. </s>
  <s xml:id="echoid-s3335" xml:space="preserve">36. </s>
  <s xml:id="echoid-s3336" xml:space="preserve">37. </s>
  <s xml:id="echoid-s3337" xml:space="preserve">aut 38. </s>
  <s xml:id="echoid-s3338" xml:space="preserve">pronunciata, quãcun tandẽ <lb/>ex illis malueris tuo accõmodare inſtituto, mox quære diſtantiã gradus Solis ab aſcen-<lb/>dente, ſaltẽ ſecundum gradus eclypticæ, eius diſtantiæ ſinum cõplementi tibi propone <lb/>ad abacũ ſupputatorium, adiungendo etiã ſinũ cõplementi alitudinis Solis, minorẽ duc <lb/>
<anchor type="note" xlink:label="note-0053-03a" xlink:href="note-0053-03"/>
in ſinum totũ, &amp; </s>
  <s xml:id="echoid-s3339" xml:space="preserve">diuide in maiorẽ ex illis duobus cõiunctis, &amp; </s>
  <s xml:id="echoid-s3340" xml:space="preserve">arcus quotiẽtis dabit arcũ <lb/>horizõtis à puncto illo; </s>
  <s xml:id="echoid-s3341" xml:space="preserve">ubi eclyptica ſecar horizontẽ uſ ad arcũ uerticalẽ, ꝗ ex Zenith <lb/>capitis per corpus ſolare ad horizontẽ uſ deducitur cõputatũ. </s>
  <s xml:id="echoid-s3342" xml:space="preserve">nume℞ illum nec abſur-<lb/>de nec temere dicemus ſeruatũ, unde ſi ſubtrahas amplitudinẽ ortus gradus aſcendẽtis <lb/>exiſtẽte tamẽ pũcto illo ſeptẽtrionali, remanet diſtãtia ☉(sun) horizõtalis q̃ſita Sin aũt pun-<lb/>ctũ ort9 meridionale fuerit, adde amplitudinẽ ei9, et habebis optatũ. </s>
  <s xml:id="echoid-s3343" xml:space="preserve">?</s>
  <s xml:id="echoid-s3344" xml:space="preserve">? Eius rei exem <lb/>
<anchor type="note" xlink:label="note-0053-04a" xlink:href="note-0053-04"/>
plũ ſit hoc tibi, rurſus ecce, ꝓpono mihi horã introniſatiõis, ubi altitudinẽ ☉(sun) ſupra hori-<lb/>zontẽ ꝑ 5. </s>
  <s xml:id="echoid-s3345" xml:space="preserve">pnunc, &amp; </s>
  <s xml:id="echoid-s3346" xml:space="preserve">diuerſas ratiões inueni 44. </s>
  <s xml:id="echoid-s3347" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3348" xml:space="preserve">52. </s>
  <s xml:id="echoid-s3349" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3350" xml:space="preserve">gradus aũt aſcẽdẽs fuit 5. </s>
  <s xml:id="echoid-s3351" xml:space="preserve">gr, <lb/>25. </s>
  <s xml:id="echoid-s3352" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3353" xml:space="preserve">♌, &amp; </s>
  <s xml:id="echoid-s3354" xml:space="preserve">diſtãtia Solis ab aſcẽdẽre 62. </s>
  <s xml:id="echoid-s3355" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3356" xml:space="preserve">59. </s>
  <s xml:id="echoid-s3357" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3358" xml:space="preserve">Angulus q̊  horizõtis &amp; </s>
  <s xml:id="echoid-s3359" xml:space="preserve">eclypti-<lb/>cæ iuxta 5. </s>
  <s xml:id="echoid-s3360" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3361" xml:space="preserve">25. </s>
  <s xml:id="echoid-s3362" xml:space="preserve">mi ♌ eſt 52. </s>
  <s xml:id="echoid-s3363" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3364" xml:space="preserve">21. </s>
  <s xml:id="echoid-s3365" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3366" xml:space="preserve">ſinũ ergo cõplementi diſtãtiæ Solis ab aſcen <lb/>dente 45424. </s>
  <s xml:id="echoid-s3367" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3368" xml:space="preserve">duco in ſinũ totũ, ꝑductũ diuido in ſinum cõplementi altitudinis Solis <lb/>
<anchor type="note" xlink:label="note-0053-05a" xlink:href="note-0053-05"/>
ſupra horizontẽ. </s>
  <s xml:id="echoid-s3369" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s3370" xml:space="preserve">70875. </s>
  <s xml:id="echoid-s3371" xml:space="preserve">quotiẽs eſt 64090. </s>
  <s xml:id="echoid-s3372" xml:space="preserve">arcus eius 39. </s>
  <s xml:id="echoid-s3373" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3374" xml:space="preserve">54. </s>
  <s xml:id="echoid-s3375" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3376" xml:space="preserve">qui ſubtractus ex <lb/>quadrãte relinquit 50. </s>
  <s xml:id="echoid-s3377" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3378" xml:space="preserve">6. </s>
  <s xml:id="echoid-s3379" xml:space="preserve">mi arcũ. </s>
  <s xml:id="echoid-s3380" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s3381" xml:space="preserve">horizontis inter gradũ aſcendẽtis &amp; </s>
  <s xml:id="echoid-s3382" xml:space="preserve">circulũ uer <lb/>ticalem Solis, at hunc numerũ dicimus ſeruatũ. </s>
  <s xml:id="echoid-s3383" xml:space="preserve">Ad hæc quæro inſuper amplitudinem <lb/>
<anchor type="note" xlink:label="note-0053-06a" xlink:href="note-0053-06"/>
5. </s>
  <s xml:id="echoid-s3384" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3385" xml:space="preserve">25. </s>
  <s xml:id="echoid-s3386" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3387" xml:space="preserve">♌ in hunc modũ, duco ſinũ declinationis illius gradus ♌ quæ eſt 18. </s>
  <s xml:id="echoid-s3388" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s3389" xml:space="preserve">58. </s>
  <s xml:id="echoid-s3390" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3391" xml:space="preserve">ſinus eius 32465 in ſinũ totũ, ꝓductũ diuido in ſinum cõplementi altitudinis po-<lb/>
<anchor type="note" xlink:label="note-0053-07a" xlink:href="note-0053-07"/>
li 66913. </s>
  <s xml:id="echoid-s3392" xml:space="preserve">quotiens eſt 48563. </s>
  <s xml:id="echoid-s3393" xml:space="preserve">cuius arcus eſt 29. </s>
  <s xml:id="echoid-s3394" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3395" xml:space="preserve">4. </s>
  <s xml:id="echoid-s3396" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3397" xml:space="preserve">amplitudo ea 5. </s>
  <s xml:id="echoid-s3398" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3399" xml:space="preserve">25. </s>
  <s xml:id="echoid-s3400" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3401" xml:space="preserve">♌ <lb/>in eleuatione 48. </s>
  <s xml:id="echoid-s3402" xml:space="preserve">graduũ. </s>
  <s xml:id="echoid-s3403" xml:space="preserve">Et quia gradus ille ♌ eſt in ſemicirculo eclypticæ ſeptentrio-<lb/>nali, ſubtrahere debeo amplitudinem eius à priori diſtantia Solis horizontali, quã abin-<lb/>terſectione eclypticæ &amp; </s>
  <s xml:id="echoid-s3404" xml:space="preserve">horizontis cõnumeraui, qui erant gra. </s>
  <s xml:id="echoid-s3405" xml:space="preserve">50. </s>
  <s xml:id="echoid-s3406" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3407" xml:space="preserve">8. </s>
  <s xml:id="echoid-s3408" xml:space="preserve">ſic à ſubtractiõe <lb/>remanẽt 21. </s>
  <s xml:id="echoid-s3409" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3410" xml:space="preserve">4. </s>
  <s xml:id="echoid-s3411" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3412" xml:space="preserve">Azimuth nempe solis ab ortu æquinoctiali uerſus meridiẽ. </s>
  <s xml:id="echoid-s3413" xml:space="preserve">At <lb/>
<anchor type="note" xlink:label="note-0053-08a" xlink:href="note-0053-08"/>
hæc quidem regula in uniuerſum uera eſt, quãdo Solis altitudo ſupra horizõtem maior <lb/>eſt altitudine eius in circulo uerticali, quam enunciato 20. </s>
  <s xml:id="echoid-s3414" xml:space="preserve">inuenire didiciſti. </s>
  <s xml:id="echoid-s3415" xml:space="preserve">Si aũt alti-<lb/>tudo Solis minor fuerit in hora propoſita ̈ ſit eius altitudo in circulo uerticali, certum <lb/>tunc eſt Solem in aliquo ſignorũ ſeptentrionaliũ eſſe, &amp; </s>
  <s xml:id="echoid-s3416" xml:space="preserve">hic iam ſubtrahe numerum ſer-<lb/>uatum ex iam inuẽta amplitudine, at manebit diſtantia solis horizontalis ſeptentrio-<lb/>nalis, hoc eſt arcus ab ortu æquinoctialis uerſus ſeptentrionẽ cõputando. </s>
  <s xml:id="echoid-s3417" xml:space="preserve">Gradũ autem <lb/>eclypticæ aſcendente exiſtente meridionali, adde amplitudinem aſcendentis ad numerũ
<pb file="0054" n="54" rhead="GENVINVS VSVS"/>
ſeruatum, &amp; </s>
  <s xml:id="echoid-s3418" xml:space="preserve">proueniet diſtantia Solis horizontalis meridionalis, id eſt ab ortu æquato-<lb/>ris uerſus meridiem connumerando.</s>
  <s xml:id="echoid-s3419" xml:space="preserve"/>
</p>
<div xml:id="echoid-div99" type="float" level="2" n="1">
<note position="right" xlink:label="note-0053-01" xlink:href="note-0053-01a" xml:space="preserve"><emph style="it">Azimutb</emph> <lb/><emph style="it">quid.</emph></note>
<note position="right" xlink:label="note-0053-02" xlink:href="note-0053-02a" xml:space="preserve"><emph style="it">@ohin</emph> <lb/><emph style="it">aus.</emph></note>
<note position="right" xlink:label="note-0053-03" xlink:href="note-0053-03a" xml:space="preserve"><emph style="it">Per arealẽ</emph> <lb/><emph style="it">introitum</emph> <lb/><emph style="it">iillud conſe-</emph> <lb/><emph style="it">queris.</emph></note>
<note position="right" xlink:label="note-0053-04" xlink:href="note-0053-04a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
<note position="right" xlink:label="note-0053-05" xlink:href="note-0053-05a" xml:space="preserve"><emph style="it">Arealiter.</emph></note>
<note position="right" xlink:label="note-0053-06" xlink:href="note-0053-06a" xml:space="preserve"><emph style="it">Arealiter.</emph></note>
<note position="right" xlink:label="note-0053-07" xlink:href="note-0053-07a" xml:space="preserve"><emph style="it">Amplitudo</emph> <lb/><emph style="it">29. gra. 4.</emph> <lb/><emph style="it">nunut</emph>.</note>
<note position="right" xlink:label="note-0053-08" xlink:href="note-0053-08a" xml:space="preserve"><emph style="it">Azimuth</emph> <lb/><emph style="it">solis 21.</emph> <lb/><emph style="it">gra. 4. mi</emph>.</note>
</div>
</div>
<div xml:id="echoid-div101" type="section" level="1" n="55">
<head xml:id="echoid-head59" xml:space="preserve">PRONVNCIATVM XLIII.</head>
<p>
  <s xml:id="echoid-s3420" xml:space="preserve">Diſtantiam Solis horizontalem à circulo uerticali diuerſa ratione indaga <lb/>re, ſed eiuſmodi quę ad oẽs ſtellas fixas &amp; </s>
  <s xml:id="echoid-s3421" xml:space="preserve">erroneas queat cõmode adhiberi.</s>
  <s xml:id="echoid-s3422" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3423" xml:space="preserve">Primum omnium hic duc ſinum complementi declinationis Solis in ſinum diſtantiæ <lb/>Solis à meridiano. </s>
  <s xml:id="echoid-s3424" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s3425" xml:space="preserve">in æquatore, ſemper pro 4. </s>
  <s xml:id="echoid-s3426" xml:space="preserve">bora 15. </s>
  <s xml:id="echoid-s3427" xml:space="preserve">gradus cõputando, productum <lb/>diuide in ſinum totũ, &amp; </s>
  <s xml:id="echoid-s3428" xml:space="preserve">quotientẽ ſepone ante te ſeorſim. </s>
  <s xml:id="echoid-s3429" xml:space="preserve">(eum inuenire didiciſti etiã pro <lb/>
<anchor type="note" xlink:label="note-0054-01a" xlink:href="note-0054-01"/>
nunc. </s>
  <s xml:id="echoid-s3430" xml:space="preserve">31. </s>
  <s xml:id="echoid-s3431" xml:space="preserve">ſiquidem diſtantia eſt Solis ab interſectione æquatoris &amp; </s>
  <s xml:id="echoid-s3432" xml:space="preserve">horizõtis) quũ arcus <lb/>eius inquiris, appone etiam ſinũ cõplementi altitudinis solis, minorem duc in ſinum to <lb/>
<anchor type="note" xlink:label="note-0054-02a" xlink:href="note-0054-02"/>
tum, productũ diuide in maiorem, quotientis arcus ex 90. </s>
  <s xml:id="echoid-s3433" xml:space="preserve">ſubtractus, relinquet diſtãtiam <lb/>Solis horizontalem quæſitam. </s>
  <s xml:id="echoid-s3434" xml:space="preserve">?</s>
  <s xml:id="echoid-s3435" xml:space="preserve">? Exemplũ habe tibi huiuſmodi. </s>
  <s xml:id="echoid-s3436" xml:space="preserve">In ipſo die introni-<lb/>
<anchor type="note" xlink:label="note-0054-03a" xlink:href="note-0054-03"/>
zationis fuit Sol in 2. </s>
  <s xml:id="echoid-s3437" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3438" xml:space="preserve">26. </s>
  <s xml:id="echoid-s3439" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3440" xml:space="preserve">II, intronizatio autem facta eſt hora 9. </s>
  <s xml:id="echoid-s3441" xml:space="preserve">ante meridiem, <lb/>declinatio Solis 20. </s>
  <s xml:id="echoid-s3442" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3443" xml:space="preserve">42. </s>
  <s xml:id="echoid-s3444" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3445" xml:space="preserve">ſicut in 5. </s>
  <s xml:id="echoid-s3446" xml:space="preserve">pronunc. </s>
  <s xml:id="echoid-s3447" xml:space="preserve">uidiſti, complementum eius 89. </s>
  <s xml:id="echoid-s3448" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s3449" xml:space="preserve">18. </s>
  <s xml:id="echoid-s3450" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3451" xml:space="preserve">ſinum ita  huius complementi 93544. </s>
  <s xml:id="echoid-s3452" xml:space="preserve">duco in ſinum diſtantiæ Solis à meridia <lb/>no, quæ eſt 45. </s>
  <s xml:id="echoid-s3453" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3454" xml:space="preserve">(quoniã hora 9. </s>
  <s xml:id="echoid-s3455" xml:space="preserve">ante meridiem facit horas 3. </s>
  <s xml:id="echoid-s3456" xml:space="preserve">ante meridiem) ſcilicet <lb/>70710. </s>
  <s xml:id="echoid-s3457" xml:space="preserve">productũ ſi diuidam in totum ſinum, ꝓueniunt in quotiente 66145. </s>
  <s xml:id="echoid-s3458" xml:space="preserve">quem dein-<lb/>ceps rurſus duco in ſinum totũ, &amp; </s>
  <s xml:id="echoid-s3459" xml:space="preserve">productũ itidem diuido in ſinum cõplementi altitudi-<lb/>nis Solis hora intronizationis, altitudinem illã habeo ex 35. </s>
  <s xml:id="echoid-s3460" xml:space="preserve">36. </s>
  <s xml:id="echoid-s3461" xml:space="preserve">37. </s>
  <s xml:id="echoid-s3462" xml:space="preserve">uel 38. </s>
  <s xml:id="echoid-s3463" xml:space="preserve">pronunc. </s>
  <s xml:id="echoid-s3464" xml:space="preserve">iam <lb/>antea inuentam 44. </s>
  <s xml:id="echoid-s3465" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3466" xml:space="preserve">52. </s>
  <s xml:id="echoid-s3467" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3468" xml:space="preserve">Complementũ eius eſt 45. </s>
  <s xml:id="echoid-s3469" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3470" xml:space="preserve">8. </s>
  <s xml:id="echoid-s3471" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3472" xml:space="preserve">ſinus uero 70876. </s>
  <s xml:id="echoid-s3473" xml:space="preserve"><lb/>quotiens dabit 93317. </s>
  <s xml:id="echoid-s3474" xml:space="preserve">arcus uero quotientis eſt 68. </s>
  <s xml:id="echoid-s3475" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3476" xml:space="preserve">56. </s>
  <s xml:id="echoid-s3477" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3478" xml:space="preserve">ſi iam arcũ illum à quadrã <lb/>te ſubtrahas, remanẽt 21. </s>
  <s xml:id="echoid-s3479" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3480" xml:space="preserve">4. </s>
  <s xml:id="echoid-s3481" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3482" xml:space="preserve">diſtantia nimirũ Solis quæſita. </s>
  <s xml:id="echoid-s3483" xml:space="preserve">Intellige tamen arcũ <lb/>horizontis à puncto intronizationis æquinoctialis &amp; </s>
  <s xml:id="echoid-s3484" xml:space="preserve">borizontis uſ ad circulũ uertica <lb/>lem, à zenith per corpus ſolare ad horizontẽ uſ deductũ. </s>
  <s xml:id="echoid-s3485" xml:space="preserve">Et hic quidem modus inue-<lb/>niendi Azimuth uſurpari poteſt in Sole &amp; </s>
  <s xml:id="echoid-s3486" xml:space="preserve">alĳs planetis, at adeo ſtellis fixis omnibus.</s>
  <s xml:id="echoid-s3487" xml:space="preserve"/>
</p>
<div xml:id="echoid-div101" type="float" level="2" n="1">
<note position="left" xlink:label="note-0054-01" xlink:href="note-0054-01a" xml:space="preserve"><emph style="it">Lateraliter</emph></note>
<note position="left" xlink:label="note-0054-02" xlink:href="note-0054-02a" xml:space="preserve"><emph style="it">Areatim.</emph></note>
<note position="left" xlink:label="note-0054-03" xlink:href="note-0054-03a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi</emph>.</note>
</div>
</div>
<div xml:id="echoid-div103" type="section" level="1" n="56">
<head xml:id="echoid-head60" xml:space="preserve">PRONVNCIATVM XLIIII.</head>
<p>
  <s xml:id="echoid-s3488" xml:space="preserve">Altitudinem Solis ſupra horizontem omni momento, &amp; </s>
  <s xml:id="echoid-s3489" xml:space="preserve">ubicun gen-<lb/>tium adhuc ſexta ratione inuenire.</s>
  <s xml:id="echoid-s3490" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3491" xml:space="preserve">Miraris forſitan quòd tam diuerſas uias inueniendi altitudinem Solis ſupra horizon <lb/>tem tibi cõmonſtro, ſed deſines uti mirari, ubi cognoueris, nos hic uſ adeo magnũla <lb/>borem fruſtra non adſumpſiſſe. </s>
  <s xml:id="echoid-s3492" xml:space="preserve">Nam &amp; </s>
  <s xml:id="echoid-s3493" xml:space="preserve">neceſſariũ id nobis uidebatur eo maxime, quod <lb/>tabulæ altitudinũ, quas lingua Arabum Almicantharat dicimus, ad complura inſtrumẽ <lb/>
<anchor type="note" xlink:label="note-0054-04a" xlink:href="note-0054-04"/>
ta eorum´ cõpoſitiones adcommodari ſolent. </s>
  <s xml:id="echoid-s3494" xml:space="preserve">Deinde non parũ etiã uſum ipſum reſpe-<lb/>ximus, ſiquidem non rarus diuerſi modi alĳs at alĳs ſunt gratiores, imò &amp; </s>
  <s xml:id="echoid-s3495" xml:space="preserve">alĳs tempo <lb/>ribus alij ſunt aptiores, quamobrẽ libuit ad hanc rem quoddã uelut copiæ cornu adcom <lb/>modare, ratio autem iſta ſic habet. </s>
  <s xml:id="echoid-s3496" xml:space="preserve">Si ſinum quem facit horizon cum circulo magno ex <lb/>Sole ad ortũ æquatoris ducto, ducas in ſinum diſtantiæ Solis à puncto interſectionis æ-<lb/>
<anchor type="note" xlink:label="note-0054-05a" xlink:href="note-0054-05"/>
quinoctialis &amp; </s>
  <s xml:id="echoid-s3497" xml:space="preserve">horizontis, productum diuidas in ſinũ totũ, arcus quotientis monſtrabit <lb/>tibi altitudinem Solis ſupra horizontem. </s>
  <s xml:id="echoid-s3498" xml:space="preserve">?</s>
  <s xml:id="echoid-s3499" xml:space="preserve">? Exemplum ſit hoc tibi, Ipſa hora introni-<lb/>
<anchor type="note" xlink:label="note-0054-06a" xlink:href="note-0054-06"/>
zationis cupio ſcire altitudinem Solis ſupra horizontẽ, eſto igitur, ut iam ex 41. </s>
  <s xml:id="echoid-s3500" xml:space="preserve">ꝓnũc. <lb/></s>
  <s xml:id="echoid-s3501" xml:space="preserve">inuenerim angulũ horizontis &amp; </s>
  <s xml:id="echoid-s3502" xml:space="preserve">circuli magni per Solem &amp; </s>
  <s xml:id="echoid-s3503" xml:space="preserve">æquatoris ortum ducti, is <lb/>eſt 70. </s>
  <s xml:id="echoid-s3504" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3505" xml:space="preserve">8. </s>
  <s xml:id="echoid-s3506" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3507" xml:space="preserve">ſinum eius 94056. </s>
  <s xml:id="echoid-s3508" xml:space="preserve">ſi ducam in ſinum diſtantiæ Solis ab ortu æquatoris <lb/>in dicto circulo computato, diſtãtiam autem illam reperi per 39. </s>
  <s xml:id="echoid-s3509" xml:space="preserve">pronunc. </s>
  <s xml:id="echoid-s3510" xml:space="preserve">ad ipſam q̊ <lb/>intronizationis horã, &amp; </s>
  <s xml:id="echoid-s3511" xml:space="preserve">eſt ſanè 48. </s>
  <s xml:id="echoid-s3512" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3513" xml:space="preserve">35. </s>
  <s xml:id="echoid-s3514" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3515" xml:space="preserve">ſinus eius eſt 74991. </s>
  <s xml:id="echoid-s3516" xml:space="preserve">productum ſi diui-<lb/>dam in ſinum totum, prouenient in quotiente 70533. </s>
  <s xml:id="echoid-s3517" xml:space="preserve">arcus illius eſt 44. </s>
  <s xml:id="echoid-s3518" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3519" xml:space="preserve">52. </s>
  <s xml:id="echoid-s3520" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3521" xml:space="preserve">illa ni <lb/>mirum altitudo Solis, quam et quin ſuperioribus pronunc. </s>
  <s xml:id="echoid-s3522" xml:space="preserve">docuimus inuenire.</s>
  <s xml:id="echoid-s3523" xml:space="preserve"/>
</p>
<div xml:id="echoid-div103" type="float" level="2" n="1">
<note position="left" xlink:label="note-0054-04" xlink:href="note-0054-04a" xml:space="preserve"><emph style="it">Almican-</emph> <lb/><emph style="it">tharat</emph>.</note>
<note position="left" xlink:label="note-0054-05" xlink:href="note-0054-05a" xml:space="preserve"><emph style="it">Lateraliter</emph></note>
<note position="left" xlink:label="note-0054-06" xlink:href="note-0054-06a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi</emph>.</note>
</div>
</div>
<div xml:id="echoid-div105" type="section" level="1" n="57">
<head xml:id="echoid-head61" xml:space="preserve">PRONVNCIATVM XLV.</head>
<p>
  <s xml:id="echoid-s3524" xml:space="preserve">Diſtantiam Solis horizontalem à circulo uerticali alio modo perquirere.</s>
  <s xml:id="echoid-s3525" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3526" xml:space="preserve">Quia iam luꝑius oſtẽdimus quidnã ſit diſtãtia ☉(sun) à circulo uerticali, ſuperfluum fuerit <lb/>idẽ hic denuo repetere, ita  inuẽtionẽ eius tantũmodo oſtẽdere libet. </s>
  <s xml:id="echoid-s3527" xml:space="preserve">Principio ꝓpone ti <lb/>bi ſinũ cõplemẽti diſtãtiæ Solis à puncto interſectiõis horizõtis &amp; </s>
  <s xml:id="echoid-s3528" xml:space="preserve">æquinoctialis, ſimili-
<pb file="0055" n="55" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
ter &amp; </s>
  <s xml:id="echoid-s3529" xml:space="preserve">ſinum complementi altitudinis Solis ſupra horizontem, quam ſex rationibus di-<lb/>
<anchor type="note" xlink:label="note-0055-01a" xlink:href="note-0055-01"/>
diciſti inuenire, minorem ex ijs duc in totum, &amp; </s>
  <s xml:id="echoid-s3530" xml:space="preserve">productum inde diuide in maiorem pro <lb/>poſitorũ ſinuum, arcus quotientis à 90. </s>
  <s xml:id="echoid-s3531" xml:space="preserve">ſubtractus, reliquam faciet diſtantiam Solis ho-<lb/>rizontalẽ ab ortu æquatoris, hoc ſcilicet quod antea Azimuth appellauimus. </s>
  <s xml:id="echoid-s3532" xml:space="preserve">?</s>
  <s xml:id="echoid-s3533" xml:space="preserve">? Eius <lb/>
<anchor type="note" xlink:label="note-0055-02a" xlink:href="note-0055-02"/>
rei gratia exemplũ hoc conſidera. </s>
  <s xml:id="echoid-s3534" xml:space="preserve">Volo ſcire diſtantiam hanc ad horam intronizationis <lb/>&amp; </s>
  <s xml:id="echoid-s3535" xml:space="preserve">quia diuerſismodis iam ſupra altitudinem Solis ſemper eandem repperi, ſcilicet 44. <lb/></s>
  <s xml:id="echoid-s3536" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3537" xml:space="preserve">52. </s>
  <s xml:id="echoid-s3538" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3539" xml:space="preserve">Complementum eius eſt 45. </s>
  <s xml:id="echoid-s3540" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3541" xml:space="preserve">8. </s>
  <s xml:id="echoid-s3542" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3543" xml:space="preserve">ſinus ipſius 70875. </s>
  <s xml:id="echoid-s3544" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3545" xml:space="preserve">hic quia maior <lb/>eſt, diuiſoris fungitur officio. </s>
  <s xml:id="echoid-s3546" xml:space="preserve">Deinde per pronunc. </s>
  <s xml:id="echoid-s3547" xml:space="preserve">39. </s>
  <s xml:id="echoid-s3548" xml:space="preserve">inueni diſtantiam Solis ab ortu <lb/>æquatoris 48. </s>
  <s xml:id="echoid-s3549" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3550" xml:space="preserve">35. </s>
  <s xml:id="echoid-s3551" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3552" xml:space="preserve">complementum ipſius 41. </s>
  <s xml:id="echoid-s3553" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3554" xml:space="preserve">25. </s>
  <s xml:id="echoid-s3555" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3556" xml:space="preserve">ſinum eius 66145. </s>
  <s xml:id="echoid-s3557" xml:space="preserve">duco <lb/>in ſinum totum, productum in diuiſorem prius cognitum diuido, &amp; </s>
  <s xml:id="echoid-s3558" xml:space="preserve">prouenient in quo <lb/>tiente 93326. </s>
  <s xml:id="echoid-s3559" xml:space="preserve">arcum illius 68. </s>
  <s xml:id="echoid-s3560" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3561" xml:space="preserve">56. </s>
  <s xml:id="echoid-s3562" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3563" xml:space="preserve">ſi ſubtraxero à 90. </s>
  <s xml:id="echoid-s3564" xml:space="preserve">remanebunt 21. </s>
  <s xml:id="echoid-s3565" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3566" xml:space="preserve">3, mi. </s>
  <s xml:id="echoid-s3567" xml:space="preserve"><lb/>Azimuth ſcilicet illud rurſus alia ratione inuentũ, ̈ ſupra in 42. </s>
  <s xml:id="echoid-s3568" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3569" xml:space="preserve">43. </s>
  <s xml:id="echoid-s3570" xml:space="preserve">propoſitiõibus.</s>
  <s xml:id="echoid-s3571" xml:space="preserve"/>
</p>
<div xml:id="echoid-div105" type="float" level="2" n="1">
<note position="right" xlink:label="note-0055-01" xlink:href="note-0055-01a" xml:space="preserve"><emph style="it">Hoc per la</emph> <lb/><emph style="it">teralẽ pro-</emph> <lb/><emph style="it">aſſum aſſe</emph> <lb/><emph style="it">queris</emph>.</note>
<note position="right" xlink:label="note-0055-02" xlink:href="note-0055-02a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſcopi</emph>.</note>
</div>
</div>
<div xml:id="echoid-div107" type="section" level="1" n="58">
<head xml:id="echoid-head62" xml:space="preserve">PRONVNCIATVM XLVI.</head>
<p>
  <s xml:id="echoid-s3572" xml:space="preserve">Angulum quem facit eclyptica cum circulo altitudinis, quem Sol ſiue <lb/>ſtella attingit, ad horam aliquam propoſitam expedite cognoſcere.</s>
  <s xml:id="echoid-s3573" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3574" xml:space="preserve">Primum omnium diſces hic inuenire angulum quem facit circulus altitudinis <lb/>cum circulo maioriducto ex polo mundiper corpus ſolare, duc ita ſinum diſtantiæ So <lb/>lis à meridie in ſinum complementi altitudinis poli, productum diuide in totum ſinum, <lb/>
<anchor type="note" xlink:label="note-0055-03a" xlink:href="note-0055-03"/>
&amp; </s>
  <s xml:id="echoid-s3575" xml:space="preserve">quotientem reſerua, ei´ adiunge ſinum complementi altitudinis Solis, minorem duc <lb/>in ſinum perfectum, &amp; </s>
  <s xml:id="echoid-s3576" xml:space="preserve">rurſus diuide productum in maiorem, arcus quotientis erit ipſe <lb/>
<anchor type="note" xlink:label="note-0055-04a" xlink:href="note-0055-04"/>
angulus, de quo iam dixi. </s>
  <s xml:id="echoid-s3577" xml:space="preserve">Quod ſi hora obſeruatiõis fuerit ante meridiem, addeangulũ <lb/>hunc inuentum ad angulum, quem eclyptica facit cum meridiano, ſed ſi pomeridiana ex <lb/>titerit, ſubtrahe iſtum angulũ ab angulo eclypticæ &amp; </s>
  <s xml:id="echoid-s3578" xml:space="preserve">meridiani, &amp; </s>
  <s xml:id="echoid-s3579" xml:space="preserve">remanebit angulus <lb/>
<anchor type="note" xlink:label="note-0055-05a" xlink:href="note-0055-05"/>
optatus. </s>
  <s xml:id="echoid-s3580" xml:space="preserve">?</s>
  <s xml:id="echoid-s3581" xml:space="preserve">? Exemplo res erit facilior, diſtantia Solis ab aſcendente ſecundum eclypti-<lb/>cam eſt 45. </s>
  <s xml:id="echoid-s3582" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3583" xml:space="preserve">ſinus eius 70710. </s>
  <s xml:id="echoid-s3584" xml:space="preserve">eum duc in ſinum cõplementi altitudinis poli, ſcilicet <lb/>66913, productum diuide in ſinum totum, &amp; </s>
  <s xml:id="echoid-s3585" xml:space="preserve">quotientem tanquam minorem rurſus duc <lb/>in totum ſinum, illud´ productum diuide in ſinum complemẽti altitudinis poli, ſcilicet <lb/>70875. </s>
  <s xml:id="echoid-s3586" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3587" xml:space="preserve">quotiens dabit 66756. </s>
  <s xml:id="echoid-s3588" xml:space="preserve">arcus eius 41. </s>
  <s xml:id="echoid-s3589" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3590" xml:space="preserve">53. </s>
  <s xml:id="echoid-s3591" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3592" xml:space="preserve">erit angulus inter circulum al <lb/>ritudinis &amp; </s>
  <s xml:id="echoid-s3593" xml:space="preserve">circulum magnum per polos mũdi ductum comprehenſus, hunc ſi addas ad <lb/>angulum quem facit eclyptica iuxta illum gradum Solis cum meridiano (quando intro <lb/>nizatïo illa ante meridiem fa cta eſt) prodibũt 120, gra. </s>
  <s xml:id="echoid-s3594" xml:space="preserve">30. </s>
  <s xml:id="echoid-s3595" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3596" xml:space="preserve">qui angulus eſt cõprehen <lb/>ſus inter circulũ altitudinis &amp; </s>
  <s xml:id="echoid-s3597" xml:space="preserve">eclypticã uerſus ſeptentrionẽ, eum ſubtrahe de ſemicircu-<lb/>lo, &amp; </s>
  <s xml:id="echoid-s3598" xml:space="preserve">remanebunt 59. </s>
  <s xml:id="echoid-s3599" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3600" xml:space="preserve">30. </s>
  <s xml:id="echoid-s3601" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3602" xml:space="preserve">at is uerus eſt angulus quem quærebamus,</s>
</p>
<div xml:id="echoid-div107" type="float" level="2" n="1">
<note position="right" xlink:label="note-0055-03" xlink:href="note-0055-03a" xml:space="preserve"><emph style="it">Lateralis</emph> <lb/><emph style="it">ingreſſus</emph>.</note>
<note position="right" xlink:label="note-0055-04" xlink:href="note-0055-04a" xml:space="preserve"><emph style="it">Arealis in-</emph> <lb/><emph style="it">greſſus</emph>.</note>
<note position="right" xlink:label="note-0055-05" xlink:href="note-0055-05a" xml:space="preserve">EXEM. <lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi</emph>.</note>
</div>
</div>
<div xml:id="echoid-div109" type="section" level="1" n="59">
<head xml:id="echoid-head63" xml:space="preserve">PRONVNCIATVM XLVII.</head>
<p>
  <s xml:id="echoid-s3603" xml:space="preserve">Eundẽ hũc angulũ eclypticę &amp; </s>
  <s xml:id="echoid-s3604" xml:space="preserve">altitudĩs circuli alio adhuc modo inueſtigare.</s>
  <s xml:id="echoid-s3605" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3606" xml:space="preserve">Propone &amp; </s>
  <s xml:id="echoid-s3607" xml:space="preserve">hic tibi ſinum complementi diſtantiæ Solis ab aſcendente, ſimul´ ſinum <lb/>
<anchor type="note" xlink:label="note-0055-06a" xlink:href="note-0055-06"/>
complementi altitudinis Solis, minorem duc in totum, productum diuide in maiorẽ nu-<lb/>
<anchor type="note" xlink:label="note-0055-07a" xlink:href="note-0055-07"/>
merum ſinuum, quotientem rurſus duc in ſinum anguli eclypticæ &amp; </s>
  <s xml:id="echoid-s3608" xml:space="preserve">horizontis quem <lb/>faciunt tempore conſiderationis, productum diuide in ſinũ totum, quotiente ſubtracto à <lb/>
<anchor type="note" xlink:label="note-0055-08a" xlink:href="note-0055-08"/>
quadrante, remanebit angulus optatus, ſicut in exemplo ſubiecto conſpicis. </s>
  <s xml:id="echoid-s3609" xml:space="preserve">?</s>
  <s xml:id="echoid-s3610" xml:space="preserve">? Fuerit <lb/>ergo in die intronizationis diſtantia Solis ab aſcẽdente 62. </s>
  <s xml:id="echoid-s3611" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3612" xml:space="preserve">59. </s>
  <s xml:id="echoid-s3613" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3614" xml:space="preserve">Complementũ <lb/>eius eſt 27, gra. </s>
  <s xml:id="echoid-s3615" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3616" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3617" xml:space="preserve">ſinum illius 45424. </s>
  <s xml:id="echoid-s3618" xml:space="preserve">tan̈ minorẽ numerũ duc in ſinũ totũ, productũ <lb/>diuide in ſinum cõplementi altitudinis Solis. </s>
  <s xml:id="echoid-s3619" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s3620" xml:space="preserve">45. </s>
  <s xml:id="echoid-s3621" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3622" xml:space="preserve">8. </s>
  <s xml:id="echoid-s3623" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3624" xml:space="preserve">is eſt 70875. </s>
  <s xml:id="echoid-s3625" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3626" xml:space="preserve">proueniũt <lb/>in quotiente 60490. </s>
  <s xml:id="echoid-s3627" xml:space="preserve">hunc iterum duc in ſinum anguli eclypticæ &amp; </s>
  <s xml:id="echoid-s3628" xml:space="preserve">horizontis iuxta gra-<lb/>dum aſcendentis, ſcilicet 5. </s>
  <s xml:id="echoid-s3629" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3630" xml:space="preserve">25. </s>
  <s xml:id="echoid-s3631" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3632" xml:space="preserve">♌ cauſſatum, quia antea ſæpius repræſentabat <lb/>52. </s>
  <s xml:id="echoid-s3633" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3634" xml:space="preserve">21. </s>
  <s xml:id="echoid-s3635" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3636" xml:space="preserve">ſinus autem eius eſt 79175, mox diuide productum in ſinum totum, &amp; </s>
  <s xml:id="echoid-s3637" xml:space="preserve">quo <lb/>tiens dabit 50743. </s>
  <s xml:id="echoid-s3638" xml:space="preserve">arcus illius erit 30. </s>
  <s xml:id="echoid-s3639" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3640" xml:space="preserve">30. </s>
  <s xml:id="echoid-s3641" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3642" xml:space="preserve">eo ſubtracto â quadra circuli, rema-<lb/>nent 59. </s>
  <s xml:id="echoid-s3643" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3644" xml:space="preserve">30. </s>
  <s xml:id="echoid-s3645" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3646" xml:space="preserve">non aliter at in exemplo ſuperioris propoſitionis.</s>
  <s xml:id="echoid-s3647" xml:space="preserve"/>
</p>
<div xml:id="echoid-div109" type="float" level="2" n="1">
<note position="right" xlink:label="note-0055-06" xlink:href="note-0055-06a" xml:space="preserve"><emph style="it">Lateraliter</emph></note>
<note position="right" xlink:label="note-0055-07" xlink:href="note-0055-07a" xml:space="preserve"><emph style="it">Lateraliter</emph></note>
<note position="right" xlink:label="note-0055-08" xlink:href="note-0055-08a" xml:space="preserve">EXEM. <lb/>PLVM <lb/><emph style="it">Epiſcopi</emph>.</note>
</div>
</div>
<div xml:id="echoid-div111" type="section" level="1" n="60">
<head xml:id="echoid-head64" xml:space="preserve">PRONVNCIATVM XLVIII.</head>
<p>
  <s xml:id="echoid-s3648" xml:space="preserve">Angulum eum ipſum quem duabus propoſitionibus oſtendimus, adhuc <lb/>alia ratione indicare.</s>
  <s xml:id="echoid-s3649" xml:space="preserve"/>
</p>
<pb file="0056" n="56" rhead="GENVINVS VSVS"/>
<p>
  <s xml:id="echoid-s3650" xml:space="preserve">Primũ hic adſume ſinũ rectũ ſecundũ diſtãtiæ Solis à gradu aſcẽdẽtis, &amp; </s>
  <s xml:id="echoid-s3651" xml:space="preserve">ſinũrectũ ſe-<lb/>
<anchor type="note" xlink:label="note-0056-01a" xlink:href="note-0056-01"/>
cundũ altitudinis ☉(sun), minorẽ duc in ſinũ ꝓfectũ, ꝓductũ diuide in maiorẽ, &amp; </s>
  <s xml:id="echoid-s3652" xml:space="preserve">arcu quotiẽ-<lb/>tis à 90. </s>
  <s xml:id="echoid-s3653" xml:space="preserve">ſubtracto, ſinũ reſidui adhuc tibi denuo ꝓpone, &amp; </s>
  <s xml:id="echoid-s3654" xml:space="preserve">ſinũ diſtãtiæ Solis ab abſcẽden <lb/>te, deinde minorem illũ ex ijs duobus duc in ſinũ totũ, ꝓductũ diuide in maiorẽ, &amp; </s>
  <s xml:id="echoid-s3655" xml:space="preserve">arcus <lb/>quotientis mõſtrabit angulũ quæſitũ. </s>
  <s xml:id="echoid-s3656" xml:space="preserve">?</s>
  <s xml:id="echoid-s3657" xml:space="preserve">?V is exemplo rem magis ob oculos poni? </s>
  <s xml:id="echoid-s3658" xml:space="preserve">Ec-<lb/>
<anchor type="note" xlink:label="note-0056-02a" xlink:href="note-0056-02"/>
ce in ſaꝑiori perſiſtẽdo, dico in ipſa hora intronizationis Solẽ abfuiſſe ab aſcendente 62 <lb/>gra. </s>
  <s xml:id="echoid-s3659" xml:space="preserve">59. </s>
  <s xml:id="echoid-s3660" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3661" xml:space="preserve">iã ita cõplementũ eius eſt 27. </s>
  <s xml:id="echoid-s3662" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3663" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3664" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3665" xml:space="preserve">ſinus uero 45424. </s>
  <s xml:id="echoid-s3666" xml:space="preserve">illũ ꝗa minor eſt <lb/>duc in ſinũ totũ, ꝓductũ diu de ꝗ 70875. </s>
  <s xml:id="echoid-s3667" xml:space="preserve">at is eſt ſinus cõplemẽti altitudinis Solis ipſa <lb/>hora intronizationis, in quotiẽte ꝓueniũt 64090. </s>
  <s xml:id="echoid-s3668" xml:space="preserve">arcũ eius 39. </s>
  <s xml:id="echoid-s3669" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3670" xml:space="preserve">52. </s>
  <s xml:id="echoid-s3671" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3672" xml:space="preserve">ſubtrahe à 90. <lb/></s>
  <s xml:id="echoid-s3673" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3674" xml:space="preserve">remanebũt 50. </s>
  <s xml:id="echoid-s3675" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3676" xml:space="preserve">8. </s>
  <s xml:id="echoid-s3677" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3678" xml:space="preserve">Reſidui huius iterũ quære ſinũ ſcilicet 76753. </s>
  <s xml:id="echoid-s3679" xml:space="preserve">eũ duc in totũ, <lb/>diuide aũt productũ in ſinum diſtantiæ Solis ab aſcendente 89087. </s>
  <s xml:id="echoid-s3680" xml:space="preserve">in quotiente proue-<lb/>niunt 86155. </s>
  <s xml:id="echoid-s3681" xml:space="preserve">arcus illius eſt 59, gra. </s>
  <s xml:id="echoid-s3682" xml:space="preserve">30. </s>
  <s xml:id="echoid-s3683" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3684" xml:space="preserve">angulus. </s>
  <s xml:id="echoid-s3685" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s3686" xml:space="preserve">quæſitus, &amp; </s>
  <s xml:id="echoid-s3687" xml:space="preserve">iã triplici uia inuẽtus.</s>
  <s xml:id="echoid-s3688" xml:space="preserve"/>
</p>
<div xml:id="echoid-div111" type="float" level="2" n="1">
<note position="left" xlink:label="note-0056-01" xlink:href="note-0056-01a" xml:space="preserve"><emph style="it">Hoc latera</emph> <lb/><emph style="it">tim aſſeque</emph> <lb/><emph style="it">ris.</emph></note>
<note position="left" xlink:label="note-0056-02" xlink:href="note-0056-02a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſcopi.</emph></note>
</div>
</div>
<div xml:id="echoid-div113" type="section" level="1" n="61">
<head xml:id="echoid-head65" xml:space="preserve">PRONVNCIATVM XLIX.</head>
<p>
  <s xml:id="echoid-s3689" xml:space="preserve">Angulũ illũ, de qq̊ hactenus diſputatũ eſt, etiamnũ diuerſa uia inquirere.</s>
  <s xml:id="echoid-s3690" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3691" xml:space="preserve">Iam nunc ſinũ cõplementi altitudinis meridianæ (gra dũ illũ uolo zodiaci, qui ſub ho-<lb/>ram huius cõſiderationis mediũ cœli attingit, cuius etiã cõplementũ nihil aliud eſt niſi <lb/>diſtãtia gradus illius à uertice capitis) duc in ſinũ anguli, quem facit eclyptica cũ meridia <lb/>
<anchor type="note" xlink:label="note-0056-03a" xlink:href="note-0056-03"/>
no iuxta punctũ illud medĳ cœli, unde cõplementũ ſumitur, productũ diuide in ſinũ totũ <lb/>quotientem ſerua in locũ aliquem ſeorſim, &amp; </s>
  <s xml:id="echoid-s3692" xml:space="preserve">ei adiunge ſinũ altitudinis Solis, minorem <lb/>ducin totũ, ꝓductũ in maiorẽ diuide, &amp; </s>
  <s xml:id="echoid-s3693" xml:space="preserve">arcus quotientis oſtẽdet quantitatẽ anguli quæſi <lb/>ti. </s>
  <s xml:id="echoid-s3694" xml:space="preserve">?</s>
  <s xml:id="echoid-s3695" xml:space="preserve">? Adcõmodemus huc etiã exemplũ ſuꝗius. </s>
  <s xml:id="echoid-s3696" xml:space="preserve">In die &amp; </s>
  <s xml:id="echoid-s3697" xml:space="preserve">hora intronizatiõis fuit in me <lb/>
<anchor type="note" xlink:label="note-0056-04a" xlink:href="note-0056-04"/>
dio cœli 16. </s>
  <s xml:id="echoid-s3698" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3699" xml:space="preserve">40. </s>
  <s xml:id="echoid-s3700" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3701" xml:space="preserve">♈, ſicut in 25. </s>
  <s xml:id="echoid-s3702" xml:space="preserve">ꝓnunc. </s>
  <s xml:id="echoid-s3703" xml:space="preserve">declinationẽ eius inueni ꝑ ꝓnunc. </s>
  <s xml:id="echoid-s3704" xml:space="preserve">5. </s>
  <s xml:id="echoid-s3705" xml:space="preserve">6. </s>
  <s xml:id="echoid-s3706" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s3707" xml:space="preserve">35. </s>
  <s xml:id="echoid-s3708" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3709" xml:space="preserve">hãc adde ad cõplemẽtũ altitudinis poli 48. </s>
  <s xml:id="echoid-s3710" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3711" xml:space="preserve">illu@ eſt 42. </s>
  <s xml:id="echoid-s3712" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3713" xml:space="preserve">ſumma igitur erit <lb/>48. </s>
  <s xml:id="echoid-s3714" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3715" xml:space="preserve">34. </s>
  <s xml:id="echoid-s3716" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3717" xml:space="preserve">iam ſi cõplementũ eius accepero 41. </s>
  <s xml:id="echoid-s3718" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3719" xml:space="preserve">26. </s>
  <s xml:id="echoid-s3720" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3721" xml:space="preserve">ea ipſa eſt diſtantia medĳ <lb/>cœli à zenith capitis, ſinum cõplementi huius 66174. </s>
  <s xml:id="echoid-s3722" xml:space="preserve">duco in ſinũ anguli, quẽ eclyptica <lb/>
<anchor type="note" xlink:label="note-0056-05a" xlink:href="note-0056-05"/>
facit cũ meridiano iuxta illum gradum medĳ cœli, hunc etiam antea uaiĳs rationibus ad <lb/>inueni, eſt autem 67. </s>
  <s xml:id="echoid-s3723" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3724" xml:space="preserve">23. </s>
  <s xml:id="echoid-s3725" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3726" xml:space="preserve">ſinus eius 92309, productũ diuido in ſinum totũ, &amp; </s>
  <s xml:id="echoid-s3727" xml:space="preserve">quo <lb/>tiens puta minorẽ duco in totum, productũ diuido in ſinum maiorem, in quotiente pro <lb/>uenient 86173, arcus eius eſt 49. </s>
  <s xml:id="echoid-s3728" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3729" xml:space="preserve">30. </s>
  <s xml:id="echoid-s3730" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3731" xml:space="preserve">angulus ille quæſitus, quoniam hora intro-<lb/>nizationis fuit ante meridiem. </s>
  <s xml:id="echoid-s3732" xml:space="preserve">Sin autem hora conſiderationis eſſet pomeridiana, angu <lb/>lus inuẽtus ſubtrahi deberet à ſemicirculo ad hoc ut remanebit quãtitas anguli quæſiti.</s>
  <s xml:id="echoid-s3733" xml:space="preserve"/>
</p>
<div xml:id="echoid-div113" type="float" level="2" n="1">
<note position="left" xlink:label="note-0056-03" xlink:href="note-0056-03a" xml:space="preserve"><emph style="it">Lateralcm</emph> <lb/><emph style="it">animaduer</emph> <lb/><emph style="it"><gap/> ingreſ-</emph> <lb/><emph style="it">ſum.</emph></note>
<note position="left" xlink:label="note-0056-04" xlink:href="note-0056-04a" xml:space="preserve"><emph style="it">Arealis bic</emph> <lb/><emph style="it">conſideran</emph> <lb/><emph style="it">dus eſt in-</emph> <lb/><emph style="it">troitus.</emph></note>
<note position="left" xlink:label="note-0056-05" xlink:href="note-0056-05a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>Epiſcopi.</note>
</div>
</div>
<div xml:id="echoid-div115" type="section" level="1" n="62">
<head xml:id="echoid-head66" xml:space="preserve">PRONVNCIATVM L.</head>
<p>
  <s xml:id="echoid-s3734" xml:space="preserve">Cognito iam gradu aſcendentis, adhuc gradum eclypticæ qui mediat <lb/>cœlum explorare.</s>
  <s xml:id="echoid-s3735" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3736" xml:space="preserve">Quære principio amplitudinem aſcendentis per 12. </s>
  <s xml:id="echoid-s3737" xml:space="preserve">pronunc. </s>
  <s xml:id="echoid-s3738" xml:space="preserve">ſinum eius duc in ſinũ <lb/>anguli horizontis &amp; </s>
  <s xml:id="echoid-s3739" xml:space="preserve">eclypticæ, productum diuide in totum ſinum, deinde arcum quoti <lb/>
<anchor type="note" xlink:label="note-0056-06a" xlink:href="note-0056-06"/>
entis ſubtrahe à 90. </s>
  <s xml:id="echoid-s3740" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3741" xml:space="preserve">ſinũ reſidui tibi propone, ſimul´ ſinum complementi altitudinis, <lb/>minorem ex ĳs duc in ſinum totũ<emph style="sub">2</emph> productũ diuide in maiorẽ, &amp; </s>
  <s xml:id="echoid-s3742" xml:space="preserve">quotientis arcũ ſubtrahe <lb/>
<anchor type="note" xlink:label="note-0056-07a" xlink:href="note-0056-07"/>
à gra du aſcendentis, hoc eſt numera tot gradus ab aſcendente cõtra ordinẽ ſignorũ, ſi-<lb/>modo tũc gradus aſcendẽtis fuerit in ſigno aliq̊ meridionali. </s>
  <s xml:id="echoid-s3743" xml:space="preserve">Sed ſi in ſeptentrionali exti <lb/>terit, accipe cõtrariũ eius, puta gradũ eclypticæ occidentem eo temporis momẽto in par <lb/>te occidentis, &amp; </s>
  <s xml:id="echoid-s3744" xml:space="preserve">adde arcũ quotientis, ſic´ ꝓueniet gradus ille ꝗ mediat cœlũ. </s>
  <s xml:id="echoid-s3745" xml:space="preserve">?</s>
  <s xml:id="echoid-s3746" xml:space="preserve">? Ex-<lb/>emplo adiũcto rem plenius intelliges. </s>
  <s xml:id="echoid-s3747" xml:space="preserve">In ipſa intronizatiõis hora fuit in aſcendente 5. <lb/></s>
  <s xml:id="echoid-s3748" xml:space="preserve">
<anchor type="note" xlink:label="note-0056-08a" xlink:href="note-0056-08"/>
gra. </s>
  <s xml:id="echoid-s3749" xml:space="preserve">25. </s>
  <s xml:id="echoid-s3750" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3751" xml:space="preserve">♌, amplitudo eius eſt 29. </s>
  <s xml:id="echoid-s3752" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3753" xml:space="preserve">4. </s>
  <s xml:id="echoid-s3754" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3755" xml:space="preserve">ſinũ eius 48563. </s>
  <s xml:id="echoid-s3756" xml:space="preserve">duco in ſinũ anguli ecly-<lb/>pticæ &amp; </s>
  <s xml:id="echoid-s3757" xml:space="preserve">horizõtis, ſiquidẽ intronizatio illa facta eſt in latitudine 48. </s>
  <s xml:id="echoid-s3758" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3759" xml:space="preserve">angulus autẽ <lb/>erit 52. </s>
  <s xml:id="echoid-s3760" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3761" xml:space="preserve">21. </s>
  <s xml:id="echoid-s3762" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3763" xml:space="preserve">ſinus eius 79175. </s>
  <s xml:id="echoid-s3764" xml:space="preserve">productum ſi diuicã in totũ, proueniẽt in quotiẽte <lb/>38449 arcũ iplſius. </s>
  <s xml:id="echoid-s3765" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s3766" xml:space="preserve">22. </s>
  <s xml:id="echoid-s3767" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3768" xml:space="preserve">37. </s>
  <s xml:id="echoid-s3769" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3770" xml:space="preserve">ſubtraho à 90. </s>
  <s xml:id="echoid-s3771" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3772" xml:space="preserve">remanẽt 67. </s>
  <s xml:id="echoid-s3773" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3774" xml:space="preserve">23. </s>
  <s xml:id="echoid-s3775" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3776" xml:space="preserve">ſinum ipſius <lb/>92309. </s>
  <s xml:id="echoid-s3777" xml:space="preserve">tã̈ maiorẽ adſeruo ꝓ diuiſore, deinde adſumo ſinũ cõplemẽti amplitudinis, q̊d <lb/>ſanè ſuit 60. </s>
  <s xml:id="echoid-s3778" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3779" xml:space="preserve">56. </s>
  <s xml:id="echoid-s3780" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3781" xml:space="preserve">ſed ſinũ eius 87405. </s>
  <s xml:id="echoid-s3782" xml:space="preserve">duco in ſinũ totũ, ꝓductũ diuido in diuiſorẽ <lb/>iam ſeruatũ, quotiens dat 94687. </s>
  <s xml:id="echoid-s3783" xml:space="preserve">arcus illius eſt 71. </s>
  <s xml:id="echoid-s3784" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3785" xml:space="preserve">15. </s>
  <s xml:id="echoid-s3786" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3787" xml:space="preserve">tot gra. </s>
  <s xml:id="echoid-s3788" xml:space="preserve">dehinc addo ad <lb/>gradũ occidentis. </s>
  <s xml:id="echoid-s3789" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s3790" xml:space="preserve">5. </s>
  <s xml:id="echoid-s3791" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3792" xml:space="preserve">25. </s>
  <s xml:id="echoid-s3793" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3794" xml:space="preserve">♒ eò ꝙ aſcendens eſt ſignũ ſeptentrionale, &amp; </s>
  <s xml:id="echoid-s3795" xml:space="preserve">arcus hic <lb/>attingit 16. </s>
  <s xml:id="echoid-s3796" xml:space="preserve">gra 40. </s>
  <s xml:id="echoid-s3797" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3798" xml:space="preserve">?</s>
  <s xml:id="echoid-s3799" xml:space="preserve">?, medium ipſum cœli quod hactenus diligenter inquiſiuimus.</s>
  <s xml:id="echoid-s3800" xml:space="preserve"/>
</p>
<div xml:id="echoid-div115" type="float" level="2" n="1">
<note position="left" xlink:label="note-0056-06" xlink:href="note-0056-06a" xml:space="preserve"><emph style="it">Lateralis</emph> <lb/><emph style="it">ingreſſus.</emph></note>
<note position="left" xlink:label="note-0056-07" xlink:href="note-0056-07a" xml:space="preserve"><emph style="it">Arealis in-</emph> <lb/><emph style="it">greſſus.</emph></note>
<note position="left" xlink:label="note-0056-08" xlink:href="note-0056-08a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>Epiſcopi.</note>
</div>
<pb file="0057" n="57" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
</div>
<div xml:id="echoid-div117" type="section" level="1" n="63">
<head xml:id="echoid-head67" xml:space="preserve">PRONVNCIATVM LI.</head>
<p>
  <s xml:id="echoid-s3801" xml:space="preserve">Arcum circuli maioris, qui per utrun polũ mundi &amp; </s>
  <s xml:id="echoid-s3802" xml:space="preserve">corpus ſolare duci-<lb/>citur, at alio nomine circulus horarius dicitur, quantus ille ſit à polo mũdi <lb/>arctico uſ ad horizontem, per ſupputationem triangularem cognoſcere.</s>
  <s xml:id="echoid-s3803" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3804" xml:space="preserve">Et ſi arcus ille per ſe magnopere neceſſarius non eſt, ad ſequens tamen pronunc. </s>
  <s xml:id="echoid-s3805" xml:space="preserve">plu <lb/>rimum conducet, operatio ita iſta ſic habet. </s>
  <s xml:id="echoid-s3806" xml:space="preserve">Propone tibi ſinum complementi altitudi <lb/>
<anchor type="note" xlink:label="note-0057-01a" xlink:href="note-0057-01"/>
nis poli, eum duc in ſinum diſtantiæ Solis à meridie, productum diuide in ſinum totum, <lb/>&amp; </s>
  <s xml:id="echoid-s3807" xml:space="preserve">quotientis arcum ſubtrahe à 90. </s>
  <s xml:id="echoid-s3808" xml:space="preserve">ſinum reſidui rurſus tibi propone, ſimul cum ſinu alti <lb/>tudinis poli, uter illorum fuerit minor, eum ducito in totum ſinum, hinc productum diui <lb/>de in maiorem, &amp; </s>
  <s xml:id="echoid-s3809" xml:space="preserve">arcus quotientis monſtrabit tibi arcum circuli maioris ducti per polos <lb/>mundi, &amp; </s>
  <s xml:id="echoid-s3810" xml:space="preserve">per locum Solis, ipſa hora conſiderationis inter polum mundi arcticum &amp; </s>
  <s xml:id="echoid-s3811" xml:space="preserve">ho <lb/>rizontem compræhenſum. </s>
  <s xml:id="echoid-s3812" xml:space="preserve">?</s>
  <s xml:id="echoid-s3813" xml:space="preserve">?Non erit (opinor) moleſtum hic tibi, ſi exemplo ſubie-<lb/>
<anchor type="note" xlink:label="note-0057-02a" xlink:href="note-0057-02"/>
cto rem tibi conemur planius oſtendere, propono hic tibi 2. </s>
  <s xml:id="echoid-s3814" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3815" xml:space="preserve">26. </s>
  <s xml:id="echoid-s3816" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3817" xml:space="preserve">II, ubi Sol fuit <lb/>ipſa hora intronizationis, ſimul etiam horam tibi præſcribo intronizationis 9. </s>
  <s xml:id="echoid-s3818" xml:space="preserve">ante me <lb/>ridiem. </s>
  <s xml:id="echoid-s3819" xml:space="preserve">diſtantia igitur Solis à meridie eſt trium horarum, quarum ſinus eſt 70710. </s>
  <s xml:id="echoid-s3820" xml:space="preserve">ſiqui <lb/>dem horæ 3. </s>
  <s xml:id="echoid-s3821" xml:space="preserve">gradus conſiciunt 45. </s>
  <s xml:id="echoid-s3822" xml:space="preserve">ſemper 15. </s>
  <s xml:id="echoid-s3823" xml:space="preserve">gradus pro hora computando. </s>
  <s xml:id="echoid-s3824" xml:space="preserve">Et quia in-<lb/>
<anchor type="note" xlink:label="note-0057-03a" xlink:href="note-0057-03"/>
tronizatio facta eſt in 48. </s>
  <s xml:id="echoid-s3825" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3826" xml:space="preserve">polaris eleuationis, complementum eius eſt 42. </s>
  <s xml:id="echoid-s3827" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3828" xml:space="preserve">ſinũ <lb/>igitur ipſius 66913. </s>
  <s xml:id="echoid-s3829" xml:space="preserve">ducin ſinum trium horarum, productum diuide in ſinum totum, &amp; </s>
  <s xml:id="echoid-s3830" xml:space="preserve"><lb/>in quotiente prouenient 74314. </s>
  <s xml:id="echoid-s3831" xml:space="preserve">arcus eius eſt 28. </s>
  <s xml:id="echoid-s3832" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3833" xml:space="preserve">14. </s>
  <s xml:id="echoid-s3834" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3835" xml:space="preserve">quibus ſubtractis à 90. </s>
  <s xml:id="echoid-s3836" xml:space="preserve">rema <lb/>nent 61. </s>
  <s xml:id="echoid-s3837" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3838" xml:space="preserve">46. </s>
  <s xml:id="echoid-s3839" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3840" xml:space="preserve">ſinus illius diuiſor efficitur, quietiam quum ſit maior ſinu altitudi-<lb/>nis poli 48. </s>
  <s xml:id="echoid-s3841" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3842" xml:space="preserve">ideo ducendus tibi eſt ſinus altitudinis poli, ſcilicet 74314. </s>
  <s xml:id="echoid-s3843" xml:space="preserve">in totum ſinũ <lb/>productum uero diuidendũ in diuiſorem iam ſeruatum. </s>
  <s xml:id="echoid-s3844" xml:space="preserve">In quotiente comperies 84349. <lb/></s>
  <s xml:id="echoid-s3845" xml:space="preserve">cuius arcus eſt 57. </s>
  <s xml:id="echoid-s3846" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3847" xml:space="preserve">31. </s>
  <s xml:id="echoid-s3848" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3849" xml:space="preserve">ille nimirum quem hactemus inquirebas, planè enim tan-<lb/>tus eſt etiam arcus huius circuli inter horizontem &amp; </s>
  <s xml:id="echoid-s3850" xml:space="preserve">polum arcticum.</s>
  <s xml:id="echoid-s3851" xml:space="preserve"/>
</p>
<div xml:id="echoid-div117" type="float" level="2" n="1">
<note position="right" xlink:label="note-0057-01" xlink:href="note-0057-01a" xml:space="preserve"><emph style="it">Introitu la-</emph> <lb/><emph style="it">terali qua-</emph> <lb/><emph style="it">drantem in</emph> <lb/><emph style="it">grediaris,</emph> <lb/><emph style="it">deinde are-</emph> <lb/><emph style="it">li.</emph></note>
<note position="right" xlink:label="note-0057-02" xlink:href="note-0057-02a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>Epiſcopi.</note>
<note position="right" xlink:label="note-0057-03" xlink:href="note-0057-03a" xml:space="preserve"><emph style="it">Intronizd-</emph> <lb/><emph style="it">tio facta eſt</emph> <lb/><emph style="it">in 48. gra.</emph> <lb/><emph style="it">eleuationis</emph> <lb/><emph style="it">poli.</emph></note>
</div>
</div>
<div xml:id="echoid-div119" type="section" level="1" n="64">
<head xml:id="echoid-head68" xml:space="preserve">PRONVNCIATVM LII.</head>
<p>
  <s xml:id="echoid-s3852" xml:space="preserve">Locum ſiue punctũ horizontis, ubi linea horaria in plano horizontali, ſi-<lb/>militer &amp; </s>
  <s xml:id="echoid-s3853" xml:space="preserve">circulus horarius in corpore ſphærico tangit horizontẽ, inuenire.</s>
  <s xml:id="echoid-s3854" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3855" xml:space="preserve">Attendenda quæ nũc docebimus tibi erũt diligenter, maxime aũt ſi te delectant cõpo <lb/>ſitiones inſtrumentorũ quæ ſolaria uocantur horizõtalia, hoc eſt, ſi in ſuperficie aliqua <lb/>plana horizonti tuo æquidiſtante cupis diuidere horas. </s>
  <s xml:id="echoid-s3856" xml:space="preserve">Adſume ita arcũ huius circu-<lb/>li horarĳ â polo mundi uſ in horizontẽ, quem ex antecedente propoſitione cognoui-<lb/>ſti, ſinum eius duc in ſinũ diſtantiæ Solis horariæ â meridie, ſiue ante ſiue poſt meridiem, <lb/>
<anchor type="note" xlink:label="note-0057-04a" xlink:href="note-0057-04"/>
productum diuide in ſinũ totum, &amp; </s>
  <s xml:id="echoid-s3857" xml:space="preserve">tunc arcus quotientis arguet arcũ horizontis interce <lb/>ptum inter meridianũ &amp; </s>
  <s xml:id="echoid-s3858" xml:space="preserve">circulũ horariũ, qui tranſit per locũ Solis &amp; </s>
  <s xml:id="echoid-s3859" xml:space="preserve">utrun polũ mun-<lb/>di. </s>
  <s xml:id="echoid-s3860" xml:space="preserve">Ne uero eſt quòd putes ſimpliciter tibi habendũ ſemper eſſe locum Solis, ſed diſtanti <lb/>am horariam tibi tantum propone, non conſiderãs, ubicun Sol ſit in zodiaco. </s>
  <s xml:id="echoid-s3861" xml:space="preserve">?</s>
  <s xml:id="echoid-s3862" xml:space="preserve">? Ex <lb/>
<anchor type="note" xlink:label="note-0057-05a" xlink:href="note-0057-05"/>
emplum huius rei tibi ſit tale. </s>
  <s xml:id="echoid-s3863" xml:space="preserve">Cupio ſcire, quo tandem intronizationis hora, quæ 3. </s>
  <s xml:id="echoid-s3864" xml:space="preserve">fuit <lb/>ante meridiẽ, uel ipſa umbra ab axe mũdi pertigerit. </s>
  <s xml:id="echoid-s3865" xml:space="preserve">ne hic opus eſt, ut conſiderem, <lb/>in quo ſigno ſiue gradu Sol fuerit, ſed tantũ adſumo ſinũ triũ horarũ, qui eſt 45 graduum <lb/>70710. </s>
  <s xml:id="echoid-s3866" xml:space="preserve">eũ duco in ſinũ arcus circuli horarĳ inter polũ mundi &amp; </s>
  <s xml:id="echoid-s3867" xml:space="preserve">horizontẽ intercluſum, <lb/>quẽ iam q̊ ex ſuperiori pronunciat. </s>
  <s xml:id="echoid-s3868" xml:space="preserve">inuentũ habeo, eſt autem 57. </s>
  <s xml:id="echoid-s3869" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3870" xml:space="preserve">31. </s>
  <s xml:id="echoid-s3871" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3872" xml:space="preserve">ſinus ipſe <lb/>84349. </s>
  <s xml:id="echoid-s3873" xml:space="preserve">Hinc ubi productũ diuido in ſinũ totũ, remanent 59643. </s>
  <s xml:id="echoid-s3874" xml:space="preserve">arcus eſt 36. </s>
  <s xml:id="echoid-s3875" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3876" xml:space="preserve">38. </s>
  <s xml:id="echoid-s3877" xml:space="preserve">mi. <lb/></s>
  <s xml:id="echoid-s3878" xml:space="preserve">At hoc eſt, quod hucuſ inueſtigauimus. </s>
  <s xml:id="echoid-s3879" xml:space="preserve">Tantum etiam in plano horizontali diſtat li <lb/>nea horæ 9 ante meridiẽ uerſus ſeptentrionem à linea meridiana, ex altera quo parte ſi <lb/>militer tantum diſtat linea horæ 3. </s>
  <s xml:id="echoid-s3880" xml:space="preserve">à linea meridiana. </s>
  <s xml:id="echoid-s3881" xml:space="preserve">Et ad hunc quidem modum ipſe ti <lb/>bi potes tabulas ſupputare, ad omnes horas &amp; </s>
  <s xml:id="echoid-s3882" xml:space="preserve">ad quaſcun eleuationes poli, ſicut in no-<lb/>ſtro opere de V mbris ad omnes polares eleuationes clare perſpicies.</s>
  <s xml:id="echoid-s3883" xml:space="preserve"/>
</p>
<div xml:id="echoid-div119" type="float" level="2" n="1">
<note position="right" xlink:label="note-0057-04" xlink:href="note-0057-04a" xml:space="preserve"><emph style="it">Illud babe-</emph> <lb/><emph style="it">tur per qua</emph> <lb/><emph style="it">drãtis late-</emph> <lb/><emph style="it">ra.</emph></note>
<note position="right" xlink:label="note-0057-05" xlink:href="note-0057-05a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>Epiſoo<unsure/>pi.</note>
</div>
</div>
<div xml:id="echoid-div121" type="section" level="1" n="65">
<head xml:id="echoid-head69" xml:space="preserve">PRONVNCIATVM LIII.</head>
<p>
  <s xml:id="echoid-s3884" xml:space="preserve">Arcũ illũ horizõtis inter meridianũ &amp; </s>
  <s xml:id="echoid-s3885" xml:space="preserve">circulũ horariũ cõprehenſum adhuc <lb/>alia quadã ratione inueſtigare, iſtũ inquã, qui per locũ Solis protenditur.</s>
  <s xml:id="echoid-s3886" xml:space="preserve"/>
</p>
<pb file="0058" n="58" rhead="GENVINVS VSVS"/>
<p>
  <s xml:id="echoid-s3887" xml:space="preserve">Si nondum è memoria tua excidit, quod per 4. </s>
  <s xml:id="echoid-s3888" xml:space="preserve">pronunciata 46 47. </s>
  <s xml:id="echoid-s3889" xml:space="preserve">48. </s>
  <s xml:id="echoid-s3890" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3891" xml:space="preserve">49. </s>
  <s xml:id="echoid-s3892" xml:space="preserve">angulũ <lb/>eclypticæ &amp; </s>
  <s xml:id="echoid-s3893" xml:space="preserve">circuli altitudinis inuenire didiciſti, dici nõ poteſt quantũ contulerit ad hanc <lb/>rem, ſimiliter quomodo angulum eclypticæ &amp; </s>
  <s xml:id="echoid-s3894" xml:space="preserve">meridiani per 26. </s>
  <s xml:id="echoid-s3895" xml:space="preserve">27 &amp; </s>
  <s xml:id="echoid-s3896" xml:space="preserve">28. </s>
  <s xml:id="echoid-s3897" xml:space="preserve">pronunc. </s>
  <s xml:id="echoid-s3898" xml:space="preserve">re-<lb/>periſti. </s>
  <s xml:id="echoid-s3899" xml:space="preserve">adhuc autem &amp; </s>
  <s xml:id="echoid-s3900" xml:space="preserve">altitudinem Solis ex 34. </s>
  <s xml:id="echoid-s3901" xml:space="preserve">35. </s>
  <s xml:id="echoid-s3902" xml:space="preserve">36. </s>
  <s xml:id="echoid-s3903" xml:space="preserve">37. </s>
  <s xml:id="echoid-s3904" xml:space="preserve">38. </s>
  <s xml:id="echoid-s3905" xml:space="preserve">ſiue etiam 44. </s>
  <s xml:id="echoid-s3906" xml:space="preserve">pronunc. </s>
  <s xml:id="echoid-s3907" xml:space="preserve">ad <lb/>inueniſti. </s>
  <s xml:id="echoid-s3908" xml:space="preserve">Si ergo ſubtrahas angulũ eclypticæ &amp; </s>
  <s xml:id="echoid-s3909" xml:space="preserve">circuli altitudinis abangulo eclypticæ <lb/>&amp; </s>
  <s xml:id="echoid-s3910" xml:space="preserve">meridiani, ducas aũt reſidui ſinum in ſinũ cõplementi altitudinis Solis, &amp; </s>
  <s xml:id="echoid-s3911" xml:space="preserve">ꝓductũ diui <lb/>
<anchor type="note" xlink:label="note-0058-01a" xlink:href="note-0058-01"/>
das in ſinum totũ, quotientis uero arcũ ſubtrahas à 90. </s>
  <s xml:id="echoid-s3912" xml:space="preserve">ſeponas inde in locũ peculiarem <lb/>tam reſidui huius ſinum, minorẽ poſtremò ex his duobus ducas in totũ, ꝓductũ diuidas <lb/>in maiorem, tunc ſanè arcus quotientis portionem tibi præſtabit circuli horarĳ inter cor <lb/>pus ſolare &amp; </s>
  <s xml:id="echoid-s3913" xml:space="preserve">horizontem cõpræhenſam. </s>
  <s xml:id="echoid-s3914" xml:space="preserve">Poſtea ſi ſinũ huius portionis ducas in ſinũ dif-<lb/>
<anchor type="note" xlink:label="note-0058-02a" xlink:href="note-0058-02"/>
ferentiæ angulorũ, quo prius etiam ſinum cõplementi altitudinis Solis multiplica ueras, <lb/>productũ uero diuidas in ſinũ totũ, arcus quotientis oſtendet tibi diſtantiã conta ctus ho <lb/>
<anchor type="note" xlink:label="note-0058-03a" xlink:href="note-0058-03"/>
rizontis &amp; </s>
  <s xml:id="echoid-s3915" xml:space="preserve">circuli horarĳ à circulo altitudinis Solis, quæ alio nomine Azimuth dici ſo-<lb/>let. </s>
  <s xml:id="echoid-s3916" xml:space="preserve">Quod ſi ergo Azimuth Solis iam antea per aliquam ex 42. </s>
  <s xml:id="echoid-s3917" xml:space="preserve">43. </s>
  <s xml:id="echoid-s3918" xml:space="preserve">aut 45. </s>
  <s xml:id="echoid-s3919" xml:space="preserve">pronunc. </s>
  <s xml:id="echoid-s3920" xml:space="preserve">in-<lb/>ueniſti, facile deinde colliges hinc ipſearcum horizontis inter meridianum &amp; </s>
  <s xml:id="echoid-s3921" xml:space="preserve">circulum <lb/>
<anchor type="note" xlink:label="note-0058-04a" xlink:href="note-0058-04"/>
horarium interceptum. </s>
  <s xml:id="echoid-s3922" xml:space="preserve">?</s>
  <s xml:id="echoid-s3923" xml:space="preserve">? Sed &amp; </s>
  <s xml:id="echoid-s3924" xml:space="preserve">hic forte exemplũ deſideras? </s>
  <s xml:id="echoid-s3925" xml:space="preserve">en hoc tibi. </s>
  <s xml:id="echoid-s3926" xml:space="preserve">Horamin-<lb/>tronizatiõis ornatiſsimi Præſulis Auguſtani, iam inueni, ſimiliter &amp; </s>
  <s xml:id="echoid-s3927" xml:space="preserve">diem, ad illud tem <lb/>pus reperi etiam angulũ eclypticæ &amp; </s>
  <s xml:id="echoid-s3928" xml:space="preserve">circuli altitudinis 69. </s>
  <s xml:id="echoid-s3929" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3930" xml:space="preserve">30. </s>
  <s xml:id="echoid-s3931" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3932" xml:space="preserve">angulum quo <lb/>eclypticæ &amp; </s>
  <s xml:id="echoid-s3933" xml:space="preserve">meridiani 101. </s>
  <s xml:id="echoid-s3934" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3935" xml:space="preserve">23. </s>
  <s xml:id="echoid-s3936" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3937" xml:space="preserve">minore à maiore ſubrracto, remanẽt 41. </s>
  <s xml:id="echoid-s3938" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3939" xml:space="preserve">53. <lb/></s>
  <s xml:id="echoid-s3940" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3941" xml:space="preserve">quæ differẽtia dicetur angulorũ, ſinũ eius 66761. </s>
  <s xml:id="echoid-s3942" xml:space="preserve">duco in ſinũ cõplementi altitudinis <lb/>Solis .</s>
  <s xml:id="echoid-s3943" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s3944" xml:space="preserve">70875. </s>
  <s xml:id="echoid-s3945" xml:space="preserve">ꝓductũ diuido in ſinum totũ, &amp; </s>
  <s xml:id="echoid-s3946" xml:space="preserve">prouenient in quotiente 47317. </s>
  <s xml:id="echoid-s3947" xml:space="preserve">cuius <lb/>arcus eſt 28. </s>
  <s xml:id="echoid-s3948" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3949" xml:space="preserve">13. </s>
  <s xml:id="echoid-s3950" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3951" xml:space="preserve">Cõplemẽtũ uero eius 61. </s>
  <s xml:id="echoid-s3952" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3953" xml:space="preserve">47 mi. </s>
  <s xml:id="echoid-s3954" xml:space="preserve">ſinus ipſius (quia maior) erit <lb/>diuiſor 88116. </s>
  <s xml:id="echoid-s3955" xml:space="preserve">Iam nunc duco ſinum altitudinis Solis (tan̈ minorem) 44. </s>
  <s xml:id="echoid-s3956" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3957" xml:space="preserve">52. </s>
  <s xml:id="echoid-s3958" xml:space="preserve">mi .</s>
  <s xml:id="echoid-s3959" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s3960" xml:space="preserve"><lb/>70530. </s>
  <s xml:id="echoid-s3961" xml:space="preserve">in ſinum totum, productum uero diuido in diuiſorem paulo ante cognitum, &amp; </s>
  <s xml:id="echoid-s3962" xml:space="preserve"><lb/>erit quotiens 80042. </s>
  <s xml:id="echoid-s3963" xml:space="preserve">arcus eius 53. </s>
  <s xml:id="echoid-s3964" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3965" xml:space="preserve">10, mi. </s>
  <s xml:id="echoid-s3966" xml:space="preserve">monſtrat diſtantiam corporis ſolaris in <lb/>circulo horario ab horizonte. </s>
  <s xml:id="echoid-s3967" xml:space="preserve">Porrò inde rurſus duco ſinum huius quotientis in ſinum <lb/>differentiæ angulorum .</s>
  <s xml:id="echoid-s3968" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s3969" xml:space="preserve">66761. </s>
  <s xml:id="echoid-s3970" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3971" xml:space="preserve">diuido productum in totum, in quotiente proueni-<lb/>ent 53419. </s>
  <s xml:id="echoid-s3972" xml:space="preserve">arcus illius eſt 32. </s>
  <s xml:id="echoid-s3973" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3974" xml:space="preserve">18. </s>
  <s xml:id="echoid-s3975" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3976" xml:space="preserve">arcus .</s>
  <s xml:id="echoid-s3977" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s3978" xml:space="preserve">horizõtis inter contactum ipſius &amp; </s>
  <s xml:id="echoid-s3979" xml:space="preserve">cir <lb/>culi horarĳ &amp; </s>
  <s xml:id="echoid-s3980" xml:space="preserve">Azimuth Solis, &amp; </s>
  <s xml:id="echoid-s3981" xml:space="preserve">quia Azimuth per 42. </s>
  <s xml:id="echoid-s3982" xml:space="preserve">43. </s>
  <s xml:id="echoid-s3983" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3984" xml:space="preserve">45. </s>
  <s xml:id="echoid-s3985" xml:space="preserve">pronunciata inueni ha <lb/>bere 21. </s>
  <s xml:id="echoid-s3986" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3987" xml:space="preserve">4. </s>
  <s xml:id="echoid-s3988" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3989" xml:space="preserve">addo utrun, &amp; </s>
  <s xml:id="echoid-s3990" xml:space="preserve">prodibũt 53. </s>
  <s xml:id="echoid-s3991" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3992" xml:space="preserve">22. </s>
  <s xml:id="echoid-s3993" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3994" xml:space="preserve">quæ diſtantia eſt huius pun-<lb/>cti horizontis ab ortu æquinoctialis, quibus ſubtractis à 90. </s>
  <s xml:id="echoid-s3995" xml:space="preserve">remanebit diſtantia eius à <lb/>meridiano 36. </s>
  <s xml:id="echoid-s3996" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s3997" xml:space="preserve">38. </s>
  <s xml:id="echoid-s3998" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s3999" xml:space="preserve">quemadmodum &amp; </s>
  <s xml:id="echoid-s4000" xml:space="preserve">ſuperiori propoſitione inueneras.</s>
  <s xml:id="echoid-s4001" xml:space="preserve"/>
</p>
<div xml:id="echoid-div121" type="float" level="2" n="1">
<note position="left" xlink:label="note-0058-01" xlink:href="note-0058-01a" xml:space="preserve"><emph style="it">Lateraliter</emph> <lb/><emph style="it">dicta quæ-</emph> <lb/><emph style="it">rẽti patẽt.</emph></note>
<note position="left" xlink:label="note-0058-02" xlink:href="note-0058-02a" xml:space="preserve">Areatim.</note>
<note position="left" xlink:label="note-0058-03" xlink:href="note-0058-03a" xml:space="preserve"><emph style="it">Lateraliter</emph></note>
<note position="left" xlink:label="note-0058-04" xlink:href="note-0058-04a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoopi.</emph></note>
</div>
</div>
<div xml:id="echoid-div123" type="section" level="1" n="66">
<head xml:id="echoid-head70" xml:space="preserve">PRONVNCIATVM LIIII.</head>
<p>
  <s xml:id="echoid-s4002" xml:space="preserve">Arcum horizontis, quem arcus horarius inter ſeipſum &amp; </s>
  <s xml:id="echoid-s4003" xml:space="preserve">meridianum <lb/>includit, adhuc alia ea´ omnium facilima ratione perquirere.</s>
  <s xml:id="echoid-s4004" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s4005" xml:space="preserve">Age fac ducas hic ſinum diſtantiæ horariæ à meridie in ſinum cõplementi altitudinis <lb/>
<anchor type="note" xlink:label="note-0058-05a" xlink:href="note-0058-05"/>
poli, productũ diuide in ſinum totũ, arcũ autẽ quotientis ſubtrahe à 90. </s>
  <s xml:id="echoid-s4006" xml:space="preserve">ſinum cõplemen <lb/>ti huius ſiue reſidui tibi propone, unà cum ſinu cõplementi diſtantiæ horariæ à meridie, <lb/>minorem ducin totum, productum in maiorem diuide, &amp; </s>
  <s xml:id="echoid-s4007" xml:space="preserve">cõplementiarcus quotientis <lb/>monſtrabit tibi arcum horizontis quæſitum. </s>
  <s xml:id="echoid-s4008" xml:space="preserve">?</s>
  <s xml:id="echoid-s4009" xml:space="preserve">?Et ſi operatio hæcomniũ facilima eſt, <lb/>
<anchor type="note" xlink:label="note-0058-06a" xlink:href="note-0058-06"/>
tamen ne hic exemplũ tibi denegare poſſum, quia igitur ſub ipſam horam nonam in-<lb/>tronizationis horæ 3. </s>
  <s xml:id="echoid-s4010" xml:space="preserve">ſunt à meridie, quæ faciũt gra. </s>
  <s xml:id="echoid-s4011" xml:space="preserve">45. </s>
  <s xml:id="echoid-s4012" xml:space="preserve">ſinus erit 70710. </s>
  <s xml:id="echoid-s4013" xml:space="preserve">eum duco in ſi-<lb/>num cõplemẽti altitudinis poli 48. </s>
  <s xml:id="echoid-s4014" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4015" xml:space="preserve">hoceſt 42. </s>
  <s xml:id="echoid-s4016" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4017" xml:space="preserve">ſinus eius eſt 66913. </s>
  <s xml:id="echoid-s4018" xml:space="preserve">ꝓductũ diui <lb/>do in totum ſinũ, unde in quotiente ꝓueniunt 47314. </s>
  <s xml:id="echoid-s4019" xml:space="preserve">arcus eius eſt 28. </s>
  <s xml:id="echoid-s4020" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4021" xml:space="preserve">14. </s>
  <s xml:id="echoid-s4022" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4023" xml:space="preserve">ſinus <lb/>aũt cõplemẽti ipſius 88102. </s>
  <s xml:id="echoid-s4024" xml:space="preserve">hũc mihi propono, ſimul &amp; </s>
  <s xml:id="echoid-s4025" xml:space="preserve">ſinũ cõplemẽti diſtantiæ horariæ <lb/>à meridie, hoc eſt 45. </s>
  <s xml:id="echoid-s4026" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4027" xml:space="preserve">ſinus eſt 70710. </s>
  <s xml:id="echoid-s4028" xml:space="preserve">hũc quia minorẽ duco in ſinũ totũ, productum <lb/>diuido in maiorem, &amp; </s>
  <s xml:id="echoid-s4029" xml:space="preserve">prodibunt in quotiente 30259. </s>
  <s xml:id="echoid-s4030" xml:space="preserve">cuius arcus eſt 5. </s>
  <s xml:id="echoid-s4031" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4032" xml:space="preserve">22. </s>
  <s xml:id="echoid-s4033" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4034" xml:space="preserve">com-<lb/>plementum ipſius 36. </s>
  <s xml:id="echoid-s4035" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4036" xml:space="preserve">38. </s>
  <s xml:id="echoid-s4037" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4038" xml:space="preserve">ſicut in 52. </s>
  <s xml:id="echoid-s4039" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4040" xml:space="preserve">53. </s>
  <s xml:id="echoid-s4041" xml:space="preserve">pronunciatis inuentum eſt.</s>
  <s xml:id="echoid-s4042" xml:space="preserve"/>
</p>
<div xml:id="echoid-div123" type="float" level="2" n="1">
<note position="left" xlink:label="note-0058-05" xlink:href="note-0058-05a" xml:space="preserve"><emph style="it">Latera qua</emph> <lb/><emph style="it">drantis boc</emph> <lb/><emph style="it">idem docẽt.</emph> <lb/><emph style="it">Illud ꝑ areã</emph> <lb/><emph style="it">diſœs.</emph></note>
<note position="left" xlink:label="note-0058-06" xlink:href="note-0058-06a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>Epiſoo<unsure/>pi.</note>
</div>
</div>
<div xml:id="echoid-div125" type="section" level="1" n="67">
<head xml:id="echoid-head71" xml:space="preserve">PRONVNCIATVM LV.</head>
<p>
  <s xml:id="echoid-s4043" xml:space="preserve">Arcum quo in circulo uerticali, inter circulum horarium &amp; </s>
  <s xml:id="echoid-s4044" xml:space="preserve">meridianum <lb/>interceptum exacta &amp; </s>
  <s xml:id="echoid-s4045" xml:space="preserve">diligenti ſupputatione indagare.</s>
  <s xml:id="echoid-s4046" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s4047" xml:space="preserve">Proderit hic arc 9 circuli uerticalis ad diuiſionẽ hora℞ in aliq̊ plano uerticali, perpen-
<pb file="0059" n="59" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
diculariter in plano horizõtis uerſus meridiẽ erecto, quales ſunt horæ quæ in horalogĳa <lb/>uiatorĳs, inde etiam uerticalibus dictis in ipſo cooperculo cõſignãtur, ſimiliter &amp; </s>
  <s xml:id="echoid-s4048" xml:space="preserve">in mu <lb/>ris directe uerſus meridiem. </s>
  <s xml:id="echoid-s4049" xml:space="preserve">Rem hãc ut plane intelligas, ecce ſi forſitan habes planum ſi <lb/>ue murũ, qui rectà meridiẽ aſpiciat, at filum ex cuius imo plumbo paruulũ depẽdet ad <lb/>hibeas, illi ſiue plano ſiue muro, quacun parte ubi linea deciderit filũ, ibi hora eſt duo-<lb/>
<anchor type="note" xlink:label="note-0059-01a" xlink:href="note-0059-01"/>
decima, reſpõdens lineæ meridianæ in plano horizontali, quoniã &amp; </s>
  <s xml:id="echoid-s4050" xml:space="preserve">hæc dici poteſt linea <lb/>meridiana uerticalis. </s>
  <s xml:id="echoid-s4051" xml:space="preserve">Porro ſi imponas illi circinũ, &amp; </s>
  <s xml:id="echoid-s4052" xml:space="preserve">inde circulum ducas quacũ uoles <lb/>magnitudine, circulus iſte uerticalis appellabitur, eo ꝙ in ſuperficie uerticali includitur. <lb/></s>
  <s xml:id="echoid-s4053" xml:space="preserve">At in hoc circulo arcus iſte quẽ nũc quærimus, ex utro latere numerat. </s>
  <s xml:id="echoid-s4054" xml:space="preserve">ſic aũt opera <lb/>tio habet. </s>
  <s xml:id="echoid-s4055" xml:space="preserve">Duc principio ſinũ diſtantiæ horariæ à meridie in ſinũ altitudinis poli, ꝓductũ <lb/>diuide in ſinũ totum, &amp; </s>
  <s xml:id="echoid-s4056" xml:space="preserve">arcũ quotientis ſubtrahe à 90. </s>
  <s xml:id="echoid-s4057" xml:space="preserve">ſinum´ reſidui tibi ꝓpone cũ ſinu <lb/>
<anchor type="note" xlink:label="note-0059-02a" xlink:href="note-0059-02"/>
cõplementi diſtãtiæ horariæ à meridie, minorẽ duc in totũ, ꝓductũ diuide in maiorem, <lb/>quotientis arcus ſubtractus de quadra circuli, relinquet arcum quæſitũ à linea meridiana <lb/>uſ ad lineã horæ propoſitæ cõputatũ. </s>
  <s xml:id="echoid-s4058" xml:space="preserve">?</s>
  <s xml:id="echoid-s4059" xml:space="preserve">? Et hicigitur in honorem &amp; </s>
  <s xml:id="echoid-s4060" xml:space="preserve">recordationem <lb/>
<anchor type="note" xlink:label="note-0059-03a" xlink:href="note-0059-03"/>
Reuerendiſsimi &amp; </s>
  <s xml:id="echoid-s4061" xml:space="preserve">ampliſsimi patris, Epiſcopi Auguſteñ. </s>
  <s xml:id="echoid-s4062" xml:space="preserve">aſſumo horã 9. </s>
  <s xml:id="echoid-s4063" xml:space="preserve">qua introniza <lb/>tus eſt, ea ſanè horis tribus diſtat à meridiano ſiue meridie, ſinũ ergo diſtantiæ à meridie <lb/>70710. </s>
  <s xml:id="echoid-s4064" xml:space="preserve">duco in ſinũ altitudinis poli 48. </s>
  <s xml:id="echoid-s4065" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4066" xml:space="preserve">74314. </s>
  <s xml:id="echoid-s4067" xml:space="preserve">ꝓductũ diuido in totũ, &amp; </s>
  <s xml:id="echoid-s4068" xml:space="preserve">quotiens ex <lb/>hibet mihi 52547. </s>
  <s xml:id="echoid-s4069" xml:space="preserve">arcus eius eſt 31. </s>
  <s xml:id="echoid-s4070" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4071" xml:space="preserve">42. </s>
  <s xml:id="echoid-s4072" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4073" xml:space="preserve">Cõplementieius ſinum 85081. </s>
  <s xml:id="echoid-s4074" xml:space="preserve">retineo <lb/>pro diuiſore, &amp; </s>
  <s xml:id="echoid-s4075" xml:space="preserve">duco ſinũ complementi diſtantiæ à meridie, tan̈ minorem, in ſinũ totũ, <lb/>productũ diuido in illũ ſeruatũ diuiſorem, &amp; </s>
  <s xml:id="echoid-s4076" xml:space="preserve">in quotiente inuenio 83109. </s>
  <s xml:id="echoid-s4077" xml:space="preserve">arcus eius eſt <lb/>56. </s>
  <s xml:id="echoid-s4078" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4079" xml:space="preserve">13. </s>
  <s xml:id="echoid-s4080" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4081" xml:space="preserve">ſubtractis ĳs à 90 remanet arcus quæſitus 33. </s>
  <s xml:id="echoid-s4082" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4083" xml:space="preserve">47. </s>
  <s xml:id="echoid-s4084" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4085" xml:space="preserve">horæ tertiæ poſt <lb/>meridiẽ, &amp; </s>
  <s xml:id="echoid-s4086" xml:space="preserve">horæ nonæ ante meridiẽ ab hora 12. </s>
  <s xml:id="echoid-s4087" xml:space="preserve">meridiei. </s>
  <s xml:id="echoid-s4088" xml:space="preserve">Nõ cælabo hic te, ut operoſum <lb/>laborem euitare queas in cõpoſitiõe tabularũ, quoniã arcus in muralibus horalogĳs etiã <lb/>ſunt arcus in horalogĳs horizõtalibus. </s>
  <s xml:id="echoid-s4089" xml:space="preserve">Exempli cauſſa, ſi forte ad omnes horas inueni-<lb/>ſti iã arcus horizõtis in eleuatione poli 48. </s>
  <s xml:id="echoid-s4090" xml:space="preserve">graduũ, ibi ſtatim habes etiam arcus omnium <lb/>horarũ circuli muralis ſeu uerticalis in eleuatione poli 42. </s>
  <s xml:id="echoid-s4091" xml:space="preserve">graduũ, ſiquidem 42. </s>
  <s xml:id="echoid-s4092" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4093" xml:space="preserve">48. </s>
  <s xml:id="echoid-s4094" xml:space="preserve">con <lb/>iunctim faciunt 90. </s>
  <s xml:id="echoid-s4095" xml:space="preserve">gradus, idem intelliges etiam in reliquis eleuationibus polaribus, q̊d <lb/>arcus uerticalis in eleuatione poli ſui complementi ſemper etiam exhibent arcus hori-<lb/>zontales. </s>
  <s xml:id="echoid-s4096" xml:space="preserve">Sic enim horizontale horalogium in eleuatione poli 36. </s>
  <s xml:id="echoid-s4097" xml:space="preserve">graduum, præſtat ſi-<lb/>mul horalogium uerticale ſeu murale in eleuatione poli 60. </s>
  <s xml:id="echoid-s4098" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s4099" xml:space="preserve">at ſic in cæteris.</s>
  <s xml:id="echoid-s4100" xml:space="preserve"/>
</p>
<div xml:id="echoid-div125" type="float" level="2" n="1">
<note position="right" xlink:label="note-0059-01" xlink:href="note-0059-01a" xml:space="preserve"><emph style="it">Per latera</emph> <lb/><emph style="it">quadrantis</emph> <lb/><emph style="it">illud depre</emph> <lb/><emph style="it">benditur.</emph></note>
<note position="right" xlink:label="note-0059-02" xlink:href="note-0059-02a" xml:space="preserve"><emph style="it">Hoc uero</emph> <lb/><emph style="it">aream.</emph></note>
<note position="right" xlink:label="note-0059-03" xlink:href="note-0059-03a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div127" type="section" level="1" n="68">
<head xml:id="echoid-head72" xml:space="preserve">PRONVNCIATVM LVI.</head>
<p>
  <s xml:id="echoid-s4101" xml:space="preserve">Arcum circuliuerticalis, quem abſcindit circulus horarum, adhuc diuer <lb/>ſo modo inueſtigare.</s>
  <s xml:id="echoid-s4102" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s4103" xml:space="preserve">Hic iam principio duc ſinum cõplementi diſtantiæ horæ ante uel poſtmeridiem à me <lb/>ridie cum ſinu altitudinis poli, &amp; </s>
  <s xml:id="echoid-s4104" xml:space="preserve">diuide productum in ſinũ totũ, quotientis arcus cõple-<lb/>
<anchor type="note" xlink:label="note-0059-04a" xlink:href="note-0059-04"/>
menti ſinum tibi propone, ſimiliter &amp; </s>
  <s xml:id="echoid-s4105" xml:space="preserve">ſinũ cõplementi altitudinis poli, minorem exĳs <lb/>duc in totum, productum diuide in maiorem, &amp; </s>
  <s xml:id="echoid-s4106" xml:space="preserve">quotientis arcũ rurſus duc in ſinũ diſtan <lb/>tiæ horariæ à meridie, &amp; </s>
  <s xml:id="echoid-s4107" xml:space="preserve">diuide productum in totum, at ſic arcus quotientis monſtra-<lb/>bit tibi arcum circuli uerticalis, non ſecus at in ſuperiori pronunciato factum uidiſti. <lb/></s>
  <s xml:id="echoid-s4108" xml:space="preserve">?</s>
  <s xml:id="echoid-s4109" xml:space="preserve">? Quamobrem eodem hic quo exemplo utemur, quod antea ad horam 9. </s>
  <s xml:id="echoid-s4110" xml:space="preserve">introniza-<lb/>
<anchor type="note" xlink:label="note-0059-05a" xlink:href="note-0059-05"/>
tionis accommodauimus. </s>
  <s xml:id="echoid-s4111" xml:space="preserve">Eſto ſit latitudo poli 48. </s>
  <s xml:id="echoid-s4112" xml:space="preserve">graduum, ſinum illius 74314. </s>
  <s xml:id="echoid-s4113" xml:space="preserve">duco in <lb/>ſinum complementi diſtantiæ horæ propoſitæ à meridie 70710. </s>
  <s xml:id="echoid-s4114" xml:space="preserve">ſi ergo productum diui-<lb/>dam in totum, prouenient in quotiẽte 52547. </s>
  <s xml:id="echoid-s4115" xml:space="preserve">complementum arcus eius eſt 58. </s>
  <s xml:id="echoid-s4116" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4117" xml:space="preserve">18 <lb/>mi. </s>
  <s xml:id="echoid-s4118" xml:space="preserve">Sinum iam illius propono 85081. </s>
  <s xml:id="echoid-s4119" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4120" xml:space="preserve">ſimul ſinum complementi altitudinis poli 42. <lb/></s>
  <s xml:id="echoid-s4121" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4122" xml:space="preserve">ſcilicet 66913. </s>
  <s xml:id="echoid-s4123" xml:space="preserve">hũc duco in totũ, productũ diuido in 85081. </s>
  <s xml:id="echoid-s4124" xml:space="preserve">quia maior eſt, &amp; </s>
  <s xml:id="echoid-s4125" xml:space="preserve">in quo <lb/>tiente reſultant 78646. </s>
  <s xml:id="echoid-s4126" xml:space="preserve">quotientem hunc rurſus duco in ſinum diſtantiæ horariæ à meri-<lb/>die, &amp; </s>
  <s xml:id="echoid-s4127" xml:space="preserve">productum diuido in totum ſinum, arcus eius eſt 33. </s>
  <s xml:id="echoid-s4128" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4129" xml:space="preserve">47. </s>
  <s xml:id="echoid-s4130" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4131" xml:space="preserve">idem planè quod <lb/>&amp; </s>
  <s xml:id="echoid-s4132" xml:space="preserve">in ſuperiori propoſitione inuentum erat.</s>
  <s xml:id="echoid-s4133" xml:space="preserve"/>
</p>
<div xml:id="echoid-div127" type="float" level="2" n="1">
<note position="right" xlink:label="note-0059-04" xlink:href="note-0059-04a" xml:space="preserve"><emph style="it">Lateralis</emph> <lb/><emph style="it">ingreſſus</emph></note>
<note position="right" xlink:label="note-0059-05" xlink:href="note-0059-05a" xml:space="preserve">EXEM. <lb/>PLVM <lb/>Epiſoo<unsure/>pi.</note>
</div>
</div>
<div xml:id="echoid-div129" type="section" level="1" n="69">
<head xml:id="echoid-head73" xml:space="preserve">PRONVNCIATVM LVII.</head>
<p>
  <s xml:id="echoid-s4134" xml:space="preserve">Angulos horarios conficere ſuper quolibet plano, quæ quidem pla-<lb/>næ ſuperficies à ſuperficie plana hotizontali inclinantur, &amp; </s>
  <s xml:id="echoid-s4135" xml:space="preserve">tamen reſpectu
<pb file="0060" n="60" rhead="GENVINVS VSVS"/>
ſuperficiei ipſius meridianiad angulos rectos ſunt compoſiæ.</s>
  <s xml:id="echoid-s4136" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s4137" xml:space="preserve">Intellige hic ſuperficies quæ directe uerſus meridiẽ uel ſeptẽtrionẽ inclinant̃, qua in re <lb/>experimentũ habes in tectis ædiũ, maxime uero ſacrarũ, quæ ita extrui ſolẽt, antiqua &amp; </s>
  <s xml:id="echoid-s4138" xml:space="preserve"><lb/>religioſa conſuetudine, ut ortũ reſpiciãt æquinoctia lis, quapropter neceſſario tecta earũ <lb/>uergunt ad meridiẽ &amp; </s>
  <s xml:id="echoid-s4139" xml:space="preserve">ſeptentrionẽ. </s>
  <s xml:id="echoid-s4140" xml:space="preserve">Si igit̃ uoles ibi lineas horarias ducere, præſcienda <lb/>tibi eſt altitudo poli, quanta ea ſit ſuper iſto plano, qua inuenta, quæres arcus horizõtis <lb/>&amp; </s>
  <s xml:id="echoid-s4141" xml:space="preserve">uerticalis inter meridianũ &amp; </s>
  <s xml:id="echoid-s4142" xml:space="preserve">circulũ horariũ, ſicut in 4. </s>
  <s xml:id="echoid-s4143" xml:space="preserve">ſuꝑioribus ꝓnunciatis edoctus <lb/>es. </s>
  <s xml:id="echoid-s4144" xml:space="preserve">Sin a ũt cupis eleuationẽ poli oim facilime inuenire, age fac ſemicirculũ tibi deſcribas <lb/>ex centro A, ipſum quo ſemicirculũ dic B C D, &amp; </s>
  <s xml:id="echoid-s4145" xml:space="preserve">diuide eundẽ more aſtronomico in <lb/>2. </s>
  <s xml:id="echoid-s4146" xml:space="preserve">qua drãtes, &amp; </s>
  <s xml:id="echoid-s4147" xml:space="preserve">quẽlibet horũ in 90. </s>
  <s xml:id="echoid-s4148" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4149" xml:space="preserve">ꝙ ſi etiã numeros huc ſpectantes adſcribere uo-<lb/>
<anchor type="note" xlink:label="note-0060-01a" xlink:href="note-0060-01"/>
les, iuſto ordine graduũ obſeruato, incipe iuxta lineã A C, &amp; </s>
  <s xml:id="echoid-s4150" xml:space="preserve">eleuationẽ polarẽ tuã pone <lb/>iuxta C, ſic em̃ in ciuitate qua ſolennis illa facta eſt intronizatio, eſt altitudo poli 48. </s>
  <s xml:id="echoid-s4151" xml:space="preserve">gr. <lb/></s>
  <s xml:id="echoid-s4152" xml:space="preserve">
<anchor type="figure" xlink:label="fig-0060-01a" xlink:href="fig-0060-01"/>
ita 48. </s>
  <s xml:id="echoid-s4153" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4154" xml:space="preserve">adſcribe literæ C, deinde <lb/>ex ordine procede per 50. </s>
  <s xml:id="echoid-s4155" xml:space="preserve">60. </s>
  <s xml:id="echoid-s4156" xml:space="preserve">70. </s>
  <s xml:id="echoid-s4157" xml:space="preserve">80. <lb/></s>
  <s xml:id="echoid-s4158" xml:space="preserve">uſ in 90. </s>
  <s xml:id="echoid-s4159" xml:space="preserve">ubi adſcribe H, mox inci-<lb/>pe iuxta D42. </s>
  <s xml:id="echoid-s4160" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4161" xml:space="preserve">retrorſum ſcribe uer <lb/>ſus H, 50. </s>
  <s xml:id="echoid-s4162" xml:space="preserve">60. </s>
  <s xml:id="echoid-s4163" xml:space="preserve">70. </s>
  <s xml:id="echoid-s4164" xml:space="preserve">80. </s>
  <s xml:id="echoid-s4165" xml:space="preserve">90. </s>
  <s xml:id="echoid-s4166" xml:space="preserve">ita ut nume-<lb/>rus hic poſtremus rurſus incidat ſuꝑ <lb/>H, deinde incipe etiam in B, &amp; </s>
  <s xml:id="echoid-s4167" xml:space="preserve">ſuper <lb/>illud pone complementum altitudi-<lb/>nispoli, puta 42. </s>
  <s xml:id="echoid-s4168" xml:space="preserve">ſiquidẽ D &amp; </s>
  <s xml:id="echoid-s4169" xml:space="preserve">B pro <lb/>uno puncto computantur, &amp; </s>
  <s xml:id="echoid-s4170" xml:space="preserve">ſic ſcri-<lb/>be uerſus C retrorſum 30. </s>
  <s xml:id="echoid-s4171" xml:space="preserve">20. </s>
  <s xml:id="echoid-s4172" xml:space="preserve">10. </s>
  <s xml:id="echoid-s4173" xml:space="preserve">0. </s>
  <s xml:id="echoid-s4174" xml:space="preserve"><lb/>ubi et repone G, quoniam à Guſ in <lb/>B ſitum eſſe debet complementum al <lb/>titudinis poli, &amp; </s>
  <s xml:id="echoid-s4175" xml:space="preserve">à Gin Caltitudo ip <lb/>ſa poli, ordire igitur iuxta literam G 0. </s>
  <s xml:id="echoid-s4176" xml:space="preserve">10. </s>
  <s xml:id="echoid-s4177" xml:space="preserve">20. </s>
  <s xml:id="echoid-s4178" xml:space="preserve">30. </s>
  <s xml:id="echoid-s4179" xml:space="preserve">40. </s>
  <s xml:id="echoid-s4180" xml:space="preserve">48. </s>
  <s xml:id="echoid-s4181" xml:space="preserve">Poſtea duc lineas duasex lite-<lb/>ra A, alteram uſ in G, alteram autem uſ ad H. </s>
  <s xml:id="echoid-s4182" xml:space="preserve">Ex litera C etiam educ æquidiſtan-<lb/>tem uerſus lineam B A D, &amp; </s>
  <s xml:id="echoid-s4183" xml:space="preserve">ex D facut DE, æquidiſtans ſit A C, ſimiliter &amp; </s>
  <s xml:id="echoid-s4184" xml:space="preserve">B F. </s>
  <s xml:id="echoid-s4185" xml:space="preserve">At <lb/>in hunc modum habebis parallelogramum ea figura, cuius hic exemplar ſubiectum eſt. </s>
  <s xml:id="echoid-s4186" xml:space="preserve"><lb/>Præterea ſcribe à B uſ in G <emph style="sc">ALTITVDO POLI SVPER VERTICEM</emph>, ab <emph style="sc">H</emph> <lb/>
<anchor type="note" xlink:label="note-0060-02a" xlink:href="note-0060-02"/>
autem in D, &amp; </s>
  <s xml:id="echoid-s4187" xml:space="preserve">à G per Cuſ ad H, ALTITVDO SVPER HORIZONTEM.</s>
  <s xml:id="echoid-s4188" xml:space="preserve"> <lb/>ſuper lineam autem DE, SEPTENTRIO:</s>
  <s xml:id="echoid-s4189" xml:space="preserve"> &amp; </s>
  <s xml:id="echoid-s4190" xml:space="preserve">ſuper lineam BF, <emph style="sc">MERIDIES</emph>. </s>
  <s xml:id="echoid-s4191" xml:space="preserve">Fi-<lb/>lum deinde cum plumbi lamina ſuſpende in centrum A, &amp; </s>
  <s xml:id="echoid-s4192" xml:space="preserve">habebis in ſtrumentum para <lb/>tum ad quemcun uſum. </s>
  <s xml:id="echoid-s4193" xml:space="preserve">Quod ſi deinceps uoles eleuationem poli ſuper inclinata ſuper <lb/>ſicie obſeruare, inſtrumentum hoc colloca cum linea F C E ſuper iſtud planum directe <lb/>ſuper lineam meridianam, &amp; </s>
  <s xml:id="echoid-s4194" xml:space="preserve">quocun ceciderit ſilum, ibi noris eſſe altitudinem poli <lb/>ſuper eadem ſuperficie. </s>
  <s xml:id="echoid-s4195" xml:space="preserve">Et ſi cadat filum ſuper aliquem giadum in altitudine uerticali, <lb/>tunc iuxta 55. </s>
  <s xml:id="echoid-s4196" xml:space="preserve">uel 56 propoſitionem fac horalogium uerticale. </s>
  <s xml:id="echoid-s4197" xml:space="preserve">Sin autem ceciderit ſu-<lb/>per gradus altitudinis poli ſupra horizontem, confice ſecundum 52. </s>
  <s xml:id="echoid-s4198" xml:space="preserve">53. </s>
  <s xml:id="echoid-s4199" xml:space="preserve">aut 54. </s>
  <s xml:id="echoid-s4200" xml:space="preserve">pronunci <lb/>atum horalogium horizontale, &amp; </s>
  <s xml:id="echoid-s4201" xml:space="preserve">erit illud rectum at accomodatum ad iſtam ſuperfici <lb/>em. </s>
  <s xml:id="echoid-s4202" xml:space="preserve">Sedſi planum deorſum fuerit inclinatum, ut ſi interiori parte alicuius tecti cupias <lb/>horalogium Solare componere, dummodo illuc radĳ Solares pertingere queant, lineæ <lb/>meridianæ, quam ſemper primo ſignari oportet, adhibe inſtrumentum cum linea B A <lb/>D, &amp; </s>
  <s xml:id="echoid-s4203" xml:space="preserve">filum monſtrabit tibi eleuationem polarem eius ſuperficiei. </s>
  <s xml:id="echoid-s4204" xml:space="preserve">Attende tamen, ut <lb/>ſemper latus B F uerſus meridiem conuertas, ſicut ex ſubiecta figura ipſe uidere potes <lb/>Quomodo autem iſtiuſmodi horalogia ſine ullo inſtrumento, at citra beneficium ta-<lb/>bularum, in quacun poſitione ſuperficierum confici &amp; </s>
  <s xml:id="echoid-s4205" xml:space="preserve">componi queãt, in noſtris libris <lb/>umbrarum habunde ſatis explicatum uidebis. </s>
  <s xml:id="echoid-s4206" xml:space="preserve">Præterea quod amplius ad horarum diui-<lb/>ſionem pertinet, ſuper quacun ſuperficie oblata, ne ſatis conſentaneum fuerit, ne <lb/>noſtri iam eſt inſtituti hocloco recenſere longius, ſed in libris noſtris umbrarum ampli-<lb/>us intelliges, ſiquidem in ĳs omnia quæ ad hanc rem referri poſſunt, adamuſsim expen-<lb/>dimus &amp; </s>
  <s xml:id="echoid-s4207" xml:space="preserve">explicauimus.</s>
  <s xml:id="echoid-s4208" xml:space="preserve"/>
</p>
<div xml:id="echoid-div129" type="float" level="2" n="1">
<note position="left" xlink:label="note-0060-01" xlink:href="note-0060-01a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
  <figure xlink:label="fig-0060-01" xlink:href="fig-0060-01a">
    <image file="0060-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0060-01"/>
  </figure>
<note position="left" xlink:label="note-0060-02" xlink:href="note-0060-02a" xml:space="preserve"><emph style="it">Quo pacto</emph> <lb/><emph style="it">eleuatio po</emph> <lb/><emph style="it">li, in ſuper</emph> <lb/><emph style="it">fiaebus de-</emph> <lb/><emph style="it">clinantibus</emph> <lb/><emph style="it">ad meridië</emph> <lb/><emph style="it">uel ſepten-</emph> <lb/><emph style="it">trienem ſit</emph> <lb/><emph style="it">inueſtigäda</emph></note>
</div>
<pb file="0061" n="61" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
  <figure>
    <image file="0061-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0061-01"/>
  </figure>
</div>
<div xml:id="echoid-div131" type="section" level="1" n="70">
<head xml:id="echoid-head74" xml:space="preserve">PRONVNCIATVM LVIII.</head>
<p>
  <s xml:id="echoid-s4209" xml:space="preserve">Cognito iam antea eclypticæ gradu, qui eſt in aſcendente, ſimiliter &amp; </s>
  <s xml:id="echoid-s4210" xml:space="preserve">habi <lb/>to gradu æquinoctialis coaſcendente, eleuationem poli inde elicere.</s>
  <s xml:id="echoid-s4211" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s4212" xml:space="preserve">Hic tibi propone gradum zodiaci qui eſt in aſcendente, quære declinationem ipſius ꝑ <lb/>5. </s>
  <s xml:id="echoid-s4213" xml:space="preserve">pronunciatũ, adſume deinde &amp; </s>
  <s xml:id="echoid-s4214" xml:space="preserve">gradũ æquinoctialis cum illo aſcendente ſimul, ſinum <lb/>
<anchor type="note" xlink:label="note-0061-01a" xlink:href="note-0061-01"/>
complementi aſcenſionis obliquæ duc in ſinũ cõplementi declinationis gradus Solis, ꝓ-<lb/>
<anchor type="note" xlink:label="note-0061-02a" xlink:href="note-0061-02"/>
ductum diuide in ſinum totum, &amp; </s>
  <s xml:id="echoid-s4215" xml:space="preserve">arcũ quotientis ſubtrahe à 90. </s>
  <s xml:id="echoid-s4216" xml:space="preserve">ſinum reſidui ſepone in <lb/>locũ peculiarẽ, unà cum ſinu declinationis gradus aſcẽdentis eclypticæ, minorẽ duc in <lb/>totũ, in maiorem aũt diuide productũ, &amp; </s>
  <s xml:id="echoid-s4217" xml:space="preserve">cõplementũ arcus quotientis erit altitudo poli, <lb/>ubi aſcenſio talis facta eſt. </s>
  <s xml:id="echoid-s4218" xml:space="preserve">?</s>
  <s xml:id="echoid-s4219" xml:space="preserve">?Exemplũ ſit hoc tibi. </s>
  <s xml:id="echoid-s4220" xml:space="preserve">Age in eo loco ubi celebrata eſt in-<lb/>
<anchor type="note" xlink:label="note-0061-03a" xlink:href="note-0061-03"/>
tronizatio, ex certa obſeruatione cognoui 5. </s>
  <s xml:id="echoid-s4221" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4222" xml:space="preserve">25. </s>
  <s xml:id="echoid-s4223" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4224" xml:space="preserve">♌ in aſcendente fuiſſe ipſa ho-<lb/>ra intronizationis, quæro igitur per 5. </s>
  <s xml:id="echoid-s4225" xml:space="preserve">pronunc. </s>
  <s xml:id="echoid-s4226" xml:space="preserve">declinationẽ aſcendentis, eã inuenio 18. <lb/></s>
  <s xml:id="echoid-s4227" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4228" xml:space="preserve">58. </s>
  <s xml:id="echoid-s4229" xml:space="preserve">mi, ſinum complementi eius 94570. </s>
  <s xml:id="echoid-s4230" xml:space="preserve">duco in ſinũ cõplementi differentiæ aſcenſio <lb/>nalis, is eſt 92432. </s>
  <s xml:id="echoid-s4231" xml:space="preserve">ſiquidẽ aſcenſio recta 5. </s>
  <s xml:id="echoid-s4232" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4233" xml:space="preserve">25. </s>
  <s xml:id="echoid-s4234" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4235" xml:space="preserve">eſt 127. </s>
  <s xml:id="echoid-s4236" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4237" xml:space="preserve">48. </s>
  <s xml:id="echoid-s4238" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4239" xml:space="preserve">ſed ☉(sun)bliqua eſt <lb/>105. </s>
  <s xml:id="echoid-s4240" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4241" xml:space="preserve">22. </s>
  <s xml:id="echoid-s4242" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4243" xml:space="preserve">Iam uero numerum minorem à maiori ſubtraho, &amp; </s>
  <s xml:id="echoid-s4244" xml:space="preserve">remanent 22. </s>
  <s xml:id="echoid-s4245" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4246" xml:space="preserve"><lb/>26. </s>
  <s xml:id="echoid-s4247" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4248" xml:space="preserve">quæ differentia dicitur aſcenſionalis, productũ ex multiplicatione diuido in totum <lb/>
<anchor type="note" xlink:label="note-0061-04a" xlink:href="note-0061-04"/>
ſinum, &amp; </s>
  <s xml:id="echoid-s4249" xml:space="preserve">in quotiente inuenio 87413. </s>
  <s xml:id="echoid-s4250" xml:space="preserve">arcus eius eſt 60. </s>
  <s xml:id="echoid-s4251" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4252" xml:space="preserve">57. </s>
  <s xml:id="echoid-s4253" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4254" xml:space="preserve">ſinũ ſui complementi
<pb file="0062" n="62" rhead="GENVINVS VSVS"/>
adſeruo pro diuiſore, is eſt 48557. </s>
  <s xml:id="echoid-s4255" xml:space="preserve">hinc ſi ſinũ declinationis 18. </s>
  <s xml:id="echoid-s4256" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4257" xml:space="preserve">58. </s>
  <s xml:id="echoid-s4258" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4259" xml:space="preserve">ſcilicet 32501 <lb/>duxero in totum, &amp; </s>
  <s xml:id="echoid-s4260" xml:space="preserve">productũ diuiſero in ipſum diuiſorẽ, tunc ſane quotiens producet <lb/>666933. </s>
  <s xml:id="echoid-s4261" xml:space="preserve">cuius arcus eſt 42. </s>
  <s xml:id="echoid-s4262" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4263" xml:space="preserve">quo ſubtracto â 90. </s>
  <s xml:id="echoid-s4264" xml:space="preserve">remanent 48. </s>
  <s xml:id="echoid-s4265" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s4266" xml:space="preserve">ipſa ſcilicet altitu <lb/>do poli, urbis Auguſtæ Vindelicorum, ubi ſolennis illa intronizatio celebrata eſt.</s>
  <s xml:id="echoid-s4267" xml:space="preserve"/>
</p>
<div xml:id="echoid-div131" type="float" level="2" n="1">
<note position="right" xlink:label="note-0061-01" xlink:href="note-0061-01a" xml:space="preserve"><emph style="it">Lateraliter</emph></note>
<note position="right" xlink:label="note-0061-02" xlink:href="note-0061-02a" xml:space="preserve"><emph style="it">Arealiter.</emph></note>
<note position="right" xlink:label="note-0061-03" xlink:href="note-0061-03a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſcopi.</emph></note>
<note position="right" xlink:label="note-0061-04" xlink:href="note-0061-04a" xml:space="preserve"><emph style="it">Lateraliter</emph></note>
</div>
</div>
<div xml:id="echoid-div133" type="section" level="1" n="71">
<head xml:id="echoid-head75" xml:space="preserve">PRONVNCIATVM LIX.</head>
<p>
  <s xml:id="echoid-s4268" xml:space="preserve">Si quis ante nouerit duo puncta eclypticæ, &amp; </s>
  <s xml:id="echoid-s4269" xml:space="preserve">arcum inter ea cõcluſum, ſi-<lb/>militer &amp; </s>
  <s xml:id="echoid-s4270" xml:space="preserve">aſcenſionem obliquam (qui gradus ſunt æquatoris cum noto iſto <lb/>loco eclypticæ in eadem regione coaſcendentes) inde quo eleuationem po <lb/>larem eius regionis, in qua fit talis aſcenſio, colligere.</s>
  <s xml:id="echoid-s4271" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s4272" xml:space="preserve">Principio hic diligenter conſidera duo illa pũcta eclypticæ, an æquales habeant decli <lb/>nationes ab æquatore ſiue nõ, ꝙ ſi æquales habuerint, ſtatim tunc operationẽ omnẽ in-<lb/>termitte, actũ enim ages, nec quicquã in ea efficies. </s>
  <s xml:id="echoid-s4273" xml:space="preserve">Sin aũt declinatiões fuerint inæqua <lb/>les, ſic age, ipſas tibi ꝓpone declinationes cũ ſuis cõplementis &amp; </s>
  <s xml:id="echoid-s4274" xml:space="preserve">ſinubus, deinde etiã ad <lb/>iunge gradus æquatoris, qui cũ illo arcu aſcenderunt ſuper horizontã (nõ ſic ut antea co <lb/>gnoſcendũ tibi ſit, quo ad nume℞, ubi tandẽ in æquinoctiali arcus iſte deſinat aut cœpe <lb/>rit, ſed ut noris, q̊t gradus cũ arcu noto eclypticæ in horizonte obliquo aſcenderint) De <lb/>inde adhuc circumſpice, an utrun illud eclypticæ punctum ſit in medietate eclypticæ <lb/>ſeptentrionali uel meridionali, &amp; </s>
  <s xml:id="echoid-s4275" xml:space="preserve">tũc operationẽ ſic aggredere. </s>
  <s xml:id="echoid-s4276" xml:space="preserve">Quære primo ad utrũ <lb/>terminũ eclypticæ aſcenſionem rectã, &amp; </s>
  <s xml:id="echoid-s4277" xml:space="preserve">eorũ diſtantiã ſepone in locũ ſingularem, quo-<lb/>niam illa erit aſcenſio recta ambo℞, eã confer ad aſcenſionem obliquã, ex obſeruatione <lb/>iam antea notã, minorem ex is ſubtrahe à maiori, q̊d reliquũ erit, dicetur differentia aſcẽ <lb/>ſionum, eius differentiæ ſinũ duc in ſinũ cõplementi maioris declinationis terminorum <lb/>
<anchor type="note" xlink:label="note-0062-01a" xlink:href="note-0062-01"/>
arcus eclypticæ, productũ diuide in ſinum perfectũ, &amp; </s>
  <s xml:id="echoid-s4278" xml:space="preserve">arcũ quotientis inquire, qui uoca <lb/>bitur inuentũ primũ. </s>
  <s xml:id="echoid-s4279" xml:space="preserve">Sinum cõplementi huius inuenti ꝓpone tibi, ſimul´ ſinũ maioris <lb/>
<anchor type="note" xlink:label="note-0062-02a" xlink:href="note-0062-02"/>
declinationis, minorem duc in ſinũ perfectũ, &amp; </s>
  <s xml:id="echoid-s4280" xml:space="preserve">ꝓductũ diuide in maiorẽ. </s>
  <s xml:id="echoid-s4281" xml:space="preserve">hinc quære ar-<lb/>cum quotientis, &amp; </s>
  <s xml:id="echoid-s4282" xml:space="preserve">inde ſubtracta declinatione maiori, remanebit inuentũ ſecundũ. </s>
  <s xml:id="echoid-s4283" xml:space="preserve">Por <lb/>
<anchor type="note" xlink:label="note-0062-03a" xlink:href="note-0062-03"/>
rò duc ſinũ cõplementi inuenti primi in ſinũ cõplemẽti inuenti ſecũdi, ꝓductũ diuide in <lb/>
<anchor type="note" xlink:label="note-0062-04a" xlink:href="note-0062-04"/>
ſinũ totũ, &amp; </s>
  <s xml:id="echoid-s4284" xml:space="preserve">quotientis arcũ ſubtrahe à 90. </s>
  <s xml:id="echoid-s4285" xml:space="preserve">ſinũ quo huius reſidui unà cũ ſinu primi in-<lb/>uenti ſepone in locũ peculiarẽ. </s>
  <s xml:id="echoid-s4286" xml:space="preserve">Minorẽ duc in totũ, ꝓductũ diuide in maiorem, &amp; </s>
  <s xml:id="echoid-s4287" xml:space="preserve">quo <lb/>
<anchor type="note" xlink:label="note-0062-05a" xlink:href="note-0062-05"/>
tientẽ rurſus duc in ſinũ cõplementi declinationis minoris, &amp; </s>
  <s xml:id="echoid-s4288" xml:space="preserve">ꝓducto in ſinũ ꝑfectũ di-<lb/>uiſo, arcus quotientis oſtẽdet altitudinẽ poli quæſitam. </s>
  <s xml:id="echoid-s4289" xml:space="preserve">?</s>
  <s xml:id="echoid-s4290" xml:space="preserve">? Nũc aũt animaduerte ad ex <lb/>
<anchor type="note" xlink:label="note-0062-06a" xlink:href="note-0062-06"/>
emplũ, q̊d in hac re tibi damus huiuſmodi. </s>
  <s xml:id="echoid-s4291" xml:space="preserve">Eſto, in loco die &amp; </s>
  <s xml:id="echoid-s4292" xml:space="preserve">hora intronizatiõſs obſer <lb/>uaui aſcenſionẽ obliquã in æꝗnoctialiab ortu Solis uſ horã &amp; </s>
  <s xml:id="echoid-s4293" xml:space="preserve">minutũ intronization-<lb/>nis. </s>
  <s xml:id="echoid-s4294" xml:space="preserve">At quũ ☉(sun) fuerit (ut ſæpe diximus) in 2. </s>
  <s xml:id="echoid-s4295" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4296" xml:space="preserve">26. </s>
  <s xml:id="echoid-s4297" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4298" xml:space="preserve">II, ego´ diligent ab ortu ☉(sun) ho <lb/>ram ex q̊cun horalogio certã cũ minutis cognouerim uſ ad tempus intronizationis, <lb/>puta horas 4. </s>
  <s xml:id="echoid-s4299" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4300" xml:space="preserve">39. </s>
  <s xml:id="echoid-s4301" xml:space="preserve">ſecũda 12. </s>
  <s xml:id="echoid-s4302" xml:space="preserve">His cõuer ſis in gradus, ecce habeo 69. </s>
  <s xml:id="echoid-s4303" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4304" xml:space="preserve">48. </s>
  <s xml:id="echoid-s4305" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4306" xml:space="preserve">quæ <lb/>aſcenſio eſt obliqua, horizõtem q̊ ſub ipſum tempus intronizationis tãgebat 5. </s>
  <s xml:id="echoid-s4307" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4308" xml:space="preserve">25 <lb/>mi. </s>
  <s xml:id="echoid-s4309" xml:space="preserve">♌. </s>
  <s xml:id="echoid-s4310" xml:space="preserve">Iam igit̃ quæro aſcẽſionem rectã ad gra. </s>
  <s xml:id="echoid-s4311" xml:space="preserve">☉(sun). </s>
  <s xml:id="echoid-s4312" xml:space="preserve">ꝑ 7. </s>
  <s xml:id="echoid-s4313" xml:space="preserve">ꝓnunc. </s>
  <s xml:id="echoid-s4314" xml:space="preserve">ea eſt 60. </s>
  <s xml:id="echoid-s4315" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4316" xml:space="preserve">21. </s>
  <s xml:id="echoid-s4317" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4318" xml:space="preserve">ſimi <lb/>liter &amp; </s>
  <s xml:id="echoid-s4319" xml:space="preserve">ſuꝑ gradũ aſcendentis .</s>
  <s xml:id="echoid-s4320" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s4321" xml:space="preserve">5. </s>
  <s xml:id="echoid-s4322" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4323" xml:space="preserve">25. </s>
  <s xml:id="echoid-s4324" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4325" xml:space="preserve">♌, ibieſt aſcenſio recta 127. </s>
  <s xml:id="echoid-s4326" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4327" xml:space="preserve">47. </s>
  <s xml:id="echoid-s4328" xml:space="preserve">mi. <lb/></s>
  <s xml:id="echoid-s4329" xml:space="preserve">ſubtracta aſcenſione minore à maiore, remanent 67. </s>
  <s xml:id="echoid-s4330" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4331" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4332" xml:space="preserve">ꝗa reſiduũ hoc aſcenſionum <lb/>recta℞ minus eſt aſcenſiõe obliqua, quã ex obſeruatione cognoui, ſubtraho illud &amp; </s>
  <s xml:id="echoid-s4333" xml:space="preserve">ma-<lb/>nent 2. </s>
  <s xml:id="echoid-s4334" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4335" xml:space="preserve">22. </s>
  <s xml:id="echoid-s4336" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4337" xml:space="preserve">differentia iſta aſcenſionalis, ſinũ eius 4129. </s>
  <s xml:id="echoid-s4338" xml:space="preserve">duco in ſinũ cõplementi <lb/>
<anchor type="note" xlink:label="note-0062-07a" xlink:href="note-0062-07"/>
declinationis maioris. </s>
  <s xml:id="echoid-s4339" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s4340" xml:space="preserve">gradus Solis, hoc eſt in 93544. </s>
  <s xml:id="echoid-s4341" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4342" xml:space="preserve">diuido in totũ ſinũ, unde pro <lb/>ueniũt in q̊tiente 3862. </s>
  <s xml:id="echoid-s4343" xml:space="preserve">inuentũ puta hoc primũ. </s>
  <s xml:id="echoid-s4344" xml:space="preserve">Arcus illius eſt 2. </s>
  <s xml:id="echoid-s4345" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4346" xml:space="preserve">13. </s>
  <s xml:id="echoid-s4347" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4348" xml:space="preserve">Cõplemen <lb/>tum uero 87. </s>
  <s xml:id="echoid-s4349" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4350" xml:space="preserve">47. </s>
  <s xml:id="echoid-s4351" xml:space="preserve">duco igitur ſinũ declinationis gra. </s>
  <s xml:id="echoid-s4352" xml:space="preserve">☉(sun) tan̈ maiorẽ declinationem <lb/>in ſinũ totũ &amp; </s>
  <s xml:id="echoid-s4353" xml:space="preserve">ꝓductũ diuido in ſinũ cõplemẽti primi inuenti. </s>
  <s xml:id="echoid-s4354" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s4355" xml:space="preserve">99925. </s>
  <s xml:id="echoid-s4356" xml:space="preserve">ſic ꝓdibunt in q̊ <lb/>tiente 35373. </s>
  <s xml:id="echoid-s4357" xml:space="preserve">in arcu faciunt 20. </s>
  <s xml:id="echoid-s4358" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4359" xml:space="preserve">43. </s>
  <s xml:id="echoid-s4360" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4361" xml:space="preserve">Vnde ſubtracta declinatione gradus aſcen-<lb/>dentis, quia minore, remanet 1. </s>
  <s xml:id="echoid-s4362" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4363" xml:space="preserve">cũ 45. </s>
  <s xml:id="echoid-s4364" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4365" xml:space="preserve">q̊d etiam ob diſcrimen uocamus inuentũ <lb/>
<anchor type="note" xlink:label="note-0062-08a" xlink:href="note-0062-08"/>
ſecundum. </s>
  <s xml:id="echoid-s4366" xml:space="preserve">Deinceps duco cõplementũ inuenti primi 99925. </s>
  <s xml:id="echoid-s4367" xml:space="preserve">in ſinũ cõplementi inuen <lb/>ti ſecundi. </s>
  <s xml:id="echoid-s4368" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s4369" xml:space="preserve">99953. </s>
  <s xml:id="echoid-s4370" xml:space="preserve">ꝓductũ diuido in totũ, &amp; </s>
  <s xml:id="echoid-s4371" xml:space="preserve">q̊tiens eſt 99878. </s>
  <s xml:id="echoid-s4372" xml:space="preserve">arcus eius 87. </s>
  <s xml:id="echoid-s4373" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4374" xml:space="preserve">11. </s>
  <s xml:id="echoid-s4375" xml:space="preserve">mi. <lb/></s>
  <s xml:id="echoid-s4376" xml:space="preserve">Complementũ ipſius 2. </s>
  <s xml:id="echoid-s4377" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4378" xml:space="preserve">49. </s>
  <s xml:id="echoid-s4379" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4380" xml:space="preserve">ſinũ eius tan̈ minorem duco in totũ, &amp; </s>
  <s xml:id="echoid-s4381" xml:space="preserve">ꝓductũ di-<lb/>uido in ſinũ inuenti primi. </s>
  <s xml:id="echoid-s4382" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s4383" xml:space="preserve">3862. </s>
  <s xml:id="echoid-s4384" xml:space="preserve">quotiẽs producet 78591. </s>
  <s xml:id="echoid-s4385" xml:space="preserve">Hũc iterum duco in ſinum
<pb file="0063" n="63" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
complementi declinationis minoris. </s>
  <s xml:id="echoid-s4386" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s4387" xml:space="preserve">5. </s>
  <s xml:id="echoid-s4388" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4389" xml:space="preserve">25. </s>
  <s xml:id="echoid-s4390" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4391" xml:space="preserve">♌, &amp; </s>
  <s xml:id="echoid-s4392" xml:space="preserve">quia declinatio eius eſt 18. </s>
  <s xml:id="echoid-s4393" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s4394" xml:space="preserve">58. </s>
  <s xml:id="echoid-s4395" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4396" xml:space="preserve">cõplementũ ipſius erit 71. </s>
  <s xml:id="echoid-s4397" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4398" xml:space="preserve">2. </s>
  <s xml:id="echoid-s4399" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4400" xml:space="preserve">ſinus atit 94570. </s>
  <s xml:id="echoid-s4401" xml:space="preserve">ꝓductũ ex hac multiplicati <lb/>
<anchor type="note" xlink:label="note-0063-01a" xlink:href="note-0063-01"/>
one diuido in ſinũ totũ, &amp; </s>
  <s xml:id="echoid-s4402" xml:space="preserve">quotiẽs dabit 74323. </s>
  <s xml:id="echoid-s4403" xml:space="preserve">arcus eſt 48. </s>
  <s xml:id="echoid-s4404" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4405" xml:space="preserve">altiudo illa poli quæſita <lb/>in loco intronizationis. </s>
  <s xml:id="echoid-s4406" xml:space="preserve">Quid ſi aũt contingat, ut alter terminus eclypticæ ſit in medie-<lb/>tate eclypticæ ſeptentrionali, alter uero in meridionali? </s>
  <s xml:id="echoid-s4407" xml:space="preserve">tunc ſanè duc ſinum differentiæ <lb/>aſcenſionũ in ſinũ cõplementi de clinationis Borealis, ꝓducto diuiſo in ſinũ totum, quo <lb/>tiens dabit inuentũ primũ. </s>
  <s xml:id="echoid-s4408" xml:space="preserve">Sinũ cõplementi huius inuenti propone tibi, &amp; </s>
  <s xml:id="echoid-s4409" xml:space="preserve">ſimul ſinũ de-<lb/>clinationis Borealis, minorem duc in totum, &amp; </s>
  <s xml:id="echoid-s4410" xml:space="preserve">productũ diuide in maiorẽ, arcui quoti-<lb/>entis adde arcũ declinationis Auſtrinæ, &amp; </s>
  <s xml:id="echoid-s4411" xml:space="preserve">collectũ hoc uocabit̃ inuentũ ſecundũ. </s>
  <s xml:id="echoid-s4412" xml:space="preserve">Poſtea <lb/>duc ſinũ complementi primi inuenti in ſinũ cõplem enti ſecundi inuenti, productũ diui-<lb/>de in ſinũ totum, quotientis arcu ex 90. </s>
  <s xml:id="echoid-s4413" xml:space="preserve">ſubtracto, reſidui ſinũ ſeorſim colloca unà cum ſi-<lb/>nu inuenti primi, minorẽ duc in totũ, productum in maiorem diuide, &amp; </s>
  <s xml:id="echoid-s4414" xml:space="preserve">quotientem ex di <lb/>uiſione prouenientem rurſus duc in ſinum cõplementi declinationis Auſtrinæ, &amp; </s>
  <s xml:id="echoid-s4415" xml:space="preserve">produ <lb/>ctum diuide cum ſinu toto, tunc arcus quotientis arguet altitudinem poli quam optabas <lb/>ſcire, nec eſt. </s>
  <s xml:id="echoid-s4416" xml:space="preserve">ꝙ hic inſuper expectes exemplum, quum neceſſarium non uideatur.</s>
  <s xml:id="echoid-s4417" xml:space="preserve"/>
</p>
<div xml:id="echoid-div133" type="float" level="2" n="1">
<note position="left" xlink:label="note-0062-01" xlink:href="note-0062-01a" xml:space="preserve"><emph style="it">Lateralis</emph> <lb/><emph style="it">ingreſſus.</emph></note>
<note position="left" xlink:label="note-0062-02" xlink:href="note-0062-02a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">primum.</emph></note>
<note position="left" xlink:label="note-0062-03" xlink:href="note-0062-03a" xml:space="preserve"><emph style="it">Arealis in-</emph> <lb/><emph style="it">greſſus.</emph></note>
<note position="left" xlink:label="note-0062-04" xlink:href="note-0062-04a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">ſecundum.</emph></note>
<note position="left" xlink:label="note-0062-05" xlink:href="note-0062-05a" xml:space="preserve"><emph style="it">Lateraliter</emph></note>
<note position="left" xlink:label="note-0062-06" xlink:href="note-0062-06a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
<note position="left" xlink:label="note-0062-07" xlink:href="note-0062-07a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">primũ gra.</emph> <lb/><emph style="it">2. mi. 13.</emph></note>
<note position="left" xlink:label="note-0062-08" xlink:href="note-0062-08a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">ſecũdũ gra.</emph> <lb/><emph style="it">1. mi. 45.</emph></note>
<note position="right" xlink:label="note-0063-01" xlink:href="note-0063-01a" xml:space="preserve"><emph style="it">Per latera.</emph> <lb/><emph style="it">lem ingreſ-</emph> <lb/><emph style="it">ſum qua-</emph> <lb/><emph style="it">drans illud</emph> <lb/><emph style="it">demõſtrat.</emph></note>
</div>
</div>
<div xml:id="echoid-div135" type="section" level="1" n="72">
<head xml:id="echoid-head76" xml:space="preserve">PRONVNCIATVM LX.</head>
<p>
  <s xml:id="echoid-s4418" xml:space="preserve">Cognito antea &amp; </s>
  <s xml:id="echoid-s4419" xml:space="preserve">gradu medĳ cœli, &amp; </s>
  <s xml:id="echoid-s4420" xml:space="preserve">ſimul perſpecta amplitudine ortiua <lb/>aſcendentis, altitudinem poli inde perquirere.</s>
  <s xml:id="echoid-s4421" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s4422" xml:space="preserve">Iam ſupra præmonuimus, ubi declinatio tanta eſt quanta amplitudo, in ea ciuitate <lb/>nullã eſſe eleuationẽ poli, q̊d ſanè omnibus cõtingit ſub æquatore habitãtibus, nequit e-<lb/>
<anchor type="note" xlink:label="note-0063-02a" xlink:href="note-0063-02"/>
nim amplitudo eſſe declinatione minor, ſed bene maior, ſi igitur maior illa fuerit, quære <lb/>angulũ quẽ facit eclyptica cũ meridiano iuxta gradũ medĳ cœli ꝑ 26. </s>
  <s xml:id="echoid-s4423" xml:space="preserve">27. </s>
  <s xml:id="echoid-s4424" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4425" xml:space="preserve">28. </s>
  <s xml:id="echoid-s4426" xml:space="preserve">ꝓnuncia <lb/>ta, angulus ille ſi fuerit quadrãte minor, tunc erit ad hanc operationẽ adcõ modatus. </s>
  <s xml:id="echoid-s4427" xml:space="preserve">ſin <lb/>autem maior extiterit, ſubtrahe eũ à ſemicirculo, &amp; </s>
  <s xml:id="echoid-s4428" xml:space="preserve">remanebit numerus quo uteris in hac <lb/>conſideratione loco anguli. </s>
  <s xml:id="echoid-s4429" xml:space="preserve">Sinum arcus illius ſeorſim pone unà cũ ſinu cõplementi am-<lb/>plitudinis ortiuæ, ſicut per 12. </s>
  <s xml:id="echoid-s4430" xml:space="preserve">pronunc. </s>
  <s xml:id="echoid-s4431" xml:space="preserve">inueniſti, minorẽ exĳs duc in totũ, productum <lb/>diuide in maiorem, &amp; </s>
  <s xml:id="echoid-s4432" xml:space="preserve">arcus quotientis tibi dabit arcũ à medio cœli uſ ad gradũ horo-<lb/>ſcopi numerãdo ſecũdũ ordinẽ ſignorũ. </s>
  <s xml:id="echoid-s4433" xml:space="preserve">At hoc uerum eſt ſi angulus medĳ cœli minor <lb/>fuerit quadrante, fit aũt id, quando gradus eclypticæ aſcendens eſt in ſignis meridionali <lb/>bus. </s>
  <s xml:id="echoid-s4434" xml:space="preserve">Si autẽ angulus meridiani &amp; </s>
  <s xml:id="echoid-s4435" xml:space="preserve">eclypticæ maior ſit recto, q̊d fit, quũ aſcendens eſt in <lb/>
<anchor type="note" xlink:label="note-0063-03a" xlink:href="note-0063-03"/>
ſignis ſeptentrionalibus, arcũ quotiẽtis minue de ſemicirculo, &amp; </s>
  <s xml:id="echoid-s4436" xml:space="preserve">reliquus manebit arcus <lb/>eclypticæ à medio cœli uſ ad caput horoſcopi. </s>
  <s xml:id="echoid-s4437" xml:space="preserve">Porrò etiã tibi propone ſinũ amplitudi <lb/>nis ortiuæ &amp; </s>
  <s xml:id="echoid-s4438" xml:space="preserve">ſinum declinationis aſcendentis, minorẽ duc in ſinũ totum, &amp; </s>
  <s xml:id="echoid-s4439" xml:space="preserve">ꝓductum di-<lb/>
<anchor type="note" xlink:label="note-0063-04a" xlink:href="note-0063-04"/>
uide in maiorem. </s>
  <s xml:id="echoid-s4440" xml:space="preserve">arcus à 90. </s>
  <s xml:id="echoid-s4441" xml:space="preserve">ſubtractus, relinquet altitudinem poli eius loci in quo am-<lb/>plitudinem obſeruaſti. </s>
  <s xml:id="echoid-s4442" xml:space="preserve">Potes idem diuerſa paulo operatione ſic exequi, ſinum ampli <lb/>tudinis ortiuæ &amp; </s>
  <s xml:id="echoid-s4443" xml:space="preserve">ſinũ cõplementi tibi propone, ſimul etiã ſinum complementi arcus in-<lb/>ter medium cœli &amp; </s>
  <s xml:id="echoid-s4444" xml:space="preserve">aſcendentis gradum, minorem duc in totum, productum in maiorem <lb/>diuide, &amp; </s>
  <s xml:id="echoid-s4445" xml:space="preserve">quotiens dabit diſtantiã medĳ cœli à 90. </s>
  <s xml:id="echoid-s4446" xml:space="preserve">gradu ab aſcendente, ad eã diſtantiã <lb/>adde declinationem medĳ cœli, ſi Borealis fuerit, uel ſubtrahe, ſi Auſtrina extiterit, quic <lb/>
<anchor type="note" xlink:label="note-0063-05a" xlink:href="note-0063-05"/>
quid inde ꝓuenerit, erit altitudo poli quæſita, ſed hic quo exemplum non negabimus <lb/>
<anchor type="note" xlink:label="note-0063-06a" xlink:href="note-0063-06"/>
tibi. </s>
  <s xml:id="echoid-s4447" xml:space="preserve">?</s>
  <s xml:id="echoid-s4448" xml:space="preserve">?Ecce ex 25. </s>
  <s xml:id="echoid-s4449" xml:space="preserve">pronunc. </s>
  <s xml:id="echoid-s4450" xml:space="preserve">inueni 16. </s>
  <s xml:id="echoid-s4451" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4452" xml:space="preserve">40. </s>
  <s xml:id="echoid-s4453" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4454" xml:space="preserve">♈ in medio cœli fuiſſe hora &amp; </s>
  <s xml:id="echoid-s4455" xml:space="preserve">lo-<lb/>co factæ intronizationis, angulũ quo eclypticæ &amp; </s>
  <s xml:id="echoid-s4456" xml:space="preserve">meridiani iuxta illum gradum eſſe <lb/>112. </s>
  <s xml:id="echoid-s4457" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4458" xml:space="preserve">37. </s>
  <s xml:id="echoid-s4459" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4460" xml:space="preserve">cognoui ꝑ 26. </s>
  <s xml:id="echoid-s4461" xml:space="preserve">27. </s>
  <s xml:id="echoid-s4462" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4463" xml:space="preserve">28. </s>
  <s xml:id="echoid-s4464" xml:space="preserve">ꝓnunciata, &amp; </s>
  <s xml:id="echoid-s4465" xml:space="preserve">quia angulus hic maior eſt qua-<lb/>drãte, ſubtraxi eũ de ſemicirculo, &amp; </s>
  <s xml:id="echoid-s4466" xml:space="preserve">remanſerunt 67. </s>
  <s xml:id="echoid-s4467" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4468" xml:space="preserve">23. </s>
  <s xml:id="echoid-s4469" xml:space="preserve">mi ſinus eorũ uoco nume℞ <lb/>introitualem. </s>
  <s xml:id="echoid-s4470" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s4471" xml:space="preserve">92309. </s>
  <s xml:id="echoid-s4472" xml:space="preserve">At quum ſinus cõplementi amplitudinis aſcendentis 87405. <lb/></s>
  <s xml:id="echoid-s4473" xml:space="preserve">minimus fuerit, nume℞ illum duxi in totũ, ꝓductũ diuiſi in ſinum introitualem, &amp; </s>
  <s xml:id="echoid-s4474" xml:space="preserve">in quo <lb/>tiente ꝓdierunt 94687. </s>
  <s xml:id="echoid-s4475" xml:space="preserve">arcus eius eſt 71. </s>
  <s xml:id="echoid-s4476" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4477" xml:space="preserve">15. </s>
  <s xml:id="echoid-s4478" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4479" xml:space="preserve">quibus à ſemicirculo ſubtractis, re-<lb/>manent 108. </s>
  <s xml:id="echoid-s4480" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4481" xml:space="preserve">43. </s>
  <s xml:id="echoid-s4482" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4483" xml:space="preserve">arcus ille eclypticæ à medio cœli uſ ad gradum aſcendentis, <lb/>tantũ quo ſi numeres â 16. </s>
  <s xml:id="echoid-s4484" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4485" xml:space="preserve">40. </s>
  <s xml:id="echoid-s4486" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4487" xml:space="preserve">♈, iuxta uerum ſignorũ ordinem, numerus tan <lb/>get 5. </s>
  <s xml:id="echoid-s4488" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4489" xml:space="preserve">25. </s>
  <s xml:id="echoid-s4490" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4491" xml:space="preserve">♌, &amp; </s>
  <s xml:id="echoid-s4492" xml:space="preserve">ſic quidẽ gradũ aſcendentẽ adhuc diuerſo â ſuꝑioribus modo in-<lb/>ueni. </s>
  <s xml:id="echoid-s4493" xml:space="preserve">Inſuper ſi ꝑ 5. </s>
  <s xml:id="echoid-s4494" xml:space="preserve">ꝓnunc. </s>
  <s xml:id="echoid-s4495" xml:space="preserve">quæro declinationẽ, inuenio uti 18. </s>
  <s xml:id="echoid-s4496" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4497" xml:space="preserve">58. </s>
  <s xml:id="echoid-s4498" xml:space="preserve">mi ſinum eius <lb/>declinationis. </s>
  <s xml:id="echoid-s4499" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s4500" xml:space="preserve">32501. </s>
  <s xml:id="echoid-s4501" xml:space="preserve">quia minorem duco in ſinũ totũ, &amp; </s>
  <s xml:id="echoid-s4502" xml:space="preserve">productũ diuido in ſinũ am-
<pb file="0064" n="64" rhead="GENVINVS VSVS"/>
plitudinis ſcilicet 48572. </s>
  <s xml:id="echoid-s4503" xml:space="preserve">in quotiente prouenient 66913. </s>
  <s xml:id="echoid-s4504" xml:space="preserve">arcus illius eſt 42. </s>
  <s xml:id="echoid-s4505" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4506" xml:space="preserve">quibus <lb/>ſubtractis à 90. </s>
  <s xml:id="echoid-s4507" xml:space="preserve">remanẽt 48. </s>
  <s xml:id="echoid-s4508" xml:space="preserve">gr. </s>
  <s xml:id="echoid-s4509" xml:space="preserve">uera illa eleuatio poli quæſita ad locũ intronizatiõis.</s>
  <s xml:id="echoid-s4510" xml:space="preserve"/>
</p>
<div xml:id="echoid-div135" type="float" level="2" n="1">
<note position="right" xlink:label="note-0063-02" xlink:href="note-0063-02a" xml:space="preserve"><emph style="it">Amplitude</emph> <lb/><emph style="it">ortus ſiue</emph> <lb/><emph style="it">occaſus de-</emph> <lb/><emph style="it">clinatione</emph> <lb/><emph style="it">nunquã mi</emph> <lb/><emph style="it">nor, ſed ma</emph> <lb/><emph style="it">ior aut æ-</emph> <lb/><emph style="it">qualis repe</emph> <lb/><emph style="it">ritur.</emph></note>
<note position="right" xlink:label="note-0063-03" xlink:href="note-0063-03a" xml:space="preserve"><emph style="it">Per aream</emph> <lb/><emph style="it">patet.</emph></note>
<note position="right" xlink:label="note-0063-04" xlink:href="note-0063-04a" xml:space="preserve"><emph style="it">Per aream</emph></note>
<note position="right" xlink:label="note-0063-05" xlink:href="note-0063-05a" xml:space="preserve"><emph style="it">Per latera.</emph></note>
<note position="right" xlink:label="note-0063-06" xlink:href="note-0063-06a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div137" type="section" level="1" n="73">
<head xml:id="echoid-head77" xml:space="preserve">PRONVNCIATVM LXI.</head>
<p>
  <s xml:id="echoid-s4511" xml:space="preserve">Cognito iam gradu medĳ cœli, ſimiliter &amp; </s>
  <s xml:id="echoid-s4512" xml:space="preserve">gradu aſcendentis, altitudi-<lb/>nem poli in de cognoſcere.</s>
  <s xml:id="echoid-s4513" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s4514" xml:space="preserve">Vbi gradũ medĳ cœli habueris, quærè deinceps angulũ eclypticæ &amp; </s>
  <s xml:id="echoid-s4515" xml:space="preserve">meridiani ꝑ 26. <lb/></s>
  <s xml:id="echoid-s4516" xml:space="preserve">27. </s>
  <s xml:id="echoid-s4517" xml:space="preserve">uel 28. </s>
  <s xml:id="echoid-s4518" xml:space="preserve">ꝓnunc. </s>
  <s xml:id="echoid-s4519" xml:space="preserve">ꝗ ſi minor fuerit ̈ 90. </s>
  <s xml:id="echoid-s4520" xml:space="preserve">erit ad hãc oꝑationem ſatis idoneus: </s>
  <s xml:id="echoid-s4521" xml:space="preserve">ſin autem <lb/>maior extiterit, ſubtrahe eum de ſemicirculo, &amp; </s>
  <s xml:id="echoid-s4522" xml:space="preserve">reliquũ erit ad cõmodũ. </s>
  <s xml:id="echoid-s4523" xml:space="preserve">Deinde ꝓpone <lb/>arcũ à medio cœliuſ ad gradũ aſcendentis, is ſi minor ſit ̈ 90. </s>
  <s xml:id="echoid-s4524" xml:space="preserve">etiã iuſtus erit: </s>
  <s xml:id="echoid-s4525" xml:space="preserve">ſin ma-<lb/>ior, ſubtractus à ſemicirculo, relinquet nume℞ aptum ad hãc oꝑationẽ, ſinum eo℞ alte℞ <lb/>duc in alte℞, ꝓductũ diuide in ſinũ totũ, arcum q̊tientis ſubtrahe à 90. </s>
  <s xml:id="echoid-s4526" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4527" xml:space="preserve">remanebit am <lb/>
<anchor type="note" xlink:label="note-0064-01a" xlink:href="note-0064-01"/>
plitudo aſcẽdẽtis. </s>
  <s xml:id="echoid-s4528" xml:space="preserve">Hinc ꝓcede ita, ut ſuꝑiori ꝓnunciato edoctus es, unum attẽde, ꝙ ſi gra <lb/>dus aſcendentis ſit in aliq̊ ſigno℞ ſeptentrionalium, tunc etiã amplitudo erit ſeptentrio-<lb/>nalis, &amp; </s>
  <s xml:id="echoid-s4529" xml:space="preserve">ſimili modo res ſe habet de meridionali. </s>
  <s xml:id="echoid-s4530" xml:space="preserve">Sciendum inſuꝑ eſt inutilem &amp; </s>
  <s xml:id="echoid-s4531" xml:space="preserve">uanam <lb/>eſſe hanc operationẽ, quũ in medio cœli fuerit principiũ ♋ uel ♑, puncta quo proxi <lb/>me coniuncta, ſiue præcedant ſiue ſequantur, quo ergo longius diſtat principium ♋ <lb/>uel ♑ à medio cœli, eo certior etexpeditior hæc erit operatio, ſed hic non neceſſarium fu <lb/>erit exemplo rem demonſtrare, quando cum ſuperiori pronunciato multum cohæret.</s>
  <s xml:id="echoid-s4532" xml:space="preserve"/>
</p>
<div xml:id="echoid-div137" type="float" level="2" n="1">
<note position="left" xlink:label="note-0064-01" xlink:href="note-0064-01a" xml:space="preserve"><emph style="it">Lateralis in</emph> <lb/><emph style="it">troitus ſimi</emph> <lb/><emph style="it">le apprehẽ</emph> <lb/><emph style="it">dit.</emph></note>
</div>
</div>
<div xml:id="echoid-div139" type="section" level="1" n="74">
<head xml:id="echoid-head78" xml:space="preserve">PRONVNCIATVM LXII.</head>
<p>
  <s xml:id="echoid-s4533" xml:space="preserve">In quacun regione, perſpecta eleuatione poli, tempus quo punctum zo <lb/>diaci ab arcu per polos mundi &amp; </s>
  <s xml:id="echoid-s4534" xml:space="preserve">arcum æquinoctialis ducto uſ ad circulũ <lb/>uerticalem moueatur, dĳudicare.</s>
  <s xml:id="echoid-s4535" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s4536" xml:space="preserve">Hic iam ꝑ circulum, qui ꝑ polos mundi &amp; </s>
  <s xml:id="echoid-s4537" xml:space="preserve">arcum æquatoris trãſit, intelliges circulum <lb/>maiorem, ꝗ circulus dicitur horæ 6. </s>
  <s xml:id="echoid-s4538" xml:space="preserve">ante meridiẽ, ꝗa quũ ☉(sun) ad eum ꝑtingit, tunc hora 6 <lb/>eſt poſt mediÀ© noctis, &amp; </s>
  <s xml:id="echoid-s4539" xml:space="preserve">6. </s>
  <s xml:id="echoid-s4540" xml:space="preserve">horæ adhuc diſtãt à meridie, ſiquidẽ tunc exacte tempus medi <lb/>um eſt int<unsure/> meridiẽ &amp; </s>
  <s xml:id="echoid-s4541" xml:space="preserve">mediũ noctis, quãdo Sol illum attingit. </s>
  <s xml:id="echoid-s4542" xml:space="preserve">Principio igitur huius oꝑa <lb/>tionis, quære ꝗ 5. </s>
  <s xml:id="echoid-s4543" xml:space="preserve">declinationẽ ꝓpoſiti puncti eclypticæ &amp; </s>
  <s xml:id="echoid-s4544" xml:space="preserve">altitudinẽ puncti dati in cir-<lb/>culo uerticali ꝗ 20. </s>
  <s xml:id="echoid-s4545" xml:space="preserve">ꝓnunc. </s>
  <s xml:id="echoid-s4546" xml:space="preserve">ſinũ cõplementi altitudinis huius in circulo uerticali ſepo-<lb/>
<anchor type="note" xlink:label="note-0064-02a" xlink:href="note-0064-02"/>
ne in locum aliquẽ ſeorſim, ſimilit<unsure/> &amp; </s>
  <s xml:id="echoid-s4547" xml:space="preserve">ſinũ cõplementi declinatiõis dati pũcti eclypticæ, <lb/>minorẽ duc in ſinum totum, ꝓductũ in maiorem diuide, &amp; </s>
  <s xml:id="echoid-s4548" xml:space="preserve">arcus q̊tientis ex 90. </s>
  <s xml:id="echoid-s4549" xml:space="preserve">ſubtra-<lb/>ctus relinquet gradus æquatoris, ꝗbus in horas horarũ´ minuta cõuerſus, habebis op <lb/>tatum. </s>
  <s xml:id="echoid-s4550" xml:space="preserve">?</s>
  <s xml:id="echoid-s4551" xml:space="preserve">? Vide exemplũ. </s>
  <s xml:id="echoid-s4552" xml:space="preserve">Cupio ſcire in loco &amp; </s>
  <s xml:id="echoid-s4553" xml:space="preserve">die intronizatiõis tempus illud cõme <lb/>
<anchor type="note" xlink:label="note-0064-03a" xlink:href="note-0064-03"/>
moratũ, declinatio ita Solis eſt 20. </s>
  <s xml:id="echoid-s4554" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4555" xml:space="preserve">42. </s>
  <s xml:id="echoid-s4556" xml:space="preserve">mi cõplementũ eius 69. </s>
  <s xml:id="echoid-s4557" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4558" xml:space="preserve">18. </s>
  <s xml:id="echoid-s4559" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4560" xml:space="preserve">ſinus ip <lb/>ſius 93544. </s>
  <s xml:id="echoid-s4561" xml:space="preserve">is (ꝗa maior) erit altitudo ☉(sun) in circulo uerticali eſt 28. </s>
  <s xml:id="echoid-s4562" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4563" xml:space="preserve">24. </s>
  <s xml:id="echoid-s4564" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4565" xml:space="preserve">ſinũ cõple <lb/>mẽti 87964. </s>
  <s xml:id="echoid-s4566" xml:space="preserve">duco in totũ, ꝓductũ in diuiſorẽ diuido, &amp; </s>
  <s xml:id="echoid-s4567" xml:space="preserve">ꝓueniũtin q̊tiente 94034. </s>
  <s xml:id="echoid-s4568" xml:space="preserve">arcus <lb/>eius eſt 70. </s>
  <s xml:id="echoid-s4569" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4570" xml:space="preserve">7. </s>
  <s xml:id="echoid-s4571" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4572" xml:space="preserve">q̊ ſu bducto à 90. </s>
  <s xml:id="echoid-s4573" xml:space="preserve">remanẽt 19. </s>
  <s xml:id="echoid-s4574" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4575" xml:space="preserve">53. </s>
  <s xml:id="echoid-s4576" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4577" xml:space="preserve">æquatoris, ho℞ ſi ſemꝑ 15 <lb/>ꝓ hora unica ſupputẽ, habebo horã 1. </s>
  <s xml:id="echoid-s4578" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4579" xml:space="preserve">19. </s>
  <s xml:id="echoid-s4580" xml:space="preserve">ſecunda 32. </s>
  <s xml:id="echoid-s4581" xml:space="preserve">tẽpus. </s>
  <s xml:id="echoid-s4582" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s4583" xml:space="preserve">illud quo Sol percurrit <lb/>ab hora 6. </s>
  <s xml:id="echoid-s4584" xml:space="preserve">uſ ad circulum uerticalem in parte orientis, quod tamen &amp; </s>
  <s xml:id="echoid-s4585" xml:space="preserve">de parte occidua <lb/>intelligendum eſt, niſi quòd tũc Sol citius circulum uerticalem attingit quàm horam 6. <lb/></s>
  <s xml:id="echoid-s4586" xml:space="preserve">poſt meridiem, at hæc operatio nihil loci habet in ſignis meridionalibus.</s>
  <s xml:id="echoid-s4587" xml:space="preserve"/>
</p>
<div xml:id="echoid-div139" type="float" level="2" n="1">
<note position="left" xlink:label="note-0064-02" xlink:href="note-0064-02a" xml:space="preserve"><emph style="it">Arealis in</emph> <lb/><emph style="it">greſſus iun</emph> <lb/><emph style="it">gitur.</emph></note>
<note position="left" xlink:label="note-0064-03" xlink:href="note-0064-03a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div141" type="section" level="1" n="75">
<head xml:id="echoid-head79" xml:space="preserve">PRONVNCIATVM LXIII.</head>
<p>
  <s xml:id="echoid-s4588" xml:space="preserve">Intellecta iã altitudine poli, adhucemetiri quanto tempore arcus aliquis <lb/>eclypticæ propoſitus à principio uſ in finem pertranſeat circulũ uerticalẽ.</s>
  <s xml:id="echoid-s4589" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s4590" xml:space="preserve">Cõſidera hic ante arcũzodiaci, an principiũ eius declinationẽ habeat maiorẽ ̈ finis <lb/>ſiue nõ, numerãdo illũ iuxta ue℞ ordinẽ ſigno℞. </s>
  <s xml:id="echoid-s4591" xml:space="preserve">Et quæſita quidẽ ꝑ 5. </s>
  <s xml:id="echoid-s4592" xml:space="preserve">declinationem u-<lb/>triuſ, adhuc inꝗre ꝑ præcedens ꝓnunc. </s>
  <s xml:id="echoid-s4593" xml:space="preserve">tempus, in q̊ quodlibet punctum principĳ &amp; </s>
  <s xml:id="echoid-s4594" xml:space="preserve">ſi <lb/>nis dati arcus, ꝓmoueatur ab hora 6. </s>
  <s xml:id="echoid-s4595" xml:space="preserve">uſ ad circulũ uerticalem. </s>
  <s xml:id="echoid-s4596" xml:space="preserve">Inueſtiga etiã utriuſ <lb/>illius puncti aſcenſionẽ rectã per 7 ꝓnunc. </s>
  <s xml:id="echoid-s4597" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4598" xml:space="preserve">ſubtrahe aſcenſionẽ minorẽ à maiori, reſi-<lb/>duũ obſerua ſeor@@m, ſubtrahe etiã tempus minimũ (tantũ duc gradus æquatoris ante cõ <lb/>uerſionem in horas) à maiori, q̊d utrun ex præcedenti ꝓnunc. </s>
  <s xml:id="echoid-s4599" xml:space="preserve">inueniſti ab hora 6. </s>
  <s xml:id="echoid-s4600" xml:space="preserve">uſ <lb/>ad cõtactum circuli uerticalis, ꝙ ſi declinatio ſinis huius arcus maior fuerit ̈ illa initĳ,
<pb file="0065" n="65" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
adde reſiduũ ad iſtud q̊d paulo ante ſe poſuiſti reliquũ aſcenſionũrecta℞. </s>
  <s xml:id="echoid-s4601" xml:space="preserve">Sed ſi declina <lb/>tio finis arcus ꝓpoſiti, ſecundũ ordinẽ ſignorũ numerãdo, minor extiterit declinatiõe ini <lb/>tĳ huius arcus, tũc ſubtrahe reſiduũ hoc â reſiduo aſcenſionũ rectarũ, ꝓ utrã hanc rationẽ <lb/>q̊d ꝓducitur tempus ipſum eſt (ſi ſemper 15. </s>
  <s xml:id="echoid-s4602" xml:space="preserve">gradus ꝓ una hora ſupputentur) in quo ar-<lb/>cus ꝓpoſitus ꝓcurrit ultra circulũ uerticalẽ. </s>
  <s xml:id="echoid-s4603" xml:space="preserve">ld omne ſic intelligendũ eſt, ꝙ ambo termi-<lb/>ni iſtius arcus ſint in medietate ſeptentrionali, fœlicius iſta oia intelliges ex adiũcto exẽ-<lb/>
<anchor type="note" xlink:label="note-0065-01a" xlink:href="note-0065-01"/>
plo. </s>
  <s xml:id="echoid-s4604" xml:space="preserve">?</s>
  <s xml:id="echoid-s4605" xml:space="preserve">?Volo ſcire quanto tꝑe arcus iſte à 2. </s>
  <s xml:id="echoid-s4606" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4607" xml:space="preserve">26. </s>
  <s xml:id="echoid-s4608" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4609" xml:space="preserve">II, ubi Sol fuit in die &amp; </s>
  <s xml:id="echoid-s4610" xml:space="preserve">hora in-<lb/>tronizatiõis uſ ad 16. </s>
  <s xml:id="echoid-s4611" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4612" xml:space="preserve">49. </s>
  <s xml:id="echoid-s4613" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4614" xml:space="preserve">II, circulũ uerticalẽ trãſcendat, aſcenſionẽ igitur re-<lb/>ctaminueni ad 2. </s>
  <s xml:id="echoid-s4615" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4616" xml:space="preserve">26. </s>
  <s xml:id="echoid-s4617" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4618" xml:space="preserve">II per 7. </s>
  <s xml:id="echoid-s4619" xml:space="preserve">ꝓnunc. </s>
  <s xml:id="echoid-s4620" xml:space="preserve">ea eſt 60. </s>
  <s xml:id="echoid-s4621" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4622" xml:space="preserve">21. </s>
  <s xml:id="echoid-s4623" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4624" xml:space="preserve">aſcenſio aũt 16. </s>
  <s xml:id="echoid-s4625" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s4626" xml:space="preserve">49. </s>
  <s xml:id="echoid-s4627" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4628" xml:space="preserve">II eſt 75. </s>
  <s xml:id="echoid-s4629" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4630" xml:space="preserve">37. </s>
  <s xml:id="echoid-s4631" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4632" xml:space="preserve">differentia earũ 15. </s>
  <s xml:id="echoid-s4633" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4634" xml:space="preserve">16. </s>
  <s xml:id="echoid-s4635" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4636" xml:space="preserve">reſiduũ ſepono ſeorſim, mox <lb/>ex præcedenti ꝓnunciato quæro tempus ab hora 6. </s>
  <s xml:id="echoid-s4637" xml:space="preserve">uſ dum 2. </s>
  <s xml:id="echoid-s4638" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4639" xml:space="preserve">26. </s>
  <s xml:id="echoid-s4640" xml:space="preserve">mi (qui Solipſe <lb/>eſt) ad circulũ perueniat uerticalem, inuenio ergo 19. </s>
  <s xml:id="echoid-s4641" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4642" xml:space="preserve">53. </s>
  <s xml:id="echoid-s4643" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4644" xml:space="preserve">At hoc ita ſeruo, non <lb/>immutans in horas. </s>
  <s xml:id="echoid-s4645" xml:space="preserve">Comperio etiam tempus illud ad 16. </s>
  <s xml:id="echoid-s4646" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4647" xml:space="preserve">49. </s>
  <s xml:id="echoid-s4648" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4649" xml:space="preserve">II, a b hora 6. </s>
  <s xml:id="echoid-s4650" xml:space="preserve">do-<lb/>nec attingat circulum uerticalem habere 29. </s>
  <s xml:id="echoid-s4651" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4652" xml:space="preserve">10. </s>
  <s xml:id="echoid-s4653" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4654" xml:space="preserve">Nunc igitur ſubtraho 19. </s>
  <s xml:id="echoid-s4655" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4656" xml:space="preserve"><lb/>53. </s>
  <s xml:id="echoid-s4657" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4658" xml:space="preserve">à 39. </s>
  <s xml:id="echoid-s4659" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4660" xml:space="preserve">10, mi. </s>
  <s xml:id="echoid-s4661" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4662" xml:space="preserve">remanent 9. </s>
  <s xml:id="echoid-s4663" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4664" xml:space="preserve">17. </s>
  <s xml:id="echoid-s4665" xml:space="preserve">quandoquidem declinatio 16. </s>
  <s xml:id="echoid-s4666" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4667" xml:space="preserve">49. </s>
  <s xml:id="echoid-s4668" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4669" xml:space="preserve"><lb/>II, maiorem 22. </s>
  <s xml:id="echoid-s4670" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4671" xml:space="preserve">50. </s>
  <s xml:id="echoid-s4672" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4673" xml:space="preserve">quàm declinatio hæc 2. </s>
  <s xml:id="echoid-s4674" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4675" xml:space="preserve">26. </s>
  <s xml:id="echoid-s4676" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4677" xml:space="preserve">II, quamper 5. </s>
  <s xml:id="echoid-s4678" xml:space="preserve">pronuncia <lb/>tum inueni eſſe 20. </s>
  <s xml:id="echoid-s4679" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4680" xml:space="preserve">42. </s>
  <s xml:id="echoid-s4681" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4682" xml:space="preserve">Iam addo 9. </s>
  <s xml:id="echoid-s4683" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4684" xml:space="preserve">17. </s>
  <s xml:id="echoid-s4685" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4686" xml:space="preserve">ad reſiduũ ſiue differẽtiam aſcen-<lb/>ſionum rectarum, ſcilicet 15. </s>
  <s xml:id="echoid-s4687" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4688" xml:space="preserve">16. </s>
  <s xml:id="echoid-s4689" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4690" xml:space="preserve">inde &amp; </s>
  <s xml:id="echoid-s4691" xml:space="preserve">prouenient 24 gra. </s>
  <s xml:id="echoid-s4692" xml:space="preserve">33. </s>
  <s xml:id="echoid-s4693" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4694" xml:space="preserve">Quibus con-<lb/>uerſis in horas &amp; </s>
  <s xml:id="echoid-s4695" xml:space="preserve">horarum minuta, habebo horã 1. </s>
  <s xml:id="echoid-s4696" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4697" xml:space="preserve">minuta ferè 38. </s>
  <s xml:id="echoid-s4698" xml:space="preserve">Quanto tꝓe arcus <lb/>ille à 2. </s>
  <s xml:id="echoid-s4699" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4700" xml:space="preserve">26. </s>
  <s xml:id="echoid-s4701" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4702" xml:space="preserve">II decurrit uſ ad 16. </s>
  <s xml:id="echoid-s4703" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4704" xml:space="preserve">49. </s>
  <s xml:id="echoid-s4705" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4706" xml:space="preserve">II, ſuper circulum uerticalem.</s>
  <s xml:id="echoid-s4707" xml:space="preserve"/>
</p>
<div xml:id="echoid-div141" type="float" level="2" n="1">
<note position="right" xlink:label="note-0065-01" xlink:href="note-0065-01a" xml:space="preserve">EXEM <lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div143" type="section" level="1" n="76">
<head xml:id="echoid-head80" xml:space="preserve">PRONVNCIATVM LXIIII.</head>
<p>
  <s xml:id="echoid-s4708" xml:space="preserve">Idem hoctempus adhucalio modo perquirere, at ea ueluti generalis eſt <lb/>regula ad totam eclypticam.</s>
  <s xml:id="echoid-s4709" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s4710" xml:space="preserve">Quum in hac operatione arcus datus ſit ſemicirculus, is ſanè uerticalem tranſcendit <lb/>in 12. </s>
  <s xml:id="echoid-s4711" xml:space="preserve">horis, at ideo nulla peculiari animaduerſione hic opus eſt. </s>
  <s xml:id="echoid-s4712" xml:space="preserve">Si autem arcus datus <lb/>eclypticæ fuerit ſemicirculo minor, eius´ termini à principio ♋ æquales habuerint re-<lb/>motiones, &amp; </s>
  <s xml:id="echoid-s4713" xml:space="preserve">ideo etiam neceſſario ab æquinoctiali ſcilicet â 90. </s>
  <s xml:id="echoid-s4714" xml:space="preserve">gradu, qui cum principio <lb/>cancri ſemper iacet in medio cœli, æquales diſtantias tunc differentia aſcenſionum, quæ <lb/>aliàs aſcenſio dati arcus recta diciſolet, eſtarcus huius temporis quem inquiris, non eſt <lb/>igitur quòd amplius labores ſolicitus, ſiquidem eo temporearcus datus percurrit circu-<lb/>lum uerticalem. </s>
  <s xml:id="echoid-s4715" xml:space="preserve">Cæterum ſi termini arcus dati inæquales habuerint diſtantias à princi-<lb/>pio Cancri, oportebit te amborum illorum aſcenſionem quærere rectam, ſimiliter &amp; </s>
  <s xml:id="echoid-s4716" xml:space="preserve">utri <lb/>uſ declinationem ab æquatore. </s>
  <s xml:id="echoid-s4717" xml:space="preserve">Deinde inquire etiam cuiuslibet termiui altitudinem <lb/>ſupra horizontem in circulo uerticali per 20. </s>
  <s xml:id="echoid-s4718" xml:space="preserve">pronunciatum, poſtea tibi propone ſinus <lb/>primi termini complementi altitudinis &amp; </s>
  <s xml:id="echoid-s4719" xml:space="preserve">complementi declinationis, minorem ex ĳs <lb/>
<anchor type="note" xlink:label="note-0065-02a" xlink:href="note-0065-02"/>
duc in totum, productum diuide in maiorem, &amp; </s>
  <s xml:id="echoid-s4720" xml:space="preserve">arcus quotientis uocabitur inuentũ <lb/>primum. </s>
  <s xml:id="echoid-s4721" xml:space="preserve">Simili modo operaberis etiam cum finali complemento termini &amp; </s>
  <s xml:id="echoid-s4722" xml:space="preserve">ſinum cõ-<lb/>
<anchor type="note" xlink:label="note-0065-03a" xlink:href="note-0065-03"/>
plementi declinationis eius, at ſic arcus quotientis dabit inuentum ſecundũ. </s>
  <s xml:id="echoid-s4723" xml:space="preserve">Porrò de-<lb/>inceps ſubtrabe inuentũ minus à maiori, &amp; </s>
  <s xml:id="echoid-s4724" xml:space="preserve">remanebit differentia inuentorũ eã adde ad <lb/>aſcenſionem rectã arcus propoſiti, quam paulo ante dixi differentiã inter aſcenſiones re <lb/>ctas duorũ terminorũ, ſi modo terminus finalis Borealior extiterit ̈ initialis, uel ſubtra <lb/>he differentiam iſtam, ſi terminus finalis meridionalior fuerit puncto initiali. </s>
  <s xml:id="echoid-s4725" xml:space="preserve">Ex hac ſiue <lb/>additione ſiue ſubtra ctione, quicquid reſultabit, arcus erit æquatoris ſimul oriens cũ ar-<lb/>cu ꝓpoſito eclypticæ circulum uerticalem ſupergreditur, tantũ ut gradus iſtos in horas <lb/>&amp; </s>
  <s xml:id="echoid-s4726" xml:space="preserve">horarũ minuta cõuertas. </s>
  <s xml:id="echoid-s4727" xml:space="preserve">Adhuc tamen, ſi arcus datus eclypticæ incipiat in principio <lb/>♈, &amp; </s>
  <s xml:id="echoid-s4728" xml:space="preserve">deſinat citra princi piũ ♎, tunc ſanè ipſum inuentum primum ſine illa ulterioriſup <lb/>putatione erit 90. </s>
  <s xml:id="echoid-s4729" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4730" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4731" xml:space="preserve">ſi finis arcus propoſiti, deſinat in principium ♎ præciſe, princi <lb/>pium autem ſuum habeat poſt principium ♈, tunc obmiſſo inuento altero, operatio fi <lb/>et ut prius. </s>
  <s xml:id="echoid-s4732" xml:space="preserve">?</s>
  <s xml:id="echoid-s4733" xml:space="preserve">? Exemplum ſit hoc tibi, ne difficultatem cauſſari nimiam queas. </s>
  <s xml:id="echoid-s4734" xml:space="preserve">Ipſo die <lb/>
<anchor type="note" xlink:label="note-0065-04a" xlink:href="note-0065-04"/>
intronizationis fuit locus ☉(sun) 2. </s>
  <s xml:id="echoid-s4735" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4736" xml:space="preserve">26. </s>
  <s xml:id="echoid-s4737" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4738" xml:space="preserve">II, nunc ergo cupio ſcire à gradu ☉(sun) uſ ad <lb/>16. </s>
  <s xml:id="echoid-s4739" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4740" xml:space="preserve">49. </s>
  <s xml:id="echoid-s4741" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4742" xml:space="preserve">Gemini, tempus iſtud, in q̊ arcus hic circulũ uerticalem ſupergreditur in
<pb file="0066" n="66" rhead="GENVINVS VSVS"/>
altitudine poliloci in q̊ facta eſt intronizatio, hactenus ſemp cõſtituimus 48. </s>
  <s xml:id="echoid-s4743" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4744" xml:space="preserve">altitu <lb/>do 2. </s>
  <s xml:id="echoid-s4745" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4746" xml:space="preserve">26. </s>
  <s xml:id="echoid-s4747" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4748" xml:space="preserve">II, in circulouerticali eſt 28. </s>
  <s xml:id="echoid-s4749" xml:space="preserve">gra.</s>
  <s xml:id="echoid-s4750" xml:space="preserve">24. </s>
  <s xml:id="echoid-s4751" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4752" xml:space="preserve">cõplementum eius 61. </s>
  <s xml:id="echoid-s4753" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4754" xml:space="preserve">36. <lb/></s>
  <s xml:id="echoid-s4755" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4756" xml:space="preserve">ſinus iſtius 87964. </s>
  <s xml:id="echoid-s4757" xml:space="preserve">declinatio autem eſt 20. </s>
  <s xml:id="echoid-s4758" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4759" xml:space="preserve">42. </s>
  <s xml:id="echoid-s4760" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4761" xml:space="preserve">cõplementũ eius 69. </s>
  <s xml:id="echoid-s4762" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4763" xml:space="preserve">18. </s>
  <s xml:id="echoid-s4764" xml:space="preserve"><lb/>mi. </s>
  <s xml:id="echoid-s4765" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4766" xml:space="preserve">ſinus 39544. </s>
  <s xml:id="echoid-s4767" xml:space="preserve">minorẽ ita ſinũ 87964. </s>
  <s xml:id="echoid-s4768" xml:space="preserve">duco in totũ, ꝓductũ diuido in maiorẽ, &amp; </s>
  <s xml:id="echoid-s4769" xml:space="preserve">ꝓ <lb/>ueniunt in quotiẽte 94034. </s>
  <s xml:id="echoid-s4770" xml:space="preserve">arcus 70. </s>
  <s xml:id="echoid-s4771" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4772" xml:space="preserve">7. </s>
  <s xml:id="echoid-s4773" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4774" xml:space="preserve">dicetur inuentũ primũ. </s>
  <s xml:id="echoid-s4775" xml:space="preserve">Declinatio termi <lb/>ni finalis 16. </s>
  <s xml:id="echoid-s4776" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4777" xml:space="preserve">49. </s>
  <s xml:id="echoid-s4778" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4779" xml:space="preserve">eſt 22. </s>
  <s xml:id="echoid-s4780" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4781" xml:space="preserve">50. </s>
  <s xml:id="echoid-s4782" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4783" xml:space="preserve">ſinus cõplementi 92163. </s>
  <s xml:id="echoid-s4784" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4785" xml:space="preserve">altitudo in circu-<lb/>lo uerticali 36. </s>
  <s xml:id="echoid-s4786" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4787" xml:space="preserve">25. </s>
  <s xml:id="echoid-s4788" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4789" xml:space="preserve">hinc proueniunt 87314. </s>
  <s xml:id="echoid-s4790" xml:space="preserve">arcus erit 60. </s>
  <s xml:id="echoid-s4791" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4792" xml:space="preserve">50. </s>
  <s xml:id="echoid-s4793" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4794" xml:space="preserve">inuentum. </s>
  <s xml:id="echoid-s4795" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s4796" xml:space="preserve"><lb/>ſecundũ, q̊d tan̈ minoris numeri ſubtraho â primo, &amp; </s>
  <s xml:id="echoid-s4797" xml:space="preserve">manent 9. </s>
  <s xml:id="echoid-s4798" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4799" xml:space="preserve">17. </s>
  <s xml:id="echoid-s4800" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4801" xml:space="preserve">At quũ <lb/>finalis terminus Borealior ſit initiali termino arcus ꝓpoſiti, addo 9 gra. </s>
  <s xml:id="echoid-s4802" xml:space="preserve">17. </s>
  <s xml:id="echoid-s4803" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4804" xml:space="preserve">ad aſcen-<lb/>ſionem rectã arcus ꝓpoſiti. </s>
  <s xml:id="echoid-s4805" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s4806" xml:space="preserve">15. </s>
  <s xml:id="echoid-s4807" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4808" xml:space="preserve">16. </s>
  <s xml:id="echoid-s4809" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4810" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4811" xml:space="preserve">proueniunt 24. </s>
  <s xml:id="echoid-s4812" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4813" xml:space="preserve">33. </s>
  <s xml:id="echoid-s4814" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4815" xml:space="preserve">quibus conuer <lb/>ſis in horas, ꝓdibũt hora una &amp; </s>
  <s xml:id="echoid-s4816" xml:space="preserve">38. </s>
  <s xml:id="echoid-s4817" xml:space="preserve">ferè minuta, ſicuti ſuperius etiam probatum fuit.</s>
  <s xml:id="echoid-s4818" xml:space="preserve"/>
</p>
<div xml:id="echoid-div143" type="float" level="2" n="1">
<note position="right" xlink:label="note-0065-02" xlink:href="note-0065-02a" xml:space="preserve"><emph style="it">Aredlis in-</emph> <lb/><emph style="it">greſſus.</emph></note>
<note position="right" xlink:label="note-0065-03" xlink:href="note-0065-03a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">primum-</emph> <lb/><emph style="it">Inuentum</emph> <lb/><emph style="it">ſecundum.</emph></note>
<note position="right" xlink:label="note-0065-04" xlink:href="note-0065-04a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div145" type="section" level="1" n="77">
<head xml:id="echoid-head81" xml:space="preserve">PRONVNCIATVM LXV.</head>
<p>
  <s xml:id="echoid-s4819" xml:space="preserve">Si in duabus regionibus altitudo poli ſitignota, &amp; </s>
  <s xml:id="echoid-s4820" xml:space="preserve">uno momento unus a-<lb/>ſcendens exiſtat, ſed ad meridianos eorum pertingat duplex eclypticæ pun <lb/>ctum etiam ignotum, adhucinſuper cognoſcere latitudines &amp; </s>
  <s xml:id="echoid-s4821" xml:space="preserve">differentiam <lb/>longitudinis earum.</s>
  <s xml:id="echoid-s4822" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s4823" xml:space="preserve">Vbiiam gradus medĳ cœli cuiuſcun regionis cognoueris, quære aſcenſionem rectã <lb/>cuiuslibet pũcti medĳ cœli, ſubtrahe deinde medium cœli aſcenſionem rectã, puta mino <lb/>rem à reliquo gradu medĳ cœli, hoc eſt à maiori, relictum inde erit differentia longitudi-<lb/>num inter utrun &amp; </s>
  <s xml:id="echoid-s4824" xml:space="preserve">quia aſcendens ambarum regionum eſt punctum eclypticæ etiam <lb/>notum, porrò in quire altitudinem poli utriuſ iuxta præſcriptum pronunc.</s>
  <s xml:id="echoid-s4825" xml:space="preserve">61. </s>
  <s xml:id="echoid-s4826" xml:space="preserve">at ſic <lb/>habebis optatum, breui exemplo rem tibi demonſtrabimus. </s>
  <s xml:id="echoid-s4827" xml:space="preserve">Eſto ut in una ciuitate medi <lb/>arit cœlum. </s>
  <s xml:id="echoid-s4828" xml:space="preserve">16. </s>
  <s xml:id="echoid-s4829" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4830" xml:space="preserve">40. </s>
  <s xml:id="echoid-s4831" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4832" xml:space="preserve">γ, in alia autem 23. </s>
  <s xml:id="echoid-s4833" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4834" xml:space="preserve">37. </s>
  <s xml:id="echoid-s4835" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4836" xml:space="preserve">γ, utrin etiam fuerit in aſcen <lb/>dente 5. </s>
  <s xml:id="echoid-s4837" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4838" xml:space="preserve">25. </s>
  <s xml:id="echoid-s4839" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4840" xml:space="preserve">♌, quæritur iam quantum eleuatus ſit polus utrin, &amp; </s>
  <s xml:id="echoid-s4841" xml:space="preserve">quæ inter am <lb/>bos locos ſit diſferentia longitudinis. </s>
  <s xml:id="echoid-s4842" xml:space="preserve">?</s>
  <s xml:id="echoid-s4843" xml:space="preserve">?Exemplum prius demonſtraui per 61. </s>
  <s xml:id="echoid-s4844" xml:space="preserve">pro-<lb/>
<anchor type="note" xlink:label="note-0066-01a" xlink:href="note-0066-01"/>
nũc. </s>
  <s xml:id="echoid-s4845" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4846" xml:space="preserve">Auguſtæ, ubi facta eſt intronizatio, altitudo poli ſupponitur 48. </s>
  <s xml:id="echoid-s4847" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4848" xml:space="preserve">ſicuti ſæpe <lb/>diximus, uerum in ignota ciuitate fuit in medio cœli 23. </s>
  <s xml:id="echoid-s4849" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4850" xml:space="preserve">37. </s>
  <s xml:id="echoid-s4851" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4852" xml:space="preserve">γ. </s>
  <s xml:id="echoid-s4853" xml:space="preserve">eodem. </s>
  <s xml:id="echoid-s4854" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s4855" xml:space="preserve">momen <lb/>to quo fuit 5. </s>
  <s xml:id="echoid-s4856" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4857" xml:space="preserve">25. </s>
  <s xml:id="echoid-s4858" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4859" xml:space="preserve">♌ in aſcendente. </s>
  <s xml:id="echoid-s4860" xml:space="preserve">aſcenſio recta 16. </s>
  <s xml:id="echoid-s4861" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4862" xml:space="preserve">40. </s>
  <s xml:id="echoid-s4863" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4864" xml:space="preserve">γ eſt 15. </s>
  <s xml:id="echoid-s4865" xml:space="preserve">gradu-<lb/>um, 21. </s>
  <s xml:id="echoid-s4866" xml:space="preserve">minutorum. </s>
  <s xml:id="echoid-s4867" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4868" xml:space="preserve">aſcenſio recta 23. </s>
  <s xml:id="echoid-s4869" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4870" xml:space="preserve">37. </s>
  <s xml:id="echoid-s4871" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4872" xml:space="preserve">γ eſt 21. </s>
  <s xml:id="echoid-s4873" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4874" xml:space="preserve">51. </s>
  <s xml:id="echoid-s4875" xml:space="preserve">minutorum. </s>
  <s xml:id="echoid-s4876" xml:space="preserve">Iam <lb/>ſi aſcenſionem minorem ſubtraho à maiori, remanet differentia 6. </s>
  <s xml:id="echoid-s4877" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4878" xml:space="preserve">30. </s>
  <s xml:id="echoid-s4879" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4880" xml:space="preserve">differentia <lb/>inquam longitudinis iſtarum duarum ciuitatum. </s>
  <s xml:id="echoid-s4881" xml:space="preserve">Mox quæro &amp; </s>
  <s xml:id="echoid-s4882" xml:space="preserve">angulũ meridiani at <lb/>eclypticæ iuxta gradũ medĳ cœli. </s>
  <s xml:id="echoid-s4883" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s4884" xml:space="preserve">23. </s>
  <s xml:id="echoid-s4885" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4886" xml:space="preserve">37. </s>
  <s xml:id="echoid-s4887" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4888" xml:space="preserve">γ, ꝗ eſt 68. </s>
  <s xml:id="echoid-s4889" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4890" xml:space="preserve">17. </s>
  <s xml:id="echoid-s4891" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4892" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4893" xml:space="preserve">diſtantiã à <lb/>medio cœli uſ ad aſcendentẽ, ꝗ ſunt 101. </s>
  <s xml:id="echoid-s4894" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4895" xml:space="preserve">48. </s>
  <s xml:id="echoid-s4896" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4897" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4898" xml:space="preserve">quũ hæc ſuꝑet 90. </s>
  <s xml:id="echoid-s4899" xml:space="preserve">ſubtraho à ſe <lb/>micirculo, &amp; </s>
  <s xml:id="echoid-s4900" xml:space="preserve">remanẽt 78. </s>
  <s xml:id="echoid-s4901" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4902" xml:space="preserve">12. </s>
  <s xml:id="echoid-s4903" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4904" xml:space="preserve">Nũc inꝗro amplitudinẽ aſcendentis in hũc modũ: <lb/></s>
  <s xml:id="echoid-s4905" xml:space="preserve">principio quæro ꝑ 26. </s>
  <s xml:id="echoid-s4906" xml:space="preserve">27. </s>
  <s xml:id="echoid-s4907" xml:space="preserve">uel 28. </s>
  <s xml:id="echoid-s4908" xml:space="preserve">angulũ quem facit eclyptica cũ meridiano iuxta gradũ <lb/>medĳ cœli, qui eſt 68. </s>
  <s xml:id="echoid-s4909" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4910" xml:space="preserve">17. </s>
  <s xml:id="echoid-s4911" xml:space="preserve">minutorũ, ſinus eſt 92902. </s>
  <s xml:id="echoid-s4912" xml:space="preserve">eũ duco in ſinũ 78. </s>
  <s xml:id="echoid-s4913" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4914" xml:space="preserve">12. </s>
  <s xml:id="echoid-s4915" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4916" xml:space="preserve"><lb/>ſcilicet 97886. </s>
  <s xml:id="echoid-s4917" xml:space="preserve">puta reſiduũ. </s>
  <s xml:id="echoid-s4918" xml:space="preserve">Poſt̈ diſtantiã medĳ cœli ab aſcendente ſubtraxi de ſemi-<lb/>
<anchor type="note" xlink:label="note-0066-02a" xlink:href="note-0066-02"/>
circulo, productũ diuido in ſinum totum, &amp; </s>
  <s xml:id="echoid-s4919" xml:space="preserve">in quotiente proueniunt 90938. </s>
  <s xml:id="echoid-s4920" xml:space="preserve">arcus eius <lb/>65. </s>
  <s xml:id="echoid-s4921" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4922" xml:space="preserve">25. </s>
  <s xml:id="echoid-s4923" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4924" xml:space="preserve">reſiduũ aũt à 90. </s>
  <s xml:id="echoid-s4925" xml:space="preserve">eſt 24. </s>
  <s xml:id="echoid-s4926" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4927" xml:space="preserve">35. </s>
  <s xml:id="echoid-s4928" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4929" xml:space="preserve">amplitudo. </s>
  <s xml:id="echoid-s4930" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s4931" xml:space="preserve">illa aſcendentis, cuius ele <lb/>uatio polaris adhuc eſt incognita. </s>
  <s xml:id="echoid-s4932" xml:space="preserve">Duco igitur ſinum declinationis aſcendentis gradus <lb/>
<anchor type="note" xlink:label="note-0066-03a" xlink:href="note-0066-03"/>
32501. </s>
  <s xml:id="echoid-s4933" xml:space="preserve">puta minorem in ſinum totum, &amp; </s>
  <s xml:id="echoid-s4934" xml:space="preserve">productũ diuido in ſinum amplitudinis 41601 <lb/>in quotiente proueniunt 78125. </s>
  <s xml:id="echoid-s4935" xml:space="preserve">arcus ipſius 51. </s>
  <s xml:id="echoid-s4936" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4937" xml:space="preserve">23. </s>
  <s xml:id="echoid-s4938" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4939" xml:space="preserve">de 90. </s>
  <s xml:id="echoid-s4940" xml:space="preserve">ſubtractus, relinquit <lb/>38. </s>
  <s xml:id="echoid-s4941" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4942" xml:space="preserve">37. </s>
  <s xml:id="echoid-s4943" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4944" xml:space="preserve">quæ eſt altitudo poli ignotæ ciuitatis, quæ ſimul cum loco intronizatio-<lb/>nis eadem hora qua illa facta eſt, in aſcendente habuit 5. </s>
  <s xml:id="echoid-s4945" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4946" xml:space="preserve">25. </s>
  <s xml:id="echoid-s4947" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4948" xml:space="preserve">♌.</s>
  <s xml:id="echoid-s4949" xml:space="preserve"/>
</p>
<div xml:id="echoid-div145" type="float" level="2" n="1">
<note position="left" xlink:label="note-0066-01" xlink:href="note-0066-01a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoopi.</emph></note>
<note position="left" xlink:label="note-0066-02" xlink:href="note-0066-02a" xml:space="preserve"><emph style="it">Lateraliter.</emph></note>
<note position="left" xlink:label="note-0066-03" xlink:href="note-0066-03a" xml:space="preserve"><emph style="it">Arealiter.</emph></note>
</div>
</div>
<div xml:id="echoid-div147" type="section" level="1" n="78">
<head xml:id="echoid-head82" xml:space="preserve">PRONVNCIATVM LXVI.</head>
<p>
  <s xml:id="echoid-s4950" xml:space="preserve">Ciuitatibus duabus eundem aſcendentem habentibus eadem hora &amp; </s>
  <s xml:id="echoid-s4951" xml:space="preserve"><lb/>momento, utriuſ etiam eleuationem poli perſpecta, differentiam longitu-<lb/>dinum inter eas concluſum inuenire.</s>
  <s xml:id="echoid-s4952" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s4953" xml:space="preserve">Facilem operationẽ hoc habet ꝓnunciatũ, quũ em̃ iam ex ſuꝑioribus ꝓnunciatis aſcẽ <lb/>
<anchor type="note" xlink:label="note-0066-04a" xlink:href="note-0066-04"/>
ſionẽ obliquã cognita habueris utriuſ loci, ſubtrahe ſtatim minorẽ à maiori, &amp; </s>
  <s xml:id="echoid-s4954" xml:space="preserve">remane <lb/>bit differentia longitudinum, idex hoc exemplo cognoſces. </s>
  <s xml:id="echoid-s4955" xml:space="preserve">?</s>
  <s xml:id="echoid-s4956" xml:space="preserve">?Auguſtæ eleuatus eſt
<pb file="0067" n="67" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
polus 48. </s>
  <s xml:id="echoid-s4957" xml:space="preserve">graduũ, eſt &amp; </s>
  <s xml:id="echoid-s4958" xml:space="preserve">alia ciuitas, quæ altitudinem poli habet 38. </s>
  <s xml:id="echoid-s4959" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4960" xml:space="preserve">37. </s>
  <s xml:id="echoid-s4961" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4962" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4963" xml:space="preserve">ea unà <lb/>cũ Auguſta ad horã intronizationis habet in aſcendent 5. </s>
  <s xml:id="echoid-s4964" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4965" xml:space="preserve">25. </s>
  <s xml:id="echoid-s4966" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4967" xml:space="preserve">♌, iam ſi quæram <lb/>ex præcedentibus ꝓnunciatis amplitudinem aſcendentis in eleuatione 38. </s>
  <s xml:id="echoid-s4968" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4969" xml:space="preserve">37. </s>
  <s xml:id="echoid-s4970" xml:space="preserve">mi. <lb/></s>
  <s xml:id="echoid-s4971" xml:space="preserve">erit illa 24. </s>
  <s xml:id="echoid-s4972" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4973" xml:space="preserve">35. </s>
  <s xml:id="echoid-s4974" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4975" xml:space="preserve">ſinum cõplementi ſui 90935. </s>
  <s xml:id="echoid-s4976" xml:space="preserve">duco in ſinum totum, productũ diui <lb/>do in ſinũ cõplementi declinationis 5. </s>
  <s xml:id="echoid-s4977" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4978" xml:space="preserve">25. </s>
  <s xml:id="echoid-s4979" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4980" xml:space="preserve">♌. </s>
  <s xml:id="echoid-s4981" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s4982" xml:space="preserve">94570. </s>
  <s xml:id="echoid-s4983" xml:space="preserve">in q̊tiente inuenio 96156 <lb/>arcus eius eſt 74. </s>
  <s xml:id="echoid-s4984" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4985" xml:space="preserve">3. </s>
  <s xml:id="echoid-s4986" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4987" xml:space="preserve">hunc ſubtraho à 90. </s>
  <s xml:id="echoid-s4988" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4989" xml:space="preserve">remanent 15. </s>
  <s xml:id="echoid-s4990" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4991" xml:space="preserve">57. </s>
  <s xml:id="echoid-s4992" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4993" xml:space="preserve">differentia. </s>
  <s xml:id="echoid-s4994" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s4995" xml:space="preserve"><lb/>aſcenſionalis, qua ſubtracta ab aſcenſione recta 5. </s>
  <s xml:id="echoid-s4996" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s4997" xml:space="preserve">25. </s>
  <s xml:id="echoid-s4998" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s4999" xml:space="preserve">♌, ſcilicet 127. </s>
  <s xml:id="echoid-s5000" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5001" xml:space="preserve">47. </s>
  <s xml:id="echoid-s5002" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5003" xml:space="preserve"><lb/>remanent 111. </s>
  <s xml:id="echoid-s5004" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5005" xml:space="preserve">50. </s>
  <s xml:id="echoid-s5006" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5007" xml:space="preserve">quæ aſcenſio eſt obliqua 5. </s>
  <s xml:id="echoid-s5008" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5009" xml:space="preserve">25. </s>
  <s xml:id="echoid-s5010" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5011" xml:space="preserve">♌ in eleuatione poli <lb/>38. </s>
  <s xml:id="echoid-s5012" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5013" xml:space="preserve">37. </s>
  <s xml:id="echoid-s5014" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5015" xml:space="preserve">Vnde ſubtraho aſcenſionem obliquã 5. </s>
  <s xml:id="echoid-s5016" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5017" xml:space="preserve">25. </s>
  <s xml:id="echoid-s5018" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5019" xml:space="preserve">♌ in eleuatione poli <lb/>48. </s>
  <s xml:id="echoid-s5020" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5021" xml:space="preserve">ſcilicet 105. </s>
  <s xml:id="echoid-s5022" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5023" xml:space="preserve">20. </s>
  <s xml:id="echoid-s5024" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5025" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5026" xml:space="preserve">remanent 6. </s>
  <s xml:id="echoid-s5027" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5028" xml:space="preserve">30. </s>
  <s xml:id="echoid-s5029" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5030" xml:space="preserve">differentia nimirum longitu-<lb/>dinis duarum iſtarum urbium, quam inquirendam propoſui.</s>
  <s xml:id="echoid-s5031" xml:space="preserve"/>
</p>
<div xml:id="echoid-div147" type="float" level="2" n="1">
<note position="left" xlink:label="note-0066-04" xlink:href="note-0066-04a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſcopi.</emph></note>
</div>
</div>
<div xml:id="echoid-div149" type="section" level="1" n="79">
<head xml:id="echoid-head83" xml:space="preserve">PRONVNCIATVM LXVII.</head>
<p>
  <s xml:id="echoid-s5032" xml:space="preserve">Cognita duarum urbium latitudine, ſimiliter &amp; </s>
  <s xml:id="echoid-s5033" xml:space="preserve">differentia ipſa longitu-<lb/>dinis, an eundem habeant uno momento aſcendentem uidere.</s>
  <s xml:id="echoid-s5034" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s5035" xml:space="preserve">Præmonitũ hic te principio uolo, ut in hac operatiõe ĳs tantũ utare regionibus, q̃lati <lb/>tudine ſua cõplementũ maximæ declinationis nõ ſuꝑgrediũtur. </s>
  <s xml:id="echoid-s5036" xml:space="preserve">Na ſi latitudines duorũ <lb/>loco℞ ſint æquales, &amp; </s>
  <s xml:id="echoid-s5037" xml:space="preserve">utra fuerit minor cõplemento maximæ declinatiõis ſolaris, tũc <lb/>fieri nõ poteſt, ut uno aliq̊ momento urbes iſtæ idem habeãt punctũ eclypticæ in aſcen-<lb/>dente. </s>
  <s xml:id="echoid-s5038" xml:space="preserve">Quũ aũt duæ ciuitates inæquales habent latitudines, tuncita ꝓcedendũ tibi erit. <lb/></s>
  <s xml:id="echoid-s5039" xml:space="preserve">Primũ ꝓpone tibi ſinũ cõplementi latitudinis minoris, &amp; </s>
  <s xml:id="echoid-s5040" xml:space="preserve">minorem duc in totũ, ꝓductũ <lb/>in maiorem diuide, arcus quotiẽtis dicetur argumentũ cõmunicationis. </s>
  <s xml:id="echoid-s5041" xml:space="preserve">Deinde duc ſi-<lb/>num cõplementi latitudinis maioris in ſinũ differentiæ lõgitudinũ duo℞ loco℞, &amp; </s>
  <s xml:id="echoid-s5042" xml:space="preserve">arcũ <lb/>
<anchor type="note" xlink:label="note-0067-01a" xlink:href="note-0067-01"/>
quotientis uocabis inuentũ primũ. </s>
  <s xml:id="echoid-s5043" xml:space="preserve">Mox etiam tibi ꝓpone linũ cõplementi primi inuen-<lb/>ti cũ ſinu latitudinis minoris, minorem duc in totũ &amp; </s>
  <s xml:id="echoid-s5044" xml:space="preserve">diuide ꝓductũ in maiorem, ab arcu <lb/>quotientis ſubtrahe latitudinẽ minorẽ, reſidui dic inuentũ ſecundũ. </s>
  <s xml:id="echoid-s5045" xml:space="preserve">Porrò inde duc ſinus <lb/>horũ inuentorũ in ſeipſos, &amp; </s>
  <s xml:id="echoid-s5046" xml:space="preserve">ꝓductũ diuide in totũ ſinũ, arcus q̊tientis de 90. </s>
  <s xml:id="echoid-s5047" xml:space="preserve">ſubtract9, <lb/>relinquet inuentũ tertiũ. </s>
  <s xml:id="echoid-s5048" xml:space="preserve">Poſtea adſume ſinus inuenti primi &amp; </s>
  <s xml:id="echoid-s5049" xml:space="preserve">tertĳ, minorẽ duc in totũ, <lb/>ꝓductũ in maiorẽ diuide, &amp; </s>
  <s xml:id="echoid-s5050" xml:space="preserve">arcus quotientis ob diſcrimen uocabitur numerus compa-<lb/>randus, is ſi minor fuerit argumento cõmunicationis iã antea inuento, argumentũ erit <lb/>tibi certũ urbes iſtas ꝓpoſitas aliq̊ momẽto totius anni die naturali idem habere punctũ <lb/>eclypticæ in aſcendente. </s>
  <s xml:id="echoid-s5051" xml:space="preserve">Sed ſi numerus cõparandus æ qualis extiterit argumento cõmu <lb/>nicationis, ſemel dũtaxat in horoſcopo cõmunicabũt. </s>
  <s xml:id="echoid-s5052" xml:space="preserve">Verumtamẽ ubi numerus cõpa-<lb/>randus ſit maior argumẽto, nõ eſt q̊d putes un̈ fieri poſſe, ut iſtæ ciuitates eodẽ inſtanti <lb/>habeãt idem punctũ eclypticæ in aſcendente: </s>
  <s xml:id="echoid-s5053" xml:space="preserve">quæ aũt nõ habent differentiã lõgitudinis, <lb/>
<anchor type="note" xlink:label="note-0067-02a" xlink:href="note-0067-02"/>
illæ poterunt q̊tidie principiũ γ &amp; </s>
  <s xml:id="echoid-s5054" xml:space="preserve">♎ ſimul habere in aſcendẽte. </s>
  <s xml:id="echoid-s5055" xml:space="preserve">?</s>
  <s xml:id="echoid-s5056" xml:space="preserve">?Video rem hanc <lb/>paulo eſſe obſcuriorẽ, ̈ q̃ ſine exemplo tibi poſſet intelligi, ꝓpono igit̃ hic rurſus locũ <lb/>intronizatiõis, is habet 48. </s>
  <s xml:id="echoid-s5057" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5058" xml:space="preserve">latitudinis, &amp; </s>
  <s xml:id="echoid-s5059" xml:space="preserve">rurſus aliã ciuitatẽ q̃ habet 6. </s>
  <s xml:id="echoid-s5060" xml:space="preserve">gr. </s>
  <s xml:id="echoid-s5061" xml:space="preserve">30. </s>
  <s xml:id="echoid-s5062" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5063" xml:space="preserve">ab <lb/>iſta lõgitudine, &amp; </s>
  <s xml:id="echoid-s5064" xml:space="preserve">latitudo illius eſt 38. </s>
  <s xml:id="echoid-s5065" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5066" xml:space="preserve">37. </s>
  <s xml:id="echoid-s5067" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5068" xml:space="preserve">Nunc iã ex præſcripto oꝑationis du-<lb/>co ſinũ maximæ declinationis Solis in totũ, &amp; </s>
  <s xml:id="echoid-s5069" xml:space="preserve">diuido in ſinũ cõplementi minoris latitu <lb/>dinis, at in q̊tiente ꝓueniunt 51033. </s>
  <s xml:id="echoid-s5070" xml:space="preserve">arcuserit 30. </s>
  <s xml:id="echoid-s5071" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5072" xml:space="preserve">41. </s>
  <s xml:id="echoid-s5073" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5074" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5075" xml:space="preserve">uocabitur argumentũ <lb/>cõmunicationis. </s>
  <s xml:id="echoid-s5076" xml:space="preserve">Deinde duco ſinũ cõplementi latitudinis maioris in ſinũ differẽtiæ lon <lb/>
<anchor type="note" xlink:label="note-0067-03a" xlink:href="note-0067-03"/>
gitudinis. </s>
  <s xml:id="echoid-s5077" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5078" xml:space="preserve">11320. </s>
  <s xml:id="echoid-s5079" xml:space="preserve">ꝓductũ diuido in totũ, &amp; </s>
  <s xml:id="echoid-s5080" xml:space="preserve">in q̊tiente ꝓueniunt 7574. </s>
  <s xml:id="echoid-s5081" xml:space="preserve">arcus eius eſt 4. <lb/></s>
  <s xml:id="echoid-s5082" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5083" xml:space="preserve">21. </s>
  <s xml:id="echoid-s5084" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5085" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5086" xml:space="preserve">dicetur inuentũ primũ, eius ſinus 99711. </s>
  <s xml:id="echoid-s5087" xml:space="preserve">erit diuiſor, ꝑ quem diuido produ-<lb/>ctũ q̊d ex multiplicatione totius &amp; </s>
  <s xml:id="echoid-s5088" xml:space="preserve">latitudinis maioris ꝓuenerat. </s>
  <s xml:id="echoid-s5089" xml:space="preserve">Arcus quotientis eſt <lb/>
<anchor type="note" xlink:label="note-0067-04a" xlink:href="note-0067-04"/>
48. </s>
  <s xml:id="echoid-s5090" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5091" xml:space="preserve">11. </s>
  <s xml:id="echoid-s5092" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5093" xml:space="preserve">inde ſubtraho latitudinem minorẽ, ut remaneat inuentũ. </s>
  <s xml:id="echoid-s5094" xml:space="preserve">ſecundũ. </s>
  <s xml:id="echoid-s5095" xml:space="preserve">9. </s>
  <s xml:id="echoid-s5096" xml:space="preserve">gr. <lb/></s>
  <s xml:id="echoid-s5097" xml:space="preserve">34. </s>
  <s xml:id="echoid-s5098" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5099" xml:space="preserve">Iam duco ſinus primi &amp; </s>
  <s xml:id="echoid-s5100" xml:space="preserve">ſecundi inuento℞ in ſeipſos, ſcilicet 98609. </s>
  <s xml:id="echoid-s5101" xml:space="preserve">in 99711. </s>
  <s xml:id="echoid-s5102" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5103" xml:space="preserve"><lb/>productum diuido in totum, quotiens erit 98324. </s>
  <s xml:id="echoid-s5104" xml:space="preserve">arcus eius de 90. </s>
  <s xml:id="echoid-s5105" xml:space="preserve">ſubtractus, relinquet <lb/>10. </s>
  <s xml:id="echoid-s5106" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5107" xml:space="preserve">30. </s>
  <s xml:id="echoid-s5108" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5109" xml:space="preserve">inuentum ſcilicet tertium. </s>
  <s xml:id="echoid-s5110" xml:space="preserve">Deinde propono ſinum inuentiprimi 7574. </s>
  <s xml:id="echoid-s5111" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0067-05a" xlink:href="note-0067-05"/>
eum duco in totum, productum uero diuido in ſinum inuenti ſecnndi, ſcilicet 18223. <lb/></s>
  <s xml:id="echoid-s5112" xml:space="preserve">quotiens erit 41562. </s>
  <s xml:id="echoid-s5113" xml:space="preserve">arcus eius 24. </s>
  <s xml:id="echoid-s5114" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5115" xml:space="preserve">34. </s>
  <s xml:id="echoid-s5116" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5117" xml:space="preserve">ſupra dictus à nobis eſt numerus compa-<lb/>randus. </s>
  <s xml:id="echoid-s5118" xml:space="preserve">Comparo igitur nunc ſiue cenſeo &amp; </s>
  <s xml:id="echoid-s5119" xml:space="preserve">æſtimo eum erga argumentum communi <lb/>cationis, qui ſi minor fuerit argumento (ita ut eſt) iudicium id mihi certum eſt, duas
<pb file="0068" n="68" rhead="GENVINVS VSVS"/>
illas cluitates inde ſingulos dies bis idem punctũ in aſcendente, uno temporis momẽto.</s>
  <s xml:id="echoid-s5120" xml:space="preserve"/>
</p>
<div xml:id="echoid-div149" type="float" level="2" n="1">
<note position="right" xlink:label="note-0067-01" xlink:href="note-0067-01a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">primum.</emph> <lb/><emph style="it">Arealis in-</emph> <lb/><emph style="it">greſſus.</emph> <lb/><emph style="it">Inuentum</emph> <lb/><emph style="it">ſecundum.</emph> <lb/><emph style="it">Lateralis</emph> <lb/><emph style="it">operatio.</emph> <lb/><emph style="it">Inuentum</emph> <lb/><emph style="it">tertium.</emph> <lb/><emph style="it">Arealis</emph> <lb/><emph style="it">proceſſus.</emph></note>
<note position="right" xlink:label="note-0067-02" xlink:href="note-0067-02a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
<note position="right" xlink:label="note-0067-03" xlink:href="note-0067-03a" xml:space="preserve"><emph style="it">Inuentũ pri</emph> <lb/><emph style="it">mũ eſt gra.</emph> <lb/><emph style="it">4. mi. 21.</emph></note>
<note position="right" xlink:label="note-0067-04" xlink:href="note-0067-04a" xml:space="preserve"><emph style="it">Inuẽtum ſe</emph> <lb/><emph style="it">cundũ ha-</emph> <lb/><emph style="it">bet gra. 9.</emph> <lb/><emph style="it">mi. 34.</emph></note>
<note position="right" xlink:label="note-0067-05" xlink:href="note-0067-05a" xml:space="preserve"><emph style="it">Inuentũ ter</emph> <lb/><emph style="it">tũ tertium</emph> <lb/><emph style="it">cõprehẽdit</emph> <lb/><emph style="it">gra. 10.</emph> <lb/><emph style="it">mi. 30.</emph></note>
</div>
</div>
<div xml:id="echoid-div151" type="section" level="1" n="80">
<head xml:id="echoid-head84" xml:space="preserve">PRONVNCIATVM LXVIII.</head>
<p>
  <s xml:id="echoid-s5121" xml:space="preserve">Si quando duæ ciuitates, quarum cognitæ ſint latitudines &amp; </s>
  <s xml:id="echoid-s5122" xml:space="preserve">longitudi-<lb/>nes, uel ſaltem differentia longitudinum, iam´ ex ſuperiori pronunciato in <lb/>uentum ſit, eas eodem momento quotidie ſemel aut bis unum habere aſcen-<lb/>dentem, punctum iam iſtud eclypticæ in aſcendente expedite indagare.</s>
  <s xml:id="echoid-s5123" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s5124" xml:space="preserve">Superiori pronunciato cõmemoratũ per nos eſt, fieri interdũ, ut duo loca ſimul habe-<lb/>ant eodẽ inſtanti unũ aſcendentẽ, uno die ſemel aut bis, quod ſi ſemel accidat die natura-<lb/>li, &amp; </s>
  <s xml:id="echoid-s5125" xml:space="preserve">locus qui Borealiorẽ latitudinẽ habet, ſit etiam orientalior, tũc principiũ ♑ in eo-<lb/>dem inſtanti iacet in utro´ horizonte. </s>
  <s xml:id="echoid-s5126" xml:space="preserve">Sed ſi locus, cuius latitudo Borealior eſt, fuerit <lb/>occidentalior eo cui cõparatur, principiũ ♋ in utro horizõte erit eodẽ momento. </s>
  <s xml:id="echoid-s5127" xml:space="preserve">At-<lb/>qui ſi cõtingit, ſicut ſuperius uiſum eſt, uno die duo puncta eclypticæ in duobus locis ſi-<lb/>mul eſſe in horizonte, tunc tibi propone numerũ comparandũ ex ſuperiori pronunciato <lb/>
<anchor type="note" xlink:label="note-0068-01a" xlink:href="note-0068-01"/>
inuentũ, eius ſinum duc in ſinũ latitudinis minoris, &amp; </s>
  <s xml:id="echoid-s5128" xml:space="preserve">productũ diuide in ſinum totum, <lb/>quotientẽ ſepone in locũ aliquẽ, unà cũ ſinu maximæ declinationis Solis, minorẽ duc in <lb/>
<anchor type="note" xlink:label="note-0068-02a" xlink:href="note-0068-02"/>
totum, ꝓductũ diuide in maiorem, arcũ quotientis ſubtrahe de 90. </s>
  <s xml:id="echoid-s5129" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5130" xml:space="preserve">reſiduũ mõſtrabit <lb/>tibi diſtantiam gradus aſcendentis à principio ♑, ſi tamẽ ciuitas iſta Borealior etiã ori-<lb/>entalior fuerit ſua cõpare, uel ab initio ♋, ſi fuerit occidentalior. </s>
  <s xml:id="echoid-s5131" xml:space="preserve">Eam diſtantiã ſi nume <lb/>res ſecũdum exigentiã rei à principio ♑ uel ♋, ſecundũ ordinẽ ſignorũ, terminus ipſius <lb/>ſiue finis dabit tibi punctũ eclypticæ in utro horizonte eodẽ temporis momẽto inuen <lb/>
<anchor type="note" xlink:label="note-0068-03a" xlink:href="note-0068-03"/>
tum. </s>
  <s xml:id="echoid-s5132" xml:space="preserve">?</s>
  <s xml:id="echoid-s5133" xml:space="preserve">? Exemplũ etiam hic dabimus, ut res fiat dilucidior, ne uideamur tan̈ in tene-<lb/>bris tantũ præceptionũ uerſari, nõ applicando ea ad uſum rei. </s>
  <s xml:id="echoid-s5134" xml:space="preserve">Propono ecce mibi iterũ <lb/>prius illud exemplũ, in quo locus alter notiſsimus ille habet in latitudine 48. </s>
  <s xml:id="echoid-s5135" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5136" xml:space="preserve">alter <lb/>38. </s>
  <s xml:id="echoid-s5137" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5138" xml:space="preserve">37. </s>
  <s xml:id="echoid-s5139" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5140" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5141" xml:space="preserve">ille quo occidentalior eſt, numerum igitur comparandum inueni eſ-<lb/>ſe 24. </s>
  <s xml:id="echoid-s5142" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5143" xml:space="preserve">34. </s>
  <s xml:id="echoid-s5144" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5145" xml:space="preserve">ſinum eius duco in ſinum complementi latitudinis minoris. </s>
  <s xml:id="echoid-s5146" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5147" xml:space="preserve">78133. <lb/></s>
  <s xml:id="echoid-s5148" xml:space="preserve">productũ diuido in ſinũ maximæ declinationis, ſi deinde arcũ quotientis ſubtraho à 90. </s>
  <s xml:id="echoid-s5149" xml:space="preserve"><lb/>remanent 35. </s>
  <s xml:id="echoid-s5150" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5151" xml:space="preserve">25. </s>
  <s xml:id="echoid-s5152" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5153" xml:space="preserve">quibus numeratis à principio ♋ (ſiquidẽ locus ille ad quem cõ <lb/>paratur alteri occidẽtalior eſt) ſecundũ ordinẽ ſignorũ finietur numerus ille in 5. </s>
  <s xml:id="echoid-s5154" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5155" xml:space="preserve">26 <lb/>mi. </s>
  <s xml:id="echoid-s5156" xml:space="preserve">♌, qui &amp; </s>
  <s xml:id="echoid-s5157" xml:space="preserve">aſcendens eſt uno temporis articulo utriuſ lociſeu ciuitatis.</s>
  <s xml:id="echoid-s5158" xml:space="preserve"/>
</p>
<div xml:id="echoid-div151" type="float" level="2" n="1">
<note position="left" xlink:label="note-0068-01" xlink:href="note-0068-01a" xml:space="preserve"><emph style="it">Lateraliter</emph></note>
<note position="left" xlink:label="note-0068-02" xlink:href="note-0068-02a" xml:space="preserve"><emph style="it">Areatim.</emph></note>
<note position="left" xlink:label="note-0068-03" xlink:href="note-0068-03a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoopi.</emph></note>
</div>
</div>
<div xml:id="echoid-div153" type="section" level="1" n="81">
<head xml:id="echoid-head85" xml:space="preserve">PRONVNCIATVM LXIX.</head>
<p>
  <s xml:id="echoid-s5159" xml:space="preserve">Quotidie ex altitudine &amp; </s>
  <s xml:id="echoid-s5160" xml:space="preserve">Azimuth Solis eleuationem poli colligere.</s>
  <s xml:id="echoid-s5161" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s5162" xml:space="preserve">Retulerit plurimũ pronũciatũ hoc diligenter obſeruare, ſiquidẽ ꝑeam quis eleuatio-<lb/>nem poli ſingulis diebus cognoſcere hoc modo. </s>
  <s xml:id="echoid-s5163" xml:space="preserve">Ex 39. </s>
  <s xml:id="echoid-s5164" xml:space="preserve">ꝓnunc. </s>
  <s xml:id="echoid-s5165" xml:space="preserve">inuentã habes diſtantiam <lb/>Solis in circulo maiori ab interſectiõe æquinoctialis &amp; </s>
  <s xml:id="echoid-s5166" xml:space="preserve">horizõtis, ex 40. </s>
  <s xml:id="echoid-s5167" xml:space="preserve">aũt angulũ quẽ <lb/>facit circulus iſte maior cũ æquatore iuxta punctũ interſectionis horizõtis obliqui &amp; </s>
  <s xml:id="echoid-s5168" xml:space="preserve">æ-<lb/>quatoris, angulũ hũc differentiæ cauſſa uoco angulũ ſuperiorẽ. </s>
  <s xml:id="echoid-s5169" xml:space="preserve">Deinde inueniſti ex 41. <lb/></s>
  <s xml:id="echoid-s5170" xml:space="preserve">ꝓnunc. </s>
  <s xml:id="echoid-s5171" xml:space="preserve">angulũ quẽ idem ille circulus efficit cũ horizõte, etiã iuxta interſectionẽ æ quato <lb/>ris &amp; </s>
  <s xml:id="echoid-s5172" xml:space="preserve">horizõtis, ſiquidẽ tres illi circuli maiores ibi cõueniunt, at is angulus dicetur infe <lb/>rior. </s>
  <s xml:id="echoid-s5173" xml:space="preserve">Quod ſi iã Sol fuerit in aliq̊ ſignorũ ſeptentrionaliũ, tunc ſubtrahe ſuperiorem an-<lb/>gulũ ab inferiori. </s>
  <s xml:id="echoid-s5174" xml:space="preserve">ſin aũt Sol in ſigno aliquo ſiet meridionali, inferiorẽ &amp; </s>
  <s xml:id="echoid-s5175" xml:space="preserve">ſuperiorẽ angu-<lb/>los ſimul addendo cõiunges, &amp; </s>
  <s xml:id="echoid-s5176" xml:space="preserve">ꝓueniet inde tibi altitudo æquatoris propoſitæ regionis <lb/>ſiue ciuitatis, cõplementũ ipſius erit altitudo poli quæſita, ſicut ex hoc exẽplo intelliges. </s>
  <s xml:id="echoid-s5177" xml:space="preserve"><lb/>?</s>
  <s xml:id="echoid-s5178" xml:space="preserve">?Eſto ut in die &amp; </s>
  <s xml:id="echoid-s5179" xml:space="preserve">hora intronizationis Auguſtæ obſeruarit quiſpiã ꝑ inſtrumentũ alti-<lb/>tudinẽ Solis 44. </s>
  <s xml:id="echoid-s5180" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5181" xml:space="preserve">52. </s>
  <s xml:id="echoid-s5182" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5183" xml:space="preserve">ſupra horizontẽ, Azimuth q̊ ipſius ab ortu æꝑnoctialis <lb/>
<anchor type="note" xlink:label="note-0068-04a" xlink:href="note-0068-04"/>
uerſus meridiẽ 21. </s>
  <s xml:id="echoid-s5184" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5185" xml:space="preserve">4. </s>
  <s xml:id="echoid-s5186" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5187" xml:space="preserve">Sol aũt eo die &amp; </s>
  <s xml:id="echoid-s5188" xml:space="preserve">hora fuit in 2. </s>
  <s xml:id="echoid-s5189" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5190" xml:space="preserve">26. </s>
  <s xml:id="echoid-s5191" xml:space="preserve">mi II, declinatio eius <lb/>ꝑ 5. </s>
  <s xml:id="echoid-s5192" xml:space="preserve">ꝓnunc. </s>
  <s xml:id="echoid-s5193" xml:space="preserve">eſt 20. </s>
  <s xml:id="echoid-s5194" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5195" xml:space="preserve">52. </s>
  <s xml:id="echoid-s5196" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5197" xml:space="preserve">Iam quæſiturus ego principio ſum quãtus ſit arcus, qui ex <lb/>☉(sun) ad interſectionẽ æquatoris &amp; </s>
  <s xml:id="echoid-s5198" xml:space="preserve">horizontis adduci poteſt, ſinũ cõplementi Azimuth. </s>
  <s xml:id="echoid-s5199" xml:space="preserve">ſ. <lb/></s>
  <s xml:id="echoid-s5200" xml:space="preserve">93316. </s>
  <s xml:id="echoid-s5201" xml:space="preserve">duco in ſinũ cõplementi altitudinis. </s>
  <s xml:id="echoid-s5202" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5203" xml:space="preserve">70875. </s>
  <s xml:id="echoid-s5204" xml:space="preserve">productũ diuido in ipſum totum, <lb/>quotientis erit 66137. </s>
  <s xml:id="echoid-s5205" xml:space="preserve">arcus illius quotientis de 90. </s>
  <s xml:id="echoid-s5206" xml:space="preserve">ſubductus, relinquet 48. </s>
  <s xml:id="echoid-s5207" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5208" xml:space="preserve">36. </s>
  <s xml:id="echoid-s5209" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5210" xml:space="preserve"><lb/>arcus ſcilicet quæſitus. </s>
  <s xml:id="echoid-s5211" xml:space="preserve">Poſt hæc inſuꝑ quæro angulũ ſuperiorẽ hoc modo, ſinũ declinati-<lb/>onis ☉(sun) 35447. </s>
  <s xml:id="echoid-s5212" xml:space="preserve">duco in totũ, ꝓductũ inde diuido in ſinũ arcus iam inuenti. </s>
  <s xml:id="echoid-s5213" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5214" xml:space="preserve">75011. </s>
  <s xml:id="echoid-s5215" xml:space="preserve">quo-
<pb file="0069" n="69" rhead="TABVLARVM SINVVM."/>
tiens eſt 47122. </s>
  <s xml:id="echoid-s5216" xml:space="preserve">arcus uero eius 28. </s>
  <s xml:id="echoid-s5217" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5218" xml:space="preserve">8. </s>
  <s xml:id="echoid-s5219" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5220" xml:space="preserve">eſt angulus iſte ſuperior. </s>
  <s xml:id="echoid-s5221" xml:space="preserve">Inferiorem porrò <lb/>ſic inquiro, ſinũ altitudinis Solis 44. </s>
  <s xml:id="echoid-s5222" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5223" xml:space="preserve">52. </s>
  <s xml:id="echoid-s5224" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5225" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5226" xml:space="preserve">70545. </s>
  <s xml:id="echoid-s5227" xml:space="preserve">tan̈ minorẽ duco in totũ, ꝓdu-<lb/>ctum diuido in ſinũ arcus inuenti 75011. </s>
  <s xml:id="echoid-s5228" xml:space="preserve">in quotiente uideo prouenire mihi 94046. </s>
  <s xml:id="echoid-s5229" xml:space="preserve">ar-<lb/>cus eius eſt 70. </s>
  <s xml:id="echoid-s5230" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5231" xml:space="preserve">8. </s>
  <s xml:id="echoid-s5232" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5233" xml:space="preserve">angulus inferior. </s>
  <s xml:id="echoid-s5234" xml:space="preserve">Et quia Sol eſt in ſigno Boreali, ſuperiorẽ an-<lb/>gulum ſubtraho ab inferiori, hoc eſt 28. </s>
  <s xml:id="echoid-s5235" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5236" xml:space="preserve">8. </s>
  <s xml:id="echoid-s5237" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5238" xml:space="preserve">à 70. </s>
  <s xml:id="echoid-s5239" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5240" xml:space="preserve">8. </s>
  <s xml:id="echoid-s5241" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5242" xml:space="preserve">ſic´ remanent 42. </s>
  <s xml:id="echoid-s5243" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s5244" xml:space="preserve">
<anchor type="note" xlink:label="note-0069-01a" xlink:href="note-0069-01"/>
cuius cõplementum eſt 48. </s>
  <s xml:id="echoid-s5245" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5246" xml:space="preserve">altitudo illa poli quæſita ad locum introniſationis.</s>
  <s xml:id="echoid-s5247" xml:space="preserve"/>
</p>
<div xml:id="echoid-div153" type="float" level="2" n="1">
<note position="left" xlink:label="note-0068-04" xlink:href="note-0068-04a" xml:space="preserve">EXEM. <lb/>PLVM <lb/><emph style="it">Epiſcopi.</emph></note>
<note position="right" xlink:label="note-0069-01" xlink:href="note-0069-01a" xml:space="preserve">EXEM. <lb/>PLVM <lb/><emph style="it">loain quo</emph> <lb/><emph style="it">facta eſt in</emph> <lb/><emph style="it">tronizatio.</emph> <lb/><emph style="it">Longitudo</emph> <lb/><emph style="it">Auguſtæ</emph> <lb/><emph style="it">ab occidẽte</emph> <lb/><emph style="it">gra. 28. mi.</emph> <lb/><emph style="it">31.</emph></note>
</div>
</div>
<div xml:id="echoid-div155" type="section" level="1" n="82">
<head xml:id="echoid-head86" xml:space="preserve">PRONVNCIATVM LXX.</head>
<p>
  <s xml:id="echoid-s5248" xml:space="preserve">Si quando duorum locorum longitudines ſunt æquales, &amp; </s>
  <s xml:id="echoid-s5249" xml:space="preserve">inſuper eorum <lb/>latitudines notæ, at inæquales, diſtantiam inter ea ſecundum uiam directã <lb/>inueſtigare.</s>
  <s xml:id="echoid-s5250" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s5251" xml:space="preserve">Quandocũ duo loca æquales habent gradus unà cum minutis in longitudine, argu <lb/>mentum rectum eſt ea ſub uno eſſe meridiano, &amp; </s>
  <s xml:id="echoid-s5252" xml:space="preserve">ſinum hunc facile colliges in meridie <lb/>aſpiciendo Solem ſub horam 12. </s>
  <s xml:id="echoid-s5253" xml:space="preserve">quòd ſi locus ille altitudinem poli habuerit maiorem ̈ <lb/>iſte alter à quo diſtantiam ſcire cupis, certum eſt eum directe poſitum eſſe uerſus ſepten <lb/>
<anchor type="note" xlink:label="note-0069-02a" xlink:href="note-0069-02"/>
trionem, at eò monſtrat umbra Solis circa horam 12. </s>
  <s xml:id="echoid-s5254" xml:space="preserve">Sed ſi pauciores habeat gradus <lb/>in latitudine, ſitus erit uerſus meridiem directe ad Solem, quum dies medius eſt, iam ſi di <lb/>ſtantiam quæris, ſubtrahe latitudinem minorem à maiori, &amp; </s>
  <s xml:id="echoid-s5255" xml:space="preserve">reſiduum tibi oſtendet di-<lb/>
<anchor type="note" xlink:label="note-0069-03a" xlink:href="note-0069-03"/>
ſtantiam iſtam locorum in gradibus, at minutis, diſtantiam hanc in miliaria rediges, <lb/>ſi pro quolibet gradu 15. </s>
  <s xml:id="echoid-s5256" xml:space="preserve">miliaria cõnumeres Germanica uel 60. </s>
  <s xml:id="echoid-s5257" xml:space="preserve">Italica, &amp; </s>
  <s xml:id="echoid-s5258" xml:space="preserve">ſemper pro 4 <lb/>minutis graduũ unum minutũ miliarium. </s>
  <s xml:id="echoid-s5259" xml:space="preserve">?</s>
  <s xml:id="echoid-s5260" xml:space="preserve">? Exemplum ſit hoc tibi: </s>
  <s xml:id="echoid-s5261" xml:space="preserve">Si in ipſo loco in-<lb/>tronizationis, ubi longitudo eſt 28. </s>
  <s xml:id="echoid-s5262" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5263" xml:space="preserve">31. </s>
  <s xml:id="echoid-s5264" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5265" xml:space="preserve">latitudo autem 48. </s>
  <s xml:id="echoid-s5266" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5267" xml:space="preserve">20. </s>
  <s xml:id="echoid-s5268" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5269" xml:space="preserve">cupio ſcire <lb/>
<anchor type="note" xlink:label="note-0069-04a" xlink:href="note-0069-04"/>
ſitum ſimul &amp; </s>
  <s xml:id="echoid-s5270" xml:space="preserve">diſtantiam Erfordiæ, propono etiam mihi gradus longitudinis Erfordiæ, <lb/>qui ſunt 28. </s>
  <s xml:id="echoid-s5271" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5272" xml:space="preserve">30. </s>
  <s xml:id="echoid-s5273" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5274" xml:space="preserve">latitudo aũt 51. </s>
  <s xml:id="echoid-s5275" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5276" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5277" xml:space="preserve">10. </s>
  <s xml:id="echoid-s5278" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5279" xml:space="preserve">habet, iam nunc conſidero, quòd lon <lb/>gitudo utriuſ eſt æqualis, eas etiam uni ſubeſſe meridiano, &amp; </s>
  <s xml:id="echoid-s5280" xml:space="preserve">quia latitudo Er-<lb/>fordieñ, maior eſt Auguſta, certus ſum, quòd Erfordia reſpectu Auguſtæ ſit Borealis, ita <lb/>ut umbra Solis hora 12. </s>
  <s xml:id="echoid-s5281" xml:space="preserve">ſub meridiem mihi mõſtret Erfordiæ ſitum, ſi dehinc ſubtraho <lb/>latitudinẽ Auguſtanã à latitudine Erfordieñ. </s>
  <s xml:id="echoid-s5282" xml:space="preserve">remanent mibi 2. </s>
  <s xml:id="echoid-s5283" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5284" xml:space="preserve">40. </s>
  <s xml:id="echoid-s5285" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5286" xml:space="preserve">quibus reſo-<lb/>lutis, habeo 40. </s>
  <s xml:id="echoid-s5287" xml:space="preserve">miliaria. </s>
  <s xml:id="echoid-s5288" xml:space="preserve">diſtãtiã Erfordiæ ab Auguſta, quæ duæ ciuitates uno temporis <lb/>
<anchor type="note" xlink:label="note-0069-05a" xlink:href="note-0069-05"/>
momẽto habẽt meridiẽ. </s>
  <s xml:id="echoid-s5289" xml:space="preserve">Nec eſt ꝙ mireris, cur hic latitudinẽ Auguſtæ poſuerim 48. </s>
  <s xml:id="echoid-s5290" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s5291" xml:space="preserve">20. </s>
  <s xml:id="echoid-s5292" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5293" xml:space="preserve">quũ tñ ſupra ſemꝑ 40. </s>
  <s xml:id="echoid-s5294" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5295" xml:space="preserve">tm̃ ſine minutis additis numerarim, ſiquidẽ ibi minuta <lb/>uolens prætermiſi, ut eò facilior tibi nota eſſet operatio, nunc ad reliqua progrediamur.</s>
  <s xml:id="echoid-s5296" xml:space="preserve"/>
</p>
<div xml:id="echoid-div155" type="float" level="2" n="1">
<note position="right" xlink:label="note-0069-02" xlink:href="note-0069-02a" xml:space="preserve"><emph style="it">Altitudo</emph> <lb/><emph style="it">poli Augu-</emph> <lb/><emph style="it">ſtana gra.</emph> <lb/><emph style="it">4 s. mi. 20.</emph></note>
<note position="right" xlink:label="note-0069-03" xlink:href="note-0069-03a" xml:space="preserve"><emph style="it">Longitudo</emph> <lb/><emph style="it">Erfordiana</emph> <lb/><emph style="it">gra. 28</emph> <lb/><emph style="it">mi. 30.</emph></note>
<note position="right" xlink:label="note-0069-04" xlink:href="note-0069-04a" xml:space="preserve"><emph style="it">Latitudo</emph> <lb/><emph style="it">uero gra.</emph> <lb/><emph style="it">51. mi. 10.</emph> <lb/><emph style="it">Diſtantia</emph> <lb/><emph style="it">inter Augu</emph> <lb/><emph style="it">ſtam &amp; Er</emph> <lb/><emph style="it">fordiam.</emph></note>
<note position="right" xlink:label="note-0069-05" xlink:href="note-0069-05a" xml:space="preserve"><emph style="it">Quare ha-</emph> <lb/><emph style="it">ctenus alti-</emph> <lb/><emph style="it">tudo poli</emph></note>
</div>
<note position="left" xml:space="preserve"><emph style="it">Auguſtana</emph> <lb/><emph style="it">per gradus</emph> <lb/><emph style="it">ſaltẽ &amp; nõ</emph> <lb/><emph style="it">ꝑ minuta e-</emph> <lb/><emph style="it">tiam propo</emph> <lb/><emph style="it">ſita ſit.</emph></note>
</div>
<div xml:id="echoid-div157" type="section" level="1" n="83">
<head xml:id="echoid-head87" xml:space="preserve">PRONVNCIATVM LXXI.</head>
<p>
  <s xml:id="echoid-s5297" xml:space="preserve">Quum loca duo uni ſubiecta ſunt meridiano, &amp; </s>
  <s xml:id="echoid-s5298" xml:space="preserve">alterius tantum nota ſit la <lb/>titudo &amp; </s>
  <s xml:id="echoid-s5299" xml:space="preserve">diſtantia ignota, inde latitudinem alterius elicere.</s>
  <s xml:id="echoid-s5300" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s5301" xml:space="preserve">Pronunciatum hoc à ſuperiori planè inuerſum eſt, ideo´ miſſa explanatione opera-<lb/>tionis, exemplum tantummodo quo ſupra uſi ſumus, adducendum erit. </s>
  <s xml:id="echoid-s5302" xml:space="preserve">?</s>
  <s xml:id="echoid-s5303" xml:space="preserve">? Eſto ut Au-<lb/>
<anchor type="note" xlink:label="note-0069-07a" xlink:href="note-0069-07"/>
guſtæ ſciam Erfordiam planè eſſe oppoſitam uerſus ſeptentrionem, diſtare quo ab ea <lb/>per 40. </s>
  <s xml:id="echoid-s5304" xml:space="preserve">miliaria Germanica, iam ergo mutatis miliaribus in gradus, ſemper 15. </s>
  <s xml:id="echoid-s5305" xml:space="preserve">miliaria <lb/>ſupputãdo pro gradu uno, habebo 2. </s>
  <s xml:id="echoid-s5306" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5307" xml:space="preserve">40. </s>
  <s xml:id="echoid-s5308" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5309" xml:space="preserve">Auguſtæ autem latitudo eſt 48. </s>
  <s xml:id="echoid-s5310" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5311" xml:space="preserve">20. <lb/></s>
  <s xml:id="echoid-s5312" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5313" xml:space="preserve">Et quia Erfordia propinquior eſt ſeptentrioni, addo 2. </s>
  <s xml:id="echoid-s5314" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5315" xml:space="preserve">40. </s>
  <s xml:id="echoid-s5316" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5317" xml:space="preserve">ad latitudinẽ Au-<lb/>guſtanam, &amp; </s>
  <s xml:id="echoid-s5318" xml:space="preserve">proueniunt Erfordiæ 51. </s>
  <s xml:id="echoid-s5319" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5320" xml:space="preserve">10. </s>
  <s xml:id="echoid-s5321" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5322" xml:space="preserve">ſed ſi locus ignotus reſpectu loci intro <lb/>nizationis Auſtralior, eiuſmodi gradus diſtantiæ ſubtrahi deberent à latitudine Augu-<lb/>ſtana, in hoc ut proueniret latitudo loci illius quæſita.</s>
  <s xml:id="echoid-s5323" xml:space="preserve"/>
</p>
<div xml:id="echoid-div157" type="float" level="2" n="1">
<note position="right" xlink:label="note-0069-07" xlink:href="note-0069-07a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">dc Auguſta</emph></note>
</div>
</div>
<div xml:id="echoid-div159" type="section" level="1" n="84">
<head xml:id="echoid-head88" xml:space="preserve">PRONVNCIATVM LXXII.</head>
<p>
  <s xml:id="echoid-s5324" xml:space="preserve">Locis duobus æqualem poli altitudinem habentibus, quæ utra ſit no-<lb/>ta, ſed ita, ut diuerſis ſubiaceant meridianis, cognita etiam differentia lon-<lb/>gitudinis, adhuc eorum inſuper diſtantiam cognoſcere.</s>
  <s xml:id="echoid-s5325" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s5326" xml:space="preserve">Res hæc multo la bore nõ eget ne moleſta operatiõe, ſed tantũ tibi propone cõple-<lb/>mentũ latitudinũ, qm̃ æqualia ſunt, deinde etiam differentiã longitudinũ, eam mediato, <lb/>ſinum´ medietatis differentiæ longitudinũ duc in ſinum cõplemẽti latitudinum, produ
<pb file="0070" n="70" rhead="GENVINVS VSVS"/>
ctum diuide in ſinumtotum, arcus quotientis duplicatus oſtendet tibi diſtantiã locorum <lb/>quæſitã. </s>
  <s xml:id="echoid-s5327" xml:space="preserve">?</s>
  <s xml:id="echoid-s5328" xml:space="preserve">?Exempli gratia. </s>
  <s xml:id="echoid-s5329" xml:space="preserve">Auguſtæ, ubi facta eſt intronizatio, lõgitudo habet 28. <lb/></s>
  <s xml:id="echoid-s5330" xml:space="preserve">
<anchor type="note" xlink:label="note-0070-01a" xlink:href="note-0070-01"/>
gra. </s>
  <s xml:id="echoid-s5331" xml:space="preserve">31. </s>
  <s xml:id="echoid-s5332" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5333" xml:space="preserve">latitudo autem 48. </s>
  <s xml:id="echoid-s5334" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5335" xml:space="preserve">20. </s>
  <s xml:id="echoid-s5336" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5337" xml:space="preserve">Vienna Auſtriæ in lõgitudine habet 35. </s>
  <s xml:id="echoid-s5338" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s5339" xml:space="preserve">8. </s>
  <s xml:id="echoid-s5340" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5341" xml:space="preserve">ſed in latitudine 48. </s>
  <s xml:id="echoid-s5342" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5343" xml:space="preserve">22. </s>
  <s xml:id="echoid-s5344" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5345" xml:space="preserve">iſtæ ergo duæ latitudines ſunt inter ſe æquales, ſiqui <lb/>dem 2. </s>
  <s xml:id="echoid-s5346" xml:space="preserve">minuta quæ ſuperſunt, nullum hic errorem ingerunt, cõplementum latitudinum <lb/>eſt 41. </s>
  <s xml:id="echoid-s5347" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5348" xml:space="preserve">40. </s>
  <s xml:id="echoid-s5349" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5350" xml:space="preserve">ſinum eius 66479. </s>
  <s xml:id="echoid-s5351" xml:space="preserve">duco in ſinum medietatis differentiæ longitudinis, <lb/>quæ eſt 3. </s>
  <s xml:id="echoid-s5352" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5353" xml:space="preserve">18. </s>
  <s xml:id="echoid-s5354" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5355" xml:space="preserve">cuius ſinus eſt 5756. </s>
  <s xml:id="echoid-s5356" xml:space="preserve">productum diuido in totum, &amp; </s>
  <s xml:id="echoid-s5357" xml:space="preserve">proueniunt in <lb/>quotiente 3826. </s>
  <s xml:id="echoid-s5358" xml:space="preserve">arcus illius eſt 2. </s>
  <s xml:id="echoid-s5359" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5360" xml:space="preserve">12. </s>
  <s xml:id="echoid-s5361" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5362" xml:space="preserve">quibus duplicatis, habeo 4. </s>
  <s xml:id="echoid-s5363" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5364" xml:space="preserve">24. </s>
  <s xml:id="echoid-s5365" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5366" xml:space="preserve">iuſta <lb/>illa diſtantia Auguſtæ &amp; </s>
  <s xml:id="echoid-s5367" xml:space="preserve">Viennæ Auſtriæ ad 66. </s>
  <s xml:id="echoid-s5368" xml:space="preserve">miliaria Germanica.</s>
  <s xml:id="echoid-s5369" xml:space="preserve"/>
</p>
<div xml:id="echoid-div159" type="float" level="2" n="1">
<note position="left" xlink:label="note-0070-01" xlink:href="note-0070-01a" xml:space="preserve"><emph style="it">EXEM-</emph> <lb/><emph style="it">PLVM</emph> <lb/><emph style="it">Epiſcopi.</emph></note>
</div>
</div>
<div xml:id="echoid-div161" type="section" level="1" n="85">
<head xml:id="echoid-head89" xml:space="preserve">PRONVNCIATVM LXXIII.</head>
<p>
  <s xml:id="echoid-s5370" xml:space="preserve">Cognitis duorũ locorum latitudine &amp; </s>
  <s xml:id="echoid-s5371" xml:space="preserve">longitudine, diſtantiam inuenire.</s>
  <s xml:id="echoid-s5372" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve"><emph style="it">Lateralis</emph> <lb/><emph style="it">ingreſſus.</emph> <lb/><emph style="it">Inuentum</emph> <lb/><emph style="it">primum.</emph> <lb/><emph style="it">Arealis in-</emph> <lb/><emph style="it">greſſus.</emph> <lb/><emph style="it">Inuentum</emph> <lb/><emph style="it">ſecundum.</emph> <lb/><emph style="it">Lateralis</emph> <lb/><emph style="it">ingreſſus.</emph></note>
<p>
  <s xml:id="echoid-s5373" xml:space="preserve">Principio hic tibi utriuſ loci nomen ꝓpone, eorum´ gradus lõgitudinis ſimul &amp; </s>
  <s xml:id="echoid-s5374" xml:space="preserve">la <lb/>titudinis, quære differentiã lõgitudinum &amp; </s>
  <s xml:id="echoid-s5375" xml:space="preserve">ipſa cõplemẽta, mox duc ſinum cõplemẽti la <lb/>titudinis maioris in ſinũ differentiæ lõgitudinis, ꝓductũ diuide in totum ſinum, arcus q̊ti <lb/>entis dicet̃ inuentũ primũ. </s>
  <s xml:id="echoid-s5376" xml:space="preserve">Deinde adſume tibi ſinum cõplementi huius inuenti primi, u-<lb/>nà cũ ſinu latitudinis minoris, minorẽ exĳs duco in ſinũ totũ, ꝓductum etiam diuide in <lb/>maiorem, &amp; </s>
  <s xml:id="echoid-s5377" xml:space="preserve">arcus q̊tientis ſubtractus à latitudine maiori, reliquũ tibi facit inuentũ ſecun <lb/>dũ. </s>
  <s xml:id="echoid-s5378" xml:space="preserve">Poſtremò ſinus utriuſ cõplementi ambo℞ inuento℞ duc in ſeipſos, ꝓductũ in totũ <lb/>diuide, arcum q̊tientis ſubtrahe à 90. </s>
  <s xml:id="echoid-s5379" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5380" xml:space="preserve">remanebit diſtantia loco℞ ꝓpoſito℞. </s>
  <s xml:id="echoid-s5381" xml:space="preserve">?</s>
  <s xml:id="echoid-s5382" xml:space="preserve">?Exem <lb/>plum in hacre tibi tale dabimus. </s>
  <s xml:id="echoid-s5383" xml:space="preserve">Propoſita lõgitudine ſimul &amp; </s>
  <s xml:id="echoid-s5384" xml:space="preserve">latitudine Auguſtæ, ſicut <lb/>
<anchor type="note" xlink:label="note-0070-03a" xlink:href="note-0070-03"/>
ſeꝗtur, cupio ſcire diſtantiã eius à Hieruſalem, quæ eſt in terra ſancta, ſic ergo propono.</s>
  <s xml:id="echoid-s5385" xml:space="preserve"/>
</p>
<div xml:id="echoid-div161" type="float" level="2" n="1">
<note position="left" xlink:label="note-0070-03" xlink:href="note-0070-03a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſoo<unsure/>pi.</emph></note>
</div>
<p>
  <s xml:id="echoid-s5386" xml:space="preserve">Auguſta Retiæ habet in longitudine 28. </s>
  <s xml:id="echoid-s5387" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5388" xml:space="preserve">31. </s>
  <s xml:id="echoid-s5389" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5390" xml:space="preserve">in latitudine 48. </s>
  <s xml:id="echoid-s5391" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5392" xml:space="preserve">20. </s>
  <s xml:id="echoid-s5393" xml:space="preserve">mi.</s>
  <s xml:id="echoid-s5394" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s5395" xml:space="preserve">Hieruſalem ciuitas Iudææ in longit. </s>
  <s xml:id="echoid-s5396" xml:space="preserve">66. </s>
  <s xml:id="echoid-s5397" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5398" xml:space="preserve">o. </s>
  <s xml:id="echoid-s5399" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5400" xml:space="preserve">in latitudine 31. </s>
  <s xml:id="echoid-s5401" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5402" xml:space="preserve">40. </s>
  <s xml:id="echoid-s5403" xml:space="preserve">mi.</s>
  <s xml:id="echoid-s5404" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s5405" xml:space="preserve">Differentia longitudinis eſt 37. </s>
  <s xml:id="echoid-s5406" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5407" xml:space="preserve">29. </s>
  <s xml:id="echoid-s5408" xml:space="preserve">mi.</s>
  <s xml:id="echoid-s5409" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s5410" xml:space="preserve">Sinus differentiæ longit. </s>
  <s xml:id="echoid-s5411" xml:space="preserve">60853. </s>
  <s xml:id="echoid-s5412" xml:space="preserve">Comple huius 52. </s>
  <s xml:id="echoid-s5413" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5414" xml:space="preserve">31. </s>
  <s xml:id="echoid-s5415" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5416" xml:space="preserve">ſinus eius 79353.</s>
  <s xml:id="echoid-s5417" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s5418" xml:space="preserve">Latitudo maior 48. </s>
  <s xml:id="echoid-s5419" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5420" xml:space="preserve">20. </s>
  <s xml:id="echoid-s5421" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5422" xml:space="preserve">ſinus 74702. </s>
  <s xml:id="echoid-s5423" xml:space="preserve">Comple 41. </s>
  <s xml:id="echoid-s5424" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5425" xml:space="preserve">40. </s>
  <s xml:id="echoid-s5426" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5427" xml:space="preserve">ſinus 96479.</s>
  <s xml:id="echoid-s5428" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s5429" xml:space="preserve">Latitudo minor 31. </s>
  <s xml:id="echoid-s5430" xml:space="preserve">gra.</s>
  <s xml:id="echoid-s5431" xml:space="preserve">40. </s>
  <s xml:id="echoid-s5432" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5433" xml:space="preserve">ſinus 52497. </s>
  <s xml:id="echoid-s5434" xml:space="preserve">Comple.</s>
  <s xml:id="echoid-s5435" xml:space="preserve">58. </s>
  <s xml:id="echoid-s5436" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5437" xml:space="preserve">29. </s>
  <s xml:id="echoid-s5438" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5439" xml:space="preserve">ſinus 5111.</s>
  <s xml:id="echoid-s5440" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s5441" xml:space="preserve">Hic iã duco ſinũ cõplementi latitudinis minoris. </s>
  <s xml:id="echoid-s5442" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5443" xml:space="preserve">85111. </s>
  <s xml:id="echoid-s5444" xml:space="preserve">in ſinũ differentiæ lõgitud. </s>
  <s xml:id="echoid-s5445" xml:space="preserve">ſ. <lb/></s>
  <s xml:id="echoid-s5446" xml:space="preserve">60853. </s>
  <s xml:id="echoid-s5447" xml:space="preserve">poſt diuiſionẽ totius ſinus, ꝓueniunt in q̊tiente 51792. </s>
  <s xml:id="echoid-s5448" xml:space="preserve">arcus eſt 31. </s>
  <s xml:id="echoid-s5449" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5450" xml:space="preserve">12. </s>
  <s xml:id="echoid-s5451" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5452" xml:space="preserve"><lb/>&amp; </s>
  <s xml:id="echoid-s5453" xml:space="preserve">dicet̃ inuentũ primũ. </s>
  <s xml:id="echoid-s5454" xml:space="preserve">Cõplementũ ipſius eſt 58. </s>
  <s xml:id="echoid-s5455" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5456" xml:space="preserve">48. </s>
  <s xml:id="echoid-s5457" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5458" xml:space="preserve">ſinus autẽ 85536. </s>
  <s xml:id="echoid-s5459" xml:space="preserve">erit diui <lb/>ſor. </s>
  <s xml:id="echoid-s5460" xml:space="preserve">Iam porrò ſinũ latitudinis minoris 52497. </s>
  <s xml:id="echoid-s5461" xml:space="preserve">duco in ſinũ totũ, ꝓductũ diuido in diui-<lb/>ſorem iã ſeruatũ, &amp; </s>
  <s xml:id="echoid-s5462" xml:space="preserve">ꝓueniunt in quotiente 61374. </s>
  <s xml:id="echoid-s5463" xml:space="preserve">arcũ illo℞. </s>
  <s xml:id="echoid-s5464" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5465" xml:space="preserve">37. </s>
  <s xml:id="echoid-s5466" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5467" xml:space="preserve">52. </s>
  <s xml:id="echoid-s5468" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5469" xml:space="preserve">ſubtraho à <lb/>latitudine maiori, &amp; </s>
  <s xml:id="echoid-s5470" xml:space="preserve">remanet inuentũ ſecundũ. </s>
  <s xml:id="echoid-s5471" xml:space="preserve">Ad extremũ adhuc duco ſinus cõplemen <lb/>to℞ utriuſ inuenti. </s>
  <s xml:id="echoid-s5472" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5473" xml:space="preserve">98336. </s>
  <s xml:id="echoid-s5474" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5475" xml:space="preserve">85536. </s>
  <s xml:id="echoid-s5476" xml:space="preserve">in ſeipſos, ꝓductũ diuido in ſinũ ꝑfectũ &amp; </s>
  <s xml:id="echoid-s5477" xml:space="preserve">ꝓueni <lb/>ent 84113. </s>
  <s xml:id="echoid-s5478" xml:space="preserve">Arcus ipſe. </s>
  <s xml:id="echoid-s5479" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5480" xml:space="preserve">57. </s>
  <s xml:id="echoid-s5481" xml:space="preserve">gr. </s>
  <s xml:id="echoid-s5482" xml:space="preserve">16. </s>
  <s xml:id="echoid-s5483" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5484" xml:space="preserve">à 90. </s>
  <s xml:id="echoid-s5485" xml:space="preserve">ſubtractus, relinꝗt 32. </s>
  <s xml:id="echoid-s5486" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5487" xml:space="preserve">44. </s>
  <s xml:id="echoid-s5488" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5489" xml:space="preserve">uerã diſtan <lb/>tiam Auguſtæ à Hieroſolymis, q̊ ad ipſam directã ꝓfectionẽ, citra montium, uallium &amp; </s>
  <s xml:id="echoid-s5490" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0070-04a" xlink:href="note-0070-04"/>
aqua℞ diuerticula, at ea diſtantia eſt 491. </s>
  <s xml:id="echoid-s5491" xml:space="preserve">miliarium Germanico℞. </s>
  <s xml:id="echoid-s5492" xml:space="preserve">Quod ſi autem cõti <lb/>gerit alte℞ locũ habere latitudinẽ Borealẽ, alte℞ Auſtralẽ, tunc duces ſinum cõplemen-<lb/>ti latitudinis ſeptentrionalis in ſinum differentiæ lõgitudinis, ꝓductum diuides in totũ, &amp; </s>
  <s xml:id="echoid-s5493" xml:space="preserve"><lb/>q̊tiens dabit inuentum primum, eius ſinum cõplementi tibi ꝓpone, ſimul´ ſinum latitu-<lb/>dinis Borealis, minorem duc in totum, ꝓductum diuide in maiorem, arcum quotiẽtis ad <lb/>de ad latitudinem meridionalem, &amp; </s>
  <s xml:id="echoid-s5494" xml:space="preserve">habebis inuentum ſecundum. </s>
  <s xml:id="echoid-s5495" xml:space="preserve">Poſtea cum illis duo-<lb/>bus inuentis operare ſicut ſupra docuimus. </s>
  <s xml:id="echoid-s5496" xml:space="preserve">Exemplum tale inuenies pronunciato 99.</s>
  <s xml:id="echoid-s5497" xml:space="preserve"/>
</p>
<div xml:id="echoid-div162" type="float" level="2" n="2">
<note position="left" xlink:label="note-0070-04" xlink:href="note-0070-04a" xml:space="preserve"><emph style="it">Diſtantia</emph> <lb/><emph style="it">Auguſtæ à</emph> <lb/><emph style="it">Hicroſoly-</emph> <lb/><emph style="it">miseſt 491.</emph> <lb/><emph style="it">miliarium</emph> <lb/><emph style="it">Germanico</emph> <lb/><emph style="it">rum.</emph></note>
</div>
</div>
<div xml:id="echoid-div164" type="section" level="1" n="86">
<head xml:id="echoid-head90" xml:space="preserve">PRONVNCIATVM LXXIIII.</head>
<p>
  <s xml:id="echoid-s5498" xml:space="preserve">Duobus locis in gradibus lõgitudinis &amp; </s>
  <s xml:id="echoid-s5499" xml:space="preserve">latitudinis cognitis, i quã mũdi ꝑtẽ <lb/>alterab altero declinet (angulũ hũc poſitiõis alio noĩe dicimus) inueſtigare.</s>
  <s xml:id="echoid-s5500" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s5501" xml:space="preserve">Quære ex ſuꝑiori ꝓnunc. </s>
  <s xml:id="echoid-s5502" xml:space="preserve">diſtantiã illo℞ duo℞ loco℞, &amp; </s>
  <s xml:id="echoid-s5503" xml:space="preserve">duc ſinum cõplementi latitu-<lb/>
<anchor type="note" xlink:label="note-0070-05a" xlink:href="note-0070-05"/>
dinis minoris in ſinũ differentiæ lõgitudinis, ꝓductũ diuide in ſinũ totum, &amp; </s>
  <s xml:id="echoid-s5504" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5505" xml:space="preserve">quotientẽ <lb/>ꝓpone tibi unà cũ ſſnu diſtantiæ loco℞, minorẽ duc in totum, ꝓductum diuide in maio-<lb/>rem, &amp; </s>
  <s xml:id="echoid-s5506" xml:space="preserve">arcus q̊tientis monſtrabit angulũ poſitionis, puta quãtum locus ille à meridie uer <lb/>ſus ortũ uel uerſus occaſum, ſimiliter à ſeptentrione uerſus orientem aut occidentem po-
<pb file="0071" n="71" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
litus ſit, Azimuth idẽ dici ſolet, de q̊ multa alibi, nũc ad exemplũ ueniamus. </s>
  <s xml:id="echoid-s5507" xml:space="preserve">?</s>
  <s xml:id="echoid-s5508" xml:space="preserve">?A loco <lb/>
<anchor type="note" xlink:label="note-0071-01a" xlink:href="note-0071-01"/>
intronizationis cupio ſcire quorſum uergat Hieruſalem, q̊ ad ſitum illũ, quẽ digito liceat <lb/>mõſtrare, res ea ſanène nulla ne exigua eſt, ſcire q̊d nun̈ uideris, &amp; </s>
  <s xml:id="echoid-s5509" xml:space="preserve">digito oſtendere <lb/>q̊ nõ ꝑtingit aſpectus, ita ꝓpoſitis gradibus latitudinũ &amp; </s>
  <s xml:id="echoid-s5510" xml:space="preserve">lõgitudinum, ſicut in ſuꝑiori <lb/>ꝓnunciato factũ eſt, inuenta etiã diſtantia 32. </s>
  <s xml:id="echoid-s5511" xml:space="preserve">gra.</s>
  <s xml:id="echoid-s5512" xml:space="preserve">44. </s>
  <s xml:id="echoid-s5513" xml:space="preserve">mi.</s>
  <s xml:id="echoid-s5514" xml:space="preserve">ſinũ differẽtiæ lõgitudinum.</s>
  <s xml:id="echoid-s5515" xml:space="preserve">ſ. <lb/></s>
  <s xml:id="echoid-s5516" xml:space="preserve">
<anchor type="note" xlink:label="note-0071-02a" xlink:href="note-0071-02"/>
60853. </s>
  <s xml:id="echoid-s5517" xml:space="preserve">duco in ſinũ cõplementi latitudinis minoris.</s>
  <s xml:id="echoid-s5518" xml:space="preserve">ſ.</s>
  <s xml:id="echoid-s5519" xml:space="preserve">85111. </s>
  <s xml:id="echoid-s5520" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5521" xml:space="preserve">diuide per totum ſinũ, q̊-<lb/>tiens dabit 51792. </s>
  <s xml:id="echoid-s5522" xml:space="preserve">quẽ ut minorẽ duco in totũ, ꝓductũ diuido in ſinũ diſtãtiæ inuentæ.</s>
  <s xml:id="echoid-s5523" xml:space="preserve">ſ. <lb/></s>
  <s xml:id="echoid-s5524" xml:space="preserve">53975. </s>
  <s xml:id="echoid-s5525" xml:space="preserve">In quotiente ꝓueniunt 95783. </s>
  <s xml:id="echoid-s5526" xml:space="preserve">arcus eius eſt 73. </s>
  <s xml:id="echoid-s5527" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5528" xml:space="preserve">18. </s>
  <s xml:id="echoid-s5529" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5530" xml:space="preserve">diſtantia Hieroſoly <lb/>mæ à meridiano uerſus ortum, ſi quãdo cupiã Auguſtæ ſitum illius digito cõmonſtrare.</s>
  <s xml:id="echoid-s5531" xml:space="preserve"/>
</p>
<div xml:id="echoid-div164" type="float" level="2" n="1">
<note position="left" xlink:label="note-0070-05" xlink:href="note-0070-05a" xml:space="preserve"><emph style="it">Per latera</emph> <lb/><emph style="it">lem obſer-</emph> <lb/><emph style="it">uationẽ idẽ</emph> <lb/><emph style="it">reperies.</emph> <lb/><emph style="it">Illud ucro</emph> <lb/><emph style="it">ꝑ arealem.</emph></note>
<note position="right" xlink:label="note-0071-01" xlink:href="note-0071-01a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">Epiſcopi.</emph></note>
<note position="right" xlink:label="note-0071-02" xlink:href="note-0071-02a" xml:space="preserve"><emph style="it">Diſtantia</emph> <lb/><emph style="it">Hieroſoly-</emph> <lb/><emph style="it">mæ à meri</emph> <lb/><emph style="it">diano Au-</emph> <lb/><emph style="it">guſtano or</emph> <lb/><emph style="it">tum uerſus</emph> <lb/><emph style="it">gra. 73. mi.</emph> <lb/><emph style="it">18.</emph></note>
</div>
</div>
<div xml:id="echoid-div166" type="section" level="1" n="87">
<head xml:id="echoid-head91" xml:space="preserve">PRONVNCIATVM LXXV.</head>
<p>
  <s xml:id="echoid-s5532" xml:space="preserve">Propoſitis locis duobus, quorum alterius tantum latitudo ſimul &amp; </s>
  <s xml:id="echoid-s5533" xml:space="preserve">longi <lb/>tudo ſit cognita, alterius autem utra ignota, angulus autem poſitionis ab al <lb/>tero conſtet unà cum diſtantia ad alterum, inſuper eleuationem poli alterius <lb/>loci, longitudinem etiam ſiue diſtantiam longitudinis indagare.</s>
  <s xml:id="echoid-s5534" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s5535" xml:space="preserve">Age hic ſinũ diſtãtiæ duc in ſinũ anguli poſitiõis, ꝓductum diuide in totũ, &amp; </s>
  <s xml:id="echoid-s5536" xml:space="preserve">arcus q̊-<lb/>
<anchor type="note" xlink:label="note-0071-03a" xlink:href="note-0071-03"/>
tientis dabit inuentũ primũ, cõplementi huius inuenti ſinum tibi ꝓpone, &amp; </s>
  <s xml:id="echoid-s5537" xml:space="preserve">ſinum cõple-<lb/>menti diſtãtiæ loco℞, minorem duc in totũ, &amp; </s>
  <s xml:id="echoid-s5538" xml:space="preserve">ꝓductũ cũ maiori diuide, arcũ uero q̊tien-<lb/>tis ſubtrahe ex 90. </s>
  <s xml:id="echoid-s5539" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5540" xml:space="preserve">reſiduum rurſus ſubtractũ de latitudine nota, dicet̃ inuentum ſecun <lb/>dum. </s>
  <s xml:id="echoid-s5541" xml:space="preserve">Quod ſi aũt locus ignotus Borealior extiterit, tunc adde reſiduo latitudinem notã, <lb/>&amp; </s>
  <s xml:id="echoid-s5542" xml:space="preserve">habebis etiã ſic inuentũ ſecundũ, Deinde duc ſinũ ſecundi inuenti in ſinum cõplementi iã inuen <lb/>primi inuenti, &amp; </s>
  <s xml:id="echoid-s5543" xml:space="preserve">deinde in totum, arcus q̊tientis mõſtrabit latitudinem loci ignoti quæſi <lb/>tam, partem eius q̊d erat inquirendũ. </s>
  <s xml:id="echoid-s5544" xml:space="preserve">Porrò inde ꝓpone tibi ſinum cõplementi iã inuen <lb/>tæ latitudinis, &amp; </s>
  <s xml:id="echoid-s5545" xml:space="preserve">ſinum inuenti primi duc in totũ, ꝓductũ diuide in maiorem, mox quære <lb/>arcum q̊tientis, ꝗ mõſtrat differentiã lõgitudinis, alte℞ id eſt q̊d quærimus. </s>
  <s xml:id="echoid-s5546" xml:space="preserve">At ſi longitu <lb/>do prioris illius loci cogniti manifeſto conſtat, &amp; </s>
  <s xml:id="echoid-s5547" xml:space="preserve">locus alter qui prius credebat̃ ignotus <lb/>uerſus ortum eſt poſitus, adde differentiã illã ad lõgitudinem loci cogniti. </s>
  <s xml:id="echoid-s5548" xml:space="preserve">Si autem locus <lb/>ignotus fuerit Orientalior, tũc ſubtrahe differentiã illã à lõgitudine ciuitatis notæ, &amp; </s>
  <s xml:id="echoid-s5549" xml:space="preserve">ha-<lb/>bebis lõgitudinem ciuitatis ignotæ cognitã at perſpectã. </s>
  <s xml:id="echoid-s5550" xml:space="preserve">?</s>
  <s xml:id="echoid-s5551" xml:space="preserve">?Videris adhuc mihi ex-<lb/>
<anchor type="note" xlink:label="note-0071-04a" xlink:href="note-0071-04"/>
plũ requirere, en damus hoc tibi. </s>
  <s xml:id="echoid-s5552" xml:space="preserve">Ecce locum factæ intronizatiõis mihi ꝓpono, ubilõgi-<lb/>tudoeſt 28. </s>
  <s xml:id="echoid-s5553" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5554" xml:space="preserve">31. </s>
  <s xml:id="echoid-s5555" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5556" xml:space="preserve">à primo meridiano qui trãſit ꝑ Canarias inſulas, unde lõgitudinis <lb/>petitur initium, latitudo quo Auguſtæ eſt 48. </s>
  <s xml:id="echoid-s5557" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5558" xml:space="preserve">20. </s>
  <s xml:id="echoid-s5559" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5560" xml:space="preserve">iam ergo ſcio Hieruſalem ab <lb/>Auguſta diſtare ꝑ 491. </s>
  <s xml:id="echoid-s5561" xml:space="preserve">miliaria Germanica, &amp; </s>
  <s xml:id="echoid-s5562" xml:space="preserve">hinc cupio cognoſcere quantum ſit eleua <lb/>tus polus Hieroſolymis, quæ ſit ibi lõgitudo, hoc eſt q̊t horis Hieroſolymiæ citius ha <lb/>beãt meridiẽ ̈ Auguſtani. </s>
  <s xml:id="echoid-s5563" xml:space="preserve">Sinus ita diſtantiæ eſt 53975, eum duco in ſinum anguli po <lb/>ſitionis, ꝗ ſit 73. </s>
  <s xml:id="echoid-s5564" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5565" xml:space="preserve">18. </s>
  <s xml:id="echoid-s5566" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5567" xml:space="preserve">ſinus eius eſt 95783. </s>
  <s xml:id="echoid-s5568" xml:space="preserve">ꝓductũ diuido in totum, &amp; </s>
  <s xml:id="echoid-s5569" xml:space="preserve">in q̊tiente ha <lb/>beo 51792. </s>
  <s xml:id="echoid-s5570" xml:space="preserve">cuius arcus erit 31. </s>
  <s xml:id="echoid-s5571" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5572" xml:space="preserve">12. </s>
  <s xml:id="echoid-s5573" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5574" xml:space="preserve">at hoc ſit inuentum primum. </s>
  <s xml:id="echoid-s5575" xml:space="preserve">Sinum diſtan <lb/>tiæ 84113. </s>
  <s xml:id="echoid-s5576" xml:space="preserve">duco in ſinum totũ, &amp; </s>
  <s xml:id="echoid-s5577" xml:space="preserve">ꝓductum diuido in ſinũ cõplementi inuenti primi, q̊ti-<lb/>ens dabit 98336. </s>
  <s xml:id="echoid-s5578" xml:space="preserve">arcus illius eſt 79. </s>
  <s xml:id="echoid-s5579" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5580" xml:space="preserve">32. </s>
  <s xml:id="echoid-s5581" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5582" xml:space="preserve">eum ſubtraho de 90.</s>
  <s xml:id="echoid-s5583" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5584" xml:space="preserve">remanent 10. </s>
  <s xml:id="echoid-s5585" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s5586" xml:space="preserve">28. </s>
  <s xml:id="echoid-s5587" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5588" xml:space="preserve">quibus ſubductis à latitudine cognita, ꝗa illa Borealior eſt, relinquuntur 37. </s>
  <s xml:id="echoid-s5589" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5590" xml:space="preserve"><lb/>52. </s>
  <s xml:id="echoid-s5591" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5592" xml:space="preserve">inuentum. </s>
  <s xml:id="echoid-s5593" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5594" xml:space="preserve">ſecundum. </s>
  <s xml:id="echoid-s5595" xml:space="preserve">Iam ſi ſinũ inuenti ſecundi 61374. </s>
  <s xml:id="echoid-s5596" xml:space="preserve">duxero in ſinum inuen <lb/>ti primi, &amp; </s>
  <s xml:id="echoid-s5597" xml:space="preserve">diuiſero in totũ, q̊tiens dabit tibi 52497. </s>
  <s xml:id="echoid-s5598" xml:space="preserve">arcus illius 31. </s>
  <s xml:id="echoid-s5599" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5600" xml:space="preserve">40. </s>
  <s xml:id="echoid-s5601" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5602" xml:space="preserve">diſſoluet <lb/>tibi hoc q̊d quæſieramus primũ, ſiquidẽ is ipſe oſtẽdit altitudinem poli in Hieruſalẽ quã <lb/>antea ignorabas. </s>
  <s xml:id="echoid-s5603" xml:space="preserve">Poſt hæc rurſus duco ſinum inuenti primi 51792. </s>
  <s xml:id="echoid-s5604" xml:space="preserve">in totum, &amp; </s>
  <s xml:id="echoid-s5605" xml:space="preserve">diuido <lb/>
<anchor type="note" xlink:label="note-0071-05a" xlink:href="note-0071-05"/>
in ſinum cõplementi latitudinis iã inuentæ Hieroſolymitanæ, &amp; </s>
  <s xml:id="echoid-s5606" xml:space="preserve">q̊tiens ꝓducit 60853. <lb/></s>
  <s xml:id="echoid-s5607" xml:space="preserve">arcus eius eſt 37. </s>
  <s xml:id="echoid-s5608" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5609" xml:space="preserve">29. </s>
  <s xml:id="echoid-s5610" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5611" xml:space="preserve">differentia illa lõgitudinis inter meridianum Auguſtenſem <lb/>&amp; </s>
  <s xml:id="echoid-s5612" xml:space="preserve">Hieroſolymitanum, hanc ſi addidero ad longitudinem Auguſteñ. </s>
  <s xml:id="echoid-s5613" xml:space="preserve">28. </s>
  <s xml:id="echoid-s5614" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5615" xml:space="preserve">31. </s>
  <s xml:id="echoid-s5616" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5617" xml:space="preserve">ꝓue <lb/>nient mihi 66. </s>
  <s xml:id="echoid-s5618" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5619" xml:space="preserve">quæ lõgitudo eſt Hieroſolymis, unde argumentũ ſumitur, quia in Hie <lb/>ruſalem duabus horis &amp; </s>
  <s xml:id="echoid-s5620" xml:space="preserve">30. </s>
  <s xml:id="echoid-s5621" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5622" xml:space="preserve">citius fiet meridies ̈ Auguſtæ. </s>
  <s xml:id="echoid-s5623" xml:space="preserve">Vnum hoc fac attendas <lb/>ſi qñ ita res tulerit, ut angulus poſitionis ſit 90. </s>
  <s xml:id="echoid-s5624" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5625" xml:space="preserve">à meridie, tunc duce@ co@@plementum <lb/>intercapedinis in ſinum latitudinis notæ, &amp; </s>
  <s xml:id="echoid-s5626" xml:space="preserve">ꝓductum diuides in ſinum perfectũ, at ſic <lb/>arcus quotientis mõſtrabit tibi latitudinẽ alterius loci, deinde cõplementum quo lati-
<pb file="0072" n="72" rhead="GENVINVS VSVS"/>
tudinis huius ſecundiloci tibi propones, ſimiliter &amp; </s>
  <s xml:id="echoid-s5627" xml:space="preserve">ſinum intercapedinis, minorem ex <lb/>ĳs duces in totum, productum diuides in minorem, &amp; </s>
  <s xml:id="echoid-s5628" xml:space="preserve">arcus quotientis dabit differenti-<lb/>am longitudinis, at iſtud ip ſum in hac re te celare noluimus.</s>
  <s xml:id="echoid-s5629" xml:space="preserve"/>
</p>
<div xml:id="echoid-div166" type="float" level="2" n="1">
<note position="right" xlink:label="note-0071-03" xlink:href="note-0071-03a" xml:space="preserve"><emph style="it">Inucntum</emph> <lb/><emph style="it">primum</emph> <lb/><emph style="it">later aliter</emph> <lb/><emph style="it">inucnies.</emph> <lb/><emph style="it">Inuentum</emph> <lb/><emph style="it">ſecundum</emph> <lb/><emph style="it">aredtim.</emph> <lb/><emph style="it">Operatio</emph> <lb/><emph style="it">lateralis.</emph> <lb/><emph style="it">Operatio</emph> <lb/><emph style="it">Arealis.</emph></note>
<note position="right" xlink:label="note-0071-04" xlink:href="note-0071-04a" xml:space="preserve">EXEM. <lb/>PLVM <lb/><emph style="it">Epiſcopi.</emph></note>
<note position="right" xlink:label="note-0071-05" xlink:href="note-0071-05a" xml:space="preserve"><emph style="it">Differentia</emph> <lb/><emph style="it">lõgitudinis</emph> <lb/><emph style="it">inter meri-</emph> <lb/><emph style="it">dianũ Au-</emph> <lb/><emph style="it">guſtẽſem et</emph> <lb/><emph style="it">Hieroſoly-</emph> <lb/><emph style="it">mitanũ est</emph> <lb/><emph style="it">gra. 37.</emph> <lb/><emph style="it">mi. 29.</emph></note>
</div>
</div>
<div xml:id="echoid-div168" type="section" level="1" n="88">
<head xml:id="echoid-head92" xml:space="preserve">PRONVNCIATVM LXXVI.</head>
<p>
  <s xml:id="echoid-s5630" xml:space="preserve">Cognita tantum unius loci propoſiti eleuatione polari ſimul &amp; </s>
  <s xml:id="echoid-s5631" xml:space="preserve">alterius, <lb/>at hinc etiam intercapedine habita inter utran, differentiam adhuc longi <lb/>tudinum &amp; </s>
  <s xml:id="echoid-s5632" xml:space="preserve">angulum poſitionis ab altero ad alterum inuenire.</s>
  <s xml:id="echoid-s5633" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s5634" xml:space="preserve">Primũ oĩm hic tibi ꝓpone gradus &amp; </s>
  <s xml:id="echoid-s5635" xml:space="preserve">ſinus cõplemento℞ utriuſ eleuationis poli, gra-<lb/>dus etiã &amp; </s>
  <s xml:id="echoid-s5636" xml:space="preserve">ſinus diſtãtiæ ſiue intercapedinis inter utrũ locum, ſiquidem certum eſt quũ <lb/>
<anchor type="note" xlink:label="note-0072-01a" xlink:href="note-0072-01"/>
intercapedo ad 90. </s>
  <s xml:id="echoid-s5637" xml:space="preserve">gradus nõ adſurgat, cõplemẽtũ alte℞ latitudinis oportere eſſe maius <lb/>intercapedine, ne eſt q̊d in hoc uſu ulterius requiras, plura aũt ſuꝑ hac re inuenies in <lb/>Mereoroſcopĳs noſtris, ſiquidẽ duo cõſcripſimus, alte℞ ſpeculare uocauimus, alterũ recti <lb/>linearũ, nũc porrò quæ cœpimus ſic proſequemur. </s>
  <s xml:id="echoid-s5638" xml:space="preserve">Numeros illos tres, puta utrun cõ-<lb/>plementũ latitudinũ &amp; </s>
  <s xml:id="echoid-s5639" xml:space="preserve">intercapedinis arcũ ita diſpone, ut unũ colloces ſuꝑ alterũ, &amp; </s>
  <s xml:id="echoid-s5640" xml:space="preserve">ma <lb/>iorem quidẽ ſupremo loco, in medio aũt mediũ, &amp; </s>
  <s xml:id="echoid-s5641" xml:space="preserve">minimũ inſimo loco, hinc ſubtrahe me <lb/>dium à maximo, &amp; </s>
  <s xml:id="echoid-s5642" xml:space="preserve">reſiduũ dicet̃ differentia prima. </s>
  <s xml:id="echoid-s5643" xml:space="preserve">Mox ſubtrahe etiã minorẽ de 90. </s>
  <s xml:id="echoid-s5644" xml:space="preserve">qđ <lb/>relinquetur, appellabitur differentia ſecunda. </s>
  <s xml:id="echoid-s5645" xml:space="preserve">Poſthæc ꝓpone tibi &amp; </s>
  <s xml:id="echoid-s5646" xml:space="preserve">ſinum cõplementi <lb/>primæ differentiæ, &amp; </s>
  <s xml:id="echoid-s5647" xml:space="preserve">inde ſubtrahe ſinum differentiæ ſecundæ, reſiduũ duc in ſinũ cõple-<lb/>menti maioris arcus, ꝓductũ diuide in ſinũ maioris, &amp; </s>
  <s xml:id="echoid-s5648" xml:space="preserve">q̊tientẽ adde ad ſinũ arcus primæ <lb/>differentiæ, ſummã illã quadrato, ſimiliter &amp; </s>
  <s xml:id="echoid-s5649" xml:space="preserve">ſinũ differentiæ ſecundæ, at hinc illa duo <lb/>quadrata ſimul adde in unã ſummã, ex ea quære radicẽ quadratã, arcus deinceps huius ra <lb/>dicis ſubtractus de 90. </s>
  <s xml:id="echoid-s5650" xml:space="preserve">relinquit argumentum operationis. </s>
  <s xml:id="echoid-s5651" xml:space="preserve">Iuxta ſinũ illius argumenti re <lb/>pone &amp; </s>
  <s xml:id="echoid-s5652" xml:space="preserve">ſinũ cõplementi maioris latitudinis, minorẽ duc in totum, &amp; </s>
  <s xml:id="echoid-s5653" xml:space="preserve">ꝓductũ diuide in <lb/>
<anchor type="note" xlink:label="note-0072-02a" xlink:href="note-0072-02"/>
maiorem, ſic arcus q̊tientis ꝓducet differentiam longitudinis quã primo quærebam. </s>
  <s xml:id="echoid-s5654" xml:space="preserve">Ad <lb/>hæc ducito &amp; </s>
  <s xml:id="echoid-s5655" xml:space="preserve">ſinũ cõplementi latitudinis minoris in ſinũ differentiæ lõgitudinis, produ-<lb/>ctum diuide in ſinũ totũ, &amp; </s>
  <s xml:id="echoid-s5656" xml:space="preserve">quotientem rurſus ſepone in aliquẽ locũ, ei´ adiunge ſinum <lb/>intercapedinis minorem duc in totũ, &amp; </s>
  <s xml:id="echoid-s5657" xml:space="preserve">ꝓductũ diuide cũ maiori, hinc arcus q̊tientis mon <lb/>ſtrat angulum poſitiõis quæſitúm. </s>
  <s xml:id="echoid-s5658" xml:space="preserve">At hæc ita demũ ueritatẽ obtinent, ſi locus ſecũdus <lb/>Auſtralior extiterit, qui ſi ſit Borealior ̈ primus &amp; </s>
  <s xml:id="echoid-s5659" xml:space="preserve">datus locus, iuxta quem angulus po <lb/>ſitionis accipitur, tunc quære angulũ poſitionis hoc modo. </s>
  <s xml:id="echoid-s5660" xml:space="preserve">Fac tibi proponas ſinũ argu-<lb/>
<anchor type="note" xlink:label="note-0072-03a" xlink:href="note-0072-03"/>
menti operationis ſuperius inuentũ, &amp; </s>
  <s xml:id="echoid-s5661" xml:space="preserve">ſintercapedinis minorũ duc in totum, &amp; </s>
  <s xml:id="echoid-s5662" xml:space="preserve">ꝓdu-<lb/>cto in maiorem diuiſo, arcus quotientis angulũ dabit poſitionis à ſeptentrione adortum, <lb/>ſi tamen locus ſecundus ſuerit orientalior, is ſi ſit occidẽtalior, numerandus erit tibi angu-<lb/>
<anchor type="note" xlink:label="note-0072-04a" xlink:href="note-0072-04"/>
lus ille à meridiano ſeptentrionali ad occaſum. </s>
  <s xml:id="echoid-s5663" xml:space="preserve">?</s>
  <s xml:id="echoid-s5664" xml:space="preserve">?Sed iã opus eſt rem exemplo plenius <lb/>excutere. </s>
  <s xml:id="echoid-s5665" xml:space="preserve">Age igitur Auguſta in latitudine habet 48. </s>
  <s xml:id="echoid-s5666" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5667" xml:space="preserve">20. </s>
  <s xml:id="echoid-s5668" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5669" xml:space="preserve">Hieruſalem aũt 31. </s>
  <s xml:id="echoid-s5670" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s5671" xml:space="preserve">40. </s>
  <s xml:id="echoid-s5672" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5673" xml:space="preserve">ab Auguſta etiã uſ in Hieruſalem ſunt 491. </s>
  <s xml:id="echoid-s5674" xml:space="preserve">miliaria, quæ faciunt 32. </s>
  <s xml:id="echoid-s5675" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5676" xml:space="preserve">44. </s>
  <s xml:id="echoid-s5677" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5678" xml:space="preserve"><lb/>nunc aſſumo numeros illos tres, cõplementum minoris latitudinis, at is numerus erit <lb/>maior, complementum latitudinis maioris medium tenebit, &amp; </s>
  <s xml:id="echoid-s5679" xml:space="preserve">intercapedo infimum lo-<lb/>cum, quia minor. </s>
  <s xml:id="echoid-s5680" xml:space="preserve">Medium porrò ſubtraho à maiori, &amp; </s>
  <s xml:id="echoid-s5681" xml:space="preserve">remanet differentia prima, mi-<lb/>norem uero à 90. </s>
  <s xml:id="echoid-s5682" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5683" xml:space="preserve">relinquitur differentia ſecunda, diſponuntur hoc modo.</s>
  <s xml:id="echoid-s5684" xml:space="preserve"/>
</p>
<div xml:id="echoid-div168" type="float" level="2" n="1">
<note position="left" xlink:label="note-0072-01" xlink:href="note-0072-01a" xml:space="preserve"><emph style="it">Meteoroſco</emph> <lb/><emph style="it">piũ abſolu-</emph> <lb/><emph style="it">tißimum in</emph> <lb/><emph style="it">Aſtronomi</emph> <lb/><emph style="it">co Cæſareo</emph> <lb/><emph style="it">ſimiliter in</emph> <lb/><emph style="it">Coſmogra-</emph> <lb/><emph style="it">phia. Com-</emph> <lb/><emph style="it">poſitiones</emph> <lb/><emph style="it">uero eiuſdẽ</emph> <lb/><emph style="it">in Plani-</emph> <lb/><emph style="it">ſphærio, li-</emph> <lb/><emph style="it">bris à nobis</emph> <lb/><emph style="it">æditis.</emph></note>
<note position="left" xlink:label="note-0072-02" xlink:href="note-0072-02a" xml:space="preserve"><emph style="it">Per latera-</emph> <lb/><emph style="it">lem introi-</emph> <lb/><emph style="it">tum ſimile</emph> <lb/><emph style="it">aſſequeris.</emph></note>
<note position="left" xlink:label="note-0072-03" xlink:href="note-0072-03a" xml:space="preserve"><emph style="it">Arealis in-</emph> <lb/><emph style="it">troitus.</emph></note>
<note position="left" xlink:label="note-0072-04" xlink:href="note-0072-04a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">diſtãtiæ in-</emph> <lb/><emph style="it">ter Augu-</emph> <lb/><emph style="it">ſtã &amp;</emph> Hie <lb/><emph style="it">ruſalem.</emph></note>
</div>
<p>
  <s xml:id="echoid-s5685" xml:space="preserve">Numerus maior 58. </s>
  <s xml:id="echoid-s5686" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5687" xml:space="preserve">20. </s>
  <s xml:id="echoid-s5688" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5689" xml:space="preserve">complementum minoris latitudinis.</s>
  <s xml:id="echoid-s5690" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s5691" xml:space="preserve">Mediuserit 41. </s>
  <s xml:id="echoid-s5692" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5693" xml:space="preserve">49. </s>
  <s xml:id="echoid-s5694" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5695" xml:space="preserve">complementum maioris latitudinis.</s>
  <s xml:id="echoid-s5696" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s5697" xml:space="preserve">Numerus minor 32. </s>
  <s xml:id="echoid-s5698" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5699" xml:space="preserve">44. </s>
  <s xml:id="echoid-s5700" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5701" xml:space="preserve">diſtantia locorum.</s>
  <s xml:id="echoid-s5702" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s5703" xml:space="preserve">Differentia prima 16. </s>
  <s xml:id="echoid-s5704" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5705" xml:space="preserve">40. </s>
  <s xml:id="echoid-s5706" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5707" xml:space="preserve">ſcilicet complementorum latitud.</s>
  <s xml:id="echoid-s5708" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s5709" xml:space="preserve">Differentia ſecunda 57. </s>
  <s xml:id="echoid-s5710" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5711" xml:space="preserve">16. </s>
  <s xml:id="echoid-s5712" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5713" xml:space="preserve">hoc eſt complementum diſtantiæ.</s>
  <s xml:id="echoid-s5714" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s5715" xml:space="preserve">Iam ꝓpono mihi ſinũ cõplemẽti primæ differentiæ. </s>
  <s xml:id="echoid-s5716" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5717" xml:space="preserve">95798. </s>
  <s xml:id="echoid-s5718" xml:space="preserve">inde ſubtraho ſinũ ſecundæ <lb/>differentiæ, puta 84119. </s>
  <s xml:id="echoid-s5719" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5720" xml:space="preserve">remanent 11679. </s>
  <s xml:id="echoid-s5721" xml:space="preserve">quẽ numerũ duco in ſinũ cõplementi maio-<lb/>ris. </s>
  <s xml:id="echoid-s5722" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5723" xml:space="preserve">52497. </s>
  <s xml:id="echoid-s5724" xml:space="preserve">ꝓductũ diuido cũ ſinu maioris. </s>
  <s xml:id="echoid-s5725" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5726" xml:space="preserve">85111. </s>
  <s xml:id="echoid-s5727" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5728" xml:space="preserve">quotiens dat 7203. </s>
  <s xml:id="echoid-s5729" xml:space="preserve">hæc addo ad <lb/>ſinũ primæ differẽtiæ, puta 28680. </s>
  <s xml:id="echoid-s5730" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5731" xml:space="preserve">ꝓueniũt 35883. </s>
  <s xml:id="echoid-s5732" xml:space="preserve">numerus hic ſi quadretur, ꝓducit <lb/>1287589689. </s>
  <s xml:id="echoid-s5733" xml:space="preserve">Mox quadrabis etiã ſinus ſecũdæ differentiæ. </s>
  <s xml:id="echoid-s5734" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5735" xml:space="preserve">84119. </s>
  <s xml:id="echoid-s5736" xml:space="preserve">facit 7076106161. <lb/></s>
  <s xml:id="echoid-s5737" xml:space="preserve">utrun hoc quadratũ cõiungo in unã ſummã, quæ erit 8363605850. </s>
  <s xml:id="echoid-s5738" xml:space="preserve">radix illius quadra <lb/>ta eſt 91453. </s>
  <s xml:id="echoid-s5739" xml:space="preserve">lã ſi arcũ radicis. </s>
  <s xml:id="echoid-s5740" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5741" xml:space="preserve">66. </s>
  <s xml:id="echoid-s5742" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5743" xml:space="preserve">8. </s>
  <s xml:id="echoid-s5744" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5745" xml:space="preserve">ſubtraxero à 90. </s>
  <s xml:id="echoid-s5746" xml:space="preserve">relinquunt̃ 23. </s>
  <s xml:id="echoid-s5747" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5748" xml:space="preserve">52. </s>
  <s xml:id="echoid-s5749" xml:space="preserve">mi.</s>
  <s xml:id="echoid-s5750" xml:space="preserve">
<pb file="0073" n="73" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
argumentum illud operationis, ſinum illius duco in ſinum totum, &amp; </s>
  <s xml:id="echoid-s5751" xml:space="preserve">productum diuido <lb/>
<anchor type="note" xlink:label="note-0073-01a" xlink:href="note-0073-01"/>
in ſinum complemẽti maioris latitudinis. </s>
  <s xml:id="echoid-s5752" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5753" xml:space="preserve">66479. </s>
  <s xml:id="echoid-s5754" xml:space="preserve">tunc arcus quotientis 37. </s>
  <s xml:id="echoid-s5755" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5756" xml:space="preserve">29. </s>
  <s xml:id="echoid-s5757" xml:space="preserve">mi. <lb/></s>
  <s xml:id="echoid-s5758" xml:space="preserve">erit differentia lõgitudinis inter meridianum Auguſtenſem &amp; </s>
  <s xml:id="echoid-s5759" xml:space="preserve">Hieruſalem, id quod pri-<lb/>mo loco ſcire uolebam. </s>
  <s xml:id="echoid-s5760" xml:space="preserve">Dehinc duco etiam ſinum differentiæ longitudinis 60853. </s>
  <s xml:id="echoid-s5761" xml:space="preserve">in ſi-<lb/>num complementi latitudinis minoris 85111. </s>
  <s xml:id="echoid-s5762" xml:space="preserve">productum diuido in ſinum intercapedi-<lb/>nis, ſcilicet 53975. </s>
  <s xml:id="echoid-s5763" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5764" xml:space="preserve">quotiens producit 95783. </s>
  <s xml:id="echoid-s5765" xml:space="preserve">cuius arcus eſt 73. </s>
  <s xml:id="echoid-s5766" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5767" xml:space="preserve">18. </s>
  <s xml:id="echoid-s5768" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5769" xml:space="preserve">angulus <lb/>hic ille poſitionis, quem ſecundo loco per hanc operationem inquirebam.</s>
  <s xml:id="echoid-s5770" xml:space="preserve"/>
</p>
<div xml:id="echoid-div169" type="float" level="2" n="2">
<note position="right" xlink:label="note-0073-01" xlink:href="note-0073-01a" xml:space="preserve"><emph style="it">Differentia</emph> <lb/><emph style="it">lõgitudinis</emph> <lb/><emph style="it">inter Augu</emph> <lb/><emph style="it">ſtã &amp; Hie</emph> <lb/><emph style="it">ruſalem.</emph> <lb/><emph style="it">Angulus</emph> <lb/><emph style="it">poſitionis</emph> <lb/><emph style="it">inter Augu</emph> <lb/><emph style="it">ſtã &amp; Hie</emph> <lb/><emph style="it">ruſalem.</emph></note>
</div>
</div>
<div xml:id="echoid-div171" type="section" level="1" n="89">
<head xml:id="echoid-head93" xml:space="preserve">PRONVNCIATVM LXXVII.</head>
<p>
  <s xml:id="echoid-s5771" xml:space="preserve">Si trium locorum nota ſit intercapedo, duo etiam loca ex ĳs cognitas ha-<lb/>beant ſuas tum latitudines tum longitudines, adhuc tertĳ longitudinem &amp; </s>
  <s xml:id="echoid-s5772" xml:space="preserve"><lb/>latitudinem, angulum´ poſitionis, inquirere.</s>
  <s xml:id="echoid-s5773" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s5774" xml:space="preserve">Propoſitis locis tribus, è ꝗbus duo habeãt lõgitudinẽ notã ſimul &amp; </s>
  <s xml:id="echoid-s5775" xml:space="preserve">latitudinẽ, tu uero <lb/>ſcias, quantũ quilibet illorũ ſit poſitus ab alĳs duobus, hinc uelis adhuc ſcire lõgitudinem <lb/>&amp; </s>
  <s xml:id="echoid-s5776" xml:space="preserve">latitudinẽ loci incogniti, conſidera principio diſtantiã unius ab alio, ſiquidẽ intercape <lb/>dinẽ duorũ cognitorũ ꝑ artẽ inueniſti, illũ aũt tertĳ loci à duobus habes ꝑ exꝑientiã, ꝓpo <lb/>ne hic tibi intercapedines illas tres, mediã ſubtrahe à maiori, reſiduũ dicetur differentia <lb/>prima, minorem quo ſubtrahe à 90. </s>
  <s xml:id="echoid-s5777" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5778" xml:space="preserve">relinquetur differentia ſecũda. </s>
  <s xml:id="echoid-s5779" xml:space="preserve">Inſuꝑ ſubducito ſi <lb/>num differentiæ ſecundæ de ſinu cõplementi differentiæ primæ, &amp; </s>
  <s xml:id="echoid-s5780" xml:space="preserve">reſiduũ duc in ſinum <lb/>complementi maioris intercapedinis, ꝓductũ diuide in ſinũ maioris intercapedinis, quo-<lb/>
<anchor type="note" xlink:label="note-0073-02a" xlink:href="note-0073-02"/>
tientem uero adde ad ſinũ differentiæ primæ, &amp; </s>
  <s xml:id="echoid-s5781" xml:space="preserve">ſummã iſtã duc in ſe quadrate, ſimiliter <lb/>&amp; </s>
  <s xml:id="echoid-s5782" xml:space="preserve">ſinum differentiæ ſecundæ, utrũ illũ numerũ qua dratũ collige in unã ſummã, &amp; </s>
  <s xml:id="echoid-s5783" xml:space="preserve">eius <lb/>radicẽ itidẽ quadratã inquire, arcũ radicis de 90. </s>
  <s xml:id="echoid-s5784" xml:space="preserve">ſubtracto relinquet̃ argumentũ oꝑatio-<lb/>nis, q̊dſeruabis in recenti memoria. </s>
  <s xml:id="echoid-s5785" xml:space="preserve">Quod ſi locus, ꝗ ignotã longitudinem habet &amp; </s>
  <s xml:id="echoid-s5786" xml:space="preserve">lati <lb/>tudinẽ, Borealior fuerit ̈ ille à q̊ ſitũ certũ ſcire cupis, &amp; </s>
  <s xml:id="echoid-s5787" xml:space="preserve">intercapedo loci notioris etiam <lb/>extiterit maior, quæres ꝑ 74. </s>
  <s xml:id="echoid-s5788" xml:space="preserve">ꝓnunc. </s>
  <s xml:id="echoid-s5789" xml:space="preserve">angulũ poſitiõis locorũ cognitorũ, eũ ſeruabis ſeor-<lb/>ſim, dehinc duces ſinũ argumenti operationis in ſinũ diſtantiæ loci primi uſ ad locum <lb/>ignotum, ꝓductũ uero diuides in totum, ſi iã arcũ q̊tientis addas ad illum antea reſerua-<lb/>tum angulũ poſitionis(quũ iſte prior ſit meridionalis) ſummã quo totã detrahas à ſemi <lb/>
<anchor type="note" xlink:label="note-0073-03a" xlink:href="note-0073-03"/>
circulo, relinquetur angulus poſitionis à primo loco ꝓpoſito uſ ad ignotũ, numerãdo <lb/>â meridiano ſeptentrionali, ſiquidẽ primus angulus poſitionis à meridiano meridionali <lb/>cõputatur, uel econtra. </s>
  <s xml:id="echoid-s5790" xml:space="preserve">Si aũt locus ignotus (qñ cõtingit, ut à loco cognito ad aliũ ꝓfe-<lb/>cto fiat) fuerit Auſtralior, &amp; </s>
  <s xml:id="echoid-s5791" xml:space="preserve">tñ intercapedo locorũ cognitorũ extiterit maior, tunc reſidu <lb/>um ꝓ ipſo angulo poſitionis habebitur, ꝗ à meridiano meridionali numeratur, hoc eſt q̊d <lb/>primo hic in ꝗrendũ erat. </s>
  <s xml:id="echoid-s5792" xml:space="preserve">Deinde duces ſinũ huius reſidui ſiue anguli poſitionis in ſinum <lb/>intercapedinis loci illius cogniti, à quo intercapedo &amp; </s>
  <s xml:id="echoid-s5793" xml:space="preserve">poſitionis angulus computantur <lb/>
<anchor type="note" xlink:label="note-0073-04a" xlink:href="note-0073-04"/>
uſ ad ignotũ, ꝓductum diuides in ſinũ totũ, &amp; </s>
  <s xml:id="echoid-s5794" xml:space="preserve">quotiens dabit inuentũ primum. </s>
  <s xml:id="echoid-s5795" xml:space="preserve">Hinc <lb/>ꝓpone tibi ſinũ cõplementi iſtius inuenti, &amp; </s>
  <s xml:id="echoid-s5796" xml:space="preserve">ſinũ cõplementi intercapedinis illorũ loco-<lb/>
<anchor type="note" xlink:label="note-0073-05a" xlink:href="note-0073-05"/>
rum, numerum minorẽ duc in totũ, &amp; </s>
  <s xml:id="echoid-s5797" xml:space="preserve">ꝓductum diuide in maiorẽ, arcum uero quotientis <lb/>ſubtrahe de 90. </s>
  <s xml:id="echoid-s5798" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5799" xml:space="preserve">remanebit inuentũ ſecundũ, iã porrò duc ſinus cõplementorũ primi &amp; </s>
  <s xml:id="echoid-s5800" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0073-06a" xlink:href="note-0073-06"/>
ſecundi in ſe, &amp; </s>
  <s xml:id="echoid-s5801" xml:space="preserve">ꝓducto in totũ diuiſo, arcus quotientis dabit tibi latitudinẽ loci incogni-<lb/>ti, q̃ ſecunda eſt utilitas ex hoc ꝓnunciato inuento. </s>
  <s xml:id="echoid-s5802" xml:space="preserve">Propterea ſi adhuc ſcire deſideras dif <lb/>ferentiã lõgitudinis, adſume ſinũ cõplementi latitudinis &amp; </s>
  <s xml:id="echoid-s5803" xml:space="preserve">ſinum primi inuenti, minorẽ <lb/>
<anchor type="note" xlink:label="note-0073-07a" xlink:href="note-0073-07"/>
duc in totũ, &amp; </s>
  <s xml:id="echoid-s5804" xml:space="preserve">ꝓductũ diuide in maiorẽ, arcus q̊tiẽtis mõſtrabit differẽtiã lõgitudinũ no <lb/>
<anchor type="note" xlink:label="note-0073-08a" xlink:href="note-0073-08"/>
ti illius loci &amp; </s>
  <s xml:id="echoid-s5805" xml:space="preserve">ignoti, ubi ſi ignotus fuerit occidentalior, tunc ſubtrahe illã differentiã à lõ. <lb/></s>
  <s xml:id="echoid-s5806" xml:space="preserve">gitudine ciuitatis notæ, ſed ſi ſit orientalior, adde eam ad longitudinem notæ ciuitatis, &amp; </s>
  <s xml:id="echoid-s5807" xml:space="preserve"><lb/>habebis longitudinem ignoti loci quo notã &amp; </s>
  <s xml:id="echoid-s5808" xml:space="preserve">perſpectã, at is tertius eſt uſus huius ꝓ <lb/>nunciati. </s>
  <s xml:id="echoid-s5809" xml:space="preserve">?</s>
  <s xml:id="echoid-s5810" xml:space="preserve">?Nunc tandem ad exempla ueniamus. </s>
  <s xml:id="echoid-s5811" xml:space="preserve">Propono igitur mihi tres ciuitates <lb/>Auguſtam, Hieruſalem, &amp; </s>
  <s xml:id="echoid-s5812" xml:space="preserve">Cracouiam Poloniæ, priores duæ mihi notæ ſunt ſecundum <lb/>longitudinem &amp; </s>
  <s xml:id="echoid-s5813" xml:space="preserve">latitudinẽ, quoniã Auguſta habet in longit. </s>
  <s xml:id="echoid-s5814" xml:space="preserve">28. </s>
  <s xml:id="echoid-s5815" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5816" xml:space="preserve">31. </s>
  <s xml:id="echoid-s5817" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5818" xml:space="preserve">in latitudine <lb/>
<anchor type="note" xlink:label="note-0073-09a" xlink:href="note-0073-09"/>
48. </s>
  <s xml:id="echoid-s5819" xml:space="preserve">gra, 20. </s>
  <s xml:id="echoid-s5820" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5821" xml:space="preserve">Hieruſalẽ aũt in longít. </s>
  <s xml:id="echoid-s5822" xml:space="preserve">66. </s>
  <s xml:id="echoid-s5823" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5824" xml:space="preserve">o. </s>
  <s xml:id="echoid-s5825" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5826" xml:space="preserve">in latitudine 301. </s>
  <s xml:id="echoid-s5827" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5828" xml:space="preserve">40. </s>
  <s xml:id="echoid-s5829" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5830" xml:space="preserve">ſed de <lb/>Cracouia nihil mihi conſtat, ne in lõgitudine ne in latitudine, unum hoc experientia <lb/>aut fama didici ab Auguſta uſ ad Cracouiam intereſſe 95. </s>
  <s xml:id="echoid-s5831" xml:space="preserve">miliaria &amp; </s>
  <s xml:id="echoid-s5832" xml:space="preserve">quartã partem
<pb file="0074" n="74" rhead="GENVINVS VSVS"/>
unius, â Cracouia uſ ad Hieruſalẽ ſunt 4 18. </s>
  <s xml:id="echoid-s5833" xml:space="preserve">miliaria Germanica cõmunia unà cũ quar <lb/>
<anchor type="note" xlink:label="note-0074-01a" xlink:href="note-0074-01"/>
ta ꝑte unius miliaris, ab Auguſta uſ ad Hieruſalẽ iã antea cognoui eſſe mili. </s>
  <s xml:id="echoid-s5834" xml:space="preserve">491. </s>
  <s xml:id="echoid-s5835" xml:space="preserve">Hic <lb/>iam principio miliaria cõuerto in gradus &amp; </s>
  <s xml:id="echoid-s5836" xml:space="preserve">minuta, ſic´ inter Auguſtã &amp; </s>
  <s xml:id="echoid-s5837" xml:space="preserve">Cracouiã e-<lb/>runt 6. </s>
  <s xml:id="echoid-s5838" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5839" xml:space="preserve">21. </s>
  <s xml:id="echoid-s5840" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5841" xml:space="preserve">quæ minima eſt intercapedo, inter Cracouiã &amp; </s>
  <s xml:id="echoid-s5842" xml:space="preserve">Hieruſalem ſunt 27. <lb/></s>
  <s xml:id="echoid-s5843" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5844" xml:space="preserve">55. </s>
  <s xml:id="echoid-s5845" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5846" xml:space="preserve">diſtãtia media inter Hieruſalẽ &amp; </s>
  <s xml:id="echoid-s5847" xml:space="preserve">Auguſtã 32. </s>
  <s xml:id="echoid-s5848" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5849" xml:space="preserve">44. </s>
  <s xml:id="echoid-s5850" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5851" xml:space="preserve">intercapedo maxĩa <lb/>media ſubtracta à maxima, relinquit 4. </s>
  <s xml:id="echoid-s5852" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5853" xml:space="preserve">49. </s>
  <s xml:id="echoid-s5854" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5855" xml:space="preserve">ſinus eius eſt 8396. </s>
  <s xml:id="echoid-s5856" xml:space="preserve">dicitur´ differen <lb/>tia prima. </s>
  <s xml:id="echoid-s5857" xml:space="preserve">Cõplemẽtum ipſius eſt 85. </s>
  <s xml:id="echoid-s5858" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5859" xml:space="preserve">16. </s>
  <s xml:id="echoid-s5860" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5861" xml:space="preserve">ſinus aũt 99646. </s>
  <s xml:id="echoid-s5862" xml:space="preserve">cõplementum numerl <lb/>maioris 83. </s>
  <s xml:id="echoid-s5863" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5864" xml:space="preserve">39. </s>
  <s xml:id="echoid-s5865" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5866" xml:space="preserve">cũ ſinu ſuo 99386. </s>
  <s xml:id="echoid-s5867" xml:space="preserve">uocat̃ differentia ſecunda, ſinũ huius differen-<lb/>tiæ ſecundæ ſubtraho â ſinu cõplementi differẽtiæ primæ. </s>
  <s xml:id="echoid-s5868" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5869" xml:space="preserve">99386. </s>
  <s xml:id="echoid-s5870" xml:space="preserve">â 99646. </s>
  <s xml:id="echoid-s5871" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5872" xml:space="preserve">relinquun <lb/>tur 260. </s>
  <s xml:id="echoid-s5873" xml:space="preserve">ea duco in ſinum cõplementi maioris intercapedinis. </s>
  <s xml:id="echoid-s5874" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5875" xml:space="preserve">84113. </s>
  <s xml:id="echoid-s5876" xml:space="preserve">ꝓductũ diuido in <lb/>ſinum maioris diſtãtiæ. </s>
  <s xml:id="echoid-s5877" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5878" xml:space="preserve">53975. </s>
  <s xml:id="echoid-s5879" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5880" xml:space="preserve">q̊tiens dabit 405. </s>
  <s xml:id="echoid-s5881" xml:space="preserve">idipſum addo ad ſinũ differentiæ <lb/>primæ, unde reſultabũt 8801. </s>
  <s xml:id="echoid-s5882" xml:space="preserve">nume℞ hunc in ſe duco quadrate, &amp; </s>
  <s xml:id="echoid-s5883" xml:space="preserve">erit q̃ @dratũ 77457601. </s>
  <s xml:id="echoid-s5884" xml:space="preserve"><lb/>ſimiliter quadratus etiã ſinus ſecundæ differentiæ. </s>
  <s xml:id="echoid-s5885" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5886" xml:space="preserve">99386. </s>
  <s xml:id="echoid-s5887" xml:space="preserve">ꝓducet ex ſe 9877576996, u-<lb/>trun ſi in ſummã unã addidero, ꝓuenient 9955034597. </s>
  <s xml:id="echoid-s5888" xml:space="preserve">hinc totius ſummæ quæro radi <lb/>cem quæ eſt 99774. </s>
  <s xml:id="echoid-s5889" xml:space="preserve">arcus eius 86. </s>
  <s xml:id="echoid-s5890" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5891" xml:space="preserve">9. </s>
  <s xml:id="echoid-s5892" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5893" xml:space="preserve">cõplemẽtum uero 3. </s>
  <s xml:id="echoid-s5894" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5895" xml:space="preserve">51. </s>
  <s xml:id="echoid-s5896" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5897" xml:space="preserve">argumentũ <lb/>illud operatiõis. </s>
  <s xml:id="echoid-s5898" xml:space="preserve">Sinum ſuum 6714. </s>
  <s xml:id="echoid-s5899" xml:space="preserve">duco in totũ, ꝓductum diuido in ſinum intercapedi-<lb/>nis Auguſtanæ et Cracouieñ. </s>
  <s xml:id="echoid-s5900" xml:space="preserve">q̃eſt 6. </s>
  <s xml:id="echoid-s5901" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5902" xml:space="preserve">21. </s>
  <s xml:id="echoid-s5903" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5904" xml:space="preserve">ſinus uero 11060. </s>
  <s xml:id="echoid-s5905" xml:space="preserve">q̊tiens 60705. </s>
  <s xml:id="echoid-s5906" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5907" xml:space="preserve">arcus <lb/>37. </s>
  <s xml:id="echoid-s5908" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5909" xml:space="preserve">23. </s>
  <s xml:id="echoid-s5910" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5911" xml:space="preserve">ĳs additis ad angulum poſitiõnis ab Auguſta uſ in Hieruſalem, quem in <lb/>74. </s>
  <s xml:id="echoid-s5912" xml:space="preserve">ꝓnunc. </s>
  <s xml:id="echoid-s5913" xml:space="preserve">inueni eſſe 73. </s>
  <s xml:id="echoid-s5914" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5915" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5916" xml:space="preserve">18. </s>
  <s xml:id="echoid-s5917" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5918" xml:space="preserve">ſumma q̊ illa ſubducta à ſemicirculo, remanent <lb/>69. </s>
  <s xml:id="echoid-s5919" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5920" xml:space="preserve">19. </s>
  <s xml:id="echoid-s5921" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5922" xml:space="preserve">angulus ille poſitionis à meridiano ſeptentrionali uerſus ortum, ab Augu <lb/>ſta Cracouiã uerſus cõputando, &amp; </s>
  <s xml:id="echoid-s5923" xml:space="preserve">hoc eſt q̊d primo erat inquirendũ. </s>
  <s xml:id="echoid-s5924" xml:space="preserve">Deinceps anguli il <lb/>lius ſinum 93554. </s>
  <s xml:id="echoid-s5925" xml:space="preserve">duco in ſinum diſtãtiæ Cracouienſis ab Auguſta. </s>
  <s xml:id="echoid-s5926" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5927" xml:space="preserve">11060. </s>
  <s xml:id="echoid-s5928" xml:space="preserve">ꝓductũ di-<lb/>
<anchor type="note" xlink:label="note-0074-02a" xlink:href="note-0074-02"/>
uido in totum, quotiens eſt 10347. </s>
  <s xml:id="echoid-s5929" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5930" xml:space="preserve">dicitur inuentum primum. </s>
  <s xml:id="echoid-s5931" xml:space="preserve">Adhuc duco ſinum cõ-<lb/>plementi diſtãtiæ Cracouiæ ab Auguſta. </s>
  <s xml:id="echoid-s5932" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5933" xml:space="preserve">99386. </s>
  <s xml:id="echoid-s5934" xml:space="preserve">in totum, &amp; </s>
  <s xml:id="echoid-s5935" xml:space="preserve">productum diuido in ſi-<lb/>num cõplementi primi inuenti. </s>
  <s xml:id="echoid-s5936" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5937" xml:space="preserve">99464. </s>
  <s xml:id="echoid-s5938" xml:space="preserve">quotiens dabit 99921. </s>
  <s xml:id="echoid-s5939" xml:space="preserve">arcus eius eſt 87. </s>
  <s xml:id="echoid-s5940" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5941" xml:space="preserve">44. <lb/></s>
  <s xml:id="echoid-s5942" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5943" xml:space="preserve">is´ de 90. </s>
  <s xml:id="echoid-s5944" xml:space="preserve">ſublatus, relinꝗt ex ſe 2. </s>
  <s xml:id="echoid-s5945" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5946" xml:space="preserve">16. </s>
  <s xml:id="echoid-s5947" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5948" xml:space="preserve">inuentũ puta ſecundũ. </s>
  <s xml:id="echoid-s5949" xml:space="preserve">Porrô inde ſub-<lb/>
<anchor type="note" xlink:label="note-0074-03a" xlink:href="note-0074-03"/>
traho arcũ ſecundi inuenti â cõplemento latitudinis Auguſtæ.</s>
  <s xml:id="echoid-s5950" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5951" xml:space="preserve">41. </s>
  <s xml:id="echoid-s5952" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5953" xml:space="preserve">40. </s>
  <s xml:id="echoid-s5954" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5955" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5956" xml:space="preserve">rema-<lb/>nent 39. </s>
  <s xml:id="echoid-s5957" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5958" xml:space="preserve">24. </s>
  <s xml:id="echoid-s5959" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5960" xml:space="preserve">ſinum cõplementi huiusreſidui. </s>
  <s xml:id="echoid-s5961" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5962" xml:space="preserve">77273. </s>
  <s xml:id="echoid-s5963" xml:space="preserve">duco in ſinum cõplementi <lb/>primi inuenti. </s>
  <s xml:id="echoid-s5964" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5965" xml:space="preserve">99464. </s>
  <s xml:id="echoid-s5966" xml:space="preserve">ꝓductum diuido in ſinũ totum, &amp; </s>
  <s xml:id="echoid-s5967" xml:space="preserve">q̊tiens erit 76858. </s>
  <s xml:id="echoid-s5968" xml:space="preserve">arcus eius <lb/>
<anchor type="note" xlink:label="note-0074-04a" xlink:href="note-0074-04"/>
50. </s>
  <s xml:id="echoid-s5969" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5970" xml:space="preserve">13. </s>
  <s xml:id="echoid-s5971" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5972" xml:space="preserve">eſt ipſa latitudo Cracouiæ quæſita. </s>
  <s xml:id="echoid-s5973" xml:space="preserve">Etiamnũ iñ ſcienda mihi eſt differen-<lb/>tia lõgitudinis inter meridianũ Auguſteñ. </s>
  <s xml:id="echoid-s5974" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5975" xml:space="preserve">Crocouieñ. </s>
  <s xml:id="echoid-s5976" xml:space="preserve">ideo duco ſinum primi inuenti <lb/>. </s>
  <s xml:id="echoid-s5977" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5978" xml:space="preserve">10343. </s>
  <s xml:id="echoid-s5979" xml:space="preserve">in totum, &amp; </s>
  <s xml:id="echoid-s5980" xml:space="preserve">diuido ꝓductũ in ſinũ cõplementi latitudinis iã inuenti. </s>
  <s xml:id="echoid-s5981" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5982" xml:space="preserve">64010. <lb/></s>
  <s xml:id="echoid-s5983" xml:space="preserve">q̊tiens ꝓducit 16164. </s>
  <s xml:id="echoid-s5984" xml:space="preserve">cuius eſt 9. </s>
  <s xml:id="echoid-s5985" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5986" xml:space="preserve">19. </s>
  <s xml:id="echoid-s5987" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5988" xml:space="preserve">ea´ differentia eſt longitudinis. </s>
  <s xml:id="echoid-s5989" xml:space="preserve">Et ꝗa Cra <lb/>couia orientalior eſt ̈ Auguſta, addo illã differentiã ad latitudinem Auguſteñ. </s>
  <s xml:id="echoid-s5990" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s5991" xml:space="preserve">28. </s>
  <s xml:id="echoid-s5992" xml:space="preserve">gr. </s>
  <s xml:id="echoid-s5993" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0074-05a" xlink:href="note-0074-05"/>
31. </s>
  <s xml:id="echoid-s5994" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s5995" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5996" xml:space="preserve">erunt Cracouiæ 37. </s>
  <s xml:id="echoid-s5997" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s5998" xml:space="preserve">50. </s>
  <s xml:id="echoid-s5999" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6000" xml:space="preserve">longitudinis, ſic iam tria illa ex unico pronun-<lb/>ciato inueni, quæ ſcitu uidebantur neceſſaria. </s>
  <s xml:id="echoid-s6001" xml:space="preserve">Si ꝓnunciatum hoc ꝓdignitate, &amp; </s>
  <s xml:id="echoid-s6002" xml:space="preserve">ut res <lb/>ipſa exigit, tractãdum hic mihi fuiſſet, multa erãt adĳcienda, q̃ operæprecium ſuerat ſcire <lb/>ueruntamen ea in alium locum reĳcimus, ubi illa plenius &amp; </s>
  <s xml:id="echoid-s6003" xml:space="preserve">fuſius explicabuntur, inte-<lb/>rim ĳs fruere fœliciter, ſatis´ ſit, cogitandi occaſionem ampliorem tibi obtuliſſe.</s>
  <s xml:id="echoid-s6004" xml:space="preserve"/>
</p>
<div xml:id="echoid-div171" type="float" level="2" n="1">
<note position="right" xlink:label="note-0073-02" xlink:href="note-0073-02a" xml:space="preserve"><emph style="it">Areatim il</emph> <lb/><emph style="it">lud cx qua-</emph> <lb/><emph style="it">drãte diſces</emph></note>
<note position="right" xlink:label="note-0073-03" xlink:href="note-0073-03a" xml:space="preserve"><emph style="it">Lateraliter</emph></note>
<note position="right" xlink:label="note-0073-04" xlink:href="note-0073-04a" xml:space="preserve"><emph style="it">Later aliter</emph></note>
<note position="right" xlink:label="note-0073-05" xlink:href="note-0073-05a" xml:space="preserve"><emph style="it">Areatim.</emph></note>
<note position="right" xlink:label="note-0073-06" xlink:href="note-0073-06a" xml:space="preserve"><emph style="it">Later aliter</emph></note>
<note position="right" xlink:label="note-0073-07" xlink:href="note-0073-07a" xml:space="preserve"><emph style="it">Areatim</emph></note>
<note position="right" xlink:label="note-0073-08" xlink:href="note-0073-08a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">de Auguſta</emph> <lb/><emph style="it">Hieruſalem</emph> <lb/><emph style="it">&amp; Craco-</emph> <lb/><emph style="it">uia.</emph></note>
<note position="right" xlink:label="note-0073-09" xlink:href="note-0073-09a" xml:space="preserve"><emph style="it">Diſtãtia in</emph> <lb/><emph style="it">ter Augu-</emph> <lb/><emph style="it">ſtam &amp;</emph> <lb/><emph style="it">Cracoui@.</emph></note>
<note position="left" xlink:label="note-0074-01" xlink:href="note-0074-01a" xml:space="preserve"><emph style="it">Diſtãtia in</emph> <lb/><emph style="it">ter Craco-</emph> <lb/><emph style="it">uiam &amp;</emph> <lb/><emph style="it">Hicruſalẽ.</emph></note>
<note position="left" xlink:label="note-0074-02" xlink:href="note-0074-02a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">primum.</emph></note>
<note position="left" xlink:label="note-0074-03" xlink:href="note-0074-03a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">ſecundum.</emph></note>
<note position="left" xlink:label="note-0074-04" xlink:href="note-0074-04a" xml:space="preserve"><emph style="it">Latitudo</emph> <lb/><emph style="it">Cracouien-</emph> <lb/><emph style="it">ſis eſt gra.</emph> <lb/><emph style="it">50. mi. 13.</emph></note>
<note position="left" xlink:label="note-0074-05" xlink:href="note-0074-05a" xml:space="preserve"><emph style="it">Longitudo</emph> <lb/><emph style="it">Cracouien-</emph> <lb/><emph style="it">ſis eſt gra.</emph> <lb/><emph style="it">37. mi. 50.</emph></note>
</div>
</div>
<div xml:id="echoid-div173" type="section" level="1" n="90">
<head xml:id="echoid-head94" xml:space="preserve">PRONVNCIATVM LXXVIII.</head>
<p>
  <s xml:id="echoid-s6005" xml:space="preserve">Arcum circuli uerticalis cõcluſum inter meridianũ &amp; </s>
  <s xml:id="echoid-s6006" xml:space="preserve">circulũ poſitiõis alicu <lb/>ius ſtellę ſiue puncti in cœlo extra eclypticã, uel in ea cõſiderarc &amp; </s>
  <s xml:id="echoid-s6007" xml:space="preserve">agnoſcere.</s>
  <s xml:id="echoid-s6008" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s6009" xml:space="preserve">Non hic iſtũ uolo angulũ poſitiõis de q̊ hactenus egi, ſed aliud quiddã eſt hic circulus <lb/>
<anchor type="note" xlink:label="note-0074-06a" xlink:href="note-0074-06"/>
poſitionis, puta ſi duxero ab interſectiõe meridiani &amp; </s>
  <s xml:id="echoid-s6010" xml:space="preserve">horizontis in parte meridionali cir <lb/>culum maiorẽ per corpus ſolare, aut alterius ſtellæ ubicun poſitæ, ſub uel ſupra horizõ <lb/>tem, uſ ad alterã interſectionẽ meridiani &amp; </s>
  <s xml:id="echoid-s6011" xml:space="preserve">horizõtis in ꝑte ſeptentrionali. </s>
  <s xml:id="echoid-s6012" xml:space="preserve">Deinde ſi <lb/>ex polo mundi alium circulũ maiorẽ ducã uerſus hunc circulũ, ſuꝑ quẽ ille cadat directe <lb/>ad angulos rectos ſphærales, quotq̊t iã gradus intercepti ſunt in illo circulo inter polum <lb/>mundi, &amp; </s>
  <s xml:id="echoid-s6013" xml:space="preserve">circulum poſitionis, idipſum ſanè uocat̃ altitudo poli ſuꝑ ſemicirculũ poſitiõis. <lb/></s>
  <s xml:id="echoid-s6014" xml:space="preserve">At hic operæpreciũ eſt noſſe declinationẽ ſtellæ ſiue pũctiunà cũ diſtãtia à meridiano. </s>
  <s xml:id="echoid-s6015" xml:space="preserve"><lb/>ea ſi minor eſt ̈ 90. </s>
  <s xml:id="echoid-s6016" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6017" xml:space="preserve">declinatio ſeptentrionalis, ſiue tũc punctũ iſtud tempore obſerua <lb/>tionis à meridiano fuerit uerſus ortũ ſiue occaſum, tunciam ducito ſinum complement@
<pb file="0075" n="75" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
declinationis in ſinum diſtantiæ à meridiano, ꝓductũ diuide in totum, arcus quotientis <lb/>
<anchor type="note" xlink:label="note-0075-01a" xlink:href="note-0075-01"/>
dicetur inuentũ primũ. </s>
  <s xml:id="echoid-s6018" xml:space="preserve">Mox duc &amp; </s>
  <s xml:id="echoid-s6019" xml:space="preserve">ſinũ minorẽ ex ſinu cõplementi huius primi inuenti <lb/>&amp; </s>
  <s xml:id="echoid-s6020" xml:space="preserve">ſinu declinationis ſtellæ uel propoſiti in totũ, ꝓductũ diuide in maiorẽ, &amp; </s>
  <s xml:id="echoid-s6021" xml:space="preserve">arcũ quoti-<lb/>entis ſubtrahe de 90. </s>
  <s xml:id="echoid-s6022" xml:space="preserve">reliquũ adde ad altitudinem poli tuæ regiõis, &amp; </s>
  <s xml:id="echoid-s6023" xml:space="preserve">habebis inuentũ ſe <lb/>cundũ. </s>
  <s xml:id="echoid-s6024" xml:space="preserve">Deinde ducito ſinus utriuſ cõplementi in ſe, ꝓductũ diuide in totũ, arcum quoti <lb/>
<anchor type="note" xlink:label="note-0075-02a" xlink:href="note-0075-02"/>
entis ſubduc de 90. </s>
  <s xml:id="echoid-s6025" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6026" xml:space="preserve">ſi ſecundũ inuentũ ſit minus ̈ 90. </s>
  <s xml:id="echoid-s6027" xml:space="preserve">remanebit tibi inuentũ tertium, <lb/>ſi aũt plus 90. </s>
  <s xml:id="echoid-s6028" xml:space="preserve">fuerit, adhuc adde arcũ quotientis, &amp; </s>
  <s xml:id="echoid-s6029" xml:space="preserve">habebis inuentũ tertium. </s>
  <s xml:id="echoid-s6030" xml:space="preserve">Porrò ad-<lb/>huc ꝓpone tibi ſinũ inuentorũ primi &amp; </s>
  <s xml:id="echoid-s6031" xml:space="preserve">tertĳ, minorẽ exĳs duc in totum, &amp; </s>
  <s xml:id="echoid-s6032" xml:space="preserve">productũ di-<lb/>uide in maiorem, arcus q̊tientis dabit portionẽ circuli uerticalis inter uerticẽ capitis &amp; </s>
  <s xml:id="echoid-s6033" xml:space="preserve"><lb/>circulum poſitionis interceptũ quẽ quærebas. </s>
  <s xml:id="echoid-s6034" xml:space="preserve">Sed ſi diſtantia puncti ꝓpoſiti uel ſtellæ à <lb/>
<anchor type="note" xlink:label="note-0075-03a" xlink:href="note-0075-03"/>
meridiano præciſe fuerit 90. </s>
  <s xml:id="echoid-s6035" xml:space="preserve">graduũ, tunc cõplementũ declinationis erit inuentũ primũ, <lb/>&amp; </s>
  <s xml:id="echoid-s6036" xml:space="preserve">latitudo regionis inuentũ ſecundũ, tertiũ uero inuenies ut antea, ſimiliter &amp; </s>
  <s xml:id="echoid-s6037" xml:space="preserve">arcũ quæ-<lb/>ſitum. </s>
  <s xml:id="echoid-s6038" xml:space="preserve">Quod ſi qũt diſtantia à meridiano maior fuerit ̈ 90. </s>
  <s xml:id="echoid-s6039" xml:space="preserve">ſubtrahe eam de ſemicirculo <lb/>ſinum quo cõplementi duc in ſinum cõplementi declinationis, ꝓductũ diuide in ſinum <lb/>
<anchor type="note" xlink:label="note-0075-04a" xlink:href="note-0075-04"/>
totũ, &amp; </s>
  <s xml:id="echoid-s6040" xml:space="preserve">quotiens dabit inuentũ primũ, cuius cõplementũ ſimul &amp; </s>
  <s xml:id="echoid-s6041" xml:space="preserve">ſinũ declinationis ſtel-<lb/>læ ſi tibi proponas, minorem uero nume℞ ducas in totum, diuidas aũt ꝓductum in maio <lb/>rem, &amp; </s>
  <s xml:id="echoid-s6042" xml:space="preserve">arcum quotientis ſubtrahas de 90. </s>
  <s xml:id="echoid-s6043" xml:space="preserve">ſimiliter &amp; </s>
  <s xml:id="echoid-s6044" xml:space="preserve">reſiduũ de latitudine regiõis, rema-<lb/>nebit inuentũ ſecundũ. </s>
  <s xml:id="echoid-s6045" xml:space="preserve">Mox ꝓcede hic, ut antea edoctus es, quãdo diſtãtia ſtellæ minor <lb/>
<anchor type="note" xlink:label="note-0075-05a" xlink:href="note-0075-05"/>
erat ̈ 90. </s>
  <s xml:id="echoid-s6046" xml:space="preserve">Operæpreciũ q̊ eſt ſcire, ꝙ qñ inuentũ ſecundũ maius eſt ̈ 90. </s>
  <s xml:id="echoid-s6047" xml:space="preserve">tunc etiã ter-<lb/>tium erit amplius eo, at ſi ita contingat, tũc ſubtrahe inuentũ tertiũ de ſemicirculo, &amp; </s>
  <s xml:id="echoid-s6048" xml:space="preserve"><lb/>inuentũ primũ etiã paulò diligẽtius cõſidera, numerũ´ minorẽ duc in totũ, &amp; </s>
  <s xml:id="echoid-s6049" xml:space="preserve">productũ <lb/>
<anchor type="note" xlink:label="note-0075-06a" xlink:href="note-0075-06"/>
diuide in maiorẽ, arcus quotientis dabit arcũ circuli uerticalis quæſitũ. </s>
  <s xml:id="echoid-s6050" xml:space="preserve">Fieri etiã poteſt, ut <lb/>inuentũ ſecundũ ſit quadra circuli, &amp; </s>
  <s xml:id="echoid-s6051" xml:space="preserve">tũc quo inuentũ tertiũ erit quadra circuli, at ſic <lb/>inuento primo habito, nõ eſt ꝙ amplius oꝑeris, ſiquidẽ illud ipſum inuentũ primũ eſt ar-<lb/>cus circuli uerticalis quæſitus. </s>
  <s xml:id="echoid-s6052" xml:space="preserve">Ethactenus ꝗdem diſſeruimus de ſtellis &amp; </s>
  <s xml:id="echoid-s6053" xml:space="preserve">punctis, quæ <lb/>declinationẽ habent ſeptentrionalẽ, nunc reliquũ eſt &amp; </s>
  <s xml:id="echoid-s6054" xml:space="preserve">de ĳsdicere quæ meridionalem <lb/>habent declinationẽ, ibi tu duc ſinum declinationis ſtellæ in ſinũ diſtantiæ ſtellæ à meri-<lb/>
<anchor type="note" xlink:label="note-0075-07a" xlink:href="note-0075-07"/>
diano, productũ diuide in ſinũ ꝑfectũ, arcus q̊tientis erit inuentũ primũ. </s>
  <s xml:id="echoid-s6055" xml:space="preserve">Deinde uter ſi-<lb/>nus fuerit maior ex cõplemento huius inuenti &amp; </s>
  <s xml:id="echoid-s6056" xml:space="preserve">declinationis, ducatur in totum, &amp; </s>
  <s xml:id="echoid-s6057" xml:space="preserve">diui <lb/>datur in alte℞. </s>
  <s xml:id="echoid-s6058" xml:space="preserve">A cõplemẽto quotientis huius ſubtrahe latitudinẽ regiõis, &amp; </s>
  <s xml:id="echoid-s6059" xml:space="preserve">manebit in-<lb/>uentum ſecundũ. </s>
  <s xml:id="echoid-s6060" xml:space="preserve">Vtriuſ huius inuẽti cõplementa duc in ſe, ꝓductũ in totũ ſinũ diuide, <lb/>&amp; </s>
  <s xml:id="echoid-s6061" xml:space="preserve">cõplementũ huius quotientis oſtendit inuentũ tertiũ, ſi iam minorẽ ſinũ primi inuen-<lb/>ti &amp; </s>
  <s xml:id="echoid-s6062" xml:space="preserve">tertĳ ducas in totum, ꝓductũ uero diuidas in maiorẽ, arcus quotientis oſtendet arcũ <lb/>
<anchor type="note" xlink:label="note-0075-08a" xlink:href="note-0075-08"/>
circuli uerticalis optatũ, &amp; </s>
  <s xml:id="echoid-s6063" xml:space="preserve">hactenus tam operoſe quæſitum. </s>
  <s xml:id="echoid-s6064" xml:space="preserve">Si aũt declinatio nulla eſt <lb/>ſtellæ uel puncti ab æquinoctiali, tunc inuentũ primũ ſit tibi diſtantia ſtellæ uel puncti à <lb/>meridiano, &amp; </s>
  <s xml:id="echoid-s6065" xml:space="preserve">inuentum ſecundũ erit cõplementũ altitudinis poli, tertium uero acquires, <lb/>ſi ſinum altitudinis poli ducas in ſinũ cõplementi diſtantiæ à meridiano, diuidas aũt in ſi-<lb/>
<anchor type="note" xlink:label="note-0075-09a" xlink:href="note-0075-09"/>
num ꝑfectũ, tunc tibi cõplementũ q̊tientis dabit inuentũ tertiũ. </s>
  <s xml:id="echoid-s6066" xml:space="preserve">Iam ſi minorem nurr e℞ <lb/>
<anchor type="note" xlink:label="note-0075-10a" xlink:href="note-0075-10"/>
ex inuento tertio &amp; </s>
  <s xml:id="echoid-s6067" xml:space="preserve">diſtãtia à meridiano ducas in totũ, &amp; </s>
  <s xml:id="echoid-s6068" xml:space="preserve">diuidas in maiorem, tunc arcus <lb/>quotientis ꝓducet arcũ circuli uerticalis inter zenith &amp; </s>
  <s xml:id="echoid-s6069" xml:space="preserve">circulũ poſitionis, qui tranſit per <lb/>
<anchor type="note" xlink:label="note-0075-11a" xlink:href="note-0075-11"/>
locum ſtellæ. </s>
  <s xml:id="echoid-s6070" xml:space="preserve">?</s>
  <s xml:id="echoid-s6071" xml:space="preserve">?Exempli loco quæram ecce in ipſo loco intronizatiõis arcum circuli <lb/>uerticalis inter zenith ſiue polum horizontis &amp; </s>
  <s xml:id="echoid-s6072" xml:space="preserve">circulum poſitiõis, qui per locũ Solis du <lb/>citur, ad horã intronizatiõis, quæ ꝗa facta eſt hora 9 ante meridiẽ ſatis fœliciter, Sol tũc <lb/>fuit in 2. </s>
  <s xml:id="echoid-s6073" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6074" xml:space="preserve">26. </s>
  <s xml:id="echoid-s6075" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6076" xml:space="preserve">II, duco igit̃ ſinum cõplementi declinatiõis loci ☉(sun). </s>
  <s xml:id="echoid-s6077" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s6078" xml:space="preserve">93544. </s>
  <s xml:id="echoid-s6079" xml:space="preserve">in ſinũ <lb/>diſtãtiæ ☉(sun) à meridie. </s>
  <s xml:id="echoid-s6080" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s6081" xml:space="preserve">70710. </s>
  <s xml:id="echoid-s6082" xml:space="preserve">ꝓductũ in totũ diuiſo, remanẽt 66145. </s>
  <s xml:id="echoid-s6083" xml:space="preserve">inuentũ illud pri-<lb/>mũ, cuius cõplementũ eſt 48. </s>
  <s xml:id="echoid-s6084" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6085" xml:space="preserve">35. </s>
  <s xml:id="echoid-s6086" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6087" xml:space="preserve">ſinus uero 74991. </s>
  <s xml:id="echoid-s6088" xml:space="preserve">Nunciã duco ſinũ declinatio <lb/>
<anchor type="note" xlink:label="note-0075-12a" xlink:href="note-0075-12"/>
nis 35347. </s>
  <s xml:id="echoid-s6089" xml:space="preserve">ꝗa minorẽ in totũ, &amp; </s>
  <s xml:id="echoid-s6090" xml:space="preserve">ꝓductum diuido in linũ cõplementi primi inuenti, ꝓue-<lb/>nient in q̊tiente 47135. </s>
  <s xml:id="echoid-s6091" xml:space="preserve">arcus eius eſt 28. </s>
  <s xml:id="echoid-s6092" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6093" xml:space="preserve">8. </s>
  <s xml:id="echoid-s6094" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6095" xml:space="preserve">is de 90. </s>
  <s xml:id="echoid-s6096" xml:space="preserve">ſubductus, relinꝗt 61. </s>
  <s xml:id="echoid-s6097" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6098" xml:space="preserve">52 <lb/>mi. </s>
  <s xml:id="echoid-s6099" xml:space="preserve">ĳs addo altitudinem poli.</s>
  <s xml:id="echoid-s6100" xml:space="preserve">ſ.</s>
  <s xml:id="echoid-s6101" xml:space="preserve">48. </s>
  <s xml:id="echoid-s6102" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6103" xml:space="preserve">20. </s>
  <s xml:id="echoid-s6104" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6105" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6106" xml:space="preserve">erit ſumma 110. </s>
  <s xml:id="echoid-s6107" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6108" xml:space="preserve">12. </s>
  <s xml:id="echoid-s6109" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6110" xml:space="preserve">dicetur´ in-<lb/>uentum ſecundum, q̊d ꝗa maius eſt ̈ 90. </s>
  <s xml:id="echoid-s6111" xml:space="preserve">ſubtraho de ſemicirculo, &amp; </s>
  <s xml:id="echoid-s6112" xml:space="preserve">remanent 69. </s>
  <s xml:id="echoid-s6113" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s6114" xml:space="preserve">48. </s>
  <s xml:id="echoid-s6115" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6116" xml:space="preserve">Cõplementũ eſt 20. </s>
  <s xml:id="echoid-s6117" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6118" xml:space="preserve">12. </s>
  <s xml:id="echoid-s6119" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6120" xml:space="preserve">cuius ſinum 34529. </s>
  <s xml:id="echoid-s6121" xml:space="preserve">duco in ſinum cõplementi in-<lb/>uenti primi 48. </s>
  <s xml:id="echoid-s6122" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6123" xml:space="preserve">35. </s>
  <s xml:id="echoid-s6124" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6125" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s6126" xml:space="preserve">74991. </s>
  <s xml:id="echoid-s6127" xml:space="preserve">ꝓductum diuido in totum, &amp; </s>
  <s xml:id="echoid-s6128" xml:space="preserve">in q̊tiente, pdeũt 25904 <lb/>arcus eius eſt 15. </s>
  <s xml:id="echoid-s6129" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6130" xml:space="preserve">cue addo 90. </s>
  <s xml:id="echoid-s6131" xml:space="preserve">gradus(eo ꝙ inuentũ ſecundũ quadrãte maius eſt) pro
<pb file="0076" n="76" rhead="GENVINVS VSVS"/>
ducetur inuentum tertium, ſcilicet 105. </s>
  <s xml:id="echoid-s6132" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6133" xml:space="preserve">quod ſemper etiam maius eſt 90. </s>
  <s xml:id="echoid-s6134" xml:space="preserve">ſiquidẽ ſe-<lb/>cundum eo eſt maius, ſubduco igitur inuentum hoc de ſemicirculo. </s>
  <s xml:id="echoid-s6135" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6136" xml:space="preserve">remanent in reſi-<lb/>duo 75. </s>
  <s xml:id="echoid-s6137" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6138" xml:space="preserve">ſinus eius eſt 96592, qui quia maior etiã diuiſor eſt, iam duco ſinũ primi in-<lb/>uenti. </s>
  <s xml:id="echoid-s6139" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s6140" xml:space="preserve">66145. </s>
  <s xml:id="echoid-s6141" xml:space="preserve">in totũ, &amp; </s>
  <s xml:id="echoid-s6142" xml:space="preserve">productũ diuido in ipſum diuiſorẽ, ꝓueniẽt in q̊tiente 68479. <lb/></s>
  <s xml:id="echoid-s6143" xml:space="preserve">cuius arcus eſt 43. </s>
  <s xml:id="echoid-s6144" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6145" xml:space="preserve">13. </s>
  <s xml:id="echoid-s6146" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6147" xml:space="preserve">arcus ille circuli uerticalis inter zenith &amp; </s>
  <s xml:id="echoid-s6148" xml:space="preserve">circulum poſitio <lb/>nis tranſeuntem per corpus Solis. </s>
  <s xml:id="echoid-s6149" xml:space="preserve">Verum hæc quæ diximus omnia, de ſtellis &amp; </s>
  <s xml:id="echoid-s6150" xml:space="preserve">punctis <lb/>illis uera ſunt, quæ ſupra horizontem cõſpiciuntur: </s>
  <s xml:id="echoid-s6151" xml:space="preserve">ſin a ũt ſub horizonte fuerint, tunc ti <lb/>bi propone punctum diametraliter ei oppoſitum, ut ſi uelim ſcire, quantum circulus poſi <lb/>tionũſub terra, qui ꝑ 2. </s>
  <s xml:id="echoid-s6152" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6153" xml:space="preserve">26. </s>
  <s xml:id="echoid-s6154" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6155" xml:space="preserve">♐ ducitur, à zenith diſtet, adſumo tũc mihi. </s>
  <s xml:id="echoid-s6156" xml:space="preserve">2. </s>
  <s xml:id="echoid-s6157" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6158" xml:space="preserve">26. </s>
  <s xml:id="echoid-s6159" xml:space="preserve"><lb/>mi. </s>
  <s xml:id="echoid-s6160" xml:space="preserve">II, &amp; </s>
  <s xml:id="echoid-s6161" xml:space="preserve">cũ eo ꝓcedo per oĩa operando ut ſupra, &amp; </s>
  <s xml:id="echoid-s6162" xml:space="preserve">ꝓdibit tandem mihi quæſitum.</s>
  <s xml:id="echoid-s6163" xml:space="preserve"/>
</p>
<div xml:id="echoid-div173" type="float" level="2" n="1">
<note position="left" xlink:label="note-0074-06" xlink:href="note-0074-06a" xml:space="preserve"><emph style="it">Circulus po</emph> <lb/><emph style="it">ſitionis ꝗd,</emph> <lb/><emph style="it">&amp; quomo</emph> <lb/><emph style="it">do imagi-</emph> <lb/><emph style="it">nandus ſit.</emph> <lb/><emph style="it">Qũo altitu</emph> <lb/><emph style="it">do poli ſuꝑ</emph> <lb/><emph style="it">ſemicirculũ</emph> <lb/><emph style="it">poſitiõis ſit</emph> <lb/><emph style="it">un aginãda</emph></note>
<note position="right" xlink:label="note-0075-01" xlink:href="note-0075-01a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">primum</emph> <lb/><emph style="it">ex lateri in</emph> <lb/><emph style="it">greſſu de-</emph> <lb/><emph style="it">prehẽſum.</emph></note>
<note position="right" xlink:label="note-0075-02" xlink:href="note-0075-02a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">ſecundum,</emph> <lb/><emph style="it">ſecũdũ are-</emph> <lb/><emph style="it">am aſſeque</emph> <lb/><emph style="it">ris.</emph></note>
<note position="right" xlink:label="note-0075-03" xlink:href="note-0075-03a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">tertium ex</emph> <lb/><emph style="it">lateribus</emph> <lb/><emph style="it">patet.</emph></note>
<note position="right" xlink:label="note-0075-04" xlink:href="note-0075-04a" xml:space="preserve"><emph style="it">Introitus d</emph> <lb/><emph style="it">realis quæ</emph> <lb/><emph style="it">ſitum oſten</emph> <lb/><emph style="it">dit.</emph></note>
<note position="right" xlink:label="note-0075-05" xlink:href="note-0075-05a" xml:space="preserve"><emph style="it">Inucntum</emph> <lb/><emph style="it">primum ꝑ</emph> <lb/><emph style="it">latera ad-</emph> <lb/><emph style="it">diſces.</emph></note>
<note position="right" xlink:label="note-0075-06" xlink:href="note-0075-06a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">ſecundum</emph> <lb/><emph style="it">areatim de</emph> <lb/><emph style="it">prebendis.</emph> <lb/><emph style="it">Operatio</emph> <lb/><emph style="it">arcalis.</emph></note>
<note position="right" xlink:label="note-0075-07" xlink:href="note-0075-07a" xml:space="preserve"><emph style="it">De ſtellis et</emph> <lb/><emph style="it">punctis ha</emph> <lb/><emph style="it">bentibus de</emph> <lb/><emph style="it">clinationẽ</emph> <lb/><emph style="it">meridionæ</emph> <lb/><emph style="it">lem.</emph></note>
<note position="right" xlink:label="note-0075-08" xlink:href="note-0075-08a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">primum ꝑ</emph> <lb/><emph style="it">areã inſpie</emph> <lb/><emph style="it">ads.</emph></note>
<note position="right" xlink:label="note-0075-09" xlink:href="note-0075-09a" xml:space="preserve"><emph style="it">Inuentũ ſe@</emph> <lb/><emph style="it">cundum.</emph></note>
<note position="right" xlink:label="note-0075-10" xlink:href="note-0075-10a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">tertim.</emph></note>
<note position="right" xlink:label="note-0075-11" xlink:href="note-0075-11a" xml:space="preserve"><emph style="it">De ſtellis ſi</emph> <lb/><emph style="it">ue punctis</emph> <lb/><emph style="it">declinatio-</emph> <lb/><emph style="it">nem ab æꝗ</emph> <lb/><emph style="it">noctiali nõ</emph> <lb/><emph style="it">habẽtibus.</emph></note>
<note position="right" xlink:label="note-0075-12" xlink:href="note-0075-12a" xml:space="preserve">EXEM-<lb/>PLVM <lb/><emph style="it">de loco So</emph> <lb/><emph style="it">lis introni-</emph> <lb/><emph style="it">zationis</emph> <lb/><emph style="it">hora.</emph></note>
</div>
</div>
<div xml:id="echoid-div175" type="section" level="1" n="91">
<head xml:id="echoid-head95" xml:space="preserve">PRONVNCIATVM LXXIX.</head>
<p>
  <s xml:id="echoid-s6164" xml:space="preserve">Altitudinem poli arctici ſuper ſemicirculum poſitionis breuiſsime &amp; </s>
  <s xml:id="echoid-s6165" xml:space="preserve">ex-<lb/>peditiſsime inueſtigare.</s>
  <s xml:id="echoid-s6166" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s6167" xml:space="preserve">Altitudo illa poliſuꝑ ſemicirculũ poſitiõis nihil aliud eſt ̈ diſtantia poli arctici ſecun <lb/>
<anchor type="note" xlink:label="note-0076-01a" xlink:href="note-0076-01"/>
dum circulum maiorẽ à ſemicirculo poſitionis, qui quidẽ circulus maior ſuꝑ ſemicirculũ <lb/>poſitionis ducitur ad angulos rectos. </s>
  <s xml:id="echoid-s6168" xml:space="preserve">Ea altitudo multũ ꝓderit ad dirigendos quin ſi-<lb/>gnificatores, ̈uis ita loꝗ Pontanus nõ ꝑmittat, nõ libet tamẽ hic à priſco uocabulo re-<lb/>cedere, melius quidẽ diceretur peragratio ſiue permeatio gradus aſcendentis, unde inqui <lb/>ritur quicquid accidit in corpore. </s>
  <s xml:id="echoid-s6169" xml:space="preserve">Peragratio igitur Solis facit ad quærendũ dignitates, <lb/>exaltationes honoris &amp; </s>
  <s xml:id="echoid-s6170" xml:space="preserve">regni ipſius nati, gradus aũt ☽ peragratio fit propter eſſe animæ, <lb/>corporis, at coniugĳ. </s>
  <s xml:id="echoid-s6171" xml:space="preserve">Quarta dehinc peragratio ſiue directio partis fortunæ, ſiue horo-<lb/>ſcopi gradus ☽ fit propter acquiſitiones &amp; </s>
  <s xml:id="echoid-s6172" xml:space="preserve">profectus ſubſtantiæ. </s>
  <s xml:id="echoid-s6173" xml:space="preserve">Vltima aũt quæ &amp; </s>
  <s xml:id="echoid-s6174" xml:space="preserve">gra <lb/>dus eſt ipſius medĳ cœli, fit ꝓpter magiſteriũ &amp; </s>
  <s xml:id="echoid-s6175" xml:space="preserve">reliquas particulares diſpoſitiones. </s>
  <s xml:id="echoid-s6176" xml:space="preserve">Pro-<lb/>
<anchor type="note" xlink:label="note-0076-02a" xlink:href="note-0076-02"/>
pter eiuſmodi directiones ſiue ꝓfectiones inuẽtus eſt circulus poſitionũ, &amp; </s>
  <s xml:id="echoid-s6177" xml:space="preserve">altitudo eius <lb/>reperta. </s>
  <s xml:id="echoid-s6178" xml:space="preserve">Porrò inquiſita iã ex ſuperiori ꝓnunc, diſtantiaà ſemicirculi à uertice capitis ſiue <lb/>zenith horizõtis in circulo uerticali, duc ſinum diſtantiæ huius in ſinũ latitudinis regio <lb/>nis, ꝓductũ diuide in ſinũ, &amp; </s>
  <s xml:id="echoid-s6179" xml:space="preserve">arcus quotientis dabit altitudinẽ poliſeptentrionalis <lb/>quæſitã ſuꝑ ſemicirculũ poſitiõis. </s>
  <s xml:id="echoid-s6180" xml:space="preserve">?</s>
  <s xml:id="echoid-s6181" xml:space="preserve">? Exemplũ hoc habe. </s>
  <s xml:id="echoid-s6182" xml:space="preserve">Ex ſuꝑiori pronunc, inueni ad <lb/>
<anchor type="note" xlink:label="note-0076-03a" xlink:href="note-0076-03"/>
horã intronziationis etiã diſtantiã ſemicirculi poſitionis à zenith, qui ductus eſt ꝑ gradũ <lb/>ſiue locum Solis 43. </s>
  <s xml:id="echoid-s6183" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6184" xml:space="preserve">13. </s>
  <s xml:id="echoid-s6185" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6186" xml:space="preserve">ſinum eius 68479. </s>
  <s xml:id="echoid-s6187" xml:space="preserve">duco in ſinum altitudinis poli 48. </s>
  <s xml:id="echoid-s6188" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s6189" xml:space="preserve">20. </s>
  <s xml:id="echoid-s6190" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6191" xml:space="preserve">ita ut eſt Auguſtæ, ſinu eius 74702. </s>
  <s xml:id="echoid-s6192" xml:space="preserve">diuiſo in perfectum, produco 51155. </s>
  <s xml:id="echoid-s6193" xml:space="preserve">cuius ar-<lb/>cus eſt 30. </s>
  <s xml:id="echoid-s6194" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6195" xml:space="preserve">46. </s>
  <s xml:id="echoid-s6196" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6197" xml:space="preserve">altitudo illa poli ſuper ſemicirculum poſitionis quæſita.</s>
  <s xml:id="echoid-s6198" xml:space="preserve"/>
</p>
<div xml:id="echoid-div175" type="float" level="2" n="1">
<note position="left" xlink:label="note-0076-01" xlink:href="note-0076-01a" xml:space="preserve"><emph style="it">Quid ſit al</emph> <lb/><emph style="it">titudo poli</emph> <lb/><emph style="it">ſuper ſemi-</emph> <lb/><emph style="it">arculum po</emph> <lb/><emph style="it">ſitionis.</emph></note>
<note position="left" xlink:label="note-0076-02" xlink:href="note-0076-02a" xml:space="preserve"><emph style="it">Qua ratio</emph> <lb/><emph style="it">ne poſitio</emph> <lb/><emph style="it">circuli ſit</emph> <lb/><emph style="it">inuenta.</emph></note>
<note position="left" xlink:label="note-0076-03" xlink:href="note-0076-03a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſcopi.</emph></note>
</div>
</div>
<div xml:id="echoid-div177" type="section" level="1" n="92">
<head xml:id="echoid-head96" xml:space="preserve">PRONVNCIATVM LXXX.</head>
<p>
  <s xml:id="echoid-s6199" xml:space="preserve">Horam diurnã ex altitudine Solis ſuꝑ horizõtẽ in omni regione cõĳcere.</s>
  <s xml:id="echoid-s6200" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s6201" xml:space="preserve">Habita altitudine Solis ſuꝑ horizontẽ, q̃re etiã declinationẽ gradus ☉(sun) ꝑ 5. </s>
  <s xml:id="echoid-s6202" xml:space="preserve">huius, &amp; </s>
  <s xml:id="echoid-s6203" xml:space="preserve">ſi <lb/>declinatio fuerit ſeptẽtrionalis, adde eã cõplemẽto altitudinis poli, uiciſsim ſubtrahe eã <lb/>ſi ſit Sol in ſigno meridionali, &amp; </s>
  <s xml:id="echoid-s6204" xml:space="preserve">ꝓueniet altitudo meridiana. </s>
  <s xml:id="echoid-s6205" xml:space="preserve">Deinde duc ſinũ altitudinis <lb/>huius meridianæ in ſinũ totũ, &amp; </s>
  <s xml:id="echoid-s6206" xml:space="preserve">diuide ꝓductũ in ſinũ cõplementi altitudinis poli, quo-<lb/>tientẽ dic inuentũ primũ. </s>
  <s xml:id="echoid-s6207" xml:space="preserve">Poſtea duc etiã ſinũ altitudinis Solis ſupra horizontẽ in ſinum <lb/>
<anchor type="note" xlink:label="note-0076-04a" xlink:href="note-0076-04"/>
totũ, &amp; </s>
  <s xml:id="echoid-s6208" xml:space="preserve">diuide ꝓductũ in ſinũ cõplementi altitudinis poli, quotiens erit inuentũ ſecundũ. <lb/></s>
  <s xml:id="echoid-s6209" xml:space="preserve">Atqui hoc inuentum ſecundũ inuenire etiã potes hoc modo. </s>
  <s xml:id="echoid-s6210" xml:space="preserve">Si ſinũ altitudinis Solis du <lb/>cas in inuentũ primũ, ꝓductũ uero diuidas in ſinũ altitudinis meridinæ, quotiens ille da-<lb/>bit quo inuentũ ſecundũ. </s>
  <s xml:id="echoid-s6211" xml:space="preserve">Vtro hoc inuẽto habito, ſubtrahe ſecundũ à priori, ſemꝑem̃ <lb/>
<anchor type="note" xlink:label="note-0076-05a" xlink:href="note-0076-05"/>
illud eſt minus, reliquum rurſus duc in totũ, &amp; </s>
  <s xml:id="echoid-s6212" xml:space="preserve">ꝓductũ diuide in ſinũ cõplemẽti declina-<lb/>tionis gradus Solis. </s>
  <s xml:id="echoid-s6213" xml:space="preserve">q̊tiens uocabit̃ inuentũ tertiũ. </s>
  <s xml:id="echoid-s6214" xml:space="preserve">q̊d ſi minus fuerit ſinu toto, ſubtrahe <lb/>ipſum à toto ſinu, &amp; </s>
  <s xml:id="echoid-s6215" xml:space="preserve">habebis arcũ tꝑis ante uel poſt meridiẽ. </s>
  <s xml:id="echoid-s6216" xml:space="preserve">Sed ſi extiterit hoc inuentũ <lb/>tertiũ maius toto ſinu, ſubtrahe hinc ſinũ totũ, &amp; </s>
  <s xml:id="echoid-s6217" xml:space="preserve">arcũ reſidui adde ad 90. </s>
  <s xml:id="echoid-s6218" xml:space="preserve">ſi´ etiã babebis <lb/>arcum antemeridianũ uel pomeridianũ, eum ſi diuides per 15. </s>
  <s xml:id="echoid-s6219" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6220" xml:space="preserve">iamiã confeceris ho <lb/>ras. </s>
  <s xml:id="echoid-s6221" xml:space="preserve">Et ſi tẽpus illud fuerit antemeridiẽ, totidẽ horas cõnumera retrorſum uerſus à 12. </s>
  <s xml:id="echoid-s6222" xml:space="preserve">ho <lb/>
<anchor type="note" xlink:label="note-0076-06a" xlink:href="note-0076-06"/>
ra: </s>
  <s xml:id="echoid-s6223" xml:space="preserve">ſed ſi ſit pomeridianũ, adde tot horas ad 12. </s>
  <s xml:id="echoid-s6224" xml:space="preserve">hoc eſt meridianã horam, &amp; </s>
  <s xml:id="echoid-s6225" xml:space="preserve">ꝓueniet ho-<lb/>ra diei quæſita. </s>
  <s xml:id="echoid-s6226" xml:space="preserve">?</s>
  <s xml:id="echoid-s6227" xml:space="preserve">? Exemplũ ni ſit etiã moleſtum tibi, eſto ut hora intronizatiõis fuerit
<pb file="0077" n="77" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
altitudo Solis in eleuatione poli 48. </s>
  <s xml:id="echoid-s6228" xml:space="preserve">graduum, 44. </s>
  <s xml:id="echoid-s6229" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6230" xml:space="preserve">52. </s>
  <s xml:id="echoid-s6231" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6232" xml:space="preserve">quando Sol tunc fuit in 2. <lb/></s>
  <s xml:id="echoid-s6233" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6234" xml:space="preserve">26. </s>
  <s xml:id="echoid-s6235" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6236" xml:space="preserve">II, ſi declinatio eius eſt 20. </s>
  <s xml:id="echoid-s6237" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6238" xml:space="preserve">42. </s>
  <s xml:id="echoid-s6239" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6240" xml:space="preserve">complementum eius erit 69. </s>
  <s xml:id="echoid-s6241" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6242" xml:space="preserve">18. </s>
  <s xml:id="echoid-s6243" xml:space="preserve"><lb/>mi. </s>
  <s xml:id="echoid-s6244" xml:space="preserve">complementum uero altitudinis poli 42. </s>
  <s xml:id="echoid-s6245" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6246" xml:space="preserve">ei addo declinationem Solis, &amp; </s>
  <s xml:id="echoid-s6247" xml:space="preserve">proue-<lb/>nient 62. </s>
  <s xml:id="echoid-s6248" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6249" xml:space="preserve">42. </s>
  <s xml:id="echoid-s6250" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6251" xml:space="preserve">cuius ſinus eſt 88861. </s>
  <s xml:id="echoid-s6252" xml:space="preserve">quem duco in totum, &amp; </s>
  <s xml:id="echoid-s6253" xml:space="preserve">productum diuido in <lb/>ſinum complementi altitudinis poli. </s>
  <s xml:id="echoid-s6254" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s6255" xml:space="preserve">66913. </s>
  <s xml:id="echoid-s6256" xml:space="preserve">quotiens eſt 132801. </s>
  <s xml:id="echoid-s6257" xml:space="preserve">inuentum primum. </s>
  <s xml:id="echoid-s6258" xml:space="preserve"><lb/>Duco etiam ſinum altitudinis Solis in totum, &amp; </s>
  <s xml:id="echoid-s6259" xml:space="preserve">diuido productum in ſinum complemẽ <lb/>ti altitudinis poli, quotiens dabit 105405. </s>
  <s xml:id="echoid-s6260" xml:space="preserve">inuentum ſecundum, ſubtraho iam hoc ab in-<lb/>uento primo, &amp; </s>
  <s xml:id="echoid-s6261" xml:space="preserve">remanent 27396. </s>
  <s xml:id="echoid-s6262" xml:space="preserve">id rurſus duco in ſinum totum, &amp; </s>
  <s xml:id="echoid-s6263" xml:space="preserve">diuido in ſinũ com <lb/>plemẽti declinationis. </s>
  <s xml:id="echoid-s6264" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s6265" xml:space="preserve">93544. </s>
  <s xml:id="echoid-s6266" xml:space="preserve">quotiens eſt 29286. </s>
  <s xml:id="echoid-s6267" xml:space="preserve">inuentum tertium, hoc quia minus <lb/>ſubtraho à toto, &amp; </s>
  <s xml:id="echoid-s6268" xml:space="preserve">remanent 70714. </s>
  <s xml:id="echoid-s6269" xml:space="preserve">arcus eius eſt 45. </s>
  <s xml:id="echoid-s6270" xml:space="preserve">gra, quibus ſubductis à 90. </s>
  <s xml:id="echoid-s6271" xml:space="preserve">reliqui <lb/>manent 45. </s>
  <s xml:id="echoid-s6272" xml:space="preserve">gra, horæ ſcilicet tres, &amp; </s>
  <s xml:id="echoid-s6273" xml:space="preserve">quando tempus iſtud fuit antemeridianum, numera <lb/>tres horas à 12. </s>
  <s xml:id="echoid-s6274" xml:space="preserve">retrorſum, at habebis horã 9. </s>
  <s xml:id="echoid-s6275" xml:space="preserve">eam qua ſolennis &amp; </s>
  <s xml:id="echoid-s6276" xml:space="preserve">fœlix illa optimi Præ <lb/>ſulis facta eſt intronizatio.</s>
  <s xml:id="echoid-s6277" xml:space="preserve"/>
</p>
<div xml:id="echoid-div177" type="float" level="2" n="1">
<note position="left" xlink:label="note-0076-04" xlink:href="note-0076-04a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">primum.</emph></note>
<note position="left" xlink:label="note-0076-05" xlink:href="note-0076-05a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">ſecundum.</emph></note>
<note position="left" xlink:label="note-0076-06" xlink:href="note-0076-06a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſcopi.</emph></note>
</div>
</div>
<div xml:id="echoid-div179" type="section" level="1" n="93">
<head xml:id="echoid-head97" xml:space="preserve">PRONVNCIATVM LXXXI.</head>
<p>
  <s xml:id="echoid-s6278" xml:space="preserve">Altitudine poli Borealis ſuper ſemicirculum poſitionis cognita, etiã arcũ <lb/>æquatoris inuenire, qui meridiano &amp; </s>
  <s xml:id="echoid-s6279" xml:space="preserve">illo ſemicirculo poſitionis includitur.</s>
  <s xml:id="echoid-s6280" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s6281" xml:space="preserve">Propone hic tibi ſinum latitudinis tuæ regionis, &amp; </s>
  <s xml:id="echoid-s6282" xml:space="preserve">ſinum altitudinis poli ſupra ſemi-<lb/>circulum poſitionis, minorem duc in totum, productum in maiorem diuide, quotientis ar <lb/>cum ſubtrahe de quadrante, &amp; </s>
  <s xml:id="echoid-s6283" xml:space="preserve">ſinum huius complemẽti, ſimiliter &amp; </s>
  <s xml:id="echoid-s6284" xml:space="preserve">ſinum complemen <lb/>ti altitudinis poli Borealis ſupra ſemicirculum poſitionis ſepone in locum aliquem, mi-<lb/>norem duc in totum, &amp; </s>
  <s xml:id="echoid-s6285" xml:space="preserve">diuide cum maiori, arcus quotientis ex 90. </s>
  <s xml:id="echoid-s6286" xml:space="preserve">ſublatus, relinquet ar <lb/>cum æ quatoris quæſitũ. </s>
  <s xml:id="echoid-s6287" xml:space="preserve">?</s>
  <s xml:id="echoid-s6288" xml:space="preserve">? Iam exemplũ hoc mihi uide, Cupio inuenire arcum æqua <lb/>
<anchor type="note" xlink:label="note-0077-01a" xlink:href="note-0077-01"/>
toris, qui inter meridianum &amp; </s>
  <s xml:id="echoid-s6289" xml:space="preserve">ſemicirculum poſitionis in ipſa hora intronizationis per <lb/>corpus Solis deductum concluſus eſt, ſinum igitur altitudinis poliſuper eundem ſemi-<lb/>circulum poſitionis inueni ex ſuperiori pronunc. </s>
  <s xml:id="echoid-s6290" xml:space="preserve">51155. </s>
  <s xml:id="echoid-s6291" xml:space="preserve">eum duco in totum, &amp; </s>
  <s xml:id="echoid-s6292" xml:space="preserve">produ-<lb/>ctum diuido in ſinum latitudinis regionis, quæ eſt ibi 48. </s>
  <s xml:id="echoid-s6293" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6294" xml:space="preserve">20. </s>
  <s xml:id="echoid-s6295" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6296" xml:space="preserve">ſinus eius eſt 74702 <lb/>quotiens producit 68478. </s>
  <s xml:id="echoid-s6297" xml:space="preserve">concludit´ 43. </s>
  <s xml:id="echoid-s6298" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6299" xml:space="preserve">13. </s>
  <s xml:id="echoid-s6300" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6301" xml:space="preserve">quibus ſubtractis de 90. </s>
  <s xml:id="echoid-s6302" xml:space="preserve">manẽt 46. <lb/></s>
  <s xml:id="echoid-s6303" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6304" xml:space="preserve">47 mi. </s>
  <s xml:id="echoid-s6305" xml:space="preserve">cuius ſinum 72876, duco in totum, &amp; </s>
  <s xml:id="echoid-s6306" xml:space="preserve">diuido in ſinum complementi altitudi-<lb/>nis poli ſuper ſemicirculũ poſitionis. </s>
  <s xml:id="echoid-s6307" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s6308" xml:space="preserve">85925. </s>
  <s xml:id="echoid-s6309" xml:space="preserve">proueniunt in quotiente 84814. </s>
  <s xml:id="echoid-s6310" xml:space="preserve">arcus ipſe <lb/>eſt 58. </s>
  <s xml:id="echoid-s6311" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6312" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6313" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6314" xml:space="preserve">quibus de 90. </s>
  <s xml:id="echoid-s6315" xml:space="preserve">ademptus, remanet 31. </s>
  <s xml:id="echoid-s6316" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6317" xml:space="preserve">59. </s>
  <s xml:id="echoid-s6318" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6319" xml:space="preserve">arcus ille æquatoris <lb/>quæſitus.</s>
  <s xml:id="echoid-s6320" xml:space="preserve"/>
</p>
<div xml:id="echoid-div179" type="float" level="2" n="1">
<note position="right" xlink:label="note-0077-01" xlink:href="note-0077-01a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſcopi.</emph></note>
</div>
</div>
<div xml:id="echoid-div181" type="section" level="1" n="94">
<head xml:id="echoid-head98" xml:space="preserve">PRONVNCIATVM LXXXII.</head>
<p>
  <s xml:id="echoid-s6321" xml:space="preserve">Quum iam altitudo poli ſuper ſemicirculum poſitionis cognitus eſt, de-<lb/>hinc arcum circuli uerticalis inter zenith &amp; </s>
  <s xml:id="echoid-s6322" xml:space="preserve">iſtum ſemicirculum poſitionis <lb/>concluſum inueſtigare.</s>
  <s xml:id="echoid-s6323" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s6324" xml:space="preserve">Non te deterreat ne moueat pronunciati huius breuitas, nam quo paucioribus uer-<lb/>bis traditur, eò tam facilius intelligetur, tamen expeditius uſurpari poterit, unde magnũ <lb/>fructum ex hac re in Aſtrolabio noſtro reportabis. </s>
  <s xml:id="echoid-s6325" xml:space="preserve">Hic ergo tibi proponeutrun ſinum <lb/>altitudinis poli tuæ regionis, &amp; </s>
  <s xml:id="echoid-s6326" xml:space="preserve">illius quo ſupra ſemicirculum poſitionis, minorẽ duc <lb/>in totum, productum diuide in maiorem, &amp; </s>
  <s xml:id="echoid-s6327" xml:space="preserve">arcus quotientis monſtrabit tibi arcum cir-<lb/>culi uerticalis, ?</s>
  <s xml:id="echoid-s6328" xml:space="preserve">? Ecce en altitudo poli Auguſtæ eſt 48. </s>
  <s xml:id="echoid-s6329" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6330" xml:space="preserve">20. </s>
  <s xml:id="echoid-s6331" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6332" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6333" xml:space="preserve">ſub horam intro <lb/>nizationis fuit altitudo poli ſuper ſemicirculum poſitionis, qui per corpus Solis ducitur <lb/>
<anchor type="note" xlink:label="note-0077-02a" xlink:href="note-0077-02"/>
30. </s>
  <s xml:id="echoid-s6334" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6335" xml:space="preserve">46. </s>
  <s xml:id="echoid-s6336" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6337" xml:space="preserve">ſinũ eius 51155. </s>
  <s xml:id="echoid-s6338" xml:space="preserve">duco in totũ, &amp; </s>
  <s xml:id="echoid-s6339" xml:space="preserve">productum diuido in ſinũ altitudinis po <lb/>li 74702. </s>
  <s xml:id="echoid-s6340" xml:space="preserve">q̊tiens erit 68479. </s>
  <s xml:id="echoid-s6341" xml:space="preserve">ipſe aũt arcus eſt 43. </s>
  <s xml:id="echoid-s6342" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6343" xml:space="preserve">13. </s>
  <s xml:id="echoid-s6344" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6345" xml:space="preserve">arcus ille quem optabam.</s>
  <s xml:id="echoid-s6346" xml:space="preserve"/>
</p>
<div xml:id="echoid-div181" type="float" level="2" n="1">
<note position="right" xlink:label="note-0077-02" xlink:href="note-0077-02a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſcopi.</emph></note>
</div>
</div>
<div xml:id="echoid-div183" type="section" level="1" n="95">
<head xml:id="echoid-head99" xml:space="preserve">PRONVNCIATVM LXXXIII.</head>
<p>
  <s xml:id="echoid-s6347" xml:space="preserve">Si arcus æquatoris à meridiano ſumatur uſ ad ſemicirculum poſitionis, <lb/>altitudinem per hoc poli ſuper ſemicirculum illum poſitionis perquirere.</s>
  <s xml:id="echoid-s6348" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s6349" xml:space="preserve">Fac age ducas æquatoris ſinum complementi iſtius arcus æquatoris in ſinum latitu-<lb/>dinis regionis, &amp; </s>
  <s xml:id="echoid-s6350" xml:space="preserve">dehinc diuide productum in totum, arcum uero quotientis ſubtrahe de <lb/>90. </s>
  <s xml:id="echoid-s6351" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6352" xml:space="preserve">ad ſinum reſidui confer ſinum complementi altitudinis poli, minorem duc in totũ <lb/>&amp; </s>
  <s xml:id="echoid-s6353" xml:space="preserve">in maiorem diuide, tunc complementum arcus quotientis dabit altitudinẽ poli quæ-
<pb file="0078" n="78" rhead="GENVINVS VSVS"/>
ſitam ſuper ſemicirculum poſitionis. </s>
  <s xml:id="echoid-s6354" xml:space="preserve">?</s>
  <s xml:id="echoid-s6355" xml:space="preserve">? Puta ſub horam intronizationis factæ, inter <lb/>
<anchor type="note" xlink:label="note-0078-01a" xlink:href="note-0078-01"/>
meridianum &amp; </s>
  <s xml:id="echoid-s6356" xml:space="preserve">ſemicirculum poſitionis, qui per corpus Solis ducitur ab ipſo æquatore, <lb/>intercepti ſunt 31. </s>
  <s xml:id="echoid-s6357" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6358" xml:space="preserve">59. </s>
  <s xml:id="echoid-s6359" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6360" xml:space="preserve">complementum huius eſt 88. </s>
  <s xml:id="echoid-s6361" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6362" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6363" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6364" xml:space="preserve">ſinus eius 84814. <lb/></s>
  <s xml:id="echoid-s6365" xml:space="preserve">hunc duco in ſinum altitudinis poli Auguſt. </s>
  <s xml:id="echoid-s6366" xml:space="preserve">74702. </s>
  <s xml:id="echoid-s6367" xml:space="preserve">productum diuido in totum, &amp; </s>
  <s xml:id="echoid-s6368" xml:space="preserve">quo <lb/>tiens dat 63358. </s>
  <s xml:id="echoid-s6369" xml:space="preserve">cuius arcus eſt 39. </s>
  <s xml:id="echoid-s6370" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6371" xml:space="preserve">19. </s>
  <s xml:id="echoid-s6372" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6373" xml:space="preserve">ſinus complementi huius ipſe eſt diuiſor. </s>
  <s xml:id="echoid-s6374" xml:space="preserve"><lb/>Iam duco ſinum complementi altitudinis poli 66479. </s>
  <s xml:id="echoid-s6375" xml:space="preserve">in totum, productum diuido in di <lb/>uiſorem, &amp; </s>
  <s xml:id="echoid-s6376" xml:space="preserve">proueniunt in quotiente 85929. </s>
  <s xml:id="echoid-s6377" xml:space="preserve">arcus eius 59. </s>
  <s xml:id="echoid-s6378" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6379" xml:space="preserve">14. </s>
  <s xml:id="echoid-s6380" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6381" xml:space="preserve">de 90. </s>
  <s xml:id="echoid-s6382" xml:space="preserve">ſubductus, <lb/>relinquit à ſe 30. </s>
  <s xml:id="echoid-s6383" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6384" xml:space="preserve">46. </s>
  <s xml:id="echoid-s6385" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6386" xml:space="preserve">altitudinem ſcilicet illam poli ſuper ſemicirculum poſitionis <lb/>quem ſcire uolebam.</s>
  <s xml:id="echoid-s6387" xml:space="preserve"/>
</p>
<div xml:id="echoid-div183" type="float" level="2" n="1">
<note position="left" xlink:label="note-0078-01" xlink:href="note-0078-01a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſcopi.</emph></note>
</div>
</div>
<div xml:id="echoid-div185" type="section" level="1" n="96">
<head xml:id="echoid-head100" xml:space="preserve">PRONVNCIATVM LXXXIIII.</head>
<p>
  <s xml:id="echoid-s6388" xml:space="preserve">Altitudinem poli ſuper ſemicirculum poſitionis per arcum æquatoris in <lb/>ter eum &amp; </s>
  <s xml:id="echoid-s6389" xml:space="preserve">meridianum concluſum, diuerſa ratione colligere.</s>
  <s xml:id="echoid-s6390" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s6391" xml:space="preserve">Propoſitio idem &amp; </s>
  <s xml:id="echoid-s6392" xml:space="preserve">quærit &amp; </s>
  <s xml:id="echoid-s6393" xml:space="preserve">præſupponit quod ſuperior, puta arcum æquatoris, ſi-<lb/>num complementi eius arcus duc in ſinum altitudinis poli, &amp; </s>
  <s xml:id="echoid-s6394" xml:space="preserve">diuide quotientem in to <lb/>
<anchor type="note" xlink:label="note-0078-02a" xlink:href="note-0078-02"/>
tum, ſinum uero complementi huius quotientis tibi propone, ſimul &amp; </s>
  <s xml:id="echoid-s6395" xml:space="preserve">ſinum arcus æ-<lb/>quatoris ſuppolìtum, minorem cum toto multiplica, &amp; </s>
  <s xml:id="echoid-s6396" xml:space="preserve">per maiorem, more ſolito, di-<lb/>uide, hinc quotientem rurſus duc in ſinum altitudinis poli, productum diuide in ſinum <lb/>perfectum, &amp; </s>
  <s xml:id="echoid-s6397" xml:space="preserve">arcus quotientis dabit altitudinem poli quæſitam ſuper ſemicirculum <lb/>poſitionis. </s>
  <s xml:id="echoid-s6398" xml:space="preserve">Exemplum cape, &amp; </s>
  <s xml:id="echoid-s6399" xml:space="preserve">in hac re tibi non moleſtum erit. </s>
  <s xml:id="echoid-s6400" xml:space="preserve">Eſto ut ſit arcus æ-<lb/>
<anchor type="note" xlink:label="note-0078-03a" xlink:href="note-0078-03"/>
quatoris, ſicut antea inter meridianum &amp; </s>
  <s xml:id="echoid-s6401" xml:space="preserve">ſemicirculum poſitionis imaginarium per lo <lb/>cum Solis ipſa hora intronizationis 31. </s>
  <s xml:id="echoid-s6402" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6403" xml:space="preserve">59. </s>
  <s xml:id="echoid-s6404" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6405" xml:space="preserve">ſinus ſui complementi eſt 84814, eũ <lb/>duco in ſinum latitudinis Auguſt. </s>
  <s xml:id="echoid-s6406" xml:space="preserve">74702. </s>
  <s xml:id="echoid-s6407" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6408" xml:space="preserve">poſt diuiſionem ſinus perfecti, quotiens ex <lb/>hibet mihi 63358. </s>
  <s xml:id="echoid-s6409" xml:space="preserve">arcus porrò eſt 39. </s>
  <s xml:id="echoid-s6410" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6411" xml:space="preserve">19. </s>
  <s xml:id="echoid-s6412" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6413" xml:space="preserve">Complementum eius 50. </s>
  <s xml:id="echoid-s6414" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6415" xml:space="preserve">41. </s>
  <s xml:id="echoid-s6416" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6417" xml:space="preserve">ſi-<lb/>nus illius eſt diuiſor 77365. </s>
  <s xml:id="echoid-s6418" xml:space="preserve">iam duco ſinum 31. </s>
  <s xml:id="echoid-s6419" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6420" xml:space="preserve">59. </s>
  <s xml:id="echoid-s6421" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6422" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s6423" xml:space="preserve">52967. </s>
  <s xml:id="echoid-s6424" xml:space="preserve">in totum, productũ <lb/>diuido in ipſum diuiſorem, &amp; </s>
  <s xml:id="echoid-s6425" xml:space="preserve">quotiens profert 68464, eum rurſus duco in ſinum altitu-<lb/>dinis poli 74702. </s>
  <s xml:id="echoid-s6426" xml:space="preserve">productum diuide in totum, &amp; </s>
  <s xml:id="echoid-s6427" xml:space="preserve">quotiens erit 51154. </s>
  <s xml:id="echoid-s6428" xml:space="preserve">cuius arcus eſt <lb/>30. </s>
  <s xml:id="echoid-s6429" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6430" xml:space="preserve">46. </s>
  <s xml:id="echoid-s6431" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6432" xml:space="preserve">altitudo illa poli ſuper ſemicirculum poſitionis inquiſita.</s>
  <s xml:id="echoid-s6433" xml:space="preserve"/>
</p>
<div xml:id="echoid-div185" type="float" level="2" n="1">
<note position="left" xlink:label="note-0078-02" xlink:href="note-0078-02a" xml:space="preserve"><emph style="it">Illud diſces</emph> <lb/><emph style="it">in quadran</emph> <lb/><emph style="it">te per intro</emph> <lb/><emph style="it">itum latera</emph> <lb/><emph style="it">lem.</emph></note>
<note position="left" xlink:label="note-0078-03" xlink:href="note-0078-03a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſcopi.</emph></note>
</div>
</div>
<div xml:id="echoid-div187" type="section" level="1" n="97">
<head xml:id="echoid-head101" xml:space="preserve">PRONVNCIATVM LXXXV.</head>
<p>
  <s xml:id="echoid-s6434" xml:space="preserve">Declinationem ſtellæ ab æquatore, ſi quam habet, cognoſcere.</s>
  <s xml:id="echoid-s6435" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s6436" xml:space="preserve">Trifariam quæri poteſt declinatio, quædam enim ftellæ ſiue puncta ſunt in arcu, qui <lb/>trãſit per polos zodiaci, &amp; </s>
  <s xml:id="echoid-s6437" xml:space="preserve">per principia ♈ &amp; </s>
  <s xml:id="echoid-s6438" xml:space="preserve">♎, quæ ſcilicet in principio ♈ uel ♎ ſunt <lb/>ſecundum longitudinem, quædam rurſus in principio ♋ uel ♑ ſunt quæ rurſus peculia-<lb/>rem habent rationẽ, &amp; </s>
  <s xml:id="echoid-s6439" xml:space="preserve">ſimiliter hinc inde extra illos circulos duos ſparſim conſpiciũtur.</s>
  <s xml:id="echoid-s6440" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s6441" xml:space="preserve">De ſtellis quæ ſunt in principio ♈ uel ♎.</s>
  <s xml:id="echoid-s6442" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s6443" xml:space="preserve">Hic ſi ſtellam aliquam conſpexeris, duc ſinum latitudinis ſtellæ in ſinum complemen <lb/>
<anchor type="note" xlink:label="note-0078-04a" xlink:href="note-0078-04"/>
ti maximæ declinationis Solis, &amp; </s>
  <s xml:id="echoid-s6444" xml:space="preserve">productum diuide in totum, arcus quotientis mon-<lb/>ſtrabit declinationem ſtellæ propoſitæ.</s>
  <s xml:id="echoid-s6445" xml:space="preserve"/>
</p>
<div xml:id="echoid-div187" type="float" level="2" n="1">
<note position="left" xlink:label="note-0078-04" xlink:href="note-0078-04a" xml:space="preserve"><emph style="it">Per laterd-</emph> <lb/><emph style="it">lem ingreſ-</emph> <lb/><emph style="it">lam aſſeque-</emph> <lb/><emph style="it">ris illud.</emph></note>
</div>
<p>
  <s xml:id="echoid-s6446" xml:space="preserve">Deĳs quæ ſunt in principio ♋ uel ♑.</s>
  <s xml:id="echoid-s6447" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s6448" xml:space="preserve">Si latitudo ſtellæ fuerit ſeptentrionalis, &amp; </s>
  <s xml:id="echoid-s6449" xml:space="preserve">ſtella ipſa in principio ♋, tunc adde maxi-<lb/>mam Solis declinationem ad latitudinem ſtellæ, &amp; </s>
  <s xml:id="echoid-s6450" xml:space="preserve">habebis eius declinationem: </s>
  <s xml:id="echoid-s6451" xml:space="preserve">ſin au-<lb/>tem latitudo ſtellæ meridionalis extiterit, ſtella exiſtente in principio ♋, &amp; </s>
  <s xml:id="echoid-s6452" xml:space="preserve">tunc latitu-<lb/>do ſit 23. </s>
  <s xml:id="echoid-s6453" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6454" xml:space="preserve">30. </s>
  <s xml:id="echoid-s6455" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6456" xml:space="preserve">ſtella declinationem nullam habebit. </s>
  <s xml:id="echoid-s6457" xml:space="preserve">Adhuc ſi latitudo ſit minor <lb/>maxima Solis declinatione, ſubtrahe tunc latitudinem ſtellæ à maxima Solis declinati <lb/>one, &amp; </s>
  <s xml:id="echoid-s6458" xml:space="preserve">remanebit declinatio ſtellæ ſeptentrionalis. </s>
  <s xml:id="echoid-s6459" xml:space="preserve">At ſi latitudo ſtellæ fuerit maior ma <lb/>xima declinatione Solis, ſubtrahes inde maximam illam Solis declinationem, &amp; </s>
  <s xml:id="echoid-s6460" xml:space="preserve">reſidu <lb/>um erit declinatio ipſa ſtellæ meridionalis. </s>
  <s xml:id="echoid-s6461" xml:space="preserve">Simili modo operare etiam ſi ſtella fuerit in <lb/>principio ♑, @iſi quòd tunc inuertenda ſunt omnia, &amp; </s>
  <s xml:id="echoid-s6462" xml:space="preserve">ubi hic ſeptentrionem habuiſti, <lb/>illic pones meridiem, &amp; </s>
  <s xml:id="echoid-s6463" xml:space="preserve">econtra.</s>
  <s xml:id="echoid-s6464" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s6465" xml:space="preserve">De ſtellis quæ alibi poſitæ ſunt extra illos duos circulos.</s>
  <s xml:id="echoid-s6466" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s6467" xml:space="preserve">Principio hic uide, an ſtella ad ♋ uel ♑ propius accedat, ſiue ſecundum ſiue contra
<pb file="0079" n="79" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
ordinem ſignorum, eius diſtantiæ ſinum duc in ſinum maximæ declinationis Solis, &amp; </s>
  <s xml:id="echoid-s6468" xml:space="preserve">di <lb/>
<anchor type="note" xlink:label="note-0079-01a" xlink:href="note-0079-01"/>
uide in totum, arcus quotientis huius ex 90. </s>
  <s xml:id="echoid-s6469" xml:space="preserve">ſubductus, relinquet inuentum primum. <lb/></s>
  <s xml:id="echoid-s6470" xml:space="preserve">Deinde propone tibi ſinum complementi primi inuenti, &amp; </s>
  <s xml:id="echoid-s6471" xml:space="preserve">ſinum complementi maxi-<lb/>
<anchor type="note" xlink:label="note-0079-02a" xlink:href="note-0079-02"/>
mæ declinationis Solis, minorem duc in totum, productum diuide in maiorem, ſinus quo <lb/>tientis ex 90. </s>
  <s xml:id="echoid-s6472" xml:space="preserve">ſubtractus, reliquum tibi faciet inuentum ſecundum: </s>
  <s xml:id="echoid-s6473" xml:space="preserve">quod etiam nomen <lb/>
<anchor type="note" xlink:label="note-0079-03a" xlink:href="note-0079-03"/>
habebit à medietate eclypticæ in qua ſtella iſta eſt, proinde ſi fuerit in medietate ſepten-<lb/>trionali, dicetur inuentum ſecundum ſeptentrionale. </s>
  <s xml:id="echoid-s6474" xml:space="preserve">Et hoc ipſum deinde adde ad lati <lb/>tudinem ſtellæ, ſi tamen ea fuerit in medietate zodiaci ſeptentrionali, &amp; </s>
  <s xml:id="echoid-s6475" xml:space="preserve">latitudo ſimili-<lb/>
<anchor type="note" xlink:label="note-0079-04a" xlink:href="note-0079-04"/>
ter ſeptentrionalis. </s>
  <s xml:id="echoid-s6476" xml:space="preserve">Aut ſubtrahe minorem â maiori, quoniam non ſint unius nominis <lb/>ſcilicet medietas zodiaci &amp; </s>
  <s xml:id="echoid-s6477" xml:space="preserve">latitudo ſtellæ, ex hac additione quicquid prouenit, aut ex <lb/>
<anchor type="note" xlink:label="note-0079-05a" xlink:href="note-0079-05"/>
ſubtractione remanet, dicetur argumentum declinationis. </s>
  <s xml:id="echoid-s6478" xml:space="preserve">Hoc ſi ex additione prodĳt, <lb/>nomen argumenti retinebit: </s>
  <s xml:id="echoid-s6479" xml:space="preserve">ſin autem ex ſubtractione ſupereſt, habebit nomen nume-<lb/>ri maioris. </s>
  <s xml:id="echoid-s6480" xml:space="preserve">Poſt hæc duces ſinum complementi inuenti primi in ſinum argumenti decli-<lb/>
<anchor type="note" xlink:label="note-0079-06a" xlink:href="note-0079-06"/>
nationis, &amp; </s>
  <s xml:id="echoid-s6481" xml:space="preserve">diuides productum in totum, arcus quotiẽtis erit declinatio ſtellæ, &amp; </s>
  <s xml:id="echoid-s6482" xml:space="preserve">ſeruat <lb/>nomen argumenti, ſiue ſeptentrionalis ſiue meridionalis. </s>
  <s xml:id="echoid-s6483" xml:space="preserve">Porrò ſi nihil in argumento <lb/>fuerit, etiam tunc declinatio erit nulla, nec eſt quod ultra labores, ſed ſi punctum ſiue <lb/>ſtella ſit in eclyptica, declinationem retinet eclypticæ, ſicut per 5. </s>
  <s xml:id="echoid-s6484" xml:space="preserve">pronunciatum inue-<lb/>nies. </s>
  <s xml:id="echoid-s6485" xml:space="preserve">?</s>
  <s xml:id="echoid-s6486" xml:space="preserve">? Exemplum non erit hic tibi contemnendum. </s>
  <s xml:id="echoid-s6487" xml:space="preserve">Adſumo ecce quartam ſtellam <lb/>
<anchor type="note" xlink:label="note-0079-07a" xlink:href="note-0079-07"/>
Agitatoris, quæ ſecundum Alfonſi regis obſeruationem habet in longitudine 19. </s>
  <s xml:id="echoid-s6488" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s6489" xml:space="preserve">59. </s>
  <s xml:id="echoid-s6490" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6491" xml:space="preserve">II, &amp; </s>
  <s xml:id="echoid-s6492" xml:space="preserve">in latitudine 20. </s>
  <s xml:id="echoid-s6493" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6494" xml:space="preserve">0. </s>
  <s xml:id="echoid-s6495" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6496" xml:space="preserve">ſeptentrionalis. </s>
  <s xml:id="echoid-s6497" xml:space="preserve">Ideo´ ſtellam hanc propono <lb/>libentius, quia ipſa hora intronizationis cum Sole penè in uno fuit circulo poſitionis, <lb/>ex ſecundo pronunciato iam inueni uerificationem ſtellæ 2. </s>
  <s xml:id="echoid-s6498" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6499" xml:space="preserve">37. </s>
  <s xml:id="echoid-s6500" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6501" xml:space="preserve">tantum nimi-<lb/>
<anchor type="note" xlink:label="note-0079-08a" xlink:href="note-0079-08"/>
rum auges planetarum &amp; </s>
  <s xml:id="echoid-s6502" xml:space="preserve">ſtellæ fixæ ſecundum ſententiam Alfonſi ab ipſius tempore <lb/>ſunt promotæ uſ ad horam intronizationis. </s>
  <s xml:id="echoid-s6503" xml:space="preserve">His ergo additis, habeo 22. </s>
  <s xml:id="echoid-s6504" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6505" xml:space="preserve">35. </s>
  <s xml:id="echoid-s6506" xml:space="preserve">min. <lb/></s>
  <s xml:id="echoid-s6507" xml:space="preserve">II, quo loci fuit illa ſtella fixa ad horam propoſitã, latitudiuem hanc ſicut omnes Aſtro-<lb/>nomifaciunt, ita retineo fixam &amp; </s>
  <s xml:id="echoid-s6508" xml:space="preserve">immotã. </s>
  <s xml:id="echoid-s6509" xml:space="preserve">Deinceps diſtantia ſtellæ à principio Can-<lb/>cri eſt 7. </s>
  <s xml:id="echoid-s6510" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6511" xml:space="preserve">25. </s>
  <s xml:id="echoid-s6512" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6513" xml:space="preserve">ſinum eius 12908. </s>
  <s xml:id="echoid-s6514" xml:space="preserve">duco in ſinum maximæ declinationis 39874. </s>
  <s xml:id="echoid-s6515" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6516" xml:space="preserve"><lb/>diuido per totum ſinum, quotiens dabit 5147. </s>
  <s xml:id="echoid-s6517" xml:space="preserve">arcus eius eſt 2. </s>
  <s xml:id="echoid-s6518" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6519" xml:space="preserve">57. </s>
  <s xml:id="echoid-s6520" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6521" xml:space="preserve">at no-<lb/>men habet intrenti primi, ſinum complementi maximæ declinationis Solis 91706. </s>
  <s xml:id="echoid-s6522" xml:space="preserve">du-<lb/>co in totum, &amp; </s>
  <s xml:id="echoid-s6523" xml:space="preserve">productum diuido in ſinum complementi primi inuenti ſcilicet 99867. </s>
  <s xml:id="echoid-s6524" xml:space="preserve"><lb/>quotiens producit 91828. </s>
  <s xml:id="echoid-s6525" xml:space="preserve">arcus eius 66. </s>
  <s xml:id="echoid-s6526" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6527" xml:space="preserve">41. </s>
  <s xml:id="echoid-s6528" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6529" xml:space="preserve">Complementum autem eius eſt in-<lb/>uentum ſecundum, &amp; </s>
  <s xml:id="echoid-s6530" xml:space="preserve">Boreale, quum ſtella ſit in ſigno Boreali. </s>
  <s xml:id="echoid-s6531" xml:space="preserve">Deinceps addo inuen-<lb/>tum ſecundum ſcilicet 23. </s>
  <s xml:id="echoid-s6532" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6533" xml:space="preserve">19. </s>
  <s xml:id="echoid-s6534" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6535" xml:space="preserve">ad latitudinem ſtellæ 20. </s>
  <s xml:id="echoid-s6536" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6537" xml:space="preserve">quando in ſeptentri-<lb/>onali plaga participant, &amp; </s>
  <s xml:id="echoid-s6538" xml:space="preserve">proueniunt 43. </s>
  <s xml:id="echoid-s6539" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6540" xml:space="preserve">19. </s>
  <s xml:id="echoid-s6541" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6542" xml:space="preserve">argumentum ſcilicet declinatio-<lb/>nis. </s>
  <s xml:id="echoid-s6543" xml:space="preserve">Iam nunc duco ſinum complementi inuenti primi 78. </s>
  <s xml:id="echoid-s6544" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6545" xml:space="preserve">3. </s>
  <s xml:id="echoid-s6546" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6547" xml:space="preserve">ſcilicet 99867. </s>
  <s xml:id="echoid-s6548" xml:space="preserve">in ſi-<lb/>num argumenti declinationis ſcilicet 68603. </s>
  <s xml:id="echoid-s6549" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6550" xml:space="preserve">diuido in totum, quotiens producet <lb/>68512. </s>
  <s xml:id="echoid-s6551" xml:space="preserve">arcus eius 43 gra. </s>
  <s xml:id="echoid-s6552" xml:space="preserve">15. </s>
  <s xml:id="echoid-s6553" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6554" xml:space="preserve">eſt ipſa declinatio ſtellæ quæſita &amp; </s>
  <s xml:id="echoid-s6555" xml:space="preserve">ſeptentrionalis, quan <lb/>doquidem argumentum nomen hoc habet, &amp; </s>
  <s xml:id="echoid-s6556" xml:space="preserve">inde illud etiam declinatio ſumit.</s>
  <s xml:id="echoid-s6557" xml:space="preserve"/>
</p>
<div xml:id="echoid-div188" type="float" level="2" n="2">
<note position="right" xlink:label="note-0079-01" xlink:href="note-0079-01a" xml:space="preserve"><emph style="it">Hoc latera</emph> <lb/><emph style="it">liter depre</emph> <lb/><emph style="it">hendis.</emph></note>
<note position="right" xlink:label="note-0079-02" xlink:href="note-0079-02a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">primum.</emph></note>
<note position="right" xlink:label="note-0079-03" xlink:href="note-0079-03a" xml:space="preserve"><emph style="it">Illud area-</emph> <lb/><emph style="it">tim aſſeque</emph> <lb/><emph style="it">ris.</emph></note>
<note position="right" xlink:label="note-0079-04" xlink:href="note-0079-04a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">ſecundum.</emph></note>
<note position="right" xlink:label="note-0079-05" xlink:href="note-0079-05a" xml:space="preserve"><emph style="it">Argumen-</emph> <lb/><emph style="it">tum decli-</emph> <lb/><emph style="it">nationis.</emph></note>
<note position="right" xlink:label="note-0079-06" xlink:href="note-0079-06a" xml:space="preserve"><emph style="it">Numerus</emph> <lb/><emph style="it">maior.</emph></note>
<note position="right" xlink:label="note-0079-07" xlink:href="note-0079-07a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſcopi.</emph></note>
<note position="right" xlink:label="note-0079-08" xlink:href="note-0079-08a" xml:space="preserve"><emph style="it">Motus au-</emph> <lb/><emph style="it">grum &amp; ſtel</emph> <lb/><emph style="it">larum fixæ</emph> <lb/><emph style="it">rum à tem-</emph> <lb/><emph style="it">pore Alfon</emph> <lb/><emph style="it">ſi, uſq; ad</emph> <lb/><emph style="it">horam in-</emph> <lb/><emph style="it">tronizatio</emph> <lb/><emph style="it">nis.</emph></note>
</div>
</div>
<div xml:id="echoid-div190" type="section" level="1" n="98">
<head xml:id="echoid-head102" xml:space="preserve">PRONVNCIATVM LXXXVI.</head>
<p>
  <s xml:id="echoid-s6558" xml:space="preserve">Declinationem ſtellæ alio &amp; </s>
  <s xml:id="echoid-s6559" xml:space="preserve">iucundiore modo perquirere.</s>
  <s xml:id="echoid-s6560" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s6561" xml:space="preserve">Conſidera primum an ſtella ſit in medietate zodiaci ſeptentrionali uel meridionali, <lb/>deinde cuinam puncto æquinoctĳ propius accedat, ut quicquid inter eſt à principio A-<lb/>rietis uſ ad finem II, id totũ principio Arietis adnumeratur, &amp; </s>
  <s xml:id="echoid-s6562" xml:space="preserve">quod à principio Can <lb/>cri eſt uſ ad principium Libræ, ad ♎ computatur. </s>
  <s xml:id="echoid-s6563" xml:space="preserve">Eam diſtantiam ſubtrahe à 90. </s>
  <s xml:id="echoid-s6564" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6565" xml:space="preserve">ſi-<lb/>num complementi uel reſidui duc in ſinum complementi latitudinis ſtellæ, peracta diui <lb/>
<anchor type="note" xlink:label="note-0079-09a" xlink:href="note-0079-09"/>
ſione ſinus perfecti, erit arcus complementi quotientis inuentum primum. </s>
  <s xml:id="echoid-s6566" xml:space="preserve">Poſtea duc <lb/>ſinum latitudinis ſtellæ in totum, &amp; </s>
  <s xml:id="echoid-s6567" xml:space="preserve">diuide in ſinum primi inuenti, arcus quotientis uo <lb/>
<anchor type="note" xlink:label="note-0079-10a" xlink:href="note-0079-10"/>
cabitur inuentum ſecundum, hoc iam adde ad maximam Solis declinationem, quum <lb/>latitudo in nomine conueniat unà cum medietate eclypticæ, ſum@a e@ erit argumen-<lb/>tum declinationis, retinebit´ nomen medietatis eclypticæ in qua eſt ſtella propoſita: <lb/></s>
  <s xml:id="echoid-s6568" xml:space="preserve">quòd ſi autem latitudo ſtellæ aliud non habuerit quàm medietas eclypticæ, inuentum
<pb file="0080" n="80" rhead="GENVINVS VSVS"/>
quo ſecundum minus fuerit maxima declinatione Solis, tunc ſubtahe inuentum ſe-<lb/>cundum de maxima Solis declinatione, &amp; </s>
  <s xml:id="echoid-s6569" xml:space="preserve">reſiduum dicetur argumentum declinationis <lb/>
<anchor type="note" xlink:label="note-0080-01a" xlink:href="note-0080-01"/>
habebit´ nomen medietatis eclypticæ: </s>
  <s xml:id="echoid-s6570" xml:space="preserve">ſed ſi inuentum ſecundum maius ſit maxima So <lb/>lis declinatione, tũc ſubtrahe hanc, &amp; </s>
  <s xml:id="echoid-s6571" xml:space="preserve">remanebit argumentum declinationis, ſimul´ ſer <lb/>uabit nomen latitudinis. </s>
  <s xml:id="echoid-s6572" xml:space="preserve">Inſuper duc ſinum argumenti in ſinum primi inuenti, &amp; </s>
  <s xml:id="echoid-s6573" xml:space="preserve">produ <lb/>
<anchor type="note" xlink:label="note-0080-02a" xlink:href="note-0080-02"/>
ctum diuide in totum, arcus quotientis dabit declinationem ſtellæ quæſitam. </s>
  <s xml:id="echoid-s6574" xml:space="preserve">?</s>
  <s xml:id="echoid-s6575" xml:space="preserve">? Vte-<lb/>mur &amp; </s>
  <s xml:id="echoid-s6576" xml:space="preserve">hic exemplo ſuperiori. </s>
  <s xml:id="echoid-s6577" xml:space="preserve">Stella ſcilicet quarta Agitatoris quæ ſita eſt ſuper ſpatulã <lb/>dextram, eius longitudo eſt 22. </s>
  <s xml:id="echoid-s6578" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6579" xml:space="preserve">35. </s>
  <s xml:id="echoid-s6580" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6581" xml:space="preserve">II. </s>
  <s xml:id="echoid-s6582" xml:space="preserve">latitudo eius 20. </s>
  <s xml:id="echoid-s6583" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6584" xml:space="preserve">ſeptentrionalis. </s>
  <s xml:id="echoid-s6585" xml:space="preserve">Com <lb/>plementum diſtantiæ ab Ariete eſt 7. </s>
  <s xml:id="echoid-s6586" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6587" xml:space="preserve">25. </s>
  <s xml:id="echoid-s6588" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6589" xml:space="preserve">ſinum eius 12908. </s>
  <s xml:id="echoid-s6590" xml:space="preserve">duco in ſinum com-<lb/>
<anchor type="note" xlink:label="note-0080-03a" xlink:href="note-0080-03"/>
plementi latitudinis 70. </s>
  <s xml:id="echoid-s6591" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6592" xml:space="preserve">ſcilicet 93969. </s>
  <s xml:id="echoid-s6593" xml:space="preserve">at extota diuiſione remanſit quotiens <lb/>12129. </s>
  <s xml:id="echoid-s6594" xml:space="preserve">cuius arcus eſt 6. </s>
  <s xml:id="echoid-s6595" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6596" xml:space="preserve">58. </s>
  <s xml:id="echoid-s6597" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6598" xml:space="preserve">complementũ uero 83. </s>
  <s xml:id="echoid-s6599" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6600" xml:space="preserve">2. </s>
  <s xml:id="echoid-s6601" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6602" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6603" xml:space="preserve">appellabitur in-<lb/>uentum primum. </s>
  <s xml:id="echoid-s6604" xml:space="preserve">Ad hæc porrò duco ſinum latitudinis ſtellæ in ſinum totum, productũ <lb/>diuido in ſinum primi inuenti, ſcilicet 99261. </s>
  <s xml:id="echoid-s6605" xml:space="preserve">quotiens ipſe 34456, cum arcuſuo, ſcilicet <lb/>20. </s>
  <s xml:id="echoid-s6606" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6607" xml:space="preserve">10. </s>
  <s xml:id="echoid-s6608" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6609" xml:space="preserve">producit inuentum ſecundum. </s>
  <s xml:id="echoid-s6610" xml:space="preserve">Et quia ſtella eſt in medietate ſeptentriona <lb/>li, ipſa quo ſtellæ latitudo ſeptentrionalis, ex additione inuenti ſecundi ad maximam <lb/>Solis declinationem, prouenerunt inde 45. </s>
  <s xml:id="echoid-s6611" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6612" xml:space="preserve">40. </s>
  <s xml:id="echoid-s6613" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6614" xml:space="preserve">argumentum puta declinationis <lb/>quod &amp; </s>
  <s xml:id="echoid-s6615" xml:space="preserve">uocatur argumentum ſeptentrionale. </s>
  <s xml:id="echoid-s6616" xml:space="preserve">Vlterius adhuc ſinum argumenti iam in-<lb/>uenti ſcilicet 69046. </s>
  <s xml:id="echoid-s6617" xml:space="preserve">duco in ſinum primi inuenti ſcilicet 99261. </s>
  <s xml:id="echoid-s6618" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6619" xml:space="preserve">diuido per totum, in-<lb/>ueni in quotiente 66536. </s>
  <s xml:id="echoid-s6620" xml:space="preserve">cuius arcus eſt 43. </s>
  <s xml:id="echoid-s6621" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6622" xml:space="preserve">15. </s>
  <s xml:id="echoid-s6623" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6624" xml:space="preserve">declinatio illa ſtellæ ſeptentriona <lb/>lis, quem hactenus quærebam.</s>
  <s xml:id="echoid-s6625" xml:space="preserve"/>
</p>
<div xml:id="echoid-div190" type="float" level="2" n="1">
<note position="right" xlink:label="note-0079-09" xlink:href="note-0079-09a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">primum.</emph></note>
<note position="right" xlink:label="note-0079-10" xlink:href="note-0079-10a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">ſecundum.</emph></note>
<note position="left" xlink:label="note-0080-01" xlink:href="note-0080-01a" xml:space="preserve"><emph style="it">Argumen-</emph> <lb/><emph style="it">tum decli-</emph> <lb/><emph style="it">nationis.</emph></note>
<note position="left" xlink:label="note-0080-02" xlink:href="note-0080-02a" xml:space="preserve"><emph style="it">Lateralis</emph> <lb/><emph style="it">operatio iã</emph> <lb/><emph style="it">dicta repe-</emph> <lb/><emph style="it">riet.</emph></note>
<note position="left" xlink:label="note-0080-03" xlink:href="note-0080-03a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſcopi.</emph></note>
</div>
</div>
<div xml:id="echoid-div192" type="section" level="1" n="99">
<head xml:id="echoid-head103" xml:space="preserve">PRONVNCIATVM LXXXVII.</head>
<p>
  <s xml:id="echoid-s6626" xml:space="preserve">Aſcenſionem rectam ſtellæ inuenire<unsure/>, puta gradum æquatoris, qui cum <lb/>ſtella propoſita meridianum ſiue horizontem rectum attingit.</s>
  <s xml:id="echoid-s6627" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s6628" xml:space="preserve">Inuenta iam ex ſuperiori pronunciato declinatione ſtellæ uel puncti alicuius, ſinum <lb/>complementi declinationis duc in ſinum totum, productum diuide in ſinum cõplemen-<lb/>
<anchor type="note" xlink:label="note-0080-04a" xlink:href="note-0080-04"/>
ti ſtellæ, arcus quotientis dicetur radix aſcenſionis: </s>
  <s xml:id="echoid-s6629" xml:space="preserve">quòd ſi longitudo ſtellæ ſit in prima <lb/>quadra zodiaci, hoc eſt à principio Arietis ad ſinem Cancri, ſubtrahe tuncradicem il-<lb/>lam à 90. </s>
  <s xml:id="echoid-s6630" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6631" xml:space="preserve">remanebit aſcenſio recta ſtellæ, quæ ſi fuerit in ſecunda quadra à principio <lb/>Cancri ad finem Virginis, addes radicem hancad 90. </s>
  <s xml:id="echoid-s6632" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6633" xml:space="preserve">rurſus habebis aſcenſionem re-<lb/>ctam ſtellæ. </s>
  <s xml:id="echoid-s6634" xml:space="preserve">Sin autem ſtella in tertia quadra inuenta fuerit, ſubtraheradicem à 90. </s>
  <s xml:id="echoid-s6635" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6636" xml:space="preserve"><lb/>reſiduum adde ad 180. </s>
  <s xml:id="echoid-s6637" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6638" xml:space="preserve">proueniet´ ſic tibi etiam aſcenſio recta: </s>
  <s xml:id="echoid-s6639" xml:space="preserve">ſed ſi in ultima <lb/>quadra extiterit, ſcilicet à Capricorno uſ ad finem Piſcium, adde radicem inuentam <lb/>ad 270. </s>
  <s xml:id="echoid-s6640" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6641" xml:space="preserve">habebis aſcenſionem rectam. </s>
  <s xml:id="echoid-s6642" xml:space="preserve">?</s>
  <s xml:id="echoid-s6643" xml:space="preserve">? Iam nunc exemplum uide. </s>
  <s xml:id="echoid-s6644" xml:space="preserve">Cupio uidere a-<lb/>
<anchor type="note" xlink:label="note-0080-05a" xlink:href="note-0080-05"/>
ſcenſionem rectam quartæ ſtellæ Agitatoris, cuius etiam declinationem inueni ex ſu-<lb/>periori pronunciato 43. </s>
  <s xml:id="echoid-s6645" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s6646" xml:space="preserve">15. </s>
  <s xml:id="echoid-s6647" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6648" xml:space="preserve">Complementum eius eſt 46. </s>
  <s xml:id="echoid-s6649" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s6650" xml:space="preserve">45. </s>
  <s xml:id="echoid-s6651" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6652" xml:space="preserve">ſinus il <lb/>lius erit diuiſor. </s>
  <s xml:id="echoid-s6653" xml:space="preserve">Inſuper aſſumo &amp; </s>
  <s xml:id="echoid-s6654" xml:space="preserve">ſinum complemẽti primi inuenti ex proximo pronun <lb/>ciato ſcilicet 6. </s>
  <s xml:id="echoid-s6655" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6656" xml:space="preserve">58. </s>
  <s xml:id="echoid-s6657" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6658" xml:space="preserve">is eſt 12129. </s>
  <s xml:id="echoid-s6659" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6660" xml:space="preserve">hunc ipſum duco in totum, at diuido in diui-<lb/>ſorem, prouenient in quotiente 16652. </s>
  <s xml:id="echoid-s6661" xml:space="preserve">arcus eius eſt 9. </s>
  <s xml:id="echoid-s6662" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6663" xml:space="preserve">35. </s>
  <s xml:id="echoid-s6664" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6665" xml:space="preserve">radix illa aſcenſionis <lb/>Et quia ſtella iſta eſt in prima quadra, ſubtraho eam à 90. </s>
  <s xml:id="echoid-s6666" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6667" xml:space="preserve">manent in reſiduo 80. </s>
  <s xml:id="echoid-s6668" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s6669" xml:space="preserve">25. </s>
  <s xml:id="echoid-s6670" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6671" xml:space="preserve">aſcenſio recta ſtellæ propoſitæ, at is ipſe gradus cum ſtella meridianum ſeume <lb/>dium cœli attingit.</s>
  <s xml:id="echoid-s6672" xml:space="preserve"/>
</p>
<div xml:id="echoid-div192" type="float" level="2" n="1">
<note position="left" xlink:label="note-0080-04" xlink:href="note-0080-04a" xml:space="preserve"><emph style="it">Iam dictum</emph> <lb/><emph style="it">depræhen-</emph> <lb/><emph style="it">ditur per a</emph> <lb/><emph style="it">realem in</emph> <lb/><emph style="it">greſſum.</emph></note>
<note position="left" xlink:label="note-0080-05" xlink:href="note-0080-05a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſcopi.</emph></note>
</div>
</div>
<div xml:id="echoid-div194" type="section" level="1" n="100">
<head xml:id="echoid-head104" xml:space="preserve">PRONVNCIATVM LXXXVIII.</head>
<p>
  <s xml:id="echoid-s6673" xml:space="preserve">Altitudinem poli ſupra horizontem quacun hora noctis, quum ſtellæ <lb/>uidentur, per totum annum ſine omni inſtrumento artificioſe dignoſcere.</s>
  <s xml:id="echoid-s6674" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s6675" xml:space="preserve">Quod hic docebimus, magni profecto faciundum eſt, ſiquidem nec memini à quo-<lb/>quam antea me illum audiuiſſe, proinde placet &amp; </s>
  <s xml:id="echoid-s6676" xml:space="preserve">illum tibi breuiter indicare. </s>
  <s xml:id="echoid-s6677" xml:space="preserve">Vnum ſci <lb/>as, quòd hic de iſtis tantummodo ſtellis dicemus´(breuitatis gratia, quæ declinationem <lb/>habent ſeptentrionalem, ſiquidem de reliquis latius diſſeruimus in noſtris libris Vmbra <lb/>rum. </s>
  <s xml:id="echoid-s6678" xml:space="preserve">Si quando uideris nocte ſtellas duas ſimul horizontem attingere, quod ſingulis fer <lb/>mè quartis ho@aru@@ contingit, quantacun tandem magnitudine fuerint illæ modo <lb/>cognoſci queant, uerifica principio loca earum per 2. </s>
  <s xml:id="echoid-s6679" xml:space="preserve">pronunciati huius, deinde quære <lb/>per 85. </s>
  <s xml:id="echoid-s6680" xml:space="preserve">uel 86. </s>
  <s xml:id="echoid-s6681" xml:space="preserve">earum declinationes, &amp; </s>
  <s xml:id="echoid-s6682" xml:space="preserve">per 87. </s>
  <s xml:id="echoid-s6683" xml:space="preserve">aſcenfionem earum rectam, arcum ſcilicet
<pb file="0081" n="81" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
æquatoris inter aſcenſiones ipſarum concluſum. </s>
  <s xml:id="echoid-s6684" xml:space="preserve">Mox ducito ſinum complementi de-<lb/>
<anchor type="note" xlink:label="note-0081-01a" xlink:href="note-0081-01"/>
clinationis minoris in ſinum differentiæ aſcenſionum illarum, productum diuide in to-<lb/>tum, arcum porrò quotientis iſtius uocabimus inuentum primum. </s>
  <s xml:id="echoid-s6685" xml:space="preserve">Poſtea ſinum mino-<lb/>rem ex ſinu minoris declinationis &amp; </s>
  <s xml:id="echoid-s6686" xml:space="preserve">complementi huius primi inuenti duc in totum, &amp; </s>
  <s xml:id="echoid-s6687" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0081-02a" xlink:href="note-0081-02"/>
productum diuide in maiorem, arcum quotientis ſubtrahe de declinatione maiori, reſi-<lb/>duum dic inuentum ſecundum. </s>
  <s xml:id="echoid-s6688" xml:space="preserve">Præterea duc ſinum complementi ſecundi inuenti in ſi-<lb/>
<anchor type="note" xlink:label="note-0081-03a" xlink:href="note-0081-03"/>
dum cõplementi primi inuenti, &amp; </s>
  <s xml:id="echoid-s6689" xml:space="preserve">diuide productum in totum, arcus quotientis pordu-<lb/>cet ipſas diſtantias ſtellarum. </s>
  <s xml:id="echoid-s6690" xml:space="preserve">Inſuper adhuc ſinum primi inuenti duc in totum, produ-<lb/>
<anchor type="note" xlink:label="note-0081-04a" xlink:href="note-0081-04"/>
ctum diuide in ſinum diſtantiæ, &amp; </s>
  <s xml:id="echoid-s6691" xml:space="preserve">arcus quotientis dabit inuentum tertium. </s>
  <s xml:id="echoid-s6692" xml:space="preserve">Ad extre-<lb/>mum duc etiam ſinum inuenti huius tertĳ in ſinum complementi declinationis maioris, <lb/>
<anchor type="note" xlink:label="note-0081-05a" xlink:href="note-0081-05"/>
producto hinc in totum diuiſo, arcus quotientis monſtrabit altitudinem poli quæſitam.</s>
  <s xml:id="echoid-s6693" xml:space="preserve"/>
</p>
<div xml:id="echoid-div194" type="float" level="2" n="1">
<note position="right" xlink:label="note-0081-01" xlink:href="note-0081-01a" xml:space="preserve"><emph style="it">Illud inueni</emph> <lb/><emph style="it">es later ali-</emph> <lb/><emph style="it">ter.</emph></note>
<note position="right" xlink:label="note-0081-02" xlink:href="note-0081-02a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">primum.</emph></note>
<note position="right" xlink:label="note-0081-03" xlink:href="note-0081-03a" xml:space="preserve"><emph style="it">Hoc area-</emph> <lb/><emph style="it">tim quæren</emph> <lb/><emph style="it">ti pater.</emph></note>
<note position="right" xlink:label="note-0081-04" xlink:href="note-0081-04a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">ſecundum.</emph></note>
<note position="right" xlink:label="note-0081-05" xlink:href="note-0081-05a" xml:space="preserve"><emph style="it">Primum ba</emph> <lb/><emph style="it">betur ꝑ late</emph> <lb/><emph style="it">ra, ſecundũ</emph> <lb/><emph style="it">uero per</emph> <lb/><emph style="it">aream.</emph></note>
</div>
<p>
  <s xml:id="echoid-s6694" xml:space="preserve">?</s>
  <s xml:id="echoid-s6695" xml:space="preserve">? Anima duerte etiam hic exemplum quod tibi dabimus. </s>
  <s xml:id="echoid-s6696" xml:space="preserve">Eſto ut Auguſtæ in loco intro <lb/>nizat onis uiſæ ſint ſtellæ duæ in horizontem ſimul oriri, quarum etiam loca ſint cogni-<lb/>ta, &amp; </s>
  <s xml:id="echoid-s6697" xml:space="preserve">altera quidem habuerit in declinatione 18. </s>
  <s xml:id="echoid-s6698" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6699" xml:space="preserve">11. </s>
  <s xml:id="echoid-s6700" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6701" xml:space="preserve">altera autem 34. </s>
  <s xml:id="echoid-s6702" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6703" xml:space="preserve">19. </s>
  <s xml:id="echoid-s6704" xml:space="preserve">mi. <lb/></s>
  <s xml:id="echoid-s6705" xml:space="preserve">quæ eſt declinatio maior. </s>
  <s xml:id="echoid-s6706" xml:space="preserve">Differentia aſcenſionum rectarum ſit 28. </s>
  <s xml:id="echoid-s6707" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6708" xml:space="preserve">25. </s>
  <s xml:id="echoid-s6709" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6710" xml:space="preserve">iam ſinũ <lb/>complementi minoris declinationis 95006. </s>
  <s xml:id="echoid-s6711" xml:space="preserve">duco in ſinum differentiæ aſcenſionum re-<lb/>ctarum ſcilicet 47588. </s>
  <s xml:id="echoid-s6712" xml:space="preserve">quotientem diuido in totum, is eſt 45211. </s>
  <s xml:id="echoid-s6713" xml:space="preserve">arcus ipſius 26. </s>
  <s xml:id="echoid-s6714" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6715" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0081-06a" xlink:href="note-0081-06"/>
53. </s>
  <s xml:id="echoid-s6716" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6717" xml:space="preserve">dicetur inuentum primum. </s>
  <s xml:id="echoid-s6718" xml:space="preserve">ſinum minoris declinationis ſcilicet 31210. </s>
  <s xml:id="echoid-s6719" xml:space="preserve">duco in <lb/>totum, productum diuido in ſinum complementi primi inuenti ſcilicet 89192. </s>
  <s xml:id="echoid-s6720" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6721" xml:space="preserve">diuido <lb/>productum in totum, quotiens producit 34991. </s>
  <s xml:id="echoid-s6722" xml:space="preserve">arcus eius eſt 20. </s>
  <s xml:id="echoid-s6723" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6724" xml:space="preserve">29. </s>
  <s xml:id="echoid-s6725" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6726" xml:space="preserve">quo ſubtra <lb/>cto à maiori declinatione ſtellarum, ſcilicet 34. </s>
  <s xml:id="echoid-s6727" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6728" xml:space="preserve">19. </s>
  <s xml:id="echoid-s6729" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6730" xml:space="preserve">remanent 13. </s>
  <s xml:id="echoid-s6731" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6732" xml:space="preserve">50. </s>
  <s xml:id="echoid-s6733" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6734" xml:space="preserve">in-<lb/>uentum ſecundum. </s>
  <s xml:id="echoid-s6735" xml:space="preserve">Porrò ſinum complem@nti huius ſecundi inuenti 97099. </s>
  <s xml:id="echoid-s6736" xml:space="preserve">duco in ſinũ <lb/>complementi primi inuenti, ſcilicet 89192. </s>
  <s xml:id="echoid-s6737" xml:space="preserve">quotientem diuido in totum, eſt autem quo-<lb/>tiens 86604. </s>
  <s xml:id="echoid-s6738" xml:space="preserve">arcus ipſius eſt 60. </s>
  <s xml:id="echoid-s6739" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6740" xml:space="preserve">complementum uero 30. </s>
  <s xml:id="echoid-s6741" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6742" xml:space="preserve">diſtantia illa duarum <lb/>ſtellarum. </s>
  <s xml:id="echoid-s6743" xml:space="preserve">lam quo duco ſinum primi inuenti 45211. </s>
  <s xml:id="echoid-s6744" xml:space="preserve">in totum, &amp; </s>
  <s xml:id="echoid-s6745" xml:space="preserve">diuido in ſinum di-<lb/>ſtantiæ, quotiens eſt 90422. </s>
  <s xml:id="echoid-s6746" xml:space="preserve">arcus illius 64, gra. </s>
  <s xml:id="echoid-s6747" xml:space="preserve">44. </s>
  <s xml:id="echoid-s6748" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6749" xml:space="preserve">inuentum tertium. </s>
  <s xml:id="echoid-s6750" xml:space="preserve">Poſtremo du-<lb/>co &amp; </s>
  <s xml:id="echoid-s6751" xml:space="preserve">ſinum complementi maioris declinationis 82593. </s>
  <s xml:id="echoid-s6752" xml:space="preserve">in ſinum tertĳ inuenti 90434. </s>
  <s xml:id="echoid-s6753" xml:space="preserve">ꝓ <lb/>ductum diuido in totum, &amp; </s>
  <s xml:id="echoid-s6754" xml:space="preserve">quotiens erit 74692. </s>
  <s xml:id="echoid-s6755" xml:space="preserve">arcus eius 48. </s>
  <s xml:id="echoid-s6756" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6757" xml:space="preserve">20. </s>
  <s xml:id="echoid-s6758" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6759" xml:space="preserve">altitudo iſta <lb/>polinon ſine magnainduſtria ad locum intronizationis quæſita &amp; </s>
  <s xml:id="echoid-s6760" xml:space="preserve">inuenta.</s>
  <s xml:id="echoid-s6761" xml:space="preserve"/>
</p>
<div xml:id="echoid-div195" type="float" level="2" n="2">
<note position="right" xlink:label="note-0081-06" xlink:href="note-0081-06a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſcopi.</emph></note>
</div>
</div>
<div xml:id="echoid-div197" type="section" level="1" n="101">
<head xml:id="echoid-head105" xml:space="preserve">PRONVNCIATVM LXXXIX.</head>
<p>
  <s xml:id="echoid-s6762" xml:space="preserve">Punctum iſtud eclypticæ cum quo ſtella ſeu punctum quoduis cœli me-<lb/>dium tangit, perſcrutari.</s>
  <s xml:id="echoid-s6763" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s6764" xml:space="preserve">Ex ſuperiori pronunciato quære aſcenſionem rectam ſtellæ, deinde per 8. </s>
  <s xml:id="echoid-s6765" xml:space="preserve">pronuncia <lb/>tum quære gradum ſiue punctum eclypticæ, qui aſcendit in ſphæra recta unà cum gradu <lb/>
<anchor type="note" xlink:label="note-0081-07a" xlink:href="note-0081-07"/>
æquatoris ſiue aſcenſione recta ſtellæ, &amp; </s>
  <s xml:id="echoid-s6766" xml:space="preserve">inuenies punctum hoc modo. </s>
  <s xml:id="echoid-s6767" xml:space="preserve">Duc ſinum com-<lb/>plementi aſcenſionis rectæ in ſinum maximæ declinationis, productum diuide in ſinum <lb/>totum, &amp; </s>
  <s xml:id="echoid-s6768" xml:space="preserve">arcum quotientis ſubtrahe de 90. </s>
  <s xml:id="echoid-s6769" xml:space="preserve">ſinus reſidui deinceps erit diuiſor. </s>
  <s xml:id="echoid-s6770" xml:space="preserve">Mox ubi <lb/>ſinum aſcenſionis recte duxeris in totum, &amp; </s>
  <s xml:id="echoid-s6771" xml:space="preserve">productum in ipſum diuiſeris diuiſorem, <lb/>
<anchor type="note" xlink:label="note-0081-08a" xlink:href="note-0081-08"/>
arcus quotientis oſtendet arcum eclypticæ, cuius extremitas mediat cœlum unà cum <lb/>ſtella propoſita. </s>
  <s xml:id="echoid-s6772" xml:space="preserve">Sin autem aſcenſio recta maior fuerit quàm 90. </s>
  <s xml:id="echoid-s6773" xml:space="preserve">operare cum comple-<lb/>mento eius, &amp; </s>
  <s xml:id="echoid-s6774" xml:space="preserve">arcum inuentum computa â principio Libræ contra ordinem ſignorum. <lb/></s>
  <s xml:id="echoid-s6775" xml:space="preserve">Et ſi aſcenſio etiamſi amplior fuerit quàm 180. </s>
  <s xml:id="echoid-s6776" xml:space="preserve">tunc arcum ipſum ſupputa à principio ♎ <lb/>ſecundum ſeriem ſignorum: </s>
  <s xml:id="echoid-s6777" xml:space="preserve">ſed ſi aſcenſio illa maior fuerit quàm 270. </s>
  <s xml:id="echoid-s6778" xml:space="preserve">numera arcum <lb/>inuentum à principio Arietis contra ſignorum ordinem. </s>
  <s xml:id="echoid-s6779" xml:space="preserve">?</s>
  <s xml:id="echoid-s6780" xml:space="preserve">? Exemplum hoc conſidera <lb/>
<anchor type="note" xlink:label="note-0081-09a" xlink:href="note-0081-09"/>
Aſſume iterum quartam ſtellam Agitatoris, quæ ſub ipſam horam intronizationis ferè <lb/>cum Sole in uno circulo poſitionis extitit, aſcenſio eius recta quam ex præcedentibus in <lb/>ueni, eſt 80. </s>
  <s xml:id="echoid-s6781" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6782" xml:space="preserve">25. </s>
  <s xml:id="echoid-s6783" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6784" xml:space="preserve">Complementum eius 9. </s>
  <s xml:id="echoid-s6785" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6786" xml:space="preserve">35. </s>
  <s xml:id="echoid-s6787" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6788" xml:space="preserve">ſinum ipſius. </s>
  <s xml:id="echoid-s6789" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s6790" xml:space="preserve">16648. </s>
  <s xml:id="echoid-s6791" xml:space="preserve">duco <lb/>in ſinum maximæ declinationis, productum diuido in totum, quotiens eſt 6639. </s>
  <s xml:id="echoid-s6792" xml:space="preserve">arcus il <lb/>lius 3. </s>
  <s xml:id="echoid-s6793" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6794" xml:space="preserve">49. </s>
  <s xml:id="echoid-s6795" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6796" xml:space="preserve">ſinus autem complementi 99778. </s>
  <s xml:id="echoid-s6797" xml:space="preserve">eſt ipſe diuiſor, ſi iam duxero ſinum <lb/>aſcenſionis rectæ 80. </s>
  <s xml:id="echoid-s6798" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6799" xml:space="preserve">25. </s>
  <s xml:id="echoid-s6800" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6801" xml:space="preserve">ſcilicet 98604. </s>
  <s xml:id="echoid-s6802" xml:space="preserve">in totum, &amp; </s>
  <s xml:id="echoid-s6803" xml:space="preserve">diuiſero in diuiſorem, quoti-<lb/>ens exhibebit mihi 98823. </s>
  <s xml:id="echoid-s6804" xml:space="preserve">cuius arcus eſt 81. </s>
  <s xml:id="echoid-s6805" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6806" xml:space="preserve">12. </s>
  <s xml:id="echoid-s6807" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6808" xml:space="preserve">eũ ſi ſupputemà principio ♈, <lb/>finietur in 21. </s>
  <s xml:id="echoid-s6809" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6810" xml:space="preserve">12. </s>
  <s xml:id="echoid-s6811" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6812" xml:space="preserve">II, cum quo etiam ſtella iſta medium attigit cœli.</s>
  <s xml:id="echoid-s6813" xml:space="preserve"/>
</p>
<div xml:id="echoid-div197" type="float" level="2" n="1">
<note position="right" xlink:label="note-0081-07" xlink:href="note-0081-07a" xml:space="preserve"><emph style="it">Illud diſces</emph> <lb/><emph style="it">ſecundum</emph> <lb/><emph style="it">latera.</emph></note>
<note position="right" xlink:label="note-0081-08" xlink:href="note-0081-08a" xml:space="preserve"><emph style="it">Hoc area-</emph> <lb/><emph style="it">tim quæren</emph> <lb/><emph style="it">ti patet.</emph></note>
<note position="right" xlink:label="note-0081-09" xlink:href="note-0081-09a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſoopi.</emph></note>
</div>
<pb file="0082" n="82" rhead="GENVINVS VSVS"/>
</div>
<div xml:id="echoid-div199" type="section" level="1" n="102">
<head xml:id="echoid-head106" xml:space="preserve">PRONVNCIATVM XC.</head>
<p>
  <s xml:id="echoid-s6814" xml:space="preserve">Amplitudinem ortiuam &amp; </s>
  <s xml:id="echoid-s6815" xml:space="preserve">occiduam ſtellarum fixarum &amp; </s>
  <s xml:id="echoid-s6816" xml:space="preserve">erraticarum <lb/>adinuenire.</s>
  <s xml:id="echoid-s6817" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s6818" xml:space="preserve">Primum omnium conſidera hic an declinatio ſtellæ, cuius amplitudinem ſcire cu-<lb/>pis, minor ſituel maior complemento eleuationis poli, cui ſi fuerit æqualis, ſcias eã ſtel <lb/>lam nec oriri, neoccidere, ſed ad momentum temporis horizontem leuiter tantũ tan-<lb/>gere: </s>
  <s xml:id="echoid-s6819" xml:space="preserve">ſed ſi illa maior extiterit, ſtelia iſta nunquàm ſub horizontem deſcendit, uerumta-<lb/>men ſi minor fuerit, tunc demum ſtella quolibet die naturali occidit &amp; </s>
  <s xml:id="echoid-s6820" xml:space="preserve">oritur, quæcun <lb/>ergo horizontem non attingit, nec ortiuam ne occiduam habet amplitudinem, ſicut in <lb/>hoc exemplo conſpicies. </s>
  <s xml:id="echoid-s6821" xml:space="preserve">?</s>
  <s xml:id="echoid-s6822" xml:space="preserve">? Superius iam tractaui ſtellam quartã Agitatoris, quòd ea <lb/>
<anchor type="note" xlink:label="note-0082-01a" xlink:href="note-0082-01"/>
ſub horam intronizationis cum Sole in uno penè ſemicirculo poſitionis fuerit, &amp; </s>
  <s xml:id="echoid-s6823" xml:space="preserve">inue-<lb/>ni declinationem ipſius ex 85. </s>
  <s xml:id="echoid-s6824" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6825" xml:space="preserve">86. </s>
  <s xml:id="echoid-s6826" xml:space="preserve">pronunciato 43. </s>
  <s xml:id="echoid-s6827" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6828" xml:space="preserve">15. </s>
  <s xml:id="echoid-s6829" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6830" xml:space="preserve">quia ergo locus introni <lb/>zationis factæ in latitudine habet tantum 48. </s>
  <s xml:id="echoid-s6831" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6832" xml:space="preserve">20. </s>
  <s xml:id="echoid-s6833" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6834" xml:space="preserve">complementum eius eſt 41. <lb/></s>
  <s xml:id="echoid-s6835" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6836" xml:space="preserve">40. </s>
  <s xml:id="echoid-s6837" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6838" xml:space="preserve">ecce iam quia declinatio ſtellæ uno gradu 35. </s>
  <s xml:id="echoid-s6839" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6840" xml:space="preserve">maior eſt, horizõtem attin <lb/>gere non poteſt, ſed Auguſtæ ſuper horizontem ſemper apparet. </s>
  <s xml:id="echoid-s6841" xml:space="preserve">Quæcun autem ſtel <lb/>
<anchor type="note" xlink:label="note-0082-02a" xlink:href="note-0082-02"/>
la declinationem habet minorem, eius amplitudinem ſic quæres. </s>
  <s xml:id="echoid-s6842" xml:space="preserve">Declinationem ſtellæ <lb/>quære per 85. </s>
  <s xml:id="echoid-s6843" xml:space="preserve">uel 86. </s>
  <s xml:id="echoid-s6844" xml:space="preserve">ſinum eius duc in totum, productum diuide in ſinum complementi <lb/>altitudinis poli, ſi complementum fuerit declinatione maius, ſi non, planè contrario <lb/>modo operare, &amp; </s>
  <s xml:id="echoid-s6845" xml:space="preserve">arcus quotientis dabit amplitudinem ſtellæ. </s>
  <s xml:id="echoid-s6846" xml:space="preserve">Atqui ut declinatiões ſtel <lb/>larum facilius inquiras, ecce tibi propono gradum Mercurĳ, in quo fuit ipſa hora intro <lb/>nizationis, puta in 10. </s>
  <s xml:id="echoid-s6847" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6848" xml:space="preserve">12. </s>
  <s xml:id="echoid-s6849" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6850" xml:space="preserve">♉, habu@´ latitudinem ab eclyptica 3. </s>
  <s xml:id="echoid-s6851" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6852" xml:space="preserve">20. </s>
  <s xml:id="echoid-s6853" xml:space="preserve">mi. <lb/></s>
  <s xml:id="echoid-s6854" xml:space="preserve">declinatio eius fuit 11. </s>
  <s xml:id="echoid-s6855" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6856" xml:space="preserve">59. </s>
  <s xml:id="echoid-s6857" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6858" xml:space="preserve">ſinus autem 40767. </s>
  <s xml:id="echoid-s6859" xml:space="preserve">eum duco in totum, &amp; </s>
  <s xml:id="echoid-s6860" xml:space="preserve">productũ <lb/>diuido in ſinum complementi loci, in quo facta eſt intronizatio, complementum iſtud <lb/>eſt 41. </s>
  <s xml:id="echoid-s6861" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6862" xml:space="preserve">40. </s>
  <s xml:id="echoid-s6863" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6864" xml:space="preserve">in quotiente proueniunt 31238. </s>
  <s xml:id="echoid-s6865" xml:space="preserve">arcus eius eſt 18. </s>
  <s xml:id="echoid-s6866" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6867" xml:space="preserve">12. </s>
  <s xml:id="echoid-s6868" xml:space="preserve">mi, amplitu-<lb/>do illa ortiua Mercurĳ quæſita, ea´ ſeptentrionalis, &amp; </s>
  <s xml:id="echoid-s6869" xml:space="preserve">tantum habet ille in amplitudi-<lb/>ne occidua.</s>
  <s xml:id="echoid-s6870" xml:space="preserve"/>
</p>
<div xml:id="echoid-div199" type="float" level="2" n="1">
<note position="left" xlink:label="note-0082-01" xlink:href="note-0082-01a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſcopi.</emph></note>
<note position="left" xlink:label="note-0082-02" xlink:href="note-0082-02a" xml:space="preserve"><emph style="it">Illud inue-</emph> <lb/><emph style="it">nitur per a</emph> <lb/><emph style="it">rcalem in-</emph> <lb/><emph style="it">greſſum.</emph></note>
</div>
</div>
<div xml:id="echoid-div201" type="section" level="1" n="103">
<head xml:id="echoid-head107" xml:space="preserve">PRONVNCIATVM XCI.</head>
<p>
  <s xml:id="echoid-s6871" xml:space="preserve">Aſcenſionem rectam ſtellarum fixarum &amp; </s>
  <s xml:id="echoid-s6872" xml:space="preserve">erraticarum quàm expeditiſ-<lb/>ſime cognoſcere.</s>
  <s xml:id="echoid-s6873" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s6874" xml:space="preserve">Hic nunc principio uide cuinam puncto æquinoctĳ, principio ſcilicet Arietis uel Li-<lb/>bræ ſtella ſit propinquior, ſecundum gradus longitudinis in eclyptica contra uel ſecun-<lb/>dum ordinem ſignorum, ſinum complementi eius diſtantiæ duc in ſinum complementi <lb/>latitudinis ſtellæ, &amp; </s>
  <s xml:id="echoid-s6875" xml:space="preserve">diuide in ſinum totum, arcus quotientis â 90. </s>
  <s xml:id="echoid-s6876" xml:space="preserve">ſublatus, reliquam ſtel <lb/>
<anchor type="note" xlink:label="note-0082-03a" xlink:href="note-0082-03"/>
læ faciet diſtantiam à principio Arietis uel Libræ ſecundum circulum directum. </s>
  <s xml:id="echoid-s6877" xml:space="preserve">ſinum <lb/>complementi huius arcus tibi propone, unà cum ſinu complementi declinationis ſtellæ, <lb/>minorem duc in totum, productum diuide in maiorem, arcus quotientis de 90. </s>
  <s xml:id="echoid-s6878" xml:space="preserve">ſubla-<lb/>
<anchor type="note" xlink:label="note-0082-04a" xlink:href="note-0082-04"/>
tus, relinquit arcum æquatoris numerando â puncto ♈ uel ♎, unde &amp; </s>
  <s xml:id="echoid-s6879" xml:space="preserve">diſtantia ſtellæ cõ <lb/>putatur, dicetur´ radix aſcenſionis, hic ſi ſolum rationis dictamen ſequaris, facile inue-<lb/>nies aſcenſionem rectam in hunc modum. </s>
  <s xml:id="echoid-s6880" xml:space="preserve">Si diſtantia ſtellæ ab initio ♈ ſecundum ordi <lb/>nem ſignorũ fuerit accepta, tunc arcus inuentus ſiue radix per ſe tibi monſtrabit aſcen-<lb/>ſionem rectam: </s>
  <s xml:id="echoid-s6881" xml:space="preserve">ſin autẽ diſtantia ab ♈ ſit cõtra ſignorũ ordinem cõnumerata, ſubtrahe <lb/>radicem illam â circulo toto, &amp; </s>
  <s xml:id="echoid-s6882" xml:space="preserve">reliquã habebis aſcenſionem rectã ſtellæ: </s>
  <s xml:id="echoid-s6883" xml:space="preserve">ſed ſi diſtantia <lb/>ſtellæ à principio ♎ numerata eſt contra ordinem ſignorum, ſubtrahes radicem à ſemi-<lb/>circulo, uerum ubi ab eodem initio ſecundum ordinem ſignorum fuerit accepta diſtan-<lb/>tia, adde radicem ad ſemicirculum. </s>
  <s xml:id="echoid-s6884" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s6885" xml:space="preserve">180. </s>
  <s xml:id="echoid-s6886" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6887" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6888" xml:space="preserve">rurſus proueniet tibi aſcenſio recta ſtel <lb/>læ. </s>
  <s xml:id="echoid-s6889" xml:space="preserve">?</s>
  <s xml:id="echoid-s6890" xml:space="preserve">? Exempli gratia, non recedemus à Mercurio, quoniã &amp; </s>
  <s xml:id="echoid-s6891" xml:space="preserve">is hora intronizationis <lb/>
<anchor type="note" xlink:label="note-0082-05a" xlink:href="note-0082-05"/>
gratus acceſsit ad locũ honoris Epiſcopi ipſius intronizationis: </s>
  <s xml:id="echoid-s6892" xml:space="preserve">diſtantia aũt eius â prin <lb/>cipio ♈ (cui erat tunc proximus) eſt 40. </s>
  <s xml:id="echoid-s6893" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6894" xml:space="preserve">12. </s>
  <s xml:id="echoid-s6895" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6896" xml:space="preserve">ſinus complementi eſt 79379. </s>
  <s xml:id="echoid-s6897" xml:space="preserve">eum <lb/>duc in ſinũ complementi latitudinis 99830. </s>
  <s xml:id="echoid-s6898" xml:space="preserve">ſiquidem latitudo eſt 3. </s>
  <s xml:id="echoid-s6899" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6900" xml:space="preserve">20. </s>
  <s xml:id="echoid-s6901" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6902" xml:space="preserve">iam ſi di-<lb/>uido per totu@, prodeunt in quotiente 75349. </s>
  <s xml:id="echoid-s6903" xml:space="preserve">arcus eius eſt 48. </s>
  <s xml:id="echoid-s6904" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6905" xml:space="preserve">14. </s>
  <s xml:id="echoid-s6906" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6907" xml:space="preserve">complemen-<lb/>tum 41. </s>
  <s xml:id="echoid-s6908" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6909" xml:space="preserve">6. </s>
  <s xml:id="echoid-s6910" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6911" xml:space="preserve">eſt diſtãtia Mercurĳ à principio ♈ ſecundum circulum maiorem. </s>
  <s xml:id="echoid-s6912" xml:space="preserve">Si-<lb/>num cõplementi huius arcus 75356, tan̈ minorẽ duco in totum, &amp; </s>
  <s xml:id="echoid-s6913" xml:space="preserve">productũ diuido in
<pb file="0083" n="83" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
ſinum complementi declinationis Mercurĳ ſcilicet 97820. </s>
  <s xml:id="echoid-s6914" xml:space="preserve">quotiens erit 77035. </s>
  <s xml:id="echoid-s6915" xml:space="preserve">arcus e-<lb/>ius 50. </s>
  <s xml:id="echoid-s6916" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6917" xml:space="preserve">23. </s>
  <s xml:id="echoid-s6918" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6919" xml:space="preserve">complementum uero 39. </s>
  <s xml:id="echoid-s6920" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6921" xml:space="preserve">37. </s>
  <s xml:id="echoid-s6922" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6923" xml:space="preserve">dicitur radix aſcenſionis, &amp; </s>
  <s xml:id="echoid-s6924" xml:space="preserve">hic <lb/>quidem aſcenſio recta Mercurĳ, quoniam diſtantia ipſius à principio ♈ ſecundum or-<lb/>dinem ſignorum numeratur.</s>
  <s xml:id="echoid-s6925" xml:space="preserve"/>
</p>
<div xml:id="echoid-div201" type="float" level="2" n="1">
<note position="left" xlink:label="note-0082-03" xlink:href="note-0082-03a" xml:space="preserve"><emph style="it">Hoc latera</emph> <lb/><emph style="it">tim aſſeque</emph> <lb/><emph style="it">ris.</emph></note>
<note position="left" xlink:label="note-0082-04" xlink:href="note-0082-04a" xml:space="preserve"><emph style="it">Iam dictum</emph> <lb/><emph style="it">habetur ꝑ</emph> <lb/><emph style="it">arcam.</emph></note>
<note position="left" xlink:label="note-0082-05" xlink:href="note-0082-05a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſcopi.</emph></note>
</div>
</div>
<div xml:id="echoid-div203" type="section" level="1" n="104">
<head xml:id="echoid-head108" xml:space="preserve">PRONVNCIATVM XCII.</head>
<p>
  <s xml:id="echoid-s6926" xml:space="preserve">Arcum ſemidiurnum ſtellæ &amp; </s>
  <s xml:id="echoid-s6927" xml:space="preserve">eius etiam aſcenſionem obliquam in æqua <lb/>tore perſpicere.</s>
  <s xml:id="echoid-s6928" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s6929" xml:space="preserve">Arcus ſtellæ diurnus eſt tantum temporis quo ſuper horizontem apparet, ideo autẽ <lb/>uocatur arcus, quoniam quodlibet punctum in cœli uirtute motus primi mobilis, circu-<lb/>lum deſcribit imaginarium æquidiſtantem æquinoctiali, &amp; </s>
  <s xml:id="echoid-s6930" xml:space="preserve">is quidem circulus æque in <lb/>24. </s>
  <s xml:id="echoid-s6931" xml:space="preserve">horas diuiditur, at æquino ctialis, earum horarum quot ſuper horizontem ma-<lb/>
<anchor type="note" xlink:label="note-0083-01a" xlink:href="note-0083-01"/>
nent alicuius regionis, arcum uocamus diurnum, medietatem ipſius, ſemidiurnum. </s>
  <s xml:id="echoid-s6932" xml:space="preserve">Quũ <lb/>ergo ex 85. </s>
  <s xml:id="echoid-s6933" xml:space="preserve">uel 86. </s>
  <s xml:id="echoid-s6934" xml:space="preserve">inuentam habes declinationem ſtellæ, &amp; </s>
  <s xml:id="echoid-s6935" xml:space="preserve">ex 90. </s>
  <s xml:id="echoid-s6936" xml:space="preserve">amplitudinem, tunc ſi <lb/>num complementi amplitudinis duc in totum, productum diuide in ſinum complemen <lb/>ti declinationis, arcum quotientis ſubtrahe de quadra circuli, reſiduum dicetur differen <lb/>tia aſcenſionalis. </s>
  <s xml:id="echoid-s6937" xml:space="preserve">quòd ſi ſtella habuerit declinationem ſeptentrionalem, addes differen <lb/>tiam hanc ad 90. </s>
  <s xml:id="echoid-s6938" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6939" xml:space="preserve">habebis arcum ſemidiurnum ſtellæ: </s>
  <s xml:id="echoid-s6940" xml:space="preserve">ſi autem declinatio ſtellæ fuerit <lb/>Auſtralis, ſubtrahes eam à 90. </s>
  <s xml:id="echoid-s6941" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6942" xml:space="preserve">rurſus manebit tempus diurnum, ſemper 15. </s>
  <s xml:id="echoid-s6943" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6944" xml:space="preserve">com <lb/>putando pro hora, facile arcum ſemidiurnum conuertes in tempus horarum, ſi duplica <lb/>ris, horæ iſtæ oſtendent tibi qua mdiu ſtelia propoſita maneat nobis conſpicua ſupra ho <lb/>rizontem, ſiue illud contingat in die ſiue in nocte, at omnis hæc noſtra ſupputatio ſic <lb/>intelligi debet, ac ſi terra tota punctum eſſet tantum reſpectu firmamenti. </s>
  <s xml:id="echoid-s6945" xml:space="preserve">Subtracta <lb/>autem hac differentia aſcenſionali ab aſcenſione recta ſtellæ (ſi tamen ſtella declinatio-<lb/>nem habuerit ſeptentrionalem) remanebit illa obliqua ſtellæ aſcenſio. </s>
  <s xml:id="echoid-s6946" xml:space="preserve">Sed ſi Auſtralis <lb/>extiterit, adde differentiam iſtam ad aſcenſionem rectam, &amp; </s>
  <s xml:id="echoid-s6947" xml:space="preserve">ſic quo proueniet obli-<lb/>qua. </s>
  <s xml:id="echoid-s6948" xml:space="preserve">At in hunc modum uno pronunciato geminam tibi quæſtionem ſolutam, tantũ <lb/>
<anchor type="note" xlink:label="note-0083-02a" xlink:href="note-0083-02"/>
nunc exemplum accipe. </s>
  <s xml:id="echoid-s6949" xml:space="preserve">?</s>
  <s xml:id="echoid-s6950" xml:space="preserve">? Quia non abeſſe ſolet Mercurius à quacunre quæ nonni <lb/>hil ponderis habet, ſed omnibus negotĳs ſeſe immiſcet, ſic´ in hac etiam intronizatio <lb/>nis ſupremum &amp; </s>
  <s xml:id="echoid-s6951" xml:space="preserve">honeſtiſsimum locum ſibi uſurpauit, age ne nos eum hinc detrude-<lb/>mus, ſiquidẽ intronizationi huic hactenus fœlix adfuit, &amp; </s>
  <s xml:id="echoid-s6952" xml:space="preserve">fauentibus ſuperis deinceps <lb/>quo proſpere cuncta adminiſtrabit. </s>
  <s xml:id="echoid-s6953" xml:space="preserve">Declinatio eius fuit iam ante inuenta per 85. </s>
  <s xml:id="echoid-s6954" xml:space="preserve">uel <lb/>86. </s>
  <s xml:id="echoid-s6955" xml:space="preserve">pronũciatum, 11. </s>
  <s xml:id="echoid-s6956" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6957" xml:space="preserve">59. </s>
  <s xml:id="echoid-s6958" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6959" xml:space="preserve">ſinum igitur eius complementi 94997. </s>
  <s xml:id="echoid-s6960" xml:space="preserve">duco in totum <lb/>&amp; </s>
  <s xml:id="echoid-s6961" xml:space="preserve">productum diuido in ſinum complementi amplitudinis, quam per 90. </s>
  <s xml:id="echoid-s6962" xml:space="preserve">pronunciatum <lb/>inueni eſſe 18. </s>
  <s xml:id="echoid-s6963" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6964" xml:space="preserve">12. </s>
  <s xml:id="echoid-s6965" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6966" xml:space="preserve">finis autem complementi eſt 97820. </s>
  <s xml:id="echoid-s6967" xml:space="preserve">quotiens 97114. </s>
  <s xml:id="echoid-s6968" xml:space="preserve">arcus ipſi <lb/>us 76. </s>
  <s xml:id="echoid-s6969" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6970" xml:space="preserve">12. </s>
  <s xml:id="echoid-s6971" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6972" xml:space="preserve">eo ſubtracto à 90. </s>
  <s xml:id="echoid-s6973" xml:space="preserve">remanent 13. </s>
  <s xml:id="echoid-s6974" xml:space="preserve">gra 48. </s>
  <s xml:id="echoid-s6975" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6976" xml:space="preserve">differentia aſcenſionalis. <lb/></s>
  <s xml:id="echoid-s6977" xml:space="preserve">Et quia declinatio Mercurĳ eſt ſeptentrionalis, addo differentiam ad 90. </s>
  <s xml:id="echoid-s6978" xml:space="preserve">ſic proueniunt <lb/>103. </s>
  <s xml:id="echoid-s6979" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6980" xml:space="preserve">48. </s>
  <s xml:id="echoid-s6981" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6982" xml:space="preserve">arcus ſcilicet ſemidiurnus, quo duplicato &amp; </s>
  <s xml:id="echoid-s6983" xml:space="preserve">in horas conuerſo, habebo <lb/>inde 13. </s>
  <s xml:id="echoid-s6984" xml:space="preserve">horas, 48. </s>
  <s xml:id="echoid-s6985" xml:space="preserve">ferè minuta, &amp; </s>
  <s xml:id="echoid-s6986" xml:space="preserve">tantum quidem temporis Mercurius ipſo die introni <lb/>zationis permanſit ſuper horizontem. </s>
  <s xml:id="echoid-s6987" xml:space="preserve">Differentiam illam ſubtraho (ſiquidem declina-<lb/>tio eſt ſeptentrionalis) ab aſcenſione recta, quam inueni per 91. </s>
  <s xml:id="echoid-s6988" xml:space="preserve">habere 39. </s>
  <s xml:id="echoid-s6989" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6990" xml:space="preserve">37. </s>
  <s xml:id="echoid-s6991" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6992" xml:space="preserve"><lb/>remanent mihi 25. </s>
  <s xml:id="echoid-s6993" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s6994" xml:space="preserve">49. </s>
  <s xml:id="echoid-s6995" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s6996" xml:space="preserve">æquinoctialis, &amp; </s>
  <s xml:id="echoid-s6997" xml:space="preserve">eo die cum Mercurio horizontem Au-<lb/>guſteñ, attigerunt.</s>
  <s xml:id="echoid-s6998" xml:space="preserve"/>
</p>
<div xml:id="echoid-div203" type="float" level="2" n="1">
<note position="right" xlink:label="note-0083-01" xlink:href="note-0083-01a" xml:space="preserve"><emph style="it">Illud inue-</emph> <lb/><emph style="it">nies introi</emph> <lb/><emph style="it">tu Areali.</emph></note>
<note position="right" xlink:label="note-0083-02" xlink:href="note-0083-02a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſcopi.</emph></note>
</div>
</div>
<div xml:id="echoid-div205" type="section" level="1" n="105">
<head xml:id="echoid-head109" xml:space="preserve">PRONVNCIATVM XCIII.</head>
<p>
  <s xml:id="echoid-s6999" xml:space="preserve">Cum quo gradu ſiue puncto eclypticæ quælibet ſtella fixa &amp; </s>
  <s xml:id="echoid-s7000" xml:space="preserve">erratica, ſi-<lb/>militer &amp; </s>
  <s xml:id="echoid-s7001" xml:space="preserve">aliud quoduis punctum imaginarium primi mobilis ſuper hori-<lb/>zontem obliquam aſcendit, uel eum tangit, aut etiam in parte occidua demer <lb/>
<anchor type="note" xlink:label="note-0083-03a" xlink:href="note-0083-03"/>
gitur, ſolerter indagare.</s>
  <s xml:id="echoid-s7002" xml:space="preserve"/>
</p>
<div xml:id="echoid-div205" type="float" level="2" n="1">
<note position="right" xlink:label="note-0083-03" xlink:href="note-0083-03a" xml:space="preserve"><emph style="it">Iam dictum</emph> <lb/><emph style="it">reperitur ꝑ</emph> <lb/><emph style="it">later alẽ in-</emph> <lb/><emph style="it">greſſum.</emph></note>
</div>
<p>
  <s xml:id="echoid-s7003" xml:space="preserve">Ex ſuperiori pronunciato inueniſti arcum æquatoris cum ſtell@ in horizõte obliqua <lb/>aſcendentẽ, ſinũ iam illius duc in ſinũ maximæ declinationis ☉(sun), ꝓductum diuide in ſinũ <lb/>
<anchor type="note" xlink:label="note-0083-04a" xlink:href="note-0083-04"/>
totum, &amp; </s>
  <s xml:id="echoid-s7004" xml:space="preserve">ſinum complementi huius quotientis uocabis inuentum primum, &amp; </s>
  <s xml:id="echoid-s7005" xml:space="preserve">illud tibi
<pb file="0084" n="84" rhead="GENVINVS VSVS"/>
propone unà cum ſinu complementi aſcenſionis obliquæ, minorem duc in totum, pro-<lb/>
<anchor type="note" xlink:label="note-0084-01a" xlink:href="note-0084-01"/>
ductum diuide in maiorem, arcum quotientis ſubtrahe de 90. </s>
  <s xml:id="echoid-s7006" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7007" xml:space="preserve">reliquum dic inuentum <lb/>ſecundum. </s>
  <s xml:id="echoid-s7008" xml:space="preserve">Poſtea duc ſinum complementi inuenti ſecundi in ſinum maximæ declina-<lb/>tionis Solis, productum diuide in totum, &amp; </s>
  <s xml:id="echoid-s7009" xml:space="preserve">arcum quotientis ſubtrahe de 90. </s>
  <s xml:id="echoid-s7010" xml:space="preserve">ſic tibi ma <lb/>
<anchor type="note" xlink:label="note-0084-02a" xlink:href="note-0084-02"/>
nebit inuentum tertium: </s>
  <s xml:id="echoid-s7011" xml:space="preserve">ſi autem in aſcendente fuerit aliquod ſignum ex ſignis aſcen-<lb/>dentibus (quod ex aſcenſione recta uel obliqua, facilime cognoſces) addes tunc inuen-<lb/>
<anchor type="note" xlink:label="note-0084-03a" xlink:href="note-0084-03"/>
tum tertium ad complementum altitudinis poli, ſumma ea ſubtra cta de ſemicirculo, re-<lb/>linquitur inuentum quartum: </s>
  <s xml:id="echoid-s7012" xml:space="preserve">ſed ſi in aſcendente ſit ſignum aliquod ex deſcendentibus, <lb/>
<anchor type="note" xlink:label="note-0084-04a" xlink:href="note-0084-04"/>
ſubtrahes à tertio inuento complementum altitudinis poli &amp; </s>
  <s xml:id="echoid-s7013" xml:space="preserve">etiam tunc remanebit in <lb/>reſiduo inuentum quartum. </s>
  <s xml:id="echoid-s7014" xml:space="preserve">Porrò inde duc ſinum inuenti quarti in ſinum complemen-<lb/>
<anchor type="note" xlink:label="note-0084-05a" xlink:href="note-0084-05"/>
ti primi inuenti, productum diuide in totum, &amp; </s>
  <s xml:id="echoid-s7015" xml:space="preserve">arcu quotientis de quadra circuli ſubtra <lb/>cto, reliquum manet inuentum quintum. </s>
  <s xml:id="echoid-s7016" xml:space="preserve">Poſtea propone tibi ſinum inuenti quinti &amp; </s>
  <s xml:id="echoid-s7017" xml:space="preserve"><lb/>primi, minorem duc in totum, productum diuide in maiorem, arcus quotientis uoca-<lb/>bitur inuentum ſextum. </s>
  <s xml:id="echoid-s7018" xml:space="preserve">Poſtremò ſinum huius ſexti inuenti duc in ſinum quarti, <lb/>
<anchor type="note" xlink:label="note-0084-06a" xlink:href="note-0084-06"/>
productum diuide in totum, &amp; </s>
  <s xml:id="echoid-s7019" xml:space="preserve">arcus quotientis tibi dabit inuentum ultimum. </s>
  <s xml:id="echoid-s7020" xml:space="preserve">Tandem <lb/>nunc adde inuentum ultimum ad ſecundum, inde proueniet tibi arcus eclypticæ, quem <lb/>
<anchor type="note" xlink:label="note-0084-07a" xlink:href="note-0084-07"/>
uocabis radicem aſcenſionis, quòd ſi ſignum aſcendens fuerit in prima quadra eclypti <lb/>cæ, ſupputa radicem à principio Arietis, &amp; </s>
  <s xml:id="echoid-s7021" xml:space="preserve">ubi finitur, ibi eſt punctum illud eclypticæ <lb/>
<anchor type="note" xlink:label="note-0084-08a" xlink:href="note-0084-08"/>
coaſcendens cum ſtella propoſita: </s>
  <s xml:id="echoid-s7022" xml:space="preserve">ſed ſi in ſecunda quadra fuerit aſcendens, numera ra <lb/>dicem à principio Libræ cõtra ordinem ſignorum, in tertia ſimiliter à principio Libræ, <lb/>ſed ſecundum ordinem uerum, in quarta iterum à principio Arietis contra ſignorum <lb/>ordinem, &amp; </s>
  <s xml:id="echoid-s7023" xml:space="preserve">finis iſtius computationis dabit tibi punctum eclypticæ aſcendens cum ſtel <lb/>la illa ſuper horizontem obliquum. </s>
  <s xml:id="echoid-s7024" xml:space="preserve">?</s>
  <s xml:id="echoid-s7025" xml:space="preserve">? Nuncrem hãc tibi exemplo cõmonſtrabimus. <lb/></s>
  <s xml:id="echoid-s7026" xml:space="preserve">
<anchor type="note" xlink:label="note-0084-09a" xlink:href="note-0084-09"/>
Retineo autem Mercurium cum declinatione ſua &amp; </s>
  <s xml:id="echoid-s7027" xml:space="preserve">aſcenſione ut prius, duco autem ſi-<lb/>num maximæ declinationis in ſinum aſcenſionis obliquæ, iam inuentæ ex proximo pro <lb/>nunciato, 25. </s>
  <s xml:id="echoid-s7028" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7029" xml:space="preserve">49. </s>
  <s xml:id="echoid-s7030" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7031" xml:space="preserve">hoc eſt 39874. </s>
  <s xml:id="echoid-s7032" xml:space="preserve">in 93549. </s>
  <s xml:id="echoid-s7033" xml:space="preserve">productum inde diuido in totum, quo <lb/>tiens erit 17364. </s>
  <s xml:id="echoid-s7034" xml:space="preserve">arcus eius 10 gra. </s>
  <s xml:id="echoid-s7035" xml:space="preserve">inuentum uocabitur primum. </s>
  <s xml:id="echoid-s7036" xml:space="preserve">Mox duco ſinum com <lb/>plementi aſcenſionis rectæ in totum, productum diuido in ſinum complementi primi in <lb/>uenti, quotiens eſt 91408. </s>
  <s xml:id="echoid-s7037" xml:space="preserve">arcus autem eius 66. </s>
  <s xml:id="echoid-s7038" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7039" xml:space="preserve">5. </s>
  <s xml:id="echoid-s7040" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7041" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7042" xml:space="preserve">complementum ipſius 23. <lb/></s>
  <s xml:id="echoid-s7043" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7044" xml:space="preserve">55. </s>
  <s xml:id="echoid-s7045" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7046" xml:space="preserve">dicetur inuentum ſecundum. </s>
  <s xml:id="echoid-s7047" xml:space="preserve">Porrò hinc duco ſinum complementi in ſinum <lb/>maximæ declinationis Solis, &amp; </s>
  <s xml:id="echoid-s7048" xml:space="preserve">quotiens dat 36450. </s>
  <s xml:id="echoid-s7049" xml:space="preserve">arcus eius eſt 21. </s>
  <s xml:id="echoid-s7050" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7051" xml:space="preserve">23. </s>
  <s xml:id="echoid-s7052" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7053" xml:space="preserve">qui-<lb/>bus ſubtractis à 90. </s>
  <s xml:id="echoid-s7054" xml:space="preserve">remanent 68. </s>
  <s xml:id="echoid-s7055" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7056" xml:space="preserve">37. </s>
  <s xml:id="echoid-s7057" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7058" xml:space="preserve">inuentum tertium. </s>
  <s xml:id="echoid-s7059" xml:space="preserve">Præterea adhuc addo in <lb/>uentum tertium ad complementum altitudinis, productum. </s>
  <s xml:id="echoid-s7060" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s7061" xml:space="preserve">110. </s>
  <s xml:id="echoid-s7062" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7063" xml:space="preserve">17. </s>
  <s xml:id="echoid-s7064" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7065" xml:space="preserve">ſubtra-<lb/>ho à ſemicirculo, &amp; </s>
  <s xml:id="echoid-s7066" xml:space="preserve">remanent 69. </s>
  <s xml:id="echoid-s7067" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7068" xml:space="preserve">43. </s>
  <s xml:id="echoid-s7069" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7070" xml:space="preserve">inuentum quartum. </s>
  <s xml:id="echoid-s7071" xml:space="preserve">lnſuper deduco ſinũ <lb/>quarti inuenti. </s>
  <s xml:id="echoid-s7072" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s7073" xml:space="preserve">93798. </s>
  <s xml:id="echoid-s7074" xml:space="preserve">in ſinum complementi primi inuenti 98480. </s>
  <s xml:id="echoid-s7075" xml:space="preserve">facta´ diuiſione in <lb/>ſioum totum, proueniunt in quotient 92372. </s>
  <s xml:id="echoid-s7076" xml:space="preserve">arcus ipſe eſt 67. </s>
  <s xml:id="echoid-s7077" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7078" xml:space="preserve">29. </s>
  <s xml:id="echoid-s7079" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7080" xml:space="preserve">is de 90. </s>
  <s xml:id="echoid-s7081" xml:space="preserve">ſub-<lb/>tractus, relinquit à ſe 22. </s>
  <s xml:id="echoid-s7082" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7083" xml:space="preserve">3. </s>
  <s xml:id="echoid-s7084" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7085" xml:space="preserve">inuentum ſcilicet quintum. </s>
  <s xml:id="echoid-s7086" xml:space="preserve">Sinum iam porrò primi <lb/>inuenti duco adbuc in totum, &amp; </s>
  <s xml:id="echoid-s7087" xml:space="preserve">productum diuido in ſinum quinti inuenti. </s>
  <s xml:id="echoid-s7088" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s7089" xml:space="preserve">38295. </s>
  <s xml:id="echoid-s7090" xml:space="preserve"><lb/>quotiens eſt 45343. </s>
  <s xml:id="echoid-s7091" xml:space="preserve">arcus eius 26. </s>
  <s xml:id="echoid-s7092" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7093" xml:space="preserve">58. </s>
  <s xml:id="echoid-s7094" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7095" xml:space="preserve">uocatur inuentum ſextum. </s>
  <s xml:id="echoid-s7096" xml:space="preserve">Poſtremò du-<lb/>co ſinum huius inuenti in ſinum quarti inuenti. </s>
  <s xml:id="echoid-s7097" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s7098" xml:space="preserve">93798. </s>
  <s xml:id="echoid-s7099" xml:space="preserve">productum diuido in totũ, quo <lb/>tiens erit 42530. </s>
  <s xml:id="echoid-s7100" xml:space="preserve">arcus eius 25. </s>
  <s xml:id="echoid-s7101" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7102" xml:space="preserve">48. </s>
  <s xml:id="echoid-s7103" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7104" xml:space="preserve">uocatur inuentum ultimum, hinc addo inuen <lb/>tum ſecundum ſ. </s>
  <s xml:id="echoid-s7105" xml:space="preserve">23. </s>
  <s xml:id="echoid-s7106" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7107" xml:space="preserve">55. </s>
  <s xml:id="echoid-s7108" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7109" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7110" xml:space="preserve">proueniunt 49. </s>
  <s xml:id="echoid-s7111" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7112" xml:space="preserve">43. </s>
  <s xml:id="echoid-s7113" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7114" xml:space="preserve">quibus iuxta modũ opera <lb/>tionis, maxime iam exiſtente ſigno aſcendente in prima quadra, numeratis à principio <lb/>♈ ſecundum ordinem ſignorum, pertingit numerus ille uſ ad 19. </s>
  <s xml:id="echoid-s7115" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7116" xml:space="preserve">43. </s>
  <s xml:id="echoid-s7117" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7118" xml:space="preserve">♉, &amp; </s>
  <s xml:id="echoid-s7119" xml:space="preserve">cũ <lb/>eo ipſo puncto Mercurius in die &amp; </s>
  <s xml:id="echoid-s7120" xml:space="preserve">loco intronizationis ſtabat in horizonte. </s>
  <s xml:id="echoid-s7121" xml:space="preserve">Quod ſi <lb/>adhuc ſcire cupis, cum quo tandem gradu eclypticæ quælibet ſtella occidat, accipe aſcen <lb/>ſionem obliquam ex 92. </s>
  <s xml:id="echoid-s7122" xml:space="preserve">pronunciato, &amp; </s>
  <s xml:id="echoid-s7123" xml:space="preserve">arcum ſemidiurnum eum duplicato, &amp; </s>
  <s xml:id="echoid-s7124" xml:space="preserve">dupla-<lb/>tum adde aſcẽſioni obliquæ, at is ipſe gradus, quem illa ſumma in æquatore attingit, <lb/>eſt in horizonte orientali, quando ſtella eſt occaſura in parte occidentis, ſi iam ꝑ 30. </s>
  <s xml:id="echoid-s7125" xml:space="preserve">pro-<lb/>nunc. </s>
  <s xml:id="echoid-s7126" xml:space="preserve">quæras gradũ eclypticæ qui cũ illo gradu aſcendit, deinde accipias gradũ ei diame <lb/>traliter oppoſitũ, habebis gradũ cum iſta ſtella occidentẽ. </s>
  <s xml:id="echoid-s7127" xml:space="preserve">Puta, aſcenſio obliqua Mercu <lb/>rĳ eſt 25. </s>
  <s xml:id="echoid-s7128" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7129" xml:space="preserve">49. </s>
  <s xml:id="echoid-s7130" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7131" xml:space="preserve">arcus aũt ſemidiurnus 130. </s>
  <s xml:id="echoid-s7132" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7133" xml:space="preserve">48. </s>
  <s xml:id="echoid-s7134" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7135" xml:space="preserve">utrũ id per ſuperiorẽ ꝓppo <lb/>ſitionẽ inueni, arcus duplicatus eſt 207. </s>
  <s xml:id="echoid-s7136" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7137" xml:space="preserve">36. </s>
  <s xml:id="echoid-s7138" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7139" xml:space="preserve">ꝗbus addo 25. </s>
  <s xml:id="echoid-s7140" xml:space="preserve">gra 49. </s>
  <s xml:id="echoid-s7141" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7142" xml:space="preserve">ſumma illa
<pb file="0085" n="85" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
eſt 233. </s>
  <s xml:id="echoid-s7143" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7144" xml:space="preserve">25. </s>
  <s xml:id="echoid-s7145" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7146" xml:space="preserve">ille ipſe gradus æquinoctialis tangit horizontem in parte occidẽtis, <lb/>quando Mercurius in die intronizationis occidit. </s>
  <s xml:id="echoid-s7147" xml:space="preserve">Igitur per 30. </s>
  <s xml:id="echoid-s7148" xml:space="preserve">quæro gradum eclypti-<lb/>cæ aſcen dentem cum 233. </s>
  <s xml:id="echoid-s7149" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7150" xml:space="preserve">25. </s>
  <s xml:id="echoid-s7151" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7152" xml:space="preserve">æquatoris in loco &amp; </s>
  <s xml:id="echoid-s7153" xml:space="preserve">horizonte intronizationis, <lb/>&amp; </s>
  <s xml:id="echoid-s7154" xml:space="preserve">inuenio 9. </s>
  <s xml:id="echoid-s7155" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7156" xml:space="preserve">4. </s>
  <s xml:id="echoid-s7157" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7158" xml:space="preserve">♏, oppoſitum eius eſt 9. </s>
  <s xml:id="echoid-s7159" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7160" xml:space="preserve">4. </s>
  <s xml:id="echoid-s7161" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7162" xml:space="preserve">♉, cum eo igitur deſcendit ☿, <lb/>quod hactenus inquirebam.</s>
  <s xml:id="echoid-s7163" xml:space="preserve"/>
</p>
<div xml:id="echoid-div206" type="float" level="2" n="2">
<note position="right" xlink:label="note-0083-04" xlink:href="note-0083-04a" xml:space="preserve"><emph style="it">Iuuentum</emph> <lb/><emph style="it">primum.</emph></note>
<note position="left" xlink:label="note-0084-01" xlink:href="note-0084-01a" xml:space="preserve"><emph style="it">Illud inue-</emph> <lb/><emph style="it">nies introi</emph> <lb/><emph style="it">tu Areal.</emph></note>
<note position="left" xlink:label="note-0084-02" xlink:href="note-0084-02a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">ſecundum.</emph></note>
<note position="left" xlink:label="note-0084-03" xlink:href="note-0084-03a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">tertium.</emph></note>
<note position="left" xlink:label="note-0084-04" xlink:href="note-0084-04a" xml:space="preserve"><emph style="it">Inuentúm</emph> <lb/><emph style="it">quartum.</emph></note>
<note position="left" xlink:label="note-0084-05" xlink:href="note-0084-05a" xml:space="preserve"><emph style="it">Hoc aſſe-</emph> <lb/><emph style="it">queris ſi</emph> <lb/><emph style="it">quadrantis</emph> <lb/><emph style="it">latera in-</emph> <lb/><emph style="it">ſpicias.</emph></note>
<note position="left" xlink:label="note-0084-06" xlink:href="note-0084-06a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">quintum.</emph></note>
<note position="left" xlink:label="note-0084-07" xlink:href="note-0084-07a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">ſextum.</emph></note>
<note position="left" xlink:label="note-0084-08" xlink:href="note-0084-08a" xml:space="preserve"><emph style="it">Inuentũ ſe-</emph> <lb/><emph style="it">ptimum &amp;</emph> <lb/><emph style="it">ultimum.</emph></note>
<note position="left" xlink:label="note-0084-09" xlink:href="note-0084-09a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſcopi.</emph></note>
</div>
</div>
<div xml:id="echoid-div208" type="section" level="1" n="106">
<head xml:id="echoid-head110" xml:space="preserve">PRONVNCIATVM XCIIII.</head>
<p>
  <s xml:id="echoid-s7164" xml:space="preserve">Proiectionem radiorum per triangularem ſupputationem colligere.</s>
  <s xml:id="echoid-s7165" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s7166" xml:space="preserve">Nemini ignotum eſſe puto, ſextilem aſpectum ſextam circuli partem, hoc eſt 60. </s>
  <s xml:id="echoid-s7167" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s7168" xml:space="preserve">concludere, idec´ quando ſtella aliqua extra eclypticam eſt 60. </s>
  <s xml:id="echoid-s7169" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7170" xml:space="preserve">tunc aſpectus eius <lb/>directe eclypticam tangit in ſuo gradu longitudinis. </s>
  <s xml:id="echoid-s7171" xml:space="preserve">Si autem diſtantia ſtellæ ab eclypti <lb/>ca maior eſt quàm 60. </s>
  <s xml:id="echoid-s7172" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7173" xml:space="preserve">aſpectus eius ſextilis eclypticam non attingit, ſed ſi minor fue <lb/>rit, tunc ſextilis eius aſpectus duobus locis eclypticam tangit, punctum iſtud quomodo <lb/>
<anchor type="note" xlink:label="note-0085-01a" xlink:href="note-0085-01"/>
cognoſces, iam tibi ediſſeram. </s>
  <s xml:id="echoid-s7174" xml:space="preserve">Sinum 30. </s>
  <s xml:id="echoid-s7175" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7176" xml:space="preserve">tibi propone &amp; </s>
  <s xml:id="echoid-s7177" xml:space="preserve">ſinum complementi lati-<lb/>tudinis, minorem duc in totum, &amp; </s>
  <s xml:id="echoid-s7178" xml:space="preserve">productum diuide in maiorem, arcus quotientis de 90 <lb/>ſubductus, quaſi digito tibi commonſtrat, quot gradus de loco lõgitudinis ſtellæ in ecly-<lb/>ptica numerare debeas antrorſum &amp; </s>
  <s xml:id="echoid-s7179" xml:space="preserve">retrorſum, ubi arcus iſte finitur, ibi ad punctum il-<lb/>lud pertingit ſextilis aſpectus ſtellæ propoſitæ, ſicut in exemplo ſubiecto patebit.</s>
  <s xml:id="echoid-s7180" xml:space="preserve"/>
</p>
<div xml:id="echoid-div208" type="float" level="2" n="1">
<note position="right" xlink:label="note-0085-01" xlink:href="note-0085-01a" xml:space="preserve"><emph style="it">Iã dicta di-</emph> <lb/><emph style="it">ſœs arcatim</emph></note>
</div>
<p>
  <s xml:id="echoid-s7181" xml:space="preserve">?</s>
  <s xml:id="echoid-s7182" xml:space="preserve">? Quarta ſtella Agitatoris, quæ cum Sole in uno ferè poſitionis circulo fuit ipſa hora <lb/>
<anchor type="note" xlink:label="note-0085-02a" xlink:href="note-0085-02"/>
intronizationis, habet in longitudine 22. </s>
  <s xml:id="echoid-s7183" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7184" xml:space="preserve">35. </s>
  <s xml:id="echoid-s7185" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7186" xml:space="preserve">♉, in latitudine 29. </s>
  <s xml:id="echoid-s7187" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7188" xml:space="preserve">ſeptent. <lb/></s>
  <s xml:id="echoid-s7189" xml:space="preserve">ſinus complementi latitudinis eſt 93969. </s>
  <s xml:id="echoid-s7190" xml:space="preserve">ſinus 30. </s>
  <s xml:id="echoid-s7191" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7192" xml:space="preserve">50000. </s>
  <s xml:id="echoid-s7193" xml:space="preserve">hunc tanquàm minorem <lb/>duco in totũ, productum diuido in 93969, in quotiente proueniunt 53215. </s>
  <s xml:id="echoid-s7194" xml:space="preserve">arcus eius <lb/>eſt 32. </s>
  <s xml:id="echoid-s7195" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7196" xml:space="preserve">9. </s>
  <s xml:id="echoid-s7197" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7198" xml:space="preserve">complementum eius 57. </s>
  <s xml:id="echoid-s7199" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7200" xml:space="preserve">51. </s>
  <s xml:id="echoid-s7201" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7202" xml:space="preserve">radix eſt radiationum, &amp; </s>
  <s xml:id="echoid-s7203" xml:space="preserve">tantum <lb/>quidem numero antrorſum ſecundum ordinem ſignorum pro radiatione finiſtra â loco <lb/>longitudinis ſtellæ, &amp; </s>
  <s xml:id="echoid-s7204" xml:space="preserve">contingit 20. </s>
  <s xml:id="echoid-s7205" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7206" xml:space="preserve">26. </s>
  <s xml:id="echoid-s7207" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7208" xml:space="preserve">♌, tantundem quo contra ordinem ſi-<lb/>gnorum pro radiatione dextra, &amp; </s>
  <s xml:id="echoid-s7209" xml:space="preserve">ibi tangit 24. </s>
  <s xml:id="echoid-s7210" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7211" xml:space="preserve">44. </s>
  <s xml:id="echoid-s7212" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7213" xml:space="preserve">♈. </s>
  <s xml:id="echoid-s7214" xml:space="preserve">Si autem ſcire deſide-<lb/>ras, in quibus gradibus eclypticæ radiatio trigona ſtellæ propoſitæ finiatur, adde 90. </s>
  <s xml:id="echoid-s7215" xml:space="preserve">ad <lb/>arcum quotientis, &amp; </s>
  <s xml:id="echoid-s7216" xml:space="preserve">ſumma iſta monſtrabit tibi arcum ante &amp; </s>
  <s xml:id="echoid-s7217" xml:space="preserve">poſt locum ſtellæ, ubi tri <lb/>nus deſinit aſpectus, ſic adde 90. </s>
  <s xml:id="echoid-s7218" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7219" xml:space="preserve">ad 32. </s>
  <s xml:id="echoid-s7220" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7221" xml:space="preserve">9. </s>
  <s xml:id="echoid-s7222" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7223" xml:space="preserve">proueniunt 122. </s>
  <s xml:id="echoid-s7224" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7225" xml:space="preserve">9. </s>
  <s xml:id="echoid-s7226" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7227" xml:space="preserve">tantum <lb/>ſi numeres ſecundum ordinem ſignorum antrorſum, radius trinus ſiniſter cadet ſuper <lb/>24. </s>
  <s xml:id="echoid-s7228" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7229" xml:space="preserve">44. </s>
  <s xml:id="echoid-s7230" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7231" xml:space="preserve">♎, &amp; </s>
  <s xml:id="echoid-s7232" xml:space="preserve">dexter tantundẽ contra ordinem ſignorum, cadet´ ſuper 20. </s>
  <s xml:id="echoid-s7233" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7234" xml:space="preserve"><lb/>26. </s>
  <s xml:id="echoid-s7235" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7236" xml:space="preserve">♒. </s>
  <s xml:id="echoid-s7237" xml:space="preserve">Radiatio autem quadrangula ſemper eſt 90. </s>
  <s xml:id="echoid-s7238" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7239" xml:space="preserve">ante &amp; </s>
  <s xml:id="echoid-s7240" xml:space="preserve">retro à loco longitu-<lb/>dinis ſtellæ, in quantalibet latitudine, non refert.</s>
  <s xml:id="echoid-s7241" xml:space="preserve"/>
</p>
<div xml:id="echoid-div209" type="float" level="2" n="2">
<note position="right" xlink:label="note-0085-02" xlink:href="note-0085-02a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſcopi.</emph></note>
</div>
</div>
<div xml:id="echoid-div211" type="section" level="1" n="107">
<head xml:id="echoid-head111" xml:space="preserve">PRONVNCIATVM XCV.</head>
<p>
  <s xml:id="echoid-s7242" xml:space="preserve">Interuallum apparitionis aut occultationis ſtellarum in arcu eclypticæ <lb/>ſubtiliter explorare.</s>
  <s xml:id="echoid-s7243" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s7244" xml:space="preserve">Arcum uiſionis dico portionem circuli maioris per uerticem regionis &amp; </s>
  <s xml:id="echoid-s7245" xml:space="preserve">centrum cor <lb/>poris Solis deducti, qui´ inter horizontem &amp; </s>
  <s xml:id="echoid-s7246" xml:space="preserve">corpus Solis concluditur, eodem plane <lb/>tempore quo ſtella apparet ex radĳs ſolaribus emergens, uel quum iam occultari incipit. <lb/></s>
  <s xml:id="echoid-s7247" xml:space="preserve">
<anchor type="note" xlink:label="note-0085-03a" xlink:href="note-0085-03"/>
Et quia iſtæ apparitiones plurimum utiles ſunt is qui de mutationibus aëris ſcribunt, <lb/>ideo docebo hic inuentionem diſtantiæ ſtellarum ſecundum longitudinem eclypticæ ad <lb/>hoc, ut talis etiam arcus uiſionis concludatur inter horizontem &amp; </s>
  <s xml:id="echoid-s7248" xml:space="preserve">corpus ſolare, prout <lb/>ſtella propoſita ſecundum magnitudinem ſplendoris ſui expoſtulat. </s>
  <s xml:id="echoid-s7249" xml:space="preserve">Quilibet enim pla <lb/>
<anchor type="note" xlink:label="note-0085-04a" xlink:href="note-0085-04"/>
neta (quando non æquali ſunt lumine omnes) peculiarem ſuum habet arcum uiſionis, <lb/>ſic ☿ gradus 10. </s>
  <s xml:id="echoid-s7250" xml:space="preserve">habet, hoc eſt, quando Solper 10. </s>
  <s xml:id="echoid-s7251" xml:space="preserve">gradus in circulo altitudinis eſt ſub <lb/>horizonte, ſiue in parte orientis, ſiue occidentis, &amp; </s>
  <s xml:id="echoid-s7252" xml:space="preserve">☿ planè in inſo ſtat horizonte, tunc <lb/>incipit occultari, aut emergit ut uideatur. </s>
  <s xml:id="echoid-s7253" xml:space="preserve">Arcus uiſionis ♀ eſt 5. </s>
  <s xml:id="echoid-s7254" xml:space="preserve">graduum, ♂ 11. </s>
  <s xml:id="echoid-s7255" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s7256" xml:space="preserve">
<anchor type="note" xlink:label="note-0085-05a" xlink:href="note-0085-05"/>
30. </s>
  <s xml:id="echoid-s7257" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7258" xml:space="preserve">♃ 10. </s>
  <s xml:id="echoid-s7259" xml:space="preserve">graduum. </s>
  <s xml:id="echoid-s7260" xml:space="preserve">variant 11. </s>
  <s xml:id="echoid-s7261" xml:space="preserve">graduum. </s>
  <s xml:id="echoid-s7262" xml:space="preserve">Vnum hic exceptum haberi uolo, quòd ſi uapor <lb/>terreſtris interpoſitus ſit talis, ut per eum interdum etiam radĳ uiſuales franguntur, tũc <lb/>
<anchor type="note" xlink:label="note-0085-06a" xlink:href="note-0085-06"/>
ſtellæ apparent quæ adhuc ſub horizonte latent, nec eſt ꝙ rideas illud, ſiquidẽ naturali-<lb/>ter ita fit, quemadmodum nos docet peſpectiua. </s>
  <s xml:id="echoid-s7263" xml:space="preserve">At ea regula eſt ad cognoſcendum ar <lb/>
<anchor type="note" xlink:label="note-0085-07a" xlink:href="note-0085-07"/>
cum eclypticæ inter horizontem &amp; </s>
  <s xml:id="echoid-s7264" xml:space="preserve">corpus ſolare contentum, qundo ſtella in horizonte
<pb file="0086" n="86" rhead="GENVINVS VSVS"/>
incipit apparere uel occultari, quære angulum eclypticæ &amp; </s>
  <s xml:id="echoid-s7265" xml:space="preserve">horizontis iuxta iſtud pun-<lb/>ctum eclypticæ, per 31, pronunciatum in parte orientis, ſi ſcire cupis apparitionem uel <lb/>occultationem matutinam, ſinus eius eſt ipſe diuiſor, deinde duc ſinum arcus uiſionis in <lb/>
<anchor type="note" xlink:label="note-0086-01a" xlink:href="note-0086-01"/>
ſinum totum, productum diuide in diuiſorem, arcus quotientis oſtendet arcum eclypti-<lb/>cæ: </s>
  <s xml:id="echoid-s7266" xml:space="preserve">ſi locum ſtellæ redigam ad horizontem, &amp; </s>
  <s xml:id="echoid-s7267" xml:space="preserve">tantum numerem ſecundum ordinem ſi-<lb/>gnorum, quantum ipſe quotiẽs habet, &amp; </s>
  <s xml:id="echoid-s7268" xml:space="preserve">umc ſi numerus hic gradum Solis non attingit, <lb/>ſtella iſta uidetur adhuc ante ortum Solis, ſcilicet aut arcus quotientis gradum Solis ap <lb/>præhendi, ſtella hæc amplius uiderinon poteſt: </s>
  <s xml:id="echoid-s7269" xml:space="preserve">ſimili quo modo operaberis in parte <lb/>occidua, niſi quòd ibi arcum quotientis numerabis contra ordinem ſignorum, quòd ſi <lb/>arcus iſte præciſe locum Solis appræhendit, eo ipſo die incipit ſtella iſta occultari, uel ex <lb/>radijs ſolaribus emergit &amp; </s>
  <s xml:id="echoid-s7270" xml:space="preserve">apparetprimum. </s>
  <s xml:id="echoid-s7271" xml:space="preserve">Quando autem planeta aliquis non præciſe <lb/>eſt in eclyptica, tunc quære per 93. </s>
  <s xml:id="echoid-s7272" xml:space="preserve">gradum, cum quo oritur in parte orientis, &amp; </s>
  <s xml:id="echoid-s7273" xml:space="preserve">angu-<lb/>
<anchor type="note" xlink:label="note-0086-02a" xlink:href="note-0086-02"/>
lum eclypticæ cũ horizonte per 32. </s>
  <s xml:id="echoid-s7274" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7275" xml:space="preserve">33. </s>
  <s xml:id="echoid-s7276" xml:space="preserve">deinde operare modo piædicto. </s>
  <s xml:id="echoid-s7277" xml:space="preserve">?</s>
  <s xml:id="echoid-s7278" xml:space="preserve">? Videa-<lb/>mus iam an ☿ die intronizationis etiam ante ortum Solis uideri oportuerit, aut an ſur-<lb/>tiuus (uti ſolet) &amp; </s>
  <s xml:id="echoid-s7279" xml:space="preserve">tacitus ad hanc uenerit intronizationem. </s>
  <s xml:id="echoid-s7280" xml:space="preserve">Inuentum habeo gradum e-<lb/>clypticæ cum quo euaſit ille ſuper horizontem per 93. </s>
  <s xml:id="echoid-s7281" xml:space="preserve">pronunciatum, is fuit 19. </s>
  <s xml:id="echoid-s7282" xml:space="preserve">gia. </s>
  <s xml:id="echoid-s7283" xml:space="preserve">43. <lb/></s>
  <s xml:id="echoid-s7284" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7285" xml:space="preserve">♉. </s>
  <s xml:id="echoid-s7286" xml:space="preserve">Deinde habeo etiam per 31. </s>
  <s xml:id="echoid-s7287" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7288" xml:space="preserve">32. </s>
  <s xml:id="echoid-s7289" xml:space="preserve">angulum quam facit eclyptica cum horizon <lb/>te iuxta gradum occidentis, is eſt 22. </s>
  <s xml:id="echoid-s7290" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7291" xml:space="preserve">41. </s>
  <s xml:id="echoid-s7292" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7293" xml:space="preserve">ſinus huius anguli eſt 38563. </s>
  <s xml:id="echoid-s7294" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7295" xml:space="preserve">quia ar-<lb/>cus uiſionis eſt 10. </s>
  <s xml:id="echoid-s7296" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7297" xml:space="preserve">ſinus quo ipſius 17364. </s>
  <s xml:id="echoid-s7298" xml:space="preserve">duco ſinum illum in totum, productum <lb/>diuido in 38563. </s>
  <s xml:id="echoid-s7299" xml:space="preserve">quotiens erit 45028. </s>
  <s xml:id="echoid-s7300" xml:space="preserve">arcus autem eius 26. </s>
  <s xml:id="echoid-s7301" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7302" xml:space="preserve">46. </s>
  <s xml:id="echoid-s7303" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7304" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7305" xml:space="preserve">tantum quidẽ <lb/>diſtare debet Sol ab horizonte ſecundum eclypticam, ut appareat ille, quod ſi propius ac <lb/>ceſſerit, non uidebitur, ſi iam à 19. </s>
  <s xml:id="echoid-s7306" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7307" xml:space="preserve">43. </s>
  <s xml:id="echoid-s7308" xml:space="preserve">mi ♉. </s>
  <s xml:id="echoid-s7309" xml:space="preserve">26. </s>
  <s xml:id="echoid-s7310" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7311" xml:space="preserve">46. </s>
  <s xml:id="echoid-s7312" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7313" xml:space="preserve">numerauero ſecundum <lb/>ordinem ſignorum, finis iſtius arcuspertinget ad 16. </s>
  <s xml:id="echoid-s7314" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7315" xml:space="preserve">29. </s>
  <s xml:id="echoid-s7316" xml:space="preserve">II, ubi oporteret eſſe So-<lb/>lem, ſi principio ſtatim uideri deberet ☿, &amp; </s>
  <s xml:id="echoid-s7317" xml:space="preserve">quò magis ☉(sun) inde receſſerit, cò diutius ap-<lb/>parebit ☿ ante Solis exortum, quia autem arcum eitis non attingit, certum eſt eum occul <lb/>to ſe proripuiſſe ultra horizontem. </s>
  <s xml:id="echoid-s7318" xml:space="preserve">Nunc uideamus an etiam ſic ſurtim ſeſe ſubduxerit <lb/>(uti plærun facit) ſub horizontem, uelan poſt Solis occaſum adhuc uideri potuerit, <lb/>primo conſidero gradum Solis, &amp; </s>
  <s xml:id="echoid-s7319" xml:space="preserve">gradum cum quo occidit ☿, quem inueni per præmiſ-<lb/>ſam eſſe 9. </s>
  <s xml:id="echoid-s7320" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7321" xml:space="preserve">4. </s>
  <s xml:id="echoid-s7322" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7323" xml:space="preserve">Ecce iam in aperto eſt, quia ☿ ante ☉(sun) occaſum ſe coniecit ſub hori <lb/>zontem, exiſtente ☉(sun) in 2. </s>
  <s xml:id="echoid-s7324" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7325" xml:space="preserve">26. </s>
  <s xml:id="echoid-s7326" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7327" xml:space="preserve">II, unde nec ulla ulteriori inquiſitione opus erit.</s>
  <s xml:id="echoid-s7328" xml:space="preserve"/>
</p>
<div xml:id="echoid-div211" type="float" level="2" n="1">
<note position="right" xlink:label="note-0085-03" xlink:href="note-0085-03a" xml:space="preserve"><emph style="it">Arcus uiſi-</emph> <lb/><emph style="it">onis Mcrcu</emph> <lb/><emph style="it">rĳ habet</emph> <lb/><emph style="it">gradus 10.</emph></note>
<note position="right" xlink:label="note-0085-04" xlink:href="note-0085-04a" xml:space="preserve"><emph style="it">Arcus uiſi</emph> <lb/><emph style="it">onis Vene-</emph> <lb/><emph style="it">ris eſt gra-</emph> <lb/><emph style="it">duums.</emph></note>
<note position="right" xlink:label="note-0085-05" xlink:href="note-0085-05a" xml:space="preserve"><emph style="it">Martis 11.</emph> <lb/><emph style="it">gra. 30. mi.</emph></note>
<note position="right" xlink:label="note-0085-06" xlink:href="note-0085-06a" xml:space="preserve"><emph style="it">Iouis gra-</emph> <lb/><emph style="it">duum 10.</emph></note>
<note position="right" xlink:label="note-0085-07" xlink:href="note-0085-07a" xml:space="preserve"><emph style="it">Saturni 11.</emph> <lb/><emph style="it">gra.</emph></note>
<note position="left" xlink:label="note-0086-01" xlink:href="note-0086-01a" xml:space="preserve"><emph style="it">Hocper a-</emph> <lb/><emph style="it">realcm in-</emph> <lb/><emph style="it">greſſum</emph> <lb/><emph style="it">quœrenti</emph> <lb/><emph style="it">apparet.</emph></note>
<note position="left" xlink:label="note-0086-02" xlink:href="note-0086-02a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſoo<unsure/>pi.</emph></note>
</div>
</div>
<div xml:id="echoid-div213" type="section" level="1" n="108">
<head xml:id="echoid-head112" xml:space="preserve">PRONVNCIATVM XCVI.</head>
<p>
  <s xml:id="echoid-s7329" xml:space="preserve">Ex altitudine ſtellæ fixæ uel planetæ ſupra horizontem etiam noctis ho-<lb/>ram elicere.</s>
  <s xml:id="echoid-s7330" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s7331" xml:space="preserve">Ad hanc rem opus tibi erit declinatione ſtellæ complemento altitudinis poli, aſcenſi <lb/>
<anchor type="note" xlink:label="note-0086-03a" xlink:href="note-0086-03"/>
one recta ſtellæ, &amp; </s>
  <s xml:id="echoid-s7332" xml:space="preserve">aſcenſione recta Solis, altitudine quo meridiana ſtellæ, altitudine eti <lb/>am ſtellæ ſuper horizontem, &amp; </s>
  <s xml:id="echoid-s7333" xml:space="preserve">complemento declinationis ſtellæ. </s>
  <s xml:id="echoid-s7334" xml:space="preserve">Duc igitur ſinum al <lb/>titudinis meridianæ in totum, productum diuide in ſinum complementi altitudinis poli, <lb/>quotiens iſte erit inuentum primum. </s>
  <s xml:id="echoid-s7335" xml:space="preserve">Duc etiam ſinum altitudinis ſtellæ ſuper horizon-<lb/>
<anchor type="note" xlink:label="note-0086-04a" xlink:href="note-0086-04"/>
tem tempore obſeruationis in totũ, productum diuide in ſinum com plementi altitudinis <lb/>poli, quotiens dicetur inuentum ſecundum, &amp; </s>
  <s xml:id="echoid-s7336" xml:space="preserve">hoc ſubtrahe à primo, quia ſemper eſt mi <lb/>nus, &amp; </s>
  <s xml:id="echoid-s7337" xml:space="preserve">reſiduum rurſus duc in ſinum totum, productũ diuide in ſinum complementi de-<lb/>clinationis ſtellæ, quotiens uocabitur inuentum tertium. </s>
  <s xml:id="echoid-s7338" xml:space="preserve">Quod ſi minus fuerit ſinu toto, <lb/>ſubtrahe illud à toto, &amp; </s>
  <s xml:id="echoid-s7339" xml:space="preserve">arcu reſidui iterũ de 90. </s>
  <s xml:id="echoid-s7340" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7341" xml:space="preserve">ſubducto, remanebit arcus diſtan-<lb/>tiæ ſtellæ à meridiano. </s>
  <s xml:id="echoid-s7342" xml:space="preserve">Sed ſi tertium illud inuentum maius extiterit ſinu toto, ſubtrahe <lb/>ſinum totũ ab eo, &amp; </s>
  <s xml:id="echoid-s7343" xml:space="preserve">ad arcum reſidui adde 90. </s>
  <s xml:id="echoid-s7344" xml:space="preserve">gra ſic´ habebis diſtantiã ſtellæ à meridi <lb/>ano: </s>
  <s xml:id="echoid-s7345" xml:space="preserve">quòd ſi ſtella fuerit in parte orientis, puta à meridiano, tunc ſubtrahe illam diſtantiã <lb/>ab aſcenſione recta ſtellæ, uerum ſi ſtella apparuerit tempore obſeruationis in medietate <lb/>cœli occidentall, adde tunc iſtam diſtantiam ſtellæ ad eius aſcenſionem rectam, &amp; </s>
  <s xml:id="echoid-s7346" xml:space="preserve">habe-<lb/>bis ex aliquo illorum modorum gradum æquatoris, qui tangit medium cœ i ipſa hora ob <lb/>ſeruationis. </s>
  <s xml:id="echoid-s7347" xml:space="preserve">Hic mihi confer illud etiam ad aſcenſionem rectam nadir Solis, hoc eſt, ſi <lb/>180. </s>
  <s xml:id="echoid-s7348" xml:space="preserve">addas ad aſcenſionem rectam, iam habes aſcenſionem nadir Solis rectam, numerũ
<pb file="0087" n="87" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
minorem ſubtrahe à maiori, &amp; </s>
  <s xml:id="echoid-s7349" xml:space="preserve">reſiduum erit diſtantia nadir Solis à media nocte, à meri-<lb/>diano eam conuerte in horas horarum´ minuta, &amp; </s>
  <s xml:id="echoid-s7350" xml:space="preserve">ſi aſcenſio recta nadir fuerit maior <lb/>quàm gradus medij cœli, ſubtrahe diſtantiã illã horarũ à 12. </s>
  <s xml:id="echoid-s7351" xml:space="preserve">horis, &amp; </s>
  <s xml:id="echoid-s7352" xml:space="preserve">remanebit hora no-<lb/>ctis quæſita. </s>
  <s xml:id="echoid-s7353" xml:space="preserve">Sed ſi aſcenſio recta nadir Solis minor extiterit quàm gradus medij cœli, <lb/>tunc oſtendet differentia horaria horas poſt medium noctis. </s>
  <s xml:id="echoid-s7354" xml:space="preserve">?</s>
  <s xml:id="echoid-s7355" xml:space="preserve">? Difficile &amp; </s>
  <s xml:id="echoid-s7356" xml:space="preserve">obſcurum <lb/>
<anchor type="note" xlink:label="note-0087-01a" xlink:href="note-0087-01"/>
uideatur hoc tibi, niſi exemplum conſideres, ecce adſumo ſpicam uirginis, declinatio e-<lb/>lus tempore introniſationis eſt 8. </s>
  <s xml:id="echoid-s7357" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7358" xml:space="preserve">16. </s>
  <s xml:id="echoid-s7359" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7360" xml:space="preserve">complementum uero 81. </s>
  <s xml:id="echoid-s7361" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7362" xml:space="preserve">44. </s>
  <s xml:id="echoid-s7363" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7364" xml:space="preserve">ſi iam <lb/>ſubtraho declinationem à complemento altitudinis poli (quia declinatio eſt meridiona <lb/>lis) remanebit altitudo ſtellæ meridiana 33. </s>
  <s xml:id="echoid-s7365" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7366" xml:space="preserve">44. </s>
  <s xml:id="echoid-s7367" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7368" xml:space="preserve">ſinum eius 55532. </s>
  <s xml:id="echoid-s7369" xml:space="preserve">duco in totũ, <lb/>productum diuido in ſinum complementi altitudinis poli 48. </s>
  <s xml:id="echoid-s7370" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7371" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s7372" xml:space="preserve">66913. </s>
  <s xml:id="echoid-s7373" xml:space="preserve">quotiens da-<lb/>
<anchor type="note" xlink:label="note-0087-02a" xlink:href="note-0087-02"/>
bit 8299. </s>
  <s xml:id="echoid-s7374" xml:space="preserve">inuentum primum. </s>
  <s xml:id="echoid-s7375" xml:space="preserve">Porrò etiam duco ſinum altitudinis ſtellæ quam inueni in <lb/>parte occidentis ad 29 gra. </s>
  <s xml:id="echoid-s7376" xml:space="preserve">14. </s>
  <s xml:id="echoid-s7377" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7378" xml:space="preserve">in nocte ante uel poſt intronizationis horam, &amp; </s>
  <s xml:id="echoid-s7379" xml:space="preserve">eſt <lb/>48836. </s>
  <s xml:id="echoid-s7380" xml:space="preserve">in totum ſinum, productum diuido in ſinum complementi Auguſtanæ quæ ſup <lb/>ponitur 48. </s>
  <s xml:id="echoid-s7381" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7382" xml:space="preserve">quotiens erit inuentum ſecundum. </s>
  <s xml:id="echoid-s7383" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s7384" xml:space="preserve">72908. </s>
  <s xml:id="echoid-s7385" xml:space="preserve">at ipſum ſubtraho de in-<lb/>
<anchor type="note" xlink:label="note-0087-03a" xlink:href="note-0087-03"/>
uento primo, &amp; </s>
  <s xml:id="echoid-s7386" xml:space="preserve">manent in reſiduo 10083. </s>
  <s xml:id="echoid-s7387" xml:space="preserve">Inſuper duco reſiduum illud etiam in ſinum <lb/>totum, productum diuido in ſinum cõplementi declinationis ſtellæ. </s>
  <s xml:id="echoid-s7388" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s7389" xml:space="preserve">98960. </s>
  <s xml:id="echoid-s7390" xml:space="preserve">quotiens <lb/>eſt 10189. </s>
  <s xml:id="echoid-s7391" xml:space="preserve">inuentum tertium: </s>
  <s xml:id="echoid-s7392" xml:space="preserve">quod quia minus eſt toto ſinu, ſubtraho de eo, &amp; </s>
  <s xml:id="echoid-s7393" xml:space="preserve">remanẽt <lb/>
<anchor type="note" xlink:label="note-0087-04a" xlink:href="note-0087-04"/>
89811. </s>
  <s xml:id="echoid-s7394" xml:space="preserve">arcus eius eſt 63, gra, 55. </s>
  <s xml:id="echoid-s7395" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7396" xml:space="preserve">quibus ſubtractis de 90. </s>
  <s xml:id="echoid-s7397" xml:space="preserve">relinquuntur 26. </s>
  <s xml:id="echoid-s7398" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7399" xml:space="preserve">5. </s>
  <s xml:id="echoid-s7400" xml:space="preserve">mi. <lb/></s>
  <s xml:id="echoid-s7401" xml:space="preserve">diſtantia ſtellæ à medio cœli, numerãdo in æquatore in aſcenſione recta ſtellæ, quum´ <lb/>ſtella iſta in hac obſeruatione ſita eſt à meridie uerſus occidentem, addere debeo differen <lb/>tiam hanc ad aſcenſionem rectam ſtellæ ſ. </s>
  <s xml:id="echoid-s7402" xml:space="preserve">194. </s>
  <s xml:id="echoid-s7403" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7404" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7405" xml:space="preserve">erunt 220. </s>
  <s xml:id="echoid-s7406" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7407" xml:space="preserve">5. </s>
  <s xml:id="echoid-s7408" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7409" xml:space="preserve">gradus ille <lb/>æquatoris qui tangit medium cœli ipſa hora intronizationis. </s>
  <s xml:id="echoid-s7410" xml:space="preserve">Scio autem certo me inue <lb/>niſſe per 7. </s>
  <s xml:id="echoid-s7411" xml:space="preserve">pronunciatum aſcenſionem rectam ☉(sun) in die intronizationis ad 60. </s>
  <s xml:id="echoid-s7412" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7413" xml:space="preserve">21. </s>
  <s xml:id="echoid-s7414" xml:space="preserve"><lb/>mi. </s>
  <s xml:id="echoid-s7415" xml:space="preserve">addo ijs ſemicirculum. </s>
  <s xml:id="echoid-s7416" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s7417" xml:space="preserve">180. </s>
  <s xml:id="echoid-s7418" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7419" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7420" xml:space="preserve">proueniunt 240. </s>
  <s xml:id="echoid-s7421" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7422" xml:space="preserve">21. </s>
  <s xml:id="echoid-s7423" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7424" xml:space="preserve">aſcenſio ſcilicet re-<lb/>cta nadir Solis, hoc eſt oppoſiti gradus Solis. </s>
  <s xml:id="echoid-s7425" xml:space="preserve">Iam nihil eſt quod agam cum aſcenſione <lb/>ſtellæ, ſed uideo utra aſcenſionum ſit maior, illa ne medij cœli, an nadir Solis, hinc mino <lb/>rem ſubtraho à maiori, hoc eſt medij cœli. </s>
  <s xml:id="echoid-s7426" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s7427" xml:space="preserve">220. </s>
  <s xml:id="echoid-s7428" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7429" xml:space="preserve">5. </s>
  <s xml:id="echoid-s7430" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7431" xml:space="preserve">à 240. </s>
  <s xml:id="echoid-s7432" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7433" xml:space="preserve">21. </s>
  <s xml:id="echoid-s7434" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7435" xml:space="preserve">remanent <lb/>20. </s>
  <s xml:id="echoid-s7436" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7437" xml:space="preserve">16. </s>
  <s xml:id="echoid-s7438" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7439" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7440" xml:space="preserve">faciunt unam horam 21. </s>
  <s xml:id="echoid-s7441" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7442" xml:space="preserve">quæ diſtantia eſt nadir Solis à medio cœli, <lb/>&amp; </s>
  <s xml:id="echoid-s7443" xml:space="preserve">quia aſcenſio recta nadir Solis uerſus orientem uergit à meridie ſupputando, ideo ſub <lb/>traho 1. </s>
  <s xml:id="echoid-s7444" xml:space="preserve">horam 21. </s>
  <s xml:id="echoid-s7445" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7446" xml:space="preserve">à 12. </s>
  <s xml:id="echoid-s7447" xml:space="preserve">horis, ſic remanet 10. </s>
  <s xml:id="echoid-s7448" xml:space="preserve">hora 39. </s>
  <s xml:id="echoid-s7449" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7450" xml:space="preserve">noctis. </s>
  <s xml:id="echoid-s7451" xml:space="preserve">Si enim nadir Solis <lb/>ita lumen haberet, uel ſtella ut ☉(sun) ipſe, horas monſtraret inſtar Solis, at ideo, quãdo op <lb/>poſitio eſt ☉(sun) &amp; </s>
  <s xml:id="echoid-s7452" xml:space="preserve">☽, ipſa ☽ etiam eſt in nadir Solis, aut certe proxima ei, ideo Luna quum <lb/>plena in omnibus horalogijs uiatorijs horas indicatut Sol, quamuis ratione latitudinis <lb/>Lunæ &amp; </s>
  <s xml:id="echoid-s7453" xml:space="preserve">uicinitatis ad horã nõnihil erroris ibi cõtingere poteſt, ſed hæc aliàs copioſius.</s>
  <s xml:id="echoid-s7454" xml:space="preserve"/>
</p>
<div xml:id="echoid-div213" type="float" level="2" n="1">
<note position="left" xlink:label="note-0086-03" xlink:href="note-0086-03a" xml:space="preserve"><emph style="it">Illud depræ</emph> <lb/><emph style="it">henditur in</emph> <lb/><emph style="it">greſſu a-</emph> <lb/><emph style="it">reali.</emph></note>
<note position="left" xlink:label="note-0086-04" xlink:href="note-0086-04a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">primum</emph> <lb/><emph style="it">Inuentum</emph> <lb/><emph style="it">ſecundum</emph> <lb/><emph style="it">Inuentum</emph> <lb/><emph style="it">tertium.</emph></note>
<note position="right" xlink:label="note-0087-01" xlink:href="note-0087-01a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſoopi.</emph></note>
<note position="right" xlink:label="note-0087-02" xlink:href="note-0087-02a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">primum</emph></note>
<note position="right" xlink:label="note-0087-03" xlink:href="note-0087-03a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">ſecundum</emph></note>
<note position="right" xlink:label="note-0087-04" xlink:href="note-0087-04a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">tertium.</emph></note>
</div>
</div>
<div xml:id="echoid-div215" type="section" level="1" n="109">
<head xml:id="echoid-head113" xml:space="preserve">PRONVNCIATVM XCVII.</head>
<p>
  <s xml:id="echoid-s7455" xml:space="preserve">Duarum ſtellarum fixarum uel errantium, diuerſas´ latitudinum deno-<lb/>minationes habentium, diſtantias ab inuicem colligere.</s>
  <s xml:id="echoid-s7456" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s7457" xml:space="preserve">Diſtantias ſtellarum hic demonſtrabimus, quarum alia meridionalem, alia latitudi-<lb/>nem habet ſeptentrionalem, in reliquis enim quæ in nomine latitudinis non differunt, <lb/>adhibebis pronunc. </s>
  <s xml:id="echoid-s7458" xml:space="preserve">70. </s>
  <s xml:id="echoid-s7459" xml:space="preserve">71. </s>
  <s xml:id="echoid-s7460" xml:space="preserve">72. </s>
  <s xml:id="echoid-s7461" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7462" xml:space="preserve">73. </s>
  <s xml:id="echoid-s7463" xml:space="preserve">ſiquidem ea diſtantias explicant ciuitatũ, de quibus <lb/>quicquid in quæſtionem &amp; </s>
  <s xml:id="echoid-s7464" xml:space="preserve">dubium uertitur, pari modo etiã hic in ſtellis diſſolui poteſt, <lb/>quum terra æque ſit corpus ſphæricum at firmamentum. </s>
  <s xml:id="echoid-s7465" xml:space="preserve">Quum autem ſunt ciuitates <lb/>duæ, quarum altera latitudinem habet Borealem, Auſtralem altera ab æquatore, earum <lb/>diſtantias ibi non docuimus inuenire per exempla, ſed ad hunc locum de induſtria diſtu-<lb/>limus, ubi per ſtellas rem hanc indicare decreuimus, quibus operatio ea non paulo etiam <lb/>eſt accommodatior, poteſt autem ad loca terreſtria conſimili quo modo applicari, ſic <lb/>igitur habet. </s>
  <s xml:id="echoid-s7466" xml:space="preserve">Sinum complementi latitudinis ſeptentrionalis duc in ſinum differentiæ <lb/>longitudinis, &amp; </s>
  <s xml:id="echoid-s7467" xml:space="preserve">diuide per totum ſinum, quotiens dicetur inuentum primum, Comple-<lb/>
<anchor type="note" xlink:label="note-0087-05a" xlink:href="note-0087-05"/>
mentum eius tibi propone &amp; </s>
  <s xml:id="echoid-s7468" xml:space="preserve">ſinum latitudinis Borealis, minorem duc in totum, produ-<lb/>ctum diuide in maiorem, arcus quotientis additus latitudini meridionali, producit inuen <lb/>tum ſecundum. </s>
  <s xml:id="echoid-s7469" xml:space="preserve">Sinus complementorum utriuſ inuenti, duc in ſç inuicem, productum <lb/>
<anchor type="note" xlink:label="note-0087-06a" xlink:href="note-0087-06"/>
diuide per ſinum totum, arcus quotientis de 90. </s>
  <s xml:id="echoid-s7470" xml:space="preserve">ſublatus, reliquas tibi facit diſtantias
<pb file="0088" n="88" rhead="GENVINVS VSVS"/>
ftellarum inquiſitas. </s>
  <s xml:id="echoid-s7471" xml:space="preserve">?</s>
  <s xml:id="echoid-s7472" xml:space="preserve">? Exempli loco iterum aſſumo Mercurſum, cuius cupio ſcire <lb/>
<anchor type="note" xlink:label="note-0088-01a" xlink:href="note-0088-01"/>
diſtantiam à quarta ſtella Agitatoris, quam ueriſicaui per 2. </s>
  <s xml:id="echoid-s7473" xml:space="preserve">pronunciatum, ſicut in <lb/>pronunciato 85. </s>
  <s xml:id="echoid-s7474" xml:space="preserve">eſt uidere, fuit autem die intronizationis ſecundum longitudinem in <lb/>22. </s>
  <s xml:id="echoid-s7475" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7476" xml:space="preserve">35. </s>
  <s xml:id="echoid-s7477" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7478" xml:space="preserve">II, habuit´ in latitudine ſeptent. </s>
  <s xml:id="echoid-s7479" xml:space="preserve">20. </s>
  <s xml:id="echoid-s7480" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7481" xml:space="preserve">Mercurius etiam ipſa hora in-<lb/>tronizationis fuit in 10. </s>
  <s xml:id="echoid-s7482" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7483" xml:space="preserve">12. </s>
  <s xml:id="echoid-s7484" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7485" xml:space="preserve">♉, habens latitudinem meridionalem 3. </s>
  <s xml:id="echoid-s7486" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7487" xml:space="preserve">20. </s>
  <s xml:id="echoid-s7488" xml:space="preserve">mi <lb/>nutorum. </s>
  <s xml:id="echoid-s7489" xml:space="preserve">Differentia igitur longitudinis eſt 42. </s>
  <s xml:id="echoid-s7490" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7491" xml:space="preserve">23. </s>
  <s xml:id="echoid-s7492" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7493" xml:space="preserve">ſinum ipſius 67408. </s>
  <s xml:id="echoid-s7494" xml:space="preserve">duco <lb/>in ſinum complementi latitudinis ſeptentrionalis, ſcilicet 20. </s>
  <s xml:id="echoid-s7495" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7496" xml:space="preserve">quæ eſt 70. </s>
  <s xml:id="echoid-s7497" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7498" xml:space="preserve">ſinus <lb/>autem 93969. </s>
  <s xml:id="echoid-s7499" xml:space="preserve">productum diuido in totum, quotiens eſt 63342. </s>
  <s xml:id="echoid-s7500" xml:space="preserve">arcus eius 39 gra. </s>
  <s xml:id="echoid-s7501" xml:space="preserve">18. </s>
  <s xml:id="echoid-s7502" xml:space="preserve">mi. <lb/></s>
  <s xml:id="echoid-s7503" xml:space="preserve">inuentum primum. </s>
  <s xml:id="echoid-s7504" xml:space="preserve">Complementũ eius eſt 50. </s>
  <s xml:id="echoid-s7505" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7506" xml:space="preserve">42. </s>
  <s xml:id="echoid-s7507" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7508" xml:space="preserve">ſinus uero 77384. </s>
  <s xml:id="echoid-s7509" xml:space="preserve">eſt ipſe diuſ <lb/>
<anchor type="note" xlink:label="note-0088-02a" xlink:href="note-0088-02"/>
ſor, iam nunc duco ſinum latitudinis ſeptentrionalis, ſcilicet 20. </s>
  <s xml:id="echoid-s7510" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7511" xml:space="preserve">34202, in totum, &amp; </s>
  <s xml:id="echoid-s7512" xml:space="preserve"><lb/>diuido in diuiſorem, quotiens erit 44197. </s>
  <s xml:id="echoid-s7513" xml:space="preserve">arcus illius 26. </s>
  <s xml:id="echoid-s7514" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7515" xml:space="preserve">14. </s>
  <s xml:id="echoid-s7516" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7517" xml:space="preserve">quibus addo latitu-<lb/>dinem Mercurij meridionalem ſcilicet 3. </s>
  <s xml:id="echoid-s7518" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7519" xml:space="preserve">20. </s>
  <s xml:id="echoid-s7520" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7521" xml:space="preserve">proueniũt inde 29. </s>
  <s xml:id="echoid-s7522" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7523" xml:space="preserve">34. </s>
  <s xml:id="echoid-s7524" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7525" xml:space="preserve">in <lb/>uentũ ſecundũ. </s>
  <s xml:id="echoid-s7526" xml:space="preserve">Complementũ ipſius eſt 60. </s>
  <s xml:id="echoid-s7527" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7528" xml:space="preserve">26. </s>
  <s xml:id="echoid-s7529" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7530" xml:space="preserve">ſinum eius 86891. </s>
  <s xml:id="echoid-s7531" xml:space="preserve">duco in ſinũ <lb/>
<anchor type="note" xlink:label="note-0088-03a" xlink:href="note-0088-03"/>
complementi primi inuenti ſcilicet 50. </s>
  <s xml:id="echoid-s7532" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7533" xml:space="preserve">42. </s>
  <s xml:id="echoid-s7534" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7535" xml:space="preserve">77384. </s>
  <s xml:id="echoid-s7536" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7537" xml:space="preserve">diuido in ſinum totum, quo <lb/>tiens eſt 67239. </s>
  <s xml:id="echoid-s7538" xml:space="preserve">arcus eius 42. </s>
  <s xml:id="echoid-s7539" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7540" xml:space="preserve">15. </s>
  <s xml:id="echoid-s7541" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7542" xml:space="preserve">quo ſubtracto de 90. </s>
  <s xml:id="echoid-s7543" xml:space="preserve">remanent 47. </s>
  <s xml:id="echoid-s7544" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7545" xml:space="preserve">45. </s>
  <s xml:id="echoid-s7546" xml:space="preserve">mi. <lb/></s>
  <s xml:id="echoid-s7547" xml:space="preserve">diſtantia nimirum iſta ſtellarum quam in hoc maxime nolui cælare, ut ſimile exemplũ <lb/>etiam in locis terreſtris imiteris.</s>
  <s xml:id="echoid-s7548" xml:space="preserve"/>
</p>
<div xml:id="echoid-div215" type="float" level="2" n="1">
<note position="right" xlink:label="note-0087-05" xlink:href="note-0087-05a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">primum</emph>.</note>
<note position="right" xlink:label="note-0087-06" xlink:href="note-0087-06a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">ſecundum</emph>.</note>
<note position="left" xlink:label="note-0088-01" xlink:href="note-0088-01a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſoopi.</emph></note>
<note position="left" xlink:label="note-0088-02" xlink:href="note-0088-02a" xml:space="preserve"><emph style="it">Inuenium</emph> <lb/><emph style="it">primum.</emph></note>
<note position="left" xlink:label="note-0088-03" xlink:href="note-0088-03a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">ſecundum</emph>.</note>
</div>
</div>
<div xml:id="echoid-div217" type="section" level="1" n="110">
<head xml:id="echoid-head114" xml:space="preserve">PRONVNCIATVM XCVIII.</head>
<p>
  <s xml:id="echoid-s7549" xml:space="preserve">Altitudinem ſtellæ ſupra horizontẽ exiſtentis, in omni regione omni´ <lb/>hora exacto calculo indagare.</s>
  <s xml:id="echoid-s7550" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s7551" xml:space="preserve">Principio duc ſinum diſtantiæ ſtellæ à meridiano in ſinum complementi declinatio-<lb/>nis, &amp; </s>
  <s xml:id="echoid-s7552" xml:space="preserve">productum diuide per totum, arcus quotientis dabit inuentum primum. </s>
  <s xml:id="echoid-s7553" xml:space="preserve">Mox <lb/>
<anchor type="note" xlink:label="note-0088-04a" xlink:href="note-0088-04"/>
propone tibi ſinum complementi huius inuenti &amp; </s>
  <s xml:id="echoid-s7554" xml:space="preserve">ſinum declinationis ſtellæ, minorem <lb/>duc in totum, productum diuide in maiorem, arcus quotientis latitudini regionis addi <lb/>tus, producit inuentum ſecundum. </s>
  <s xml:id="echoid-s7555" xml:space="preserve">Nunc iam duc ſinum complementi inuenti ſecundi <lb/>
<anchor type="note" xlink:label="note-0088-05a" xlink:href="note-0088-05"/>
in ſinum complementi inuenti primi, productum diuide in totum, arcus quotientis o-<lb/>ſtendit altitudinem ſtellæ ſupra horizontem. </s>
  <s xml:id="echoid-s7556" xml:space="preserve">?</s>
  <s xml:id="echoid-s7557" xml:space="preserve">? Exemplum hic tibi cape huiuſmodi. <lb/></s>
  <s xml:id="echoid-s7558" xml:space="preserve">Adſumo ecce ſpicam uirginis per quam antea in nocte intronizationis horam obſerua <lb/>
<anchor type="note" xlink:label="note-0088-06a" xlink:href="note-0088-06"/>
ui per altitudinem, iam uero ex ipſa hora quæro altitudinem. </s>
  <s xml:id="echoid-s7559" xml:space="preserve">Declinatio ita ſpicæ eſt <lb/>8. </s>
  <s xml:id="echoid-s7560" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7561" xml:space="preserve">26. </s>
  <s xml:id="echoid-s7562" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7563" xml:space="preserve">merid. </s>
  <s xml:id="echoid-s7564" xml:space="preserve">complementum aũt 81. </s>
  <s xml:id="echoid-s7565" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7566" xml:space="preserve">44. </s>
  <s xml:id="echoid-s7567" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7568" xml:space="preserve">ſinum ipſius 98960. </s>
  <s xml:id="echoid-s7569" xml:space="preserve">duco in ſi-<lb/>num diſtantiæ ſtellæ à meridie, quam exempli loco accipio 26. </s>
  <s xml:id="echoid-s7570" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7571" xml:space="preserve">5 mi. </s>
  <s xml:id="echoid-s7572" xml:space="preserve">ſinus eius eſt <lb/>43967. </s>
  <s xml:id="echoid-s7573" xml:space="preserve">productum diuido in totum, quotiens producit 43509. </s>
  <s xml:id="echoid-s7574" xml:space="preserve">arcus ip ſius eſt 25. </s>
  <s xml:id="echoid-s7575" xml:space="preserve">gra. <lb/></s>
  <s xml:id="echoid-s7576" xml:space="preserve">48. </s>
  <s xml:id="echoid-s7577" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7578" xml:space="preserve">inuentum illud primum. </s>
  <s xml:id="echoid-s7579" xml:space="preserve">Porrò ſinum declinationis 14378. </s>
  <s xml:id="echoid-s7580" xml:space="preserve">duco in totum, diui-<lb/>
<anchor type="note" xlink:label="note-0088-07a" xlink:href="note-0088-07"/>
do deinde productum in ſinum complementi primi inuenti, quotiens erit 15970. </s>
  <s xml:id="echoid-s7581" xml:space="preserve">arcus <lb/>iſtius eſt 9. </s>
  <s xml:id="echoid-s7582" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7583" xml:space="preserve">12. </s>
  <s xml:id="echoid-s7584" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7585" xml:space="preserve">quibus addo eleuationẽ poli 48. </s>
  <s xml:id="echoid-s7586" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7587" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7588" xml:space="preserve">ſumma fit 57. </s>
  <s xml:id="echoid-s7589" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7590" xml:space="preserve">12. </s>
  <s xml:id="echoid-s7591" xml:space="preserve">mi. <lb/></s>
  <s xml:id="echoid-s7592" xml:space="preserve">inuentum ſecundum. </s>
  <s xml:id="echoid-s7593" xml:space="preserve">Adhuc ſinum complementi ſecundi inuenti duco in ſinum primi <lb/>
<anchor type="note" xlink:label="note-0088-08a" xlink:href="note-0088-08"/>
inuenti. </s>
  <s xml:id="echoid-s7594" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s7595" xml:space="preserve">54170. </s>
  <s xml:id="echoid-s7596" xml:space="preserve">in 90031. </s>
  <s xml:id="echoid-s7597" xml:space="preserve">productum diuido in totum. </s>
  <s xml:id="echoid-s7598" xml:space="preserve">quotiens erit 48770. </s>
  <s xml:id="echoid-s7599" xml:space="preserve">arcus eius <lb/>eſt 29. </s>
  <s xml:id="echoid-s7600" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7601" xml:space="preserve">14. </s>
  <s xml:id="echoid-s7602" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7603" xml:space="preserve">altitudo iſta ſtellæ.</s>
  <s xml:id="echoid-s7604" xml:space="preserve"/>
</p>
<div xml:id="echoid-div217" type="float" level="2" n="1">
<note position="left" xlink:label="note-0088-04" xlink:href="note-0088-04a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">primum.</emph></note>
<note position="left" xlink:label="note-0088-05" xlink:href="note-0088-05a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">ſecundum</emph>.</note>
<note position="left" xlink:label="note-0088-06" xlink:href="note-0088-06a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſcopi</emph>.</note>
<note position="left" xlink:label="note-0088-07" xlink:href="note-0088-07a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">primum</emph>.</note>
<note position="left" xlink:label="note-0088-08" xlink:href="note-0088-08a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">ſecundum</emph>.</note>
</div>
</div>
<div xml:id="echoid-div219" type="section" level="1" n="111">
<head xml:id="echoid-head115" xml:space="preserve">PRONVNCIATVM XCIX.</head>
<p>
  <s xml:id="echoid-s7605" xml:space="preserve">Diſtantiam ſtellæ horizontalem à circulo meridiano omni hora in-<lb/>ueſtigare.</s>
  <s xml:id="echoid-s7606" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s7607" xml:space="preserve">Ad inueniendum autem azimuth ſtellæ propone tibi ſinum complementi altitudinis <lb/>ſtellæ iam per præmiſſam inuentæ, &amp; </s>
  <s xml:id="echoid-s7608" xml:space="preserve">ſinum inuenti primi quem per præcedentem inue <lb/>niſti, minorem duc in totum, productum diuide in maiorem, arcus quotientis dabit azi <lb/>muth ſtellæ, quod alio nomine dicimus diſtantiam horizõtalem â meridiano. </s>
  <s xml:id="echoid-s7609" xml:space="preserve">?</s>
  <s xml:id="echoid-s7610" xml:space="preserve">? Ex-<lb/>
<anchor type="note" xlink:label="note-0088-09a" xlink:href="note-0088-09"/>
empli gratia. </s>
  <s xml:id="echoid-s7611" xml:space="preserve">Ex ſuperiori pronunciato inueni inuentum primum, ſinum eius 43509. <lb/></s>
  <s xml:id="echoid-s7612" xml:space="preserve">duco in ſinum totum, &amp; </s>
  <s xml:id="echoid-s7613" xml:space="preserve">productum diuido in ſinum complementi altitudinis ſtellæ iam <lb/>ex ſuperiori pron<unsure/>un@iato inuentæ. </s>
  <s xml:id="echoid-s7614" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s7615" xml:space="preserve">43509. </s>
  <s xml:id="echoid-s7616" xml:space="preserve">quotiens eius eſt 47713. </s>
  <s xml:id="echoid-s7617" xml:space="preserve">arcus autem 29. </s>
  <s xml:id="echoid-s7618" xml:space="preserve"><lb/>gra. </s>
  <s xml:id="echoid-s7619" xml:space="preserve">55. </s>
  <s xml:id="echoid-s7620" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7621" xml:space="preserve">talis eſt dictantia ſtellæ à meridiano uerſus occaſum.</s>
  <s xml:id="echoid-s7622" xml:space="preserve"/>
</p>
<div xml:id="echoid-div219" type="float" level="2" n="1">
<note position="left" xlink:label="note-0088-09" xlink:href="note-0088-09a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſcopi</emph>.</note>
</div>
<pb file="0089" n="89" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
</div>
<div xml:id="echoid-div221" type="section" level="1" n="112">
<head xml:id="echoid-head116" xml:space="preserve">PRONVNCIATVM C.</head>
<p>
  <s xml:id="echoid-s7623" xml:space="preserve">Quocun anni tempore etiam in pauculis diebus per ſtellam incognitam <lb/>&amp; </s>
  <s xml:id="echoid-s7624" xml:space="preserve">exortum Solis, maximam Solis declinationem dignoſcere.</s>
  <s xml:id="echoid-s7625" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s7626" xml:space="preserve">Vtuideas exactè finem reſpondere principio, &amp; </s>
  <s xml:id="echoid-s7627" xml:space="preserve">utrun diligentiſsime à nobis eſſe <lb/>præſcripta omnia, pulcherrimum &amp; </s>
  <s xml:id="echoid-s7628" xml:space="preserve">utiliſsimum pronunciatum in hunc locum cõſulto <lb/>diſtulimus, ubi admiratione quo dignum eſt declinationem Solis maximam per totũ <lb/>annum inueniri poſſe, ne tunc tantum quando circa principia eſt ♋ uel ♑. </s>
  <s xml:id="echoid-s7629" xml:space="preserve">Ita ſic ꝓ <lb/>cede. </s>
  <s xml:id="echoid-s7630" xml:space="preserve">Primum tibi ob oculos pone ſtellam aliquam etiam ignotam in quocun ſit illa ſi <lb/>gno uel gradu, &amp; </s>
  <s xml:id="echoid-s7631" xml:space="preserve">diligenter conſidera quando attingit meridianum, ſit etiam ad manus <lb/>tibi clepſydra aliqua certa uel aqua uel harena dimetiens horas, aut quodcun horologi <lb/>um etiam ferreum, quum´ ſtella propoſita meridianum atringit, horologium tuum tibi <lb/>compone, ſingulas horas &amp; </s>
  <s xml:id="echoid-s7632" xml:space="preserve">minuta obſeruans, eò uſ dum Sol ad horizontem pertin-<lb/>gat, eam horam attende diligentius, at cum aliquo in ſtrumento obſerua amplitudi-<lb/>nem ortus Solis. </s>
  <s xml:id="echoid-s7633" xml:space="preserve">Deinde poſt aliquot dies conſidera rurſus quando ſtella propoſita tan <lb/>gat meridianum, at inde horas obſerua uſ ad Solis ortum, ſimiliter &amp; </s>
  <s xml:id="echoid-s7634" xml:space="preserve">amplitudinem <lb/>ſicut prius attende, at ſic facies in occaſu Solis &amp; </s>
  <s xml:id="echoid-s7635" xml:space="preserve">eius amplitudine, unum hoc uide, ut <lb/>utra hæc obſeruatio fiat in una quarta zodiaci, quotquot interim dies interueniant, ho <lb/>ras deinde illas quæ minus ſunt ſubtrahe à maioribus, &amp; </s>
  <s xml:id="echoid-s7636" xml:space="preserve">reſiduum ſepone in locum <lb/>aliquem ſeorſim, dicetur´ reſiduum, reſiduum horarum, mox ad quamlibet amplitu-<lb/>nem quære declinationem Solis ab æquatore per 13. </s>
  <s xml:id="echoid-s7637" xml:space="preserve">pronunciatum, ſimiliter &amp; </s>
  <s xml:id="echoid-s7638" xml:space="preserve">differen <lb/>tiam aſcenſionalem ad quamlibet amplitudinem per 15 pronunciatum. </s>
  <s xml:id="echoid-s7639" xml:space="preserve">Inſuper adde <lb/>differentiam horariam &amp; </s>
  <s xml:id="echoid-s7640" xml:space="preserve">differentiam aſcenſionalem maiorem, &amp; </s>
  <s xml:id="echoid-s7641" xml:space="preserve">â ſumma illa ſubtra-<lb/>he rurſus differentiam aſcenſionalem minorem, reſiduum eſt ipſa aſcenſio recta inter lo-<lb/>ca Solis in quo erat tempore obſeruationis. </s>
  <s xml:id="echoid-s7642" xml:space="preserve">Ecce iam tria habes per quæ inuenies ma-<lb/>ximam Solis declinationem, puta duas declinationes Solis &amp; </s>
  <s xml:id="echoid-s7643" xml:space="preserve">aſcenſionem rectam in <lb/>duo loca Solis. </s>
  <s xml:id="echoid-s7644" xml:space="preserve">Iam duc ſinum complementi minoris declinationis in ſinum aſcenſionis <lb/>
<anchor type="note" xlink:label="note-0089-01a" xlink:href="note-0089-01"/>
rectæ, &amp; </s>
  <s xml:id="echoid-s7645" xml:space="preserve">eſt differentia longitudinis in æquatore, quæ inter duos meridianos per Solem <lb/>tempore obſeruationis deductos includitur, productum diuide in totum, arcus quotien <lb/>tis eſt inuentum primum. </s>
  <s xml:id="echoid-s7646" xml:space="preserve">Mox propone tibi complementum inuenti primi, &amp; </s>
  <s xml:id="echoid-s7647" xml:space="preserve">ſinum <lb/>
<anchor type="note" xlink:label="note-0089-02a" xlink:href="note-0089-02"/>
minoris declinationis, minorem duc in totum, diuide etiam productum in maiorem, ar <lb/>cum quotientis illius ſubtrahe à declinatione maiori, reſiduum uocabitur inuentum ſe-<lb/>cundum. </s>
  <s xml:id="echoid-s7648" xml:space="preserve">Super hæc etiam duc ſinus complementorum primi &amp; </s>
  <s xml:id="echoid-s7649" xml:space="preserve">ſecundi inuenti in ſe, <lb/>productum diuide in totum, arcus quotientis de 90. </s>
  <s xml:id="echoid-s7650" xml:space="preserve">ſublatus, relinquet arcum eclypticæ <lb/>â loco Solis primæ obſeruationis uſ ad locum Solis, in quo erat in ſecunda obſeruati-<lb/>one. </s>
  <s xml:id="echoid-s7651" xml:space="preserve">Porrò inde duc ſinum primi inuenti in totum, productum diuide in ſinum huius <lb/>diſtantiæ locorum Solis, arcus quotientis dabit inuentum tertium, eius ſinum itidem <lb/>
<anchor type="note" xlink:label="note-0089-03a" xlink:href="note-0089-03"/>
duc in ſinum complementi maioris declinationis Solis, qui quidem in duabus ijs obſer-<lb/>uationibus ſit inuenta, productum diuide in totum, arcus quotientis de 90. </s>
  <s xml:id="echoid-s7652" xml:space="preserve">ſubtractus, <lb/>relinquet maximam declinationem eclypticæ abæquinoctiali. </s>
  <s xml:id="echoid-s7653" xml:space="preserve">?</s>
  <s xml:id="echoid-s7654" xml:space="preserve">? Sed quo piaculo hic <lb/>
<anchor type="note" xlink:label="note-0089-04a" xlink:href="note-0089-04"/>
tandem tibi exemplum dabimus ? </s>
  <s xml:id="echoid-s7655" xml:space="preserve">aut nonne religio fuerit, in gratiam &amp; </s>
  <s xml:id="echoid-s7656" xml:space="preserve">honorem <lb/>ampliſsimi &amp; </s>
  <s xml:id="echoid-s7657" xml:space="preserve">Reuerendiſsimi patris &amp; </s>
  <s xml:id="echoid-s7658" xml:space="preserve">Præſulis Auguſtani, hic ubi maxime opus eſt, <lb/>non meminiſſe celeberrimæ intronizationis, qua hactenus per omnia exempla uſi ſu <lb/>mus? </s>
  <s xml:id="echoid-s7659" xml:space="preserve">Eſto igitur, ut hora intronizationis Auguſtæ, ubi &amp; </s>
  <s xml:id="echoid-s7660" xml:space="preserve">facta eſt in altitudine poli <lb/>48. </s>
  <s xml:id="echoid-s7661" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s7662" xml:space="preserve">obſeruarim bis amplitudinem Solis forte per 45. </s>
  <s xml:id="echoid-s7663" xml:space="preserve">aut 46. </s>
  <s xml:id="echoid-s7664" xml:space="preserve">dies cõſequenter, uſus <lb/>ad hoc clepſydra, adhibita in hac ſtella medij cœli, à momento obſeruationis primæ <lb/>uſ ad contactum Solis &amp; </s>
  <s xml:id="echoid-s7665" xml:space="preserve">horizontis inuenerim 1. </s>
  <s xml:id="echoid-s7666" xml:space="preserve">horam, 40. </s>
  <s xml:id="echoid-s7667" xml:space="preserve">minut. </s>
  <s xml:id="echoid-s7668" xml:space="preserve">Deinde forſitan <lb/>poſt 45. </s>
  <s xml:id="echoid-s7669" xml:space="preserve">dies habita obſeruatione altera, ſub contactum eiuſdem ſtellæ cum meridiano <lb/>uſ ad ortum Solis, repererim tres horas, 30. </s>
  <s xml:id="echoid-s7670" xml:space="preserve">minuta, 12. </s>
  <s xml:id="echoid-s7671" xml:space="preserve">ſecunda. </s>
  <s xml:id="echoid-s7672" xml:space="preserve">Iam ita ſubtraho <lb/>unam horam, 40. </s>
  <s xml:id="echoid-s7673" xml:space="preserve">minu. </s>
  <s xml:id="echoid-s7674" xml:space="preserve">à 3. </s>
  <s xml:id="echoid-s7675" xml:space="preserve">horis, 30. </s>
  <s xml:id="echoid-s7676" xml:space="preserve">min. </s>
  <s xml:id="echoid-s7677" xml:space="preserve">12. </s>
  <s xml:id="echoid-s7678" xml:space="preserve">ſecundis, &amp; </s>
  <s xml:id="echoid-s7679" xml:space="preserve">remanet 1. </s>
  <s xml:id="echoid-s7680" xml:space="preserve">liora cum 50. </s>
  <s xml:id="echoid-s7681" xml:space="preserve">mi. <lb/></s>
  <s xml:id="echoid-s7682" xml:space="preserve">12. </s>
  <s xml:id="echoid-s7683" xml:space="preserve">ſecundis, quibus in gradus mutatis, habeo 27. </s>
  <s xml:id="echoid-s7684" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s7685" xml:space="preserve">33. </s>
  <s xml:id="echoid-s7686" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7687" xml:space="preserve">at eam Jifferentiam di-<lb/>co horariam. </s>
  <s xml:id="echoid-s7688" xml:space="preserve">In priore itidem obſeruatione inueni amplitudinem ortus Solis 9. </s>
  <s xml:id="echoid-s7689" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7690" xml:space="preserve">51. </s>
  <s xml:id="echoid-s7691" xml:space="preserve"><lb/>mi. </s>
  <s xml:id="echoid-s7692" xml:space="preserve">ſimul´ ꝑ 13. </s>
  <s xml:id="echoid-s7693" xml:space="preserve">pronunc. </s>
  <s xml:id="echoid-s7694" xml:space="preserve">repperi declinationẽ ☉(sun) 6. </s>
  <s xml:id="echoid-s7695" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7696" xml:space="preserve">34. </s>
  <s xml:id="echoid-s7697" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7698" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7699" xml:space="preserve">differentiã aſcenſio-
<pb file="0090" n="90" rhead="GENVINVS VSVS"/>
nalem per 15. </s>
  <s xml:id="echoid-s7700" xml:space="preserve">pronunciatum 7. </s>
  <s xml:id="echoid-s7701" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7702" xml:space="preserve">22. </s>
  <s xml:id="echoid-s7703" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7704" xml:space="preserve">In altera autem obſeruatione fuit amplitudo <lb/>31. </s>
  <s xml:id="echoid-s7705" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7706" xml:space="preserve">53. </s>
  <s xml:id="echoid-s7707" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7708" xml:space="preserve">unde ſequitur declinatio eius 20. </s>
  <s xml:id="echoid-s7709" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7710" xml:space="preserve">42. </s>
  <s xml:id="echoid-s7711" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7712" xml:space="preserve">ſimul &amp; </s>
  <s xml:id="echoid-s7713" xml:space="preserve">differentia aſcenſi <lb/>onalis 24. </s>
  <s xml:id="echoid-s7714" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7715" xml:space="preserve">49. </s>
  <s xml:id="echoid-s7716" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7717" xml:space="preserve">Iam addo maiorem differentiam aſcenſionalem. </s>
  <s xml:id="echoid-s7718" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s7719" xml:space="preserve">24. </s>
  <s xml:id="echoid-s7720" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7721" xml:space="preserve">49. </s>
  <s xml:id="echoid-s7722" xml:space="preserve">mi. <lb/></s>
  <s xml:id="echoid-s7723" xml:space="preserve">ad differentiam horariam. </s>
  <s xml:id="echoid-s7724" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s7725" xml:space="preserve">27. </s>
  <s xml:id="echoid-s7726" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7727" xml:space="preserve">33. </s>
  <s xml:id="echoid-s7728" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7729" xml:space="preserve">ſumma erit 52. </s>
  <s xml:id="echoid-s7730" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7731" xml:space="preserve">22. </s>
  <s xml:id="echoid-s7732" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7733" xml:space="preserve">hic ſubtraho rur-<lb/>ſus differentiam aſcenſionalem, &amp; </s>
  <s xml:id="echoid-s7734" xml:space="preserve">remanent 45. </s>
  <s xml:id="echoid-s7735" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7736" xml:space="preserve">aſcenſio illa recta inter utrun pun <lb/>ctum eclypticæ, in quo Sol fuit tempore obſeruato. </s>
  <s xml:id="echoid-s7737" xml:space="preserve">At reliquum nihil inde deſidero <lb/>ad hanc operationem, niſi duas iſtas declinationes &amp; </s>
  <s xml:id="echoid-s7738" xml:space="preserve">aſcenſionem illam rectam, duco igi <lb/>tur ſinum complementi minoris declinationis 99343. </s>
  <s xml:id="echoid-s7739" xml:space="preserve">in ſinum diſtantiæ aſcenſionis re <lb/>ctæ. </s>
  <s xml:id="echoid-s7740" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s7741" xml:space="preserve">43. </s>
  <s xml:id="echoid-s7742" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7743" xml:space="preserve">70710. </s>
  <s xml:id="echoid-s7744" xml:space="preserve">productum diuido in totum, quotiens eſt 70245. </s>
  <s xml:id="echoid-s7745" xml:space="preserve">arcus eius erit <lb/>
<anchor type="note" xlink:label="note-0090-01a" xlink:href="note-0090-01"/>
44. </s>
  <s xml:id="echoid-s7746" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7747" xml:space="preserve">38. </s>
  <s xml:id="echoid-s7748" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7749" xml:space="preserve">inuentum primum. </s>
  <s xml:id="echoid-s7750" xml:space="preserve">Porrò hinc aſſumo ſinum minoris declinationis, eum <lb/>duco in totum, productum diuido in ſinum complementi inuenti primi, &amp; </s>
  <s xml:id="echoid-s7751" xml:space="preserve">in quotiente <lb/>proueniunt 16070. </s>
  <s xml:id="echoid-s7752" xml:space="preserve">arcus eius eſt 9. </s>
  <s xml:id="echoid-s7753" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7754" xml:space="preserve">15. </s>
  <s xml:id="echoid-s7755" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7756" xml:space="preserve">quibus ſubductis à maxima declinatione <lb/>obſeruationis factæ, quæ eſt 20. </s>
  <s xml:id="echoid-s7757" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7758" xml:space="preserve">42. </s>
  <s xml:id="echoid-s7759" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7760" xml:space="preserve">inuentum ſecundum. </s>
  <s xml:id="echoid-s7761" xml:space="preserve">Poſtea duco ſinus com <lb/>
<anchor type="note" xlink:label="note-0090-02a" xlink:href="note-0090-02"/>
plementorum utriuſ inuenti in ſe. </s>
  <s xml:id="echoid-s7762" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s7763" xml:space="preserve">98009. </s>
  <s xml:id="echoid-s7764" xml:space="preserve">in 71161. </s>
  <s xml:id="echoid-s7765" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7766" xml:space="preserve">diuido in ſinum totum, quoti <lb/>ens erit 69744. </s>
  <s xml:id="echoid-s7767" xml:space="preserve">arcus autem 44. </s>
  <s xml:id="echoid-s7768" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7769" xml:space="preserve">13. </s>
  <s xml:id="echoid-s7770" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7771" xml:space="preserve">quibus itidem à toto ſublatis, remanent 45. <lb/></s>
  <s xml:id="echoid-s7772" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7773" xml:space="preserve">42. </s>
  <s xml:id="echoid-s7774" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7775" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7776" xml:space="preserve">tot ſanè gradibus Sol in eclyptica per ambas obſeruationes conſtitit. </s>
  <s xml:id="echoid-s7777" xml:space="preserve">De-<lb/>inde duco etiam ſinum primi inuenti rurſus in totum, ac diuido in ſinum complementi <lb/>
<anchor type="note" xlink:label="note-0090-03a" xlink:href="note-0090-03"/>
primi inuenti, quotiens dabit 68012. </s>
  <s xml:id="echoid-s7778" xml:space="preserve">arcus eius eſt ipſum inuentum tertium. </s>
  <s xml:id="echoid-s7779" xml:space="preserve">Sinum illũ <lb/>poſtremo duco in ſinum complemẽti maioris declinationis, &amp; </s>
  <s xml:id="echoid-s7780" xml:space="preserve">diuido per totum ſinum, <lb/>in quotiente inuenio 91696. </s>
  <s xml:id="echoid-s7781" xml:space="preserve">arcus eius eſt 66. </s>
  <s xml:id="echoid-s7782" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7783" xml:space="preserve">30. </s>
  <s xml:id="echoid-s7784" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7785" xml:space="preserve">quibus à 90. </s>
  <s xml:id="echoid-s7786" xml:space="preserve">ſubtractis, rema-<lb/>nent 23. </s>
  <s xml:id="echoid-s7787" xml:space="preserve">gra. </s>
  <s xml:id="echoid-s7788" xml:space="preserve">30. </s>
  <s xml:id="echoid-s7789" xml:space="preserve">mi. </s>
  <s xml:id="echoid-s7790" xml:space="preserve">Ecce quàm exacte iam inueni declinationem maximam Solis, quã <lb/>aliàs per totum annum duobus tantum diebus ſolent inquirere ubi uſuuenire poteſt, ut <lb/>per multos annos illis diebus Sol cœlo ſereno tamdiu uix conſpiciatur, at in hunc mo <lb/>dum propoſitionibus ijs centum finis eſto, ſint hæ lucubrationes noſtræ ſic concluſæ in <lb/>honorem ampliſsimi patris &amp; </s>
  <s xml:id="echoid-s7791" xml:space="preserve">Epiſcopi Auguſteñ. </s>
  <s xml:id="echoid-s7792" xml:space="preserve">at inuſum omnium ſtudioſorum <lb/>Mathematices &amp; </s>
  <s xml:id="echoid-s7793" xml:space="preserve">Aſtronomiæ.</s>
  <s xml:id="echoid-s7794" xml:space="preserve"/>
</p>
<div xml:id="echoid-div221" type="float" level="2" n="1">
<note position="right" xlink:label="note-0089-01" xlink:href="note-0089-01a" xml:space="preserve"><emph style="it">Lateralis</emph> <lb/><emph style="it">ingreſſus</emph> <lb/><emph style="it">ſimile oſters</emph> <lb/><emph style="it">dit</emph>.</note>
<note position="right" xlink:label="note-0089-02" xlink:href="note-0089-02a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">primum-</emph> <lb/><emph style="it">Inuentum</emph> <lb/><emph style="it">ſecundum</emph></note>
<note position="right" xlink:label="note-0089-03" xlink:href="note-0089-03a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">tertium.</emph></note>
<note position="right" xlink:label="note-0089-04" xlink:href="note-0089-04a" xml:space="preserve">EXEM-<lb/>PLVM <lb/>E<emph style="it">piſoo<unsure/>pi.</emph></note>
<note position="left" xlink:label="note-0090-01" xlink:href="note-0090-01a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">Primum.</emph></note>
<note position="left" xlink:label="note-0090-02" xlink:href="note-0090-02a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">ſecundum.</emph></note>
<note position="left" xlink:label="note-0090-03" xlink:href="note-0090-03a" xml:space="preserve"><emph style="it">Inuentum</emph> <lb/><emph style="it">tertium.</emph></note>
</div>
</div>
<div xml:id="echoid-div223" type="section" level="1" n="113">
<head xml:id="echoid-head117" xml:space="preserve">FINIS.</head>
<p>
  <s xml:id="echoid-s7795" xml:space="preserve">Norimbergæ apud Iohan. </s>
  <s xml:id="echoid-s7796" xml:space="preserve">Petreium, <lb/>Anno M. </s>
  <s xml:id="echoid-s7797" xml:space="preserve">D. </s>
  <s xml:id="echoid-s7798" xml:space="preserve">XLI.</s>
</p>
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<pb file="0094" n="94"/>
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  </div></text>
</echo>
author	Klaus Thoden <kthoden@mpiwg-berlin.mpg.de>
date	Wed, 29 Nov 2017 16:55:37 +0100
parents	22d6a63640c6
children