Mercurial > hg > mpdl-xml-content
view texts/XML/echo/la/Clavius_1591_DP9UZA52.xml @ 31:edf6e8fcf323 default tip
Removing DESpecs directory which deserted to git
| author | Klaus Thoden <kthoden@mpiwg-berlin.mpg.de> |
|---|---|
| date | Wed, 29 Nov 2017 16:55:37 +0100 |
| parents | 22d6a63640c6 |
| children |
line wrap: on
line source
<?xml version="1.0" encoding="utf-8"?><echo xmlns="http://www.mpiwg-berlin.mpg.de/ns/echo/1.0/" xmlns:de="http://www.mpiwg-berlin.mpg.de/ns/de/1.0/" xmlns:dcterms="http://purl.org/dc/terms" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:echo="http://www.mpiwg-berlin.mpg.de/ns/echo/1.0/" xmlns:xhtml="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.0RC"> <metadata> <dcterms:identifier>ECHO:DP9UZA52.xml</dcterms:identifier> <dcterms:creator identifier="GND:118880632">Clavius, Christoph</dcterms:creator> <dcterms:title xml:lang="la">In Sphaeram Ioannis de Sacro Bosco commentarius</dcterms:title> <dcterms:date xsi:type="dcterms:W3CDTF">1591</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> <parameters>despecs = 1.1.2</parameters> </metadata> <text xml:lang="la" type="free"> <div xml:id="echoid-div1" type="section" level="1" n="1"><pb file="000" n="1"/> <pb file="001" n="2"/> <pb file="002" n="3"/> <pb file="003" n="4"/> <pb file="004" n="5"/> <pb file="005" n="6"/> </div> <div xml:id="echoid-div2" type="section" level="1" n="2"> <head xml:id="echoid-head1" xml:space="preserve">CHRISTOPHORI <lb/>CLAVII BAMBERGENSIS <lb/>EX SOCIETATE IESV <lb/>IN SPH AERAM IOANNIS <lb/>DE SACRO BOSCO <lb/>COMMENTARIVS,</head> <head xml:id="echoid-head2" xml:space="preserve">Nunc tertio ab ipſo Auctore recognitus, & pleriſque <lb/>in locis locupletatus.</head> <head xml:id="echoid-head3" xml:space="preserve">PERMISSV SVPERIORVM.</head> <figure> <image file="005-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/005-01"/> </figure> </div> <div xml:id="echoid-div3" type="section" level="1" n="3"> <head xml:id="echoid-head4" xml:space="preserve">VENETIIS, MD XCI.</head> <p> <s xml:id="echoid-s1" xml:space="preserve">Apud Ioan. </s> <s xml:id="echoid-s2" xml:space="preserve">Baptiſtam Ciotum Senenſem, ſub ſign<unsure/>o Mineruæ.</s> <s xml:id="echoid-s3" xml:space="preserve"/> </p> <pb file="006" n="7"/> <handwritten/> </div> <div xml:id="echoid-div4" type="section" level="1" n="4"> <head xml:id="echoid-head5" xml:space="preserve">AD LECTOREM.</head> <p> <s xml:id="echoid-s4" xml:space="preserve">VT maior fructus ex noſtris commentarijs in ſphæram perciperetur, <lb/>addidimus in gratiam ſtudioſorum, pręter auctoris expoſitionem, <lb/>cum multa alia, tum hæc præcipue, quæ ſequuntur.</s> <s xml:id="echoid-s5" xml:space="preserve"/> </p> <note style="it" position="right" xml:space="preserve"> <lb/>1 # <emph style="sc">Tractationem</emph> figurarum Iſoperim etrarum octodecim propoſitionibus abſolutam <lb/># pag. # 81.ad 104 <lb/>2 # <emph style="sc">Qva</emph> arte declinationes ſtellarum ex earum longitudinibus, & latitudinibus cogni-<lb/># tis per ſinus ſint ſupputandæ. # 183 <lb/>3 # <emph style="sc">Historiam</emph> & ſententiam propriam de ſtella noua, quæ anno 1572. apparuitin <lb/># Caſſiopeia. # pag. 191. <lb/>4 # <emph style="sc">Digressionem</emph> de arenæ numero ex Archimede. # pag. 217 <lb/>5 # <emph style="sc">Qva</emph> ratione inueſtiganda ſit declinatio, cuiuſlibet puncti Eclipticæ ex doctrina Si-<lb/># nuum. # pag. 263 <lb/>6 # <emph style="sc">Qva</emph> induſtria interuallum inter quaſcunque duas ciuitates, quarum longitudo, <lb/># & latitudo nota ſit, tam Geometrice per lineas, quàm ex ſinubus inueniatur. <lb/># pag. # 290. & 293 <lb/>7 # <emph style="sc">Item</emph> quomodo ſ@@pputandæ ſint per ſinus Latitudines ortiuæ, atque occiduæ. # pag. 300 <lb/>8 # <emph style="sc">Deinde</emph> qua via aſcenſiones rectæ, & ohliquæ omnium punctorum, ſeu arcuum Ecli <lb/># pticæ ex ſinuum doctrina reperiantur. # pag. 328. & 337 <lb/>9 # <emph style="sc">Rvrsvs</emph> quo pacto quantitates dierum, & noctium per totum annum in omni Climate <lb/># inquirantur per ſinus. # pag. 406. & 407 <lb/>10 # <emph style="sc">Ad</emph> hæc, Tabulas ad rem Aſtronomicam perneceſſarias. Vt Tabulam omnium ſtellarũ <lb/># fixarum, cum ſingularum longitudine, latitudine, magnitudine, & ſitu in conſtella-<lb/># tionibus. qua in re ſecuti ſumus ordinem omnium Aſteriſmorum, ſiue Conſtellatio-<lb/># num, ut ab antiqui ſſimis Aſtronomis ſunt obſeruatæ. Tabulam reducendi gradus <lb/># ad Horas, & contra. Tabulam declinationum punctorum Eclipticæ multo copioſio-<lb/># rem quàm ab alijs edita eſt: quippe quæ per quina Minuta progrediatur. Tabulam <lb/># aſcenſionum rectarum. Tabulas aſcenſionalium differentiarum ad omnes poli eleua-<lb/># tiones. Tabulam aſcenſionum obliquarum ad varias altitudines poli. Tabulam ar-<lb/># cuum ſemidiurnorum ad plurimas poli eleuationes ſupputatam. pag. 151. 231. 264. <lb/># 330. 340. 348. & 408. # pag. 432 <lb/>11 # <emph style="sc">Dispvtationem</emph> perutilem de orbibus Eccentricis, & Epicyclis contra non-<lb/># nullos philoſophos. # pag. 432 <lb/>12 # <emph style="sc">Postremo</emph> Theoricas omnium planetar um digeſtas in tabulas, quæ eorum or-<lb/># bes, motus, & paſſiones, necnon definitiones terminorum Aſtronomicorum comple-<lb/># ctumtur. # pag. 464 <lb/></note> <handwritten/> </div> <div xml:id="echoid-div5" type="section" level="1" n="5"> <head xml:id="echoid-head6" xml:space="preserve">MAX-PLANCK-INSTITUT <lb/>FÜR WISSENSCHAFTSGESCHICHTE</head> <head xml:id="echoid-head7" xml:space="preserve">Bibliothek</head> <handwritten/> <pb file="007" n="8"/> <figure> <image file="007-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/007-01"/> </figure> </div> <div xml:id="echoid-div6" type="section" level="1" n="6"> <head xml:id="echoid-head8" xml:space="preserve">IO. IA COBO <lb/>TONIALO VIRO <lb/>ERVDITISSIMO.</head> <head xml:id="echoid-head9" style="it" xml:space="preserve">IO. BAPTISTA CIOTVS S.P.D.</head> <p> <s xml:id="echoid-s6" xml:space="preserve"><emph style="sc">ETsi</emph> omnes artes, quæ libero <lb/>homine dignæ ſunt, omnesq; <lb/></s> <s xml:id="echoid-s7" xml:space="preserve">ſcientiæ in ſummo honore a-<lb/>pud omnes gentes ſemper ha-<lb/>bitæ ſint: </s> <s xml:id="echoid-s8" xml:space="preserve">quæ tamen hanc hu <lb/>ius Dei templi, quod incoli-<lb/>mus, fabricam contemplatur, & </s> <s xml:id="echoid-s9" xml:space="preserve">illius cognitio-<lb/>nem tradit, tanto interuallo cæteris antecedit, vt <lb/>cæteræ huius quodammodo pediſſequę uidean <lb/>tur. </s> <s xml:id="echoid-s10" xml:space="preserve">Propius enim perducit illos, qui in hu-<lb/>iuſmodi contemplatione uitæ ocium terunt, <lb/>ad illius, qui Mundum condidit, cognitionem. </s> <s xml:id="echoid-s11" xml:space="preserve"><lb/>Quo quid melis? </s> <s xml:id="echoid-s12" xml:space="preserve">Quid honeſtius? </s> <s xml:id="echoid-s13" xml:space="preserve">Quid homi-<lb/>num generi conducibilius? </s> <s xml:id="echoid-s14" xml:space="preserve">Præterea rem longe <pb file="008" n="9"/> præſtantiorem, & </s> <s xml:id="echoid-s15" xml:space="preserve">in illa perpetua conuerſione <lb/>firmiorem, hæc diſciplina, quàm cæterę comple <lb/>ctitur. </s> <s xml:id="echoid-s16" xml:space="preserve">Propter hanc cauſam qui hac ratione Mũ <lb/>dum contemplatur, non ſolum in Dei cognitio-<lb/>nem faciliùs uenit, ſed ſui ipſius: </s> <s xml:id="echoid-s17" xml:space="preserve">quod illi priſci <lb/>Philoſophi plurimi faciebant. </s> <s xml:id="echoid-s18" xml:space="preserve">Nullum enim a-<lb/>liud eſt Dei opus, quod ubiq́ue, & </s> <s xml:id="echoid-s19" xml:space="preserve">ſemper tam <lb/>excellenti ratione omnibus pene noſtris ſenſi-<lb/>bus pateat, & </s> <s xml:id="echoid-s20" xml:space="preserve">ſui Factoris ſapientiam prædicet, <lb/>quàm hoc Mundi ornamentum, & </s> <s xml:id="echoid-s21" xml:space="preserve">hęcrerũ om <lb/>nium vniuerſitas. </s> <s xml:id="echoid-s22" xml:space="preserve">Quæ nos quoque nobis pe-<lb/>neob oculos pc<unsure/>r<unsure/> ſpeculum ponit. </s> <s xml:id="echoid-s23" xml:space="preserve">Nihil enim <lb/>aliud eſt homo, ut Græci uoluerunt, quàm <lb/>μικρόκοσμος. </s> <s xml:id="echoid-s24" xml:space="preserve">Hanc autem rem cum ſine controuer <lb/>ſia Chriſtophorus Clauius noſtræ tempeſtatis <lb/>mathematicorum Princeps ita tractet in ſuis <lb/>commentarijs in ſphæram Ioannis de ſacro Bo-<lb/>ſco, ut nihil addi poſse uideatur (ut Roma teſta-<lb/>tur, quæ iam ter, u<unsure/>el quater illos impreſsit) mihi <lb/>faciendum exiſtimaui, ut hic quoq; </s> <s xml:id="echoid-s25" xml:space="preserve">Venetijs eoſ <lb/>dem nouis figuris, & </s> <s xml:id="echoid-s26" xml:space="preserve">diligenti correctione meis <lb/>typis imprimendos curarem, & </s> <s xml:id="echoid-s27" xml:space="preserve">tali viro illos <lb/>conſecrarem, qui tum alijs, tum hoc ſtudio, tum <lb/>uita, & </s> <s xml:id="echoid-s28" xml:space="preserve">morib. </s> <s xml:id="echoid-s29" xml:space="preserve">iã in numero Heroũ, & </s> <s xml:id="echoid-s30" xml:space="preserve">Semideo <lb/>rum ſit collocatus. </s> <s xml:id="echoid-s31" xml:space="preserve">Ex omnibus autem, qui in <pb file="009" n="10"/> mentem mihi uenerint, qui hac tempeſtate qui-<lb/>dem pauciſsimi ſunt, qui illis rebus, quæ perfi-<lb/>ciunt hominem tecum ſit conferendus, inueni <lb/>neminem. </s> <s xml:id="echoid-s32" xml:space="preserve">mitto litteras Latinas, & </s> <s xml:id="echoid-s33" xml:space="preserve">Græcas qui-<lb/>bus tantopere delectaris, ut non ſint indigna do <lb/>ctiſſimorum virorum auribus, quæ tum proſa <lb/>oratione, tum uerſibus cõſcribis: </s> <s xml:id="echoid-s34" xml:space="preserve">mitto nobilita <lb/>tem, morũ, facilitatem, uitę integritatem Philo-<lb/>ſophię ſtudia, & </s> <s xml:id="echoid-s35" xml:space="preserve">cætera huiuſmodi, quęin prõ-<lb/>ptu ſunt, & </s> <s xml:id="echoid-s36" xml:space="preserve">omnibus patent, quid dicendum eſ-<lb/>ſet de caritate, & </s> <s xml:id="echoid-s37" xml:space="preserve">officijs, quibus quoſq; </s> <s xml:id="echoid-s38" xml:space="preserve">peritiſ-<lb/>ſimos Mathematicos complecteris? </s> <s xml:id="echoid-s39" xml:space="preserve">Nonne om <lb/>nia tua ſemper illis patent? </s> <s xml:id="echoid-s40" xml:space="preserve">Hęc omnia, & </s> <s xml:id="echoid-s41" xml:space="preserve">alia hu <lb/>iuſmodi nõ mediocria, non vulgaria, ſed ſumma <lb/>cũ in te ſint, me profecto tuarũ laudũ enume-<lb/>ratione ne dum celebratione, deterrent. </s> <s xml:id="echoid-s42" xml:space="preserve">Ne mi-<lb/>nus igitur dicam quam te talem virum de-<lb/>cet, de tuis laudibus hactenus: </s> <s xml:id="echoid-s43" xml:space="preserve">aliàs fortaſ-<lb/>ſe, ſi qua mihiſe offeretur occaſio commoda <lb/>(quemadmodum ſpero,) diffuſius explicabun-<lb/>tur hæc, quę hoc loco uix enumerantur Illud fit <lb/>in hac epiſtola poſtremũ, vt hoc opus, quod tibi <lb/>dico, atque conſecro hilari uultu ſuſcipias, ac <lb/>tueare. </s> <s xml:id="echoid-s44" xml:space="preserve">Vale Veronę decus, iterum uale. <lb/></s> <s xml:id="echoid-s45" xml:space="preserve">Venetijs. </s> <s xml:id="echoid-s46" xml:space="preserve">Kalend. </s> <s xml:id="echoid-s47" xml:space="preserve">Septemb. </s> <s xml:id="echoid-s48" xml:space="preserve">M. </s> <s xml:id="echoid-s49" xml:space="preserve">D. </s> <s xml:id="echoid-s50" xml:space="preserve">XCI.</s> <s xml:id="echoid-s51" xml:space="preserve"/> </p> <pb file="010" n="11"/> <pb file="011" n="12"/> </div> <div xml:id="echoid-div7" type="section" level="1" n="7"> <head xml:id="echoid-head10" xml:space="preserve">INDEX RERVM, ET VERBORVM, <lb/>QV AE HIS COMMENTARIIS <lb/>CONTINENTVR.</head> <figure> <image file="011-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/011-01"/> </figure> <note position="right" xml:space="preserve"> <lb/>A <lb/><emph style="sc">ABraham</emph> Aegyptios docuiſse <lb/>Arithmeticã, & Aſtrologiã. # 3. <lb/>Acceptiones Zodiaci variæ. <lb/># pag. # 252. ad 254 <lb/>Acceſſus & receſſus ſphæræ o-<lb/># ctauæ quomodo fiat. # 56 <lb/>Acceſſus, & receſſus in octaua ſphæra quo-<lb/># modo deprehenſus. # 63 <lb/>Achillini ſententia de numero, & motu cę <lb/># lorum, eiusq́; confutatio. # 48 <lb/>Admirabilis ſphæra Archimedis. # 17 <lb/>Aequalis, ſiue æquinoctialis hora quæ. # 405 <lb/>Aequans circulus planetarum quid, & cur <lb/># ſit excogitatus. # 459. & 460 <lb/>Aequator, vel æquinoctialis circulus quid <lb/># & vnde dictus, & eius officia, atque utili-<lb/># tates quæ. # 225. ad 232 <lb/>Aequator, quo modo in cœlo deſcribi con <lb/># cipiatur. # 225 <lb/>Aequatoris altitudinem æqualem eſſe com <lb/># plemento altitudinis poli, hoc eſt, diſtan <lb/># tiæ Zenith à polo mundi. # 302 <lb/>Aequatoris altitudo qũo cognoſcatur. ibi. <lb/>Aequatoris gradus cur dicãtur tẽpora. # 248 <lb/>Aequator quare ſit regula, & menſura or-<lb/># tus, & occaſus ſignorum. # 321 <lb/>Aequatorem vniformiter aſcendere ſupra <lb/># quemcunque Horizontem. # 219 <lb/>Aequinoctia, & ſolſtitia mutare ſedes in Ca <lb/># lendario, & quare. # 274. & 275 <lb/>Aequinoctialia puncta quæ. # 23. & 274 <lb/>Aequinoctialis circulus, ſiue Aequator <lb/># quid, & cur ſic dictus, eiusq́; officia quæ. <lb/># pag. # 225. ad 232 <lb/>Aequinoctialis circuli, vel æquatoris uaria <lb/># nomina. # 227 <lb/>Aequinoctialis circulus quomodo in cęlo <lb/># deſcribatur. <lb/>Aequinoctialis, ſiue æquai<unsure/>i<unsure/>s hora quæ. # 405 <lb/>Aequinoctialis, ſiue uerus ortus, & occaſus <lb/># quid. # 300 <lb/>Aequinoctiorum Colurus quid. # 23. & 260. <lb/>Aequinoctium cur in ſphæra recta ſemper <lb/># fiat. # 401. & 402 <lb/>Aequinoctium in ſphæra obliqua, cur bis <lb/># tantum contingat. # 402. & 404 <lb/>Aequinoctium cur in ſphæra obliqua fiat, <lb/># Sole exiſtente in æquatore. # 227 <lb/>Aequinoctium quomodo intelligatur fier<unsure/>i <lb/># bis in anno in uniuerſa terra. # ibid. <lb/>Aer quanto minor ſit, quàm terra, & ignis. <lb/># pag. # 130. & 131 <lb/>Aeris, & ignis figura. # 134 <lb/>Aeris tres regiones quo modo ſint diſpoſi <lb/># tæ quoad craſſitiem. # 38 <lb/>Aerea ſigna Zodiaci, quæ. # 238 <lb/>Aeris regionis tres. # 38 <lb/>Aeris craſſities quanta ſit. # 130. & 131 <lb/>Aeſtiui, & hyemalis ſolſtitij pũcta quæ. # 260 <lb/>Aetheræ regionis proprietates. # 39 <lb/>Aethereæ regionis figura, ac forma. # 72 <lb/>Aetherea regio cur ſic dicta. # 39 <lb/>Aetates animantiũ præcipuè<unsure/> quatuor. # 241 <lb/>Alpetragij ſententia de numero, & motu <lb/># cœlorum, eiuſq́ confutatio. # 48 <lb/>Altitudo ęquatoris quo modo ex altitudi-<lb/># ne poli inueſtigetur. # 302 <lb/>Altitudinem ęquatoris ęqualem eſſe com <lb/># plemento altitudinis poli, ſiue diſtantię <lb/># Zenith à polo mundi. # ibid. <lb/>Altitudinem poli in quocunq; loco ęqua-<lb/># lem eſſe latitudini eiuſdem loci, hoc eſt, <lb/># diſtantię Zenith ab ęquatore. # 298 <lb/>Altitudo poli quo modo ex altitudine So-<lb/># lis meridiana inueniatur. # 279 <lb/>Altitudo Solis meridiana, uel alia quæui’s <lb/>\\</note> <pb file="012" n="13"/> </div> <div xml:id="echoid-div8" type="section" level="1" n="8"> <head xml:id="echoid-head11" style="it" xml:space="preserve">INDEX.</head> <note position="right" xml:space="preserve"> # quo modo inueſtigetur. # ibid. Altitudo ſtellæ meridiana<unsure/> quid. # 278 Ambitus cœlorum ſecundum concauum, # & conuexum. # 216 Ambitum terræ ſumendum eſſe penes cir- # culum maximum. # 199 Ambitus terræ ſecundum Macrobium, & # Eratoſthenem. # 198 Ambitus terræ uarius ſecundum varios au- # ctores, & quarr. # 211. vſque ad 215. Ambitus terræ ſecundum Ariſtotelem. # 211 Ambitum terræ ſecũdum Ptolemæum ma- # gis receptum eſſe. # 212 Ambitus terræ quibus uijs exploretur. # 119. ad 203. Amphiſcij, Heteroſcij, & Periſcij qui ſint. # pag. # 313 Amplitudo ortiua, uel occidua quid, & # quomodo inueniatur per ſinus. # 300 Amplitudinẽ ortiuam, uel occiduã eandẽ # eſſe in quaternis punctis Eclipticæ. # ibid. Anaximandrum Mileſium fuiſſe primũ in- # uentorem Zodiaci. # 233 Animantiũ ætates quatuor præcipuæ. # 241 Anni quatuor temporum qualitates. # 238 Anni quatuor tempora Ver, Aeſtas, Autũ- # nus, & Hyems, quibus partibus Zodiaci # reſpondeant. # 239 Annum Iulij Cæſaris, & Eccleſiaſticum ve # ro maiorem eſſe. # 275 Annus in Calẽdario Romano cur à ſolſti- # tio brumali incipiat. # 243 Antarcticũ polum nullas circum ſe habe- # re ſtellas. # 181 Anticipationis ęquinoctiorum, & ſoIſtitio # rum in Calendario, quæ cauſa ſit. # 275 Antipodes cur non cadant. # 196 Antipodes noſtros eandem nobiſcũ habe- # re latitudinem, ſed diuerſi nominis. # 283 Antiqui cur putarint aſtra caſu ferri. # 433. Apparens Horizon quid. # 297 Apparentiæ uariæ quibus Aſtronomi im- # pulſi ſunt, ut Eccentricos orbes, & Epicy # clos in cœlis eſſe crederent. # 532. ad 458 Apparens, & uerus ortus, occaſusq́; ꝗd. # 318 Apparentiæ duæ contra metum ſtellarum # fixarum ab occaſu in ortum ſuper polos # Zodiaci, earumq́ue ſolutio. # 61. & 62 Aqua quo pacto à terra inſſu Dei receſſe- # rit, ut apparet arida. # 31. & 32 Aqua cur nõ ambiat totã terram. # 31. & 32 Aquam & terram unum globum conſtitue # re. # 117. ad 134 Aqua cur non occupet centrum mundi, # quemadmodum terra. # 126 Aquam eſſe ſphæricam. # 114. ad 116 Aquea ſigna Zodiaci quæ ſint. # 238 Archimedis demõſtratio, aquam eſſe ſphæ # ricam. # 116. & 117 Archimedis ſphæra admirabilis. # 17 Archimedis proportio inter circunferen- # tiam circuli, eiuſq́; diametrum. # 205 Archimedis proportionẽ inter circunferẽ- # tiam circuli, eiuſq́; diametrũ, date circũ- # ferentiam maiorẽ ex nota diametro, dia # metrum vero minorem ex nota circunfe # rentia, quàm re ipſa ſit. # 207 Arcticus, & antarcticus circulus. # 23. 303. # & 304. Arcticus, & antarcticus circulus ſecundum # Græcos. # 304 Arcticus, & antarcticus polus, eorumque # varia nomina. # 18. 227. & 228. Arcus æquales Eclipticæ, ſeu Zediaci, æ- # qualiterq́; ab alterutro punctorũ æqui- # noctialiũ remotos habere æquales aſcen # ſiones in quauis ſphæra obliqua. # 336 Arcus æquales Eclipticæ, ſeu Zodiaci, æ- # qualiterq. ab alterutro punctorum ſolſti # tialium remotos habere aſcẽſiones ſimul # ſumptas in quauis obliqua ſphæra ęqua # les eorundem arcuum aſcenſionibus ſi- # mul ſumptis in ſphæra recta. # 335 Arcus æquales Eclipticæ, & oppoſitos ha- # bere aſcenſiones ſimul ſumptas in qua- # uis ſphęra obliqua ęquales eorundem ar # cuũ aſcenſionibus ſimul ſumptas in ſphæ # ra recta. # 334. & 335 Arcus æquales Eclipticæ, & oppoſitos ha- # bere aſcenſiones in ſphæra recta æqua- # les. # 324. & 326. Arcus ęquales, Eclipticę, ęqualiterq́; à quo # uis quatuor punctorũ Card. diſtãtes hẽre # aſcenſiones in ſphæra recta ęquales. # 324 Arcus cuiuſuis, uel pũcti Eclipticę, uel etiã # ſtellæ aſcenſio, & deſcenſio quid ſit. # 321</note> <pb file="013" n="14"/> </div> <div xml:id="echoid-div9" type="section" level="1" n="9"> <head xml:id="echoid-head12" style="it" xml:space="preserve">INDEX.</head> <note position="right" xml:space="preserve"> Arcus cuiuſuis Eclipticæ aſcenſio recta, # & obliqua quid ſit tam ſecundum aucto- # rem, quàm ſecundũ Ptolemęum, & alios # Aſtronomos. # 322 Arcu s cuiuſuis, aut puncti Eclipticæ ab al- # terutro æquinoctio numerati aſcenſio in # ſphæra recta quo pacto per ſinus inueſti # getur. # 328. & 329 Arcus cuiuſuis, aut puncti Eclipticæ aſcen- # ſio in ſphæra recta quo pacto ex tabula # aſcenſionum rectarum eliciatur. # 332 Arcus cuiuſuis, aut puncti Eclipticæ aſcen # ſionalis differẽtia in ſphęra obliqua quo # pacto per ſinus ſupputetur. # 337 Arcus cuiuſuis, aut puncti Eclipticæ ab al- # terutro ęquinoctio numerati aſcenſio in # ſphęra obliqua quo pacto ex differentia # aſcenſionali reperiatur. # ibid. Arcus cuiuſuis, aut puncti Eclipticæ aſcen # ſio in ſphæra obliqua quo pacto ex tabu # la aſcenſionũ obliquarum eliciatur. # 339 Arcus cuiuſuis, aut puncti Ecliplicæ à prin # cipio Arietis numerati deſcenſio in ſphę # ra obliqua quo pacto reperiatur. # ibid. Arcus cuiuſuis Eclipticæ aſcenſionũ æqua # lem eſſe deſcẽſioni eiuſdem in ſphęra re # cta: Immo & mediationi cœli in qualibet # ſphæra tam obliqua, quàm recta. # 328 Arcus cuiuſuis, ſeu puncti Eclipticæ Aſcen # ſionalem differentiam eandẽ eſſe, quę eſt # inter arcus ſemidiurnos ſphæræ rectæ, & # obliquę, Sole in illo puncto Eclipticę cõ # morante. # 406 Arc<emph style="sub">9</emph><unsure/> cuiuſuis eclipticæ aſcẽſionẽ ęqualẽ eſ # ſe deſcẽſioni arcus oppoſiti, & ęqualis in # quacũq; ſphęra ſiue recta, ſiue obliqua. # 336 Arcus cuiuſuis eclipticæ aſcẽſionem, & de- # ſcenſionẽ ſimul ęquales eſſe aſcẽſioni, & # deſcẽſioni ſimul arcus oppoſiti, & æqua- # lis in quacunq. ſphæra tam recta, quam # obliqua. # ibid. Arcus cuiuſuis eclipticæ aſcenſionem in # ſphæra obliqua inæqualem eſſe deſcen # ſioni eiuſdem. # ibid. Arcus Coluri inter tropicos, & circulos po # lares quantus ſit. # 305. & 306 Arcus cuiuſuis complementum quid. # 300 Arcum Eclipticæ ab initio Arietis, & Li- # bræ, uſq; ad finem Geminorũ, & Sagitta- # rij numeratorum maiores ſemper partes # oriri in ſphæra recta, quã quadrantũ Ae- # quatoris conterminalium: Arcuum uero # eclipticæ ab initio Cancri, & Capricorni # uſq; ad finem Virginis, & Piſcium nume- # ratorum minores. # 326. & 327 Arc<emph style="sub">9</emph> dierũ & noctiũ artificialiũ ꝗd ſint. # 401 Arcus diurnus quo pacto ex aſcenſione ob # liqua ſupputetur. # 406 Arcus Eclipticæ à principio Arietis, uſq; ad # finẽ Virginis minores habere aſcenſiones # in ſphæra obliqua, quàm in recta; arc<emph style="sub">9</emph> ve # ro à principio Libræ uſq; ad finẽ Piſciũ # maiores, & tanto maiores pręciſe, quan- # to illi minores habent. # 333. & 334 Arcus Eclipticæ ſemper apparẽtes æquales # eſſe arcubus ſemꝑ occultis in locis inter # circulum polarem, & polũ, dies autẽ con # tinuos noctibus continuis inęquales. # 421 Arcũ eclipticæ à principio Arietis uſq; ad # finẽ Virginis numeratorũ maiores ſemꝑ # partes oriri in ſphæra obliqua, ꝗ̃ medie- # tatũ Aequatoris conterminalium: Arcuũ # Eclipticæ à principio Libræ uſq; ad finẽ # Piſcium numeratorum minores. # 333 Arcus eclipticæ ſemꝑ apparens, uel ſemper # latẽs, in locis inter circulum polarem, & # polũ, quo pacto inueſtigetur. # 440. & 421 Arcus ſemidiurnus qua rõne ex differẽtia ĩ # ter arcũ ſemidiurnũ ſphęrę rectę, & arcũ # ſemidiurnũ ſphęrę obliquæ reperiat̃. # 406 Arcus ſemidiurnus qua ratione per ſinus # inueſtigetur. # 407 Arcus ſeminocturnus, tẽpus meridiei, & no # ctis, tempus ortus, more Italorum, quo # pacto ex arcu ſemidiurno colligatur. # 407 Arcus Firmamenti interceptus inter duos # radios uiſuales ęquidiſtãtes, quorũ alter # è centro terrę dicitur, alter uero terram # contingit, quantus fit. # 145 Arcuum ſemidiurnorum tabula quo pacto # componatur. # 407 Arcuũ ſemidiurnorũ tabula à gr. 26. & uſq; # ad grad. 56. # 408. ad 413 Arcus totales Eclipticæ inter 4. pũcta Car- # dinalia adęquari ſuis aſcẽſionib<emph style="sub">9</emph> in ſphę # ra recta, ſed eorum partes minimè. # 323</note> <pb file="014" n="15"/> </div> <div xml:id="echoid-div10" type="section" level="1" n="10"> <head xml:id="echoid-head13" style="it" xml:space="preserve">INDEX.</head> <note position="right" xml:space="preserve"> Arcus totales eclipticæ inter duo puncta # æquinoctialia adæquari ſuis aſcenſioni- # bus in ſphæra obliqua, ſed eorum partes # minime. # 332. & 333 Area figuræ quid. # 82 Area cuiuſuis circuli quo modo reperia- # tur. # 208 Area trianguli cuiuſcunq; cui parallelo- # grammo rectangulo æqualis ſit. # 82 Area cuiuſcunq; figurę regularis cui paral # lelogrammo rectangulo æqualis ſit. # 83 Area cuiuſcunq; figuræ regularis cui triã # gulo rectangulo ſit æqualis. # 84 Area circuli cuiuſuis cui parallelogram- # mo rectangulo ſit æqualis. # 85 Area ſphæræ cuiuſuis cui ſolido rectangu # lo ſit ęqualis. # 100. & 101 Arenę numerus in toto mundo cõprehen # ſus, quo pacto inueſtigetur. # 217 Argumenta Auerrois, eiuſq́; ſectatorũ ad # uerſus eccẽtricos, & epicyclos, eorumq́ # ſolutio. # 453. ad 458 Argumẽta duo aduerſus motum ſtellarũ # fixarum ab occaſu in ortum ſuper polos # Zodiaci, eorumque ſolutio. # 61. & 62 Argumentum primi cap. eiuſq́; diuiſio. # 13 Argumentũ ſecũdi cap. eiuſq́; diuiſio. # 221 Argumentum tertij cap. eiuſq́. diuiſio. # 315 Argumentum quarti capitis. # 431 Aries cur principium Zodiaci ponatur. # pag. # 240. ad 242 Arietis principium nobilius eſſe tribus re # liquis punctis cardinalibus Zodiaci. # 241 Ariſtotelis demonſtratio aquam eſſe ſphæ # ricam. # 116 Ariſtotelis ſententiam de circulo Lacteo # ueram non eſſe. # 306 Arithmetica circa quid verſetur. # 1 Artificiales dies & noctes in ſphæra recta # omnes inter ſe æquales eſſe. # 401. & 402 Artificiales dies in hyeme minores eſſe in # ciuitate borealiori, quam in ciuitate mi # nus boreali: in æſtate autem maiores, & # quare. # 403 Artificiales duos dies quoſcunque ab al- # terutro ſolſtitio ęqualiter diſtãtes inter # ſe æquales eſſe in ſphæra obliqua. # ibid. Artificialis dies quicunq; cui nocti artifi- # ciali æqualis ſit. # ibid. Artificialis diei, & noctis arcus quid. # 401 Artificialis dies, & nox quid, & cur penes # Horizõtc̃ eius ꝗ̃titas ſumat̃. # 269. & 401 Artiſicialis diei, noctiſq́; quantitas, qua ra # tione ex ſphęra materiali deprehẽdatur # pag. # 229 Artificialis diei quantitas quo pacto ex a- # ſcenſione obliqua ſupputetur. # 406 Artificialis Horizon quid. # 297 Aſcendens, & deſcendẽs ſemicirculus ecli # pticæ quid. # 243 Aſcenſio, & deſcenſio cuiuslibet arcus, aut # pũcti eclipticę, uel etiam ſtellę, quid ſit # apud Aſtronomos. # 321 Aſcenſio, & deſcenſio cuiuſuis arcus ecli- # pticæ cur definiatur ab Aſtronomis per # Aequatorem. # ibid. Aſcenſio, & deſcenſio recta, uel obliqua # cuiuſuis arcus eclipticę quid tã ſecundũ # auctorem, quàm ſecũdum Ptolemæum, # & alios Aſtronomos. # 322 Aſcenſio cuiuſuis arcus, ſeu puncti eclipti # cæ in ſphęra recta ab alterutro ęquino # ctio nnmerati, quo pacto per ſinus ex- # ploretur. # 328. & 329 Aſcenſio cuiuſuis arcus, ſeu puncti eclipti- # cę in ſphæra recta quo pacto ex tabula # aſcẽſionum rectarum cognoſcatur. # 332 Aſcenſionum obliquarum tabulæ quo pa- # cto conſtruantur. # 338 Aſcenſionum obliquarum tabulæ à grad. # 36. uſque ad grad. 60. # 348. ad 397 Aſcenſionum rectarum tabula quo pacto # componatur. # 329 Aſcenſionum rectarum tabula. # 330. & 331 Aſcenſionalis differentia cuiuſuis arcus, # aut puncti eclipticæ in ſphęra obliqua # quo pacto per ſinus ſupputetur. # 337 Aſcenſionalium differentiarum tabula. # pag. # 340. ad 347 Aſcenſio cuiuſuis arcus, aut puncti eclipti # cæ ab alterutro ęquinoctio numerati in # ſphæra obliqua quo pacto ex differẽtia # aſcenſionali reperiatur. # 337 Aſcenſio cuiuſuis arcus aut puncti eclipti # cę in ſphęra obliqua quo pacto ex tabu # la aſcẽſionum obliquarum eruatur. # 339</note> <pb file="015" n="16"/> </div> <div xml:id="echoid-div11" type="section" level="1" n="11"> <head xml:id="echoid-head14" style="it" xml:space="preserve">INDEX</head> <note position="right" xml:space="preserve"> Aſcenſionem cuiuſuis arcus eclipticæ in # ſphæra recta æqualẽ eſſe deſcẽſioni eiuſ # dẽ: Immo & meditationi cæli in quali- # bet ſphęra tam obliqua,@ quã recta. # 328. Aſcenſionalẽ differentiam cuiuſuis arcus # ſeu pũcti eclipticæ eandem eſſe, quę eſt # inter arcus ſemidiurnos ſphęrę rectæ, # & obliquę, Sole in illo pũcto eclipticæ # commorante # 406 Aſcenſionẽ cuiuſuis arcus eclipticæ æqua # lẽ eſſe deſcẽſioni arcus oppoſiti, & ęqua # lis in quacunq; ſphęra tam recta, quam # obliqua # 336 Aſcenſionẽ, & deſcenſionẽ ſimul cuiuſuis # arcus eclipticæ æquales eſſe aſcenſioni, # & deſcenſioni ſimul arcus oppoſiti, & # æqualis in quacũque ſphæra tam recta, # quàm obliqua # ibid. Aſcenſionem cuiuſuis arcus eclipticæ in # ſphæra obliqua inæqualem eſſe deſcen # ſioni eiuſdem # ibid. Aſcenſiones arcuum eclipticę æqualium, # æqualiter que ab alterutro punctorum # æquinoctialium remotorũ æquales eſſe # in qualibet ſphæra obliqua # ibid. Aſcenſiones arcuum eclipticæ æqualium, # æqualiterq; ab alterutro pũctorum ſol- # ſtitialium remotorum ſimul ſumptas in # quauis obliqua ſphęra eſſe æquales aſcẽ # ſionibus eorundem arcuum ſimul ſum # ptis in ſphæra recta # 335 Aſcenſiones arcuũ eclipticæ oppoſitorũ, # & æqualium ſimul ſumptas in qualibet # ſphæra obliqua æquales eſſe aſcenſioni- # bus eorundem arcuum ſimul ſumptis in # ſphæra recta # 334. & 335 Aſcenſiones arcuum eclipticæ æqualium, # & oppoſitorum in ſphæra recta eſſe æ- # quales # 324. & 326 Aſcenſiones arcuum eclipticæ æqualium, # æqualiterq; diſtantiũ à quouis quatuor # punctorum Cardinalium in ſphæra re- # cta eſſe æquales # 324 Aſcẽſionem, & deſcenſionẽ ſimul cuiuſuis # arcus eclipticæ in ſphęra obliqua æqua # les eſſe aſcẽſioni, & deſcẽſioni ſimul eiuſ # dem arcus in ſphæra recta # 336. & 337 Aſpectus aſtrorum diametralis, triãgularis # quadratus, & hexagonus quid # 240 Aſpectus diuerſitas quid # 65 Aſpectus diuerſirates duorũ aſtrorũ in eo- # dẽ cælo eandem altitudinẽ ſupra Hori- # zontem habentiũ eſſe æquales. # 65. & 66 Aſpectus diuerſitatẽ eiuſdẽ aſtri, quo pro- # pinquius eſt Horizonti, eo eſſe maiorẽ, # adeo ut in Horizonte aſtrum exiſtens # habeat maximam, in uertice uero capi- # tis nullam # 66 Aſpectus diuerſitatẽ aſtri, ꝙ terræ propin- # quius eſt, ubicunq, in cęlo exiſtat, maio # rem eſſe ea, quam habet aſtrum lõgius # à terra diſtans, eundemq́; locũ uerum, # ſeu uiſum cum priore obtinens. # 66. & 67 Aſpectus diuerſitatem Lunæ in diuerſis cli # matib. cauſam eſſe, cur eclipſis Solis fiat # interdum in uno climate, & in alio nõ, # & maior in uno, quàm in alio # 463 Aſſis, eiuſque partes # 248 Aſteriſmus, ſiue conſtellatio quid # 148 Aſteriſmi, ſiue conſtellationes 48. in tabu- # las digeſtæ, in quibus continentur lon- # gitudines, latitudines, & magnitudines # ſtellarum # 151. ad 180 Aſtra cur maiora appareãt iuxta Horizon- # tem poſita, quàm in medio cæli # 107 Aſtra caſu ferri, cur antiqui putarint. # 433 Aſtra regulariter moueri # 434. & 435 Aſtra borealia, atque auſtralia quæ. # pag. # 219. 255. & 256 Aſtra omnia eſſe rotunda, ac ſphærica. # 108 Aſtra neq; orientia, neque occidẽtia quæ, # & quomodo cognoſcantur. # 301. & 302 Aſtronomia quid # 4 Aſtronomia ab Aſtrologia quomodo dif- # ferat # 5 Aſtronomia circa quid uerſetur. # 2. & 12 Aſtronomiæ inuentores # 3 Aſtronomiæ partes # 5 Aſtronomi cur diem à meridiano inchoẽt # pag. # 278. 279. & 282 Aſtronomiæ præſtantia ex obiecto, & mo # do demonſtrandi # 6 Aſtronomiæ utilitates uariæ # 7. ad 10 Aſtronomi quo pacto ſtellarum numerũ # indagarint # 148 Aſtronomi quo modo dicãt, omnia eſſe in</note> <pb file="016" n="17"/> </div> <div xml:id="echoid-div12" type="section" level="1" n="12"> <head xml:id="echoid-head15" style="it" xml:space="preserve">INDEX</head> <note position="right" xml:space="preserve"> # aliquo ſigno # 254 Aſtronomi uarij # 4 Aſtronomi quibus phęnomenis, aut appa # rentijs impulſi ſunt, ut Eccentricos or- # bes & Epicyclos in cœlis eſſe crederẽt. # pag. # 432. ad 458 Aſtronomicus ortus, & occaſus quid, & # quomodo à Poetico differat # 319 Aſtronomi cur diuiſio ne ſexagenaria utan # tur # 246 Aſtronomi cur definiant ortũ, & occaſum # arcuum Zo diaci per Aequatorem # 321 Aſtronomicus dies, ęqualis, uel mediocris # quid # 400 Aſtrorũ declinationes quo pacto per ſinus # ſupputentur # 183. ad 185 Aſtrorum magnitudines tam in diametris # reſpectu diametri terrę, quàm in ſolidi- # tate reſpectu terræ # 186. ad 191 Aſtrorum diametri viſuales quid # 71 Auſtralem partem mundi ignobiliorem # eſſe boreali # 241 Auſtralem partem mundi eſſe ſiniſtram, # borealem uero dextram # ibid. Auſtralem partem cœli prope polum an- # tarcticũ nullas habere ſtellas. # 181. & 241 Auſtralia aſtra, & Borealia quæ. # 229. 255. # & 256 Auſtralis, borealisq́ue pars cœli, & terræ # quę # ibid. Auſtralis borealisque pars Zodiaci, & ſi- # gna auſtralia, ac borealia quę # ibid. Augis, & oppoſiti Augis linea quid. # 433 Auguſtini Ricij ſententia de numero, & # & motu cœlorum, eiuſq; conſutatio # 50 Aux, Augiſque oppoſitum in planetis # quid # 431. & 433 Axis ſphæræ quid, & quomodo à diame- # tro ſphæræ differat # 17. & 18 B BOREALEM partem mundi nobilio- # rem eſſe auſtrali # 241 Borealem partem mundi eſſe dextram, au # ſtralem uero ſiniſtram # ibid. Borealẽ partem cęli prope polũ atcticum # plurib. ſtellis ex ornatam eſſe, quàm au- # ſtralem prope polum antarcticum. # ibid. Borealia aſtra, atque auſtralia quæ. # 229. # 255. & 256 Borealis, atque auſtralis pars cœli, & terrę # quæ # ibid. Borealis, atque auſtralis pars Zodiaci, & ſi- # gna borealia, atque auſtralia quæ. # 250. # 255. & 256 C CÆLESTES imagines 48. in quibus # continentur longitudines, longitudi # nes, & magnitudines ſtellarũ. # 151. ad 180 Cœleſtibus Zonis quomodo Zonæ terre- # ſtres ſuppoſitæ ſint # 311 Cœleſtia corpora omnium nobiliſſima. # 6 Cœlum aqueum, glaciale, ſeu Chryſtalli- # num # 45 Cœlum empyreum ſecundum Theologos # ibidem Cœlum empyreum dari, quibus indicijs # probetur à nonnullis # 45. & 46 Cœlos plures eſſe, quàm unum # 42 Cœlos plures eſſe, quàm octo # 43 Cœlos plures eſſe, quàm nouem # 44 Cœlos mobiles eſſe decem, & qua ratione # colligantur # 44. & 45 Cœlorum motus duplex, ab ortu in occa- # ſum, & ab occaſu in ortum # 40. & 51 Cœlornm motus ab ortu in occaſum, & # ab occaſu in ortum, quomodo intelli- # gatur # 40 Cœleſtium motuum harmonia # 41 Cœlorum motus diuturnus cui cœlo tri- # buatur # 41. & 51 Cœlos inferiores rapti motu diurno à pri # mo mobili # ibid. Cœleſtium motuũ periodi. # 41. & 55. ad 57 Cœlorũ motus ab occaſu in ortum nõ ha- # bere ordinatã proportionẽ inter ſe. # 49 Cœleſtium motuum uariæ opiniones, ea- # rumq́ue confutatio # 46. ad 51 Cœleſtium motuum propria noſtra ſen- # tentia # 51. ad 55 Cœlorũ motus ab ortu in occasũ, & ab oc # caſu in ortũ nõ eſſe contrarios. # 52. & 54 Cœlos oẽs ſimpliciter moueri ab ortu in # occaſum, iuferiores aũt ab occaſu in or # tum ſecũdum quid, & qũo intelligatur, # & qua ratione id fieri poſſit. # 53. ad 55 Cœlos ſuper eoſdẽ polos moueri poſſe ab</note> <pb file="017" n="18"/> </div> <div xml:id="echoid-div13" type="section" level="1" n="13"> <head xml:id="echoid-head16" style="it" xml:space="preserve">INDEX</head> <note position="right" xml:space="preserve"> # ortu in occaſum, & ab occaſu in ortum: # immo quoſdam orbes ita moueri: Et cur # non moueantur omnes ſuper eoſdem po- # los. # 55 Cælorum motus ab ortu in occaſum, & ab # occaſu in ortum, qua ratione dici poſſint # contrarij. # 54 Cælos omnes ab ortu in occaſum ſimplici- # ter moueri, quo pacto deprehenſum ſit. # pag. # 57. & 58 Cælos inferiores ab occaſu in ortum moue # ri ſecundum quid, & ſuper polos Zodiaci # quomodo obſeruatum ſit. # 58. ad 61 Cælum cuiuſque planetæ ex pluribus orb<unsure/>i- # bus componi # 433 Cælum quodlibet ſuo motu inferiorem or # bem ſibi contiguum, & concentricum ſe- # cum rapere. # 56. & 447 Cęlum ſtellarum fixarũ moueritriplici mo # tu, a b ortu in occaſum, ab occaſu in ortũ, # & motu trepidationic, ſiue acceſſus, & re- # ceſſus. # 56 Cælum ſtellarũ fixarum moueri motu tre- # pidationis, ſiue acceſſus, & receſſus, quo pa # cto deprehenſum ſit. # 62. & 63 Cæleſtium motuum periodi penes quos or # bes intelligendi ſint. # 57 Cælos eſſe immediatos inter ſe. # 20. 63. & 64 Cælorum ordo ſecundum Ariſtarchum Sa- # mium, & Nicolaum Copernicum. # 64 Cælorum ordo ſecundum Platonem, Ari- # ſtotelem, & Aegyptios. # ibid. Cælorum ordo ſecundum Aſtronomos re- # centiores, & qua ratione colligatur. pag. # 64. ad 71 Cęlum moueri, & ſecum deferre ſtellas, nõ # autem ipſum quieſcere, & ſtellas moueai, # ut piſces in mari. # 72. ad 75 Cælum eſſe rotundum, & ſphæricum. # 75. ad # 80. & 104. ad 108 Cælum æqualiter a quouis puncto ſupe ſi- # ciei terræ nõ diſtare, niſi quoad ſensũ. # 107 Cælum cur a nobis longius uideatur diſta- # re iuxta Horizontem, quam prope uerti- # cem capitis. # 108 Cæli pars dextra, & ſiniſtra ſecundum ua- # rios. # 310 Cælum diuidi in hæmiſphæriũ boreale, at- # que auſtrale primum ab Aequatore, dein- # de a Zodiaco, poſtremo a Verticali pro- # prie dicto. # 256 Cælorum diſtantiæ a centro terræ, eorum- # que ambitus. # 215. & 216 Cæleſtium domorum circuli. # 218 Cæleſtium orbium, & motuum theoricæ in # tabulas redactæ. # 464. ad 483 Calippum, & Eudoxum diuiſiſſe ſphæras cę # leſtes in orbes concentricos. # 435 Calendarii Romani initium cura Solſtitio # Brumali ſumatur potius, quàm ab Aequi- # noctio Verno. # 243 Calendariũ Romanũ cur nõ eiſdem diebus # indicet æquinoctia, & ſolſtitia. # 274. & 275 Caput, & cauda Draconis Lunæ. # 469 Cardines mundi. # 19 Cardinalia puncta in Zodiaco quæ. pagina<unsure/> # 23. & 241 Caſus cuiuſuis planetæ quod ſignum Zodia # ci dicatur. # 244 Cen@@@ in Vniuerſo, ſecundum aliquos, eſ- # ſe tria, unum @@@@@, alterum aquæ, & ter- # tium totius Vniuerſi. # 117. & 118 Centrum figuræ regularis quid. # 82 Centrum grauitatis quid. # 121 Centrum grauitatis quo pacto in quolibet # corpore inueniatur. # ibid. Centrum grauitatis in terra, & aqua idem # eſſe, quod magnitudinis. # 122. & 123 Centrum ſphærę quid. # 17 Centrũ terræ, & aquæ unũ & idẽ eſſe, quo- # ad ſuperficies conuexas. # 117. ad 134 Cholerica ſigna Zodiaci quæ. # 238 Chronicus ortus, & occaſus ſiderum ſecun- # dum poeras quid. # 314. ad 316 Circuli circunferentia quam proportionẽ # habeat ad diametrum. # 205 Circuli decem ſphærę. # 22. & 221 Circuli, & ſphæræ dignitates uatiæ. # 77 Circulos cæleſtes in primo mobili eſſe con<unsure/> # cipiendos. # 226 Circuli cuiuſque in ſphæra polus quid. # 22 Circuli dierum Naturalium qui. # 400. & 402<unsure/> Circuli intrinſeci, & extrinſeci ſphæræ qui. # pag. # 225 Circuli maximi in ſphæra ad non maximũ # proportio qua ratione inueſtigetur. # 304</note> <pb file="018" n="19"/> </div> <div xml:id="echoid-div14" type="section" level="1" n="14"> <head xml:id="echoid-head17" style="it" xml:space="preserve">INDEX</head> <note position="right" xml:space="preserve"> Circulom quẽlibet in tot partes diuidi, in # quot Zodiacus diuiditur. # 248 Circulos cæleſtes multiplices eſſe apud A- # ſtronomos # 221. & 222 Circuli Verticales, Horarij, domorum cæle # ſtium, poſitionum, declinationum, & lati- # tudinum qui. # 222. & 223 Circulorum ſphæræ diuiſio ſecundum Pro # clum. # 225 Circulorum ſphęræ proprietates nonnul- # læ. # 223. & 214 Circulorum parallelorum in ſphæra offi- # cia. # 307. & 308 Circuli cęleſtes cur in gradus 360. diuidan # tur. # 246 Circuli polares. # 303. & 304 Circuli polares ſecundum Græcos. # ibid. Circulus arcticus, & antarcticus. 23. # 303. # & 304 Circulus declinationis ſtellæ quid. # 257 Circulus Eccentricus quid. # 433 Circulus latitudinis ſtellæ quid. # 256 Circulus lacteus in @@@, & unde habeat cã # dorem. # 306 Girculum lacteum eſſe in Firmamento, nõ # autem in aere, ut falſo Ariſtoteles credi- # dit. # ibid. Circulus lacteus per quas conſtellationes # incedat. # 306. & 307 Circulum uiſualem Solis ad circulũ uiſua- # lem Veneris habere proportionem centu # plam. # 70 Circulum capaciſſimum eſſe inter figuras # Iſoperimetras. # 77. ad 80. & 96 Circulus ſemper apparentium, & ſemper la # tentium maximus. # 301 Circulus quicunque cui triangulo rectan- # gulo æqualis ſit. # 83 Circulus quicunque cui parallelogrammo # rectangulo æqualis ſit. # 84 Circulus maximus, & non maximus, ſiue # maior, & minor in ſphæra quid. # 22. 222. & # 223. Circuli paralleli in terra quanto ſpatio in- # ter ſe diſtantes a Ptolemæo, & alijs Aſtro # nomis deſcribantur. # 428 Circuli paralleli quot à Sole in anno de- # ſcribantur. # 400. & 401 Circulos parallelos a Sole plures deſcribi # ab Ariete ad Libram, qua<unsure/>m a Libra ad A- # rietem, & quare. # 401 Circulus Aequans planetæ quid, & cur ſit # excogitatus. # 459. & 460 Circum ferentia circuli@ qua ratione ex dia- # metro, & diameter uiciſſim ex circumfe- # rentia eliciatur. # 205. ad 207 Circumferentię cuiuſuis circuli ad diame- # trum proportio ſecundum Archimedem # quæ ſit. # 205 Circumferentiæ circulorum ex eodem con # tro deſcriptorum comprehẽſę inter duas # rectas è centro egredientes eſſe ſimiles. # 203. & 204. Circumferentiam cuiuſuis circuli ex nota # diametro reperiri maiorẽ, diametrũ uero # ex nota circũferẽtia maiorẽ, quã re ipſa ſit # ſecundũ proportionem Archimedis inter # circumferentiã circuli, & diametrum. # 207 Ci@it@@ propoſita in quanam Zona ſit, quo # pacto cognoſcatur. # 312 Ciuitatum latitudo quid. # 283 Ciuitatum latitudo duplex, borealis, & au- # ſtralis. # ibid. Ciuitatum longitudo quid. # 277. 278. & 282 Ciuitates plures eundem Meridianum ha- # bere poſſe, quoad ſenſum, tam ab ortu in # occaſum, quã a ſeptẽtrione in auſtrũ. # 277 Citatum longitudines a quo Meridiano in # cipiant. # ibid. Ciuitatũ plurimarũ longitudines, latitudi- # nesque in tabulam digeſtæ. # 285. ad 289 Ciuitates eandem latitudinem, uel longitu # dinem habentes quæ. # 283 Ciuitatum diſtãtias penes circulum maxia # mum eſſe accipiendas. # 290 Ciuitatum diſtantiæ quo pacto inueſtigen- # tur. # 290. ad 295 Ciuitatis cuiuſq; latitudinem æqualem eſ- # ſe altitudini poli eiuſdem. # 299 Clima a Zona quomodo differat. # 428 Clima quid. # 423. & 424 Climatũ diuiſio unde pendeat. # 424. ad 426 Climata quot a Veteribus ſint conſtituta. # 423 Climatum tabula ſecundum Veteres. # 426. # & 427</note> <pb file="019" n="20"/> </div> <div xml:id="echoid-div15" type="section" level="1" n="15"> <head xml:id="echoid-head18" style="it" xml:space="preserve">INDEX.</head> <note position="right" xml:space="preserve"> Climata quot a recentioribus conſtituan- # tur. # 428 Climatum tabula ſecundum recentiores. # pag. # 429. & 430 Columnæ duæ, in quibus filij Adam ſcien- # tias inſcripſerunt, ne perirent. # 5 Coluri qui circuli ſint, & unde dicti. # 23. # & 258. Coluri arcus inter tropicos, & circulos po- # lares, quantus ſit. # 305. & 306 Coluri ſolſtitiorum, & æquinoctiorum offi # cia. # 261. ad 269 Coluros nullos circulos dici poſſe in ſphæ # ra recta. # 259 Colurus æquinoctiorum quid. # 23. & 260 Colurus ſolſtitiorum quid. # 23. & 259 Combinatio num uariæ regulæ, quibus co- # gnoſcatur, quotnam modis plures res in- # ter ſe poſſint comparari. # 34. & 35 Communia ſigna Zodiaci quæ. # 236. & 139 Complementum cuiuſuis arcus quid. # 300 Concentricos orbes eſſe 77. uel 79. ex ſen- # tentia Hieronymi Fracaſtorij. # 449 Concentricis orbibus nõ poſſe omnia phæ # nomena defendi. # 432. ad 458 Concentricis orbibus poſitis, ut uult Fra- # caſtorius, multa abſurda ſequi. # 449 Conicam eſſe umbram terræ. # 461 Conuexa ſuperficies cuiuſlibet ſphæræ quo # pacto reperiatur. # 208 Conſtellatio, ſiue Aſteriſmus quid. # 148 Cõſtellationes, ſiue Aſteriſmi. 48. in quibus # continentur longitudines, latitudines, & # magnitudines ſtellarum. # 151. ad 180 Corpora cæleſtia omnium nobiliſſima. # 6 Corpora ſimplicia eſſe quinq; Vniuerſum # totum componentia. # 135 Corporum quinque regulariũ figuræ quo # pacto Elementis, & cœlo tribuãtur a Pla # tone. # 134 Corpus, ſiue ſolidum planis ſuperficiebus # contentũ, & ſphæræ circũſcriptibile, ſiue # in quo ſphæra inſeribi poſſit, cui ſolido # rectangulo ſit æquale. # 99 Coſmicus ortus, & occaſus ſiderum ſecun- # dum poetas quid. # 314. ad 316 Coſmicus ortus, & occaſus ad quid condu- # cat. # 319 Craſſities aeris quanta fit. # 131. & 232 Crucem, quam ſtellæ prope polum antar- # cticum exprimere vulgo dicuntur, eſſe in # Centauro. # 181 D <emph style="sc">DEcem</emph> circuli ſphæræ. # 22. & 221 # Declinatio ſtellæ cuiusvis quid. # 229 # & 256. Declinatio ſtellæ cuiuſuis quo circulo ma # maximo menſuretur. # 257 Declinationis ſtellæ circulus quid. # ibid. Declinationum circuli qui. # 223 Declinationes ſtellarum quaratione per ſi # nus ſupputentur. # 183. ad 185 Declinationes punctorum Eclipticæ qua ra # tione per ſinus ſupputentur. # 263 Declinationum omnium punctorum Ecli- # pticæ tabula. # 264 Declinationem quaternorum punctorum # Eclipticæ eſſe eandem. # 257 Declinationum, & latitudinum ſtellarũ va- # riæ habitudines. # ibid. Declinatio Solis maxima q<unsure/>d, & quãta. # 262 Declinatio maxima Solis quo pacto inue- # ſtigetur. # 262. & 263 Declinationem Solis maximam Borealem # æqualem eſſe maximæ declinationi eiuſ # dem auſtrali. # 273 Declinationes omnium pũctorum Eclipti- # cæ quomodo ex tabula Declinationum # inueniantur. # 272. & 273 Declinationes punctorum Eclipticæ æqua # liter ab æquinoctialibus punctis dictan- # tium æquales eſſe. # 257 Decuplam proportionem inter elementa # non eſſe. # 129. & 130 Deſcendens, & aſcẽdens ſemicirculus Ecli- # pticæ quid. # 243 Deſcenſio, & aſcenſio cuiuſlibet arcus, aut # pũcti. Eclipticæ, uel etiam ſtellæ, quid ſit # apud Aſtronomos. # 321 Deſcenſio, & aſcenſio cuiuſuis arcus Ecli- # pticæ cur ab Aſtronomis definiatur per # Aequatorem. # ibid. Deſcenſio, & aſcenſio recta, uel obliqua cu- # iuſuis arcus Eclipticæ quid tam ſecun- # dum auctorem, quàm ſecundum Ptole-</note> <pb file="020" n="21"/> </div> <div xml:id="echoid-div16" type="section" level="1" n="16"> <head xml:id="echoid-head19" style="it" xml:space="preserve">INDEX</head> <note position="right" xml:space="preserve"> # mæum, & alios Aſtronomos. # 322 Deſcenſionem cuiuſuis arcus Eclipticæ in # ſphæra recta æqualem eſſe aſcẽſioni eiuſ # dem in eadcm ſphęra: Immo & mediatio # ni cæli in qualibet ſphæra tam obliqua, # quàm recta. # 328 Deſcẽſionem cuiuſuis arcus Eclipticæ æqua # lem eſſe aſcẽſioni arcus oppoſiti, & æqua # lis in quacunque ſphæra tam recta, quàm # obliqua. # 336 Deſcenſionem, & aſcenſionem ſimul cuiuſ- # uis arcus Eclipticæ æquales eſſe deſcẽſio # ni, & aſcenſioni ſimul arcus oppoſiti, & # æqualis in quacunque ſphæra tam recta, # quàm obliqua. # ibid. Deſcenſionem cuiuſuis arcus Eclipticæ in # ſphęra obliqua inæqualem eſſe aſcenſio- # ni eiuſdem. # ibid. Deſcenſio cuiuſuis arcus, aut pũcti Eclipti- # cæ à principio Arietis numerati quo pa- # cto in ſphæra obliqua reperiatur. # 349 Deſcenſionem, & aſcenſionem ſimul cuiuſ- # uis arcus Eclipticæ in ſphæi<unsure/>a obliqua æ- # quales eſſe deſcẽſioni, & aſcenſioni ſimul # eiuſdem arcus in ſphæra recta. # 336. & 733 Deferens orbis planetæ cuiuſuis # 458 Deferens caput, & caudam Dratonis Lunæ # quis orbis ſit. # 460 Detrimentum cuiuſuis planetę quod ſignũ # Zodiaci dicatur. # 244 Dextrum, & ſiniſtrum in cælo uariæ ſumi. # pag. # 310 Diameter ſphæræ quid, & quomodo ab axe # diſſerat. # 18 Diametri cuiuſuis circuli ad circumferen- # tiam proportio ſecundum Archimedem # quæ ſit. # 205 Diameter circuli cuiuſuis ex circũferẽtia, # & viciſſim circũf<unsure/>erentia ex diametro quo # pacto eliciatur. # 205. ad 207 Diametrum circuli cuiuſuis ex nota circũ- # ferentia reperiri minorem, circumferen # tiam vero ex nota diametro maiorem, # quàm reipſa ſit, ſecundum proportionẽ # Archimedis inter circumferẽtiam, & dia # metrum. pag. # 207 Diametrum viſualem Solis ad diametrum # viſualem Veneris eſſe decuplam. # 71 Diametri terræ quantitas uaria ſecundu@ # varios. # 212<unsure/> Diametri uiſuales aftrorum quid. # 71 Dies, & nox artificialis quid, & cur penes # Horizontem eius quantitas ſumatur. # 299 # & 401 Diei, & noctis artificialis quantitas qua ra- # tione ex ſphæra materiali deprendatur. # pag. # 229 Diei artificialis quantitas quo pacto ex # aſcenſione obliqua ſupputetur. # 316 Dies naturales eſſe inæquales, & quare. # 399 Dierum, & noctium artif<unsure/>icialiũ arcus quid # ſint. # 401 Dies naturalis quid. # 399 Dierum Naturaliũ circuli qui. # 400 & 401 Diei uaria initia apud uarias gentes. # 278 Dies artificiales in hyeme minores eſſe in # ciuitate borealiori, quàm in ciuitate mi- # nus boreali, in æſtate autem maiores, & # quare. # 403 Dies duos artificiales quoſcunque ab alte- # rutro ſolſtitio æqualiter diſtantes inter # ſe eſſe æquades in ſphæra obliqua. # ibi. Dies, & noctes artificiales in ſphæra recta # omnes eſſe intet ſe æquales. # 401. & 402 Dies ar<unsure/>tificiales, & noctes in ſphæra obli- # qua eſſe inæquales. # 402 Dies artificialis quicunq; cui nocti artificia # li ſit æqualis. # 403 Diem cur Aſtronomi inchoent à Meridia- # no. # 279. & 282 Dies continuos inter polum, & circulum # polarem noctibus continuis ęquales non # eſſe. # 421 Diei continuæ quantitas inter polum, & # circulum polarem quo pacto inquiratur. # pag. # 420. & 421 Differentia latitudinum ciuitatũ quid. # 283 Differentia longitudinum ciuitatum quid- # ibidem Differentiæ aſcenſionales quo pacto per ſi- # nus ſupputentur. # 337. & 338 Differentiarum aſcenſionalium tabula. pa- # gina. # 340 ad 347 Differentiam aſcenſionalem cuiuſuis arcus # ſeu puncti Eclipticæ eãdem eſſe, quæ eſt # inter arcus ſemidiurnos ſphęræ rectę, &</note> <pb file="021" n="22"/> </div> <div xml:id="echoid-div17" type="section" level="1" n="17"> <head xml:id="echoid-head20" style="it" xml:space="preserve">INDEX.</head> <note position="right" xml:space="preserve"> # obliquæ, Sole in illo puncto Eclipticę # commorante. # 406 Differentia inter arcũ ſemidiurnũ ſphęrę # rectæ, & arcũ ſemidiurnũ ſphærę obli- # quæ, quo pacto per ſinus reperiat̃. ibi. Dimenſionęs in quantitate eſſe tm̃ tres, # & quare # 15 Dimẽſi ones magnitudinũ fieri debere ꝑ # lineas perpendiculares, & quare # 14 Directio planetæ quid. # 460 Directus planeta quando dicatur<unsure/>. ibidem Directa, Retrograda, uel Stationaria cur # non dicatur Luna. # 461 Diſtantiam duorũ locorum in terra men # ſurãdam eſſe per circulũ maximũ. # 290 Diſtantia inter duas ſtellas ciuitates quo pacto # inueſtigetur. # 290 ad 295 Diſtantia inter duas ſtellas quomodo in- # ueniatur. # 293 Diſtãtiæ cęlorũ à cẽtro terræ. # 215. & 216 Diſtantiã Zenith ab Aequatore ubiq. ter # rarum ęqualem eſſe altitudini poli ſu- # pra Horizontem. # 302 Diſtantiam polorũ Zodiaci à polis mũdi # æqualem eſſe maximę declinationi So # lis.pag. # 273. & 305 Diuerſitas aſpectus quid. # 65 Diuerſitates aſpectus duorum aſtrorũ in # eodem cęlo eãdẽ altitudinẽ ſupra Ho # rizontẽ habẽtiũ eſſe ęquales. # 65. & 66 Diuerſitatem aſpectus eiuſdẽ aſtri, quo ꝓ # pinquius eſt Horizõti, eo eſſe maiorẽ, # adeo ut in Horizonte aſtrum exiſtens # habeat maximam, in uertice vero capi # tis nullam. # 66 Diuerſitatem aſpectus aſtri, quod terræ # propinquius eſt, ubicun<unsure/>q. in cęlo exi- # ſtat, maiorem eſſe ea, ꝗ̃ hẽt aſtrũ lõgi’ # à terra diſtãs, eundemq́ue locũ ſiue ve- # rũ, ſiue visũ cũ priore obtinẽs. # 66. & 67 Diuerſitatẽ aſpectus Lunę in diuerſis Cli # matibus cãm eſſe, cur Eclipſis Solis fiat # interdũ in vno Climate, & in alio nõ, # & maior interdũ in vno ꝗ̃ in alio. # 451 Diuiſio diſciplinarum Mathematicarũ. # 1 Diuiſio horarum. # 405 Diuiſiones varię circulorum ſphærę. # 212 # ad 216 Diuiſio ſphæræ ſecundum ſubſtantiam. # 19 Diuiſio ſexagenaria cur celebris apud A- # ſtronomos. # 246 Diuiſio ſphærę ſecundum accidens. # 21 Diuiſio Zodiaci in 12. ſigna cur facta ſit. # pag. # 237 ad 240 Diuiſio ſigni in 30. gradus. & totius Zo- # diaci in 360. # 246 Diuiſio Zodiaci ſecundum longitudinẽ # quæ ſit. # ibidem Diuiſio Zodiaci in gradus 360. cur facta # ſit. pag. # 246 Diuiſio Zodiaci ſecundum latitudinem. # pag. # 248 & 249 Domorum cęleſtium circuli qui. # 213 Domus plànetarum quæ ſigna Zodiaci eſ # ſe dicantur. # 244 Dom<emph style="sub">9</emph> principalior cuiuſuis planæ quod # ſignum Zodiaci ſit, & quòd domus mi # nus principalis. # ibidem Draconis Lunæ caput. # 459 & 460 Draconis Lunę cauda. # ibidem Duodenarij numeri dignitas # 240 E <emph style="sc">ECcentricvs</emph> orbis ſimplici- # ter quid. # 422 # Eccẽtrici orbes f<unsure/>m ꝗd ꝗ ſint. # Ibid. Eccẽtricis orbib<emph style="sub">9</emph>, & Epicylis ſphæras pla # netarum conſtare f<unsure/>m Ptolomęũ. # 425 Eccentricus circulus in planetis ꝗd. # 423 Eccentricos orbes ſimpliciter, & ſecundũ # quid, unà cum concentricis, & Epicy- # clis in omnibus cælis eſſe 33. tm̃. # 450 Eccentricis oribibus, & Epicylis poſitis # quo pacto phænomena defendi poſ- # ſint. pag. # 422 ad 458 Eclipſim cur Sol à Luna, non autem à Ve # nere, & Mercurio patiatur. # 70 & 71 Eclipſim Lunæ eſſe interpoſitionẽ terræ # iter Solẽ, ac Lunã, & quare. # 250 & 462 Eclipſis Lunę quid, & quando fiat. # ibid. Eclipſis Lunę cur non in omni plenilu- # nio fiat. # 460 Eclipſim Lunæ eſſe uniuerſalem in tota # terra. # 460. & 461 Eclipſis Solis quid, & quando fiat. # ibid.</note> <pb file="022" n="23"/> </div> <div xml:id="echoid-div18" type="section" level="1" n="18"> <head xml:id="echoid-head21" style="it" xml:space="preserve">INDEX.</head> <note position="right" xml:space="preserve"> Eclipſis Solis cur nõ in omni Nouilunio # fiat. # ibidem Ecl@pſim Solis non eſſe uniuerſalem in # tota terra. # ibidem Eclipſim Solis in Paſſione Domini fuiſ- # ſe miraculoſam. # ibidem Eclipſim cur ſtellæ fixę, & tres ſuperiores # planetę non patiantur ob interpoſitio # nem terrę inter Solem, & ipſos. # 190 Ecliptica quid, & vnde dicta. # 250 Ecliptica qũo in cœlo concipiatur deſcri # bi. # 251 Eclipticæ varia nomina. # ibidem Eclipticę officia uaria, & vtilitates. # 256 # ad 259. Eclipticæ punctorum declinationes quo # modo per ſinus ſupputentur. # 255 Eclipticæ quaterna puncta eandem habe # re declinationem. # 258 Eclipticę aſcendens, & deſcendens ſemi- # circulus quid. # 243 Eclipticæ borealis, & auſtralis ſemicircu- # lus quid. # 252 Eclipticæ puncta ab ęquinoctialibus pun # ctis æqualiter diſtantia æquales habe- # re declinationes. # 258 Eclipticæ duas medietates inter ęquino # ctialia puncta poſitas ad æquari ſuis a- # ſcenſionibus in ſphęra obliqua, ſed ea # rum partes minime. # 332 & 333 Eclipticam eſſe viam Solis, quàm nunꝗ̃ # relinquit. # 251 & 252 Eclipticam menſuram eſle motus ab oc- # caſu in ortum. # 256 Eclipticam cauſam eſſe eclipſium. # ibid. Eclipticam cauſam eſſe inæqualitatis die # rũ & noctiũ, ac viciſſicudinis tꝑum. # ibi. Elementa quid. # 29 & 30 Elementa viciſſim à ſemetipſis alterari, & # corrumpi. # ibid. Elemẽta decuplam proportionem inter # ſe non habere. # 129. & 130. Elementa omnia, pręter terram, moueri # ab ortu in occaſum. # 32 Elementa nullam continuam proportio # nem inter ſe habere. # 130 Elementarem regionem continuę altera # tioni eſſe obnoxiam. # 29 Elementaris regio quę. # ibidem Elementaris regionis forma ac figura. # 31. # & 134 Elementorum & numerus, & ordo qũo # à philoſophis colligatur. # 33. ad 37 Eleuatio poli ſupra Horizõtẽ quo pacto # ex altitudine meridiana inueniat̃. # 279 Eleuatio Æquatoris qua ratione ex a@ti- # dine poli inueſtigetur. # 302 Eleuationem poli ęqualem eſſe latitudi # ni eiuſdem loci, hoc eſt, diſtantię ze- # nith ab Æquatore. # 298 Eleuationem Æquatoris æqualem eſſe # complemẽto altitudinis poli, hoc eſt, # diſtantię Zenit à polo mundi. # 302 Empyreum cęlum ſecũdũ Theologos. # 45 Empyreum cœlum dari, quibus indicijs # probetur à nonnullis. # 45. & 46 Epicyclus quid. # 433. Exaltatio planerę cuiuſuis quodnam ſi- # gnum Zodiaci dicatur. # 244 F <emph style="sc">FIgvrae</emph> area quid. # 82 # Figurę Iſoperimetrę quę. # 78. & 81 # Figura, & forma aeris, & Ignis. # 134 Figura, & forma elementaris regionis. # 31 # & 134. Figura, & forma ęthereę regionis. # 39. et 72 Figura regularis quid, & eius centrum ꝗ<unsure/> # pag. # 81: & 82 Figura ſolida rectangula quid # ibidem Figura regularis q̃libet cui parallelogrã- # mo rectangulo ſit ęqualis. # 83 Figura regularis quęlibet cui triangulo # rectangulo ſit ęqualis. # ibidem Figurarum Iſoperimetrar<unsure/>ũ regulariũ eã # maiorẽ eſſe, q̃ plures angulos, plurave # latera continet. # 86 & 87 Figurarũ Iſoperimetrarũ latera numero # ęqualia habentium maximam & ęqui- # lateram eſſe, & ęquiãgulam. # 93. ad 96 Figuris omnibus rectilineis regularibus # circulum, qui ęqualẽ ambitũ habeat, # maiorem eſſe. # 97 Figuratũ oĩum rectilinearũ circulum, ꝗ # ęqualẽ ambitũ habeat, maximũ eſſe. # 98</note> <pb file="023" n="24"/> </div> <div xml:id="echoid-div19" type="section" level="1" n="19"> <head xml:id="echoid-head22" style="it" xml:space="preserve">INDEX.</head> <note position="right" xml:space="preserve"> Firmamentum quid, & cur ſic dicatur. # 20 Firmamenti arcus inter duos radios viſua # les, quorũ unus à centro terræ, alter ei # æquidiſtans, & terrã tangens, ex ſuper- # ficie terræ exire intelligitur, interce- # ptus, quantus ſit. # 145 Firmamenti ſuperficies concaua quot ſtel # las primæ magnitudinis cõtinere poſ- # ſit. # 189 Firmamenti ambitus, & diſtantia à cẽtro # terræ tam ſecundum concauum, quàm # ſecundum conuexum. # 216 Firmamentum triplici motu moueri. # 56 Fixa ſigna Zodiaci quæ dicantur. # 239 Fixæ ſtellæ cur ſic ſint dictæ. # 21 Fixas ſtellas uiſu notabiles eſſe. # 1022. # 148. & 181 Franciſci Maurolyci ratio inueſtigandi # ambitus terreni. # 202 G <emph style="sc">GEometria</emph> circa quid uerſe- # tur. # 1 Glaciale cœlum, ſiue aqueum, aut # cryſtallinum. # 45 Globum unum ex terra, & aqua confici. # pag. # 117. ad 134 Globum unum cõſtitui ex terra & aqua, # quomodo intelligendum ſit. # 126 Globus ex terra, & aqua conſectus cui cõ # parari poſſit. # 127 Gradus, ac Minuta graduum, quo pacto # ad Horas, & Minuta horarum reuocẽ- # tur. # 231. & 232 Gradus quid, & quot ſint in Zodiaco tã # ſecundum longitudinem, quàm ſecun # dum latitudinem, & quare. # 247. ad 249 Gradus Aequatoris cur Tempora dican- # tur. # 248 Gradus unus quot Minuta, Secunda, Ter # tia, &c. comprehendat. # 245. & 247 Gradus unus circuli maximi ĩ terra quot # ſtadia, aut milliaria cõprehendat, ſecũ- # dum uarios. # 211. ad 214 H <emph style="sc">HAeitabilis</emph> portio terræ # quãta ſtatuatur ab auctore. # 423 Habitabilem portionem terræ maiorem # eſſe, quàm ab auctore conſtituitur. # 428 Habitabiles eſſe Zonas frigidas, & torri- # dam. # 311 Habitabiles Zonæ ab antiquis quæ dictæ # ſint. # 309 Habitantibus ſub Aequatore quid acci- # dat. # 414. & 415 Habitantibus inter Aequatorem, & Tro- # picum cancri quid accidat. # 416 Habitantibus ſub Tropico Cancri quid # accidat. # 416. & 417 Habitantibus inter Tropicum Cancri, # & circulum arcticum quid accidat. # pag. # 417. & 418 Habitantibus ſub circulo arctico quid # accidat. # 418. & 419 Habitantibus inter circulum arcticum, & # polum quid accidat. # 419. & 420 Habitantibus ſub polo quid accidat. # pag. # 422 Habitudines variæ parallelorum ſemper # apparentium, ſemperq́; latentium ma # ximorum. # 301 Habitudines uariæ declinationum, & la- # titudinum ſtellarum. # 257 Heliace oriri aliqua ſtella quando dica- # tur. # 317 Heliacus ortus, & occaſus ſecundum poe # tas quid. # 315. ad 317 Heliacus ortus, & occaſus qua in parte cę # li fiat. # 317 Hemiſphærium uiſum, ſiue ſuperum, & # non uiſum ſiue inferum. # 299 Hemiſphærium boreale, & auſtrale trib. # modis ſumi apud Aſtronomos, & pe- # nes quos circulos maximos utrumque # accipiatur. # 257 Heteroſcij, Amphiſcij, & Periſcij, qui # ſint. # 313 Homines olim tamdiu uixiſſe beneficio # Dei, ut rebus Aſtronomicis poſſent ua # care. # 3 Hora æqualis, ſiue æquinoctialis: natura- # lis, planetaria, temporalisue quid, & # cur ſic dicatur. # 405 Horæ, ac Minuta horarum, quo pacto ad # Gradus, & Minuta Graduum reuocen-</note> <pb file="024" n="25"/> </div> <div xml:id="echoid-div20" type="section" level="1" n="20"> <head xml:id="echoid-head23" style="it" xml:space="preserve">INDEX.</head> <note position="right" xml:space="preserve"> # tur. # 231. & 232 Horarum inæqualium duo genera. # 405 Horarum inæqualium quantitas quomo # do cognoſcatur. # 405. & 406 Horarij circuli qui ſint. # 221 Horizon quid, & cur ſic dictus, & alia eius # nomina. # 23. & 295 Horizon apparens, ſiue ſenſibilis quid. # pag. # 297 Horizon artificialis quid. # 26. & 297 Horizon naturalis, rationalisue quid. # pag. # 297 Horizon ſenſibilis quantum ſpatium cõ # plectatur in terra. # 297 Horizõ quomodo in terra mutetur, quã # tum ad ſenſum. # 295 Horizontem rationalem ſolum partiri # cęlum bifariam, Geometrice loquen- # do. # 297 Horizon rectus, & obliquus quid. # 26. # & 297 Horizontes tot eſſe debere, quot ſunt Me # ridiani. # 295 Horizontis polum eſſe Zenith. # 298 Horizontis officia, & utilitates uariæ. # 299 ad 302 Horizontem concipiendum eſſe immobi # lem. # 295 I <emph style="sc">IGnea</emph> ſigna Zodiaci quæ ſint. # 238 Immobilitatis terræ ſecundum ua- # rios uariæ cauſæ, earumq́ue confu- # tatio. # 197 Immobilitatis terræ uera cauſa. # 194 Inæqualis hora, plane<unsure/>taria, naturalis, tẽ- # porali ſve quid. # 405 Inæqualium horarum duo genera, & # quo pacto earum quantitas cognoſca- # tur. # ibidem Ingreſſus ſolis in ſigna zodiaci quibus # diebus contingat. # 276 Inſcriptio huius operis. # 11 Inſtrumenta Aſtronomica uaria. # 5 Intentio auctoris in hac ſphæra. # 11. & 12 Interuallum inter duas ciuitates quo pa # cto reperiatur. # 290. ad 295 Interuallum inter duas ſtellas quo pacto # inueſtigetur. # 293 Inuentores Aſtronomiæ primi qui fue- # rint. # 3 Inuentores primi ſphæræ materialis qui. # pag. # 17 Ioannes de ſacro boſco quo tempore flo- # ruerit, & cur hanc ſphæram conſcri- # pſerit. # 2 Iſoperimetrę figuræ quæ. # 78. & 81 Iſoperimetrarum figurarum maximum # eſſe circulum. # 97 Iſoperimetrarum figurarum regularium # eam eſſe maiorem, quæ plures angulos # pluraue latera continet. # 86. & 87 Iſoperimetrarum figurarum latera nume # ro æqualia habentiũ maximã & æqui- # lateram eſſe, & æquiangulam. # 93. & 96 Iſoperimetrorum parallelogrammorum # maius illud eſſe, quod eſt rectangu- # lum. # 79. & 80 Iſoperimetrorum triangulorum eandem # baſim habentium Iſoſceles maius eſſe # non Iſoſcele. # 88 Iſoperimetrarum figurarum ſolidarum, # quæ planis ſuperficiebus cõtineantur, circaq́ue ſphæras circumſcriptibilia # ſint, maximam eſſe ſphæram. # 102 Iſoperimetrarũ figurarum ſolidatũ circa # ſphæras circumſcriptibilium, quæ ſu- # perficiebus conicis cõtineantur, ita ut # omnia latera conica ſint æqualia, ſph@ # ram eſſe maximam. # 102. & 103 Iſoſceles triangulum Iſoperimetrum al- # teri triangulo non Iſoſceli ſuper ean- # dem baſim quo pacto conſtruatur. # 87 Iſoſcelia duo triãgula, & ſimilia inter ſe, # Iſoperimetra aũt alijs duo bus triangũ # lis Iſoſcelibus nõ ſimilibus ſuper eaſ- # dem baſes qua ratione cõ@truantur. # 90 Iſoſcelia duo triãgula ſimilia ſu ꝑ inęqua # libus baſibus cõſtituta, utraque ſimul # maiora eſſe duob. triãgulis Iſoſcelibus, # vtriuſq; ſimul, quæ habeant eaſdẽ ba- # ſes cũ prioribus, ſintq́ue diſſimilia qui # dem inter ſe, at Iſoperimetra priorib. # duobus, nec non quatuor latera inter # ſe habeant æqualia. # 91. & 92</note> <pb file="025" n="26"/> </div> <div xml:id="echoid-div21" type="section" level="1" n="21"> <head xml:id="echoid-head24" style="it" xml:space="preserve">INDEX.</head> <note position="right" xml:space="preserve"> L <emph style="sc">LActevs</emph> circulus in cęlo. # 290 Lacteus circulus unde habeat can- # dorem. # ibidem Lacteum circulum eſſe in Firmamento, # non autem in aere, vt falſo Ariſtoteles # credit. # ibidem Latera ędificiorum nõ eſſe parallela, ſed # protracta coire in centro mundi. # 132 Latitudinum, & longitudinum ciuitatũ # tabula. # 285. ad 289 Latitudo ciuitatum quid. # 283 Latitudo ciuitatum duplex, borealis, & # auſtralis. # ibidem Latitudo ſtellarum quid. # 256 Latitudo ſtellarum duplex, borealis, & # auſtralis. # ibidem Latitudo ſtellarum quo circulo maximo # menſuretur. # ibidem Latitudo, & longitudo in Vniuerſo quo # modo a philoſophis accipiatur. # 284 Latitudo ortiua, & occidua Solis, uel cu- # iuſuis puncti Eclipticæ quid, & quo pa # cto inueniatur per ſinus. # 300 Latitudo ſtellarum ab earundem declina # tione quomodo differat. # 256 Latitudo Zodiaci quanta ſit, & cur ei tri # buatur. # 248. & 249 Latitudo Zonæ cuiuſlibet quanta ſit. # 312 Latitudinem cuiuſlibet Zonæ eſſe eandẽ, # quo ad omnes partes, longitudinem # autem nequaquam. # ibidem Latitudinem cuiuſuis loci, ideſt, diſtãt@ã # Zenith ab Aequatore, æqualẽ eſſe alti # tudini poli ſupra Horizõtẽ. # 298. & 299 Latitudinum circuli qui ſint. # 222. & 25<unsure/>6 Latitudinum, & declinationum ſtellarũ # uarię habitudines. # 257 Lineas rectas ex circũferentijs circulorũ # circa idem centrum deſcriptorum in- # tercipere arcus ſimiles. # 203. & 204 Locales mot<emph style="sub">9</emph> ſimplices eẽ tres. # 36. & 453 Locorum diſtantiam in terra penes circu # lum maximum ſumendam eſſe. # 290 Locorum diſtantia in terra quo pacto in # ueſtigetur. # 290. ad 295 Locus uerus cuiuſuis ſtellæ in Zodiaco # quid. # 258 Locus uerus, & uiſus aſtri quid. # 65 Longitudinum, & latitudinum ciuitatũ # tabula. # 285. ad 289 Longitudo ſtellæ quid. # 150. & 256 Longitudo ſtellæ quo circulo maximo # menſuretur. # 256 Longitudines, & latitudines ſtellatũ, quo # pacto ex tabulis eliciantur. # 181 Lõgitudo ſtellarum uera quid, & quo pa # cto inueniatur. # ibidem Lõgitudo, & latitudo ĩ<unsure/> Vniuerſo quo pa # cto apud philo ſophos ſumatur. # 284 Longitudo cuiuslibet Zonę tam in princi # pio, quàm in fine, quo pacto reperia- # tur.pag. # 312 Longitudinem cuiusuis Zonæ non eſſe # eandem, quo ad omnes partes. # ibidem Longitudines ciuitatum per eclipſes cer # tiſſime inueniri. # 284 Longitudines ciuitatum unde incipiant. # pag. # 278. & 283 Longitudines, latitudines, & magnitudi- # nes ſtellarũ ĩ tabulas digeſtę. # 151 ad 180 Luna cur non dicatur ſtationaria, directa, # uel retrograda. # 461 Luna cur Solẽ eclipſet, cum ipſo ſit mul- # to minor. # 71 Lunæ eclipſis quid, & quando fiat. # 250 # & 462 Luna cur non ſingulis menſibus patiatur # eclipſim. # 462 Lunæ eclipſim eſſe interpoſitionem terrę # inter Lunam, & Solem. # 250. & 462 Lunę eclipſim eſſe uniuerſalẽ in tota ter # ra, Solis autem non. # 462. & 463 Lunam inter planetas infim um habere # locum. # 68 Lunam minorem eſſe Sole, & terra, quo- # modo demonſtretur. # 190. & 191 Lucani locus emendatus. # 309 M <emph style="sc">MAcrobii</emph>, & Eratoſthenis de # ambitu terræ ſententia. # 211 Magnitudinum tria tantum eſſe # genera, & quare. # 13. & 15</note> <pb file="026" n="27"/> </div> <div xml:id="echoid-div22" type="section" level="1" n="22"> <head xml:id="echoid-head25" style="it" xml:space="preserve">INDEX.</head> <note position="right" xml:space="preserve"> Mare innumeris inſulis eſſe reſperſum. # 119. 125. 127. & 128. Mare minus eſſe, quàm terram. # 32. & 130. Mare quo pacto a terra ſeparatum ſit, cũ # Deus dixit. [cõgregentur aquæ in locũ # vnum, & appareat arida] variæ ſenten- # tiæ, earumq́ue confutatio. # 31 Mare quo pacto à terra receſſerit, vt appa # reret arida, verior ſententia. # 32 Maris profunditas quanta fit vt pluri- # mum. # pag. 130 Maris ſuperficiem ſub ſuperficie terræ, ſi # vtraque compleretur, æquali ſemper # diſtantia contineri. # 126 Materialis ſphæra cur ab Aſtronomis in- # uenta ſit. # 11 Mathematicarum diſciplinarum diuiſio. # pag. # 1 Mathematicos metiri omnia linea perpẽ # diculari, & quare. # 14 Matutinus, ac Veſpertinus ortus, & occa- # ſus. # 318 Maxima declinatio Solis quomodo inue # ſtigetur. # 262. & 263 Maxima Solis declinatio quid, & quanta. # pag. # 259. & 262 Maximam Solis declinationem boream # æqualem eſſe maximæ declinationi # eiuſdem auſtrali, # 273 Maximam Solis declinationem æqualem # eſſe diſtantiæ poli Zodiaci à polo mun # di. # 274 Maximus, & nõ maximuscirculus, ſiue ma # ior, & minor in ſphæra ꝗd. # 22. 221. 222 Maximi circuli in ſphæra ad nõ maximũ # proportio quo pacto inueſtigetur. # 304 Maximus parallelorũ ſemper apparentiũ, # ſemperq́ue latentium quid. # 301 Medietatem cœli vbique cõſpici, quomo # do intelligendum ſit. # 136. & 137 Nediocres dies qui ſint. # 400 Melancholica ſigna Zodiaci quæ ſint. # pag. # 238. Menſuræ variæ Mathematicorũ, & quara # tione vna in aliã trãſmutetur. # 209. 210 Menſuræ Mathematicorum quomodo in # telligendæ ſint. # ibid. Mercurium inter aſtra eſſe minimum, So # lem uero maximum. # 189 Mercurium cõuenienter collocari ſupra # Lunam, & infra Venerem. # 69 Mercurius cur Solẽ non eclipſet # 70. & 71 Meridiana linea quo pacto inueniat̃. # 280 Meridiana vna linea inuenta, quo pacto # innumeræ aliæ in eodem loco inueniã # tur. # pag. 281 # Meridiana ſtellæ altitudo quid. # 278 Meridiana Solis altitudo, vel alia quæcũ # que, quo pacto obſeruetur. # 279 Meridiana altitudo Solis quo pacto exhi # beat altitudinem poli. # ibid em Meridianus circulus quid, eiusq́; omnia # varia, & cur ſic dicatur. # 23. & 276 Meridianum cuiuſque loci eſſe inſtar Ho # rizontis recti. # 282 Meridianum concipiendum eſſe immobi # lem # 276 Meridiani circuli officia, & vtilitates ua- # riæ. # pag. 278. & 279 Meridiani in quanto ſpatio terræ muten # tur ſenſibiliter. # 277 Meridiani ſecundum Ptolemæũ, & Coſ- # mographos quot ſint. # 277 Meridiani unde initium ſumant. # ibid. Meridiani cur tãtum 12. vt plurimum in # mappis mundi deſcribantur à Coſmo- # graphis. # ibid. Meridiei, medię noctis, & ortus Solis té- # pus, more Italorum, quo pacto ex arca # ſemidiurno cognoſcatur. # 417 Meridionalis pars cœli quæ. # 229. & 253 Meridionalia ſigna Zodiaci, & borealia # quæ. # 251 Meridionales planetæ, & borales quãdo # dicantur. # 252 Mixtorum quinque genera. # 31 Mobilia ſigna Zodiaci quæ ſint. # 239 Motus cœlorum duplex, ab ortu in occa- # ſum, & ab occaſu in ortum. # 40. & 51 Motuum cœleſtium variæ opiniones, ea- # rumq́ue conſutatio. # 46. ad 51 Motuũ cęleſtiũ noſtra ſentẽtia. # 51. ad 55 Motus cęlorum ab ortu in occaſum, & ab # occaſu in ortum, quo pacto intelliga- # tur. # pag. 40 Motuum cæleſtium harmonia. # 41</note> <pb file="027" n="28"/> </div> <div xml:id="echoid-div23" type="section" level="1" n="23"> <head xml:id="echoid-head26" style="it" xml:space="preserve">INDEX.</head> <note position="right" xml:space="preserve"> Motus cęlorum ab ortu in occaſum, & ab # occaſu in ortum non eſſe contrarios. # pag. # 52. & 54 Motus diurnus cui cęlo tribuat̃ # 41. & 51 Motu diurno omnes cælos inferiores ra # pi à primo mobili. # ibidem Motuum cæleſtiũ periodi # 41. & 55. ad 57 Motuus omnium cælorum fieri ſimplici # ter ab ortu in occasũ, inferiores uero # cælos ſub primo mobili moueri ab oc- # caſu in ortũ f<unsure/>m quid, qũo intellrgatur, # & qua ratione id fieri poſſit. # 53. ad 55 Motus cælorum ab occaſu in ortum non # habere ordinatam proportionem in- # ter ſe. # pag. 49 Motus cælorum ab ortu in occaſum, & ab # occaſu in ortũ ſuper eoſdem polos fie- # r<unsure/>i poſſe: immo quoſdam orbes ita mo- # ueri, Et cur non omnes moueantur ſu # per eoſdem polos. # 55 Mot<emph style="sub">9</emph> eælorum ab ortu in occaſum, & ab # occaſu in ortum, qua ratione dici poſ- # ſint contratij. # 64 Motum cælorum omnium ſimpliciter ab # ortu in occaſum fieri, quo pacto depre # henſum ſit. # 57. & 58 Motum cęlorũ inferiorũ ſub primo mo- # bili fieri ſecundũ quid, & ſuꝑ polos Zo # diaci, quomodo obſeruatũ ſit. # 59. & 61 Motus triplex Firmamenti, ab ortu in oc # caſum, ab occaſu in ortum, & trepida- # tionis, ſiue acceſſus, & receſſus. # 56 Motus trepidationis quomodo fiat. # Ibid. Motus trepidationis in Firmamẽto quo # pacto deprehenſus ſit. # 62. & 63 Motuum cæleſtium periodi penes quos # orbes intelligendi ſint. # 57 Motus verus ſtellæ, & linea veri motus # quid. # 258 Motus cælorũ ab ortu in occaſum, & ab # occaſu in ortum quibus exemplis de- # claretur. # 54 Motuum, & orbium cæleſtium theoricæ # in tabulas digeſtæ, unà cum terminis # Aſtronomicis, & pafſionibus planeta- # rum. # 464 ad 483 Mundus quid. # 28 Mundum Verno tꝑe fuiſſe creatum. # 273 Mundus triplex, Vltramundanus, cęleſtis, # & Sublunaris. # 29 Mundi totius forma ac figura. # 28 Muſica circa quid uerſetur. # 2 N NAdir cuiuſque loci quid. # 23 Nadir Solis quid. # 461 Naturales dies quid, coſq́ue inæ- # quales eſſe, & quare. # 399 Naturales dies qua arte ad æqualitatem # redigantur ab Aſtronomis. # 400 Naturalium dierum circuli qui # Ibi. Naturalis hora, ſiue planetaria, uel inæ- # qualis, aut temporalis quid. # 405 Naturalis horæ ꝗ̃titas quo pacto cogno- # ſcatur. # 405. & 406 Naturalis Horizon quid, & cur ſic dica- # tur. # 297 Noctis artiſicialis arcus quid. # 401 Noctes continuas inter polum, & circulũ # arcticum minores eſſe diebus cõtinuis # reſpondentibus, & quare. # 421 Nox artificialis quid. # 401 Nomina, & ordo 12. ſignorũ Zodiaci. # 236 Numeri duodenarij dignitas. # 240 Numerus, & ordo corporum uniuerſum # mundum componentium. # 71 Numerum elemẽtorum, & ordo qua via # colligatur. # 33. ad 38 Numerus orbiũ cœleſtium varius, & quo # pacto colligatur. # 42. ad 46 Numerus & ordo fignorum Zodiaci. # 236 Numerus arenæ in toto mundo cõprehẽ # ſus qua ratione inueſtigetur. # 217 O OBiectiones duæ aduerſus motũ ftel # larum fixarũ ab occaſu in ortũ ſu # ꝑ polos Zodiaci ex apparẽtijs de- # ſumptæ, earumq́ue ſolutio. # 61. & 62 Oceani, & matis profunditas quanta ſit # vt plurimum. # 130 Oceani ſupeificiem ſub terræ ſuperficie, # ſi vtraque compleretur, ęquali ſemper # diſtantia contineri. # 126</note> <pb file="028" n="29"/> </div> <div xml:id="echoid-div24" type="section" level="1" n="24"> <head xml:id="echoid-head27" style="it" xml:space="preserve">INDEX.</head> <note position="right" xml:space="preserve"> Oceanum, etiamſi omnia alia maria addã # tur, minorem eſſe, quàm terram. # 129 Oceanũ innumeris pene inſulis reſpersũ # eſſe. # 119. 125. 127. & 128. Oculum in edito monte cõſtitutum plus # uidere poſſe, quàm cęli medietatem, & # quare. # 145 Officia, & utilitates Æquinoctialis cir- # culi. # 228 ad 230 Officia, & utilitates Eclipticæ, vel Zodia- # ci. # 255. ad 258 Officia, & vtilitates Colurorũ. # 261. ad 276 Officia, & vtilitates Meridiani. # 278. ad 284 Officia, & utilitates Horizontis. # 299 ad # 302 Officia, & utilitates circulor<unsure/>ũ parallelo- # rum, nempe Tropicorum, & polarium # circulorum. # 307. & 308 Oppoſita ſigna in ſphæra recta habere ę- # quales aſcenſiones. # 323. & 326 Oppoſitum Augis quid. # 431. & 433 Orbem cęleſtem quemcunq. ſuo motu ra # pere inferiorem ſibi contiguum, & con # centricum. # 56. & 447 Orbes augẽ planetæ deferẽtes ꝗ ſint. # 459 Orbes eccentrici ſecundum quid. # 432 Orbes eccentricos ſimpliciter, & ſecundũ # quid, vnà cum concẽtricis, & epicyclis # in omnibus cęlis eſſe 33. tantum. # 450 Orbes totales planetarũ ex pluribus orbi # bus partialibus componi. # 433 Orbis Eccentricus ſimpliciter in planetis # quid. # 432 Orbis a ſphæra quomodo differat. # 29 Orbis eccentricus Deferẽs planetam, aut # Epicyclum. # 433 Orbib. eccẽtricis, & epicyclis poſitis quo # pacto phęnomena defendãt̃ # 432. & 458 Orbibus eccentricis, & epicyclis ſphæras # planetarum conſtare ſecundum Ptole # mæum. pag. # 435 Orbium cæleſtiũ, & motuũ theoricę in ta # bulasredactę, vnà cũ terminis Aſtrono # micis, & paſſionib. planetarum # 464. ad # 483 Ordo cęlorum ſecundum Ariſtarchum, # & Copernicum. # 64 Ordo cęlorum ſecũdum Aſtronomos re- # cẽtiores, & ꝗbus uijs colligat̃. # 64. ad 72 Ordo cælorum ſecũdũ Platonem, Ariſto # relem, & Ægyptios. # 64 Ordo, quẽ auctor ſeruat in hac ſphæra. # 11 Ordo elementorum qua ratione a philo # ſophis ſit collectus. # 33 ad 37 Oriens, &Occidẽs abſolutũ, ac reſpectiuũ # pag. # 282 Ortiua, & occidua latitudo ſtellę quid, # & quo pacto per ſinus ſupponatur. # 300 Ortus, & occaſus Aſtronomicus quid. # pag. # 321 Ortus, & occaſus rectus, atque obliquus # ſigni quid, & cur ſic dictus. # 322 Ortus, & occaſus rectus, & obliquus ꝗd # tam ſecundum auctorem, quàm ſecũdũ # Ptolemęum, & alios Aſtronomos. # ibi. Ortus, & occaſus ſtellæ quid. # 315 Ortus, & occaſus uerus, ſiue ęquinoctialis # quid. # 300 Ort<emph style="sub">9</emph>, & occaſus apud Poetas triplex, Coſ # mic<emph style="sub">9</emph>, Chronic<emph style="sub">9</emph>, & Heliac<emph style="sub">9</emph>. # 314. ad 318 Ortus, & occaſus uerus, atque Apparens # quid. # 318 Ortus, & occaſus Matutinus, ac Veſperti- # nus quid. # ibidem Ortus, & occaſus ab Aſtronomis cur per # Aequatorem definiatur. # 321 Ortus, & occaſus ſignorũ quomodo fiant # in ſphæra recta. # 323. ad 331 Ortus, & occaſus ſignorũ quomodo fiant # in ſphæra obliqua. # 331. ad 398 P <emph style="sc">PAralleli</emph> circuli in terra quã # to ſpatio ĩter ſe diſtãtes a Ptolomęo # & alijs Aſtronomis deſcribatur. # 428 Paralleli circuli quota Sole in anno de- # ſcribantur. # 400. & 401 Paralleli quatuor minores quo pacto in # terra Zonas diſtinguant. # 308. ad 313 Paralleli quinque in ſphara qui ſint. # 308 Parallelogrammorum Iſoperimetrorum, # quod rectangulum eſt, maius eſſe non # rectangulo. # 79. & 80 Parallelorum circulorum, nempe Tropi- # corum, & circulorum polarium offi- # cia, atque utilitates. # 307. & 308 Parallelorum ſꝑ apparentium maximus,</note> <pb file="029" n="30"/> </div> <div xml:id="echoid-div25" type="section" level="1" n="25"> <head xml:id="echoid-head28" style="it" xml:space="preserve">INDEX.</head> <note position="right" xml:space="preserve"> # & ſemper I<unsure/>atentium maximus, ꝗd # 301 Parallelorũ ſꝑ apparentium, ſemperq́. la # tẽtiũ maximorũ habitudines uarię. # ibi. Parallelos plures deſcribi à Sole cõmorã # te in ſignis borealibus, quàm eodem ſi # gna auſtralia percurrente, & quare. # 401 Partes Aſtronomiæ # 5 Pars cæli dextra, & ſiniſtra, quæ ſecundũ # philoſophos, Coſmographos, Aſtrono # mos, & Poetas. # 310 Partes Aſſis quæ ſint. # 248 Pauimenta ad libellam conſtructa nõ eſ # ſe plana. # 132 Periodi motuuw<unsure/> cæleſtiũ. # 41 & 55. ad 57 Periſcij, Amphiſcij, & Heteroſcij, ꝗ ſint. # pag. # 313 Perpendicula omnia in centro mũdi coi # re. # 132 Perpendiculari linea omnia a Mathema # ticis menſurari, & quare. # 14 Phlegmatica ſigna Zodiaci, & aquea, quę # pag. # 238 Phyſicũ ſignum Zodiaci, & cõe quid. # 237 Planetas, præter Solem, non ſemper eſſe # ſub Ecliptica. # 250. 251 Planetã in aliquo ſigno eſſe quot modis # dicatur. # 252 ad 254 Planetæ ſtatio, directio, aut retrograda- # tio quid. # 460. & 461 Planeta quando dicatur ſtationarius, di- # rectus, aut retrogradus. # ibid. Planetarum ordo ſecundum Ariſtarchũ # Samium, & Nicolaum Copernicũ # 64 Planetarum ordo ſecundum Platonem, # Ariſtotelem, & Ægyptios. # ibidem Planetarum ordo ſecũdum Aſtronomos # recentiores, & quibus uijs colligatur. # 64. ad 71 Planetæ unde ſic dicti. # 21 Planetę cuiuſuis domus quod ſignum Zo # diaci eſſe dicatur. # 244 Planetę boreales, & auſtrales quando di # cantur. # 229. & 252 Planetarum dominium in ſingulis horis # diei. pag. # 80 Planetæ quo pacto dies hebdomadæ de- # nominent. # ibidem Planetaria hora, uel inæqualis, Natura # aut temporalis, quæ eiuſq́. quantitas # pacto cognoſcatur. # 405 Planetæ cuiuſuis exaltatio, caſus, & detri # mẽtum, quod ſignum Zodiaci dicatur. # pag. # 244 Planetæ quo pacto inſignis borealib<emph style="sub">9</emph> exi # ſtẽtes dici aliquando poſſint auſtrales, # boreales uero, qñ in auſtralibus ſignis # exiſtunt. # 255 Planetarũ Theoricæ in cabulas digeſtæ. # pag. # 464 ad 483 Planetas in orbibus ecentricis moueri, ꝓ<unsure/> # babilius eſſe, quàm eos in concentricis # orbibus ferri. # 432. ad 458 Poeticus ortus, & occaſus ſtellarum ꝗd, # & quotuplex. # 314 ad 318 Polares circuli qui. # 303. & 304 Polares circuli ſecundum Græcos ꝗ. # 304 Polarium circulorũ officia & utilitates. # pag. # 307. & 308 Polus arcticus, & antarcticus, eorumq́. ua # ria nomina. # 18. 227. & 228 Polus circuli cuiuſuis in ſphęra quid. # 22 Poli ſphæræ, & mundi. # 17. ad 19 Poli altitudo ſupra Horizontem quo pa- # cto ex altitudine meridiana Solis eli- # ciatur. # pag. 279 Poli altitudinẽ in quocunq. loco æqualẽ # eſſe latitudini eiuſdẽ loci. # 298 & 299 Polorum Zodiaci diſtantiam à polis mun # di ęqualem eſſe maximæ declinationi # Solis pag. # 274 Poſſidonij ratio inueſtigandi ambitus ter # reni. # 201 Practica Aſtronomia quæ. # 5 Profunditas maris quanta ſit ut plurimũ. # pag. # 130 Proœmium auctoris in ſphæram. # 11 Proportionem decuplam inter elementa # non eſſe. # 130. & 131 Propo@tionem nullam continuam ſerua- # ri inter elementa. # 131 Proportio circuli maximi ad non maxi- # mum quomodo reperiatur. # 304 Proportio Archimedis inter circumferẽ # tiam circuli, &eius diametrum, q̃. # 205 Proportionem Archimedis inter circũfe # rentiã circuli, eiuſq́. diametrũ, dare cir</note> <pb file="030" n="31"/> </div> <div xml:id="echoid-div26" type="section" level="1" n="26"> <head xml:id="echoid-head29" style="it" xml:space="preserve">INDEX.</head> <note position="right" xml:space="preserve"> # cumferentiã maiorem ex nota diame- # tro, diametrum vero minorẽ ex nota # circumferentia, quàm re ipſa ſit. # 207 Proportiones diametrorum ſtellarum ad # diametrum terræ. # 186. & 187 Proportiones ſtellar<unsure/>ũ ad terrã. # 187. & 188 Proprietates aliquot Æthæreæ regionis # pag. # 39 Proprietates nonnullæ circulorũ in ſphæ # ra. # 222. & 223 Ptolemæi ratio, quòd terra ſit in medio # mundi. # 137. ad 143 Puncta æquinoctialia quæ. # 23. & 241 Puncta Cardinalia in cœlo quę. # 241 Puncta Solſtitialia quæ # 23. & 241 Punctorum Eclipticę declinationes quo # pacto per ſinus ſupputentur. # 263 Punctorum Eclipticę aſcenſiones in ſphę # ra tam recta, quàm obliqua, quomodo # ſe habeant, & qua ratione inueſtigen- # tur. pag. # 319 ad 408 Pyramis quælibet cui paralleiepipedo æ- # qualis ſit. # 98 Q <emph style="sc">QVadrantes</emph> quatuor Ecli # pticæ à quatuor punctis Cardi- # nalibus inchoatos adæquari # ſuis aſcenſionibus in ſphæra recta, par # tes autem eorum nequaquam. # 323 Quadrantes quatuor Zodiaci quibus an- # ni temporibu<unsure/>s reſpondeant. # 239 Quadrantum Eclipticę à punctis ęquino # ctialibus inchoatorum vſque ad pũcta # ſolſtitialia maiores ſemper partes ori- # ri in ſphęra recta, quàm quadrantũ Æ- # quatoris reſpondentium. # 326. & 327 Quadrantũ Eclipticæ a punctis ſolſtitiali # bus inchoatorum uſq. ad puncta ęqui- # noctialia minores ſemper partes oriri # in ſphęra recta, quàm quadrãtum Æ- # quatoris reſpondentium. # 317 Qualitates quatuor anni temporum. # 238 Quinta eſſentia apud Ariſtotelem, & phi # loſophos, idẽ quod ætherea regio. # 39 Quantitatis cõtinuæ tria tantum eſſe ge # nera, & quare. # 13. & 15 R <emph style="sc">RAtionalis</emph> Horizon quid. # pag. # 297 Recta, &obliqua ſphęra q̃. # 32. ad 28 Rectus, & obliquus Horizon, Finiens, aut # Finitor quid. # 26. & 297 Rectus, & obliquus ortus, atque occaſus # ſigni quid, & cur ſic dictus. # 322 Regio ætherea, & elementaris quę. # 29 Regiones aeris tres, & quomodo ſint di- # ſpoſitę, quoad craſſitiem. # 38 Regionis elementaris forma, ac figura. # pag. # 29. ad 32<unsure/> Regionis ęthereę forma, ac figura # 39. & # 40 Regularis figura quid, & quod eius cẽtrũ # ſit. # 81 & 82 Regularis figura quæcunque cui paralle- # logrammo rectangulo ſit ęqualis # 83 Regularis figura quęcunque cui triangu # lo rectangulo ſit æqualis. # ibidem Regularium figurarum Iſoperimetratũ # maiorem illam eſſe, quæ plures angu- # los, plura ve latera contineat. # 86. & 87 Regulatium figurarum omnium circulũ, # qui æqualem habeat ambitum, maxi- # mum eſſe. # 98 Regularium quinque corporum figuras # qua ratione elementis, & cęlo tribue- # rit Plato. pag. # 134 S <emph style="sc">SEmicircvlvs</emph> Eclipticæ, uel # Zodiaci aſcendens, & deſcendens # quid. pag. # 243 Semicirculos Eclipticæ à punctis ęquino # ctialibus inchoatos adæquari ſuis aſcẽ # ſionibus in ſphæra obliqua, partes aũt # eorum nequaquam. # 332. & 333 Semicirculi Eclipticę ab Ariete inchoati<unsure/> # uſque ad Libram maiores ſemꝑ partes # oriri in ſphæra obliqua, quàm ſemicir # culi Æquatoris reſpondentis. # 333 Semirculi Eclipticæ a Libra ĩ<unsure/>choati uſq. # ad Arierẽ minores ſemper partes ori- # ri in ſphæra obliqua, quà<unsure/>m ſemirculi # Aequatoris reſpondentis. # ibidem</note> <pb file="031" n="32"/> </div> <div xml:id="echoid-div27" type="section" level="1" n="27"> <head xml:id="echoid-head30" style="it" xml:space="preserve">INDEX.</head> <note position="right" xml:space="preserve"> Semidiametri cœlorum quantæ ſint tam # ſecundum concauum, quàm ſecundum # conuexum. # 215 Semidiametri terræ quantitas uaria ſecũ # dum uarios. # 214 Semidiurni temporis tabulæ pro uariis # poli eleuationibus. # 408. ad 413 Semidiurnus arcus quo pacto inueſtige- # tur. # 407. & 408 Semidiurnus arcus quo pacto arcum ſe- # minocturnum, tempus meridiei, & tem # pus ortus Solis, more Italorum, exhi- # beat. # 408 Senſibilis Horizon quid. # 297 Senſum decipi, dum iudicat, cœlum terrę # imminere, ut furnum, & terram iuxta # Horizontem contingere. # 129 Septentrionalem partem mundi dextram # eſſe, & nobiliorem. # 241 Septentrionales, & auſtrales planetæ, uel # ſtellæ quomodo dicantur. # 229. & 252 Septentrionalis, & auſtralis pars cęli quę. # pag. # 252 Septentrionalis Zodiaci pars, & auſtralis # quæ. # 251. & 256 Septentrionalia, & auſtralia ſigna Zodia- # ci quæ. # 251 Sexagenaria diuiſio cur celebris apud # Aſtronomos. # 246 Signa Zodiaci Ignea & Cholerica, Ter- # rea & Melancholica, Aerea, & Sangui- # nea, Aquea & Phlegmatica quæ. # 238 Signa Zodiaci Mobilia, Fixa, & Commu # nia quæ. # 239 Signa Zodiaci cur ab animalibus deno- # minentur. # 225 Signa Zodiaci borealia, & auſtralia quæ. # pag. # 251 Signa Zodiaci cur 12. eorumque ordo, ac # nomina. # 235. ad 240 Signa Zodiaci ſex qualibet die, totidem- # que qualibet nocte oriri, ſex autem oc- # cidere. # 404 Signa Zodiaci cur ab Ariete incipiant. # pag. # 240. ad 245 Signa Zodiaci ſex in ſphæra obliqua oriri # recte, & ſex oblique, quo modo ſit in- # relligendum. # 404. & 405 Signi uaria acceptiones, & omnia, quæ in # mũdo ſunt, quomodo in aliquo ſigno # dicantur eſſe. # 262. ad 254 Signorum ortus, & occaſus tam in ſphæ- # ra recta, quàm in obliqua quomodo ſe # habeant. # 323. ad 398 Signum phyſicum, & commune Zodiaci # quid. # 237 Sol cur à Luna, non autem à Mercurio, # Venere eclipſetur. # 70 Sol, & ſtellæ cur maiores appareant iux- # ta Horizontem, ꝗ̃ in medio cœli. # 108 Solẽ in ſemicirculo Zodiaci boreali exi # ſtentẽ plures parallellos ad motũ diur # num deſcribere, quàm in ſemicirculo # auſtrali, & quare. # 401 Solem omuium aſtrorum eſſe maximum, # Mercurium autem minimum. # 189 Solem maiorem eſſe terra, ac Luna, quo- # modo demonſtretur. # 190 Solẽ ſemper ſub Ecliptica moueri, alios # autem planetas non. Et quomodo hoc # deprehenſum ſit. # 250. & 251 Sol quibus diebus ſigna Zodiaci ingre- # diatur. # 276 Sol in qua gradu Zodiaci exiſtat plus mi # nus. qua arte deprehendatur. # ibidem Solem conue nienter in medio planetarũ # ſtatui. # 68. & 69 Solis altitudo quomodo inueſtiget̃. # 279 Solis maxima declinatio quid, & quanta # ſecundum uarios. # 259. & 262 Solis maxima declinatio quo pacto inue # ſtigetur. # 262. & 263 Solis maximas declinationes inter ſe æ- # quales eſſe. # 267 Solis maximas declinationes æquales eſ- # ſe diſtantiis polorum Zodiaci à polis # mundi. # 267. & 305 Solſtitialia puncta quæ, & cur ſic dicta. # 23. 260. & 261 Solſtitium quid. # 261 Solſtitia, & Æquinoctia cur ſedes mutent # in Calendario. # 268 Sphæra Archimedis admirabilis. # 17 Sphæra materialis cur inuenta ab Aſtro- # nomis. # 11 Sphæra quo pacto ab orbe differat. # 19</note> <pb file="032" n="33"/> </div> <div xml:id="echoid-div28" type="section" level="1" n="28"> <head xml:id="echoid-head31" style="it" xml:space="preserve">INDEX.</head> <note position="right" xml:space="preserve"> Sphæra quælibet cui parallepipedo ſit # æqualis. # 100 Sphæra recta, & obliqua quid. # 22.ad # 28 Sphęra recta cur perpetuum habeat ęqui # noctium. # 401. & 402 Sphæra obliqua cur bis tãtũ in anno ha- # beat ęquinoctium. # 402 Sphęrę definitio tã Euclidis, quàm Theo # doſij. # 13. ad 17 Sphæræ diuiſio ſecundum accidens. # 22 Sphęrę diuiſio ſecundum fubſtantiam # 19 Sphæræ materialis deſcrip tio. # 17 Sphæræ, & circuli dignitates uariæ. # 77 Sphæræ materialis compoſitio. # 24. & 25 Sphæræ axis quid, & quo modo a diame- # troſphęræ differat. # 17. & 18 Sphæræ materialis inuentores qui. # 17 Sphæræ poli qui, eorumq́ue uaria nomi # na. pag. # 17. & 18 Sphærę ſupeificies conuexa, & tota ſolidi # tas, quomodo inueniatur. # 208. & 209 Sphęralis angulus quid. # 260 Sphæram omnibus corporibus ſibi Iſope- # rimetris, quæ planis ſuperficiebus con # tineantur, circaq́. alias ſphæras circum # ſcriptibilia ſint, maiorem eſſe. # 101 Sphærã omnibus corporibus ſibi Iſoperi # metris, & circa alias ſphæras circũſcri- # ptibilibus, q̃ ſuperficiebus conicis con # tineantur, ita ut latera conica omnia # ſint æqualia, maiorem eſſe. # 102 Sphęrarum cęleſtium numerus, motus va # rij, & ordo. # 42. ad 71 Stella quæuis in quo ſigno, & gradu Zo- # diaci ſit, quo pacto ex tabula ſtellarum # fixarum cognoſcatur. # 182 Stellæ aſcenſio, & deſcenſio quid. # 315 Stellæ cur plures in hyeme appareant, ꝗ̃ # in ęſtate. # 149 Stellę fixę, & planetæ ſupra Solem cur nõ # patiantur Eclipſim & interpoſitionem # terræ inter Solem, & ipſos. # 190 Stellę fixę, cur ſic dictæ. # 21 Stellæ primę magnitudinis quot requirã # tur ut repleant cõcauũ firmamẽti. # 189 Stellæ ſemper apparentes ſemperq laten # tes in qualibet regione quę, & quomõ # cognoſcantur. # 301 & 302 Stellarum numerus quãtus, & quo pacto # ab Aſtronomis inueſtigatus ſit. # 148 Stellarum differentię ſex, quo ad magni # tudinem, & quot in qualibet differen- # tia comprehendantur. # 148 & 149 Stellarum magnitudo, & quo ad diame- # tros, & quo ad ſoliditates, ſi cum terra # comparentur. # 185. ad 191 Stellas non moueri per ſe, ſed ad motum # cæli, in quo ſunt. # 73. ad 76 Stellas omnes eſſe ſphæricas. # 109 Stellis fixis triplicem ineſſe motum # 56 Stellam nouam quæ anno 1572. apparuit # i Caſſiopeia, i Firmamẽto extitiſſe # 193 Subiectum huius ſphærę idem eſſe, quòd # Aſtronomiæ, & quodnam illud ſit. # 12 Superficiem maris ſub ſupeificie terræ, ſi # vtraque compleretur, ęquali ſemper di # ſtantia contineri. # 125. & 126 Superficies cuiuſq. circuli; & cõuexa ſu ꝑ # ficies ſphęrę quo pacto reperiat̃. # 208 T TABVLA conſtellationum 48. cõ- # tinens ſtellarum numerum, & @@- # tum, longitudines, & latitudines, # ac magnitudines. # 151. ad 180 Tabula, qua Aequatoris gradus in horas, # & uiciſſim horæ in gradus permutan- # tur. pag. # 231 Tabula partium Aſſis. # 248 Tabula docens, quot minuta, ſecũda, ter- # tia, & c. vnus grad@ Zodiaci: Et quot gra # uus, Minuta, Secunda, Tertia, & c. totus # Zodiacus complectatur. # 247 Tabula declinationum punctorum Ecli- # pticæ. # 264 Tabula longitudinum, & latitudinem ci- # uitatum præcipuarum. # 285 Tabula differentiarum aſcenſionalium, P # oibus eleuationibus poli. # 340 ad 347 Tabula aſcéſio num rectarum. # 330 & 331 Tabula aſcenſionum obliquarum pro ua # rijs poli altitudinibus. # 341 ad 407 Tabula ſemidiurnorum arcuum pro ua- # rijs latitudinibus. # 408 ad 413</note> <pb file="033" n="34"/> </div> <div xml:id="echoid-div29" type="section" level="1" n="29"> <head xml:id="echoid-head32" style="it" xml:space="preserve">INDEX.</head> <note position="right" xml:space="preserve"> Tabula maximorum dierum, vbi plus ele # uatur pluribus gradibus, quã # 66. 411 Tabula Climatum ſecundũ Veteres. # 426 Tabula Climatum ſecundũ Recentiores. # pag. # 429 Tabulę proportionũ diametrorum ſtella # rum fixarum, & planetarũ ad diametrũ # terrę: Et proportionum magnitudinũ # ſtellarum, & planetarum ad magnitu- # dinem terræ. # 186. ad 187 Tempora quatuor anni quibus quadrãti # bu@ Zodiaci reſpondeant. # 239 Terra quanta ſit cum ſingulis cęlis com- # parata. # 190 Terra cur ſenſui appareat plana. # 114 Terra cur ſola occupet centrum mundi, # & non etiam aqua. # 126 Terram, & aquam vnum globum conſti- # tuere. # 117. ad 134 Terrã cum aqua cõſtituere vnum globũ, # quomodo ſit intelligendum. # 126 Terram in centro mundi eſſe collocatam. # pag. # 135. ad 143 Terram eſſe inſtar centri, & pũcti reſpectu # Firmamenti. # 143. ad 148 # Terram rotundam eſſe, ac ſphæricam. # pag. # 109. ad 114 Terrã in medio mũdi immobilẽ eſſe, & q̃ # ſit huius immobilitatis cã. # 195. ad 198 Terram non eſſe cauam. # 114 Terram Sole eſſe minorem, maiorẽ vero # Luna, qua ratione demonſtretur. # 190 Terræ ambitus, diameter, & ſuperficies # conuexa ſecundum varios. # 211 ad 214 Terræ ambit us quibus vijs inueſtigetur. # pag. # 199. ad 206 Terræ quanta pars dicatur habitabilis ab # auctore. # 423 Terrę maiorem partem eſſe habitabilem, # quàm ab auctore ponitur. # 428 Theoricæ planetarum iu tabulas digeſtæ. # pag. # 464 ad 483 Tractatio figurarum Iſoperimetrarũ con # tinens propoſitiones 18. # 8@. ad 103 Trepidationis motus octauæ ſphæræ quo # modo fiat. # 56 Trepidationis motus in octaua ſphęra # quo indicio deprehenſus ſit. # 62. & 63 Triãgula duo Iſoſcelia ſimilia ſuper inæ- # qualibus baſibus cõſtituta, vtraq ſimul@ # maiora eẽ duobus triãgulis Iſoſcelib@, # vtriuſq. ſimul, quę habeant eaſdẽ baſes # cũ prioribus, ſintq́ue d@ſſimilia quidẽ # inter ſe, at Iſoperimetra prioribus duo # bus nec non quatuor latera inter ſe ha # beant æqualia. # 90 & 91 Triãguli rectanguli proprietas quædam. # pag. # 85 Triangulis duobus Iſoſcelibus datis, quo # rum baſes inæquales ſint, duoq́; latera # vnius æqualia duobus lateribus alte- # rius; ſu ꝗ eiſdẽ baſibus duo alia triãgu- # la Iſoſcelia inter ſe quidẽ ſimilia, prio- # ribus vero Iſoperimetra quo pacto cõ # ſtruantur. pag. # 90 Triangulorum eandem baſim, habentiũ, # quod Iſoſceles eſt, maius eſſe eo, quod # noneſt Iſoſceles. # 88 Triangulorum duorum rectãgulorum ſi # milium proprietas quædam. # 89 Triangulum Iſoſceles alteri nõ Iſoſceli # Iſoperimetrum ſuper eandẽ baſim con # ſtituere. # 87 Triangulum quodcunque cui parallelo- # grammo rectangulo ſit æquale. # 82 Tropici qui ſiut, & quomodo deſcriban- # tur, eorumq́ue varia nomina. # 303 Tropicorũ officia, & vtil@tates. # 307. & 308 Tropicos duos, & duos polares circulos # diſtinguere in cœlo, & in terra quinq; # Zonas. # 308 ad 314 V VAs quodcunq. plus aquæ recipere # ad radices editiſſi mi mõtis, quàm # in cacumine. # 133 Velocitas motus cęli incomprehẽſibilis, # quibuſdam exemplis declaratur. # 216 Venerẽ non poſſe Solẽ eclipſare. # 70. & 7@ Veneris circulum viſualem ſubcen@uplũ # eſſe circuli viſualis Solis. # 70 Veneris diametrũ viſualem ſubdecuplam # eſſe viſualis diametri Solis. # ibid. Venus quando dicatur Lucifer, & quãdo # Heſperus. # 318</note> <pb file="034" n="35"/> </div> <div xml:id="echoid-div30" type="section" level="1" n="30"> <head xml:id="echoid-head33" style="it" xml:space="preserve">INDEX.</head> <note position="right" xml:space="preserve"> Vertex loci. # 23. & 259 Verticalem circulum ſecare cęlũ in hemi # ſphærium boreale, & auſtrale. # 256 Verticales circuli qui. # 221 Verus, & viſus locus aſtri in cęlo quid. # 65 Verus locus ſtellæ in Zodiaco ꝗd, & quo # modo cognoſcatur. # 258 Verus motus ſtellæ, & linea veri motus # quid ſit. # ibidem Verus, & Appatens ortus quid. # 318 Verus, ſiue æꝗnoctialis ortus, & occaſus # quid. # 300 Veſpertinus, ac Matutinus ortus, & occa- # ſus quid. # 318 Viſualis diameter, & circulus aſtri quid. # pag. # 70 Vtilitates Aequatoris, Zodiaci, Coluro- # rũ, Meridiani, Horizõtis, tropicorum, # & polarium circulorum. # Lege # Officia eorundem. Z <emph style="sc">ZEnith</emph>, ſeu vertex loci. 23. & 259 # Zenith loci pofito ſub Aequatore, de # indeinter Aequatorẽ, & tropicorũ Cã # cri, Itẽ ſub Tropico Cãcri, Itẽ inter tro # picum Cancri & circulum arcticũ, Poſt # hæc ſub circulo arctico Rurſus inter # circulum arcticum, & polum, & poſtre- # mo ſub polo quid accidat ratione or- # tus, & occaſus ſiderum. # 414 ad 423 Zenith tãtum diſtare ab Aequatore, quã # ta eſt altitudo poli. # 298. & 299 Zodiacus quid, cur ſic dictus, quare, & à # quo primum inuentus. # 233 Zodiacus cur obliquum habeat ſitum in # cęlo, & ſphæra. # 236 Zodiaci acceptiones variæ. # 252 ad 254 Zodiaci diuiſio in gradus. # 245 Zodiaci initium cur ab Ariete ſumatur. # pag. # 240. ad 242. Zodiaci officia, & vtilitates. # 255 Zodiaci pars borealis, & auſtralis fignaq́ # borealia, & auſtralia. # 251 Zodiaci quadrantes quibus anni tempori # bus reſpondeant. # 239 Zodiaci ſemicirculus aſcendẽns, & deſcẽ # dens. # 243 Zodiaci ſigna cur ab animalibus denomi # nentur. # 234. & 235 Zodiaci ſigna quo ordine dicantur plane # tarum domus. # 244 Zodiaci varia nomina. # 235 Zodiaci latitudo quanta ſit, & cur ei tri- # buatur. # 248. & 249 Zodiaci polos tãtum abeſſe à<unsure/> polis mu<unsure/>n- # di, quanta eſt maxima Solis declinatio # 276. & 305 Zodiaci ſigna, ſeu arcus quomodo ſecun- # dum Aſtronomos oriãtur, & occidant # tam in ſphæra recta, quàm in obliqua. # 323 ad 398. Zodiaci nomen cuius cęli Zodiaco magis # conueniat. # 235 Zodiacus duplex, Mobilis, & fixus, ſeu im- # mobilis. # 52. & 53 Zodiacus cur in 12. ſigna diſtribui ſoleat. # pag. # 237. ad 240 Zodiacus cur in 360. gradus diuidat̃. # 246 Zodiacus quot gradus, Minuta, Secunda, # &c. comprehendat. # 247 Zodiacum in nullo Horizonte vniformi # ter oriri. # 310 Zodiacũ varios angulos cũ quolibet Ho # rizonte conſtituere. # 233. & 320 Zona à Climate quomodo differat. # 428 Zona torrida, tem perata, & frigida quid. # pag. # 309 Zonæ quid, & quibus parallelis conftituã # tur. # 308 Zonæ quinque cœleſ@es, & totidem terre # ſtres. # 308. & 309 Zonæ terreſtres quo pacto cęleftibus ſint # ſuppoſitæ. # 311 Zonam quamuis eſſe eiuſdem latitudinis. # quoad omnes partes, nõ autem eiuſdẽ # longitudinis. # 312 Zonarum varia nomina. # 310 Zonarum latitudines, & lõgitudines quo # modo inueſtigentur. # 312 </note> </div> <div xml:id="echoid-div31" type="section" level="1" n="31"> <head xml:id="echoid-head34" xml:space="preserve">FINIS INDICIS.</head> <pb file="035" n="36"/> <pb file="036" n="37"/> <pb file="037" n="38"/> </div> <div xml:id="echoid-div32" type="section" level="1" n="32"> <head xml:id="echoid-head35" xml:space="preserve">CHRISTOPHORI <lb/>CLAVII BAMBERGENSIS <lb/>EX SOCIETATE IESV,</head> <head xml:id="echoid-head36" style="it" xml:space="preserve">In Sphæram Io ANNIS de Sacro Boſco.</head> <figure> <image file="037-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/037-01"/> </figure> </div> <div xml:id="echoid-div33" type="section" level="1" n="33"> <head xml:id="echoid-head37" style="it" xml:space="preserve">PRAEFATIO.</head> <p> <s xml:id="echoid-s52" xml:space="preserve"><emph style="sc">VAriis</emph> modis, (vt Auctor eſt Proclus Dia <lb/>dochus in Commentarijs, quos in primũ <lb/>librum Euclidis conſcripſit) antiqui Philo-<lb/>ſophi diſciplinas Mathematicas partiti fue <lb/>re: </s> <s xml:id="echoid-s53" xml:space="preserve">Inter quorum omnium diuiſiones ea, <lb/>quæ Pithagoreis adſcribitur, & </s> <s xml:id="echoid-s54" xml:space="preserve">quã ſequũ-<lb/>tur Plato, Ariſtoteles, Boetius, alijq́; </s> <s xml:id="echoid-s55" xml:space="preserve">grauiſ-<lb/>ſimi Philoſophi cum veteres, tum etiam re <lb/>centiores, celeberrima ſemper extitit; </s> <s xml:id="echoid-s56" xml:space="preserve">qua quidem omnes <lb/>diſciplinę Mathematicæ in quatuor præcipua genera, puta <lb/> <anchor type="note" xlink:label="note-037-01a" xlink:href="note-037-01"/> in Arithmeticam, Geometriam, Muſicam, & </s> <s xml:id="echoid-s57" xml:space="preserve">Aſtronomiam <lb/>diſtribuuntur; </s> <s xml:id="echoid-s58" xml:space="preserve">neque id ſine ratione factum eſſe exiſtimandum <lb/>eſt. </s> <s xml:id="echoid-s59" xml:space="preserve">Cum. </s> <s xml:id="echoid-s60" xml:space="preserve">n. </s> <s xml:id="echoid-s61" xml:space="preserve">uniuerſæ facultates Mathematicæ circa quantitatẽ uer <lb/>ſentur, duplex autem ſit quantitas, diſcreta, atque continua; </s> <s xml:id="echoid-s62" xml:space="preserve">Rur <lb/>ſus quantitas diſcreta uel abſolute, ac per ſe, uel comparatione al-<lb/>terius conſiderari poſsit; </s> <s xml:id="echoid-s63" xml:space="preserve">Pari rõne quantitas continua uel ut im-<lb/>mobilis, uel ut mobilis, ſub cognitionẽ noſtrã cadat; </s> <s xml:id="echoid-s64" xml:space="preserve">Iure optimo <lb/>effectũ eſt, ut quatuor præcipuæ Mathematicæ diſciplinæ cõſti-<lb/>tuerẽtur, quæ de duplici quãtitate ſub duplici utriuſq; </s> <s xml:id="echoid-s65" xml:space="preserve">conſidera-<lb/>tione diſputarent, cuiuſmodi ſunt illæ quattuor iam enumeratæ.</s> <s xml:id="echoid-s66" xml:space="preserve"/> </p> <div xml:id="echoid-div33" type="float" level="2" n="1"> <note position="right" xlink:label="note-037-01" xlink:href="note-037-01a" xml:space="preserve">Diuiſio Ma <lb/>thematica-<lb/>r<unsure/>@m diſci-<lb/>plinatum.</note> </div> <p> <s xml:id="echoid-s67" xml:space="preserve"><emph style="sc">Arithmetica</emph> ſiquidem circa quantitatem diſcretam, <lb/>hoc eſt, numerũ abſolute ac per ſe conſideratũ uerſatur, paſsiones <lb/>eius, & </s> <s xml:id="echoid-s68" xml:space="preserve">totã numerorum uim unà cum arte numerãdi diffuſe, ac di <lb/>ligenter inquirens, explicansq́ue. </s> <s xml:id="echoid-s69" xml:space="preserve"><emph style="sc">Geometria</emph> deinde de <lb/>quantitate cõtinua immobili diſſerit, & </s> <s xml:id="echoid-s70" xml:space="preserve">terræ aliarumq́; </s> <s xml:id="echoid-s71" xml:space="preserve">rerũ ma- <pb o="2" file="038" n="39" rhead="Comment in I. Cap. Sphæræ"/> gnitudines metiri docet. </s> <s xml:id="echoid-s72" xml:space="preserve"><emph style="sc">Mvsica</emph> vero circa quantitatem di <lb/>ſcretam, hoc eſt, numerum, facta comparatione cum alio, veſatur, <lb/>ſonorumq́; </s> <s xml:id="echoid-s73" xml:space="preserve">concentus, atq; </s> <s xml:id="echoid-s74" xml:space="preserve">harmoniã conſiderat. </s> <s xml:id="echoid-s75" xml:space="preserve"><emph style="sc">Astrono-<lb/>mia</emph> demũ de quãtitate cõtinua, magnitudineve mobili diſputa <lb/>tionẽ inſtituit, & </s> <s xml:id="echoid-s76" xml:space="preserve">cœli, aſtrorumq́; </s> <s xml:id="echoid-s77" xml:space="preserve">motus inuariabiles perſcrutatur.</s> <s xml:id="echoid-s78" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s79" xml:space="preserve"><emph style="sc">Harvm</emph> aũt quatuor diſciplinarum Mathematicarum (ex qui <lb/>bus quidem oẽs aliæ quouis modo de quantitate agẽtes manant, <lb/>ac propagãtur) latiſsime patẽs eſt Aſtronomia ob multitudinẽ re-<lb/>rũ, quas cõſiderat, & </s> <s xml:id="echoid-s80" xml:space="preserve">obid digniſsima ſimul, ac iucũdiſsima ab om <lb/>nibus ſemper habita eſt; </s> <s xml:id="echoid-s81" xml:space="preserve">vt in nullã alterã ſcientiã plus ſtudij, labo <lb/>ris, ac diligẽtiæ cõtulerint antiqui Philoſophi, quã in hanc vnam <lb/>Aſtronomiã. </s> <s xml:id="echoid-s82" xml:space="preserve">Sed quoniã ſucceſſu tẽporis plurimi ab hac egregia <lb/>diſciplina lõgitudine librorũ, ac difficultate rei perteriti abhorre <lb/>bãt, ita vt pene iã collaberetur; </s> <s xml:id="echoid-s83" xml:space="preserve">Ideo <emph style="sc">Ioannes de</emph> <emph style="sc">Sacro</emph> B<emph style="sc">O <lb/> <anchor type="note" xlink:label="note-038-01a" xlink:href="note-038-01"/> SCO</emph> natione Anglus, egregius ſua tẽpeſtate Philoſophus, ac Ma-<lb/>thematicus, qui floruit circa annũ Domini M.</s> <s xml:id="echoid-s84" xml:space="preserve">CC.</s> <s xml:id="echoid-s85" xml:space="preserve">XXXII. </s> <s xml:id="echoid-s86" xml:space="preserve">volens <lb/>huic malo ſuccurrere, in cõmunẽ ſtudioſorum vtilitatẽ ex probatiſ <lb/>ſimis, ſele ctiſsimisq́; </s> <s xml:id="echoid-s87" xml:space="preserve">Aſtronomis, Ptolemæo, Alphragano, Albate-<lb/>gnio, & </s> <s xml:id="echoid-s88" xml:space="preserve">pleriſq. </s> <s xml:id="echoid-s89" xml:space="preserve">aliis compendiũ quoddã exiguum vniuerſæ Aſtro <lb/>nomię quod eſſet veluti introductio quędã ad ſcriptores Aſtrono <lb/>mię, grauiores, ea, qua potuit, diligẽtia conſcripſit; </s> <s xml:id="echoid-s90" xml:space="preserve">quod quidẽ ad <lb/>noſtra uſq; </s> <s xml:id="echoid-s91" xml:space="preserve">tempora magnũ ſemper in ſcholis omnibus obtinuit <lb/>nomen. </s> <s xml:id="echoid-s92" xml:space="preserve">Hoc igitur opuſculũ uiſum eſt nobis in gratiã ſtudioſorũ <lb/>annotationibus copioſioribus illuſtrare, in quibus conati ſumus, <lb/>quantũ fieri potuit, ſententiã primũ auctoris ſimpli ci narratione <lb/>explanare; </s> <s xml:id="echoid-s93" xml:space="preserve">Deinde ea, quæ ipſe videt̃ omiſiſſe, ſupplere; </s> <s xml:id="echoid-s94" xml:space="preserve">& </s> <s xml:id="echoid-s95" xml:space="preserve">quæ ni-<lb/>mis ſuccincte docuit, lõgiore ſermone dilucidare, inſiſtẽs sẽper ve <lb/>ſtigiis antiquorũ Aſtronomorũ, addentes inſuper obſeruationes <lb/>nõnullas recentiorũ, ut perfectius intelligi poſsint ea, quæ ab aliis <lb/>obſcure dicta ſuere de motibus cœlorum, & </s> <s xml:id="echoid-s96" xml:space="preserve">forma totius mundi.</s> <s xml:id="echoid-s97" xml:space="preserve"/> </p> <div xml:id="echoid-div34" type="float" level="2" n="2"> <note position="left" xlink:label="note-038-01" xlink:href="note-038-01a" xml:space="preserve">Quo tempo <lb/>re loan. de <lb/>Sacro Bo-<lb/>@co florue-<lb/>rit, & cur <lb/>hoc cõpen <lb/>diũ Aſtro-<lb/>nomiæ cõ-<lb/>ſaripſerit.</note> </div> <p> <s xml:id="echoid-s98" xml:space="preserve"><emph style="sc">Vervm</emph> ante quam ad auctorẽ ipſum accedamus interpretan <lb/>dum, operæpretium erit, pauca prius de Aſtronomia in vniuerſum <lb/>præfari, ut paratori aĩo, alacrioriq́; </s> <s xml:id="echoid-s99" xml:space="preserve">ad hanc ſcientiã ſtudioſi acce <lb/>dãt. </s> <s xml:id="echoid-s100" xml:space="preserve">Hæc autẽ in quatuor capita diſtinguemus; </s> <s xml:id="echoid-s101" xml:space="preserve">In primo breuiter <lb/>docebimus, qui nã fuerint primi huius diſciplinæ inuẽtores, & </s> <s xml:id="echoid-s102" xml:space="preserve">qui <lb/>potiſsimũ in ea auctores excelluerint: </s> <s xml:id="echoid-s103" xml:space="preserve">In ſecundo, quibus partibus <lb/>vniuerſa hęc ſcientia Aſtronomia cõtineatur, aperimus: </s> <s xml:id="echoid-s104" xml:space="preserve">In tertio <lb/>de p̃ſtãtia, dignitateq́. </s> <s xml:id="echoid-s105" xml:space="preserve">Aſtronomię diſputabimus: </s> <s xml:id="echoid-s106" xml:space="preserve">In quarto deniq. <lb/></s> <s xml:id="echoid-s107" xml:space="preserve">de eiuſdẽ utilitate, ac neceſsitate in mediũ nonnulla adducemus.</s> <s xml:id="echoid-s108" xml:space="preserve"/> </p> <pb o="3" file="039" n="40" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div36" type="section" level="1" n="34"> <head xml:id="echoid-head38" xml:space="preserve">DEINVENTORIBVS ASTRONOMIÆ</head> <p style="it"> <s xml:id="echoid-s109" xml:space="preserve"><emph style="sc">Nemini</emph> dubium eſſe debet, Aſtronomiæ primos inuentores extitiſſe humani <lb/> <anchor type="note" xlink:label="note-039-01a" xlink:href="note-039-01"/> generis progenitores, ac propagatores, Adamum dico, Noe, Abrahamum, & </s> <s xml:id="echoid-s110" xml:space="preserve">cæteros <lb/>huiuſmodi, a quibus etiam alias omnes diſciplinas honeſtas originem duxiſſe, teſtantur <lb/>æntiquiſſimæ hiſtoriæ. </s> <s xml:id="echoid-s111" xml:space="preserve">Nam vt ſcribit Ioſephus antiquitatum Iudaicarum lib. </s> <s xml:id="echoid-s112" xml:space="preserve">1. </s> <s xml:id="echoid-s113" xml:space="preserve">cap. </s> <s xml:id="echoid-s114" xml:space="preserve">4. <lb/></s> <s xml:id="echoid-s115" xml:space="preserve">oum prædixiſſet Adam filijs ſuis exterminationem rerum omnium, vnam ignis virtute, <lb/>alteram vero aquarum vi, ac multitudine fore venturam, illi pertimeſcentes, ne diſcipli <lb/> <anchor type="note" xlink:label="note-039-02a" xlink:href="note-039-02"/> @a rerum cœleſti um, quàm primi adinuenerunt, dilaberetur ab hominibus, aut ante-<lb/>quam ad notitiam veniret, deperiret, duas fecere columnas, aliam quidem ex lateribus, <lb/>aliam vero ex lapidibus, & </s> <s xml:id="echoid-s116" xml:space="preserve">in ambabus, quæ inuenerant, conſcripſerunt, vt ſi conſtru-<lb/>sta ex lateribus exterminaretur ab imbribus, lapidea permanens præberet hominibus <lb/>ſcripta de rebus cæleſt ibus; </s> <s xml:id="echoid-s117" xml:space="preserve">quàm columnam lapidem refert Ioſephus hucuſque in Sy <lb/>ria con ſeruari ſi vero lapidea columna ab igne conſumeretur, laterita illæſa remane-<lb/>ret, ſcientiamq́. </s> <s xml:id="echoid-s118" xml:space="preserve">aſtrorum mortalibus exhiberet. </s> <s xml:id="echoid-s119" xml:space="preserve">Idem Ioſephus cap. </s> <s xml:id="echoid-s120" xml:space="preserve">8. </s> <s xml:id="echoid-s121" xml:space="preserve">eiuſdem lib. </s> <s xml:id="echoid-s122" xml:space="preserve">affir <lb/>mat, ideo antiquos illos patres tam longam duxiſſe vitam, vt vacare poßent rebus Aſtro <lb/>@omicis. </s> <s xml:id="echoid-s123" xml:space="preserve">ac Geometricis, cuius quidem verba hæc<unsure/> ſunt.</s> <s xml:id="echoid-s124" xml:space="preserve"/> </p> <div xml:id="echoid-div36" type="float" level="2" n="1"> <note position="right" xlink:label="note-039-01" xlink:href="note-039-01a" xml:space="preserve">Inuentores <lb/>primi Aſtro <lb/>nomiæ qui <lb/>fueri@t.</note> <note position="right" xlink:label="note-039-02" xlink:href="note-039-02a" xml:space="preserve">Duæ colum <lb/>nę, in qui-<lb/>bus filij A-<lb/>dam ſcien-<lb/>tias inſcri-<lb/>pſerunt, ne <lb/>diluuio pe-<lb/>rirent, quæ <lb/>fuerint.</note> </div> <p> <s xml:id="echoid-s125" xml:space="preserve"><emph style="sc">Nvllvm</emph> autem ad uitam modernam, & </s> <s xml:id="echoid-s126" xml:space="preserve">annorum breuitatem, qui-<lb/> <anchor type="note" xlink:label="note-039-03a" xlink:href="note-039-03"/> bus nunc uiuimus, uitam comparans antiquorũ, putet falſa, quæ de illis ſunt <lb/>dicta, & </s> <s xml:id="echoid-s127" xml:space="preserve">eo quòd nunc uita tanto non ducatur tempore, credat nequaquam il <lb/>los ad uitæ illius longitudinem perueniſſe. </s> <s xml:id="echoid-s128" xml:space="preserve">Illi nam que, cum eſſent religioſi, <lb/>& </s> <s xml:id="echoid-s129" xml:space="preserve">ab ipſo Deo facti, cumque eis pabula opportuniora ad maiustempus exiſte <lb/>rent præparata, tantorum annorum circulis rite uiuebant. </s> <s xml:id="echoid-s130" xml:space="preserve">Deinde propter <lb/>uirtutes, & </s> <s xml:id="echoid-s131" xml:space="preserve">glorioſas utilitates, quas iugiter perſcrutabantur, id eſt, Aſtrolo-<lb/>giam, & </s> <s xml:id="echoid-s132" xml:space="preserve">Geometriam, Deus eis ampliora uiuendi ſpacia condonauit, quæ non <lb/>ediſcere potuiſſent, niſi ſexcentis uiuerent annis. </s> <s xml:id="echoid-s133" xml:space="preserve">Per tot enim annorum cur-<lb/> <anchor type="note" xlink:label="note-039-04a" xlink:href="note-039-04"/> ricula magnus annus impletur. </s> <s xml:id="echoid-s134" xml:space="preserve">Rurſus in eodom lib. </s> <s xml:id="echoid-s135" xml:space="preserve">cap. </s> <s xml:id="echoid-s136" xml:space="preserve">15. </s> <s xml:id="echoid-s137" xml:space="preserve">Abrahamum uirum <lb/>iuſtum, & </s> <s xml:id="echoid-s138" xml:space="preserve">magnum, in cęleſlibus rebus expertum nominat. </s> <s xml:id="echoid-s139" xml:space="preserve">Et cap. </s> <s xml:id="echoid-s140" xml:space="preserve">16. </s> <s xml:id="echoid-s141" xml:space="preserve">teſtatur, eum <lb/>primum inſtruxiſſe Aegyptios in Arithmetica, & </s> <s xml:id="echoid-s142" xml:space="preserve">Syderum ſcientia. </s> <s xml:id="echoid-s143" xml:space="preserve">Ita enim de eo <lb/>ſcribit. </s> <s xml:id="echoid-s144" xml:space="preserve">Arnhmeticam quoque eis (id oſt, Aegyptijs) contulit, & </s> <s xml:id="echoid-s145" xml:space="preserve">quęde Aſtro-<lb/>logia ſunt, ipſe contradidit. </s> <s xml:id="echoid-s146" xml:space="preserve">Nam ante aduentum Abraham in Aegyptum <lb/>hæc Aegyptii penitus ignorabant. </s> <s xml:id="echoid-s147" xml:space="preserve">A Chaldæis enim hæc plantata noſcuntur <lb/>in Aegypto, unde etiam perueniſſe noſcuntur ae Græcos. </s> <s xml:id="echoid-s148" xml:space="preserve"><emph style="sc">Constat</emph> igi-<lb/>tur, Aflronomiam ſcientiam eſſe antiquiſſimam, cum ante diluuium, immo ſub initium <lb/>mundi extiterit, ut iure optimo cum omnibus alijs artibus, ac diſciplinis de antiquita-<lb/>te poſſit decertare, quandoquidem nullam legimus fuiſſe antiquiorem. </s> <s xml:id="echoid-s149" xml:space="preserve">Hinc fit, ut <lb/>ij auctores, qui in hiſt orijs leguntur fuiße primi Aſtronomiæ inuentores, ipſampe-<lb/>tius iamdiu inuentam, im<unsure/>mo a primordijs mundi exortam illuſtraſſe, nouisq́ue addi-<lb/>tionibus adauxiſſe cenſendi ſint, quàm adinueniſſe; </s> <s xml:id="echoid-s150" xml:space="preserve">& </s> <s xml:id="echoid-s151" xml:space="preserve">ob id primos eos huius diſcipli-<lb/>nę au ctores appellatos eße.</s> <s xml:id="echoid-s152" xml:space="preserve"/> </p> <div xml:id="echoid-div37" type="float" level="2" n="2"> <note position="right" xlink:label="note-039-03" xlink:href="note-039-03a" xml:space="preserve">Cur Deus<unsure/> <lb/>primis pa-<lb/>rentibus tã <lb/>longęuam <lb/>vir<unsure/>am pro-<lb/>rogauerit, <lb/>ex Ioſephi <lb/>ſententia.</note> <note position="right" xlink:label="note-039-04" xlink:href="note-039-04a" xml:space="preserve">Abraha@ <lb/>Aegyptios <lb/>docuit Ari-<lb/>thmeticam. <lb/>& Aſtrono-<lb/>miam.</note> </div> <p style="it"> <s xml:id="echoid-s153" xml:space="preserve"><emph style="sc">Caetervm</emph> cui potiſſimum hæc inuentio, ſeu potius amplificatio Aſtronomiæ <lb/> <anchor type="note" xlink:label="note-039-05a" xlink:href="note-039-05"/> ſit adſcribenda, magna inter auctores fuit ſemper controue: </s> <s xml:id="echoid-s154" xml:space="preserve">fia, & </s> <s xml:id="echoid-s155" xml:space="preserve">aahuc ſub iudice lis <lb/>eſt. </s> <s xml:id="echoid-s156" xml:space="preserve">Quidam enimeam attribuunt Aegyptijs; </s> <s xml:id="echoid-s157" xml:space="preserve">quidam Aßyrijs; </s> <s xml:id="echoid-s158" xml:space="preserve">quidam Babylonijs; </s> <s xml:id="echoid-s159" xml:space="preserve">qui-<lb/>dam uero eam primum ab Aethiopis inuentã fuiſse aſſerunt, eo quod ſub Aequinoctia-<lb/>li circulo degentes ſereniſſimo ſemper cœlo ſruuntiur, ex quo facile ſyderum curſus ob-<lb/>ſeruare poſſunt. </s> <s xml:id="echoid-s160" xml:space="preserve">Non inficiantur tamen hi auctores, Aegyptios eam poſtea magis per-<lb/>ſpicuam, illuſtriorem q́ue reddidiſſe. </s> <s xml:id="echoid-s161" xml:space="preserve">Neque uero deſunt, qui Atlantem huius diſcipli- <pb o="4" file="040" n="41" rhead="Comment. in I. Cap. Sphæræ"/> næ primum inuentorem faciunt, uoluntq́ue inde fabulam illam originem traxiſſe, ip-<lb/>ſum uidelicet humeris ſuis cœlum ſuſtinuiſſe, quòd primus eurſum Solis, & </s> <s xml:id="echoid-s162" xml:space="preserve">Lunæ, <lb/>ſyderumq́ue omnium conuerſiones, rationesq́ue vigore animi, ſolertiaq́ue curaſſet tra-<lb/>dendas hominibus. </s> <s xml:id="echoid-s163" xml:space="preserve">De quo ſic ſcribit Diodorus Siculus lib. </s> <s xml:id="echoid-s164" xml:space="preserve">4. </s> <s xml:id="echoid-s165" xml:space="preserve">Ferunt Atlantẽ Aſtrolo <lb/>giæ fuiſſe peritiſſimum, deq́; </s> <s xml:id="echoid-s166" xml:space="preserve">ſphæra primum inter homines diſputaſſe; </s> <s xml:id="echoid-s167" xml:space="preserve">qua ex <lb/>re uiſus eſt cœlum ſuis humeris ſuſtinere, locum præbente fabulis ſphæræ in-<lb/>uentione. </s> <s xml:id="echoid-s168" xml:space="preserve">De eodem B. </s> <s xml:id="echoid-s169" xml:space="preserve">Auguſt. </s> <s xml:id="echoid-s170" xml:space="preserve">lib. </s> <s xml:id="echoid-s171" xml:space="preserve">18. </s> <s xml:id="echoid-s172" xml:space="preserve">de Ciuit. </s> <s xml:id="echoid-s173" xml:space="preserve">Dei ſic ait. </s> <s xml:id="echoid-s174" xml:space="preserve">Atlas magnus fuiſſe <lb/>Aſtrologus dicitur, unde occaſionem fabula inuenit, ut eum cœlum portare <lb/>confingeretur. </s> <s xml:id="echoid-s175" xml:space="preserve">Vult quoque Euſebius Cæſarienſis in præparatione Euangelica, E-<lb/>noch, & </s> <s xml:id="echoid-s176" xml:space="preserve">Atlantem eſſe unum & </s> <s xml:id="echoid-s177" xml:space="preserve">eundem hominem: </s> <s xml:id="echoid-s178" xml:space="preserve">ſed ex hiſtorijs conſtat, Atlantem <lb/>D C C. </s> <s xml:id="echoid-s179" xml:space="preserve">annis, ut minimum, eſſe iuniorem. </s> <s xml:id="echoid-s180" xml:space="preserve">Cælius Rhodiginus lib. </s> <s xml:id="echoid-s181" xml:space="preserve">18. </s> <s xml:id="echoid-s182" xml:space="preserve">lectionum anti-<lb/>quarum putat, Aſtronomiam primum à Sidonijs propter uſum nauigationis fuiſſe in-<lb/>uentam. </s> <s xml:id="echoid-s183" xml:space="preserve">Sicut enim Geometriæ prima fundamentaiecerunt Aegyptij ob rationem menſu <lb/>randorum agrorum, quam habere non poterant ſine Geometria: </s> <s xml:id="echoid-s184" xml:space="preserve">& </s> <s xml:id="echoid-s185" xml:space="preserve">Phænices ob frequẽ <lb/>tes mercaturas, commerciaq́ue prima Arithmetices rudimenta tradidiſſe exiſtimantur: <lb/></s> <s xml:id="echoid-s186" xml:space="preserve">Ita etiam Sidonij propter aſſiduam nauigationem, qua utebantur, Aſtronomiam prim@ <lb/>inueniſſe creduntur, quoniam ſine hac ſcientia nauigationis uſus conſiſtere minimc po-<lb/>teſt: </s> <s xml:id="echoid-s187" xml:space="preserve">hanc tamen poſtea mirum in modum auxerunt Chaldæi, Perſæ, Indi, Aegyptij, <lb/>Græci, necnon Arabes quamplurimi.</s> <s xml:id="echoid-s188" xml:space="preserve"/> </p> <div xml:id="echoid-div38" type="float" level="2" n="3"> <note position="right" xlink:label="note-039-05" xlink:href="note-039-05a" xml:space="preserve">Qui dican-<lb/>t<unsure/>ur eſſe pri-<lb/>mi inuento <lb/>res Aſtrono <lb/>miæ à ſcri-<lb/>ptoribus.</note> </div> <p style="it"> <s xml:id="echoid-s189" xml:space="preserve">QVIC QVID tandem ſit de primis inuentoribus Aſtronomiæ, clarum eſt, at-<lb/>quecertum, complures inſignes auctores in ea excelluiſſe, è quibus recenſebo duntaxat <lb/> <anchor type="note" xlink:label="note-040-01a" xlink:href="note-040-01"/> magis præcipuos. </s> <s xml:id="echoid-s190" xml:space="preserve">In primis floruit in ea Atlas Promethei frater, rex Mauritaniæ in <lb/>Aegypto natus, e<unsure/>amq́ue tradidit Herculi, qui in hac diſciplina tantum dicitur profeciſ-<lb/>ſe, ut ob doctrinam rerum cæleſtium, qua præditus erat, cælum ab Atlante ſuſceptum <lb/>humeris ſuis ſuſtinuiſſe prædicetur, magnaq́ue eum eße gloria potitum hiſtoriæ teſten-<lb/>tur, quòd ſphæram aſtrorum primus in Græciam tranſtulerit. </s> <s xml:id="echoid-s191" xml:space="preserve">His poſtmodum pluri-<lb/>miinſignes Aſtrologi ſucceſſerunt, ut Anaximander Mileſius, Thales Mileſius, Pytha-<lb/>goras Samius, Eudoxus Cnidius tempore Platonis auditor Aegyptiorum, & </s> <s xml:id="echoid-s192" xml:space="preserve">Chaldæo-<lb/>rum, Callippus, Architas Tarentinus, Euclides Megarenſis, Aratus Solænſis, Timocha-<lb/>res Alexandrinus, Abrachis, qui alio nomine Hipparchus dicitur, licet plerique diuer-<lb/>ſum exiſtiment Abrachim ab Hipparcho, Eratoſthenes Atenienſis, Archimedes Syra-<lb/>cuſanus, Soſigenes, Iulius Cæſar, qui opera Soſigenis annum ad Solis curſum accomo<unsure/>-<lb/>dauit, Andromacus Cretenſis, qui dicitur eſſe inuentor Theoricarum, Proclus Diado-<lb/>chus, Menelaus Romanus, qui & </s> <s xml:id="echoid-s193" xml:space="preserve">Mileus Geometra, Theodoſius Tripolita auctor triũ <lb/>librorum de ſphæricis elementis, Ptolemæus omnium peritiſſimus, Theon Alexandri-<lb/>nus, Pappus Alexandrinus, Albumaſar, Almeon Arabs, Abraham Aueneſre, Al-<lb/>bategnius, Thebith inuentor motus trepidationis in octaua ſphæra, qui anni M C X L. <lb/></s> <s xml:id="echoid-s194" xml:space="preserve">poſt Ptolemæum floruit, Hali, Geber Hiſpalenſis, Alphraganus, Alphonſus rex Hiſpæ <lb/>m<unsure/>iæ, anno Domini M C C L. </s> <s xml:id="echoid-s195" xml:space="preserve">à quo tabulæ Alphonſinæ nomen deſumpſerunt, Geor-<lb/>gius Peurbachius, Ioannes de Regiomonte, Ioannes Vernerus Norimbergenſis, Ioan-<lb/>nes Blanchinus Ferrarienſis, qui etiam tabulas Aſtronomicas compoſuit, Ioannes Stofle-<lb/>rinus, Nicolaus Copernicus, Franciſcus Maurolycus Siculus Abbas, & </s> <s xml:id="echoid-s196" xml:space="preserve">Petrus No-<lb/>mius Salacienſis Luſitanus, & </s> <s xml:id="echoid-s197" xml:space="preserve">alij pene innumeri.</s> <s xml:id="echoid-s198" xml:space="preserve"/> </p> <div xml:id="echoid-div39" type="float" level="2" n="4"> <note position="left" xlink:label="note-040-01" xlink:href="note-040-01a" xml:space="preserve">Varij aucto <lb/>res, qui in <lb/>Aſtrono-<lb/>mia florue <lb/>@@nt.</note> </div> </div> <div xml:id="echoid-div41" type="section" level="1" n="35"> <head xml:id="echoid-head39" xml:space="preserve">DEPARTIBVS ASTRONOMIÆ.</head> <p style="it"> <s xml:id="echoid-s199" xml:space="preserve">VT RECTIVS colligamus, quaſnam partes ſub ſe comprehendat Aſtrono-<lb/> <anchor type="note" xlink:label="note-040-02a" xlink:href="note-040-02"/> mia, non incongrue à nominis explicatione ſumemus exordium. </s> <s xml:id="echoid-s200" xml:space="preserve">Scientia igitur hæc <pb o="5" file="041" n="42" rhead="Ioan. de Sacro Boſco."/> de rebus cæleſtibus, quæ Aſtronomia appellatur, iuxta nominis rationem, etymologiam-<lb/>q́ue nihil aliud ſi gniſicare videtur, quàm aſtrorum rationem, ac legem, ita ut Aſtrono-<lb/>mia idem ſit, quod ſyderum ſcientia. </s> <s xml:id="echoid-s201" xml:space="preserve">Diſſerit enim de ſyderum motibus, motuumq́ue <lb/>certis, & </s> <s xml:id="echoid-s202" xml:space="preserve">perpetuis vicibus, ac legibus, ordine ſtellarum, atque cœlorum ſitu, ac poſitu, or <lb/>tu, & </s> <s xml:id="echoid-s203" xml:space="preserve">occaſu, multitudine, ac magnitudine, diſtantia à terra, & </s> <s xml:id="echoid-s204" xml:space="preserve">à ſe inuicem, mutuo con-<lb/>greſſu, eclipſibus, & </s> <s xml:id="echoid-s205" xml:space="preserve">alijs huiuſmodi. </s> <s xml:id="echoid-s206" xml:space="preserve">Hæc ab alijs appellari ſolet Aſtrologia. </s> <s xml:id="echoid-s207" xml:space="preserve">Hac <lb/>enim tempeſtate pro eadem ſcientia uſurpantur fere Aſtronomia, & </s> <s xml:id="echoid-s208" xml:space="preserve">Aſtrologia, & </s> <s xml:id="echoid-s209" xml:space="preserve"><lb/>idcirco nos quoque hiſce nominibus ſine diſcrimine in his noſtris commentarijs vtemur; <lb/></s> <s xml:id="echoid-s210" xml:space="preserve">quamuis nonnulli Mathematicorum id diſcriminis inter hæc vocabula conſticuendum eſ <lb/> <anchor type="note" xlink:label="note-041-01a" xlink:href="note-041-01"/> ſe uelint, ut Aſtronomia eam doctrinam ſignificet, quæ motus cœlorum, aſtrorumq́ue <lb/>conſiderat; </s> <s xml:id="echoid-s211" xml:space="preserve">Aſtrologia uero illi arti accommodetur, quæ ex conuerſionibus cœlorum, <lb/>& </s> <s xml:id="echoid-s212" xml:space="preserve">coniunctionibus aſtrorum, oppoſitionibusve euentus prædicit futuros, & </s> <s xml:id="echoid-s213" xml:space="preserve">præſenſio-<lb/>nes quaſdam, ſignificationesq́ue ad valetudinem, & </s> <s xml:id="echoid-s214" xml:space="preserve">rem familiarem tuendam accomo-<lb/>datas.</s> <s xml:id="echoid-s215" xml:space="preserve"/> </p> <div xml:id="echoid-div41" type="float" level="2" n="1"> <note position="left" xlink:label="note-040-02" xlink:href="note-040-02a" xml:space="preserve">Aſtrono-<lb/>mia quid.</note> <note position="right" xlink:label="note-041-01" xlink:href="note-041-01a" xml:space="preserve">Aſtrono-<lb/>mia, & A-<lb/>ſtrologia, <lb/>quo pacto <lb/>inter ſe dif <lb/>ferant.</note> </div> <p style="it"> <s xml:id="echoid-s216" xml:space="preserve">DIVIDITVR autem Aſtronomia in Theoricam, ideſt, contemplatricem; </s> <s xml:id="echoid-s217" xml:space="preserve">& </s> <s xml:id="echoid-s218" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-041-02a" xlink:href="note-041-02"/> Practicam, hoc eſt, operantem, & </s> <s xml:id="echoid-s219" xml:space="preserve">agentem. </s> <s xml:id="echoid-s220" xml:space="preserve">Theorica conſiderat uniuerſam mundi ma-<lb/>chinam, ut in ſe eſt, deſcribens conſtitutionem mundi, diuidensq́ue totam mundi compa-<lb/>gem in ætheream, & </s> <s xml:id="echoid-s221" xml:space="preserve">elementarem regionem: </s> <s xml:id="echoid-s222" xml:space="preserve">Deinde inueſtigat numerum, magnitudi-<lb/>nem, & </s> <s xml:id="echoid-s223" xml:space="preserve">motum omnium corporum cæleſtium, ſtellarum omnium, ac planetarum ortus, <lb/>obitusq́ue ſpeculatur: </s> <s xml:id="echoid-s224" xml:space="preserve">Pari ratione omnium conſtellationum, & </s> <s xml:id="echoid-s225" xml:space="preserve">ſignorum figuras, & </s> <s xml:id="echoid-s226" xml:space="preserve">ima <lb/>gines conſiderat, veraque loca tam ſtellarum fixarum, quam errantium, quas Planetas <lb/>vocant, numerorum docet calculo ſupputare: </s> <s xml:id="echoid-s227" xml:space="preserve">Similiter planetarum progreſſus, ſtatus, <lb/>regreſſus, coniunctiones, oppoſitiones unà cum eclipſihus luminarium, Solis uidelicet, ac <lb/>Lunæ, & </s> <s xml:id="echoid-s228" xml:space="preserve">id genus alia propemodum infinita, diligentiſſime inquirit. </s> <s xml:id="echoid-s229" xml:space="preserve">Atque hæc Aſtro <lb/>nomia explicatur partim in Almageſto, ſeu magna conſtructione Ptolemæi, vel etiam in <lb/>Epitome Ioannis regiomontani, in opere Aſtronomino Albategnij, in opuſculo Alphra-<lb/>ni, in Theoricis planetarum Georgij Peurbachij, in reuolutionibus cæleſtibus Nicolai <lb/>Copernici, & </s> <s xml:id="echoid-s230" xml:space="preserve">in aliorum fere innumerabilium auctorum uoluminibus: </s> <s xml:id="echoid-s231" xml:space="preserve">Partim inſtru-<lb/>mentis quamplurimis ab Aſtronomis ſumma induſtria ad hoc inuentis, ut motus cæle-<lb/>ſtes nobis ob oculos ponerent, quale eſt Aſtrolabium uulgare, ſeu planiſphærium Ptole <lb/>mæi, Aſtrolabium Gemmæ F<unsure/>risij catholicum. </s> <s xml:id="echoid-s232" xml:space="preserve">ſeu uniuerſale, Planiſphærium Ioannis <lb/>de Roias uniuerſale quoque, Annulus Aſtronomicus, Quadrans, Torquetum, Radius <lb/>Aſtronomicus, & </s> <s xml:id="echoid-s233" xml:space="preserve">id genus alia: </s> <s xml:id="echoid-s234" xml:space="preserve">Partim denique docetur Theorica Aſtronomia in e@ <lb/>parte, quæ dici ſolet tabularis eo quod per numeros in tabulas digeſtos Aſtronomi cœlo-<lb/>rum motus ſcrutentur quales ſunt tabulæ Alphonſi regis Hiſpaniæ, Ioannis Regiomon-<lb/>tani, Ioannis Blanchini Ferrarienſis, Nicolai Copernici, quæ tabulæ Prutenicæ nuncupæ <lb/>ri ſolent, & </s> <s xml:id="echoid-s235" xml:space="preserve">multorum aliorum.</s> <s xml:id="echoid-s236" xml:space="preserve"/> </p> <div xml:id="echoid-div42" type="float" level="2" n="2"> <note position="right" xlink:label="note-041-02" xlink:href="note-041-02a" xml:space="preserve">Diuiſio A <lb/>ſtronomiæ <lb/>in Theori-<lb/>cam, & Pra <lb/>cticam.</note> </div> <p style="it"> <s xml:id="echoid-s237" xml:space="preserve">PRACTICA vero Aſtronomia, quam alij Iudiciariam, ſeu Prognoſticam, id <lb/>@ſt, Diuinatricem dicunt, omnia iſta ad uſum uitæ humanæ accomodat. </s> <s xml:id="echoid-s238" xml:space="preserve">Contemplatur <lb/>enim complexiones, & </s> <s xml:id="echoid-s239" xml:space="preserve">naturas tum ſignorum, conſtellationumq́ue, tum etiam Plane-<lb/>tarum, reliquarumq́ue ſtellarum, explicatq́ue quænam ſigna ſint calida, quæ frigida, <lb/>quæ temperata, quæ maſculina, quæ fœminina, & </s> <s xml:id="echoid-s240" xml:space="preserve">id genus alia. </s> <s xml:id="echoid-s241" xml:space="preserve">Rurſus ex motibus <lb/>orbium, & </s> <s xml:id="echoid-s242" xml:space="preserve">ſtellarum futuros euentus in hiſce inferiorib{us} prædicit. </s> <s xml:id="echoid-s243" xml:space="preserve">Verum q́uoniam <lb/> <anchor type="note" xlink:label="note-041-03a" xlink:href="note-041-03"/> huic Aſtronomiæ parti multi multa temerarie, ac perperam auſi ſunt adijcere, adeo que <lb/>hanc partem prognoſticam amplificare uoluerunt, ut ſit iam res omnino ſuperſtitioſa, <lb/>e<unsure/>xoſaq́ue, & </s> <s xml:id="echoid-s244" xml:space="preserve">merito ab Eccleſia ſuſpecta habeatur, mirumq́ue in modum à B. </s> <s xml:id="echoid-s245" xml:space="preserve">Auguſtino <lb/>damnata in libris de Doctrina Chriſtiana; </s> <s xml:id="echoid-s246" xml:space="preserve">propterea nihil omnino de ea nobis dicen-<lb/>dum exiſtimo<unsure/>, niſi quòd illam funditus euertunt Ioan. </s> <s xml:id="echoid-s247" xml:space="preserve">Picus Mirandulanus libris 12.</s> <s xml:id="echoid-s248" xml:space="preserve"> <pb o="6" file="042" n="43" rhead="Comment. in 1. Cap. Sphæræ"/> aduerſus Aſtrologos conſcriptis: </s> <s xml:id="echoid-s249" xml:space="preserve">Franciſcus Picus eius nepos in libris de Præn<unsure/>otio@e. <lb/></s> <s xml:id="echoid-s250" xml:space="preserve">Antonius Bernardus Mirandulanus Epiſcopus Caſertanus lib. </s> <s xml:id="echoid-s251" xml:space="preserve">22. </s> <s xml:id="echoid-s252" xml:space="preserve">23. </s> <s xml:id="echoid-s253" xml:space="preserve">& </s> <s xml:id="echoid-s254" xml:space="preserve">24. </s> <s xml:id="echoid-s255" xml:space="preserve">Mono-<lb/>machiæ. </s> <s xml:id="echoid-s256" xml:space="preserve">Michael Medina lib. </s> <s xml:id="echoid-s257" xml:space="preserve">2. </s> <s xml:id="echoid-s258" xml:space="preserve">de recta in Deum fide, cap. </s> <s xml:id="echoid-s259" xml:space="preserve">1. </s> <s xml:id="echoid-s260" xml:space="preserve">& </s> <s xml:id="echoid-s261" xml:space="preserve">Iulius Syrenius in <lb/>libris de Fato.</s> <s xml:id="echoid-s262" xml:space="preserve"/> </p> <div xml:id="echoid-div43" type="float" level="2" n="3"> <note position="right" xlink:label="note-041-03" xlink:href="note-041-03a" xml:space="preserve">Aſtrologia <lb/>iudicia@ia <lb/>res eſt ſu-<lb/>per<unsure/>ſtitioſa.</note> </div> </div> <div xml:id="echoid-div45" type="section" level="1" n="36"> <head xml:id="echoid-head40" xml:space="preserve">DEPRÆSTANTIA ASTRONOMIÆ.</head> <p style="it"> <s xml:id="echoid-s263" xml:space="preserve">CVM ex duobus nob ilitas alicuius ſcientiæ, auctore Ariſtotele, ſumi debeat, nem-<lb/>pe ex præſtantia ſubiecti, de quo agit, & </s> <s xml:id="echoid-s264" xml:space="preserve">ex certitudine demonſtrationum, quibus ea, <lb/>quæ conſiderat, confirmat, (Ait enim, eam ſcientiam eſſe præſtantiorem, nobiliorem-<lb/> <anchor type="note" xlink:label="note-042-01a" xlink:href="note-042-01"/> q́ue, quæ vel circa res præſtantiores uerſatur, vel quæ certior eſt,) quanta ſi@ <lb/>Aſtronomiæ dignitas, ac excellentia, haud obſcure ex vtroque capite cognoſci poteſt. <lb/></s> <s xml:id="echoid-s265" xml:space="preserve">Si namque ſubiectum, ſeu materiam Aſtronomiæ ſpectemus, ſupremum eipropemodum<unsure/> <lb/> <anchor type="note" xlink:label="note-042-02a" xlink:href="note-042-02"/> locum inter reliquas omnes diſciplinas humanas, ſeu lumine naturali acquiſitas, con-<lb/>cedendum eſſe, fateri neceſſe eſt. </s> <s xml:id="echoid-s266" xml:space="preserve">Agit enim hæc ſcientia de corporibus cœleſtibus, quæ <lb/>omnium nobiliſſima ſunt multas ob cauſas. </s> <s xml:id="echoid-s267" xml:space="preserve">P R I M O quidem, quoniam, ſecundum <lb/>philoſophos. </s> <s xml:id="echoid-s268" xml:space="preserve">ſunt ingenerabilia, ac incorruptibilia, omnisq́ue alterationis corrumpen-<lb/>tis expertia, omni denique motu ſubſtantiam eorum aliquo modo variante immutabi-<lb/>lia, cuiuſmodi non ſunt reliqua corpora, de quibus Philoſophus naturalis diſputat. <lb/></s> <s xml:id="echoid-s269" xml:space="preserve">Nam licet elementa, vt vult Ariſtoteles cum philoſophis, ſecundum ſe tota non poſ-<lb/>ſint generari aut corrumpi, ſecundum tamen partes eorùm continuæ ſunt generatio-<lb/>ni, corruptioniq́ue obnoxia. </s> <s xml:id="echoid-s270" xml:space="preserve">S E C V N D O, quia corpora cęleſiia ſunt cauſa omnium <lb/>horum inferiorum, vt placet Ariſt. </s> <s xml:id="echoid-s271" xml:space="preserve">@. </s> <s xml:id="echoid-s272" xml:space="preserve">Meteor. </s> <s xml:id="echoid-s273" xml:space="preserve">vbi ait, Neceſſe eſſe mundum inferiorem <lb/>ſuperioribus lationibus continuari, vt omnis inde virtus deriuetur. </s> <s xml:id="echoid-s274" xml:space="preserve">Item 8. </s> <s xml:id="echoid-s275" xml:space="preserve">Phyſ. </s> <s xml:id="echoid-s276" xml:space="preserve"><lb/>aſſerit, omnia produci mediante motu cœli, ob idq́ue motum cœleſtem, vitam omnium <lb/>@ntium nuncupare non dubitauis. </s> <s xml:id="echoid-s277" xml:space="preserve">Rurſus 2. </s> <s xml:id="echoid-s278" xml:space="preserve">de cœlo affirmat, cœlum in hæc inferio-<lb/>ra agere mediante lumine, & </s> <s xml:id="echoid-s279" xml:space="preserve">motu, Poſtremo 2. </s> <s xml:id="echoid-s280" xml:space="preserve">de Gener. </s> <s xml:id="echoid-s281" xml:space="preserve">& </s> <s xml:id="echoid-s282" xml:space="preserve">corrup. </s> <s xml:id="echoid-s283" xml:space="preserve">teſtatur, pro-<lb/>pter motũ Solis, & </s> <s xml:id="echoid-s284" xml:space="preserve">aliorum planetarum in circulo obliquo, ideſt, in Zodiaco, fierigene-<lb/>rationes, & </s> <s xml:id="echoid-s285" xml:space="preserve">corruptiones in hiſce inferioribus; </s> <s xml:id="echoid-s286" xml:space="preserve">Idemq́ue pleriſque alijs in locis affir-<lb/>mat, cui ferè totus philoſophorum cætus aſtipulatur. </s> <s xml:id="echoid-s287" xml:space="preserve">T E R T I O, quoniam corpo-<lb/>ra cæleſtia ſunt propinquiora nobiliſſimo ac primo enti, puta Deo glorioſo; </s> <s xml:id="echoid-s288" xml:space="preserve">Immo <lb/>ſecundum Auerroem corpus cæleſte eſt mediator, ac ligamentum ſuperiorum cum in-<lb/>ferioribus, & </s> <s xml:id="echoid-s289" xml:space="preserve">locus æternorum, ac diuinorum. </s> <s xml:id="echoid-s290" xml:space="preserve">Omnes etenim philoſophi, ac natio-<lb/>nes, etiam quantumuis barbaræ, in cœlo Deumtanquam in ſede collocant propria. </s> <s xml:id="echoid-s291" xml:space="preserve"><lb/>Quamuis enim Deus non huic isel illi loco ſit alligatus, ſed ubiuis locorum (quod nullis <lb/>alijs conuenit rebus) exiſtat; </s> <s xml:id="echoid-s292" xml:space="preserve">ponitur tamen in cœlo, tanquam in nobiliori mundi parte, <lb/>@bi maxime ſuam omnipotentiam, & </s> <s xml:id="echoid-s293" xml:space="preserve">bonitatem manifeſtat, ut Theologi aſſerunt.</s> <s xml:id="echoid-s294" xml:space="preserve"/> </p> <div xml:id="echoid-div45" type="float" level="2" n="1"> <note position="left" xlink:label="note-042-01" xlink:href="note-042-01a" xml:space="preserve">Aſtrono-<lb/>mię p@æſtã <lb/>tiaex ſub-<lb/>iecto.</note> <note position="left" xlink:label="note-042-02" xlink:href="note-042-02a" xml:space="preserve">Cæleſtia <lb/>corporaom <lb/>nium ſunt <lb/>nobiliſſi-<lb/>ma.</note> </div> <p style="it"> <s xml:id="echoid-s295" xml:space="preserve">QVARTO, ac poſtremo, quia inter alia omnia corpora nobiliſſimum locum, ſis-<lb/>premum uidelicet, poſſident cœleſtia corpora; </s> <s xml:id="echoid-s296" xml:space="preserve">Quo<unsure/> autem corpora ſunt ſuperiora, eo etiã <lb/>nobiliora exiſtimari debent, ut philoſophi omnes fatentur. </s> <s xml:id="echoid-s297" xml:space="preserve">Vt enim terra omnium ele-<lb/>mentorum infimum eſt in ſitu & </s> <s xml:id="echoid-s298" xml:space="preserve">loco; </s> <s xml:id="echoid-s299" xml:space="preserve">ita quoque in dignitate poſtremum exiſtit: </s> <s xml:id="echoid-s300" xml:space="preserve">Cui <lb/>in nobilitate ſuccedit aqua, quia, ſuperiorem occupat locum: </s> <s xml:id="echoid-s301" xml:space="preserve">Deinde ſequitur aer, quo-<lb/>niam ſua leuitate aquam tranſcendit: </s> <s xml:id="echoid-s302" xml:space="preserve">Vltimo ignis principatum inter omnia elementa <lb/>@btinet, cum ſit ſupra omnia collocatus. </s> <s xml:id="echoid-s303" xml:space="preserve">Accedit etiam ad dignitatem corporum cœle-<lb/>ſtium, quod habent accidentia nobiliſſima, nimirum & </s> <s xml:id="echoid-s304" xml:space="preserve">motum, & </s> <s xml:id="echoid-s305" xml:space="preserve">figuram circularem, <lb/>vt ſuo loco oſtendemus, lumen, & </s> <s xml:id="echoid-s306" xml:space="preserve">alia huiuſmodi: </s> <s xml:id="echoid-s307" xml:space="preserve">vt non immerito Ariſtoteles hęc co<unsure/>r-<lb/>pora videatur duina nuncupaſſe.</s> <s xml:id="echoid-s308" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">Aſtrono-<lb/>miæ digni-<unsure/></note> <p style="it"> <s xml:id="echoid-s309" xml:space="preserve">QVOD ſi modum d@monſtrandi, quo vtitur Aſtronomia, conſideremus, nemo @@ <pb o="7" file="043" n="44" rhead="Ioan. de Sacro Boſco."/> gabit, om@es naturales diſciplinas ab hac ſcientia longe ſuperari. </s> <s xml:id="echoid-s310" xml:space="preserve">Adhibet enim ad <lb/> <anchor type="note" xlink:label="note-043-01a" xlink:href="note-043-01"/> ea confirmanda, de quibus agit, demonſtrationes efficaciſſimas, Geometricas nimi-<lb/>rum, & </s> <s xml:id="echoid-s311" xml:space="preserve">Arithmeticas, quæ ex ſententia omnium philoſophe<unsure/>rum primum certitudi <lb/>nis gradum obtinent. </s> <s xml:id="echoid-s312" xml:space="preserve">Quare non ſine ratione ex vt<unsure/>roque capite, nempe nobilitate <lb/>ſubiecti, & </s> <s xml:id="echoid-s313" xml:space="preserve">certitudine demonſtrandi, voluit Ptolemaus ad initium Almageſti. <lb/></s> <s xml:id="echoid-s314" xml:space="preserve">Aſtronomiam ſimpliciter inter reliquas ſcientias eße primam. </s> <s xml:id="echoid-s315" xml:space="preserve">Ait enim ph@loſo-<lb/>phiam naturalem & </s> <s xml:id="echoid-s316" xml:space="preserve">Metaphyſicam, ſi modum demonſtrandi illarum ſpectemus appel-<lb/>landas potius eſſe coniecturas, quam ſcientias, propter multitudinem, & </s> <s xml:id="echoid-s317" xml:space="preserve">diſcrepantiam <lb/>opinio@um.</s> <s xml:id="echoid-s318" xml:space="preserve"/> </p> <div xml:id="echoid-div46" type="float" level="2" n="2"> <note position="right" xlink:label="note-043-01" xlink:href="note-043-01a" xml:space="preserve">tas ex m@-<lb/>do demon-<lb/>ſtrandi.</note> </div> </div> <div xml:id="echoid-div48" type="section" level="1" n="37"> <head xml:id="echoid-head41" xml:space="preserve">DE VTILITATE ASTRONOMIÆ.</head> <p style="it"> <s xml:id="echoid-s319" xml:space="preserve">QV ANT A ſit huius præſtantiſſimæ ſcientiæ vtilitas, immo vero neceſſitas, vix <lb/>explicari poteſt; </s> <s xml:id="echoid-s320" xml:space="preserve">Ad omnes ſiquidem diſciplinas videtur Aſtronomia viam quodam-<lb/> <anchor type="note" xlink:label="note-043-02a" xlink:href="note-043-02"/> modo parare, & </s> <s xml:id="echoid-s321" xml:space="preserve">aditum monſtrare ſecurum. </s> <s xml:id="echoid-s322" xml:space="preserve">Conducit enim in primis plurimum ſacræ <lb/>Theologiæ. </s> <s xml:id="echoid-s323" xml:space="preserve">Nam conſideratione orbium cœleſtium, ac motuum ſemper eodem modo, & </s> <s xml:id="echoid-s324" xml:space="preserve"><lb/>inuariabiliter ſeſe habentium, cognoſcitur magnitudo, exceli<unsure/>entiaq́; </s> <s xml:id="echoid-s325" xml:space="preserve">creatoris ipſorum: <lb/></s> <s xml:id="echoid-s326" xml:space="preserve">Vt non immerito Ptolemæus in principio Almageſti, ſecundum traditionem Arabum <lb/>aſſeruerit, hanc vnam ſcientiam eße viam, ac ſemitam ad ſciendum Deum altiſſimum.</s> <s xml:id="echoid-s327" xml:space="preserve"/> </p> <div xml:id="echoid-div48" type="float" level="2" n="1"> <note position="right" xlink:label="note-043-02" xlink:href="note-043-02a" xml:space="preserve">Aſtr@no-<lb/>miæ utilitas <lb/>ad Theolo-<lb/>giam.</note> </div> <p style="it"> <s xml:id="echoid-s328" xml:space="preserve">A qua ſententia non abeſt D. </s> <s xml:id="echoid-s329" xml:space="preserve">Paulus ad Rom. </s> <s xml:id="echoid-s330" xml:space="preserve">1. </s> <s xml:id="echoid-s331" xml:space="preserve">vbi ait, Inuiſibilia Dei à crea-<lb/>tura mundi@ perea, quæ facta ſunt, intellecta conſpiciuntur, &</s> <s xml:id="echoid-s332" xml:space="preserve">c. </s> <s xml:id="echoid-s333" xml:space="preserve">Quo in loco <lb/>cum omnes res creatas, tum maxime videtur corpora cœleſtia intellexiſſe. </s> <s xml:id="echoid-s334" xml:space="preserve">Hæc ete-<lb/>nim ſua pulchritudine, magnitudine, & </s> <s xml:id="echoid-s335" xml:space="preserve">multitudine, ſuorumq́ue motuum, & </s> <s xml:id="echoid-s336" xml:space="preserve">influxuũ <lb/>mira varietate, ac ſtabilitate perpetua, mirum in modum Dei glorioſi bonitatem, <lb/>ſapientiam, ac prouidentiam commendant, atque in eius cognitionem, amorem, ac <lb/>admirationem maxime nos inducunt; </s> <s xml:id="echoid-s337" xml:space="preserve">Quod egregie teſtatur regius prophet<unsure/>a Dauid, <lb/>c um dicit. </s> <s xml:id="echoid-s338" xml:space="preserve">Cęli enarrant gloriam Dei, & </s> <s xml:id="echoid-s339" xml:space="preserve">opera manuum eius ennunciat fir<unsure/>ma-<lb/>mentum. </s> <s xml:id="echoid-s340" xml:space="preserve">Item. </s> <s xml:id="echoid-s341" xml:space="preserve">Quoniam uidebo cęlos tuos, operadigitorum tuo@um, Lunam <lb/>& </s> <s xml:id="echoid-s342" xml:space="preserve">ſtellas, quæ tu fundaſti. </s> <s xml:id="echoid-s343" xml:space="preserve">Cui ſententiæ fauet id, quod ſcriptum eſt Sap. </s> <s xml:id="echoid-s344" xml:space="preserve">cap. </s> <s xml:id="echoid-s345" xml:space="preserve">13. <lb/></s> <s xml:id="echoid-s346" xml:space="preserve">vbi de corporibus cæleſtibus ita legitur. </s> <s xml:id="echoid-s347" xml:space="preserve">Qui horum pulchru@dine delectati Deos <lb/>putauerunt, ſciant, quanto his crcator eorum ſpecioſior eſt; </s> <s xml:id="echoid-s348" xml:space="preserve">A magnitudine <lb/>enim ſpeciei, & </s> <s xml:id="echoid-s349" xml:space="preserve">creaturæ cognoſcibiliter potera@ creator horum u@deri. </s> <s xml:id="echoid-s350" xml:space="preserve">Ex <lb/>quo factum eſt, vt Aſironomia, quæ de præſtantiſſimis iſtis corporibus diſputat à ple-<lb/>riſque Theologia naturalis uocetur.</s> <s xml:id="echoid-s351" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s352" xml:space="preserve">INSERVIT etiam Metaphyſicæ hæc diſciplina, quia auctoritate Aſtrologorum <lb/> <anchor type="note" xlink:label="note-043-03a" xlink:href="note-043-03"/> Ariſtoteles lib. </s> <s xml:id="echoid-s353" xml:space="preserve">12. </s> <s xml:id="echoid-s354" xml:space="preserve">Meiaphyſices ex numero orbium collegit numerum in elligentia-<lb/>rum; </s> <s xml:id="echoid-s355" xml:space="preserve">Pari ratione ex motibus orbium cœleſtium virtus & </s> <s xml:id="echoid-s356" xml:space="preserve">ſubſtantia intelligenti<unsure/>arum, <lb/>quæ illos mouent, maxime inueſtigari, ac percipi poteſt.</s> <s xml:id="echoid-s357" xml:space="preserve"/> </p> <div xml:id="echoid-div49" type="float" level="2" n="2"> <note position="right" xlink:label="note-043-03" xlink:href="note-043-03a" xml:space="preserve">Aſtrono-<lb/>mię utilitas <lb/>ad Meta-<lb/>phyſicam. <lb/>Phyſicam, <lb/>Medicinã, <lb/>Poeticã, & <lb/>Nauticam.</note> </div> <p style="it"> <s xml:id="echoid-s358" xml:space="preserve">NON parum quoque confert hæc ſcientia ad naturalem philoſophiam, quoniam <lb/>multa deſumit philoſophus ab Aſtronomis inuenta, ac demonſirata, vt videre eſt in <lb/>2. </s> <s xml:id="echoid-s359" xml:space="preserve">lib. </s> <s xml:id="echoid-s360" xml:space="preserve">de cælo, & </s> <s xml:id="echoid-s361" xml:space="preserve">alijs libris Ariſtotelis. </s> <s xml:id="echoid-s362" xml:space="preserve">Deinde quia ex motu cæleſti inuariabili inueſtiga <lb/>@it Ariſtoteles 8. </s> <s xml:id="echoid-s363" xml:space="preserve">Phyſ. </s> <s xml:id="echoid-s364" xml:space="preserve">primum motorem æternum, omnisq́ mutationis expertem.</s> <s xml:id="echoid-s365" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s366" xml:space="preserve">MEDICINAE vero adeo conducit Aſtronomia, vt Galenus Medicorum prin-<lb/>ceps ægrot<unsure/>os moneat, ne ſe committant manibus medicorum Aſtrologiam ignorantium: <lb/></s> <s xml:id="echoid-s367" xml:space="preserve">Nam, ait medicamenta parum, aut nihil proſunt temporibu@ incongruis exh@b@ta; </s> <s xml:id="echoid-s368" xml:space="preserve">Immo<unsure/> <lb/>vero ſæpenumero nocere ſolent: </s> <s xml:id="echoid-s369" xml:space="preserve">Hæc autem tempora ex planetarum duntaxat motibus, <lb/>qui ad Aſtronomum pertinent, cognoſci poſſunt.</s> <s xml:id="echoid-s370" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s371" xml:space="preserve">QVID porro poetæ efficerent, ſi hac præclara diſciplina eßent prorſus deſtituti@@ <lb/>Nam quid eorum poemata, aut ſcripta præclari, aut egregij habent, quod aſtrorum <pb o="8" file="044" n="45" rhead="Comment. in 1. Cap. Sphæræ"/> motibus, ortu & </s> <s xml:id="echoid-s372" xml:space="preserve">occaſu ſignorum, ac ſtellarum non ſit ref<unsure/>ertum? </s> <s xml:id="echoid-s373" xml:space="preserve">Adde quod nem@ <lb/>antiquorum poemata intelliget, niſi prius optime in Aſtronomiæ ſtudio fuerit uer-<lb/>ſatus.</s> <s xml:id="echoid-s374" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s375" xml:space="preserve">ARS quoque Nautica tantum humano generi utilis, ac neceſſaria, nulla ratione fi <lb/>nes ſuos abſque præſidio Aſi<unsure/>ronomiæ digne poteſt tueri, ut ingenue fatentur omnes Nau <lb/>ticæ artis ſcriptores.</s> <s xml:id="echoid-s376" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s377" xml:space="preserve">ACCEDIT etiam, quod uiris in eccleſiaſtica dignitate conſtitutis perneceſſa-<lb/> <anchor type="note" xlink:label="note-044-01a" xlink:href="note-044-01"/> ria eſt Aſtronomia, teſte B. </s> <s xml:id="echoid-s378" xml:space="preserve">Au<unsure/>guſtino, ad congreſſus, oppoſitionesq́ue luminarium, ad <lb/>mobilia feſta, & </s> <s xml:id="echoid-s379" xml:space="preserve">id genus alia decus, & </s> <s xml:id="echoid-s380" xml:space="preserve">ſtatum Eccleſiæ reſpicientia, accuratius diſcu-<lb/>tienda; </s> <s xml:id="echoid-s381" xml:space="preserve">Ob cuius Aſtronomiæ neglectum factum eſt, ut hactenus uſque ad annum Do <lb/>mini M. </s> <s xml:id="echoid-s382" xml:space="preserve">D L X X X I I I. </s> <s xml:id="echoid-s383" xml:space="preserve">à uera ſacri Paſchatis obſeruatione, aliarumq́ue celebri-<lb/>tatum mobilium tantum plerumque exorbitauerimus, ut Iudæi, Tureæ, & </s> <s xml:id="echoid-s384" xml:space="preserve">cæteræ gen-<lb/>tes mirum in modum ignorantiæ nos arguerint; </s> <s xml:id="echoid-s385" xml:space="preserve">Quod quidem plurimi, ac grauiſſimi <lb/>Mathematici ſæpius, ac quidem uehementer deplorarunt. </s> <s xml:id="echoid-s386" xml:space="preserve">Cui tamen malo Nicolaus V. <lb/></s> <s xml:id="echoid-s387" xml:space="preserve">Leo X. </s> <s xml:id="echoid-s388" xml:space="preserve">& </s> <s xml:id="echoid-s389" xml:space="preserve">plerique alij Pontifices maximi dicuntur ſæpe remedium uoluiſſe adhibe-<lb/>re, ſi modo tunc temporis eximiorum, ac præſtantium Aſtronomorum eis copia fuiſſet, <lb/>quibus tute curam emendandi Calendarij, corrigendiq́ue potuiſſent committere. </s> <s xml:id="echoid-s390" xml:space="preserve">Ha-<lb/>bet etenim Aſtronomia inter cęteras propemodum infinitas, hanc etiam inſignem utili-<lb/>tatem, quod anni certas metas, & </s> <s xml:id="echoid-s391" xml:space="preserve">partium anni iuſtam deſcriptionem, notatis diligen-<lb/>ter æquinoctijs, & </s> <s xml:id="echoid-s392" xml:space="preserve">ſolſtitijs veris, demonſtrat, menſtrua ſpacia definit, dierum noctium-<lb/>q́ue uices, & </s> <s xml:id="echoid-s393" xml:space="preserve">interualla, & </s> <s xml:id="echoid-s394" xml:space="preserve">quantitates accuratiſſime metitur, atque diſtinguit. </s> <s xml:id="echoid-s395" xml:space="preserve">Diui-<lb/>na autem bonitate, ac prouidentia factum tandem eſt, ut noſtris temporibus Grego-<lb/>@ius X I I I. </s> <s xml:id="echoid-s396" xml:space="preserve">Pontifex Optimus Maximus, vltimam manum Calendarij Romani corre-<lb/>ctioni appoſuerit, æquinoctiaq́ue, ac ſolſtitia ad tempora concilij Nicæni reduxerit. </s> <s xml:id="echoid-s397" xml:space="preserve"><lb/>Quo fit, ut ſacroſanctum Paſcha, cum reliquis feſtis mobilibus in poſterum recte ſe<unsure/>m-<lb/>per iuxta decreta Sanctorum Patrum, ac Romanorum Pontificum ſimus celebraturi. </s> <s xml:id="echoid-s398" xml:space="preserve"><lb/>Qua in re & </s> <s xml:id="echoid-s399" xml:space="preserve">ego annis non paucis, iußu eiuſdem Summi Pontificis, non parum ſtudij, <lb/>atque operæ collocaui.</s> <s xml:id="echoid-s400" xml:space="preserve"/> </p> <div xml:id="echoid-div50" type="float" level="2" n="3"> <note position="left" xlink:label="note-044-01" xlink:href="note-044-01a" xml:space="preserve">Aſtro<unsure/>no <lb/>@ia neceſ-<lb/>ſaria eſt ꝑ <lb/>ſonis eccl<unsure/>e <lb/>ſ<unsure/>iaſticis.</note> </div> <p style="it"> <s xml:id="echoid-s401" xml:space="preserve">EST præterea Aſtronomia uelutifons, & </s> <s xml:id="echoid-s402" xml:space="preserve">origo Coſmographiæ; </s> <s xml:id="echoid-s403" xml:space="preserve">quoniam ſine hu-<lb/> <anchor type="note" xlink:label="note-044-02a" xlink:href="note-044-02"/> ius ſcientię auxilio deſcriptio globi terreni, doctrina de locorum interuallis, deq́ue re-<lb/>gionum deſignatione, & </s> <s xml:id="echoid-s404" xml:space="preserve">cætera huiuſmodi, quæ mirabile ornamentum, ſimul, ac utilita-<lb/>tem omnibus rebuspub. </s> <s xml:id="echoid-s405" xml:space="preserve">afferunt, nullo pacto poteſt perfecte haberi.</s> <s xml:id="echoid-s406" xml:space="preserve"/> </p> <div xml:id="echoid-div51" type="float" level="2" n="4"> <note position="left" xlink:label="note-044-02" xlink:href="note-044-02a" xml:space="preserve">Aſtrono-<lb/>miæ utili-<lb/>tas ad Coſ-<lb/>m<unsure/>ographiã.</note> </div> <p style="it"> <s xml:id="echoid-s407" xml:space="preserve">OMITTO, quod hæc ſcientia ſumme eſt neceſſaria ad reipub. </s> <s xml:id="echoid-s408" xml:space="preserve">adminiſtratio-<lb/> <anchor type="note" xlink:label="note-044-03a" xlink:href="note-044-03"/> nem, ut ad agriculturam, ad bella gerenda, & </s> <s xml:id="echoid-s409" xml:space="preserve">alia huiuſmodi; </s> <s xml:id="echoid-s410" xml:space="preserve">Cuius rei multa no<unsure/>-<lb/>bis exempla hiſtoriæ proponunt. </s> <s xml:id="echoid-s411" xml:space="preserve">Sulpitius enim ob ſcientiam eclipſis lunaris, quæ ſo-<lb/>lum in Aſtrologia edocetur, ingenti metu exercitum totum liberaſſe perhibetur: <lb/></s> <s xml:id="echoid-s412" xml:space="preserve">Quod idem de Pericle Athenienſe, necnon Dione Siciliæ rege teſtantur hiſtorici. </s> <s xml:id="echoid-s413" xml:space="preserve">At <lb/>vero Nicias Athenienſium imperator ob huius rei ignorationem metu perculſus <lb/>claſſem portu educere non eſt auſus, haud par@o reipub. </s> <s xml:id="echoid-s414" xml:space="preserve">Athenienſis incommodo, <lb/>& </s> <s xml:id="echoid-s415" xml:space="preserve">iactura.</s> <s xml:id="echoid-s416" xml:space="preserve"/> </p> <div xml:id="echoid-div52" type="float" level="2" n="5"> <note position="left" xlink:label="note-044-03" xlink:href="note-044-03a" xml:space="preserve">Aſtrono <lb/>@iæ utili-<lb/>@as ad reip. <lb/>@dminiſtra-<lb/>tionem.</note> </div> <p style="it"> <s xml:id="echoid-s417" xml:space="preserve">NEQVE uero prætereundum eſt, quod non ita multos ante annos (ut refert 10. <lb/></s> <s xml:id="echoid-s418" xml:space="preserve">de Roias in epiſtola ad Carolum V. </s> <s xml:id="echoid-s419" xml:space="preserve">Imperatorem, quam commentarijs ſuis in plani-<lb/>ſphærium uniuerſale præfixit) Colonus ductor exercitus Ferdinandi regis Hiſpa-<lb/>niarum ſuperioribus annis, quibus nouus orbis Indiæ Occidentalis detectus eſt atque <lb/>exploratus, apud Iamaicam inſulam totum exercitum Chriſtianorum ab imminente <lb/>morte huius diuinæ diſciplinæ auxilio eripuit. </s> <s xml:id="echoid-s420" xml:space="preserve">Cum enim uniuerſus Hiſpanorum <lb/>exercitus in ultimo iam uitæ periculo eſſet conſtitutus, neque Dux à Iamaicenſibus <lb/>alimenta ullo poßet modo impetrare, (Hac enim ratione ſperabant Barbari exerci- <pb o="9" file="045" n="46" rhead="Ioan. de Sacro Boſco."/> tum Chriſtianorum facile ſine armis poſſe expugnari) rectoribus Iamaienſium nun <lb/>ciari iubet, ni ſibi, ſuisq́ue omnibus neceſſaria ad victum ſubminiſtrent, plurima illis <lb/>ac ſuprema mala imminere: </s> <s xml:id="echoid-s421" xml:space="preserve">In cuius rei teſtimonium non mulio poſt Lunam eos ob-<lb/>ſcuratam eße viſuros, quam quidem ipſe in Aſtronomia eximie verſatus iamiam de-<lb/>fecturam cognoſcebat. </s> <s xml:id="echoid-s422" xml:space="preserve">Contempſerunt quidem primo Barbari iußa Ducis Chriſtia-<lb/>ni, ac minas: </s> <s xml:id="echoid-s423" xml:space="preserve">At cum ad conſtitutum ab ipſo tempus Lunam deficere ſenſim conſpice-<lb/>rent, neque huius rei cauſam intelligerent, illius tum verbis primum fidem præ-<lb/>bentes, & </s> <s xml:id="echoid-s424" xml:space="preserve">commeatum Chriſtianis affatim ſubminiſtrarunt, & </s> <s xml:id="echoid-s425" xml:space="preserve">ad ipſius Ducis, cæte-<lb/>rorumq́; </s> <s xml:id="echoid-s426" xml:space="preserve">militum pedes prouoluti, vti ſibi ignoſcerent, obnixe efflagitarunt. </s> <s xml:id="echoid-s427" xml:space="preserve">Taceo <lb/>multa alia exempla ſimilia; </s> <s xml:id="echoid-s428" xml:space="preserve">vt non immerito Ptolemæus aſſeruiſſe videatur, op@imum <lb/>Aſtrologum multum malum prohibere, & </s> <s xml:id="echoid-s429" xml:space="preserve">ſapientem Aſtronomum multum bonum ho-<lb/>minibus poſſe procurare.</s> <s xml:id="echoid-s430" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s431" xml:space="preserve"><emph style="sc">Ad</emph> omnes has laudes accedit, quod ſemper hæc ſcientia de rebù<unsure/>s cęleſtibus, ni <lb/> <anchor type="note" xlink:label="note-045-01a" xlink:href="note-045-01"/> mirum Aſtronomia, habita fuerit in magno pretio. </s> <s xml:id="echoid-s432" xml:space="preserve">Thales etiam Mileſius ita hac ar-<lb/>te delectabatur, vt pauper omnino philoſopharetur, nullamq́ue rei familiaris curam <lb/>habere videretur; </s> <s xml:id="echoid-s433" xml:space="preserve">qui cum ab ignauis, vt fieri ſolet, quaſi ſui ipſius eſſet oblitus, de <lb/>@ideretur, edoctus miram illius anni fertilitatem ab Aſtrologia, omnes in agro Mi-<lb/>leſio oleas, antequam florere cœpiſſent, coemiſſe dicitur, ditiſſimusq́ue euaſiſſe; </s> <s xml:id="echoid-s434" xml:space="preserve">Qua in <lb/>@e oſtendere Milesijs volebat, prudentem virum, & </s> <s xml:id="echoid-s435" xml:space="preserve">ſapientem, pecuniam, ſi velit, fa-<lb/>cere poſſe.</s> <s xml:id="echoid-s436" xml:space="preserve"/> </p> <div xml:id="echoid-div53" type="float" level="2" n="6"> <note position="right" xlink:label="note-045-01" xlink:href="note-045-01a" xml:space="preserve">Aſtrone<unsure/>-<lb/>mia apud <lb/>veteres in <lb/>magno pre <lb/>tio fuit.</note> </div> <p style="it"> <s xml:id="echoid-s437" xml:space="preserve"><emph style="sc">Sillentio</emph> prætermitto, quod apud Aegyptios nulli ſaceraotes, nulliq́; </s> <s xml:id="echoid-s438" xml:space="preserve">Pon-<lb/>tifices creabantur, niſi Mathematici; </s> <s xml:id="echoid-s439" xml:space="preserve">(Ita enim Aſtrologos per Antonomaſiam nomi-<lb/>nabant) Nulli apud Lacedæmonios regibus aſſidebant, niſi Mathematici; </s> <s xml:id="echoid-s440" xml:space="preserve">Nulli apud <lb/>Perſ{as} ſalutabantur Reges, niſi Mathematici; </s> <s xml:id="echoid-s441" xml:space="preserve">Immo princeps philoſophorum Ariſtote-<lb/>les ad Alexandrum Magnum ita ſcripſiſſe fertur; </s> <s xml:id="echoid-s442" xml:space="preserve">(quod tamen abſit ab homine Chri-<lb/>ſtiano) O rex clementiſſime nec ſurgas, nec ſedeas, nec cibum ſumas, aut potum, peni-<lb/>tusq́; </s> <s xml:id="echoid-s443" xml:space="preserve">nihilſine periti Mathematici conſilio, ſi fieri poteſt, facias.</s> <s xml:id="echoid-s444" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s445" xml:space="preserve"><emph style="sc">Hac</emph> diſciplina Dionyſium Areopagitam ob eclipſim Solis factam in plenilunio, <lb/>quæ naturæ viribus tunc fieri non poterat, Domini paſſionem denunciaße legimus, <lb/>quando exclamauit, Aut Deus naturæ patitur, a@t mundi machina diſſoluetur. </s> <s xml:id="echoid-s446" xml:space="preserve">Vn-<lb/>de paulo poſt, prædicatione Pauli Apoſtoli ad Chriſti fidem eſt conuerſus. </s> <s xml:id="echoid-s447" xml:space="preserve">Hanc, ſi <lb/>Ioſepho credimus, Abraham primus Aegyptijs tradidit ſacerdotibus: </s> <s xml:id="echoid-s448" xml:space="preserve">hac populi Dei <lb/>ductor ille eximius Moyſes excelluit, vt teſtatur B. </s> <s xml:id="echoid-s449" xml:space="preserve">Steph. </s> <s xml:id="echoid-s450" xml:space="preserve">in Actis Apof<unsure/>tolorum dicens, <lb/>eum fuiße inſtructum in omni ſapientia Aegyptiorum, quæ quidem potiſſimum in <lb/>Aſtronomia conſiſtebat.</s> <s xml:id="echoid-s451" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s452" xml:space="preserve"><emph style="sc">His</emph> omnibus laudibus adde, nullam eſſe perfectionem, qua magis delectati ſint <lb/> <anchor type="note" xlink:label="note-045-02a" xlink:href="note-045-02"/> maximi quique Reges, & </s> <s xml:id="echoid-s453" xml:space="preserve">Imperatores, quàm Aſtronomia: </s> <s xml:id="echoid-s454" xml:space="preserve">Fuit enim illis hæc diſci-<lb/>plina familiariſſima, cuius rei teſtes ſunt tam qui priſcis ſeculis vixerunt, quàm <lb/>qui noſtro ſeculo. </s> <s xml:id="echoid-s455" xml:space="preserve">Nam fuit iſtud ſtudium Aſtronomicum ſummæ curæ Iulio Cæſari <lb/>Romanorum Imperatori, qui vt hiſtoriæ perhibent, ex Aegypto ſecum adduxit Soſi-<lb/>genem Mathematicum inſignem & </s> <s xml:id="echoid-s456" xml:space="preserve">peritum, cuius opera plurimum eſt vſus in ordina-<lb/>tione anni ad curſum Solis; </s> <s xml:id="echoid-s457" xml:space="preserve">atque ab eo tempore cæperunt artęs Mathematicæ in Ita <lb/>lia diligentius coli. </s> <s xml:id="echoid-s458" xml:space="preserve">Hic Cæſar tantum eſt hoc ſtudio delectatus, vt ipſemet de ſeipſo <lb/>apud Lucanum dixerit.</s> <s xml:id="echoid-s459" xml:space="preserve"/> </p> <div xml:id="echoid-div54" type="float" level="2" n="7"> <note position="right" xlink:label="note-045-02" xlink:href="note-045-02a" xml:space="preserve">Aſtrono-<lb/>mia ſemper <lb/>delectati. <lb/>ſunt Reges, <lb/>& Impera-<lb/>tores.</note> </div> <p> <s xml:id="echoid-s460" xml:space="preserve">. </s> <s xml:id="echoid-s461" xml:space="preserve">. </s> <s xml:id="echoid-s462" xml:space="preserve">. </s> <s xml:id="echoid-s463" xml:space="preserve">. </s> <s xml:id="echoid-s464" xml:space="preserve">. </s> <s xml:id="echoid-s465" xml:space="preserve">media inter prælia ſemper <lb/>Stellarum, cęliq́; </s> <s xml:id="echoid-s466" xml:space="preserve">plagis, ſuperisq́; </s> <s xml:id="echoid-s467" xml:space="preserve">vacaui.</s> <s xml:id="echoid-s468" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s469" xml:space="preserve"><emph style="sc">Hvnc</emph> ſecutus eſt Adrianus Imperator adeo in motibus aſtrorum uerſatus, vt <lb/>ſingulis annis ipſi conſcripſiße prognoſticon referant hiſtoriæ.</s> <s xml:id="echoid-s470" xml:space="preserve"/> </p> <pb o="10" file="046" n="47" rhead="Comment. in I. Cap. Sphæræ"/> <p style="it"> <s xml:id="echoid-s471" xml:space="preserve">QVID dicam de Alphonſo<unsure/> rege Hiſpaniar<unsure/>um? </s> <s xml:id="echoid-s472" xml:space="preserve">qui adeo doctus in aſtrorum ſcieu<unsure/>-<lb/>tia extitit, vt inſigne opus tabularum Aſtronomicarum compoſuerit.</s> <s xml:id="echoid-s473" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s474" xml:space="preserve">PRAETEREO ex recentioribus Carolum Quintum Imperatorem ſemper Au-<lb/>guſtum, & </s> <s xml:id="echoid-s475" xml:space="preserve">Ferdinandum eius fratrem, qui mirum in modum his ſtudijs, aſtronomi-<lb/>eisq́; </s> <s xml:id="echoid-s476" xml:space="preserve">inſtrumentis ſunt recreati: </s> <s xml:id="echoid-s477" xml:space="preserve">quorum exemplum imitati ſunt Philippus Hiſpania-<lb/>rum rex: </s> <s xml:id="echoid-s478" xml:space="preserve">Maximilianus Imperator: </s> <s xml:id="echoid-s479" xml:space="preserve">Philibertus Dux Sabaudiæ, & </s> <s xml:id="echoid-s480" xml:space="preserve">plerique alij, qui ad <lb/>huc ſuperſtites viuunt.</s> <s xml:id="echoid-s481" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s482" xml:space="preserve">ACCEDIT huc etiam, quòd ex nulla alia ſcientia humana tanta voluptas, <lb/> <anchor type="note" xlink:label="note-046-01a" xlink:href="note-046-01"/> & </s> <s xml:id="echoid-s483" xml:space="preserve">delectatio capitur, quanta ex Aſtronomia; </s> <s xml:id="echoid-s484" xml:space="preserve">Quid enim iucundius eſſe poteſt, quid <lb/>amœnius, quid ſuauius, quid denique delectabilius, quàm illam tot, & </s> <s xml:id="echoid-s485" xml:space="preserve">tantorum lu-<lb/>minum venuſtiſſimam, atque ordinatisſimam ſeriem oculis perluſtrare? </s> <s xml:id="echoid-s486" xml:space="preserve">Nihil enim <lb/>in hac vita eſſe, quod magis animum hominis oblectet, plurimi & </s> <s xml:id="echoid-s487" xml:space="preserve">grauiſſimi aucte<unsure/>-<lb/>res affirmant, vt iam mirum videri non debeat, cur aliqui duodecim integros annos, <lb/>aliqui quadraginta, aliqui plures, paucioresvein montibus ſub Dio tranſegerint, con-<lb/>ſiderandarum ſtellarum cauſa: </s> <s xml:id="echoid-s488" xml:space="preserve">Immo diuinus Plato ſolum Aſtronomiæ cauſa oculos no-<lb/>bis eſſe conceſſos, aſſerere non eſt veritus. </s> <s xml:id="echoid-s489" xml:space="preserve">Ad quod Ouidius poetarum ingenioſiſſimus <lb/>videtur alludere, dum ſic canit.</s> <s xml:id="echoid-s490" xml:space="preserve"/> </p> <div xml:id="echoid-div55" type="float" level="2" n="8"> <note position="left" xlink:label="note-046-01" xlink:href="note-046-01a" xml:space="preserve">Ex n<unsure/>ulla <lb/>f<unsure/>ciẽtia ma-<lb/>ſ<unsure/>or volu-<lb/>ptas percipi <lb/>tur, quàm <lb/>ex Aftrono-<lb/>@ia.</note> </div> <p> <s xml:id="echoid-s491" xml:space="preserve">Finxit in effigiem moderantum cuncta Deorum, <lb/>Pronaq́; </s> <s xml:id="echoid-s492" xml:space="preserve">cum ſpectent animalia cætera terram, <lb/>Os homini ſublime dedit, cęlumq́; </s> <s xml:id="echoid-s493" xml:space="preserve">videre <lb/>Iuſſit, & </s> <s xml:id="echoid-s494" xml:space="preserve">erectos ad ſydera tollere vultus.</s> <s xml:id="echoid-s495" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s496" xml:space="preserve">Et alio in loco.</s> <s xml:id="echoid-s497" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s498" xml:space="preserve">Felices animæ, quibus hæc cognoſcere primum, <lb/>Inq́; </s> <s xml:id="echoid-s499" xml:space="preserve">domos ſuperas ſcandere cura fuit.</s> <s xml:id="echoid-s500" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s501" xml:space="preserve">Et paulo poſt.</s> <s xml:id="echoid-s502" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s503" xml:space="preserve">Admouere oculis diſtantia ſydera noſtris, <lb/>Aetheraq́. </s> <s xml:id="echoid-s504" xml:space="preserve">ingenio ſuppoſuereſuo.</s> <s xml:id="echoid-s505" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s506" xml:space="preserve">Sic petitur cœlum, non vt ferat Oſſam olympus, <lb/>Summaq́; </s> <s xml:id="echoid-s507" xml:space="preserve">Peliacus ſydera tangat apex.</s> <s xml:id="echoid-s508" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s509" xml:space="preserve">IN hac enim pulcherrima arte ea Luſt<unsure/>antur, quibus maius, aut pulchrius exce-<lb/>gitari pote<unsure/>ſt nihil; </s> <s xml:id="echoid-s510" xml:space="preserve">In hac animi noſtrirapiuntur, atque abſtrahuntur à rebu@ <lb/>huius terreſtris orbis nunquam in eodem ſtatu permanentibus ad ea, quæ <lb/>nulli corruptionibus ſubiacent; </s> <s xml:id="echoid-s511" xml:space="preserve">In hac contemptis terreni huius <lb/>puncti anguſtijs, per aera ſpaciosũ, inter aureos ſoles, argen <lb/>teas, mutabilesq́. </s> <s xml:id="echoid-s512" xml:space="preserve">Lunas, ac lucida ſydera, mira dulcedi <lb/>ne, & </s> <s xml:id="echoid-s513" xml:space="preserve">iucunditate vagatur animus. </s> <s xml:id="echoid-s514" xml:space="preserve">Atque hæc <lb/>pauca ex multis, quæ de laudibus, vtilitateq́; <lb/></s> <s xml:id="echoid-s515" xml:space="preserve">huius eximiæ diſciplinæ afferri poſſent, <lb/>dicta ſufficiant. </s> <s xml:id="echoid-s516" xml:space="preserve">Nunc ad aucto<unsure/>-<lb/>rem ſphæræ explicandum <lb/>accedamus.</s> <s xml:id="echoid-s517" xml:space="preserve"/> </p> <pb file="047" n="48"/> </div> <div xml:id="echoid-div57" type="section" level="1" n="38"> <head xml:id="echoid-head42" xml:space="preserve">PROOEMIVM <lb/>IOANNIS DE SACRO <lb/>BOSCO.</head> <p style="it"> <s xml:id="echoid-s518" xml:space="preserve"><emph style="sc">TRactatvm</emph> de Sphæraquatuor capitulis diſtin-<lb/> <anchor type="note" xlink:label="note-047-01a" xlink:href="note-047-01"/> guimus, dicturi primo compoſitionem ſphærę, quid ſit <lb/>ſphæra, quid ſit eius centrum, quid axis ſphæræ, quid ſit <lb/>polus mundi, quot ſint ſphęræ, quæ ſit forma mundi.</s> <s xml:id="echoid-s519" xml:space="preserve"/> </p> <div xml:id="echoid-div57" type="float" level="2" n="1"> <note position="right" xlink:label="note-047-01" xlink:href="note-047-01a" xml:space="preserve">Quem or<unsure/>d<unsure/>i <lb/>nem ſerue@ <lb/>auctor in <lb/>ſphęra tra-<lb/>denda.</note> </div> <p style="it"> <s xml:id="echoid-s520" xml:space="preserve"><emph style="sc">In</emph> ſecundo de circulis, ex quibus ſphæra materialis <lb/>componitur, & </s> <s xml:id="echoid-s521" xml:space="preserve">illa ſupercæleſtis, quæ per iſtam repræ-<lb/>ſentatur, componi intelligitur.</s> <s xml:id="echoid-s522" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s523" xml:space="preserve"><emph style="sc">In</emph> tertio de ortu, & </s> <s xml:id="echoid-s524" xml:space="preserve">occaſu ſignorum, & </s> <s xml:id="echoid-s525" xml:space="preserve">de diuerſitate dierum, & </s> <s xml:id="echoid-s526" xml:space="preserve"><lb/>noctium, & </s> <s xml:id="echoid-s527" xml:space="preserve">diuiſione climatum.</s> <s xml:id="echoid-s528" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s529" xml:space="preserve"><emph style="sc">In</emph> quarto de circulis, & </s> <s xml:id="echoid-s530" xml:space="preserve">motibus Planetarum, & </s> <s xml:id="echoid-s531" xml:space="preserve">de cauſis <lb/>eclipſium.</s> <s xml:id="echoid-s532" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div59" type="section" level="1" n="39"> <head xml:id="echoid-head43" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s533" xml:space="preserve"><emph style="sc">INscrieitvr</emph> hic libellus de Sphera, id eſt, de figuta quadam <lb/> <anchor type="note" xlink:label="note-047-02a" xlink:href="note-047-02"/> globoſa, ſeu rotunda varios, & </s> <s xml:id="echoid-s534" xml:space="preserve">diuerſos circulos continente, quæ <lb/>ſphæra materialis ſolet nuncupari, inuenta miro artificio ad hoc, <lb/>vt aliquam de rebus cœleſtibus habere notitiam poſſimus. </s> <s xml:id="echoid-s535" xml:space="preserve">Quo-<lb/>niam enim in noſtra poteſtate non eſt, cęlos, quando libuerit, <lb/>aſcendere, vt ibi gradus, circulosq́ue conſideratos viſu percipiamus, eoſq́ue <lb/>reuoluamus, vndecunq. </s> <s xml:id="echoid-s536" xml:space="preserve">& </s> <s xml:id="echoid-s537" xml:space="preserve">quocunq; </s> <s xml:id="echoid-s538" xml:space="preserve">voluerimus: </s> <s xml:id="echoid-s539" xml:space="preserve">Rurſus neq. </s> <s xml:id="echoid-s540" xml:space="preserve">hõis ætas ſuſſicie <lb/>expectare ea omnia, quæ in cœlo futura ſunt, neq; </s> <s xml:id="echoid-s541" xml:space="preserve">vllus hominum, dum viuit, <lb/>ea omnia, quæ pręſentia ſunt, intueri poteſt: </s> <s xml:id="echoid-s542" xml:space="preserve">Amplius, nũc hic dies exiſtit, illic <lb/>nox: </s> <s xml:id="echoid-s543" xml:space="preserve">His modo Sol oritur, vel alia ſtella quæuis, illis vero occidit: </s> <s xml:id="echoid-s544" xml:space="preserve">Hi ſub ſphæ <lb/>ra obliqua, illi ſub recta degunt: </s> <s xml:id="echoid-s545" xml:space="preserve">& </s> <s xml:id="echoid-s546" xml:space="preserve">deniq. </s> <s xml:id="echoid-s547" xml:space="preserve">nullus omnibus in locis habitare ſi <lb/>mul eodem tempore poteſt; </s> <s xml:id="echoid-s548" xml:space="preserve">quæ tamen omnia requiruntur, vt aliquam poſſi-<lb/>mus cognitionem habere eorum, quæ in cœleſti illa regione fiunt: </s> <s xml:id="echoid-s549" xml:space="preserve">Idcirco ma <lb/> <anchor type="note" xlink:label="note-047-03a" xlink:href="note-047-03"/> gna induſtria, ſummoq́; </s> <s xml:id="echoid-s550" xml:space="preserve">ingenio, excogitarunt artifices huius diſciplinæ mira <lb/>eruditione præditi materiale ali quod inſtrumentum, quod nobis omnia illa, <lb/>quæ in cęlo imaginamur, & </s> <s xml:id="echoid-s551" xml:space="preserve">ſcire deſideramus, ob oculos poneret. </s> <s xml:id="echoid-s552" xml:space="preserve">Tale igitur <lb/>inſtrumentum appellatur Sphæra materialis, de qua inſcripſit ſuum libellum <lb/>auctor hic, non quod quaſi ex proprio inſtituto de hac velit diſſerere: </s> <s xml:id="echoid-s553" xml:space="preserve">Princi-<lb/> <anchor type="note" xlink:label="note-047-04a" xlink:href="note-047-04"/> palis enim eius intentio eſt in hoc libello agere de ſphæra illa cęleſti, in cuius <lb/>gratiam hæc materialis eſt inuenta. </s> <s xml:id="echoid-s554" xml:space="preserve">Sed quoniam, vt diximus, notitia eorum <lb/>quæ in cęlo apparent, acquiti minime poteſt abſque ſphæræ materialis vſu, <lb/>ideo ſu<unsure/>um libellum de hac ſphæra inſcripſit, ita tamen, vt omnia, quæ de hac <lb/>ſphæra dicentur, ad illam cęleſtem ſphæram referantur.</s> <s xml:id="echoid-s555" xml:space="preserve"/> </p> <div xml:id="echoid-div59" type="float" level="2" n="1"> <note position="right" xlink:label="note-047-02" xlink:href="note-047-02a" xml:space="preserve">Inſcriptio <lb/>huius ope-<lb/>ris.</note> <note position="right" xlink:label="note-047-03" xlink:href="note-047-03a" xml:space="preserve">Cur ab A-<lb/>ſtronomis <lb/>ſphæra m@ <lb/>terialis in-<lb/>uenta ſint.</note> <note position="right" xlink:label="note-047-04" xlink:href="note-047-04a" xml:space="preserve">Præcipuæ <lb/>in hoc lib. <lb/>agitur de <lb/>ſphæra cæ-<lb/>leſti.</note> </div> <note position="right" xml:space="preserve">Intentio <lb/>auctoris.</note> <p> <s xml:id="echoid-s556" xml:space="preserve"><emph style="sc">Totvm</emph> igitur ſtudium auctoris poſitum eſt in eo, ut per ſphæram mate- <pb o="12" file="048" n="49" rhead="Comment. in I. Cap. Sphæræ"/> rialem declaret nobis conſtitutionem, & </s> <s xml:id="echoid-s557" xml:space="preserve">figuram totius mundi, doceatq́ue, <lb/>quomodo cœleſtia corpora moueantur, qua ratione ſtellæ, & </s> <s xml:id="echoid-s558" xml:space="preserve">ſigna oriantur, <lb/>occidantq́ue, quid denique ex hoc ortu conſequatur, quantum ad dies, & </s> <s xml:id="echoid-s559" xml:space="preserve">no-<lb/>ctes in varijs climatibus; </s> <s xml:id="echoid-s560" xml:space="preserve">Ita vt iſte tractatus ſit fere compendium vniuerſæ <lb/>Aſtronomiæ. </s> <s xml:id="echoid-s561" xml:space="preserve">Quare non incongrue idem huius libelli ſtatuemus ſubiectum, <lb/>quod totius Aſtronomiæ, nempe Corpus cœleſte mobile circa medium. </s> <s xml:id="echoid-s562" xml:space="preserve">Nam <lb/> <anchor type="note" xlink:label="note-048-01a" xlink:href="note-048-01"/> iuxta placita ph loſophorum ſubiectum alicuius libri tres debet habere con-<lb/>ditiones; </s> <s xml:id="echoid-s563" xml:space="preserve">primo, vt partes ſubiectæ, ac paſſiones eius, quod ſubiectum dicitur, <lb/>in illo lib. </s> <s xml:id="echoid-s564" xml:space="preserve">declarentur; </s> <s xml:id="echoid-s565" xml:space="preserve">Secundo, vt omnia, quæ in eo tractatu dicuntur, ad <lb/>ipſum ſubiectum referantur; </s> <s xml:id="echoid-s566" xml:space="preserve">Tertio, vt id, quod ſubiectum illius libri conſtitui <lb/>tur, diſtinguat librum, ſeu ſcientiam illam ab omnibus alijs: </s> <s xml:id="echoid-s567" xml:space="preserve">Quæ quidem om <lb/>nes conditiones corpori cœleſti mobili circa medium reſpectu iſtius libelli cõ <lb/>ueniunt. </s> <s xml:id="echoid-s568" xml:space="preserve">Inueſtigantur enim in eo corporis cœleſtis mobilis partes ſubiectæ, <lb/>videlicet cœli particulares, quotnam ſint numero, & </s> <s xml:id="echoid-s569" xml:space="preserve">paſſiones eius diligentiſ-<lb/>ſime explicantur, vt motus, ſitus, figura, quantitats, & </s> <s xml:id="echoid-s570" xml:space="preserve">huiuſmodi alia. </s> <s xml:id="echoid-s571" xml:space="preserve">Deinde <lb/>omnia, quæ hic tractantur, per attributionem ad corpus cœleſte mobile circa <lb/>medium conſiderantur, vt quod terra, & </s> <s xml:id="echoid-s572" xml:space="preserve">aqua rotũdum corpus eſſiciant, quod <lb/>terra ſit in medio mundi ſita immobilis, & </s> <s xml:id="echoid-s573" xml:space="preserve">punctum exiſtat reſpectu firmamen <lb/>ti, & </s> <s xml:id="echoid-s574" xml:space="preserve">id genus alia; </s> <s xml:id="echoid-s575" xml:space="preserve">neque enim ratio eorum, quæ apparent in corporibus cœ-<lb/>leſtibus, aſſignari poſſet ſine his. </s> <s xml:id="echoid-s576" xml:space="preserve">Atque hæc fuit cauſa, cur Ptolemæus in Al-<lb/>mageſto, & </s> <s xml:id="echoid-s577" xml:space="preserve">auctor noſter, Alphraganus, & </s> <s xml:id="echoid-s578" xml:space="preserve">cæteri omnes Aſtronomi multa di-<lb/>xer@t de quatuor elementis, præcipue uero de terra, vt nimirum facilius poſ <lb/>ſent motus cœleſtes, qui circa terram tanquam centrum fiunt, declarare. </s> <s xml:id="echoid-s579" xml:space="preserve">Poſtre <lb/>mo per corpus cœleſte mobile circa medium diſtinguitur hic libellus ab om-<lb/>nibus aliis diſciplinis, Quamuis enim Ariſtoteles quoque de cœlo agat in lib. <lb/></s> <s xml:id="echoid-s580" xml:space="preserve">de cœlo, tamen alia id ratione facit, quàm Aſtrologus. </s> <s xml:id="echoid-s581" xml:space="preserve">Philoſophus ſiquidem <lb/>præcipue naturam, ac ſubſtantiam cœli conatur inueſtigare, & </s> <s xml:id="echoid-s582" xml:space="preserve">ſi quid de mo-<lb/>tu cęli in particulari aſſerit, id totum ab Aſtrologis emendicat: </s> <s xml:id="echoid-s583" xml:space="preserve">Aſtrologus ve <lb/>ro de eodem corpore cœleſti agit hac præciſa ratione, qua circa medium Vni-<lb/>uerſi eſt mobile, vt videlicet aſſignet periodos, & </s> <s xml:id="echoid-s584" xml:space="preserve">varietates omnium motuũ, <lb/>in telligendo ſemper motum tantummodo localẽ Nam cœleſtia corpora alios <lb/>motus, vt alterationẽ, ſaltem corrumpentem, augmentationem, diminutionẽ, <lb/>generationem, & </s> <s xml:id="echoid-s585" xml:space="preserve">corrumptionem, ſecundum philoſophos, non admittunt.</s> <s xml:id="echoid-s586" xml:space="preserve"/> </p> <div xml:id="echoid-div60" type="float" level="2" n="2"> <note position="left" xlink:label="note-048-01" xlink:href="note-048-01a" xml:space="preserve">Subiectum <lb/>Aſtrono-<lb/>miæ, & hu-<lb/>ius libri, <lb/>quod.</note> </div> <p> <s xml:id="echoid-s587" xml:space="preserve"><emph style="sc">Inhoc igitvr</emph> Proœmio declarat nobis auctor ſuam intentio-<lb/>nem, proponitq́ue modum procedendi, diuidens totum tractatum in quatuor <lb/> <anchor type="note" xlink:label="note-048-02a" xlink:href="note-048-02"/> capita. </s> <s xml:id="echoid-s588" xml:space="preserve">In quorum primo ait ſe declaraturum partes ſphęrę, & </s> <s xml:id="echoid-s589" xml:space="preserve">quæ ſit forma <lb/>mundi, quod quidem eſt digniſſimum ſcitu. </s> <s xml:id="echoid-s590" xml:space="preserve">Quomodo enim non erit iucun-<lb/>diſſimum ſimul, ac utiliſſimum, noſſe, quonã pacto huius mundi machina, qua <lb/>tegimur, continemur, & </s> <s xml:id="echoid-s591" xml:space="preserve">in qua aſſidue uitã degimus, conſtructa ſit atque di-<lb/>ſpoſita? </s> <s xml:id="echoid-s592" xml:space="preserve">In ſecundo pollicetur ſe dicturũ de circulis ſphæræ. </s> <s xml:id="echoid-s593" xml:space="preserve">In tertio, & </s> <s xml:id="echoid-s594" xml:space="preserve">quar-<lb/>to aſſerit, ſe diſputaturũ de motibus aſtrorum, hoc eſt, de ortu & </s> <s xml:id="echoid-s595" xml:space="preserve">occaſu ſigno-<lb/>rum, ſtellarumq́ue. </s> <s xml:id="echoid-s596" xml:space="preserve">Verum quoniam duplex poteit eſſe de motibus cœleſtibus <lb/>tractatio; </s> <s xml:id="echoid-s597" xml:space="preserve">Altera, quæ inquirit, atque explicat primum motum, qui proprius <lb/>eſt, & </s> <s xml:id="echoid-s598" xml:space="preserve">peculiaris primo mobili ab ortu in occaſum, rapitq́ue omnes alios orbes <lb/>ſecũ ſpatio uigintiquatuor horarũ: </s> <s xml:id="echoid-s599" xml:space="preserve">Altera uero conſiderat, & </s> <s xml:id="echoid-s600" xml:space="preserve">declarat motum <lb/>ſecundũ, qui peculiaris eſt, & </s> <s xml:id="echoid-s601" xml:space="preserve">proprius aliis cœlis infra primũ mobile, fitq́; </s> <s xml:id="echoid-s602" xml:space="preserve">ab <lb/>occaſu in ortũ; </s> <s xml:id="echoid-s603" xml:space="preserve">Contranituntur enim quodammodo ſinguli orbes inferiores, <lb/>f<unsure/>ingulis etiam, ac proprijs motibus primo illi motui, à quo trahuntur ab ortu <pb o="13" file="049" n="50" rhead="Ioan. de Sacro Boſco."/> in occaſum: </s> <s xml:id="echoid-s604" xml:space="preserve">Idcirco auctor noſter uolens utramque tractationem breuiter <lb/>perſtringere, in tertio cap. </s> <s xml:id="echoid-s605" xml:space="preserve">agit de primo illo motu, & </s> <s xml:id="echoid-s606" xml:space="preserve">de omnibus, quæ ra-<lb/>tione illius accidunt in uariis regionibus, nempe de ortu, & </s> <s xml:id="echoid-s607" xml:space="preserve">occaſu ſignorum, <lb/>quę à primo mobili perpetuo ab ortu in occaſum deferuntur: </s> <s xml:id="echoid-s608" xml:space="preserve">Item de diuerſi-<lb/>tate dierum, ac noctium, quę ob diuerſum ortum, obitumque ſignorum diuer-<lb/>ſis in locis uaria exiſtit; </s> <s xml:id="echoid-s609" xml:space="preserve">& </s> <s xml:id="echoid-s610" xml:space="preserve">denique de climatibus, in quibus huiuſmudi diuer-<lb/>ſitas reperitur, diſſerit. </s> <s xml:id="echoid-s611" xml:space="preserve">In quarto uero cap. </s> <s xml:id="echoid-s612" xml:space="preserve">diſputat de circulis, orbibus, & </s> <s xml:id="echoid-s613" xml:space="preserve">moti <lb/>bus planetarum, & </s> <s xml:id="echoid-s614" xml:space="preserve">de cauſis eclipſium Solis, & </s> <s xml:id="echoid-s615" xml:space="preserve">Lunæ, & </s> <s xml:id="echoid-s616" xml:space="preserve">de iis, quę ratione ſecũ <lb/>di motus contingunt. </s> <s xml:id="echoid-s617" xml:space="preserve">Atque ita’<unsure/> compendio quodam uidetur hoc libello totã <lb/>ſcientiam de rebus cœleſtibus fuiſse complexus.</s> <s xml:id="echoid-s618" xml:space="preserve"/> </p> <div xml:id="echoid-div61" type="float" level="2" n="3"> <note position="left" xlink:label="note-048-02" xlink:href="note-048-02a" xml:space="preserve">Quid in <lb/>@ngulis ca-<lb/>pitibus hu-<lb/>ius lib. con-<lb/>@ineatur.</note> </div> </div> <div xml:id="echoid-div63" type="section" level="1" n="40"> <head xml:id="echoid-head44" xml:space="preserve">CAPVT PRIMVM.</head> <p style="it"> <s xml:id="echoid-s619" xml:space="preserve"><emph style="sc">SPhaera</emph> igitur ab Euclide ſic deſcribitur. </s> <s xml:id="echoid-s620" xml:space="preserve">Sphæra eſt <lb/>tranſitus circunferentiæ dimidij circuli, quæ fixa diametro <lb/>eouſque circunducitur, quouſque ad locum ſuum redeat. </s> <s xml:id="echoid-s621" xml:space="preserve">Id eſt. <lb/></s> <s xml:id="echoid-s622" xml:space="preserve">Sphæra eſt tale rotundum, & </s> <s xml:id="echoid-s623" xml:space="preserve">ſolidum, quod deſcribitur ab ar-<lb/>cuſemicirculi circunducto,</s> </p> </div> <div xml:id="echoid-div64" type="section" level="1" n="41"> <head xml:id="echoid-head45" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s624" xml:space="preserve">HOc primum caput continet principia, ac fundamenta totius <lb/> <anchor type="note" xlink:label="note-049-01a" xlink:href="note-049-01"/> Aſtronomiæ, de quibus etiã doctiſſime diſſerit Ptolemæus in pri <lb/>ma Dictione ſuę magnæ conſtructionis. </s> <s xml:id="echoid-s625" xml:space="preserve">Diuidi autem poterit cõ-<lb/>modiſſimæ in quatuor præcipuas partes. </s> <s xml:id="echoid-s626" xml:space="preserve">Prima pars continet <lb/>quinque definitiones, duas quidem ſphæræ: </s> <s xml:id="echoid-s627" xml:space="preserve">tertiam centri ſphæ <lb/>ræ; </s> <s xml:id="echoid-s628" xml:space="preserve">quartam ipſius axis mundi; </s> <s xml:id="echoid-s629" xml:space="preserve">& </s> <s xml:id="echoid-s630" xml:space="preserve">quintam polorum mundi.</s> <s xml:id="echoid-s631" xml:space="preserve"><unsure/></s> </p> <div xml:id="echoid-div64" type="float" level="2" n="1"> <note position="right" xlink:label="note-049-01" xlink:href="note-049-01a" xml:space="preserve">Quod in <lb/>primo capi <lb/>te Sphæræ <lb/>agatur.</note> </div> <p> <s xml:id="echoid-s632" xml:space="preserve"><emph style="sc">In</emph> ſecunda parte continentur diuiſiones quædam ſphæræ: </s> <s xml:id="echoid-s633" xml:space="preserve">In tertia, quænã <lb/>ſit mundi forma, explicatur: </s> <s xml:id="echoid-s634" xml:space="preserve">In quarta denique quaſdam concluſiones de cœ-<lb/>leſti, & </s> <s xml:id="echoid-s635" xml:space="preserve">elementari regione auctor demonſtrat.</s> <s xml:id="echoid-s636" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s637" xml:space="preserve"><emph style="sc">Vt</emph> autem duæ ſphæræ definitiones intelligantur, aduertendum eſt, aqud <lb/> <anchor type="note" xlink:label="note-049-02a" xlink:href="note-049-02"/> Mathematicos tria genera quantitatũ duntaxat reperiri: </s> <s xml:id="echoid-s638" xml:space="preserve">Sub primo continen-<lb/>tur omnes lineæ, quarum extremitates ſunt puncta: </s> <s xml:id="echoid-s639" xml:space="preserve">Sub ſecundo includnntur <lb/>omnes ſuperficies, quæ lineis terminantur: </s> <s xml:id="echoid-s640" xml:space="preserve">Tertium denique genus corpora, <lb/>ſeu ſolida complectitur, quorum extrema ſunt ſuperficies. </s> <s xml:id="echoid-s641" xml:space="preserve">Linea eſt longitu-<lb/> <anchor type="note" xlink:label="note-049-03a" xlink:href="note-049-03"/> do ſine latitudine, vnam tantum habens dimenſionem, qua ſecundũ longum <lb/>diuiditur. </s> <s xml:id="echoid-s642" xml:space="preserve">Superficies vero eſt latitudo proſunditatis expers, duas duntaxat <lb/> <anchor type="note" xlink:label="note-049-04a" xlink:href="note-049-04"/> recipiens dimenſiones, vnam ſecundum longitudinem, alteram ſecundum la-<lb/>titudinem. </s> <s xml:id="echoid-s643" xml:space="preserve">Corpus denique, ſiue ſolidum eſt magnitudo tres admittens dimen <lb/> <anchor type="note" xlink:label="note-049-05a" xlink:href="note-049-05"/> ſiones, longitudinem uidelicet, latitudinem, & </s> <s xml:id="echoid-s644" xml:space="preserve">craſſitiem ſeu profunditatem: <lb/></s> <s xml:id="echoid-s645" xml:space="preserve">Neq. </s> <s xml:id="echoid-s646" xml:space="preserve">alia magnitudo, ſiue quantitas à Mathematico præter has tres conſide-<lb/>ratur, quod plures dar<unsure/>i non poſsint, cũ nec plures dimenſiones tribus prędi-<lb/>ctis queant reperiri. </s> <s xml:id="echoid-s647" xml:space="preserve">Quod quidem ad initium librorum de cęlo Ariſtoteles li <lb/>cet conetur multis rationibus probabilibus confirmare, Mathematici tame n <lb/>idipſum unica demonſtratione clariſſima oſtendunt, quam libuit hic appone- <pb o="14" file="050" n="51" rhead="Comment. in I. Cap. Sphæræ"/> re, quod apud paucos reperiatur bene explicata.</s> <s xml:id="echoid-s648" xml:space="preserve"/> </p> <div xml:id="echoid-div65" type="float" level="2" n="2"> <note position="right" xlink:label="note-049-02" xlink:href="note-049-02a" xml:space="preserve">Quãtitatis <lb/>tria tãtum <lb/>ſunt genc-<lb/>ra.</note> <note position="right" xlink:label="note-049-03" xlink:href="note-049-03a" xml:space="preserve">Linea q@</note> <note position="right" xlink:label="note-049-04" xlink:href="note-049-04a" xml:space="preserve">Superficies <lb/>quid.</note> <note position="right" xlink:label="note-049-05" xlink:href="note-049-05a" xml:space="preserve">Corpus <lb/>quid.</note> </div> <p> <s xml:id="echoid-s649" xml:space="preserve"><emph style="sc">Sciendvm</emph>eſt igitur, omnia commenſurari linea perpendiculari à<unsure/> <lb/> <anchor type="note" xlink:label="note-050-01a" xlink:href="note-050-01"/> Mathematicis, ita vt tam longa dicatur eſſe quælibet magnitudo, quanta eſt <lb/>perpendicularis ducta ab vno extremo figuræ ad aliud extremũ; </s> <s xml:id="echoid-s650" xml:space="preserve">Vt in hoc pro <lb/> <anchor type="figure" xlink:label="fig-050-01a" xlink:href="fig-050-01"/> poſito parallelogrammo A B C D, <lb/>longitudo erit linea perpendicula-<lb/>ris L M, ducta à puncto L, lateris <lb/>A D, ad latus oppoſitum B C, pro-<lb/>tractum, vel perpendicularis A F. <lb/></s> <s xml:id="echoid-s651" xml:space="preserve">Pari ratione latitudinem cuiuſuis <lb/>quantitatis tantã dicunt eſſe, quan-<lb/>ta eſt perpendicularis educta ab v-<lb/>no latere ad aliud; </s> <s xml:id="echoid-s652" xml:space="preserve">Vt propoſiti pa-<lb/>rallelogrammi latitudo erit perpen <lb/>dicularis B E, alatere A B, ad latus <lb/>D C, protractum extenſa. </s> <s xml:id="echoid-s653" xml:space="preserve">Profundi-<lb/>tas denique ſeu craſſities, altitudove cuiuſcunque corporis tanta eſſe iudica-<lb/>tor, quanta eſt perpendicularis producta ab vna parte ad aliã. </s> <s xml:id="echoid-s654" xml:space="preserve">Quamobrem Eu <lb/>clides pulcherrime ad initium ſexti lib. </s> <s xml:id="echoid-s655" xml:space="preserve">deſiniens altitudinem cuiuſq; </s> <s xml:id="echoid-s656" xml:space="preserve">figuræ <lb/>dixit: </s> <s xml:id="echoid-s657" xml:space="preserve">Eam eſſe lineam perpendicularem à vertice ad baſim deductam.</s> <s xml:id="echoid-s658" xml:space="preserve"/> </p> <div xml:id="echoid-div66" type="float" level="2" n="3"> <note position="left" xlink:label="note-050-01" xlink:href="note-050-01a" xml:space="preserve">Mat<unsure/>hema-<lb/>tici omnia <lb/>metiuntur <lb/>linea perpẽ <lb/>diculari.</note> <figure xlink:label="fig-050-01" xlink:href="fig-050-01a"> <image file="050-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/050-01"/> </figure> </div> <p> <s xml:id="echoid-s659" xml:space="preserve"><emph style="sc">Ratio</emph> vero, cur omnia Mathematici metiantur linea perpendiculari, <lb/> <anchor type="note" xlink:label="note-050-02a" xlink:href="note-050-02"/> ea eſt, quà<unsure/>m Ptolemæus aſſerit in libello, quem de Analemmate conſcripſit, & </s> <s xml:id="echoid-s660" xml:space="preserve"><lb/>quam Simplicius accepit ex libro eiuſdem Ptolemæi de Dimenſiones: </s> <s xml:id="echoid-s661" xml:space="preserve">quoniã <lb/>videlicet menſura alicuius rei debet eſſe ſtata, determinataq́; </s> <s xml:id="echoid-s662" xml:space="preserve">& </s> <s xml:id="echoid-s663" xml:space="preserve">non indeſini <lb/>ta: </s> <s xml:id="echoid-s664" xml:space="preserve">Inter cũctas autem lineas rectas, penes quas ſumitur omnis menſura, ſola <lb/>linea perpendicularis eſt certæ, determinatæq́; </s> <s xml:id="echoid-s665" xml:space="preserve">longitudinis, aliæ autem om-<lb/>nes indeterminatæ. </s> <s xml:id="echoid-s666" xml:space="preserve">Vt in ſuperiore parallelogrammo, linea perpendicularis <lb/>BE, penes quam ſumpſimus latitudinem figuræ, inter omnes lineas, quæ à late <lb/>re A B, duci poſſunt ad latus D C, ſiue vlterius protractum ſit, ſiue non, ſola <lb/>eſt ſtatæ, atq; </s> <s xml:id="echoid-s667" xml:space="preserve">inuariabilis quãtitatis; </s> <s xml:id="echoid-s668" xml:space="preserve">A quocunq. </s> <s xml:id="echoid-s669" xml:space="preserve">enim puncto lateris A B, du-<lb/>xeris ad latus D C, lineam perpendicularem, hæc prorſus eandem habebit lon <lb/>gitudinem, quàm perpendicularis B E, qualis eſt perpendicularis G H. </s> <s xml:id="echoid-s670" xml:space="preserve">Nam <lb/>cum G B F H, (vt manifeſto conſtat ex primo lib. </s> <s xml:id="echoid-s671" xml:space="preserve">Euclidis) ſit parallelogram-<lb/>mum, erunt latera oppoſita B E, G H, æqualia, & </s> <s xml:id="echoid-s672" xml:space="preserve">ſic de alijs; </s> <s xml:id="echoid-s673" xml:space="preserve">Quod minime <lb/> <anchor type="note" xlink:label="note-050-03a" xlink:href="note-050-03"/> contingit in alijs lineis, quæ non perpendiculares ſunt: </s> <s xml:id="echoid-s674" xml:space="preserve">Ex quo cunque enim <lb/>puncto lateris A B, ad latus D C, duci poſſunt innumeræ lineę non perpendi-<lb/>culares, quarum vna altera maior eſt, & </s> <s xml:id="echoid-s675" xml:space="preserve">omnibus minor exiſtit perpendicula-<lb/>ris ab eodem puncto deducta, vt manifeſtum eſt in lineis G H, G I, G K. </s> <s xml:id="echoid-s676" xml:space="preserve">Quod <lb/> <anchor type="note" xlink:label="note-050-04a" xlink:href="note-050-04"/> cum ita ſit, non ſine magno cõſilio, immo ipſa Natura duce, mẽſuræ quantia-<lb/> <anchor type="figure" xlink:label="fig-050-02a" xlink:href="fig-050-02"/> tum capiuntur penes lineas parpendicula-<lb/>res, quæ ſolæ terminatæ ſunt, atque inuaria <lb/>biles: </s> <s xml:id="echoid-s677" xml:space="preserve">non autẽ ſecundum alias, quæ infini-<lb/>tis modis poſſunt duci, modo breuiores, <lb/>modo longiores; </s> <s xml:id="echoid-s678" xml:space="preserve">Sicut etiam non ſolum <lb/>apud Mathematicos, verum etiam apud <lb/>vulgus ſpacia, & </s> <s xml:id="echoid-s679" xml:space="preserve">itinerum interualla iux-<lb/>ta lineas rectas ſumuntur, quæ breuiſſimæ <lb/>ſunt, & </s> <s xml:id="echoid-s680" xml:space="preserve">non penes circulares, quæ ſexcen- <pb o="15" file="051" n="52" rhead="Ioan. de Sacro Boſco."/> ris modis vatiari poſſunt. </s> <s xml:id="echoid-s681" xml:space="preserve">V tſpacium interiectum inter A, & </s> <s xml:id="echoid-s682" xml:space="preserve">B, puncta, tantum <lb/>eſſe definitur, quanta eſt linea recta A C B, non autem, quanta eſt circularis <lb/>A D B, aut A E B, aut A F B; </s> <s xml:id="echoid-s683" xml:space="preserve">quoniam hæ non ſunt eiuſdem longitudinis, ſed <lb/>vna eſt altera maior: </s> <s xml:id="echoid-s684" xml:space="preserve">recta vero ſemper eadem eſt, & </s> <s xml:id="echoid-s685" xml:space="preserve">omnium, quæ ex pun A, <lb/>ad punctum B, duci poſſunt, breuiſfima.</s> <s xml:id="echoid-s686" xml:space="preserve"/> </p> <div xml:id="echoid-div67" type="float" level="2" n="4"> <note position="left" xlink:label="note-050-02" xlink:href="note-050-02a" xml:space="preserve">@ur a Ma-<lb/>thematicis <lb/>omnia mẽ-<lb/>ſurentur li <lb/>n<unsure/>ea perpen <lb/>diculari.</note> <note position="left" xlink:label="note-050-03" xlink:href="note-050-03a" xml:space="preserve">34. primi.</note> <note position="left" xlink:label="note-050-04" xlink:href="note-050-04a" xml:space="preserve">19. primi.</note> <figure xlink:label="fig-050-02" xlink:href="fig-050-02a"> <image file="050-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/050-02"/> </figure> </div> <p> <s xml:id="echoid-s687" xml:space="preserve"><emph style="sc">Hoc</emph> igitur ita oſtẽſo, omnia videlicet cõmenſurari linea perpendiculari, <lb/>facile demonſtrabitur, tres tantum eſſe dimenſiones ex natura rei in vnaquaq. <lb/></s> <s xml:id="echoid-s688" xml:space="preserve"> <anchor type="note" xlink:label="note-051-01a" xlink:href="note-051-01"/> re corporea, vnã videlicet ſecundum longitudinem, alteram ſecundum latitu-<lb/>dinem, & </s> <s xml:id="echoid-s689" xml:space="preserve">tertiam ſecundum profunditatem: </s> <s xml:id="echoid-s690" xml:space="preserve">Cuius rei cauſa eſt, quoniam ad <lb/>quoduis punctum in aliquo corpore ſuſceptum ſolum tres lineæ perpendicu-<lb/>Iares: </s> <s xml:id="echoid-s691" xml:space="preserve">ita vt quælibet illarum ad reliquas duas ſit ad angulos rectos, conſtitui <lb/>poſſunt, nõ plures, quarum duæ quomodolibet ſumptæ exiſtent in vna cadem <lb/>q́ue ſuperficie, reliqua vero in alia diuerſa. </s> <s xml:id="echoid-s692" xml:space="preserve">Penes vnã itaq. </s> <s xml:id="echoid-s693" xml:space="preserve">harum linearũ ac-<lb/>cipitur longitudo corporis, penes aliam latitudo, & </s> <s xml:id="echoid-s694" xml:space="preserve">penes tertiã altitudo, ſeu <lb/>profunditas. </s> <s xml:id="echoid-s695" xml:space="preserve">Ex quibus conſtat, curnã corpori tres tantum inſint dimenſiones. <lb/></s> <s xml:id="echoid-s696" xml:space="preserve">Quare non inepte quidam ſic corpus deſinire ſolent. </s> <s xml:id="echoid-s697" xml:space="preserve">Corpus, ſeu ſolidum eſt <lb/>magnitudo, in qua tres lineæ recte ſe inuicem ad angulos rectos interſecãtes <lb/>in vno, eodemq́ue puncto protrahi poſſunt: </s> <s xml:id="echoid-s698" xml:space="preserve">in ſuperficie enim ſolum duæ poſ-<lb/>ſunt. </s> <s xml:id="echoid-s699" xml:space="preserve">Quod autem ad quoduis punctum tres poſſint lineæ duci, ita vt quæli-<lb/>bet ad reliquas duas ſit perpendicularis, ita demonſtrabimus. </s> <s xml:id="echoid-s700" xml:space="preserve">In ſuperiori figu-<lb/>ra, vbi duæ rectæ AB, BE, ſeſe ad angulos rectos ſecantin B, ſi ex B, intelliga <lb/>tur ad planum, in quo illæ rectæ exiſtunt, (ſemper enim duæ rectæ ſe interſecã <lb/>tes in vno plano ſunt) excitari recta linea ad angulos rectos, erit hæc ad utran <lb/>que A B, B E, perpendicularis, ex defin. </s> <s xml:id="echoid-s701" xml:space="preserve">3. </s> <s xml:id="echoid-s702" xml:space="preserve">lib, 11. </s> <s xml:id="echoid-s703" xml:space="preserve">Eucl. </s> <s xml:id="echoid-s704" xml:space="preserve">ac proinde, & </s> <s xml:id="echoid-s705" xml:space="preserve">utraque <lb/>uiciſſim ad hanc perpendicularis erit. </s> <s xml:id="echoid-s706" xml:space="preserve">Ex quo efficitur, quamlibet ad reliquas <lb/>duas eſſe perpendicularem. </s> <s xml:id="echoid-s707" xml:space="preserve">Nullam autem aliam ad has tres poſſe perpendicu <lb/>larem eſſe, hoc modo perſpicuum faciemus. </s> <s xml:id="echoid-s708" xml:space="preserve">Ducatur, ſi fieri poteſt: </s> <s xml:id="echoid-s709" xml:space="preserve">quarta li-<lb/>nea ex B, perpendicularis ad rectas A B, B E: </s> <s xml:id="echoid-s710" xml:space="preserve">quæ neceſſario ad planũ, in quo <lb/>ſunt rectę A B, B E, recta erit. </s> <s xml:id="echoid-s711" xml:space="preserve">Cum ergo & </s> <s xml:id="echoid-s712" xml:space="preserve">tertia linea excitate ſit ad idem <lb/>planum recta, ducentur duæ rectæ lineæ ex puncto B, ad idem planum perpea <lb/>diculares ad eaſdem partes, quod fieri non poteſt.</s> <s xml:id="echoid-s713" xml:space="preserve"/> </p> <div xml:id="echoid-div68" type="float" level="2" n="5"> <note position="right" xlink:label="note-051-01" xlink:href="note-051-01a" xml:space="preserve">Cur tãtum <lb/>tres ſint di <lb/>menſiones.</note> </div> <p> <s xml:id="echoid-s714" xml:space="preserve"><emph style="sc">His</emph> rite intellectis, facile duæ definitiones ſphæræ percipiẽtur. </s> <s xml:id="echoid-s715" xml:space="preserve">Ita namq. <lb/></s> <s xml:id="echoid-s716" xml:space="preserve">habet prima definitio, quã auctor ſe deſumpſiſſe teſtatur ab Euclide. </s> <s xml:id="echoid-s717" xml:space="preserve">[Sphæra <lb/> <anchor type="note" xlink:label="note-051-02a" xlink:href="note-051-02"/> eſt tranſituscircumferentiæ dimidij circuli, quæ fixa diametro, eouſque circunduci-<lb/>t<unsure/>ur, quouſque ad locum ſuum redit,] Id eſt, vt auctor ipſe declarat. </s> <s xml:id="echoid-s718" xml:space="preserve">[Sphæra eſt-<lb/>tale rotundum, ſeu ſolidum, quod deſeribitur ab arcu ſemicirculi circunducto.</s> <s xml:id="echoid-s719" xml:space="preserve">] Ne-<lb/>que enim ſphæra eſt tranſitus, ſeu reuolutio ipſa, ſed efficitur ex eiuſmodi trã <lb/>ſitu, ſeu reuolutione; </s> <s xml:id="echoid-s720" xml:space="preserve">Ita ut hæc prædicatio, Sphæra eſt tranſitus, ſit cauſalis, <lb/>minime uero formalis. </s> <s xml:id="echoid-s721" xml:space="preserve">Eſt enim ſenſus, quòd ſphæra eſt tale ſolidum, quod ab <lb/>arcu ſemicirculi, ſua quidem diametro immobili, & </s> <s xml:id="echoid-s722" xml:space="preserve">fixa manente, una comple <lb/>ta reuolutione circunſcribi intelligitur: </s> <s xml:id="echoid-s723" xml:space="preserve">Id autem Solidum circunſcribi intel-<lb/>ligitur, quod continue ab arcu circunducto tãgitur. </s> <s xml:id="echoid-s724" xml:space="preserve">Vt ſi ſumatur argilla, aut <lb/>quæuis alia materia tractabilis, cui diameter aliqua pro matetiæ ſpiſſitudine <lb/>inſeratur, & </s> <s xml:id="echoid-s725" xml:space="preserve">ad huius diametri extremitates ſemicirculi circunferentia utrin-<lb/>que applicata circunducatur, donec ad eum locum, ex quo dimoueri cœpit, te <lb/>uertatur, tolletur omnis inæqualitas argillæ, effi cieturq́ue figura ſphærica, ſi-<lb/>ue rotunda. </s> <s xml:id="echoid-s726" xml:space="preserve">Tale igitur corpus rotundum à circunferentia ſemicirculi deſcri-<lb/>ptum, Sphæra appellatur.</s> <s xml:id="echoid-s727" xml:space="preserve"/> </p> <div xml:id="echoid-div69" type="float" level="2" n="6"> <note position="right" xlink:label="note-051-02" xlink:href="note-051-02a" xml:space="preserve">Explicatio <lb/>ſuperioris <lb/>definitio-<lb/>nis ſphæræ.</note> </div> <pb o="16" file="052" n="53" rhead="Comment. in I. Cap. Sphæræ"/> <p> <s xml:id="echoid-s728" xml:space="preserve"><emph style="sc">Vervm</emph> dicet aliquis, cum circunferentia ſemicirculi ſit linea quædam <lb/> <anchor type="note" xlink:label="note-052-01a" xlink:href="note-052-01"/> curua omnis latitudinis expers, ex ductu autẽ, ſeu motu cuiuſuis lineæ imagi-<lb/>nario, omnium Mathematicorum conſenſu, non efficiatur niſi ſuperficies, qui <lb/>fieri poteſt, ut ſphæra, quæ eſt ſolidum quippam, vt & </s> <s xml:id="echoid-s729" xml:space="preserve">auctor ipſe in declaratio <lb/>ne ſuæ definitionis aſſeruit, & </s> <s xml:id="echoid-s730" xml:space="preserve">mox iterum ex Theodoſio ſubiungetur, gignatur <lb/>ex ductu, ſeu reuolutione, circumactione ve circunferentię ſemicirculi? </s> <s xml:id="echoid-s731" xml:space="preserve">nam <lb/> <anchor type="note" xlink:label="note-052-02a" xlink:href="note-052-02"/> ex tali circũductu ſola ſuperficies extima ſphæræ procreatur. </s> <s xml:id="echoid-s732" xml:space="preserve">Cui oecurrendũ <lb/>eſt, definitionem hanc Euclidis non eſſe fideliterab auctore recitatam. </s> <s xml:id="echoid-s733" xml:space="preserve">Eucli-<lb/>des enim in lib. </s> <s xml:id="echoid-s734" xml:space="preserve">11. </s> <s xml:id="echoid-s735" xml:space="preserve">defin. </s> <s xml:id="echoid-s736" xml:space="preserve">4. </s> <s xml:id="echoid-s737" xml:space="preserve">non dixit, Sphęram effici ex conuerſione circunfe <lb/>rentiæ ſemicirculi circa diametrũ, ſed ex ductu. </s> <s xml:id="echoid-s738" xml:space="preserve">ac reuolutione totius ſemicir-<lb/> <anchor type="note" xlink:label="note-052-03a" xlink:href="note-052-03"/> culi, quem quidem conſtat eſſe ſu perficiem. </s> <s xml:id="echoid-s739" xml:space="preserve">Quamobrem ſicut ex reuolutione <lb/>lineę rectæ finitæ circa alterũ extremum fixum deſcribitur circulus, ita vt ipſa <lb/>linea ſuperficiem efficiat, punctum vero alterum extremum circunferentiam <lb/>deſignet: </s> <s xml:id="echoid-s740" xml:space="preserve">ſic quoque ex circumactione quidem ſuperficiei ſemicirculi procrea-<lb/>bitur ſolidita@ ſphæræ, ex reuolutione uero ſemicircunferentiæ ſuperficies ex-<lb/>tima rotunda; </s> <s xml:id="echoid-s741" xml:space="preserve">atque hac ratione perfectum corpus ſphæricum naſcitur.</s> <s xml:id="echoid-s742" xml:space="preserve"/> </p> <div xml:id="echoid-div70" type="float" level="2" n="7"> <note position="left" xlink:label="note-052-01" xlink:href="note-052-01a" xml:space="preserve">Dubitatio <lb/>eõtra ſupe-<lb/>riorem de-<lb/>finitionem <lb/>auctoris.</note> <note position="left" xlink:label="note-052-02" xlink:href="note-052-02a" xml:space="preserve">Solutio du-<lb/>bitationis.</note> <note position="left" xlink:label="note-052-03" xlink:href="note-052-03a" xml:space="preserve">Definitio <lb/>ſphęrę ab <lb/>Eucl. tradi-<lb/>ta.</note> </div> <p style="it"> <s xml:id="echoid-s743" xml:space="preserve"><emph style="sc">Sphaera</emph> etiam à Theodoſio ſic deſcribitur; </s> <s xml:id="echoid-s744" xml:space="preserve">Sphæra eſt ſolidum <lb/> <anchor type="note" xlink:label="note-052-04a" xlink:href="note-052-04"/> quoddam una ſuperficie cotentum, in cuius medio punctus eſt, à quo omnes <lb/>lineæ ductæ ad circunferentiam ſunt æquales.</s> <s xml:id="echoid-s745" xml:space="preserve"/> </p> <div xml:id="echoid-div71" type="float" level="2" n="8"> <note position="left" xlink:label="note-052-04" xlink:href="note-052-04a" xml:space="preserve">Alia ſphę-<lb/>ræ defini-<lb/>tio tradita <lb/>à Thedo-<lb/>ſio.</note> </div> </div> <div xml:id="echoid-div73" type="section" level="1" n="42"> <head xml:id="echoid-head46" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s746" xml:space="preserve"><emph style="sc">Haec</emph> eſt ſecunda ſphæræ definitio deſumpta ex Theodoſio de ſphæri-<lb/>cis elementis; </s> <s xml:id="echoid-s747" xml:space="preserve">in aqua quidem tres particulæ continentur. </s> <s xml:id="echoid-s748" xml:space="preserve">Prima eſt [ſolidum] <lb/> <anchor type="note" xlink:label="note-052-05a" xlink:href="note-052-05"/> id eſt, corpus, poniturq́; </s> <s xml:id="echoid-s749" xml:space="preserve">ad differentiam figurarum planarum, cuiuſmodi eſt <lb/>circulus, quadratum, &</s> <s xml:id="echoid-s750" xml:space="preserve">c. </s> <s xml:id="echoid-s751" xml:space="preserve">Secunda [una ſuperficie contentum] apponitur ad ex-<lb/>cludendas figuras ſolidas pluribus ſuperficiebus comprehenſas, qualis eſt rota <lb/>currus, lapis molaris, pyramis, cubus, &</s> <s xml:id="echoid-s752" xml:space="preserve">c. </s> <s xml:id="echoid-s753" xml:space="preserve">Sed quoniam duplex eſt ſuperficies, <lb/>una plana, quæ ex omni parte linea recta adæquate poteſt cõmenſurari, ut eſt <lb/>ſuperficies alicuius muri bene cõplanati, uel tabulæ uel papyri bene extenſæ: <lb/></s> <s xml:id="echoid-s754" xml:space="preserve">Altera curua, quæ undique linea recta menſurari nequit; </s> <s xml:id="echoid-s755" xml:space="preserve">Atq; </s> <s xml:id="echoid-s756" xml:space="preserve">hæc uel eſt con <lb/>caua, ut eſt interior ſuperficies alicuius hydriæ; </s> <s xml:id="echoid-s757" xml:space="preserve">uel conuexa, cuiuſmodi eſt <lb/>exterior ſuperficies hydriæ, uel pilæ; </s> <s xml:id="echoid-s758" xml:space="preserve">Sphæra ſuperficie curua, eaq́; </s> <s xml:id="echoid-s759" xml:space="preserve">conuexa & </s> <s xml:id="echoid-s760" xml:space="preserve"><lb/>unica continetur. </s> <s xml:id="echoid-s761" xml:space="preserve">Tertia denique particula eſt [in cuius medio, &</s> <s xml:id="echoid-s762" xml:space="preserve">c.</s> <s xml:id="echoid-s763" xml:space="preserve">] adiungi-<lb/>turq́ue ad differentiam plurimorum ſolidorum una quidem ſuperficie conten <lb/>torum, in quibus tamen tale punctum aſſignari minime poteſt: </s> <s xml:id="echoid-s764" xml:space="preserve">quale eſt cor-<lb/>pus ouale, lenticulare, & </s> <s xml:id="echoid-s765" xml:space="preserve">alia huiuſmodi.</s> <s xml:id="echoid-s766" xml:space="preserve"/> </p> <div xml:id="echoid-div73" type="float" level="2" n="1"> <note position="left" xlink:label="note-052-05" xlink:href="note-052-05a" xml:space="preserve">Explicatio <lb/>definitio-<lb/>nis ſphærę <lb/>à Theodoſ. <lb/>@aditæ.</note> </div> <p> <s xml:id="echoid-s767" xml:space="preserve"><emph style="sc">Qvod</emph> ſi hanc deſinitionem cum priore conferamus, reperiemus illam fa-<lb/>bricandæ ſphærę modum, induſtriamq́; </s> <s xml:id="echoid-s768" xml:space="preserve">nobis præbere: </s> <s xml:id="echoid-s769" xml:space="preserve">hanc uero ſphæræ iam <lb/> <anchor type="note" xlink:label="note-052-06a" xlink:href="note-052-06"/> ſabricatæ ſubſtantiam explicare, ob idq́; </s> <s xml:id="echoid-s770" xml:space="preserve">illã potius deſcriptionẽ, hanc uero de <lb/>finitionem dicẽdã eſſe. </s> <s xml:id="echoid-s771" xml:space="preserve">Quam quidem definitionem Theodoſij deſumptam ex <lb/>Tymęo Platonis eleganter expreſſit Cicero in lib. </s> <s xml:id="echoid-s772" xml:space="preserve">de Vniuerſitate his uerbis <lb/>de mundo loquens. </s> <s xml:id="echoid-s773" xml:space="preserve">Ergo globoſus eſt fabricatus, quod σ φ {αι}ρώ{ει}δες Græci vocant, <lb/>cuius omnis extremitas paribus à medio radijs attingitur. </s> <s xml:id="echoid-s774" xml:space="preserve">Conuenit enim hęc etiam <lb/>definitio uniuerſo mundo; </s> <s xml:id="echoid-s775" xml:space="preserve">Mundus ſiquidem eſt ſphęra ſolida, cum nihil in <lb/>ipſo uacuum exiſtat, ſed omnia corporibus ſint repleta à mundi conuexitate <pb o="17" file="053" n="54" rhead="Ioan. de Sacro Boſco."/> vſque ad eius contrum, vt in 4. </s> <s xml:id="echoid-s776" xml:space="preserve">Phyſ. </s> <s xml:id="echoid-s777" xml:space="preserve">Ariſtoteles probat.</s> <s xml:id="echoid-s778" xml:space="preserve"/> </p> <div xml:id="echoid-div74" type="float" level="2" n="2"> <note position="left" xlink:label="note-052-06" xlink:href="note-052-06a" xml:space="preserve">Cõparatio <lb/>duarũ ſphæ <lb/>ræ definitio <lb/>nũ interſe.</note> </div> <p> <s xml:id="echoid-s779" xml:space="preserve"><emph style="sc">Vervm</emph> ſi rem diligentius introſpiciamus, ambæ prædictæ definitiones <lb/>ſphæræ potius cuilibet globo, ſeu pilæ accõmodari poſſunt, quam ſphæræ illi, <lb/>de qua l@bellum inſcripſit auctor, & </s> <s xml:id="echoid-s780" xml:space="preserve">de qua præcipue nobis eſt futura diſputa-<lb/>tio; </s> <s xml:id="echoid-s781" xml:space="preserve">idcirco aliã deſcriptionẽ adducemus hoc modo. </s> <s xml:id="echoid-s782" xml:space="preserve">Sphæra (de qua agendũ <lb/> <anchor type="note" xlink:label="note-053-01a" xlink:href="note-053-01"/> nobis eſt) eſt inſtrumentum quod dã rotundum, in quo varij circuli armil lęve <lb/>continentur, quibus cęlorum motus, & </s> <s xml:id="echoid-s783" xml:space="preserve">totius mundi ſitus commodiſſime expli <lb/>cantur. </s> <s xml:id="echoid-s784" xml:space="preserve">Quale nimirum eſt inſtrumentum, quod ſphæram materialem dicunt.</s> <s xml:id="echoid-s785" xml:space="preserve"/> </p> <div xml:id="echoid-div75" type="float" level="2" n="3"> <note position="right" xlink:label="note-053-01" xlink:href="note-053-01a" xml:space="preserve">Deſcriptio <lb/>ſphæræ ma <lb/>@erialis, de <lb/>qua hic agi <lb/>tur.</note> </div> <note position="right" xml:space="preserve">Qui dican-<lb/>tur inuẽto <lb/>res primi <lb/>ſphæræ ma <lb/>terialis.</note> <p> <s xml:id="echoid-s786" xml:space="preserve"><emph style="sc">Qvi</emph> autem fuerint pulcherrimi iſtius inſtrumenti inuentores primi, non <lb/>ſatis conſtat. </s> <s xml:id="echoid-s787" xml:space="preserve">Quidam enim putant, Atlantem ſphæram primum reperiſſe; </s> <s xml:id="echoid-s788" xml:space="preserve">De <lb/>inde eam tranſportatam fuiſſe in Græciam ab Her@ule, vt auctor eſt Plinius. <lb/></s> <s xml:id="echoid-s789" xml:space="preserve">Quidam vero, utidem teſtatur, Anaximandrum M@leſium primum inuentorẽ <lb/>faciunt. </s> <s xml:id="echoid-s790" xml:space="preserve">Laertius Diogenes Muſæo hanc inuentionem aſcribit. </s> <s xml:id="echoid-s791" xml:space="preserve">Alij denique <lb/>alios inuentores faciunt; </s> <s xml:id="echoid-s792" xml:space="preserve">inter quos etiam connumeratur Architas Tarẽtinus <lb/>non ignobilis Scriptor. </s> <s xml:id="echoid-s793" xml:space="preserve">Cicero tamen, & </s> <s xml:id="echoid-s794" xml:space="preserve">Maternus teſtantur, Archimedem <lb/>Sytacuſanum Mathematicum ſubtiliſſimũ inuentorem primum extitiſſe ſphæ <lb/>ræ in trumẽtalis, quæ ſphærã illam cęleſtem ad viuum repræſentaret. </s> <s xml:id="echoid-s795" xml:space="preserve">Nam vt <lb/>nobis cęlorum cõpoſitionem, ordinationem, motusq́ue eorum ob oculos po-<lb/> <anchor type="note" xlink:label="note-053-03a" xlink:href="note-053-03"/> neret, fabricauit, inquiunt, ſphæram quandam vitream omnino trãſparentem <lb/>tanto artificio, vt in ea planetarũ globi, præcipue Solis, ac Lunæ, proprijs mo-<lb/>tibus in diuerſas mundi plagas incederent non ſecus, ac in cęlo ipſo mouẽtur: <lb/></s> <s xml:id="echoid-s796" xml:space="preserve">ita perfecte, & </s> <s xml:id="echoid-s797" xml:space="preserve">ad amuſſim ſphæram cęleſtem imitabatur ſphæra hæc vitrea ab <lb/>Archimede ſumma induſtria, ac arte conſtructa. </s> <s xml:id="echoid-s798" xml:space="preserve">De qua ſphæra Claudianus <lb/>poeta elegantiſſimum Epigramma conſcripſit, quod libuit hic apponere.</s> <s xml:id="echoid-s799" xml:space="preserve"/> </p> <div xml:id="echoid-div76" type="float" level="2" n="4"> <note position="right" xlink:label="note-053-03" xlink:href="note-053-03a" xml:space="preserve">Sphęra ad <lb/>mirabilis <lb/>Archime-<lb/>dis.</note> </div> <p style="it"> <s xml:id="echoid-s800" xml:space="preserve">Iuppiter in paruo cum cerneret æthera vitro.</s> <s xml:id="echoid-s801" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s802" xml:space="preserve">Riſit, & </s> <s xml:id="echoid-s803" xml:space="preserve">ad ſuperos talia dicta dedit.</s> <s xml:id="echoid-s804" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s805" xml:space="preserve">Huccine mortalis progreßa potentia curę.</s> <s xml:id="echoid-s806" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s807" xml:space="preserve">Iam meus in fragili luditur orbe labor.</s> <s xml:id="echoid-s808" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s809" xml:space="preserve">Iura poli, rerumq́; </s> <s xml:id="echoid-s810" xml:space="preserve">fidem, legesq́; </s> <s xml:id="echoid-s811" xml:space="preserve">Deorum</s> </p> <p style="it"> <s xml:id="echoid-s812" xml:space="preserve">Ecce Syracuſius tranſtulit arte ſenex.</s> <s xml:id="echoid-s813" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s814" xml:space="preserve">Incluſus varijs famulatur ſpiritus aſtris,</s> </p> <p style="it"> <s xml:id="echoid-s815" xml:space="preserve">Et viuum certis motibus urget opus.</s> <s xml:id="echoid-s816" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s817" xml:space="preserve">Percurrit proprium mentitus Signifer annum,</s> </p> <p style="it"> <s xml:id="echoid-s818" xml:space="preserve">Et ſimulata nouo Cinthia menſe redit.</s> <s xml:id="echoid-s819" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s820" xml:space="preserve">Iamq; </s> <s xml:id="echoid-s821" xml:space="preserve">ſuum uoluens audax induſiria mundum</s> </p> <p style="it"> <s xml:id="echoid-s822" xml:space="preserve">Gaudet, & </s> <s xml:id="echoid-s823" xml:space="preserve">humana ſidera mente regit.</s> <s xml:id="echoid-s824" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s825" xml:space="preserve"><emph style="sc">Et</emph> ille punctus dicitur centrum ſpheræ. </s> <s xml:id="echoid-s826" xml:space="preserve">Linea uero recta tranſiens <lb/> <anchor type="note" xlink:label="note-053-04a" xlink:href="note-053-04"/> per centrum ſphæræ, applicans extremitates ſuas ad circunferentiam <lb/>ex utraque parte, circa quam ſphæra uoluitur, dicitur axis ſphærę. </s> <s xml:id="echoid-s827" xml:space="preserve">Duo <lb/>uero puncta axem terminantia dicuntur poli ſphærę.</s> <s xml:id="echoid-s828" xml:space="preserve"/> </p> <div xml:id="echoid-div77" type="float" level="2" n="5"> <note position="right" xlink:label="note-053-04" xlink:href="note-053-04a" xml:space="preserve">Centrum, <lb/>axis, & poli <lb/>ſphærę qd.</note> </div> </div> <div xml:id="echoid-div79" type="section" level="1" n="43"> <head xml:id="echoid-head47" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s829" xml:space="preserve"><emph style="sc">Declarat</emph> hic tribus reliquis definitionibus, quid ſit centrum ſphę-<lb/>ræ, quid axis, quid denique ſint poli ſphæræ; </s> <s xml:id="echoid-s830" xml:space="preserve">quæ omnia perſpicua ſunt in <lb/>auctore.</s> <s xml:id="echoid-s831" xml:space="preserve"/> </p> <pb o="18" file="054" n="55" rhead="Comment. in I. Cap. Sphæræ"/> <p> <s xml:id="echoid-s832" xml:space="preserve"><emph style="sc">Centrvm</emph> ſphæræ Euclides in lib. </s> <s xml:id="echoid-s833" xml:space="preserve">12. </s> <s xml:id="echoid-s834" xml:space="preserve">ita deſcribit. </s> <s xml:id="echoid-s835" xml:space="preserve">Centrum ſphæræ <lb/> <anchor type="note" xlink:label="note-054-01a" xlink:href="note-054-01"/> eſt idem, quod & </s> <s xml:id="echoid-s836" xml:space="preserve">ſemirculi, à cuius reuolutione ſphęra effici intelligitur.</s> <s xml:id="echoid-s837" xml:space="preserve"/> </p> <div xml:id="echoid-div79" type="float" level="2" n="1"> <note position="left" xlink:label="note-054-01" xlink:href="note-054-01a" xml:space="preserve">Centrũ, & <lb/>axis ſphærę <lb/>quid ſecun <lb/>dum Eucli-<lb/>dem.</note> </div> <p> <s xml:id="echoid-s838" xml:space="preserve"><emph style="sc">Axem</emph> uero ita definit Euclides loco citato. </s> <s xml:id="echoid-s839" xml:space="preserve">Axis ſphæræ eſt quieſcens <lb/>illa linea, circa quam ſemicirculus, ex cuius nimirum circumactione ſphæra <lb/>conficitur) co nuertitur. </s> <s xml:id="echoid-s840" xml:space="preserve">Proclus autem Diadochus ſic. </s> <s xml:id="echoid-s841" xml:space="preserve">Axis mundi (quem nos <lb/>iam ſphæram eſſe diximus) vocatur dimetiens ipſius, circa quam uoluitur. </s> <s xml:id="echoid-s842" xml:space="preserve">Ex <lb/>his vero omnibus definitionibus perſpicuum eſt, non omnem lineam, quæ per <lb/>centrum ſphæræ tranſiens extremitates ſuas ad circunferentiam ex utraq; </s> <s xml:id="echoid-s843" xml:space="preserve">par <lb/>te applicat, axem dici, (quamuis diameter dicatur) niſi circa eam ſphæra volua <lb/>tur. </s> <s xml:id="echoid-s844" xml:space="preserve">Multo enim plura complectitur diameter, quam axis, cũ axis ſit quid infe-<lb/>rius, Diameter uero quid ſuperius: </s> <s xml:id="echoid-s845" xml:space="preserve">Omnis ſiquidem axis diameter eſt, at non <lb/> <anchor type="note" xlink:label="note-054-02a" xlink:href="note-054-02"/> contra; </s> <s xml:id="echoid-s846" xml:space="preserve">Quoniam in ſphæra cęleſti ſolæ eæ diametri axes dici poſſunt, circa <lb/>quas fit aliquis motus, quę quidem paucæ ſunt, & </s> <s xml:id="echoid-s847" xml:space="preserve">pręcipuus axis eſt ille, qui <lb/>protenditur à ſeptentrione per mediam terram uerſus auſtrum: </s> <s xml:id="echoid-s848" xml:space="preserve">Innumeræ ta-<lb/>men diametri aſſignari poſſunt. </s> <s xml:id="echoid-s849" xml:space="preserve">omnes nimirum lineæ per centrũ ſphæræ tran <lb/>ſeuntes; </s> <s xml:id="echoid-s850" xml:space="preserve">immo & </s> <s xml:id="echoid-s851" xml:space="preserve">planæ figuræ diametros habent, vt circulus, &</s> <s xml:id="echoid-s852" xml:space="preserve">c. </s> <s xml:id="echoid-s853" xml:space="preserve">non autem <lb/>axem. </s> <s xml:id="echoid-s854" xml:space="preserve">Axis etenim in ſolidis duntaxat corporibus reperitur. </s> <s xml:id="echoid-s855" xml:space="preserve">Poteſt tamen <lb/>quæuis diameter dici quoque axĩs, quia circa eam circumuolui poteſt ſphęra, <lb/>quemadmodum circa axem mundi, licet re ipſa non moueatur. </s> <s xml:id="echoid-s856" xml:space="preserve">Sic apud Geo-<lb/>metras, atque Aſtronomos quilibet circulus in ſphæra habere dicitur axem <lb/>proprium, circa quem nimirum circulariter, atque vniformiter moueretur, ſi <lb/>deberet moueri, quamuis actu non moueatur. </s> <s xml:id="echoid-s857" xml:space="preserve">Huiuſmodi axis eſt diameter <lb/>ſphæræ per centrum circuli ducta, & </s> <s xml:id="echoid-s858" xml:space="preserve">ad angulos rectos plano eiuſdem circuli <lb/>inſiſtens. </s> <s xml:id="echoid-s859" xml:space="preserve">Dicitur autem illa diameter, circa quam cęlum, ſeu ſphæra conuer-<lb/>titur, axis, ſumpta ſimilitudine ab axe ligneo, ſuper quẽ rota alicuius currus <lb/>contorquetur; </s> <s xml:id="echoid-s860" xml:space="preserve">deriuaturq́; </s> <s xml:id="echoid-s861" xml:space="preserve">hoc nomen ab agendo, id eſt, mouendo, quia uide-<lb/>licet circa eum mundus ſine intermiſſione circumagitur. </s> <s xml:id="echoid-s862" xml:space="preserve">Quem nobis Mani-<lb/>lius poeta eleganter depinxit his carminibus.</s> <s xml:id="echoid-s863" xml:space="preserve"/> </p> <div xml:id="echoid-div80" type="float" level="2" n="2"> <note position="left" xlink:label="note-054-02" xlink:href="note-054-02a" xml:space="preserve">Diſcrimen <lb/>inter dia-<lb/>metrum, & <lb/>axẽ ſphę ę.</note> </div> <p style="it"> <s xml:id="echoid-s864" xml:space="preserve">Aera per gelidum tenuis deducitur axis,</s> </p> <p style="it"> <s xml:id="echoid-s865" xml:space="preserve">Libratumq́; </s> <s xml:id="echoid-s866" xml:space="preserve">gerit diuerſo cardine Mundum,</s> </p> <p style="it"> <s xml:id="echoid-s867" xml:space="preserve">Sidereus medium circa quem voluitur orbis.</s> <s xml:id="echoid-s868" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s869" xml:space="preserve">Aeternosq́; </s> <s xml:id="echoid-s870" xml:space="preserve">rotat curſus immotus, . </s> <s xml:id="echoid-s871" xml:space="preserve">. </s> <s xml:id="echoid-s872" xml:space="preserve">. </s> <s xml:id="echoid-s873" xml:space="preserve">. </s> <s xml:id="echoid-s874" xml:space="preserve">.</s> <s xml:id="echoid-s875" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s876" xml:space="preserve">Axe quoque cęlum, terramq́; </s> <s xml:id="echoid-s877" xml:space="preserve">ſuſtineri finxerunt antiqui. </s> <s xml:id="echoid-s878" xml:space="preserve">Vnde Cicero ait. <lb/></s> <s xml:id="echoid-s879" xml:space="preserve">Terra, quę tranſiecto axe ſuſtinetur. </s> <s xml:id="echoid-s880" xml:space="preserve">Ad quod alludit Lucanus, quando Cæſa-<lb/>ri ſedem in cęlo commonſtrat, ita ſcribens.</s> <s xml:id="echoid-s881" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s882" xml:space="preserve">Aetheris immenſi partem ſi preſſeris unam,</s> </p> <p style="it"> <s xml:id="echoid-s883" xml:space="preserve">Sentiet axis onus librati pondera cæli.</s> <s xml:id="echoid-s884" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s885" xml:space="preserve"><emph style="sc">Qvoniam</emph> uero duo ſunt poli mundi; </s> <s xml:id="echoid-s886" xml:space="preserve">duo uidelicet puncta axem ter-<lb/> <anchor type="note" xlink:label="note-054-03a" xlink:href="note-054-03"/> minãtia; </s> <s xml:id="echoid-s887" xml:space="preserve">Ille, qui nobis hic Europa degẽtibus ſemper apparet, conſpicuusq́ue <lb/>exiſtit, dicitur Borealis, ſiue Boreus, Septentrionalis, Aquiloniusve: </s> <s xml:id="echoid-s888" xml:space="preserve">Ab <lb/>Aſtronomis autem appellatur polus Arcticus, id eſt, Vrſinus, a conſtellatione <lb/>quadam infigni, quæ Gręce dicitur ἀρκτὸς, Latine vrſa, perpetuoq́; </s> <s xml:id="echoid-s889" xml:space="preserve">circa po-<lb/>lum hunc conuertitur. </s> <s xml:id="echoid-s890" xml:space="preserve">Hunc quoque pleręque nationes uocant Nort; </s> <s xml:id="echoid-s891" xml:space="preserve">Italis <lb/>uero Tramontana dicitur. </s> <s xml:id="echoid-s892" xml:space="preserve">Alter uero polus Auſtralis dicitur, uel Auſtrinus, <lb/>Meridionalis, uel Notius; </s> <s xml:id="echoid-s893" xml:space="preserve">Aſtronomi uocant Antarcticum, quod per diame-<lb/>trum oppoſitus ſit polo Arctico. </s> <s xml:id="echoid-s894" xml:space="preserve">Hic nunquam à nobis conſpicitur; </s> <s xml:id="echoid-s895" xml:space="preserve">Semper <lb/>enim tantum ſub noſtro hemiſphęrio deliteſcit, quantum alter ſupra idem he- <pb o="19" file="055" n="56" rhead="Ioan. de Sacro Boſco."/> miſphærium attollitur, ut hic Romæ 42. </s> <s xml:id="echoid-s896" xml:space="preserve">ferme grad. </s> <s xml:id="echoid-s897" xml:space="preserve">Vtrumque hunc polum <lb/>pulchre deſcribit Virgilius, cum ait.</s> <s xml:id="echoid-s898" xml:space="preserve"/> </p> <div xml:id="echoid-div81" type="float" level="2" n="3"> <note position="left" xlink:label="note-054-03" xlink:href="note-054-03a" xml:space="preserve">@oli. mũdi.</note> </div> <p style="it"> <s xml:id="echoid-s899" xml:space="preserve">Hic Vertex nobis ſemper ſublimis, at illum</s> </p> <p style="it"> <s xml:id="echoid-s900" xml:space="preserve">Sub pedib{us} ſtyx atra videt, manesq́. </s> <s xml:id="echoid-s901" xml:space="preserve">profundi.</s> <s xml:id="echoid-s902" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s903" xml:space="preserve">A Nautis uterq; </s> <s xml:id="echoid-s904" xml:space="preserve">polus ſtella maris, ſeu ſtella nautarum dicitur, non qd po-<lb/>li ipſi ſint ſtellæ, ſed quod prope ipſos ſint ſtellæ quædam ita propinque, vt vix <lb/> <anchor type="note" xlink:label="note-055-01a" xlink:href="note-055-01"/> moueri cernantur, (quamuis iuxta polum Antarcticum nulla ſtella inſignis de <lb/>prehenſa ſit, quæ minus, quam grad. </s> <s xml:id="echoid-s905" xml:space="preserve">30. </s> <s xml:id="echoid-s906" xml:space="preserve">ab ipſo polo abſit) quarum ea quæ po <lb/>lo Arctica uiciniſſima eſt, in extremitate caudæ urſæ minoris exiſtit; </s> <s xml:id="echoid-s907" xml:space="preserve">quæ uero <lb/>Antarctico polo vicinior obſeruatur, in extremo pede ſiniſtro Cẽtauri poſita <lb/>eſt. </s> <s xml:id="echoid-s908" xml:space="preserve">Quoniam vero ad has ſtellas Nautæ reſpicientes itinera ſua per medium <lb/>mare dirigunt, propterea utraque ſtella maris, uel Nautarum dici conſueuit.</s> <s xml:id="echoid-s909" xml:space="preserve"/> </p> <div xml:id="echoid-div82" type="float" level="2" n="4"> <note position="right" xlink:label="note-055-01" xlink:href="note-055-01a" xml:space="preserve">Stella m@-<lb/>ris idem, <lb/>quod po-<lb/>lus.</note> </div> <p> <s xml:id="echoid-s910" xml:space="preserve"><emph style="sc">Dicvntvr</emph> autem poli a uerbo Græco, πολέω, quod ſignificat uerto <lb/> <anchor type="note" xlink:label="note-055-02a" xlink:href="note-055-02"/> ſeu circumago; </s> <s xml:id="echoid-s911" xml:space="preserve">Circa enim illa duo puncta tota mundi machina indeſinenter <lb/>circumuoluitur. </s> <s xml:id="echoid-s912" xml:space="preserve">Porro nonnulli hæc duo puncta Vertices, ſeu Cardines mun-<lb/>di appellant: </s> <s xml:id="echoid-s913" xml:space="preserve">Sicut enim ianua circa cardines voluitur, ita etiam tota mundi <lb/>ſtructura circa dicta puncta, quæ ſola immobilia ſunt, conuertitur.</s> <s xml:id="echoid-s914" xml:space="preserve"/> </p> <div xml:id="echoid-div83" type="float" level="2" n="5"> <note position="right" xlink:label="note-055-02" xlink:href="note-055-02a" xml:space="preserve">Vnde dicti <lb/>ſint poli.</note> </div> </div> <div xml:id="echoid-div85" type="section" level="1" n="44"> <head xml:id="echoid-head48" xml:space="preserve">DIVISIO SPHÆRÆ MVNDI.</head> <p style="it"> <s xml:id="echoid-s915" xml:space="preserve"><emph style="sc">SPhaera</emph> autem mundi dupliciter diuiditur, ſecundum ſub-<lb/>ſtantiam, et ſecundum accidens. </s> <s xml:id="echoid-s916" xml:space="preserve">Secundum ſubſtantiam, in ſphę <lb/> <anchor type="note" xlink:label="note-055-03a" xlink:href="note-055-03"/> ras nouem; </s> <s xml:id="echoid-s917" xml:space="preserve">Scilicet, ſphæram nonam, quę primus motus, ſiue <lb/>primum mobile dicitur: </s> <s xml:id="echoid-s918" xml:space="preserve">& </s> <s xml:id="echoid-s919" xml:space="preserve">in ſphæram ſtellarum fixarum, quæ <lb/>firmamentum nuncupatur: </s> <s xml:id="echoid-s920" xml:space="preserve">& </s> <s xml:id="echoid-s921" xml:space="preserve">in ſeptem ſphæras ſeptem planetarum qua-<lb/>rum quædam ſunt maiores, quędam minores, ſecundum quod plus accedunt <lb/>uel recedunt à firmamento. </s> <s xml:id="echoid-s922" xml:space="preserve">Vnde inter illas ſphæras ſphæra Saturni maxi <lb/>ma, ſphæra uero Lunæ minima exiſtit.</s> <s xml:id="echoid-s923" xml:space="preserve"/> </p> <div xml:id="echoid-div85" type="float" level="2" n="1"> <note position="right" xlink:label="note-055-03" xlink:href="note-055-03a" xml:space="preserve">Diuiſi@ <lb/>ſphære ſe-<lb/>cũdum ſub <lb/>ſtantiam.</note> </div> </div> <div xml:id="echoid-div87" type="section" level="1" n="45"> <head xml:id="echoid-head49" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s924" xml:space="preserve"><emph style="sc">Haecest</emph> ſecunda pars huius capitis, in qua duæ duiſiones ſphæræ <lb/>mundi afferuntur, una ſecundum ſubſtantiam, altera ſecundum accidens. <lb/></s> <s xml:id="echoid-s925" xml:space="preserve"> <anchor type="note" xlink:label="note-055-04a" xlink:href="note-055-04"/> Secundum ſubſtantiam diuidit auctor ſphæram mundi in nouem ſphæras. </s> <s xml:id="echoid-s926" xml:space="preserve">In <lb/>qua diuiſione non ſumitur ſphæra, vt complectitur omnia corpora mundum <lb/>uniuerſum componentia, cęlos uidelicet, & </s> <s xml:id="echoid-s927" xml:space="preserve">elementa; </s> <s xml:id="echoid-s928" xml:space="preserve">Sic enim plures eſſent <lb/>ſphæræ, quam nouem, vt paulo poſt erit manifeſtum, quando de numero cælo <lb/>rum, & </s> <s xml:id="echoid-s929" xml:space="preserve">elementorum eorumq́. </s> <s xml:id="echoid-s930" xml:space="preserve">ordine diſputabimus: </s> <s xml:id="echoid-s931" xml:space="preserve">Sed accipitur pro ſphęra <lb/>cæleſti, quæ quidem conſtat, ſeu continetur duabus ſuperficiebus, conuexa ni <lb/>mirum exteriore, & </s> <s xml:id="echoid-s932" xml:space="preserve">concaua interiore, diciturq́ue proprie orbis; </s> <s xml:id="echoid-s933" xml:space="preserve">Hoc namq <lb/> <anchor type="note" xlink:label="note-055-05a" xlink:href="note-055-05"/> differt orbis a ſphæra, quod hæc ad centrum vſq. </s> <s xml:id="echoid-s934" xml:space="preserve">tota ſit ſolida, unicaque tan <lb/>tum ſuperficie, puta conuexa exteriore concludatur, orbis autem non rta, ſed <lb/>duabus finiatur ſuperficiebus, una exteriore, & </s> <s xml:id="echoid-s935" xml:space="preserve">altera interiore, quales ſunt <lb/>omnes cæli.</s> <s xml:id="echoid-s936" xml:space="preserve"/> </p> <div xml:id="echoid-div87" type="float" level="2" n="1"> <note position="right" xlink:label="note-055-04" xlink:href="note-055-04a" xml:space="preserve">Sphæra hic <lb/>diuiſa ſu-<lb/>mitur pro <lb/>ſphæra c@-<lb/>leſti.</note> <note position="right" xlink:label="note-055-05" xlink:href="note-055-05a" xml:space="preserve">Differentia <lb/>inter orbẽ, <lb/>& ſphærã. <lb/>Sphę@a, ſeu <lb/>orbis cæle-<lb/>ſtis duobus <lb/>modis acci-<lb/>pitur.</note> </div> <p> <s xml:id="echoid-s937" xml:space="preserve"><emph style="sc">Sed</emph> quoniam ſphæra, ſeu orbis cæleſtis duobus modis ſumi poteſt; </s> <s xml:id="echoid-s938" xml:space="preserve">uno <lb/>modo pro quolibet orbe diuiſo ab alio, ſiue ſit concentricus mundo, ſiue eccẽ <pb o="20" file="056" n="57" rhead="Comment. in I. Cap. Sphæræ"/> tricus, hoc eſt, ſiue idem cum mundo centrum poſſideat, ſiue diuerſum: </s> <s xml:id="echoid-s939" xml:space="preserve">quo <lb/>pacto quilibet Planeta plures orbes continere dicitur, quorum tractatio, & </s> <s xml:id="echoid-s940" xml:space="preserve">con <lb/>ſideratio ad Theoricas planetarum ſpectat, quamuis etiam auctor noſter eos <lb/>breuiſſime capite 4. </s> <s xml:id="echoid-s941" xml:space="preserve">perſtringere conetur: </s> <s xml:id="echoid-s942" xml:space="preserve">Alio modo ſumitur ſphæra cœleſtis <lb/>pro orbe totali ab alijs diuiſo, qui undequaque a mundi centro æquidiſtat, & </s> <s xml:id="echoid-s943" xml:space="preserve"><lb/>tam ſecundum conuexum, quàm ſecundum concauum mundo cõcẽtricus exi-<lb/>ſtit, conficiturq́. </s> <s xml:id="echoid-s944" xml:space="preserve">ex pluribus orbibus particularibus, qui ordinantur ad motum <lb/>planetæ, quo pacto quiuis planeta unum proprium, & </s> <s xml:id="echoid-s945" xml:space="preserve">peculiarem orbem habe <lb/> <anchor type="note" xlink:label="note-056-01a" xlink:href="note-056-01"/> re dicitur, continentem alios orbes partiales partim concentricos, partim ec-<lb/>centricos, ut in Theoricis planetarum fiet perſpicuum. </s> <s xml:id="echoid-s946" xml:space="preserve">Hoc igitur modo poſte <lb/>riore accipitur in hac diuiſione ſphæra, pro orbe uidelicet cæleſti integro con <lb/>tinente plures alios partiales ad motũ planetæ ordinatos, ſiue hi concentrici <lb/>ſint, ſiue eccentrici. </s> <s xml:id="echoid-s947" xml:space="preserve">Diuidit itaque auctor ſphæram ita acceptam in 9. </s> <s xml:id="echoid-s948" xml:space="preserve">ſphæras <lb/>nempe in ſphæram nonam, quę primus motus, ſiue primum mobile dicitur: </s> <s xml:id="echoid-s949" xml:space="preserve">& </s> <s xml:id="echoid-s950" xml:space="preserve"><lb/>in ſphæram ſtellarum fixarum, quæ Firmamentum nuncupatur, & </s> <s xml:id="echoid-s951" xml:space="preserve">in ſeptem <lb/>ſphæras ſeptem planetarum, videlicet in ſphærã Saturni, louis, Martis, Solis, <lb/>Veneris, Mercurij, & </s> <s xml:id="echoid-s952" xml:space="preserve">Lunæ. </s> <s xml:id="echoid-s953" xml:space="preserve">Hanc tamen diuiſionem paulo poſt examinabimus, <lb/>quoniam Aſtronomi recentiores plures ſphæras cæleſtes conſtituunt.</s> <s xml:id="echoid-s954" xml:space="preserve"/> </p> <div xml:id="echoid-div88" type="float" level="2" n="2"> <note position="left" xlink:label="note-056-01" xlink:href="note-056-01a" xml:space="preserve">Quo pacto <lb/>accipiatur <lb/>ſphæra cæle <lb/>ſtis in hac <lb/>diuiſione.</note> </div> <p> <s xml:id="echoid-s955" xml:space="preserve"><emph style="sc">Svnt</emph> autem omnes orbes cæleſtes contigui prorſus, & </s> <s xml:id="echoid-s956" xml:space="preserve">immediati inter <lb/> <anchor type="note" xlink:label="note-056-02a" xlink:href="note-056-02"/> ſe, ita vt ſemper ſuperior inferiorem includat, nihilq́ue inter vnum atque alte <lb/>rum ſit medium, non ſecus ac in tunicis cæparum uidemus ſuperiorem vndiq. <lb/></s> <s xml:id="echoid-s957" xml:space="preserve">circundare inferiorem; </s> <s xml:id="echoid-s958" xml:space="preserve">quod quidem ita eſſe demonſtrabimus, cũ de ordine cæ <lb/>lorum diſputabimus. </s> <s xml:id="echoid-s959" xml:space="preserve">Quare cum omne corpus continens maius ſit corpore <lb/>contento, quo ad ambitum, recte ſubiungit auctor, ſphærarum cęleſtium quaſ-<lb/>dam eſſe maiores, & </s> <s xml:id="echoid-s960" xml:space="preserve">quaſdam minores, ſecundum quod plus accedunt, uel re-<lb/>cedunt a Firmamento. </s> <s xml:id="echoid-s961" xml:space="preserve">Erit enim hac ratione ſphæra nona omnium maxima; </s> <s xml:id="echoid-s962" xml:space="preserve"><lb/>Deinde firmamentum maius erit ſphæra Saturni, quę ſtatim ſubſequitur, & </s> <s xml:id="echoid-s963" xml:space="preserve">ſic <lb/>deinceps, donec ad ſphæram Lunæ, quæ infima eſt; </s> <s xml:id="echoid-s964" xml:space="preserve">deueniamus. </s> <s xml:id="echoid-s965" xml:space="preserve">Hæc namque <lb/>omnium ſphærarum minima eſt.</s> <s xml:id="echoid-s966" xml:space="preserve"/> </p> <div xml:id="echoid-div89" type="float" level="2" n="3"> <note position="left" xlink:label="note-056-02" xlink:href="note-056-02a" xml:space="preserve">Orbes cæle-<lb/>ſtes inter ſe <lb/>@õtigui sũt.</note> </div> <p> <s xml:id="echoid-s967" xml:space="preserve"><emph style="sc">Dicitvr</emph> nona ſphæra ab auctore, & </s> <s xml:id="echoid-s968" xml:space="preserve">alijs Aſtronomis primus motus, <lb/> <anchor type="note" xlink:label="note-056-03a" xlink:href="note-056-03"/> ſeu primum mobile, quoniam, vt ipſi putãt, nullum aliud cælum mobile ſupra <lb/>ipſam exiſtit, ſuoq́. </s> <s xml:id="echoid-s969" xml:space="preserve">motu uelociſſimo, ut ſuo loco dicemus, omnes alias inſe-<lb/>riores ſphæras, quas ambit, ſecum rapit ab ortu in occaſum ſpacio vigintiqua-<lb/>tuor horarum. </s> <s xml:id="echoid-s970" xml:space="preserve">Quamuis autem nonam ſphæram, quam auctor hic putat eſſe <lb/>ſupremam, ac primum mobile, ſine diſcrimine poſſimus dicere & </s> <s xml:id="echoid-s971" xml:space="preserve">primam ſphæ <lb/>ram, & </s> <s xml:id="echoid-s972" xml:space="preserve">nonam, ſiue ultimam; </s> <s xml:id="echoid-s973" xml:space="preserve">Primam quidem ordine naturę, quia proprior eſt <lb/>primo enti, qua ratione ſphæra Lunæ vltima exiſtit, cum a primo ente ſit re-<lb/>motiſſima; </s> <s xml:id="echoid-s974" xml:space="preserve">Nonam uero ultimamve, quo ad nos, quia uidelicet remotior a no-<lb/>bis exiſtit, quo pacto Lunæ ſphæra, quoniam nobis eſt propinquior, dicetur eſ-<lb/>ſe prima: </s> <s xml:id="echoid-s975" xml:space="preserve">Non tamen ab Aſtronomis dici conſueuit vltimus motus, ſeu ulti-<lb/>mum mobile, ſed ſolum primus motus, vel primum mobile, ob dignitatem, & </s> <s xml:id="echoid-s976" xml:space="preserve"><lb/>præſtant@am, quam habet circunſerendo ſphæras inferiores ſecum ſuo motu <lb/>proprio, qua in re primatum habere videtur.</s> <s xml:id="echoid-s977" xml:space="preserve"/> </p> <div xml:id="echoid-div90" type="float" level="2" n="4"> <note position="left" xlink:label="note-056-03" xlink:href="note-056-03a" xml:space="preserve">Nona ſphę-<lb/>ra cur dica-<lb/>t<unsure/>ur primũ <lb/>mobile, ſeu <lb/>primus mo-<lb/>@us.</note> </div> <note position="left" xml:space="preserve">Octaua <lb/>ſphæ@a cur <lb/>dicatur Fir-<lb/>mamẽtum, <lb/>& ſphæra <lb/>ſi<unsure/>ellarum <lb/>ſixarum.</note> <p> <s xml:id="echoid-s978" xml:space="preserve"><emph style="sc">Appellat</emph> quoque auctor cum Aſtronomis ſphæram, quæ eſt octa-<lb/>ua quo ad nos, Firmamentum, & </s> <s xml:id="echoid-s979" xml:space="preserve">ſphæram ſtellarum fixarum. </s> <s xml:id="echoid-s980" xml:space="preserve">Firmamentum <lb/>quidem, quia ſicut munimẽtum, vallum, aut mœnia in extremis partibus poſi-<lb/>ta cingunt, muniunt, ac firmant ciuitatem, ſic etiam octaua ſphæra, quæ Fir-<lb/>mamentum nuncupatur, & </s> <s xml:id="echoid-s981" xml:space="preserve">quam antiquitas omnis ſupremum, ac extremum <pb o="21" file="057" n="58" rhead="Ioan de Sacro Boſco."/> @@e<unsure/>lum putauit, ſirmat, continet, ambit; </s> <s xml:id="echoid-s982" xml:space="preserve">& </s> <s xml:id="echoid-s983" xml:space="preserve">quaſi munit non ſolum reliquas <lb/>ſphæras inferiores omnes, verum etiam omnia, quæcunque in mundo uniuer <lb/>ſo exiſtunt: </s> <s xml:id="echoid-s984" xml:space="preserve">Vel etiam dicitur Firmamentum, quoniam uidelicet continet ſtel-<lb/>las firmius hærentes, ut mox dicetur. </s> <s xml:id="echoid-s985" xml:space="preserve">At uero ſphæram ſtellarum ſixarum no-<lb/>minat, quia defert, circumuehit, & </s> <s xml:id="echoid-s986" xml:space="preserve">continet omnes ſtellas fixas. </s> <s xml:id="echoid-s987" xml:space="preserve">Quæ quidem <lb/>ſtellæ non ideo fixę dicuntur, quod non moueantur, aut quod fixę prorſus <lb/> <anchor type="note" xlink:label="note-057-01a" xlink:href="note-057-01"/> permaneant. </s> <s xml:id="echoid-s988" xml:space="preserve">Hoc enim falſum eſt, cum experientia compertum ſit clariſſime, <lb/>eas moueri, vt ſuo loco dicetur. </s> <s xml:id="echoid-s989" xml:space="preserve">Neque etiam fixę dicuntur, quòd non mo-<lb/>ueantur, niſi ad motum orbis, in quo ſunt: </s> <s xml:id="echoid-s990" xml:space="preserve">Hac enim ratione Planetę quoq. <lb/></s> <s xml:id="echoid-s991" xml:space="preserve">fixi dici deberent, cum ſolum ad motum orbium, in quibus exiſtunt, circunfe-<lb/>rantur, ut poſtea oſtendemus. </s> <s xml:id="echoid-s992" xml:space="preserve">Sed ideo appellantur fixę, quod ſem per eundem <lb/>inter ſe ſitum, ordinem, atque diſtantiam ſeruent, quod quidem tum anti-<lb/>quorum Aſtronomorum obſeruationes, puta Prolemęi, Albategnij, cætero-<lb/>rumq́ue, tum etiam recentiorum manife ſtiſſi me nobis declarant. </s> <s xml:id="echoid-s993" xml:space="preserve">Semper nam <lb/>que ſtellæ illuſtris illius conſtellationis, quæ Orion nuncupatur, eundem in-<lb/>ter ſe ſitum, ordinem, ac diſtantiam cuſtodiunt, ut nimirum tres ſtellæ cingu-<lb/>lum Orionis conſtituentes perpetuo lineam quaſi rectam conficiant. </s> <s xml:id="echoid-s994" xml:space="preserve">Idemq́. </s> <s xml:id="echoid-s995" xml:space="preserve">in <lb/>ſtellis Vrſæ maioris, & </s> <s xml:id="echoid-s996" xml:space="preserve">minoris, & </s> <s xml:id="echoid-s997" xml:space="preserve">denique aliarum conſtellationum obſerua <lb/>tum fuit: </s> <s xml:id="echoid-s998" xml:space="preserve">Qua de re lege Prolemæum Dictione 7. </s> <s xml:id="echoid-s999" xml:space="preserve">Almageſti, & </s> <s xml:id="echoid-s1000" xml:space="preserve">Ioannem de <lb/>Regiomonte in epitoma eiuſdem Dictionis, ubi plurimæ ſtellarum obſerua-<lb/>tiones in medium proferuntur, ex quibus perſpicue colligitur, ſtellas Fir-<lb/>mamenti eundem ſemper ordinem, ac ſitum ſeruare inter ſe. </s> <s xml:id="echoid-s1001" xml:space="preserve">Ob eandem quo-<lb/>que rationem a Græcis dicta eſt octaua hæc ſphæra ἀπλανὴς, quaſi non vaga, <lb/>inerrabilisq́ue, quia nimirum omnes ſtellæ in ea infixæ ſine vllo errore, permi-<lb/>ſtioneve procedunt.</s> <s xml:id="echoid-s1002" xml:space="preserve"/> </p> <div xml:id="echoid-div91" type="float" level="2" n="5"> <note position="right" xlink:label="note-057-01" xlink:href="note-057-01a" xml:space="preserve">Stellæ Fi@-<lb/>mamenti <lb/>cur fixæ di-<lb/>cantur.</note> </div> <p> <s xml:id="echoid-s1003" xml:space="preserve"><emph style="sc">Postremo</emph> reliquæ ſeptem ſphæræ, quarum ſingulæ ſingulas conti-<lb/> <anchor type="note" xlink:label="note-057-02a" xlink:href="note-057-02"/> nent ſtellas, planetarum ſtellæ uocantur, quoniam deferunt ſtellas, ſiue aſtra, <lb/>qui planetæ ſunt dicti, id eſt, aſtra erratica, ſeu E@rones, non quòd ita in cœlo <lb/>oberrent, ut non ordinato, certo, & </s> <s xml:id="echoid-s1004" xml:space="preserve">determinato motu uehantur: </s> <s xml:id="echoid-s1005" xml:space="preserve">Hac enim <lb/>ratione non poſſet de illis haberi ſcientia, quod uerum non eſt, cum habeãt cer <lb/>tas motuũ periodos: </s> <s xml:id="echoid-s1006" xml:space="preserve">Sed ob id aſtra erratica uocantur, quod neque ipſa inter ſe <lb/>eandem ſemper habeant diſtantiam, neq. </s> <s xml:id="echoid-s1007" xml:space="preserve">cum ſtellis fixis octaui orbis eundem <lb/>ſeruent ordinem. </s> <s xml:id="echoid-s1008" xml:space="preserve">Quod quidem luce clarius intuemur quotidie in Sole, ac Lu <lb/>na. </s> <s xml:id="echoid-s1009" xml:space="preserve">Modo enim hi duo Planetæ inter ſe omnino coniunguntur, ut ſit in Noui <lb/>lunijs, modo alter alteri opponitur, ac maxime alter ab altero recedit, vt in <lb/>Plenilunijs contingit, modo magis, modo minus propinqui inter ſe conſpiciũ <lb/>tur. </s> <s xml:id="echoid-s1010" xml:space="preserve">Rurſus modo prope hanc ſtellam fixam octaui orbis, ſeu Firmamenti ap-<lb/>parent, modo prope illam: </s> <s xml:id="echoid-s1011" xml:space="preserve">Atque idem prorſus in reliquis planetis fuit obſer <lb/>uatum. </s> <s xml:id="echoid-s1012" xml:space="preserve">Nunc enim recto videntur incedere curſu, nunc retrocedere, & </s> <s xml:id="echoid-s1013" xml:space="preserve">in con-<lb/>trariam partem niti. </s> <s xml:id="echoid-s1014" xml:space="preserve">Nunc occultari, & </s> <s xml:id="echoid-s1015" xml:space="preserve">deliteſcere, ob propinquitatem Solis; <lb/></s> <s xml:id="echoid-s1016" xml:space="preserve">Deinde cum Sol ab eis recedit, uel ipſi a Sole, rurſus prodire in lucem, ſeſeq́. </s> <s xml:id="echoid-s1017" xml:space="preserve"><lb/>aperire, & </s> <s xml:id="echoid-s1018" xml:space="preserve">depromere. </s> <s xml:id="echoid-s1019" xml:space="preserve">Nunc antecedere Solem. </s> <s xml:id="echoid-s1020" xml:space="preserve">Nunc eundem ſubſequi. </s> <s xml:id="echoid-s1021" xml:space="preserve">Nunc <lb/>uelociſſimo curſu quaſi incitari. </s> <s xml:id="echoid-s1022" xml:space="preserve">Nunc vero ita retardari, ut ne moueri qui-<lb/>dem exiſtimantur, ſed in eodem prorſus Zodiaci loco conſiſtere. </s> <s xml:id="echoid-s1023" xml:space="preserve">Nunc deniq. </s> <s xml:id="echoid-s1024" xml:space="preserve"><lb/>in ſeptentrionem excurrere. </s> <s xml:id="echoid-s1025" xml:space="preserve">Nunc in meridiem. </s> <s xml:id="echoid-s1026" xml:space="preserve">De qua re plura in Theoricis <lb/>planetarum exponuntur. </s> <s xml:id="echoid-s1027" xml:space="preserve">Hanc igitur ob cauſam ita ſtellæ in cælo oberrare ui <lb/>dentur, ut caſu quodam, ac fato agi iudicentur. </s> <s xml:id="echoid-s1028" xml:space="preserve">Quapropter ab Aſtronomis <lb/>Planetæ meritò nuncupantur.</s> <s xml:id="echoid-s1029" xml:space="preserve"/> </p> <div xml:id="echoid-div92" type="float" level="2" n="6"> <note position="right" xlink:label="note-057-02" xlink:href="note-057-02a" xml:space="preserve">Sphæræ Pl@ <lb/>neta rũ @@t <lb/>ſic dictæ.</note> </div> <pb o="22" file="058" n="59" rhead="Comment. in I. Cap. Sphæræ"/> <p style="it"> <s xml:id="echoid-s1030" xml:space="preserve"><emph style="sc">Secvndvm</emph> accidens autem diuiditur in ſphæram rectam, & </s> <s xml:id="echoid-s1031" xml:space="preserve">ſphæ-<lb/> <anchor type="note" xlink:label="note-058-01a" xlink:href="note-058-01"/> ram obliquam. </s> <s xml:id="echoid-s1032" xml:space="preserve">Illi autem dicuntur habere ſphæram rectam, qui manent ſub <lb/>Aequinoctiali, ſi aliquis ibi manere poſſit. </s> <s xml:id="echoid-s1033" xml:space="preserve">Et dicitur eis recta, quia neuter <lb/>polorum magis altero illis eleuatur. </s> <s xml:id="echoid-s1034" xml:space="preserve">Vel quoniam eorum Horizon interſe-<lb/>cat Aequino ctialem, & </s> <s xml:id="echoid-s1035" xml:space="preserve">interſecatur ab eodem ad angulos rectos ſphærales. <lb/></s> <s xml:id="echoid-s1036" xml:space="preserve">Illiuero dicuntur habere ſphæram obliquam, quicunque habitant citra Ae-<lb/>quinoctialem, uel ultra. </s> <s xml:id="echoid-s1037" xml:space="preserve">Illis enim ſupra Horizontem alter polorum ſemper <lb/>eleuatur, alter uero ſemper deprimitur: </s> <s xml:id="echoid-s1038" xml:space="preserve">Vel quoniam illorum Horizon ar-<lb/>tificialis interſecat Aequinoctialem, & </s> <s xml:id="echoid-s1039" xml:space="preserve">interſecatur ab eodem ad angulos <lb/>impares, & </s> <s xml:id="echoid-s1040" xml:space="preserve">obliquos.</s> <s xml:id="echoid-s1041" xml:space="preserve"/> </p> <div xml:id="echoid-div93" type="float" level="2" n="7"> <note position="left" xlink:label="note-058-01" xlink:href="note-058-01a" xml:space="preserve">Diuiſio <lb/>ſphæræ ſe-<lb/>cundum ac <lb/>cidens.</note> </div> </div> <div xml:id="echoid-div95" type="section" level="1" n="46"> <head xml:id="echoid-head50" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s1042" xml:space="preserve"><emph style="sc">Dividit</emph> iam ſphæram ſecundum accidens in ſphæram rectam, & </s> <s xml:id="echoid-s1043" xml:space="preserve">obli-<lb/>quam. </s> <s xml:id="echoid-s1044" xml:space="preserve">Sed quoniam ea, quæ in hac diuiſione dicuntur, & </s> <s xml:id="echoid-s1045" xml:space="preserve">quæ deinceps ſequũ <lb/>tur, intelligi non poſſunt, niſi prius qui iam circuli ſphæræ cognoſcantur, quo-<lb/>rum in ſequentibus frequenter fit mentio; </s> <s xml:id="echoid-s1046" xml:space="preserve">operæpretium me facturum puto, <lb/>ſi breuiter, & </s> <s xml:id="echoid-s1047" xml:space="preserve">generatim circulos ſphæræ explicauero, plura de illis, eorumque <lb/>officijs, nominibusq́ue in 2. </s> <s xml:id="echoid-s1048" xml:space="preserve">cap. </s> <s xml:id="echoid-s1049" xml:space="preserve">diſputaturus, ubi de eiſdem differit auctor: <lb/></s> <s xml:id="echoid-s1050" xml:space="preserve">Nunc enim tantum rudi minerua vocabula circulorum exponam.</s> <s xml:id="echoid-s1051" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div96" type="section" level="1" n="47"> <head xml:id="echoid-head51" xml:space="preserve">DE CIRCVLIS SPHAERAE.</head> <p> <s xml:id="echoid-s1052" xml:space="preserve"><emph style="sc">GIrcvli</emph> ſphæræ ſunt 10. </s> <s xml:id="echoid-s1053" xml:space="preserve">quorum hæc ſunt nomina. </s> <s xml:id="echoid-s1054" xml:space="preserve">Aequino-<lb/> <anchor type="note" xlink:label="note-058-02a" xlink:href="note-058-02"/> ctialis, Zodiacus, Colurus ſolſtitiorum, Colurus æquinoctiorum, <lb/>Meridianus, Horizon, Tropicus Cancri, Tropicus Capricorni, <lb/>Circulus arcticus, & </s> <s xml:id="echoid-s1055" xml:space="preserve">circulus antarcticus. </s> <s xml:id="echoid-s1056" xml:space="preserve">Priores ſex, maiores di-<lb/>cuntur, ſiue maximi, poſteriores quatuor, minores, ſiue non maxi-<lb/> <anchor type="note" xlink:label="note-058-03a" xlink:href="note-058-03"/> mi. </s> <s xml:id="echoid-s1057" xml:space="preserve">Maior circulus dicitur is, qui idem centrum cum ſphæra obtinet, ipſamq́ue <lb/>ſphæram in duo hemiſphæria æqualia diuidit: </s> <s xml:id="echoid-s1058" xml:space="preserve">Minor uero circulus appellatur <lb/>ille, qui diuerſum centrum a ſphæræ centro poſſidet, ſphæramq́ue in duo ſeg-<lb/>menta inæqualia patitur. </s> <s xml:id="echoid-s1059" xml:space="preserve">Cæterum quilibet circulus ſphæræ, ſiue maior, ſiue <lb/>minor, duos dicitur habere polos, circa quos, ſi moueretur, uniformiter ferre-<lb/>tur. </s> <s xml:id="echoid-s1060" xml:space="preserve">Immo ex polis ipſis omnes circuli in ſuperficie ſphæræ deſcribuntur. </s> <s xml:id="echoid-s1061" xml:space="preserve">Eſt. </s> <s xml:id="echoid-s1062" xml:space="preserve">n. <lb/></s> <s xml:id="echoid-s1063" xml:space="preserve">polus cuiuslibet circuli fphæræ, punctum illud in conuexa ſuperficie ſphæræ, a <lb/> <anchor type="note" xlink:label="note-058-04a" xlink:href="note-058-04"/> quo omnes lineæ rectę ad circunferentiam circuli ductę ſunt ęquales. </s> <s xml:id="echoid-s1064" xml:space="preserve">Nam <lb/>cum ex polo circuli circunferentia deſcribatur, neceſſe eſt, vt polus ęqualiter re <lb/>cedat ab omnibus punctis illius circunferentię.</s> <s xml:id="echoid-s1065" xml:space="preserve"/> </p> <div xml:id="echoid-div96" type="float" level="2" n="1"> <note position="left" xlink:label="note-058-02" xlink:href="note-058-02a" xml:space="preserve">Decem cir-<lb/>@uli ſphęrę.</note> <note position="left" xlink:label="note-058-03" xlink:href="note-058-03a" xml:space="preserve">Maior cir<unsure/>-<lb/>@ulus ſphæ-<lb/>ræ, & mi-<lb/>@or quid.</note> <note position="left" xlink:label="note-058-04" xlink:href="note-058-04a" xml:space="preserve">Polus circu <lb/>li in ſphæra <lb/>quid,</note> </div> <p> <s xml:id="echoid-s1066" xml:space="preserve"><emph style="sc">Æqvinoctiali</emph> scirculus in ſphæra dicitur ille maior, qui ex mun <lb/> <anchor type="note" xlink:label="note-058-05a" xlink:href="note-058-05"/> di polis eſt deſcriptus, ęqualiterq́. </s> <s xml:id="echoid-s1067" xml:space="preserve">ab vtroque polo mundi ſecundum omnes <lb/>ſui partes remouetur.</s> <s xml:id="echoid-s1068" xml:space="preserve"/> </p> <div xml:id="echoid-div97" type="float" level="2" n="2"> <note position="left" xlink:label="note-058-05" xlink:href="note-058-05a" xml:space="preserve">Aequino-<lb/>ctialis.</note> </div> <p> <s xml:id="echoid-s1069" xml:space="preserve"><emph style="sc">Zodiacvs</emph> circulus eſt quoque maior, deſcriptus ex polis diſtantibu@ <lb/> <anchor type="note" xlink:label="note-058-06a" xlink:href="note-058-06"/> a mundi polis quarta parte, & </s> <s xml:id="echoid-s1070" xml:space="preserve">inſuper nonageſima unius quadrantis, hoc eſt, <lb/>partibus 47. </s> <s xml:id="echoid-s1071" xml:space="preserve">ex 180. </s> <s xml:id="echoid-s1072" xml:space="preserve">in quas quadrans diuidi intelligitur, qui ſecat ęquinoctia-<lb/>lem, ſecaturq́ue uiciſſim ab eodem in duas medietates, oblique tamen; </s> <s xml:id="echoid-s1073" xml:space="preserve">ita ut <lb/>Zodiacus ad Æquinoctialem ſit inclinatus, unaq́ue medietas uergat ad ſepte@ <pb o="23" file="059" n="60" rhead="Ioan. de Sacro Boſco."/> trionem, altera ad auſtrũ. </s> <s xml:id="echoid-s1074" xml:space="preserve">Punctum autem medium vtriuſq. </s> <s xml:id="echoid-s1075" xml:space="preserve">medietatis recedat <lb/>ab Aequinoctiali tantum, quantum poli Zodiaci a polis mundi recedunt; </s> <s xml:id="echoid-s1076" xml:space="preserve">quę <lb/>quidem diſtantia continet grad. </s> <s xml:id="echoid-s1077" xml:space="preserve">23. </s> <s xml:id="echoid-s1078" xml:space="preserve">& </s> <s xml:id="echoid-s1079" xml:space="preserve">ſemis. </s> <s xml:id="echoid-s1080" xml:space="preserve">Appellamus gradum particulam <lb/>unam cuiuſuis circuli diuiſi in 360. </s> <s xml:id="echoid-s1081" xml:space="preserve">partes. </s> <s xml:id="echoid-s1082" xml:space="preserve">In tot enim partes quemlibet circu <lb/>lum partiuntur Aſtronomi. </s> <s xml:id="echoid-s1083" xml:space="preserve">Cęterum in Zodiaco conſiderantur quatuor pun <lb/>cta pręcipua, quorum duo dicuntur Aequinoctialia, duo uero Solſtitialia. <lb/></s> <s xml:id="echoid-s1084" xml:space="preserve">Æquinoctialia ſunt illa, quibus Zodiacus Æquinoctialem ſecat: </s> <s xml:id="echoid-s1085" xml:space="preserve">Solſtitialia. </s> <s xml:id="echoid-s1086" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-059-01a" xlink:href="note-059-01"/> vero duo illa, quæ maxime diximus ab Æquinoctiali remoueri. </s> <s xml:id="echoid-s1087" xml:space="preserve">Rurſus puncto-<lb/>rum ęquinoctialium illud, quod polo arctico eſt ad dexteram, (ſi nimirum me <lb/>dietas Zodiaci, quę in Septentrionem inclinat, in ſuperiori hemiſphęrio con-<lb/>ſtituatur) uel in occidenre ponitur, Vernum dicitur, eſtq́. </s> <s xml:id="echoid-s1088" xml:space="preserve">principium A@ietis: <lb/></s> <s xml:id="echoid-s1089" xml:space="preserve">Alterum vero, quod eidem polo eſt ad ad ſiniſtram, (eũdem ſitum habente ſpę <lb/>ra) uel in oriente ponitur, Autumnale uocatur, eſtq́ue principium Librę. </s> <s xml:id="echoid-s1090" xml:space="preserve">Vel@ <lb/>ſi mauis, punctum illud Zodiaci ſpectat ad Vernum ęquinoctium, quod prin-<lb/>cipium eſt ſemicirculi ad polum arcticum vergentis, procedendo ab occaſu in <lb/>ortum: </s> <s xml:id="echoid-s1091" xml:space="preserve">terminus uero eiuſdem ſemirculi, hoc eſt, punctum illud Zodiaci ad <lb/>ęquinoctium Autumnale pertinet, quod principium eſt ſemirculi alterius ad <lb/>antarcticum polum inclinantis, progrediendo etiam ab occaſu in ortum. </s> <s xml:id="echoid-s1092" xml:space="preserve">Solſti <lb/>tialium quoq. </s> <s xml:id="echoid-s1093" xml:space="preserve">punctorum illud, quod ab æquinoctiali in ſeptentrionem rece-<lb/>dit, ęſtiuum appellatur, eſtq́. </s> <s xml:id="echoid-s1094" xml:space="preserve">principium Cancri: </s> <s xml:id="echoid-s1095" xml:space="preserve">Reliquum uero, quod ad au-<lb/>ſtrum ſecedit, nuncupatur hybernum, eſtq́. </s> <s xml:id="echoid-s1096" xml:space="preserve">principium Capricorni. </s> <s xml:id="echoid-s1097" xml:space="preserve">Atque hęc <lb/>quatuor pũcta diligenter ſunt notãda, vt alij circuli ſphęræ intelligi poſſint.</s> <s xml:id="echoid-s1098" xml:space="preserve"/> </p> <div xml:id="echoid-div98" type="float" level="2" n="3"> <note position="left" xlink:label="note-058-06" xlink:href="note-058-06a" xml:space="preserve">Zodiacus</note> <note position="right" xlink:label="note-059-01" xlink:href="note-059-01a" xml:space="preserve">Pũcta æqu@ <lb/>noctialia, <lb/>& ſolſtiti@-<lb/>lia.</note> </div> <p> <s xml:id="echoid-s1099" xml:space="preserve"><emph style="sc">Colvrvs</emph> Solſtitiorum eſt ille circulus, qui per polus mundi, polos Zo <lb/> <anchor type="note" xlink:label="note-059-02a" xlink:href="note-059-02"/> diaci, & </s> <s xml:id="echoid-s1100" xml:space="preserve">puncta Solſtitialia incedit.</s> <s xml:id="echoid-s1101" xml:space="preserve"/> </p> <div xml:id="echoid-div99" type="float" level="2" n="4"> <note position="right" xlink:label="note-059-02" xlink:href="note-059-02a" xml:space="preserve">Colu@ Sol-<lb/>ſtitiorum.</note> </div> <p> <s xml:id="echoid-s1102" xml:space="preserve"><emph style="sc">Colvrvs</emph> Æquinoctiorum eſt circulus ille, qui per polos mundi, & </s> <s xml:id="echoid-s1103" xml:space="preserve">pun <lb/>cta ęquinoctialia ingreditur, non autem per polos Zodiaci.</s> <s xml:id="echoid-s1104" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1105" xml:space="preserve"><emph style="sc">Meridianvs</emph> circuius eſt ille, qui per mundi polos, & </s> <s xml:id="echoid-s1106" xml:space="preserve">uerticem loci <lb/> <anchor type="note" xlink:label="note-059-03a" xlink:href="note-059-03"/> ducitur, ſupereminetq́ue alijs maioribus circulis in ſphęra materiali. </s> <s xml:id="echoid-s1107" xml:space="preserve">Eſt autem <lb/>vertex loci, punctum in cęlo, quod directe ſuprapoſitum eſt illi loco, quale eſt <lb/> <anchor type="note" xlink:label="note-059-04a" xlink:href="note-059-04"/> illud, quod oſtendit cacumen alicuius turris, ſi ad cęlum uſque extenderetur: <lb/></s> <s xml:id="echoid-s1108" xml:space="preserve">Siue illud, quod uertici capitis cuiusuis hominis imminet. </s> <s xml:id="echoid-s1109" xml:space="preserve">Hoc autem pun-<lb/> <anchor type="note" xlink:label="note-059-05a" xlink:href="note-059-05"/> ctum Arabes dicunt Zenith: </s> <s xml:id="echoid-s1110" xml:space="preserve">Oppoſitum uero punctum per diametrum, quod <lb/>eadem turris oſtendit, ſi in alteram cęli partem intelligatur excurrere, appel-<lb/>lant Nadir.</s> <s xml:id="echoid-s1111" xml:space="preserve"/> </p> <div xml:id="echoid-div100" type="float" level="2" n="5"> <note position="right" xlink:label="note-059-03" xlink:href="note-059-03a" xml:space="preserve">Colurùs æ-<lb/>quinoctio-<lb/>rum.</note> <note position="right" xlink:label="note-059-04" xlink:href="note-059-04a" xml:space="preserve">Meridia-<lb/>nus.</note> <note position="right" xlink:label="note-059-05" xlink:href="note-059-05a" xml:space="preserve">Vertex lo-<lb/>ci, ſeu Ze-<lb/>nith.</note> </div> <p> <s xml:id="echoid-s1112" xml:space="preserve"><emph style="sc">Horizon</emph>, eſt circulus maior eſt uertice loci, tanquam polo, deſcriptus, <lb/> <anchor type="note" xlink:label="note-059-06a" xlink:href="note-059-06"/> qui alijs etiam circulis in materiali ſphęra ſupereminet, diuiditq́ue Meridia-<lb/>num, ab eodemq́ue diuiditur ad angulos rectos ſphęrales: </s> <s xml:id="echoid-s1113" xml:space="preserve">ſeparatque hemi-<lb/>ſphærium viſum a non uiſo.</s> <s xml:id="echoid-s1114" xml:space="preserve"/> </p> <div xml:id="echoid-div101" type="float" level="2" n="6"> <note position="right" xlink:label="note-059-06" xlink:href="note-059-06a" xml:space="preserve">Nadir lo@ <lb/>Horizon.</note> </div> <p> <s xml:id="echoid-s1115" xml:space="preserve"><emph style="sc">Tropicvs</emph> Cancri dicitur ille circulus minor, qui ex parte poli Arctici <lb/> <anchor type="note" xlink:label="note-059-07a" xlink:href="note-059-07"/> ęquidiſtat Æquinoctiali, tranſitq́ue per illud punctum Zodiaci maxime ab Æ-<lb/>quinoctiali remotum, quod principium Cancri ſupra diximus nominari.</s> <s xml:id="echoid-s1116" xml:space="preserve"/> </p> <div xml:id="echoid-div102" type="float" level="2" n="7"> <note position="right" xlink:label="note-059-07" xlink:href="note-059-07a" xml:space="preserve">Tropicus <lb/>Canc@i.</note> </div> <p> <s xml:id="echoid-s1117" xml:space="preserve"><emph style="sc">Tropicvs</emph> Capricorni uocatur ille minor circulus, qui ex parte poli <lb/> <anchor type="note" xlink:label="note-059-08a" xlink:href="note-059-08"/> Antar ctici Æquinoctiali ęquidiſtat, tranſitq́ue per illud punctum Zodiaci, <lb/>quod ſupra monuimus appellari principium Capricorni.</s> <s xml:id="echoid-s1118" xml:space="preserve"/> </p> <div xml:id="echoid-div103" type="float" level="2" n="8"> <note position="right" xlink:label="note-059-08" xlink:href="note-059-08a" xml:space="preserve">Tropicus <lb/>Capricorni.</note> </div> <p> <s xml:id="echoid-s1119" xml:space="preserve"><emph style="sc">Arcticvs</emph> circulus eſt minor, qui prope polum arcticum deſcriptus eſt <lb/>per polum Zodiaci parallelus exiſtens Aequinoctiali.</s> <s xml:id="echoid-s1120" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">Circulus ac <lb/>cticus.</note> <p> <s xml:id="echoid-s1121" xml:space="preserve"><emph style="sc">Antarcticvs</emph> circulus eſt quoq. </s> <s xml:id="echoid-s1122" xml:space="preserve">minor, qui iuxta polum antarcti-<lb/> <anchor type="note" xlink:label="note-059-10a" xlink:href="note-059-10"/> cũ incedit per alterum Zodiaci polum, ęquidiſtãs etiam Æquinoctiali circulo.</s> <s xml:id="echoid-s1123" xml:space="preserve"/> </p> <div xml:id="echoid-div104" type="float" level="2" n="9"> <note position="right" xlink:label="note-059-10" xlink:href="note-059-10a" xml:space="preserve">Circulus <lb/>antarcticus</note> </div> <pb o="24" file="060" n="61" rhead="Comment. in I. Cap. Sphæræ"/> <p> <s xml:id="echoid-s1124" xml:space="preserve"><emph style="sc">Exemplvm</emph> omnium circulorum, quos explicauimus, habes vtcunque <lb/>in propoſita ſigura A B C D, in qua E, principium Cancri. </s> <s xml:id="echoid-s1125" xml:space="preserve">F, principium Ca-<lb/>pricorni. </s> <s xml:id="echoid-s1126" xml:space="preserve">G, principium Arietis. </s> <s xml:id="echoid-s1127" xml:space="preserve">H, principium Libræ. </s> <s xml:id="echoid-s1128" xml:space="preserve">A B C D, Meridianus. <lb/></s> <s xml:id="echoid-s1129" xml:space="preserve">B. </s> <s xml:id="echoid-s1130" xml:space="preserve">Zenith. </s> <s xml:id="echoid-s1131" xml:space="preserve">D, Nadir. </s> <s xml:id="echoid-s1132" xml:space="preserve">A H C G, Horizon. </s> <s xml:id="echoid-s1133" xml:space="preserve">A B C, hemiſpheriũ uiſum. </s> <s xml:id="echoid-s1134" xml:space="preserve">A D C, he-<lb/>miſphærium non uiſum. </s> <s xml:id="echoid-s1135" xml:space="preserve">K, L, poli Zodiaci, & </s> <s xml:id="echoid-s1136" xml:space="preserve">c. </s> <s xml:id="echoid-s1137" xml:space="preserve">Sed omnia hæc clarius perci-<lb/>pientur ex inſtrumento materiali.</s> <s xml:id="echoid-s1138" xml:space="preserve"/> </p> <figure> <image file="060-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/060-01"/> </figure> <p> <s xml:id="echoid-s1139" xml:space="preserve"><emph style="sc">Qvonia@</emph> vero de ſphæræ circulis verba fecimus, non abs re fuerit, pa@ <lb/> <anchor type="note" xlink:label="note-060-01a" xlink:href="note-060-01"/> cis indicare, quonam pacto ex ipſis ſphæra materialis ſit componenda, vel ob <lb/>hanc ſolam utilitatem, ut iudicium ferre poſſimus de quacunque ſphæra, num <lb/>rite ſit fabricata, & </s> <s xml:id="echoid-s1140" xml:space="preserve">compoſita. </s> <s xml:id="echoid-s1141" xml:space="preserve">Primo igitur parentur ex aliqua materia tres <lb/>circuli inter ſe omnino æquales, diuiſiq́; </s> <s xml:id="echoid-s1142" xml:space="preserve">in 360. </s> <s xml:id="echoid-s1143" xml:space="preserve">partes æquales, quas gradus <lb/>diximus appellari. </s> <s xml:id="echoid-s1144" xml:space="preserve">Horum duo ita coniungantur, ut ſe inuicem ad angulos æ-<lb/>@uales, nimitum rectos ſphærales ſecent in duobus punctis, per quæ extenda@ <pb o="25" file="061" n="62" rhead="Ioan. de Sacro Boſco."/> @xis mundi; </s> <s xml:id="echoid-s1145" xml:space="preserve">eruntq́; </s> <s xml:id="echoid-s1146" xml:space="preserve">hi circuli duo Coluri. </s> <s xml:id="echoid-s1147" xml:space="preserve">Deinde in unoquoque Coluro, a <lb/>polis mundi numerentur 90. </s> <s xml:id="echoid-s1148" xml:space="preserve">gradus, & </s> <s xml:id="echoid-s1149" xml:space="preserve">in nonageſimo cuiuſque gradu appli-<lb/>cetur tertius circulus, nempe Æquinoctialis, qui hac ratione ab vtroq; </s> <s xml:id="echoid-s1150" xml:space="preserve">polo <lb/>æque remotus erit. </s> <s xml:id="echoid-s1151" xml:space="preserve">Poſt hæc ab Aequinoctiali uerſus vtrumq polum numerẽ <lb/>tur in Coluris gr. </s> <s xml:id="echoid-s1152" xml:space="preserve">23. </s> <s xml:id="echoid-s1153" xml:space="preserve">& </s> <s xml:id="echoid-s1154" xml:space="preserve">ſemis, & </s> <s xml:id="echoid-s1155" xml:space="preserve">in terminis numerationum applicentur duo <lb/>tropici, quorum ꝗ̃titatem facile habebis, ſi prius diametro eorum accipias, du-<lb/>cendo videlicet lineam rectam a fine numerationis unius Coluri ad finem nu <lb/>merationis eiuſdem Coluri verſus eundem tamen polum. </s> <s xml:id="echoid-s1156" xml:space="preserve">Eodem pacto nume <lb/>ratis totidem partibus ab utroq. </s> <s xml:id="echoid-s1157" xml:space="preserve">polo Æquinoctialem uerſus in eiſdem Colu-<lb/>ris, conſtituentur circuli Polares, nimirum Arcticus, & </s> <s xml:id="echoid-s1158" xml:space="preserve">Antarcticus, quorum <lb/>diametros non diſſimili arte reperies. </s> <s xml:id="echoid-s1159" xml:space="preserve">Rurſus paretur circulus Zodiacus ambi-<lb/>tu quidem æqualis tribus prædictis circulis maioribus, latitudine uero ab eiſ-<lb/>dem differens: </s> <s xml:id="echoid-s1160" xml:space="preserve">Debet enim in latitudine continere 12. </s> <s xml:id="echoid-s1161" xml:space="preserve">gradus, in quorum me-<lb/>dio depingitur linea dicta Ecliptica, diſtans ab extremitatibus Zodiaci 6. </s> <s xml:id="echoid-s1162" xml:space="preserve">gr. </s> <s xml:id="echoid-s1163" xml:space="preserve">ut <lb/>in 2. </s> <s xml:id="echoid-s1164" xml:space="preserve">c. </s> <s xml:id="echoid-s1165" xml:space="preserve">docebimus: </s> <s xml:id="echoid-s1166" xml:space="preserve">Hic autem circulus ita applicetur, accommodeturve, ut to-<lb/>tus circulus oblique ſecet Aequinoctioalẽ in duobus illis punctis, in quibus al <lb/>ter Colurus eundem Aequinoctialem ſecat. </s> <s xml:id="echoid-s1167" xml:space="preserve">Linea vero ecliptica utrumq́. </s> <s xml:id="echoid-s1168" xml:space="preserve">tro-<lb/>picũ contingat in alijs duobus pũctis, in quibus reliquus Colurus tropicos ſe-<lb/>cat, quorũ unũ ſumitur uerſus unũ polũ, aliud vero illi per diametrũ oppoſitũ <lb/>uerſus alterũ. </s> <s xml:id="echoid-s1169" xml:space="preserve">Deniq. </s> <s xml:id="echoid-s1170" xml:space="preserve">in hunc modũ Meridianus, atq. </s> <s xml:id="echoid-s1171" xml:space="preserve">Horizon conſtituantur, <lb/>& </s> <s xml:id="echoid-s1172" xml:space="preserve">ad inuicem adaptentur, ut intra ipſos fixos & </s> <s xml:id="echoid-s1173" xml:space="preserve">immobiles tota ſphæra hacte-<lb/>nus conſtructa libere circumuolui queat, hac tñ lege, vt hi duo circuli ſeſe mu <lb/>tuo ad rectos angulos interſecent, & </s> <s xml:id="echoid-s1174" xml:space="preserve">Meridianus circa ſuos polos (qui ſunt cõ-<lb/>munes ſectiones Horizontis cũ Æquinoctiali) moueatur in hũc finẽ, ut omnib. <lb/></s> <s xml:id="echoid-s1175" xml:space="preserve">poſſit eleuationibus poli inſeruire ſphæra, hoc eſt, ut uterq. </s> <s xml:id="echoid-s1176" xml:space="preserve">polus magis depri <lb/>mi, eleuatiq́; </s> <s xml:id="echoid-s1177" xml:space="preserve">poſſit pro ratione altitudinis poli. </s> <s xml:id="echoid-s1178" xml:space="preserve">In nõnullis ſphæris Horizon <lb/>nunc deprimitur, nunc eleuatur ob eundẽ finẽ, Meridiano immobili exiſtente, <lb/>ſed prior mihi modus magis placet. </s> <s xml:id="echoid-s1179" xml:space="preserve">Atq. </s> <s xml:id="echoid-s1180" xml:space="preserve">ita tota ſphæra materialis cõfecta, & </s> <s xml:id="echoid-s1181" xml:space="preserve"><lb/>abſoluta erit. </s> <s xml:id="echoid-s1182" xml:space="preserve">Nam circulos Planetarũ, qui ſolẽt in nõnullis ſphæris apponi, ita <lb/>ut moueantur ſemper ſub Zodiaco & </s> <s xml:id="echoid-s1183" xml:space="preserve">circa polos Zodiaci, quilibet propria in-<lb/>duſtria facile ſphæræ imponet: </s> <s xml:id="echoid-s1184" xml:space="preserve">Nos enim hic tm̃ præcipuos ſphæræ circulos <lb/>tractamus. </s> <s xml:id="echoid-s1185" xml:space="preserve">Hæc itaque dicta ſint in genere de circulis, quos Aſtronomi in cęlo <lb/>conſiderant. </s> <s xml:id="echoid-s1186" xml:space="preserve">Nunc ad auctoris diuiſionem reuertamur.</s> <s xml:id="echoid-s1187" xml:space="preserve"/> </p> <div xml:id="echoid-div105" type="float" level="2" n="10"> <note position="left" xlink:label="note-060-01" xlink:href="note-060-01a" xml:space="preserve">Cõpoſi@ <lb/>ſphęræ ma-<lb/>@@alis.</note> </div> <p> <s xml:id="echoid-s1188" xml:space="preserve">I<emph style="sc">L. L. I</emph> autem dicuntur, &</s> <s xml:id="echoid-s1189" xml:space="preserve">c] Diuiſa ſphæra ſecundum accidens (in qua di-<lb/> <anchor type="note" xlink:label="note-061-01a" xlink:href="note-061-01"/> n<unsure/>iſione ſphęra ſumitur pro tota mũdi ſphęra) in ſphęrã rectam, & </s> <s xml:id="echoid-s1190" xml:space="preserve">obliquam, <lb/>declarat iam vtram que partem diuiſionis. </s> <s xml:id="echoid-s1191" xml:space="preserve">Dicit igitur, illos ſphęram rectam <lb/>habere, qui manent ſub Aequinoctiali circulo, ſi aliquis ibi manere poſſit: <lb/></s> <s xml:id="echoid-s1192" xml:space="preserve">Quod ideo adiunxit, quoniam multi grauiſſimi viri & </s> <s xml:id="echoid-s1193" xml:space="preserve">Philoſophi, & </s> <s xml:id="echoid-s1194" xml:space="preserve"><emph style="sc">A</emph> ſtrolo <lb/>gi, necnõ Theologorum plerique dubitarunt, eſſetne ſub Aequinoctiali cir-<lb/>culo habitatio, immo plurimi cum antiquis pro certo affirmarunt, ſub circu-<lb/>lo Ae quinoctiali non eſſe habitationẽ, ob nimiũ calorẽ, quem Sol perpetuo <lb/>ibi decurrens efficit: </s> <s xml:id="echoid-s1195" xml:space="preserve">Similisq́; </s> <s xml:id="echoid-s1196" xml:space="preserve">dubitatio fieri poſſet de polis mundi; </s> <s xml:id="echoid-s1197" xml:space="preserve">Non em̃ <lb/>pauci fuerunt, neq; </s> <s xml:id="echoid-s1198" xml:space="preserve">modo deſunt, qui negent, ibi poſſe homines degere, ob fri <lb/>gus intolerabile, quod illic ob nimiam Solis remotionẽ, atq; </s> <s xml:id="echoid-s1199" xml:space="preserve">abſentiam per-<lb/>petuo exiſtit. </s> <s xml:id="echoid-s1200" xml:space="preserve">Qua de re nonnihil dicemus ad finem 2. </s> <s xml:id="echoid-s1201" xml:space="preserve">cap. </s> <s xml:id="echoid-s1202" xml:space="preserve">Nunc vero certũ <lb/> <anchor type="note" xlink:label="note-061-02a" xlink:href="note-061-02"/> ſit, & </s> <s xml:id="echoid-s1203" xml:space="preserve">indubitatum, experientijs multorum deprehenſum eſſe, tam ſub Aequi-<lb/>noctiali circulo, quà<unsure/>m ſub polis, ſaltem ſub polo Arctico, homines habitare.</s> <s xml:id="echoid-s1204" xml:space="preserve"/> </p> <div xml:id="echoid-div106" type="float" level="2" n="11"> <note position="right" xlink:label="note-061-01" xlink:href="note-061-01a" xml:space="preserve">Quomodo <lb/>ſphæra ſu-<lb/>mat<unsure/>ur in <lb/>poſteriori <lb/>diuiſione, <lb/>Qui dican. <lb/>tur habcre <lb/>ſphęram re <lb/>ctam.</note> <note position="right" xlink:label="note-061-02" xlink:href="note-061-02a" xml:space="preserve">Terra ſub <lb/>Aequino-<lb/>ctiali, & po <lb/>lis eſt habi-<lb/>tabilis.</note> </div> <p> <s xml:id="echoid-s1205" xml:space="preserve">Et dieitur eis recta, &</s> <s xml:id="echoid-s1206" xml:space="preserve">c.</s> <s xml:id="echoid-s1207" xml:space="preserve">] Duabus de cauſis ait ſphæram illorum, qui ſub <pb o="26" file="062" n="63" rhead="Comment. in I. Cap. Sphæræ"/> Æquinoctiali degunt, dici rectam; </s> <s xml:id="echoid-s1208" xml:space="preserve">Vel, quia neuter polorum magis altero <lb/> <anchor type="note" xlink:label="note-062-01a" xlink:href="note-062-01"/> illis ſupra Horizontem eleuatur: </s> <s xml:id="echoid-s1209" xml:space="preserve">Vel, quoniam illorum Horizon interſecat <lb/>Aequinoctialem, & </s> <s xml:id="echoid-s1210" xml:space="preserve">ab eodem interſecatur ad angulos rectos ſphęrales.</s> <s xml:id="echoid-s1211" xml:space="preserve"/> </p> <div xml:id="echoid-div107" type="float" level="2" n="12"> <note position="left" xlink:label="note-062-01" xlink:href="note-062-01a" xml:space="preserve">@ur ſub <lb/>Aequino-<lb/>ctiali degẽ-<lb/>tes dicãtur <lb/>habereſphę <lb/>ram rectã.</note> </div> <p> <s xml:id="echoid-s1212" xml:space="preserve"><emph style="sc">Hinc</emph> factum eſt, vt quidem ſphæram rectam definieriut dicentes, Eam´eſ <lb/>ſe, in qua vterque polus inſiſtit, & </s> <s xml:id="echoid-s1213" xml:space="preserve">innititur Horizonti, vel, in qua Aequinoctia <lb/>lis, (qui medium inter polos locum exacte obtinet) cum Horizonte rectos con <lb/> <anchor type="note" xlink:label="note-062-02a" xlink:href="note-062-02"/> ſtituit angulos ſphæricos, uel, in qua uterque polus in Horizonte iacet, & </s> <s xml:id="echoid-s1214" xml:space="preserve">Ae-<lb/>quinoctialis ſupra verticem capitis directe eminet, uel, in qua Horizontem u-<lb/>terque polus contingit. </s> <s xml:id="echoid-s1215" xml:space="preserve">Sphęram rectam ſortita eſt magna pars Africæ, & </s> <s xml:id="echoid-s1216" xml:space="preserve">Indiæ <lb/>occidentalis, nempe ea pars, quæ Peru dicitur; </s> <s xml:id="echoid-s1217" xml:space="preserve">Inſulę quoque Moluccæ, Inſula <lb/>Taprobena, & </s> <s xml:id="echoid-s1218" xml:space="preserve">Inſula D. </s> <s xml:id="echoid-s1219" xml:space="preserve">Thomæ. </s> <s xml:id="echoid-s1220" xml:space="preserve">Nulla autem pars Europæ rectæ ſphęrę eſt ſu <lb/> <anchor type="note" xlink:label="note-062-03a" xlink:href="note-062-03"/> biecta.</s> <s xml:id="echoid-s1221" xml:space="preserve"/> </p> <div xml:id="echoid-div108" type="float" level="2" n="13"> <note position="left" xlink:label="note-062-02" xlink:href="note-062-02a" xml:space="preserve">Variæ de <lb/>ſeriptiones <lb/>ſphæræ re-<lb/>ctæ.</note> <note position="left" xlink:label="note-062-03" xlink:href="note-062-03a" xml:space="preserve">Quæ regio-<lb/>nes ſphærã <lb/>rectam ha-<lb/>beant.</note> </div> <p> <s xml:id="echoid-s1222" xml:space="preserve"><emph style="sc">Illi</emph> uero dicuntur, &</s> <s xml:id="echoid-s1223" xml:space="preserve">c.</s> <s xml:id="echoid-s1224" xml:space="preserve">] Sphæram obliquam, inquit, illi habent, quicun-<lb/>que citra, uel vltra Æquinoctialem habitant. </s> <s xml:id="echoid-s1225" xml:space="preserve">Subiungit deinde cauſam, curnã <lb/> <anchor type="note" xlink:label="note-062-04a" xlink:href="note-062-04"/> his dicatur obliqua ſphęra: </s> <s xml:id="echoid-s1226" xml:space="preserve">quoniam videlicet alter polorum ſemper ſupra Ho-<lb/>rizontẽ attollitur, alter uero ſemper deprimitur; </s> <s xml:id="echoid-s1227" xml:space="preserve">Vnde obliquũ uidetur ſitum <lb/>habere ſphæra: </s> <s xml:id="echoid-s1228" xml:space="preserve">Vel certe, quoniam illorum Horizon artificialis interſecat Ae-<lb/>quinoctialem, & </s> <s xml:id="echoid-s1229" xml:space="preserve">ab eodem interſecatur ad angulos obliquos, & </s> <s xml:id="echoid-s1230" xml:space="preserve">inæquales.</s> <s xml:id="echoid-s1231" xml:space="preserve"/> </p> <div xml:id="echoid-div109" type="float" level="2" n="14"> <note position="left" xlink:label="note-062-04" xlink:href="note-062-04a" xml:space="preserve">Qui dican-<lb/>tur habere <lb/>ſphærã obli <lb/>quã, & cur.</note> </div> <p> <s xml:id="echoid-s1232" xml:space="preserve"><emph style="sc">Appellat</emph> Horizontem ſphęræ obliquæ artificialem, eam fortaſſis ob <lb/>cauſam, quod admodum variabilis exiſtat, & </s> <s xml:id="echoid-s1233" xml:space="preserve">non naturaliter ſphęram diuidat. <lb/></s> <s xml:id="echoid-s1234" xml:space="preserve"> <anchor type="note" xlink:label="note-062-05a" xlink:href="note-062-05"/> Solus enim Horizon ſphæræ rectę, cum tranſeat per vtrunq. </s> <s xml:id="echoid-s1235" xml:space="preserve">mundi polum, ui-<lb/>detur per ſeſe, & </s> <s xml:id="echoid-s1236" xml:space="preserve">quodammodo naturaliter ſphæram diuidere. </s> <s xml:id="echoid-s1237" xml:space="preserve">Nam hoc pacto <lb/>ſortitur ſphæra directum & </s> <s xml:id="echoid-s1238" xml:space="preserve">proprium ſitum, neque talis Horizon unquam ua-<lb/>riari poteſt, ut aliqui habere poſſint Horizontem magis rectam, alij minus re-<lb/>ctum. </s> <s xml:id="echoid-s1239" xml:space="preserve">At uero in Horizonte ſphæræ obliquę, cum non tranſeat per polos mun <lb/>di ſed ſupra ipſum ſemper alter attollatur, alter ſub ipſo deprimatur, obliquæ <lb/>uidetur collocari ſphæra, & </s> <s xml:id="echoid-s1240" xml:space="preserve">non naturaliter. </s> <s xml:id="echoid-s1241" xml:space="preserve">Accedit etiam, quod Horizon <lb/>ſphęræ obliquæ pro arbitrio, & </s> <s xml:id="echoid-s1242" xml:space="preserve">uoluntate hominum habitancium in terra va-<lb/>riabilis propemodum infinitis modis exiſtit. </s> <s xml:id="echoid-s1243" xml:space="preserve">Quo enim magis ad polum quis <lb/>accedit, eo magis obliquum Horizontem habeat neceſſe eſt. </s> <s xml:id="echoid-s1244" xml:space="preserve">Quare non imme-<lb/>rito Horizon obliquę ſphęrę quodammodo artificialis appellari poteſt, ut di-<lb/>ſtinguatur ab Horizonte ſphęrę rectæ, qui quaſi naturalis eſt ipſi ſphæræ. </s> <s xml:id="echoid-s1245" xml:space="preserve">Cum <lb/>enim in ipſo vterq. </s> <s xml:id="echoid-s1246" xml:space="preserve">mundi polus exiſtat, vĩ naturaliter in ipſo ſphæra moueri.</s> <s xml:id="echoid-s1247" xml:space="preserve"/> </p> <div xml:id="echoid-div110" type="float" level="2" n="15"> <note position="left" xlink:label="note-062-05" xlink:href="note-062-05a" xml:space="preserve">Cur Hori-<lb/>zon ſphæræ <lb/>o<unsure/>bliquæ di-<lb/>ctus ſi@ ab <lb/>auctore ar-<lb/>@ific<unsure/>ialis.</note> </div> <p> <s xml:id="echoid-s1248" xml:space="preserve"><emph style="sc">Obliqvam</emph> Sphęram alij definiunt dicentes, eam eſſe, in qua alter po-<lb/> <anchor type="note" xlink:label="note-062-06a" xlink:href="note-062-06"/> lorum mundi ſupra Horizontem eleuatus eminet, alter infra Horizontem de <lb/>cumbit, & </s> <s xml:id="echoid-s1249" xml:space="preserve">ſubſidit: </s> <s xml:id="echoid-s1250" xml:space="preserve">Vel, in qua Aequinoctialis cum Horizonte angulos efficit, <lb/>& </s> <s xml:id="echoid-s1251" xml:space="preserve">conformat obliquos, obtuſum quidem eum, qui polum exaltatum reſpicit, <lb/>acutum uero, qui ad polum uergit occultum. </s> <s xml:id="echoid-s1252" xml:space="preserve">Sphæram obliquam nacti ſunt <lb/>omnes inhabitantes Europam, ut ſunt Hiſpani, Galli, Itali, Germani, Gręci, Po <lb/> <anchor type="note" xlink:label="note-062-07a" xlink:href="note-062-07"/> loni, & </s> <s xml:id="echoid-s1253" xml:space="preserve">maior pars Africæ, & </s> <s xml:id="echoid-s1254" xml:space="preserve">Indię occidentalis, necnon tota Aſia.</s> <s xml:id="echoid-s1255" xml:space="preserve"/> </p> <div xml:id="echoid-div111" type="float" level="2" n="16"> <note position="left" xlink:label="note-062-06" xlink:href="note-062-06a" xml:space="preserve">Variæ de-<lb/>fcription es <lb/>ſphæræ ob-<lb/>liquæ.</note> <note position="left" xlink:label="note-062-07" xlink:href="note-062-07a" xml:space="preserve">Quæ regio-<lb/>nes habeãr <lb/>ſphærã ob-<lb/>@i<unsure/>quam.</note> </div> <p> <s xml:id="echoid-s1256" xml:space="preserve"><emph style="sc">Non</emph> ſolum Sphęra, verum etiam orbis, ſeu Mundus, Item Horizon, Fi-<lb/>niensve, ſeu Finitor ab auctoribus dici ſolet rectus & </s> <s xml:id="echoid-s1257" xml:space="preserve">obliquus. </s> <s xml:id="echoid-s1258" xml:space="preserve">Solent namque <lb/>dicere, Germanos, Italos, Gallos, & </s> <s xml:id="echoid-s1259" xml:space="preserve">Hiſpanos habitare in orbe obli quo: </s> <s xml:id="echoid-s1260" xml:space="preserve">Pari ra <lb/>tione Horizontem, ſeu Finitorem, mundum, uel ſphęram illos habere obli-<lb/> <anchor type="note" xlink:label="note-062-08a" xlink:href="note-062-08"/> quam, &</s> <s xml:id="echoid-s1261" xml:space="preserve">c.</s> <s xml:id="echoid-s1262" xml:space="preserve"/> </p> <div xml:id="echoid-div112" type="float" level="2" n="17"> <note position="left" xlink:label="note-062-08" xlink:href="note-062-08a" xml:space="preserve">Qui ſub <lb/>polis habi-<lb/>tant, habẽt <lb/>ſpheram ob <lb/>liquam.</note> </div> <p> <s xml:id="echoid-s1263" xml:space="preserve"><emph style="sc">Qvod</emph> ſi quis interroget, qualem ſphęram dicantur habere ij, qui dire-<lb/>cte ſub polis habitant; </s> <s xml:id="echoid-s1264" xml:space="preserve">reſpondendum erit, eos, ex auctoris ſententia habere <lb/>ſphęram obliquam. </s> <s xml:id="echoid-s1265" xml:space="preserve">Nam licet eorum Horizon, cum ſit idem prorſus, qui <pb o="27" file="063" n="64" rhead="Ioan. de Sacro Boſco."/> Aequinoctialis, nullo modo cum ſecet, quare nec ad rectos, nec ad obliquos an <lb/>gulos, tamen alter polotum ipſis maxime extollitur, alter vero maxime depri-<lb/>mitur; </s> <s xml:id="echoid-s1266" xml:space="preserve">Vnde ex hac parte maxime obliquam ſphęram habere cenſendi erunt. <lb/></s> <s xml:id="echoid-s1267" xml:space="preserve">Non deſunt tamen, qui eos in ſphęra recta habitare aſſerant, quod eorum Hori <lb/>zon non eſſiciat obliquos angulos cum Aequinoctialia. </s> <s xml:id="echoid-s1268" xml:space="preserve">Verum hoc eodem ar-<lb/>gumento concludetur, eos non in ſphęra recta degere, quoniam eorum Hori-<lb/>zon non conſſituit angulos rectos cum Aequinoctiali, ſed omnino cum eo co-<lb/>incidit. </s> <s xml:id="echoid-s1269" xml:space="preserve">Quare meo iudicio rectus cum auctore dicemus, eos in ſphęra obliqua <lb/>habitare, quia ſaltem vna cauſa ſphęrę obliquę illis cõgruit, nulla autem ſphę-<lb/>ræ rectę. </s> <s xml:id="echoid-s1270" xml:space="preserve">Quod etiam indicant definitiones aliorum traditę de ſphæ-<lb/>ra recta & </s> <s xml:id="echoid-s1271" xml:space="preserve">obliqua.</s> <s xml:id="echoid-s1272" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1273" xml:space="preserve"><emph style="sc">Origo</emph> autem, & </s> <s xml:id="echoid-s1274" xml:space="preserve">cauſa huius diuiſionis ſphęrę in rectam, & </s> <s xml:id="echoid-s1275" xml:space="preserve">obliquam <lb/> <anchor type="note" xlink:label="note-063-01a" xlink:href="note-063-01"/> eſt rotunditas terrę. </s> <s xml:id="echoid-s1276" xml:space="preserve">Cum enim vt ſuo loco demonſtrabimus, terra ſit rotunda, <lb/>ſit, vt ſitus polorum, & </s> <s xml:id="echoid-s1277" xml:space="preserve">totius ſphęrę mutetur in diuerſis terrę partibus, ita vt <lb/>homines uerſus alterum polorum procedentes ſemper eum magis ac magis <lb/>eleuatum intueantur; </s> <s xml:id="echoid-s1278" xml:space="preserve">Quod non accideret, ſi terra eſſet plana. </s> <s xml:id="echoid-s1279" xml:space="preserve">Præterea, quo-<lb/>niam ubicunque homo fuerit, & </s> <s xml:id="echoid-s1280" xml:space="preserve">in quacunque orbis terreni parte extiterit, <lb/>ſemper uidet mediam partem cœli, ſecluſis montium, & </s> <s xml:id="echoid-s1281" xml:space="preserve">uallium impedimen-<lb/>tis, ut a Ptolemęo, Alphragano, & </s> <s xml:id="echoid-s1282" xml:space="preserve">alijs Aſtronomis uarijs eſt phęnomenis com <lb/>pertum, quam quidem medietatem viſam a non uiſa dirimit Horizon; </s> <s xml:id="echoid-s1283" xml:space="preserve">Effici-<lb/>tur, ut in qua regione unus polus in Horizonte iacet, alter ẽt in eodẽ exiſtat. <lb/></s> <s xml:id="echoid-s1284" xml:space="preserve">Item quantum alter polorum ſupra Horizontem attollitur, alter quoque ran-<lb/>tum ſub eodem deprimatur; </s> <s xml:id="echoid-s1285" xml:space="preserve">Alias aut plus, aut minus, quà<unsure/>m medietatem cęli <lb/>conſpiceremus, cum poli per dimidiam cęli partem a ſe inuicem diſtent, nem-<lb/>pe qui per diametrum mundi opponantur. </s> <s xml:id="echoid-s1286" xml:space="preserve">Quare neceſſe eſt, ut homo in ali-<lb/>qua magna campi planitie conſtitutus habeat aut utrumque mundi polum (re-<lb/>motis omnibus impedimentis montium ac uallium) in Horizonte iacentem, <lb/>quando nimirum Horizon per mundi polos incedit, aut unum eleuatum, & </s> <s xml:id="echoid-s1287" xml:space="preserve">al <lb/>terum depreſſum, quando uidelicet Horizon per polos mundi minime tran-<lb/>ſit. </s> <s xml:id="echoid-s1288" xml:space="preserve">Ex his igitur omnibus euidenter conſtat ratio diuiſionis ſphęrę in rectam & </s> <s xml:id="echoid-s1289" xml:space="preserve"><lb/>obliquam.</s> <s xml:id="echoid-s1290" xml:space="preserve"/> </p> <div xml:id="echoid-div113" type="float" level="2" n="18"> <note position="right" xlink:label="note-063-01" xlink:href="note-063-01a" xml:space="preserve">Rotũditas <lb/>terræ cauſa <lb/>eſt ſphæræ <lb/>rectæ & ob<unsure/>-<lb/>liquę.</note> </div> <p> <s xml:id="echoid-s1291" xml:space="preserve"><emph style="sc">Dicta</emph> eſt ab auctore prior illa diuiſio, qua diſtribuitur ſphęra cęle-<lb/> <anchor type="note" xlink:label="note-063-02a" xlink:href="note-063-02"/> ſtis in nouem ſphęras, eſſe ſecundum ſubſtantiam, quoniam eſt diuiſio ſuperio-<lb/>ris in ſua inferiora, nempe cœli in cœlos particulares; </s> <s xml:id="echoid-s1292" xml:space="preserve">non ſecus ac fi diuide-<lb/>remus animal in hominem, leonem, equum, & </s> <s xml:id="echoid-s1293" xml:space="preserve">cętera animalia. </s> <s xml:id="echoid-s1294" xml:space="preserve">Vel certe, <lb/>quia eſt diuiſio Totius in ſuas partes integrantes, nempe totius regionis cœ-<lb/>leſtis in cœlos ſingulos, ex quibus ipſa conflatur, non aliter quam ſi diuide-<lb/>retur homo in caput, pectus, crura, brachia, & </s> <s xml:id="echoid-s1295" xml:space="preserve">cętera membra, ex quibus con-<lb/>ſtituitur. </s> <s xml:id="echoid-s1296" xml:space="preserve">Poſterior autem hæc diuiſio ſphæræ in rectam, & </s> <s xml:id="echoid-s1297" xml:space="preserve">obliquam ſphæram <lb/>uocata eſt ſecundum accidens, quia in ea non diuiditur ſphæra in fibi eſſen-<lb/>tialia, ut in priori, ſed in accidentalia, quæ nimirum illi accidunt, habita ra-<lb/>tione eorum, qui in ſphæra uitam degunt. </s> <s xml:id="echoid-s1298" xml:space="preserve">Dicitur namque ſphæra recta, <lb/>uel obliqua reſpectu habitantium ſub ipſa, quod quidem accidit ſphæræ. </s> <s xml:id="echoid-s1299" xml:space="preserve">Tam <lb/>enim eſſet ſphæra, ſi nullus in ea habitaret, quam nunc eſt; </s> <s xml:id="echoid-s1300" xml:space="preserve">non eſſet autem re <lb/>cta, uel obliqua, quoniam nullus eſſet Horizon, quem degentes in terra ſolum <lb/>conſiderare conſuenerunt. </s> <s xml:id="echoid-s1301" xml:space="preserve">Eſt igitur diuiſio hæc ſimilis illi, qua diuideretur <lb/>animal in album, nigrum, &</s> <s xml:id="echoid-s1302" xml:space="preserve">c. </s> <s xml:id="echoid-s1303" xml:space="preserve">quam quidem conſtat eſſe diuiſionem ſecun-<lb/>dum accidens.</s> <s xml:id="echoid-s1304" xml:space="preserve"/> </p> <div xml:id="echoid-div114" type="float" level="2" n="19"> <note position="right" xlink:label="note-063-02" xlink:href="note-063-02a" xml:space="preserve">Prior diui<unsure/>-<lb/>ſio cur dica<unsure/> <lb/>tur ſecun-<lb/>dum ſub-<lb/>ſtantiam, <lb/>poſtetior <lb/>autem ſe-<lb/>co<unsure/>ndum as<unsure/> <lb/>tidens.</note> </div> <pb o="28" file="064" n="65" rhead="Comment. in I. Cap. Sphæræ"/> <p> <s xml:id="echoid-s1305" xml:space="preserve"><emph style="sc">In</emph> priori fign <lb/> <anchor type="figure" xlink:label="fig-064-01a" xlink:href="fig-064-01"/> ra hic appoſita e<unsure/>-<lb/>xemplum habes <lb/>ſphæræ rectę: </s> <s xml:id="echoid-s1306" xml:space="preserve">In <lb/>poſteriori uero <lb/>ſphęræ obliquæ. <lb/></s> <s xml:id="echoid-s1307" xml:space="preserve">Manifeſte autem <lb/>uides in ſphæra <lb/>recta axem mun-<lb/>di coĩcidere cum <lb/>Horizonte, cum <lb/>ab eo non diffe-<lb/>rat; </s> <s xml:id="echoid-s1308" xml:space="preserve">ac proinde utrumque polum in Horizonte iacere. </s> <s xml:id="echoid-s1309" xml:space="preserve">In obliqua uero axem <lb/>mundi ab Horizonte differre, ac propterea unum polum ſupra Horizontem eſ <lb/>ſe exaltatum, alterum vero ſub eodem depreſſum.</s> <s xml:id="echoid-s1310" xml:space="preserve"/> </p> <div xml:id="echoid-div115" type="float" level="2" n="20"> <figure xlink:label="fig-064-01" xlink:href="fig-064-01a"> <image file="064-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/064-01"/> </figure> </div> <p style="it"> <s xml:id="echoid-s1311" xml:space="preserve"><emph style="sc">Vniversalis</emph> autem mundi machina in duo diuidit ur, in æthe-<lb/> <anchor type="note" xlink:label="note-064-01a" xlink:href="note-064-01"/> ream ſcilicet, & </s> <s xml:id="echoid-s1312" xml:space="preserve">elementarem regionem.</s> <s xml:id="echoid-s1313" xml:space="preserve"/> </p> <div xml:id="echoid-div116" type="float" level="2" n="21"> <note position="left" xlink:label="note-064-01" xlink:href="note-064-01a" xml:space="preserve">Diuiſio mũ <lb/>di in ærhe-<lb/>ream, & ele <lb/>mentarem <lb/>z<unsure/>egionem.</note> </div> </div> <div xml:id="echoid-div118" type="section" level="1" n="48"> <head xml:id="echoid-head52" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s1314" xml:space="preserve"><emph style="sc">Traditvrvs</emph> iam auctor in hac tertia capitis parte formam totius <lb/>mundi, diuidit prius vniueiſam mundi machinam in duo, Videlicet in regio-<lb/>nem elementarem, & </s> <s xml:id="echoid-s1315" xml:space="preserve">ætheream, ex quibus tanquam partibus tota mundi ma-<lb/>china conflatur. </s> <s xml:id="echoid-s1316" xml:space="preserve">In qua diuiſione Mundi machina capitur pro congerie, & </s> <s xml:id="echoid-s1317" xml:space="preserve">co-<lb/>agmentatione omnium corporum ſuperiorum, & </s> <s xml:id="echoid-s1318" xml:space="preserve">inferiorum. </s> <s xml:id="echoid-s1319" xml:space="preserve">Eſt enim mun-<lb/> <anchor type="note" xlink:label="note-064-02a" xlink:href="note-064-02"/> dus perfecta & </s> <s xml:id="echoid-s1320" xml:space="preserve">abſoluta omnium rerum congeries, & </s> <s xml:id="echoid-s1321" xml:space="preserve">ornamentum. </s> <s xml:id="echoid-s1322" xml:space="preserve">Vnde a <lb/>Græcis κόσμος dicitur ab ornatu. </s> <s xml:id="echoid-s1323" xml:space="preserve">Quem duabus definitionibus Ariſtoteles in <lb/>libello de mundo cap. </s> <s xml:id="echoid-s1324" xml:space="preserve">2. </s> <s xml:id="echoid-s1325" xml:space="preserve">(ſi tamen Ariſtotelis eſt libellus) deſcribit, quarum <lb/>prior hæc eſt. </s> <s xml:id="echoid-s1326" xml:space="preserve">Mundus eſt compages conſtans ex cœlo, terra, & </s> <s xml:id="echoid-s1327" xml:space="preserve">reliq uis naturis, <lb/>quæ in his contiuentur: </s> <s xml:id="echoid-s1328" xml:space="preserve">poſterior autem ita habet. </s> <s xml:id="echoid-s1329" xml:space="preserve">Mundus eſt corporum or-<lb/>dinatio, & </s> <s xml:id="echoid-s1330" xml:space="preserve">diſtributio, quæ a Deo, & </s> <s xml:id="echoid-s1331" xml:space="preserve">propter Deum conſeruatur.</s> <s xml:id="echoid-s1332" xml:space="preserve"/> </p> <div xml:id="echoid-div118" type="float" level="2" n="1"> <note position="left" xlink:label="note-064-02" xlink:href="note-064-02a" xml:space="preserve">Mundus <lb/>quid.</note> </div> <note position="left" xml:space="preserve">Mundusſe <lb/>cundũ mul <lb/>tos philoſo <lb/>phos æter-<lb/>nus puta@. <lb/>Mundus ſe <lb/>cundum fi <lb/>dem Catho <lb/>licã factus <lb/>e<unsure/>ſt.</note> <p> <s xml:id="echoid-s1333" xml:space="preserve"><emph style="sc">Mvndvm</emph> quidam philoſophi æternum putauerunt, ſine principio, ac <lb/>fine, vt Ariſtoteles, eiusq́ue ſectatores non pauci. </s> <s xml:id="echoid-s1334" xml:space="preserve">Plinius quoque li. </s> <s xml:id="echoid-s1335" xml:space="preserve">1. </s> <s xml:id="echoid-s1336" xml:space="preserve">natura-<lb/>lis hiſtoriæ cap. </s> <s xml:id="echoid-s1337" xml:space="preserve">1. </s> <s xml:id="echoid-s1338" xml:space="preserve">idem ſentit, cum dicit, [Mundum, & </s> <s xml:id="echoid-s1339" xml:space="preserve">hoc, quod nomine alio <lb/>cælum appellare libuit, cuius circumflexu teguntur cuncta, numen eſſe credi par eſt, <lb/>æternum, immenſum, neque genitum, neque interiturum vnquam.</s> <s xml:id="echoid-s1340" xml:space="preserve">] Fides tamen ca-<lb/>tholica docet mũdum incepiſſe, creatumq́. </s> <s xml:id="echoid-s1341" xml:space="preserve">fuiſſe, atque conditum a Deo Opt. <lb/></s> <s xml:id="echoid-s1342" xml:space="preserve">Max. </s> <s xml:id="echoid-s1343" xml:space="preserve">ex nihilo, ſolo uerbo, vt eſſet domicilium humanæ naturæ, in qua ipſe <lb/>innoteſcere, & </s> <s xml:id="echoid-s1344" xml:space="preserve">conſpici voluit. </s> <s xml:id="echoid-s1345" xml:space="preserve">Vt legimus cap. </s> <s xml:id="echoid-s1346" xml:space="preserve">1. </s> <s xml:id="echoid-s1347" xml:space="preserve">Geneſ. </s> <s xml:id="echoid-s1348" xml:space="preserve">Immo & </s> <s xml:id="echoid-s1349" xml:space="preserve">Plato in Ty-<lb/>mæo tradit, Deum eſſe mundi opificem. </s> <s xml:id="echoid-s1350" xml:space="preserve">Rurſus nonnulli philoſophi, inter <lb/>quos fuit Democritus, innumerabiles eſſe mundos cenſebant, alios extra a-<lb/>lios, quaſi pilas, ſeu globos. </s> <s xml:id="echoid-s1351" xml:space="preserve">Eſt enim forma mundi rotunda, & </s> <s xml:id="echoid-s1352" xml:space="preserve">globoſa, ut po-<lb/>ſtea dicetur: </s> <s xml:id="echoid-s1353" xml:space="preserve">Quod cum Anaxarchus Democriti diſeipulus Alexandro Ma-<lb/>gnoretuliſſet, ingemuiſſe fertur Alexander dicens: </s> <s xml:id="echoid-s1354" xml:space="preserve">Heu me miſerum, qui ne <lb/>uno quidem adhuc potius ſum. </s> <s xml:id="echoid-s1355" xml:space="preserve">Ariſtoteles tamen, & </s> <s xml:id="echoid-s1356" xml:space="preserve">Theologi noſtri ſen-<lb/>tiunt, vnum duntaxat eſſe mundum, quamuis Deus Opt. </s> <s xml:id="echoid-s1357" xml:space="preserve">Max. </s> <s xml:id="echoid-s1358" xml:space="preserve">infinitos mun-<lb/>dos ſua potentia abſoluta ſecundum Theologos poſſit producere.</s> <s xml:id="echoid-s1359" xml:space="preserve"/> </p> <pb o="29" file="065" n="66" rhead="Ioan. de Sacro Boſco."/> <p> <s xml:id="echoid-s1360" xml:space="preserve"><emph style="sc">Antiqvi</emph> porro philoſophi, & </s> <s xml:id="echoid-s1361" xml:space="preserve">grauiſſimi Theologi omnia, quæcunque <lb/> <anchor type="note" xlink:label="note-065-01a" xlink:href="note-065-01"/> exiſtunt, in tria genera partiti ſunt, adeo ut triplicem eſſe mundum aſſerue-<lb/>rint, nempe Vltramundanum, Cæleſtem, & </s> <s xml:id="echoid-s1362" xml:space="preserve">Sublunarem. </s> <s xml:id="echoid-s1363" xml:space="preserve">Vltramundanum <lb/>Theologi Angelicum, philoſophi Intellectualem nuncupant, comprehen-<lb/>dentem Deum Opt. </s> <s xml:id="echoid-s1364" xml:space="preserve">Max. </s> <s xml:id="echoid-s1365" xml:space="preserve">cum omnibus intelligentijs. </s> <s xml:id="echoid-s1366" xml:space="preserve">Cæleſtis ex orbibus, & </s> <s xml:id="echoid-s1367" xml:space="preserve"><lb/>ſphæris cæleſtibus, quotquot ſunt, integratur, & </s> <s xml:id="echoid-s1368" xml:space="preserve">vſitato vocabulo cælum appel <lb/>latur. </s> <s xml:id="echoid-s1369" xml:space="preserve">Sublunaris denique, quem nos incolimus, dicitur is, qui omnia, quæ in <lb/>tra totius cæli Lunaris concauum repoſita ſunt, vt ſunt elementa, animalia, res <lb/>inanimatæ &</s> <s xml:id="echoid-s1370" xml:space="preserve">c. </s> <s xml:id="echoid-s1371" xml:space="preserve">complectitur.</s> <s xml:id="echoid-s1372" xml:space="preserve"/> </p> <div xml:id="echoid-div119" type="float" level="2" n="2"> <note position="right" xlink:label="note-065-01" xlink:href="note-065-01a" xml:space="preserve">Mũdus tri-<lb/>plex, Vltra-<lb/>mundan’, <lb/>Cæleſtis, & <lb/>Sublunaris.</note> </div> <p> <s xml:id="echoid-s1373" xml:space="preserve"><emph style="sc">Noster</emph> igitur auctor relinquens mundum VItramundanum, quo-<lb/>niam eius conſideratio ab Aſtrologo aliena eſt, & </s> <s xml:id="echoid-s1374" xml:space="preserve">potius ad Metaphyſicum, <lb/>uel Theologum ſpectat, diuiſit mundum, vt complectitur cæleſtem, & </s> <s xml:id="echoid-s1375" xml:space="preserve">Sublu-<lb/>narem, in duo hæc membra, ex quibus ueluti partibus integratur, nempe in<unsure/> <lb/>regionem Elementarem, & </s> <s xml:id="echoid-s1376" xml:space="preserve">Æthæream. </s> <s xml:id="echoid-s1377" xml:space="preserve">Vocauit autem has duas potiſſimas <lb/>Mundi partes regiones, propter communem fortaſſis loquendi modum, quo <lb/>ſolemus orbem hunc terrenum, in quo nos degimus, in varias regiones diſtri-<lb/>buere. </s> <s xml:id="echoid-s1378" xml:space="preserve">Vtriuſque porro regionis tam Elementaris, quam Aethereæ formam no <lb/>bis explic<unsure/>abit, ac figuram.</s> <s xml:id="echoid-s1379" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">Elementa-<lb/>ris regionis <lb/>forma ac fi-<lb/>gura.</note> <p style="it"> <s xml:id="echoid-s1380" xml:space="preserve"><emph style="sc">Elementaris</emph> quidem alterationi continuæ peruia exiſtens, in <lb/>quatuor diuiditur.</s> <s xml:id="echoid-s1381" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s1382" xml:space="preserve">Eſt enim terra tanquam mundi centrum in medio omnium poſita, circa <lb/>quam aqua; </s> <s xml:id="echoid-s1383" xml:space="preserve">circa aquam aer; </s> <s xml:id="echoid-s1384" xml:space="preserve">circa aerem ignis illic purus, & </s> <s xml:id="echoid-s1385" xml:space="preserve">non turbi-<lb/>dus orbem Lunæ attingens, ut ait Ariſtoteles in libro Meteororum. </s> <s xml:id="echoid-s1386" xml:space="preserve">Sic <lb/>enim ea diſpoſuit Deus glorioſus, & </s> <s xml:id="echoid-s1387" xml:space="preserve">ſublimis.</s> <s xml:id="echoid-s1388" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s1389" xml:space="preserve">Et hæc quatuor elementa dicuntur, quę uiciſſim a ſemetipſis alter an-<lb/>tur, corrumpuntur, & </s> <s xml:id="echoid-s1390" xml:space="preserve">generantur.</s> <s xml:id="echoid-s1391" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s1392" xml:space="preserve">Sunt autem elementa corpora ſimplicia, quæ in partes diuerſarum for-<lb/>marum minime diuidi poſſunt, ex quorum commixtione diuerſæ gener ato-<lb/>rum ſpecies fiunt.</s> <s xml:id="echoid-s1393" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s1394" xml:space="preserve">Quorum trium quodlibet terram orbiculariter undique circundat, niſi <lb/>quantum ſiccitas terræ humori aquæ obſiſtit, ad uitam animantium tuen-<lb/>dam.</s> <s xml:id="echoid-s1395" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s1396" xml:space="preserve">Omnia etiam, præter terram, mobilia exiſtunt, quæ, ut centrum mundi <lb/>ponderoſitate ſui magnum extremorum motum undique æqualiter fugiens, <lb/>rotundæ ſphęrę medium poſſidet.</s> <s xml:id="echoid-s1397" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div121" type="section" level="1" n="49"> <head xml:id="echoid-head53" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s1398" xml:space="preserve"><emph style="sc">Incipit</emph> hic agere de regione elementari, ſeu (quod idem eſt) de mun-<lb/>do Sublunari, eiusq́; </s> <s xml:id="echoid-s1399" xml:space="preserve">formam, ac diſpoſitionem oſtendit. </s> <s xml:id="echoid-s1400" xml:space="preserve">Sex autem breuiſſi-<lb/>me circa hanc regionem exequitur.</s> <s xml:id="echoid-s1401" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1402" xml:space="preserve"><emph style="sc">Primo</emph> aſſignat quandam proprietatem elementaris regionis, quod ni-<lb/> <anchor type="note" xlink:label="note-065-03a" xlink:href="note-065-03"/> mirum continuæ alterationi exiſtit peruia, id eſt, dans locum, & </s> <s xml:id="echoid-s1403" xml:space="preserve">aditum altera <lb/>tionibus, quæ in ipſa fiunt. </s> <s xml:id="echoid-s1404" xml:space="preserve">Nomine vero alterationis intellige omnem trãſmu <lb/>tationẽ naturalem, ut generationem, corruptionem, augmentationem, dimi- <pb o="30" file="066" n="67" rhead="Comment. in I. Cap. Sphæræ"/> nutionem, motum localem & </s> <s xml:id="echoid-s1405" xml:space="preserve">alterationem proprie dictam, qualis eſt calefa-<lb/>ctio, frigefactio, &</s> <s xml:id="echoid-s1406" xml:space="preserve">c. </s> <s xml:id="echoid-s1407" xml:space="preserve">& </s> <s xml:id="echoid-s1408" xml:space="preserve">denique omnem motum ſubſtantiam rei aliquo modo <lb/>variantem. </s> <s xml:id="echoid-s1409" xml:space="preserve">Eſt enim elementaris regio pars illa uniuerſi, in qua continuæ fiunt <lb/>rerum tranſmutationes.</s> <s xml:id="echoid-s1410" xml:space="preserve"/> </p> <div xml:id="echoid-div121" type="float" level="2" n="1"> <note position="right" xlink:label="note-065-03" xlink:href="note-065-03a" xml:space="preserve">Elementa-<lb/>ris regio cõ <lb/>tinuæ alte-<lb/>rationi ob-<lb/>nexia eſt.</note> </div> <p> <s xml:id="echoid-s1411" xml:space="preserve"><emph style="sc">Secvndo</emph> elementarem regionem in quatuor membra partitur, vide-<lb/>licet in Terram, Aquam, Aerem, & </s> <s xml:id="echoid-s1412" xml:space="preserve">Ignem, ubi etiam harum partium ordi-<lb/> <anchor type="note" xlink:label="note-066-01a" xlink:href="note-066-01"/> nem, quem in Vniuerſo obtinent, oſtendit dicens, terram tanquam mundi cea <lb/>trum in medio omnium ſitam eſſe. </s> <s xml:id="echoid-s1413" xml:space="preserve">Dixit [tanquam centrum] quoniam cum ter-<lb/>ra quantitatem ac molem habeat ingentem, ſi abſolute conſideretur, uerum <lb/>centrum eſſe nequit. </s> <s xml:id="echoid-s1414" xml:space="preserve">Centrum etenim circuli cuiuſuis, uel ſphæræ punctũ eſt <lb/>indiuiſibile omni carens magnitudine. </s> <s xml:id="echoid-s1415" xml:space="preserve">Sed quoniam tota terræ magnitudo, li-<lb/>cet immenſa nobis appareat, reſpectu totius cæli eſt inſtar puncti, ut poſtea <lb/>demonſtrabitur, merito tanquam centrum dici poterit. </s> <s xml:id="echoid-s1416" xml:space="preserve">Deinde aſſerit circa <lb/>terram eſſe aquam; </s> <s xml:id="echoid-s1417" xml:space="preserve">quod intelligendum eſt de naturali loco aquæ. </s> <s xml:id="echoid-s1418" xml:space="preserve">Conue-<lb/>nit enim naturæ aquæ, ut ambiat terram: </s> <s xml:id="echoid-s1419" xml:space="preserve">Cur vero nunc non ambiat, mox di-<lb/>cemus) circa aquam aerem; </s> <s xml:id="echoid-s1420" xml:space="preserve">& </s> <s xml:id="echoid-s1421" xml:space="preserve">denique circa aerem ignem exiſtere illic purum, <lb/>& </s> <s xml:id="echoid-s1422" xml:space="preserve">non turbidum, orbem Lunæ attingentem. </s> <s xml:id="echoid-s1423" xml:space="preserve">Dicitur autem ignis illic purus, & </s> <s xml:id="echoid-s1424" xml:space="preserve"><lb/>non turbidus a philoſophis ob tres cauſas, quarum prima eſt; </s> <s xml:id="echoid-s1425" xml:space="preserve">quia illuc va-<lb/>pores aſcendere non poſſunt, qui illum impurum, & </s> <s xml:id="echoid-s1426" xml:space="preserve">turbidum reddant: </s> <s xml:id="echoid-s1427" xml:space="preserve">Secun-<lb/>da cauſa eſt propter differentiam inter illum ignem, & </s> <s xml:id="echoid-s1428" xml:space="preserve">noſtrum hunc inferio-<lb/>rem, qui non purus, ſed mixtus eſſe dicitur, cum non ſit in ſuo loco naturali; <lb/></s> <s xml:id="echoid-s1429" xml:space="preserve">Idcirco namque permiſcetur continue cum aere, in quo exiſtit, habetq́. </s> <s xml:id="echoid-s1430" xml:space="preserve">ali-<lb/>mentum terrenum, quo turbidus, ac impurus efficitur: </s> <s xml:id="echoid-s1431" xml:space="preserve">ignis autem in propria <lb/>ſphæra eſt immixtus, rarus, & </s> <s xml:id="echoid-s1432" xml:space="preserve">purus; </s> <s xml:id="echoid-s1433" xml:space="preserve">Cuius rei ſignum eſſe poteſt, quod ob <lb/>maximam ſui raritatem, ac puritatem ibi non collucet; </s> <s xml:id="echoid-s1434" xml:space="preserve">Vnde etiam non ui-<lb/>detur: </s> <s xml:id="echoid-s1435" xml:space="preserve">Tertia cauſa ſumitur reſpectu aliorum elementorum, quæ non pura <lb/>exiſtunt; </s> <s xml:id="echoid-s1436" xml:space="preserve">Aqua enim cum terra promiſcue commiſcetur; </s> <s xml:id="echoid-s1437" xml:space="preserve">Aer vero impurus à <lb/>continuo aſcenſu vaporum ex terra, & </s> <s xml:id="echoid-s1438" xml:space="preserve">aqua redditur; </s> <s xml:id="echoid-s1439" xml:space="preserve">Ignis autem cum nul-<lb/>lo, præcipue apud concauum Lunæ, permiſcetur. </s> <s xml:id="echoid-s1440" xml:space="preserve">Quamombrem Ariſtoteles 1. </s> <s xml:id="echoid-s1441" xml:space="preserve"><lb/>Meteor. </s> <s xml:id="echoid-s1442" xml:space="preserve">dixit, Aut nullibi ſimplex elementum eſt, aut ſi alicubi eſt, in loco <lb/>ignis erit. </s> <s xml:id="echoid-s1443" xml:space="preserve">Quod ſi petas ab auctore cauſam huius ordinis, cur uidelicet terra <lb/>ſit infima, deinde ſupra eam aqua, &</s> <s xml:id="echoid-s1444" xml:space="preserve">c. </s> <s xml:id="echoid-s1445" xml:space="preserve">reſpondet huius ordinis cauſam eſſe <lb/>Deũ glorioſum, qui ea ita diſpoſuit, uoluitq́; </s> <s xml:id="echoid-s1446" xml:space="preserve">hoc elementum illo ſuperius eſſe.</s> <s xml:id="echoid-s1447" xml:space="preserve"/> </p> <div xml:id="echoid-div122" type="float" level="2" n="2"> <note position="left" xlink:label="note-066-01" xlink:href="note-066-01a" xml:space="preserve">Ordo Ele-<lb/>mẽtorum.</note> </div> <p> <s xml:id="echoid-s1448" xml:space="preserve"><emph style="sc">Tertio</emph> ait has quatu or elementaris regionis partes Elementa appel-<lb/> <anchor type="note" xlink:label="note-066-02a" xlink:href="note-066-02"/> lari, quæ viciſſim a ſemetipſis alterantur, corrumpuntur, & </s> <s xml:id="echoid-s1449" xml:space="preserve">generantur. </s> <s xml:id="echoid-s1450" xml:space="preserve">Mo-<lb/>do enim ex terra fit aqua, ex aqua aer, & </s> <s xml:id="echoid-s1451" xml:space="preserve">ex aere ignis, & </s> <s xml:id="echoid-s1452" xml:space="preserve">contra, idq́. </s> <s xml:id="echoid-s1453" xml:space="preserve">conti-<lb/>nue: </s> <s xml:id="echoid-s1454" xml:space="preserve">Ob quam rationem regio elementaris a philoſophis ſphæra actiuorum <lb/>& </s> <s xml:id="echoid-s1455" xml:space="preserve">paſſiuorum eſt appellata. </s> <s xml:id="echoid-s1456" xml:space="preserve">Quod non ſic intelligas, quod ita hæc elementa <lb/>inter ſe pugnent, vt vnum elementum totum aliud corrumpat, hoc enim <lb/>falſum eſt, ſed quod pars unius interdum alteret, & </s> <s xml:id="echoid-s1457" xml:space="preserve">corrumpat partem alte-<lb/>rius, ſuæq́; </s> <s xml:id="echoid-s1458" xml:space="preserve">ſpeciei formam in eius materiam introducat.</s> <s xml:id="echoid-s1459" xml:space="preserve"/> </p> <div xml:id="echoid-div123" type="float" level="2" n="3"> <note position="left" xlink:label="note-066-02" xlink:href="note-066-02a" xml:space="preserve">Elementa <lb/>uiciſſim a <lb/>ſemetipſis <lb/>alterantur, <lb/>@orrumpũ-<lb/>@ur, &c.</note> </div> <p> <s xml:id="echoid-s1460" xml:space="preserve"><emph style="sc">Qvarto</emph> definit elementa dicens, Elementa eſſe corpora ſimplicia, <lb/> <anchor type="note" xlink:label="note-066-03a" xlink:href="note-066-03"/> quæ in partes diuerſarum formarum minime diuidi poſſunt, ex quorum com-<lb/>mixtione diuerſæ generatorum ſpecies fiunt. </s> <s xml:id="echoid-s1461" xml:space="preserve">Quam quidem definitionem ex <lb/>Auicenna deſum @ſit. </s> <s xml:id="echoid-s1462" xml:space="preserve">Dicuntur elementa [corpora] vt diſtinguantur contra <lb/>materiam primam, quæ corpus non eſt. </s> <s xml:id="echoid-s1463" xml:space="preserve">Dicuntur [corpora ſimplicia] non quod <lb/>careant compoſitione ex materia & </s> <s xml:id="echoid-s1464" xml:space="preserve">forma; </s> <s xml:id="echoid-s1465" xml:space="preserve">hoc enim falſum eſſet, ſed quod <lb/>non componantur ex alijs corporibus, ſicut mixta corpora componuntur ex <pb o="31" file="067" n="68" rhead="Ioan. de Sacro Boſco."/> eſementis, & </s> <s xml:id="echoid-s1466" xml:space="preserve">in eadẽ reſoluuntur. </s> <s xml:id="echoid-s1467" xml:space="preserve">Id vero, quod additur. </s> <s xml:id="echoid-s1468" xml:space="preserve">[quæ in partes diuer-<lb/>ſarum, &</s> <s xml:id="echoid-s1469" xml:space="preserve">c.</s> <s xml:id="echoid-s1470" xml:space="preserve">] deſumptum eſt ex 5. </s> <s xml:id="echoid-s1471" xml:space="preserve">lib. </s> <s xml:id="echoid-s1472" xml:space="preserve">Metaph. </s> <s xml:id="echoid-s1473" xml:space="preserve">cap. </s> <s xml:id="echoid-s1474" xml:space="preserve">3. </s> <s xml:id="echoid-s1475" xml:space="preserve">ſigniſicatq́ue elementa non <lb/>reſolui in res diuerſarum formarũ, quo pacto mixta reſoluuntur in elementa: <lb/></s> <s xml:id="echoid-s1476" xml:space="preserve">Vel ſignificat, in diuiſione elementorum non poſſe aſſignari partes diſſimila-<lb/>res, cum ſint corpora Homogenea, ideſt, ſimilis generis, rationisve. </s> <s xml:id="echoid-s1477" xml:space="preserve">quo pacto <lb/>alia corpora diuiduntur in partes diſſimilares, cum ſint Heterogenea, id eſt, <lb/> <anchor type="note" xlink:label="note-067-01a" xlink:href="note-067-01"/> alterius ſeu diuerſi generis, rationisve. </s> <s xml:id="echoid-s1478" xml:space="preserve">Pro eo denique, quod ſequitur [ex quo <lb/>rum commixtione, &</s> <s xml:id="echoid-s1479" xml:space="preserve">c.</s> <s xml:id="echoid-s1480" xml:space="preserve">] id tantum ſciendum eſt, quinque eſſe mixtorum genera, <lb/>quæ ex diuerſa elementorum miſcibilium proportione interſe, contempera-<lb/>mentoq́ue proueniunt. </s> <s xml:id="echoid-s1481" xml:space="preserve">Io primo, & </s> <s xml:id="echoid-s1482" xml:space="preserve">inſimo gradu ſunt illa mixta, quę dici ſo-<lb/>lent a philoſophis mixta imperfecta, appellanturq́ue impreſſiones Meteorolo <lb/>gicę, quia in ſublimifiunt, ut ſunt pluuię, grando, nix, tonitrua, fulgur, & </s> <s xml:id="echoid-s1483" xml:space="preserve">cęte <lb/>ra huiuſmodi. </s> <s xml:id="echoid-s1484" xml:space="preserve">In ſecundo gradu ſunt lapides, mineralia, & </s> <s xml:id="echoid-s1485" xml:space="preserve">corpora foſſilia, quę <lb/>mixta inanimata uocantur: </s> <s xml:id="echoid-s1486" xml:space="preserve">In tertio gradu ſunt uegetabilia, ut planta anima-<lb/>lia: </s> <s xml:id="echoid-s1487" xml:space="preserve">In quinto denique, & </s> <s xml:id="echoid-s1488" xml:space="preserve">ſupremo gradu homines continentur.</s> <s xml:id="echoid-s1489" xml:space="preserve"/> </p> <div xml:id="echoid-div124" type="float" level="2" n="4"> <note position="left" xlink:label="note-066-03" xlink:href="note-066-03a" xml:space="preserve">Elementa <lb/>quid.</note> <note position="right" xlink:label="note-067-01" xlink:href="note-067-01a" xml:space="preserve">Mixtorum <lb/>quinque ge <lb/>nera.</note> </div> <note position="right" xml:space="preserve">Elemẽtor@ <lb/>figuræ.</note> <p> <s xml:id="echoid-s1490" xml:space="preserve"><emph style="sc">Qvinto</emph> oſtendit figuras elementorum dicens, unumquodque trium <lb/>elementorum orbiculariter circundare terram, ita ut ignis ambiat circulari-<lb/>ter aerem, aer aquam & </s> <s xml:id="echoid-s1491" xml:space="preserve">terram: </s> <s xml:id="echoid-s1492" xml:space="preserve">Et quoniam aer debebat circundare aquam, <lb/>& </s> <s xml:id="echoid-s1493" xml:space="preserve">aqua terram, cuius contrarium cernimus; </s> <s xml:id="echoid-s1494" xml:space="preserve">Aqua enim non totam terram, <lb/>circumit, ſed duo hęc elementa, nempe terra & </s> <s xml:id="echoid-s1495" xml:space="preserve">aqua unum efficiunt globum <lb/>ut paulo poſt oſtendemus; </s> <s xml:id="echoid-s1496" xml:space="preserve">Affert duas cauſas, cur aqua totam terram non am-<lb/>biat, quarum prima efficiens eſt & </s> <s xml:id="echoid-s1497" xml:space="preserve">naturalis, nempe ſiccitas terrę, quę con-<lb/>tinue, inquit, in humidum aqueum agens aquam diminuit, aut ſaltem reſi-<lb/>ſit, ne totam terram operiat orbemq́; </s> <s xml:id="echoid-s1498" xml:space="preserve">perficiat. </s> <s xml:id="echoid-s1499" xml:space="preserve">Verum hæc cauſa ualde ineffi-<lb/>cax exiſtit? </s> <s xml:id="echoid-s1500" xml:space="preserve">Quomodo enim tanta eſſe poteſt terrę ſiccitas, ut tanto elemen-<lb/>to aquæ ualeat reſiſtere, præſertim potentiori, & </s> <s xml:id="echoid-s1501" xml:space="preserve">ſuperiori ſe ſuapte natura? <lb/></s> <s xml:id="echoid-s1502" xml:space="preserve">Immo & </s> <s xml:id="echoid-s1503" xml:space="preserve">cum experientia pugnat, ſiccitatẽ à ſe humorem propellere, cum po-<lb/>tius illum corripiat, & </s> <s xml:id="echoid-s1504" xml:space="preserve">attrahat, ut cernimus in cineribus, & </s> <s xml:id="echoid-s1505" xml:space="preserve">alijs huiuſmodi <lb/>rebus ſiccis. </s> <s xml:id="echoid-s1506" xml:space="preserve">Secunda cauſa finalis eſt, & </s> <s xml:id="echoid-s1507" xml:space="preserve">ſupernaturalis, Diuina ſcilicet pro-<lb/>uidentia. </s> <s xml:id="echoid-s1508" xml:space="preserve">Deus enim, ut in Geneſi legitur, aquas terra ſegregauit ad quorun-<lb/>dam animalium vitam tuendam. </s> <s xml:id="echoid-s1509" xml:space="preserve">Antequam enim Deus Opt. </s> <s xml:id="echoid-s1510" xml:space="preserve">Max. </s> <s xml:id="echoid-s1511" xml:space="preserve">dixiſſet, Con <lb/>gregentur aquæ in locum unum, circundabat aqua, ſecundum Theologos, to-<lb/>tam terram; </s> <s xml:id="echoid-s1512" xml:space="preserve">luſſu autem Dei receſſit aqua, & </s> <s xml:id="echoid-s1513" xml:space="preserve">apparuit arida. </s> <s xml:id="echoid-s1514" xml:space="preserve">Quo autem mo-<lb/> <anchor type="note" xlink:label="note-067-03a" xlink:href="note-067-03"/> do id iuſſu Dei factũ ſit, uariæ extant ſententiæ. </s> <s xml:id="echoid-s1515" xml:space="preserve">Quidam em̃ dicunt, Terram <lb/>in ſuo quidẽ loco permanſiſſe, Aquam uero ſupra terram eſſe eleuatam, ita vt <lb/>ſi deflueret, totam iterum terrã cooperiret: </s> <s xml:id="echoid-s1516" xml:space="preserve">Neque vero, cur nunc nõ defluat, <lb/>terramq́; </s> <s xml:id="echoid-s1517" xml:space="preserve">operiat, inter eos conuenit. </s> <s xml:id="echoid-s1518" xml:space="preserve">Multi enim exiſtimant, miraculo, & </s> <s xml:id="echoid-s1519" xml:space="preserve">po-<lb/>tentia Dei fieri, ne aqua deflluens orbem terrarum cooperiat, In q́ua ſententia <lb/>uidetur etiam eſſe B. </s> <s xml:id="echoid-s1520" xml:space="preserve">Hieron. </s> <s xml:id="echoid-s1521" xml:space="preserve">motus auctoritate ſcripturæ. </s> <s xml:id="echoid-s1522" xml:space="preserve">Dicitur enim Pro-<lb/>uerb. </s> <s xml:id="echoid-s1523" xml:space="preserve">8. </s> <s xml:id="echoid-s1524" xml:space="preserve">& </s> <s xml:id="echoid-s1525" xml:space="preserve">Pſal. </s> <s xml:id="echoid-s1526" xml:space="preserve">103. </s> <s xml:id="echoid-s1527" xml:space="preserve">Deum aquis terminum poſuiſſe, quem non tranſirent. <lb/></s> <s xml:id="echoid-s1528" xml:space="preserve">Alij uero nolentes concedere hoc continuum miraculum, ridiculam prorſus <lb/>& </s> <s xml:id="echoid-s1529" xml:space="preserve">nullius momenti cauſam adducunt. </s> <s xml:id="echoid-s1530" xml:space="preserve">Dicunt enim circa polum arcticum eſ-<lb/>ſe ſtellas quaſdam, nimirum in Vrſa, Dracone, &</s> <s xml:id="echoid-s1531" xml:space="preserve">c. </s> <s xml:id="echoid-s1532" xml:space="preserve">tantæ efficacitatis, & </s> <s xml:id="echoid-s1533" xml:space="preserve">uirtutis <lb/>in hæc inferiora, ut ab hac parte terræ habitabili in Septentionem uergente <lb/>Oceanum propellant, & </s> <s xml:id="echoid-s1534" xml:space="preserve">coerceant, ne iterum terram obruat. </s> <s xml:id="echoid-s1535" xml:space="preserve">Alij arbitrantes <lb/>multo maiorem eſſe quantitatem aquæ, quàm terræ, dicunt, Aquam ob ingen <lb/>tem ſui molem propellere grauitate ſua terram extralocum ſuum naturalem, <pb o="32" file="068" n="69" rhead="Comment in I Cap. Sphæræ"/> ipſam uero occupare centrum mundi, adeo ut Te@ra in mari quaſi natare vi-<lb/>deatur. </s> <s xml:id="echoid-s1536" xml:space="preserve">Et hi auctores omnes putant, totam hanc terram uerſus polum arcti-<lb/>cum eſſe aquis delectam, reliquam vero terræ pattem uerſus antarcticum po-<lb/>lum totam eſſe mari oppletam: </s> <s xml:id="echoid-s1537" xml:space="preserve">quod hodiernæ nauigantium experientiæ re-<lb/>pugnat, ut poſtea dicemus. </s> <s xml:id="echoid-s1538" xml:space="preserve">Alij denique adhuc concedentes aquam multo eſ <lb/>ſe maiorem ipſa terra, immo decuplo maiorem, aſſerunt totam terram eſſe ue <lb/>luti ſpongiam quandam, (cuius rei, aiunt, ſignum eſſe poteſt, quod ſtatim re-<lb/>peritur aqua in omni loco, ubi terra fodiatur) eſſeq́; </s> <s xml:id="echoid-s1539" xml:space="preserve">multis cauernis, atque <lb/>concauitatibus repletã; </s> <s xml:id="echoid-s1540" xml:space="preserve">Ex quo, aiunt, fit, ut aquæ cum tota terra permiſcean-<lb/>tur, & </s> <s xml:id="echoid-s1541" xml:space="preserve">in cõcauitatibus illis recip@ãtur. </s> <s xml:id="echoid-s1542" xml:space="preserve">Quate minor pars aquæ, quàm ſit terra, <lb/>remanebit ſupra terrã; </s> <s xml:id="echoid-s1543" xml:space="preserve">quare mirum non eſt, quod amplius aqua terram ob-<lb/>ruere nequeat In quam ſententiam multi Peripatetici Ariſtotelem trahere co <lb/>nantur. </s> <s xml:id="echoid-s1544" xml:space="preserve">Verum etiamſi concedamus concauitates ingentes in terra, impoſſi-<lb/>bile eſt, aquam decies maiorem eſſe ipſa terra; </s> <s xml:id="echoid-s1545" xml:space="preserve">Hac enim ratione, quamuis to-<lb/>tus globus terrenus eſſet aqua, fieri non poſſet, quin maior portio aquæ, quàm <lb/>ſit terra, exiſteret ſupra terram; </s> <s xml:id="echoid-s1546" xml:space="preserve">cum ad huc nouem partes aquæ ex decem ſu-<lb/>pereſſent. </s> <s xml:id="echoid-s1547" xml:space="preserve">Accedit etiam, quod multo minor ſit aqua quàm terra, vt poſtea <lb/>oſtendemus. </s> <s xml:id="echoid-s1548" xml:space="preserve">Omnes igitur hæ ſententiæ & </s> <s xml:id="echoid-s1549" xml:space="preserve">rationi, & </s> <s xml:id="echoid-s1550" xml:space="preserve">experientijs manifeſtiſſi <lb/>mis repugnant, quod magis perſpicuum fiet, cum de rotunditate terræ & </s> <s xml:id="echoid-s1551" xml:space="preserve">aquæ <lb/>egerimus. </s> <s xml:id="echoid-s1552" xml:space="preserve">Qua propter modus, quo iuſſu Dei ſegregatæ fuerunt aquæ, ut ap <lb/> <anchor type="note" xlink:label="note-068-01a" xlink:href="note-068-01"/> pareret Arida, magis mihi placet is, quem explicat S. </s> <s xml:id="echoid-s1553" xml:space="preserve">Ioan Damaſcenus ſum-<lb/>mæ auctoritatis apud Theologos uir, lib. </s> <s xml:id="echoid-s1554" xml:space="preserve">2. </s> <s xml:id="echoid-s1555" xml:space="preserve">de orthodoxa fide capit. </s> <s xml:id="echoid-s1556" xml:space="preserve">9. </s> <s xml:id="echoid-s1557" xml:space="preserve">& </s> <s xml:id="echoid-s1558" xml:space="preserve">10. </s> <s xml:id="echoid-s1559" xml:space="preserve">& </s> <s xml:id="echoid-s1560" xml:space="preserve"><lb/>quem ſequitur Iacobus de Valentijs epiſcopus; </s> <s xml:id="echoid-s1561" xml:space="preserve">Terram nimirum a Deo Opt. <lb/></s> <s xml:id="echoid-s1562" xml:space="preserve">Max. </s> <s xml:id="echoid-s1563" xml:space="preserve">perfecte rotundam, ac globoſam, abſque vllis concauitatibus, vallibus, <lb/>montibus, & </s> <s xml:id="echoid-s1564" xml:space="preserve">eminentijs eſſe conditam, totamq́ue aquis circundatam; </s> <s xml:id="echoid-s1565" xml:space="preserve">At ue-<lb/>ro poſtea, cum Deus dixit, [congregentur aquæ in locum vnum, &</s> <s xml:id="echoid-s1566" xml:space="preserve">c.</s> <s xml:id="echoid-s1567" xml:space="preserve">] ob uitam ani-<lb/>mantium quorundam diuino iuſſu concauitates in terra factas eſſe, & </s> <s xml:id="echoid-s1568" xml:space="preserve">in eas <lb/>omnem aquarum uim, tanquam in ſuas congregationes conueniſſe, variaq́ue <lb/>maria in diuerſis terræ partibus illico exorta eſſe, atque ex partibus illi terræ <lb/>extractis montes eſſe factos. </s> <s xml:id="echoid-s1569" xml:space="preserve">Huic ſententiæ nonnulli adiungunt, Aquas in <lb/>principio mundi fuiſſe rariſſimas, ſed poſtea iuſſu Dei fuiſſe condenſatas, re-<lb/>ceptasq́ue in dictis concauitatibus, ut mirum non ſit, quod minores nunc ſint <lb/>quàm terra. </s> <s xml:id="echoid-s1570" xml:space="preserve">Quomodocunque denique id factum ſit, diſputandum alijs relin-<lb/>quamus; </s> <s xml:id="echoid-s1571" xml:space="preserve">nobis autem nunc certum ſit, terram & </s> <s xml:id="echoid-s1572" xml:space="preserve">aquam unum efficere glo-<lb/>bum: </s> <s xml:id="echoid-s1573" xml:space="preserve">quod quidem paulo infra demonſtrabitur ex uarijs experientijs; </s> <s xml:id="echoid-s1574" xml:space="preserve">atque <lb/>hanc eſſe cauſam, cur iam aqua totam terram non ambiat, immo nec poſſit am-<lb/>bire, cum duo hęc elementa vnam, eandemq́; </s> <s xml:id="echoid-s1575" xml:space="preserve">ſuperficiem conuexã habeant, at-<lb/>que ambo ſua grauitate naturaliter ad totius uniuerſi centrum tendant.</s> <s xml:id="echoid-s1576" xml:space="preserve"/> </p> <div xml:id="echoid-div125" type="float" level="2" n="5"> <note position="right" xlink:label="note-067-03" xlink:href="note-067-03a" xml:space="preserve">Variæ ſen-<lb/>tentiæ quo <lb/>pacto aqua <lb/>à terra re-<lb/>ceſſerit, ur <lb/>apparere@ <lb/>arida.</note> <note position="left" xlink:label="note-068-01" xlink:href="note-068-01a" xml:space="preserve">Verior ſen-<lb/>tentia expli <lb/>cãs, quo pa <lb/>cto aqua à <lb/>terra ſepara <lb/>ta ſit.</note> </div> <p> <s xml:id="echoid-s1577" xml:space="preserve"><emph style="sc">Sexsto</emph> ac ultimo docet, omnia elementa præter terram [quæ vt cen-<lb/> <anchor type="note" xlink:label="note-068-02a" xlink:href="note-068-02"/> trum mundi ponderoſitate ſui magnum extremorum motum, nempe cælorum, vn dique <lb/>æqualiter fugiens, rotundæ ſphæræ, hoc eſt, mundi medium poſſidet] exiſtere mobilia. <lb/></s> <s xml:id="echoid-s1578" xml:space="preserve">Quod non ſic intelligas, quaſi nullo modo terra ſit mobilis; </s> <s xml:id="echoid-s1579" xml:space="preserve">Hoc enim fal-<lb/>ſum eſt, cum extra ſuum locum poſita maximo impetu ad naturalem ſuum lo <lb/>cum recurrat: </s> <s xml:id="echoid-s1580" xml:space="preserve">Sed quod propter grauitatem immenſam non moueatur circu-<lb/>lariter in ſuo loco, ut reliqua elementa. </s> <s xml:id="echoid-s1581" xml:space="preserve">Ignis etenim, & </s> <s xml:id="echoid-s1582" xml:space="preserve">ſuprema pars ae-<lb/>ris, immo, ut nonnulli experimento conſtare affirmant, bona pars Ocea-<lb/>ni motu primi mobilis ab oriente in occidentem, propter eorum leuitatem, & </s> <s xml:id="echoid-s1583" xml:space="preserve"><lb/>mobilitatem, feruntur.</s> <s xml:id="echoid-s1584" xml:space="preserve"/> </p> <div xml:id="echoid-div126" type="float" level="2" n="6"> <note position="left" xlink:label="note-068-02" xlink:href="note-068-02a" xml:space="preserve">Terra im-<lb/>mobilis eſt, <lb/>alia uero e-<lb/>lemẽta mo-<lb/>uentur ab <lb/>ortu in oc-<lb/>caſum.</note> </div> <pb o="33" file="069" n="70" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div128" type="section" level="1" n="50"> <head xml:id="echoid-head54" xml:space="preserve">DE NVMERO ET ORDINE ELEMENTORVM.</head> <p> <s xml:id="echoid-s1585" xml:space="preserve"><emph style="sc">QVoniam</emph> vero auctor noſter docuit, quatuor eſſe elementa, <lb/>nõ abs re fuerit, paucis aperire, quibus potiſſimũ rationibus philo <lb/>ſophi colligant. </s> <s xml:id="echoid-s1586" xml:space="preserve">quatuor elementa eſſe: </s> <s xml:id="echoid-s1587" xml:space="preserve">Deinde nõnihil de ordi <lb/> <anchor type="note" xlink:label="note-069-01a" xlink:href="note-069-01"/> ne, ac ſitu eorundem referre. </s> <s xml:id="echoid-s1588" xml:space="preserve">Prima igitur ratio, qua philoſophi <lb/>probant, quatuor eſſe elementa, ſumitur ex qualitatib primis, quas <lb/>dicit Ariſtoteles 2. </s> <s xml:id="echoid-s1589" xml:space="preserve">de Gñatio ne eſſe quatuor, duas actiuas, nempe caliditatẽ, & </s> <s xml:id="echoid-s1590" xml:space="preserve"><lb/>frigiditatẽ: </s> <s xml:id="echoid-s1591" xml:space="preserve">duas vero paſſiuas, nimirũ ſiccitatem, & </s> <s xml:id="echoid-s1592" xml:space="preserve">humiditatem. </s> <s xml:id="echoid-s1593" xml:space="preserve">Eſt autem ra <lb/> <anchor type="figure" xlink:label="fig-069-01a" xlink:href="fig-069-01"/> tio talis. </s> <s xml:id="echoid-s1594" xml:space="preserve">Tot ſunt elementa, quot ſunt cõbinationes harũ quatuor primarum <lb/>qualitatum poſſibiles, ideſt, quot modis primæ hæ quatuor qualitates inter ſe <lb/>poſſunt cõiungi, ſeſeq́; </s> <s xml:id="echoid-s1595" xml:space="preserve">mutuo compati, vt loco citato ait Ariſtoteles: </s> <s xml:id="echoid-s1596" xml:space="preserve">Atqui <lb/>ſunt ſolũ quatuor combinationes poſſibiles, igitur & </s> <s xml:id="echoid-s1597" xml:space="preserve">quatuor erunt elemen-<lb/>ta. </s> <s xml:id="echoid-s1598" xml:space="preserve">Minor patet, quia ad ſummum inter quatuor illas qualitates, ſi binas ſem-<lb/>per ſumpſerimus, ſex tantũ fieri poſſunt combinationes, vt caliditatis cum ſicci-<lb/>tate, ex qua conſtituitur Ignis, qui calidus eſt in ſummo gradu, ſiccus vero in <lb/>remiſſo: </s> <s xml:id="echoid-s1599" xml:space="preserve">humiditatis cũ caliditate, ex qua habemus aerem, qui ſumme humi- <pb o="34" file="070" n="71" rhead="Comment. in I. Cap. Sphæræ"/> dus, remiſſe autem calidus exiſtit: </s> <s xml:id="echoid-s1600" xml:space="preserve">frigiditatis cum humiditate, ex qua philoſo-<lb/>phi aquam colligunt, quam frigidam dicunt in ſummo, humidam vero remiſ-<lb/>ſe: </s> <s xml:id="echoid-s1601" xml:space="preserve">ſiccitatis cum frigiditate, ex qua terra conficitur, quæ in ſummo ſicca, frigi-<lb/>da uero remiſſe eſſe prædicatur: </s> <s xml:id="echoid-s1602" xml:space="preserve">caliditatis cum frigiditate: </s> <s xml:id="echoid-s1603" xml:space="preserve">& </s> <s xml:id="echoid-s1604" xml:space="preserve">humiditatis cum <lb/>ſiccitate. </s> <s xml:id="echoid-s1605" xml:space="preserve">Sed quoniam duæ hæ poſtremæ combinationes impoſſibiles ſunt, <lb/>cum ſint contrariorum; </s> <s xml:id="echoid-s1606" xml:space="preserve">quorum ea eſt natura, vt vnum alterum ſemper expel-<lb/>lat: </s> <s xml:id="echoid-s1607" xml:space="preserve">Neque enim una, eademq́ue res numero calida, & </s> <s xml:id="echoid-s1608" xml:space="preserve">frigida; </s> <s xml:id="echoid-s1609" xml:space="preserve">neque humida <lb/>ſimul, & </s> <s xml:id="echoid-s1610" xml:space="preserve">ſicca eſſe poteſt; </s> <s xml:id="echoid-s1611" xml:space="preserve">idcirco inutiles cenſentur, neque quicquam ex eis cõ <lb/>ſtitui poteſt. </s> <s xml:id="echoid-s1612" xml:space="preserve">Hæ autem omnes combinationes luce clarius in figura propoſi-<lb/>ta conſpiciuntur. </s> <s xml:id="echoid-s1613" xml:space="preserve">Quod autem diximus, unam qualitatem in quolibet elemẽ <lb/>to eſſe in ſummo gradu, & </s> <s xml:id="echoid-s1614" xml:space="preserve">in remiſſo alteram, intelligendum eſt ex ſententia <lb/>@uorunda<unsure/>m philoſophorum. </s> <s xml:id="echoid-s1615" xml:space="preserve">Multi enim arbitrantur, utramque qualitatem in <lb/>quouis elemento eſſe in ſummo grad@</s> </p> <div xml:id="echoid-div128" type="float" level="2" n="1"> <note position="right" xlink:label="note-069-01" xlink:href="note-069-01a" xml:space="preserve">Quatuor e@ <lb/>ſe elemen-<lb/>ta, probatu@ <lb/>ex cõbina-<lb/>tionibus <lb/>primaru@ <lb/>qualitatũ</note> <figure xlink:label="fig-069-01" xlink:href="fig-069-01a"> <image file="069-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/069-01"/> </figure> </div> <note position="left" xml:space="preserve">Digreſſio <lb/>pulcherri-<lb/>ma de rerũ <lb/>cõbinatio--<lb/>nibus, fiue <lb/>cõparatio--<lb/>nibus.</note> <p> <s xml:id="echoid-s1616" xml:space="preserve"><emph style="sc">Qvoniam</emph> vero diximus, inter quatuor res non poſſe fieri plures com-<lb/>binationes, quàm ſex, ſi binæ tantum ſemper ſumantur, uiſum mihi eſt, paulo <lb/>uberius explicare, quotnam combinationes huiuſmodi fieri poſsint inter quot-<lb/>cunque res propoſitas; </s> <s xml:id="echoid-s1617" xml:space="preserve">Ad multa enim conducit huiuſce rei notitia, eſtq́ue per <lb/>ſe iucundiſſima. </s> <s xml:id="echoid-s1618" xml:space="preserve">Propoſito ergo numero aliquarum rerum, multiplicetur is <lb/>per numerum proxime minorem. </s> <s xml:id="echoid-s1619" xml:space="preserve">Nam producti numeri medietas indicabit <lb/> <anchor type="note" xlink:label="note-070-02a" xlink:href="note-070-02"/> numerum combinationum, quæ fieri poſſunt inter res propoſitas. </s> <s xml:id="echoid-s1620" xml:space="preserve">Vt in propo-<lb/>ſito exemplo, quoniam ſunt quatuor qualitates primæ, ſi multiplicentur 4. </s> <s xml:id="echoid-s1621" xml:space="preserve">per <lb/>3. </s> <s xml:id="echoid-s1622" xml:space="preserve">officientur 12. </s> <s xml:id="echoid-s1623" xml:space="preserve">quare ſex combinationes inter ipſas fieri poſſunt. </s> <s xml:id="echoid-s1624" xml:space="preserve">Quòd ſi fue-<lb/>rint quinque res combinandæ, multiplicanda ſunt 5. </s> <s xml:id="echoid-s1625" xml:space="preserve">per 4. </s> <s xml:id="echoid-s1626" xml:space="preserve">Nam producti me-<lb/>dietas, nempe 10. </s> <s xml:id="echoid-s1627" xml:space="preserve">oſtendet numerum combinationum: </s> <s xml:id="echoid-s1628" xml:space="preserve">quot uidelicet Porphy <lb/>rius inter quinque prædicabilia inſtituit.</s> <s xml:id="echoid-s1629" xml:space="preserve"/> </p> <div xml:id="echoid-div129" type="float" level="2" n="2"> <note position="left" xlink:label="note-070-02" xlink:href="note-070-02a" xml:space="preserve">Quot com-<lb/>binationes <lb/>fieri poſ-<lb/>f<unsure/>int inter <lb/>quotcunq; <lb/>res, ſi binæ <lb/>ſ<unsure/>umantur.</note> </div> <p> <s xml:id="echoid-s1630" xml:space="preserve"><emph style="sc">Potest</emph> hæc regula tradita in duas diſtrahi, prout ſcilicet numerus re-<lb/>rum par, uel impar fuerit. </s> <s xml:id="echoid-s1631" xml:space="preserve">Sienim numerus rerum fuerit par, multiplicandus <lb/>erit numerus proxime minor per medietatem numeri rerum: </s> <s xml:id="echoid-s1632" xml:space="preserve">Nam productus <lb/>numerus continuo oſtendet combinationum numerum. </s> <s xml:id="echoid-s1633" xml:space="preserve">Vt ſi ſcire lubet, quo@ <lb/>fieri poſſint combinationes inter 10. </s> <s xml:id="echoid-s1634" xml:space="preserve">res, multiplicabuntur 9. </s> <s xml:id="echoid-s1635" xml:space="preserve">per 5. </s> <s xml:id="echoid-s1636" xml:space="preserve">ut fiant 45. <lb/></s> <s xml:id="echoid-s1637" xml:space="preserve">quot nimirum combinationes fieri inter decem res poſſunt. </s> <s xml:id="echoid-s1638" xml:space="preserve">Si uero numerus <lb/>rerum extiterit impar, multiplicandus is erit per medietatem numeri proxime<unsure/> <lb/>minoris; </s> <s xml:id="echoid-s1639" xml:space="preserve">Hac enim ratione numerus procreatus indicabit, quot fieri poſſintcõ <lb/>binationes. </s> <s xml:id="echoid-s1640" xml:space="preserve">Vt ſi res fuerint 15. </s> <s xml:id="echoid-s1641" xml:space="preserve">Multiplicatis 15. </s> <s xml:id="echoid-s1642" xml:space="preserve">per 7. </s> <s xml:id="echoid-s1643" xml:space="preserve">efficietur numerus con <lb/>binationum inter ipſas, nempe 105. </s> <s xml:id="echoid-s1644" xml:space="preserve">Inter 9. </s> <s xml:id="echoid-s1645" xml:space="preserve">uero res fient combinationes 36. </s> <s xml:id="echoid-s1646" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s1647" xml:space="preserve">fic de cæteris.</s> <s xml:id="echoid-s1648" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1649" xml:space="preserve"><emph style="sc">Qvod</emph> ſi ſcire placuerit, quotcunque rebus propoſitis, quot fimpliciter <lb/> <anchor type="note" xlink:label="note-070-03a" xlink:href="note-070-03"/> coniunctiones ex ipſis poſſint fieri, non ſolum intelligendo, quando binæ ſu-<lb/>muntur, ut in præcedenti regula, ſed etiam quando ternæ, quaternæ, quinæ, <lb/>&</s> <s xml:id="echoid-s1650" xml:space="preserve">c. </s> <s xml:id="echoid-s1651" xml:space="preserve">hoc eſt, quotnã modis diſtinctis inter ſeſe poſſint cõparari; </s> <s xml:id="echoid-s1652" xml:space="preserve">efficietur id hac <lb/>arte, & </s> <s xml:id="echoid-s1653" xml:space="preserve">regula. </s> <s xml:id="echoid-s1654" xml:space="preserve">Accipiantur tot numeri, incipiendo ab unitate, in dupla propo@ <lb/>tione, quot res ſunt propoſitæ, & </s> <s xml:id="echoid-s1655" xml:space="preserve">à ſumma omnium illorum ſubtrahatur nume <lb/>rus rerum: </s> <s xml:id="echoid-s1656" xml:space="preserve">Reliquus enim numerus indicabit, quotnam comparationes diuerſę <lb/>effici poſſint.</s> <s xml:id="echoid-s1657" xml:space="preserve">|Facile aũt habebitur ſumma quotcunq. </s> <s xml:id="echoid-s1658" xml:space="preserve">numerorum duplæ pro-<lb/>portionis ab 1. </s> <s xml:id="echoid-s1659" xml:space="preserve">incipientis, ſi ultimus numerus duplicetur, & </s> <s xml:id="echoid-s1660" xml:space="preserve">ex producto unitas <lb/>abijciatur. </s> <s xml:id="echoid-s1661" xml:space="preserve">Vt ſi lubeat ſcire ſummam horum numerorum in dupla proportio-<lb/>ne, 1. </s> <s xml:id="echoid-s1662" xml:space="preserve">2. </s> <s xml:id="echoid-s1663" xml:space="preserve">4. </s> <s xml:id="echoid-s1664" xml:space="preserve">8. </s> <s xml:id="echoid-s1665" xml:space="preserve">16. </s> <s xml:id="echoid-s1666" xml:space="preserve">32. </s> <s xml:id="echoid-s1667" xml:space="preserve">64. </s> <s xml:id="echoid-s1668" xml:space="preserve">duplicandus erit numerus ultimus 64. </s> <s xml:id="echoid-s1669" xml:space="preserve">ut fiant 128. </s> <s xml:id="echoid-s1670" xml:space="preserve">@ <lb/>quibus reiecta unitate, remanent 127. </s> <s xml:id="echoid-s1671" xml:space="preserve">pro ſumma omnium illorum numerorũ, <pb o="35" file="071" n="72" rhead="Ioan. de Sacro Boſco."/> hoc eſt, unitates 127. </s> <s xml:id="echoid-s1672" xml:space="preserve">in illis continentur. </s> <s xml:id="echoid-s1673" xml:space="preserve">Sed hac de plura in noſtra Arithme-<lb/> <anchor type="note" xlink:label="note-071-01a" xlink:href="note-071-01"/> tica Practica ſcripſimus. </s> <s xml:id="echoid-s1674" xml:space="preserve">Exemplum combinationum in ſupradictis quatuor <lb/>qualitatibus. </s> <s xml:id="echoid-s1675" xml:space="preserve">Numeri in dupla proportione iuxta nume rum rerum erunt 4. </s> <s xml:id="echoid-s1676" xml:space="preserve">ni <lb/>mirum 1. </s> <s xml:id="echoid-s1677" xml:space="preserve">2. </s> <s xml:id="echoid-s1678" xml:space="preserve">4. </s> <s xml:id="echoid-s1679" xml:space="preserve">8. </s> <s xml:id="echoid-s1680" xml:space="preserve">quorum ſumma eſt 15. </s> <s xml:id="echoid-s1681" xml:space="preserve">abiectis ergo 4. </s> <s xml:id="echoid-s1682" xml:space="preserve">remanent 11. </s> <s xml:id="echoid-s1683" xml:space="preserve">Totigitur <lb/>modis diuerſis coniungi poterunt quatuor primæ qualitates, uidelicet hæ, ca-<lb/>liditas, frigiditas: </s> <s xml:id="echoid-s1684" xml:space="preserve">caliditas, ſiccitas caliditas, humiditas: </s> <s xml:id="echoid-s1685" xml:space="preserve">frigiditas, ſiccitas: </s> <s xml:id="echoid-s1686" xml:space="preserve">frigi-<lb/>ditas, humiditas: </s> <s xml:id="echoid-s1687" xml:space="preserve">ſiccitas, humiditas: </s> <s xml:id="echoid-s1688" xml:space="preserve">caliditas, ſrigiditas, ſiccitas: </s> <s xml:id="echoid-s1689" xml:space="preserve">caliditas, ſicci-<lb/>tas, humiditas: </s> <s xml:id="echoid-s1690" xml:space="preserve">frigiditas, ſiccitas, humiditas: </s> <s xml:id="echoid-s1691" xml:space="preserve">caliditas, frigiditas, humiditas: </s> <s xml:id="echoid-s1692" xml:space="preserve">& </s> <s xml:id="echoid-s1693" xml:space="preserve"><lb/>demum caliditas, frigiditas, ſiccitas, humiditas. </s> <s xml:id="echoid-s1694" xml:space="preserve">Neque fieri poteſt, ut alia com-<lb/>paratio efficiatur, quæ a omnibus iſtis differat. </s> <s xml:id="echoid-s1695" xml:space="preserve">Non. </s> <s xml:id="echoid-s1696" xml:space="preserve">n. </s> <s xml:id="echoid-s1697" xml:space="preserve">hæ duæ, caliditas, frigidi-<lb/>tas: </s> <s xml:id="echoid-s1698" xml:space="preserve">frigiditas, caliditas, cum ordo tantum mutetur, & </s> <s xml:id="echoid-s1699" xml:space="preserve">non res, diſtinctæ eſſe cen <lb/>ſentur Hac rõne inter quinque res, ut inter quinque prædicabilia, 26. </s> <s xml:id="echoid-s1700" xml:space="preserve">poſſunt <lb/>fieri diuerſæ comparationes. </s> <s xml:id="echoid-s1701" xml:space="preserve">Nam ſumma horum numerorum 1. </s> <s xml:id="echoid-s1702" xml:space="preserve">2. </s> <s xml:id="echoid-s1703" xml:space="preserve">4. </s> <s xml:id="echoid-s1704" xml:space="preserve">8. </s> <s xml:id="echoid-s1705" xml:space="preserve">16. </s> <s xml:id="echoid-s1706" xml:space="preserve">eſt 31. <lb/></s> <s xml:id="echoid-s1707" xml:space="preserve">Ablatis aũt 5. </s> <s xml:id="echoid-s1708" xml:space="preserve">relinquuntur 26. </s> <s xml:id="echoid-s1709" xml:space="preserve">Hæc porro regula multum conducit Aſtrolo-<lb/>gis, ut ſciant oẽs cõiunctiones diuerſas, quæ fieri poſſunt inter ſeptem planetas. </s> <s xml:id="echoid-s1710" xml:space="preserve"><lb/>Iuxta. </s> <s xml:id="echoid-s1711" xml:space="preserve">n. </s> <s xml:id="echoid-s1712" xml:space="preserve">artificium prædictum coniungi poſſunt, ſeu uariari modis 120. </s> <s xml:id="echoid-s1713" xml:space="preserve">quos lõ <lb/>gũ eſſet recenſere. </s> <s xml:id="echoid-s1714" xml:space="preserve">Pari rõne cognoſcetur, quot dictiones ſiue utiles, ſiue inuti <lb/>les, ex 23. </s> <s xml:id="echoid-s1715" xml:space="preserve">literis alphabeti poſſint conſtitui, hoc eſt, quot modis dictæ 13. </s> <s xml:id="echoid-s1716" xml:space="preserve">lite-<lb/>ræ inter ſe coniungi poſſint, ita ut ſemper ſint diuerſæ coniunctiones, ſiue pro-<lb/>@unciari poſſint, ſiue non. </s> <s xml:id="echoid-s1717" xml:space="preserve">Fient em̃ ex 23. </s> <s xml:id="echoid-s1718" xml:space="preserve">literis dictiones, ſiue diuerſæ coniun <lb/>c<unsure/>tiones, numero 8388584. </s> <s xml:id="echoid-s1719" xml:space="preserve">Nam ultimus numerus, uidelicet ui<unsure/>ceſimus tertius <lb/>proportionis duplæ eſt, 4194304. </s> <s xml:id="echoid-s1720" xml:space="preserve">& </s> <s xml:id="echoid-s1721" xml:space="preserve">ideo ſumma omnium numerorum erit <lb/>8388607. </s> <s xml:id="echoid-s1722" xml:space="preserve">Reiectis igitur 23. </s> <s xml:id="echoid-s1723" xml:space="preserve">remanent 8388584. </s> <s xml:id="echoid-s1724" xml:space="preserve">&</s> <s xml:id="echoid-s1725" xml:space="preserve">c. </s> <s xml:id="echoid-s1726" xml:space="preserve">Verũ eſt, plures dictiones <lb/>fieri poſſe, ſiue literarum coniunctiones, ſi literæ in quauis coninctione permu <lb/>tentur inter ſeſe. </s> <s xml:id="echoid-s1727" xml:space="preserve">Vt hoc aggregatum, ſe coniunctio literarum, <emph style="sc">Ave</emph>, ſex modis <lb/>uariari põt, uidelicet, <emph style="sc">Ave</emph>, <emph style="sc">Aev</emph>, <emph style="sc">Vae</emph>, <emph style="sc">Vea</emph>, <emph style="sc">Eva</emph>, <emph style="sc">Eav</emph>, qui quidem <lb/>modi ſumpti ſunt à nobis in regula pro una duntaxat coniunctione, quoniam <lb/>omnes hi modi eaſdem continent literas, quamuis inter ſe locum mutent.</s> <s xml:id="echoid-s1728" xml:space="preserve"/> </p> <div xml:id="echoid-div130" type="float" level="2" n="3"> <note position="left" xlink:label="note-070-03" xlink:href="note-070-03a" xml:space="preserve">Quot com-<lb/>binationes <lb/>fieri poſ-<lb/>fint inter <lb/>quotcunq; <lb/>res abſolu-<lb/>te, ſi non ſo <lb/>l<unsure/>um binæ, <lb/>ſed etiam <lb/>@ernæ, qua-<lb/>ternæ, qui-<lb/>@æ, &c. ſu-<lb/>mantur<unsure/>.</note> <note position="right" xlink:label="note-071-01" xlink:href="note-071-01a" xml:space="preserve">Qũo ſcia-<lb/>tur ſumma<unsure/> <lb/>quorcũque <lb/>numerorũ <lb/>proportie<unsure/>-<lb/>nis duplæ <lb/>ab 1<unsure/>. incip@ <lb/>entis.</note> </div> <p> <s xml:id="echoid-s1729" xml:space="preserve"><emph style="sc">Si</emph> vero propoſitus fuerit numerus rerũ, & </s> <s xml:id="echoid-s1730" xml:space="preserve">operæpretiũ ſit indagare, quotnã <lb/> <anchor type="note" xlink:label="note-071-02a" xlink:href="note-071-02"/> modis illæ inter ſe poſſint cõmutari, manente tñ ſemper eodẽ numero rerum, <lb/>id hac conſequeris regula. </s> <s xml:id="echoid-s1731" xml:space="preserve">Cape tot numeros in ſerie naturali, quot ſunt res, <lb/>initio facto ab unitate, & </s> <s xml:id="echoid-s1732" xml:space="preserve">illos omnes inter ſe multiplica; </s> <s xml:id="echoid-s1733" xml:space="preserve">Procreatus em̃ nume <lb/>rus oſtendet propoſitum. </s> <s xml:id="echoid-s1734" xml:space="preserve">Vt duæ res, v. </s> <s xml:id="echoid-s1735" xml:space="preserve">g. </s> <s xml:id="echoid-s1736" xml:space="preserve">A, B, duobus modis uariari poſſunt. <lb/></s> <s xml:id="echoid-s1737" xml:space="preserve">Nam quæuis primũ occupabit locũ, hoc modo, A B, B A, qm̃ hi numeri 1. </s> <s xml:id="echoid-s1738" xml:space="preserve">2. </s> <s xml:id="echoid-s1739" xml:space="preserve">in-<lb/>rer ſe multiplicati efficiunt 1. </s> <s xml:id="echoid-s1740" xml:space="preserve">Attres res poſsũt ſex modis uariari. </s> <s xml:id="echoid-s1741" xml:space="preserve">Nã hi nume <lb/>ri 1. </s> <s xml:id="echoid-s1742" xml:space="preserve">2. </s> <s xml:id="echoid-s1743" xml:space="preserve">3. </s> <s xml:id="echoid-s1744" xml:space="preserve">multiplicati inter ſe faciũt 6. </s> <s xml:id="echoid-s1745" xml:space="preserve">Ratio huius eſt, qm̃ unaquæq; </s> <s xml:id="echoid-s1746" xml:space="preserve">res primũ <lb/>tenebit locũ ſemel, & </s> <s xml:id="echoid-s1747" xml:space="preserve">reliquæ duæ bis poſsũt, ut dixi<unsure/>mus, mutari inter ſeſe. </s> <s xml:id="echoid-s1748" xml:space="preserve">Ita <lb/>quoq; </s> <s xml:id="echoid-s1749" xml:space="preserve">quatuor res uigintiquatuor modis uariari poſsũt; </s> <s xml:id="echoid-s1750" xml:space="preserve">cũ hi numeri 1. </s> <s xml:id="echoid-s1751" xml:space="preserve">2. </s> <s xml:id="echoid-s1752" xml:space="preserve">3. </s> <s xml:id="echoid-s1753" xml:space="preserve">4. </s> <s xml:id="echoid-s1754" xml:space="preserve"><lb/>inter ſe multiplicati faciãt 24. </s> <s xml:id="echoid-s1755" xml:space="preserve">Ratio eſt, quia unaquęq; </s> <s xml:id="echoid-s1756" xml:space="preserve">res ſemel primũ occu-<lb/>pabit locũ, & </s> <s xml:id="echoid-s1757" xml:space="preserve">reliquæ tres ſexies, ut diximus, inter ſe uariari poſſunt, Eadem uia <lb/>colliges 10. </s> <s xml:id="echoid-s1758" xml:space="preserve">res poſſe ordinẽ inter ſe uariare modis 36.</s> <s xml:id="echoid-s1759" xml:space="preserve">8800. </s> <s xml:id="echoid-s1760" xml:space="preserve">ꝙ hi numeri 1. </s> <s xml:id="echoid-s1761" xml:space="preserve">2. </s> <s xml:id="echoid-s1762" xml:space="preserve"><lb/>3. </s> <s xml:id="echoid-s1763" xml:space="preserve">4. </s> <s xml:id="echoid-s1764" xml:space="preserve">5. </s> <s xml:id="echoid-s1765" xml:space="preserve">6. </s> <s xml:id="echoid-s1766" xml:space="preserve">7. </s> <s xml:id="echoid-s1767" xml:space="preserve">8. </s> <s xml:id="echoid-s1768" xml:space="preserve">9. </s> <s xml:id="echoid-s1769" xml:space="preserve">10. </s> <s xml:id="echoid-s1770" xml:space="preserve">inter ſe multiplicati gignant hunc numerũ 3628800. </s> <s xml:id="echoid-s1771" xml:space="preserve">Res ue-<lb/>ro undecim, modis 39916800. </s> <s xml:id="echoid-s1772" xml:space="preserve">inter ſe; </s> <s xml:id="echoid-s1773" xml:space="preserve">qm̃ hi numeri 1. </s> <s xml:id="echoid-s1774" xml:space="preserve">2. </s> <s xml:id="echoid-s1775" xml:space="preserve">3. </s> <s xml:id="echoid-s1776" xml:space="preserve">4. </s> <s xml:id="echoid-s1777" xml:space="preserve">5. </s> <s xml:id="echoid-s1778" xml:space="preserve">6. </s> <s xml:id="echoid-s1779" xml:space="preserve">7. </s> <s xml:id="echoid-s1780" xml:space="preserve">8. </s> <s xml:id="echoid-s1781" xml:space="preserve">9. </s> <s xml:id="echoid-s1782" xml:space="preserve">10. </s> <s xml:id="echoid-s1783" xml:space="preserve">11. </s> <s xml:id="echoid-s1784" xml:space="preserve"><lb/>multiplicati inter ſe procreant numerũ prædictũ. </s> <s xml:id="echoid-s1785" xml:space="preserve">Poſtquam igitur per docu-<lb/>mentũ præcedens omnes coniunctiones uigintitriũ literarum alphabeti cogi-<lb/>tæ fuerint, ſi inquiratur per hanc regulã, quot modis literæ uniuſcuiuſq; </s> <s xml:id="echoid-s1786" xml:space="preserve">con-<lb/>iunctionis inter ſe cõmutari poſſint, habebitur numerus omniũ dictionum uti <lb/>liũ & </s> <s xml:id="echoid-s1787" xml:space="preserve">inutilium, dummodo in una dictione nulla litera bis, uel ter, &</s> <s xml:id="echoid-s1788" xml:space="preserve">c. </s> <s xml:id="echoid-s1789" xml:space="preserve">accipia- <pb o="36" file="072" n="73" rhead="Comment. in I. Cap. Sphæræ"/> tur. </s> <s xml:id="echoid-s1790" xml:space="preserve">Sic em̃ multo plures adhuc dictiones fieri poſſent. </s> <s xml:id="echoid-s1791" xml:space="preserve">Hac ratione ex ultima <lb/>coniunctione uiginti trium literarum inter ſeſe conſtituentur permutationes <lb/>25852016738884976640000. </s> <s xml:id="echoid-s1792" xml:space="preserve">& </s> <s xml:id="echoid-s1793" xml:space="preserve">tamen nulla litei<unsure/>a bis ſumitur <lb/>quod uix credibile eſt. </s> <s xml:id="echoid-s1794" xml:space="preserve">Placuit hæc de cõbinationibus inſerere huic loco, qm̃ <lb/>mẽtio facta fuerat cõbinationũ, & </s> <s xml:id="echoid-s1795" xml:space="preserve">à paucis huiuſmodi regulæ expiicari ſolent.</s> <s xml:id="echoid-s1796" xml:space="preserve"/> </p> <div xml:id="echoid-div131" type="float" level="2" n="4"> <note position="right" xlink:label="note-071-02" xlink:href="note-071-02a" xml:space="preserve">Quot mo-<lb/>dis quotcũ <lb/>que res in-<lb/>ter ſe poſ <lb/>ſint cõmu <lb/>tari, manẽ <lb/>te ſemper <lb/>eodem nu <lb/>mero rerũ</note> </div> <p> <s xml:id="echoid-s1797" xml:space="preserve"><emph style="sc">Secvndam</emph> rationem, qua probatur quaternarius elementorum nume-<lb/> <anchor type="note" xlink:label="note-072-01a" xlink:href="note-072-01"/> rus, ſumunt philoſophi à leuitate & </s> <s xml:id="echoid-s1798" xml:space="preserve">grauitate. </s> <s xml:id="echoid-s1799" xml:space="preserve">Omne em̃ corpus ſimplex, in <lb/>quod mixta reſoluuntur, (cuiuſmodi eſt elementũ) aut graue exiſtit, aut leue: <lb/></s> <s xml:id="echoid-s1800" xml:space="preserve">Si graue, aut graue eſt ſimpliciter, vt terra; </s> <s xml:id="echoid-s1801" xml:space="preserve">aut graue ſecundum quid, vt aqua; </s> <s xml:id="echoid-s1802" xml:space="preserve"><lb/>Si leue, uel eſt leue ſimpliciter, ut ignis; </s> <s xml:id="echoid-s1803" xml:space="preserve">uel leue ſecundum quid, vt aer. </s> <s xml:id="echoid-s1804" xml:space="preserve">Atque <lb/>ita colliguntur quatuor hæc elementa. </s> <s xml:id="echoid-s1805" xml:space="preserve">Dicitur autem Aqua grauis ſecundum <lb/>quid, quia licet reſpe ctu ignis, & </s> <s xml:id="echoid-s1806" xml:space="preserve">aeris exiſtat grauis, reſpectu tamen terræ quo-<lb/> <anchor type="note" xlink:label="note-072-02a" xlink:href="note-072-02"/> dam modo leuis eſt, cũ terra ſit grauior, quàm aqua: </s> <s xml:id="echoid-s1807" xml:space="preserve">Potius vero dicitur grauis <lb/>quàm leuis, quoniam ſolum reſpectu unius elementi, puta terræ, dicitur leuis; <lb/></s> <s xml:id="echoid-s1808" xml:space="preserve">At reſpectu aliorum duorum grauis appellatur, & </s> <s xml:id="echoid-s1809" xml:space="preserve">reipſa grauitatem in ſe con <lb/>tiner, non autem leuitatem. </s> <s xml:id="echoid-s1810" xml:space="preserve">Pari ratione nuncupatur aer leuis ſecundũ quid, <lb/>quoniam licet reſpectu terræ, & </s> <s xml:id="echoid-s1811" xml:space="preserve">aquæ ſit leuis, reſpectu tamen ignis quodam-<lb/>modo grauis exiſtit, cũ illo leuior multo ſit ignis; </s> <s xml:id="echoid-s1812" xml:space="preserve">Denominatur vero potius le-<lb/>uis, quàm grauis, quia reſpectu unius duntaxat elemẽti, uidelicet ignis, grauis <lb/>uocatur; </s> <s xml:id="echoid-s1813" xml:space="preserve">At uero reſpectu alio rũ duorũ leuis, & </s> <s xml:id="echoid-s1814" xml:space="preserve">reipſa cõtinet in ſe leuitatẽ, mi <lb/>nime aũt grauitatẽ, cũ ſemper ad locũ ſublimẽ, niſi impediatur, ſuo motu tẽdat.</s> <s xml:id="echoid-s1815" xml:space="preserve"/> </p> <div xml:id="echoid-div132" type="float" level="2" n="5"> <note position="left" xlink:label="note-072-01" xlink:href="note-072-01a" xml:space="preserve">Quatuor <lb/>eſſe elemẽ-<lb/>ta, cõfirma <lb/>tur à leui-<lb/>tate, & gra-<lb/>uitate.</note> <note position="left" xlink:label="note-072-02" xlink:href="note-072-02a" xml:space="preserve">Cur aqua <lb/>dicatur gra <lb/>uis ſecũ dũ <lb/>quid, & aer <lb/>leuis ſecun <lb/>dum quid.</note> </div> <p> <s xml:id="echoid-s1816" xml:space="preserve"><emph style="sc">Tertia</emph> ratio deſumitur ex motibus localibus ſimplicibus Sunt etenim, <lb/> <anchor type="note" xlink:label="note-072-03a" xlink:href="note-072-03"/> Auctore Ariſtotele in libro de cælo, tres tantum motus locales ſimplices; </s> <s xml:id="echoid-s1817" xml:space="preserve">Pri-<lb/>mus fit circa mediũ, qualis eſt circularis, qui conuenit cæleſtibus corporibus: <lb/></s> <s xml:id="echoid-s1818" xml:space="preserve">Secundus eſt à medio: </s> <s xml:id="echoid-s1819" xml:space="preserve">Tertius ad mediũ; </s> <s xml:id="echoid-s1820" xml:space="preserve">atque hi duo motus poſteriores recti <lb/>ſunt. </s> <s xml:id="echoid-s1821" xml:space="preserve">Iam uero ita philoſophi ratiocinantur. </s> <s xml:id="echoid-s1822" xml:space="preserve">Tot ſunt corpora ſimplicia, quæ <lb/>recto motu feruntur, (ut cælum excludamus, quod motu recto non agitatur) <lb/>quot ſunt motus recti ſimplices: </s> <s xml:id="echoid-s1823" xml:space="preserve">(Omnis ſiquidẽ motus ſimplex alicui corpori <lb/>ſimplici debetur; </s> <s xml:id="echoid-s1824" xml:space="preserve">& </s> <s xml:id="echoid-s1825" xml:space="preserve">contra, omne corpus ſimplex motu ſimplici moueri eſt a-<lb/>ptũ.) </s> <s xml:id="echoid-s1826" xml:space="preserve">Sunt aũt quatuor huiuſmodi motus, duo ſcilicet à medio, hoc eſt, à centro <lb/>mundi: </s> <s xml:id="echoid-s1827" xml:space="preserve">quor<unsure/>ũ vnus eſt à medio ſimpliciter, tribuiturq́. </s> <s xml:id="echoid-s1828" xml:space="preserve">igni, qui omnium leuiſ-<lb/>ſimus eſt; </s> <s xml:id="echoid-s1829" xml:space="preserve">alter à medio ſecundum quid, qui aeri conceditur, cum non ſit tam <lb/>leuis, quàm ignis, leuior uero, quàm terra, & </s> <s xml:id="echoid-s1830" xml:space="preserve">aqua: </s> <s xml:id="echoid-s1831" xml:space="preserve">Et duo ad medium, ſiue ad <lb/>centrum mundi, quorum is, qui ſimpliciter eſt ad medium, conuenit terræ ob <lb/>ſummã grauitatẽ: </s> <s xml:id="echoid-s1832" xml:space="preserve">Ille uero, qui eſt ad mediũ ſecundũ quid, aquæ adſcribitur, <lb/>quippe quæ nõ tam grauis exiſtat, quàm terra, grauior aũt igne, & </s> <s xml:id="echoid-s1833" xml:space="preserve">aere. </s> <s xml:id="echoid-s1834" xml:space="preserve">Sunt igi <lb/>tur hæc tantum elementa. </s> <s xml:id="echoid-s1835" xml:space="preserve">Aliæ rationes ex philoſophia naturali petantur.</s> <s xml:id="echoid-s1836" xml:space="preserve"/> </p> <div xml:id="echoid-div133" type="float" level="2" n="6"> <note position="left" xlink:label="note-072-03" xlink:href="note-072-03a" xml:space="preserve">Quatuor <lb/>eſſe elemẽ-<lb/>@a, probatur <lb/>ex motibus <lb/>localibus</note> </div> <p> <s xml:id="echoid-s1837" xml:space="preserve"><emph style="sc">Ordo</emph> & </s> <s xml:id="echoid-s1838" xml:space="preserve">ſitus elementorũ ex tribus quoq. </s> <s xml:id="echoid-s1839" xml:space="preserve">potiſſimũ colligi poteſt. </s> <s xml:id="echoid-s1840" xml:space="preserve">Primo <lb/> <anchor type="note" xlink:label="note-072-04a" xlink:href="note-072-04"/> ex leuitate, & </s> <s xml:id="echoid-s1841" xml:space="preserve">grauitate ipſorum. </s> <s xml:id="echoid-s1842" xml:space="preserve">Quo. </s> <s xml:id="echoid-s1843" xml:space="preserve">n. </s> <s xml:id="echoid-s1844" xml:space="preserve">unũaltero leuius eſt, eo ad ſublimio-<lb/>rem locum aſcendit, & </s> <s xml:id="echoid-s1845" xml:space="preserve">quo grauius, eo ad inferiorem. </s> <s xml:id="echoid-s1846" xml:space="preserve">Cum ergo ignis ob maxi <lb/>mã ſui raritatẽ ſit ſumme leuis, ſupremus ei debebitur locus, qui quidẽ eſt ſub <lb/>cõcauo Lunæ: </s> <s xml:id="echoid-s1847" xml:space="preserve">Proximũ huic locũ adeptus eſt aer, cũ ſit cæteris duobus elemen-<lb/>tis leuior, minus vero leuis, quàm ignis: </s> <s xml:id="echoid-s1848" xml:space="preserve">Huic proxime ſuccedit aqua: </s> <s xml:id="echoid-s1849" xml:space="preserve">Eſt enim <lb/>grauiorigne, & </s> <s xml:id="echoid-s1850" xml:space="preserve">aere, leuior uero quàm terra: </s> <s xml:id="echoid-s1851" xml:space="preserve">Infimum denique locũ, qui eſt pro <lb/> <anchor type="note" xlink:label="note-072-05a" xlink:href="note-072-05"/> pe centrum Vniuerſi, iure ſibi Terra uendicat, cum ſit omnium grauiſima.</s> <s xml:id="echoid-s1852" xml:space="preserve"/> </p> <div xml:id="echoid-div134" type="float" level="2" n="7"> <note position="left" xlink:label="note-072-04" xlink:href="note-072-04a" xml:space="preserve">Ordo ele-<lb/>mentorum <lb/>colligitur <lb/>exleuitate, <lb/>& grauita-<lb/>te.</note> <note position="left" xlink:label="note-072-05" xlink:href="note-072-05a" xml:space="preserve">Ordo ele-<lb/>menior<unsure/>um <lb/>colligitur <lb/>ex proprie-<lb/>tatibus illo <lb/>rum.</note> </div> <p> <s xml:id="echoid-s1853" xml:space="preserve"><emph style="sc">Secvndo</emph> ex conuenientia elementorum in proprietatibus. </s> <s xml:id="echoid-s1854" xml:space="preserve">Quanto <lb/>enim aliqua magis conueniunt in proprietatibus, tanto etiam propinquiora, <lb/>& </s> <s xml:id="echoid-s1855" xml:space="preserve">uiciniora inter ſe ſunt in loco. </s> <s xml:id="echoid-s1856" xml:space="preserve">Vnde cum terram uideamus infimã tenuiſſe <pb o="37" file="073" n="74" rhead="Ioan. de Sacro Boſco."/> ſedem, aquam vero terræ ſimiliorem eſſe, quàm aerem; </s> <s xml:id="echoid-s1857" xml:space="preserve">cum aer prorſus terræ <lb/>aduerſetur, in nullaq́ue qualitate cum ipſa conueniat, aqua vero in frigidita-<lb/>te concordet cum terra, non immerito aquam ſupra terram immediate collo-<lb/>cauit natura. </s> <s xml:id="echoid-s1858" xml:space="preserve">Eadem ratione ſupra aquam commode aerem ponemus, cum <lb/>conueniat cum aqua in humiditate, ignis uero in nulla qualitate aquæſit ſimi-<lb/>lis, ſed ei omnino ſit contrarius. </s> <s xml:id="echoid-s1859" xml:space="preserve">Supra aerem denique ignem haud iniuria cõ-<lb/>ſtituemus; </s> <s xml:id="echoid-s1860" xml:space="preserve">cum in caliditate conueniat cum aere. </s> <s xml:id="echoid-s1861" xml:space="preserve">Accedit ad hoc, quòd cum <lb/>ignis, & </s> <s xml:id="echoid-s1862" xml:space="preserve">aqua, ſimiliter aer, & </s> <s xml:id="echoid-s1863" xml:space="preserve">terra, ſint contraria, quia prorſus contrarias obti-<lb/>nent qualitates, immediate poſita eſſe nequeunt; </s> <s xml:id="echoid-s1864" xml:space="preserve">Idcirco natura ſolertiſſima <lb/>media elementa interpoſuit, quæ in qualitatibus cum utroque contrariorum <lb/>cõmunicant, aerem uidelicet inter ignem & </s> <s xml:id="echoid-s1865" xml:space="preserve">aquam; </s> <s xml:id="echoid-s1866" xml:space="preserve">aquam vero inter terram <lb/>& </s> <s xml:id="echoid-s1867" xml:space="preserve">aerem; </s> <s xml:id="echoid-s1868" xml:space="preserve">Atque hac ratione ſymbolizantia inter ſe exiſtunt elementa. </s> <s xml:id="echoid-s1869" xml:space="preserve">Quòd <lb/>ſi quis petat, cur potius aqua ſit terram immediate ſecuta, & </s> <s xml:id="echoid-s1870" xml:space="preserve">non potius ignis; <lb/></s> <s xml:id="echoid-s1871" xml:space="preserve">deinde aer, & </s> <s xml:id="echoid-s1872" xml:space="preserve">poſtremo aqua, cum hoc etiam ordine ſeruentur dictæ conueniẽ <lb/>tiæ elementorum in qualitatibus, quoniam ſemper media elementa contrarijs <lb/>ſunt interpoſita: </s> <s xml:id="echoid-s1873" xml:space="preserve">Reſpondendum eſt, duplici id ratione eſſe factum. </s> <s xml:id="echoid-s1874" xml:space="preserve">Primo qui-<lb/>dem, quoniam cum uideamus terram omnium grauiſſimam infimum poſſediſſe <lb/>locum, naturalis ratio exigere uidetur, vt ignis omnium leuiſſimus ſupremum <lb/>occupet locum: </s> <s xml:id="echoid-s1875" xml:space="preserve">quare non immediate cum ſubſequiterram decebat: </s> <s xml:id="echoid-s1876" xml:space="preserve">Secundo <lb/>vero, quoniam cum aqua ſit labilis admodum, & </s> <s xml:id="echoid-s1877" xml:space="preserve">fluxibilis, non poteſt conſiſte-<lb/>re, niſi duro alicui corpori innitatur, qualis eſt terra: </s> <s xml:id="echoid-s1878" xml:space="preserve">Iure igitur optimo aqua <lb/>ſupra terram immediate eſt collocata.</s> <s xml:id="echoid-s1879" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1880" xml:space="preserve"><emph style="sc">Tertio</emph> ex ſenſu atque experimento. </s> <s xml:id="echoid-s1881" xml:space="preserve">Videmus namque quotidie ignẽ <lb/> <anchor type="note" xlink:label="note-073-01a" xlink:href="note-073-01"/> ſupra terram, aquam, & </s> <s xml:id="echoid-s1882" xml:space="preserve">aerem ferri naturaliter, cum ſemper pyramidem conſti <lb/>tuat eius figura; </s> <s xml:id="echoid-s1883" xml:space="preserve">Quare locus eius naturalis ſupra omnia hæc eſſe debet. </s> <s xml:id="echoid-s1884" xml:space="preserve">Vi-<lb/>demus etiam aerem naturaliter ſupra terram, & </s> <s xml:id="echoid-s1885" xml:space="preserve">aquam aſcendere, ut pater in <lb/>terræ motu. </s> <s xml:id="echoid-s1886" xml:space="preserve">Fit enim terræ motus ob vehementiam aeris incluſi in uiſceribus <lb/>terræ, conantisq́ue ſupra terram, & </s> <s xml:id="echoid-s1887" xml:space="preserve">aquam in ſuum locum aſcendere. </s> <s xml:id="echoid-s1888" xml:space="preserve">Hoc <lb/>etiam conſtat in ampullis aeris in aqua ſurſum ſcaturientibus, ut uidere eſt in <lb/>paludibus, ſi quis baculum fundo infigat. </s> <s xml:id="echoid-s1889" xml:space="preserve">Ratio igitur exigit, ut aer ſupra <lb/>terram, & </s> <s xml:id="echoid-s1890" xml:space="preserve">aquam, ac ſub igne collocetur. </s> <s xml:id="echoid-s1891" xml:space="preserve">Videmus tandem aquam in aere poſi <lb/>tam deſcendere, & </s> <s xml:id="echoid-s1892" xml:space="preserve">terram in aqua collocatam deorſum quoque tendere. </s> <s xml:id="echoid-s1893" xml:space="preserve">Qua <lb/>propter non ſine ratione naturalis locus aquæ ſub aere, & </s> <s xml:id="echoid-s1894" xml:space="preserve">terræ ſub aqua eſſe <lb/>concludetur.</s> <s xml:id="echoid-s1895" xml:space="preserve"/> </p> <div xml:id="echoid-div135" type="float" level="2" n="8"> <note position="right" xlink:label="note-073-01" xlink:href="note-073-01a" xml:space="preserve">Ordo ele-<lb/>mentorum <lb/>colligitur <lb/>ab experiẽ-<lb/>tia.</note> </div> <p> <s xml:id="echoid-s1896" xml:space="preserve"><emph style="sc">Svnt</emph> tamen nonnulli, inter quoseſt Cardanus, qui negant ſuper aerem <lb/> <anchor type="note" xlink:label="note-073-02a" xlink:href="note-073-02"/> exiſtere ignem, eo quod minime à nobis cernatur: </s> <s xml:id="echoid-s1897" xml:space="preserve">immo, inquiunt, ſi ibi eſſet, <lb/>combureret hæc inferiora. </s> <s xml:id="echoid-s1898" xml:space="preserve">Itaque hi non concedunt ignem alium elementa-<lb/>rem, præter hunc inferiorem, quo nos utimur. </s> <s xml:id="echoid-s1899" xml:space="preserve">Verum id negotij philoſophis <lb/>relinquamus: </s> <s xml:id="echoid-s1900" xml:space="preserve">Hoc ſatis erit nunc noſſe, multo probabiliorem, & </s> <s xml:id="echoid-s1901" xml:space="preserve">magis commu-<lb/>nem eſſe ſententiam eorum, qui cum Ariſtotele ignem ſub concauo Lunæ, tan-<lb/>quam in ſuo loco naturali, ſtaruunt: </s> <s xml:id="echoid-s1902" xml:space="preserve">Quod autem non cernatur, prouenit ex <lb/>nimia eius raritate; </s> <s xml:id="echoid-s1903" xml:space="preserve">quoniam enim admodum purus eſt, & </s> <s xml:id="echoid-s1904" xml:space="preserve">in materia rariori, <lb/>quàm aer, ideo conſpici non poteſt; </s> <s xml:id="echoid-s1905" xml:space="preserve">immo aer ipſe, qui denſior eſt, uideri mini <lb/>me poteſt: </s> <s xml:id="echoid-s1906" xml:space="preserve">Quòd uero hæc inferiora non comburat, ex eadem raritate accidit: <lb/></s> <s xml:id="echoid-s1907" xml:space="preserve">Ignis enim in rariſſima materia exiſtens non poteſt habere tantam comburen-<lb/> <anchor type="note" xlink:label="note-073-03a" xlink:href="note-073-03"/> di vim; </s> <s xml:id="echoid-s1908" xml:space="preserve">fouet tamen mirum in modum ſuo calore hæcinferiora.</s> <s xml:id="echoid-s1909" xml:space="preserve"/> </p> <div xml:id="echoid-div136" type="float" level="2" n="9"> <note position="right" xlink:label="note-073-02" xlink:href="note-073-02a" xml:space="preserve">Cardanus <lb/>negat ele-<lb/>mentum <lb/>ignis ſub <lb/>cõcauo Lu <lb/>nę eſſe.</note> <note position="right" xlink:label="note-073-03" xlink:href="note-073-03a" xml:space="preserve">Aer in tres <lb/>regiones di <lb/>ſtribuitur à <lb/>philoſophis</note> </div> <p> <s xml:id="echoid-s1910" xml:space="preserve"><emph style="sc">De</emph> Figuris porro horum elementorum poſtea eſt ſermo futurus: </s> <s xml:id="echoid-s1911" xml:space="preserve">Nunc ve <lb/>r<unsure/>o id tantum annotatione dignum eſt, aerem à philoſophis in tresregiones di- <pb o="38" file="074" n="75" rhead="Comment. in I. Cap. Sphæræ"/> ſtribui. </s> <s xml:id="echoid-s1912" xml:space="preserve">In ſupremam ſcilicet, mediam, & </s> <s xml:id="echoid-s1913" xml:space="preserve">infimam. </s> <s xml:id="echoid-s1914" xml:space="preserve">Suprema, in qua cometas de-<lb/>ferri conſpicimus, propter motum eius continuum, quem habet à primo mo-<lb/>bili, & </s> <s xml:id="echoid-s1915" xml:space="preserve">ignis uicinitatem, & </s> <s xml:id="echoid-s1916" xml:space="preserve">ſolarium radiorum continuam emiſſionem per ean<unsure/> <lb/>dem, calida ſemper exiſtit. </s> <s xml:id="echoid-s1917" xml:space="preserve">Pari ratione infima nobis uicinior à multiplici ſo-<lb/>larium radiorum reſſexione caleſcit: </s> <s xml:id="echoid-s1918" xml:space="preserve">Media uero regio ob magnam ab igne <lb/>diſtantiam, & </s> <s xml:id="echoid-s1919" xml:space="preserve">ad quam radiorum ſolarium reflexiones peruenire nequeũt, ſem <lb/> <anchor type="figure" xlink:label="fig-074-01a" xlink:href="fig-074-01"/> per eſt frigida, ut oſtendunt impreſſiones Meteorologicæ ibidem generatæ; <lb/></s> <s xml:id="echoid-s1920" xml:space="preserve">quæ ſunt frigidæ, quales ſunt pluuiæ, nix, grando, &</s> <s xml:id="echoid-s1921" xml:space="preserve">c. </s> <s xml:id="echoid-s1922" xml:space="preserve">Cæterum, poſito toto <lb/>orbe aereo uniformi, ita ut tam ſecundum concauum, quàm ſecundum con-<lb/>uexum idem cum mundo centrum habeat, probabile ſatis uidetur, media ae-<lb/>ris regionem latiorem, & </s> <s xml:id="echoid-s1923" xml:space="preserve">denſiorem eſſe iuxta polos mundi, ob caloris debi-<lb/>litatem, quã maxima Solis abſentia ibi efficit, & </s> <s xml:id="echoid-s1924" xml:space="preserve">ob nimiũ frigus, quod ibi per-<lb/>petuo exiſtit: </s> <s xml:id="echoid-s1925" xml:space="preserve">Partes vero eiuſdẽ mediæ regionis medias inter vtrunque mundi <lb/>polum, ut ſub Aequinoctiali, ob caloris abundantiã, quam perpetua ſolis præ-<lb/>ſentia ibidem efficit, conſtringi; </s> <s xml:id="echoid-s1926" xml:space="preserve">& </s> <s xml:id="echoid-s1927" xml:space="preserve">uiceuerſa partes ſupremæ, & </s> <s xml:id="echoid-s1928" xml:space="preserve">infimæ regio-<lb/>nis circa mundi polos reſtringi, partes uero earundem medias inter utrum-<lb/>que polum dilatari. </s> <s xml:id="echoid-s1929" xml:space="preserve">Quod quidem clare ex figura appoſita elicere potes: </s> <s xml:id="echoid-s1930" xml:space="preserve">In <lb/>qua etiam ſitum, & </s> <s xml:id="echoid-s1931" xml:space="preserve">ordinem elementorum contueberis. </s> <s xml:id="echoid-s1932" xml:space="preserve">Immo fortaſſis neque <pb o="39" file="075" n="76" rhead="Ioan. de Sacro Boſco."/> Ignis uniformis eſt in denſitate, cum propter uelocitatem motus, quo ab ortu <lb/>in occaſum rapitur, facile aerem ſibi ſubiectum in ſe poſſit tranſmutare.</s> <s xml:id="echoid-s1933" xml:space="preserve"/> </p> <div xml:id="echoid-div137" type="float" level="2" n="10"> <figure xlink:label="fig-074-01" xlink:href="fig-074-01a"> <image file="074-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/074-01"/> </figure> </div> <p style="it"> <s xml:id="echoid-s1934" xml:space="preserve"><emph style="sc">Circa</emph> elementarem uero regionem ætherea regio lucida, ab omni <lb/> <anchor type="note" xlink:label="note-075-01a" xlink:href="note-075-01"/> uariatione ſua immutabili eſſentia immunis exiſtens, motu continuo circu <lb/>lariter incedit: </s> <s xml:id="echoid-s1935" xml:space="preserve">Et hæc à philoſophis quinta nuncupatur eſſentia.</s> <s xml:id="echoid-s1936" xml:space="preserve"/> </p> <div xml:id="echoid-div138" type="float" level="2" n="11"> <note position="right" xlink:label="note-075-01" xlink:href="note-075-01a" xml:space="preserve">Aethere@ <lb/>regio.</note> </div> </div> <div xml:id="echoid-div140" type="section" level="1" n="51"> <head xml:id="echoid-head55" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s1937" xml:space="preserve"><emph style="sc">Postqvam</emph> egit auctor de forma regionis elementaris, aggreditur di-<lb/>ſputationem de forma ætherea regionis. </s> <s xml:id="echoid-s1938" xml:space="preserve">Cuius quinque illuſtres proprieta-<lb/> <anchor type="note" xlink:label="note-075-02a" xlink:href="note-075-02"/> tes in principio affert, quibus à regione elementari ſeparatur, acdiſiungitur. <lb/></s> <s xml:id="echoid-s1939" xml:space="preserve">Prima eſt, quòd ſit circa elementarem regionem; </s> <s xml:id="echoid-s1940" xml:space="preserve">qua in re comparatur cum ele <lb/>mentari, tanquam continens cum contento, diciturq́ue locus totius elementa <lb/>ris regionis: </s> <s xml:id="echoid-s1941" xml:space="preserve">Omnis autem locus, quò ſuperior, eò etiam nobilior à philoſo-<lb/>phis creditur, corpusq́ue in eo exiſtens præſtantius; </s> <s xml:id="echoid-s1942" xml:space="preserve">quia à corruptibilibus hi-<lb/>ſce inferioribus magis remouetur, & </s> <s xml:id="echoid-s1943" xml:space="preserve">diuinis illis orbium motoribus optima, <lb/>& </s> <s xml:id="echoid-s1944" xml:space="preserve">feliciſſima ſemper uita fruentibus propinquius, atque uicinius exiſtit. </s> <s xml:id="echoid-s1945" xml:space="preserve">Secun <lb/>da proprietas eſt, quòd ſit lucida; </s> <s xml:id="echoid-s1946" xml:space="preserve">qua longe ſuperat elementarem regionem. </s> <s xml:id="echoid-s1947" xml:space="preserve"><lb/>Lux enim multo nobilior eſt proprietatibus elementorum; </s> <s xml:id="echoid-s1948" xml:space="preserve">Hæ namque acti-<lb/>uæ ſunt, & </s> <s xml:id="echoid-s1949" xml:space="preserve">paſſiuæ, inuicemq́ue contrariæ; </s> <s xml:id="echoid-s1950" xml:space="preserve">adeo ut mutua earum pugna res hæ <lb/>inferiores omnes ad interitum, & </s> <s xml:id="echoid-s1951" xml:space="preserve">corruptionem deducantur; </s> <s xml:id="echoid-s1952" xml:space="preserve">Lux uero omnis <lb/>contrarij expers cunctis hiſce inferioribus uitam, Eſſe, ac durationem influit. </s> <s xml:id="echoid-s1953" xml:space="preserve"><lb/>Accedit etiam, quòd lux eſt obiectum ſenſus nobiliſſimi, puta Viſus; </s> <s xml:id="echoid-s1954" xml:space="preserve">Et circa il <lb/>lam tota unaex diſciplinis Mathematicis, eaq́ue pulcherrima, nempe Perſpecti <lb/>ua, eſt occupata. </s> <s xml:id="echoid-s1955" xml:space="preserve">Tertia proprietas eſt, quòd ætherea regio careat omni motu <lb/>ſubſtantiam eius uariante. </s> <s xml:id="echoid-s1956" xml:space="preserve">Ætherea namque regio, ſiue cęleſtis, nec alterari, <lb/>nec augeri, diminuive, nec generari, corrumpive poteſt, ſecundum philoſophos; </s> <s xml:id="echoid-s1957" xml:space="preserve"><lb/>cuius oppoſitum ſupra de elementis aſſeruimus: </s> <s xml:id="echoid-s1958" xml:space="preserve">quoniã hæc in perpetua tranſ-<lb/>mutatione uerſantur. </s> <s xml:id="echoid-s1959" xml:space="preserve">Quarta proprietas eſt, quòd moueatur ætherea regio <lb/>perpetuo & </s> <s xml:id="echoid-s1960" xml:space="preserve">continuo motu circulari ſine ulla interruptione; </s> <s xml:id="echoid-s1961" xml:space="preserve">qui motus apud <lb/>philoſophos inter omnes alios primus eſt, ac nobiliſſimus; </s> <s xml:id="echoid-s1962" xml:space="preserve">eſtq́ue cauſa conti-<lb/>nuæ generationis, corruptionisq́ue in his inferioribus. </s> <s xml:id="echoid-s1963" xml:space="preserve">Motus autem elemento <lb/>rum rectus eſt ſuapte natura, qui cito finem facit. </s> <s xml:id="echoid-s1964" xml:space="preserve">Quinta, & </s> <s xml:id="echoid-s1965" xml:space="preserve">ultima proprietas <lb/> <anchor type="note" xlink:label="note-075-03a" xlink:href="note-075-03"/> eſt, ꝙ à philoſophis ætherea regio nuncupetur Quinta eſſentia. </s> <s xml:id="echoid-s1966" xml:space="preserve">Neq. </s> <s xml:id="echoid-s1967" xml:space="preserve">n. </s> <s xml:id="echoid-s1968" xml:space="preserve">cœlum, <lb/>ut uult Ariſtoteles, eſt elementũ, aut ex elementis compoſitũ, confectũve, ſed <lb/>eſt corpus alterius cuiuſdã immixtæ naturæ à quatuor elementis ualde ſemotę. <lb/></s> <s xml:id="echoid-s1969" xml:space="preserve">Vnde ut à quatuor elementis diſtingueretur, Quinta eſſentia eſt appellata.</s> <s xml:id="echoid-s1970" xml:space="preserve"/> </p> <div xml:id="echoid-div140" type="float" level="2" n="1"> <note position="right" xlink:label="note-075-02" xlink:href="note-075-02a" xml:space="preserve">Proprieta-<lb/>tes æthereę<unsure/> <lb/>regionis.</note> <note position="right" xlink:label="note-075-03" xlink:href="note-075-03a" xml:space="preserve">Quinta eſ-<lb/>ſentia.</note> </div> <note position="right" xml:space="preserve">Aethere a <lb/>regio cur <lb/>ſic dicta.</note> <p> <s xml:id="echoid-s1971" xml:space="preserve"><emph style="sc">Dicitvr</emph> autem Quinta hæc natura, hoc eſt, cęleſtis regio, Ætherea, <lb/>auctore Ariſtotele, ab {αἰ} {εὶ} id eſt, ſemper, & </s> <s xml:id="echoid-s1972" xml:space="preserve">θ έ ω, quod ſignificat uoluo, aut cur <lb/>ro; </s> <s xml:id="echoid-s1973" xml:space="preserve">quia cęleſtia corpora, quæ illam regionem conſtituunt, ſemper, ac perpe-<lb/>tuo uoluuntur, & </s> <s xml:id="echoid-s1974" xml:space="preserve">rotantur. </s> <s xml:id="echoid-s1975" xml:space="preserve">Quidem tamen uolunt, inter quos referuntur A-<lb/>naxagoras, & </s> <s xml:id="echoid-s1976" xml:space="preserve">Cicero, dici Aethereã, ab {αἴ} θ ω hoc eſt, flagro, fulgeo; </s> <s xml:id="echoid-s1977" xml:space="preserve">Eſt etenim <lb/>ætherea regio lucida ſemper, ac fulgida.</s> <s xml:id="echoid-s1978" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s1979" xml:space="preserve"><emph style="sc">Cvivs</emph> nouem ſunt ſphęrę, ſicut in proximo pertractatum eſt. </s> <s xml:id="echoid-s1980" xml:space="preserve">Sci-<lb/> <anchor type="note" xlink:label="note-075-05a" xlink:href="note-075-05"/> licet Lunę, Mercurij, Veneris, Solis, Martis, Iouis, Saturni, Stellarum <pb o="40" file="076" n="77" rhead="Comment. in I. Cap. Sphæræ"/> fixarum, & </s> <s xml:id="echoid-s1981" xml:space="preserve">cęli ultimi. </s> <s xml:id="echoid-s1982" xml:space="preserve">Iſtarum autem ſphærarum quælibet ſuperior in-<lb/>feriorem ſphærice circund at. </s> <s xml:id="echoid-s1983" xml:space="preserve">Quarum quidem duo ſunt motus; </s> <s xml:id="echoid-s1984" xml:space="preserve">unus eſt cœ <lb/>li ultimi ſuper duas axis extremitates, ſcilicet polum arcticum, & </s> <s xml:id="echoid-s1985" xml:space="preserve">antar-<lb/> <anchor type="note" xlink:label="note-076-01a" xlink:href="note-076-01"/> cticum, ab oriente per occidentem iterum rediens in orientem, quem Ae-<lb/>quinoctialis circulus per medium diuidit. </s> <s xml:id="echoid-s1986" xml:space="preserve">Eſt etiam alius inferiorum ſphæ-<lb/>rarum motus per obliquum huic oppoſitus ſuper polos ſuos diſtantes à pri-<lb/>mis 23. </s> <s xml:id="echoid-s1987" xml:space="preserve">gradibus, & </s> <s xml:id="echoid-s1988" xml:space="preserve">33. </s> <s xml:id="echoid-s1989" xml:space="preserve">minutis.</s> <s xml:id="echoid-s1990" xml:space="preserve"/> </p> <div xml:id="echoid-div141" type="float" level="2" n="2"> <note position="right" xlink:label="note-075-05" xlink:href="note-075-05a" xml:space="preserve">Ordo ſphæ-<lb/>rarum cæ-<lb/>leſtium.</note> <note position="left" xlink:label="note-076-01" xlink:href="note-076-01a" xml:space="preserve">Sphærarum <lb/>cæleſtium <lb/>duo ſunt <lb/>motus.</note> </div> </div> <div xml:id="echoid-div143" type="section" level="1" n="52"> <head xml:id="echoid-head56" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s1991" xml:space="preserve"><emph style="sc">Repetit</emph> diuiſionem æthereæ regionis, qua paulo ante ſphæram mun-<lb/>di ſecundum ſubſtantiam diuiſerat in nouem cœlos, quorum nomina, ordine-<lb/>q́ue hic recenſet.</s> <s xml:id="echoid-s1992" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1993" xml:space="preserve"><emph style="sc">Moventvr</emph> autem, ait, omnes ſphæræ cęleſtes duobus præcipuis mo-<lb/>tibus, quorum primus cœlo ultimo, ſeu primo mobili attribuitur, qui fit ſuper <lb/>duos mundi polos, arcticum ſcilicet, & </s> <s xml:id="echoid-s1994" xml:space="preserve">antarcticum, ab oriente in occidentem <lb/> <anchor type="note" xlink:label="note-076-02a" xlink:href="note-076-02"/> iterum ad orientem rediens. </s> <s xml:id="echoid-s1995" xml:space="preserve">Illud autem cœlum dicitur moueri ab oriente in <lb/>occidentem, quod ab oriente uerſus meridiem, hoc eſt, verſus eam partem Me <lb/>ridiani circuli, quæ ſupra Horizontem extat, in occidentem tendit, & </s> <s xml:id="echoid-s1996" xml:space="preserve">rurſus ab <lb/>occidente uerſus mediam noctem, id eſt, uerſus eam partem circuli Meridiani, <lb/>quæ ſub Horizonte latet, in orientem reuoluitur. </s> <s xml:id="echoid-s1997" xml:space="preserve">Cœlum autem illud ab occi <lb/>dente in orientem moueri dicitur, quod ab occidente uerſus meridiem in o-<lb/>rientem tendit, & </s> <s xml:id="echoid-s1998" xml:space="preserve">rurſus ab oriente uerſus mediam noctem in occidentem re-<lb/>labitur. </s> <s xml:id="echoid-s1999" xml:space="preserve">Quod diligenter notandum eſt, ut facile motus ab oriente in occiden-<lb/>tem à motu ab occidente in orientem diſcernatur: </s> <s xml:id="echoid-s2000" xml:space="preserve">quo niam prior ſub terra etiã <lb/>fit ab occidente in orientem, & </s> <s xml:id="echoid-s2001" xml:space="preserve">poſterior ab oriente in occidentem; </s> <s xml:id="echoid-s2002" xml:space="preserve">& </s> <s xml:id="echoid-s2003" xml:space="preserve">tamen <lb/>prior dicitur ab ortu in occaſum, ac poſterior ab occaſu in ortum: </s> <s xml:id="echoid-s2004" xml:space="preserve">quia ille ſu-<lb/>pra terram fit ab ortu in occaſum, hic uero ab occaſu in ortum. </s> <s xml:id="echoid-s2005" xml:space="preserve">Hunc aũt motũ <lb/>ab oriente in occidentem Aequinoctialis circulus, ait auctor, per medium diui <lb/>dit: </s> <s xml:id="echoid-s2006" xml:space="preserve">Nam cum motus diuidatur ad diuiſionem mobilis, vt habetur 6. </s> <s xml:id="echoid-s2007" xml:space="preserve">Phyſ. </s> <s xml:id="echoid-s2008" xml:space="preserve">Pri <lb/>mum autem mobile à circulo Aequinoctiali diuidatur in duas partes æquales, <lb/>uti ſupra diximus, neceſſe eſt, ut idem circulus motum eiuſdem primi mobilis, <lb/>quod eſt ſecundum noſtrum auctorem nona ſphæra, quodq́ue fertur ſecundum <lb/>Aequinoctialem circulum, in duas æquales partes diſtribuat.</s> <s xml:id="echoid-s2009" xml:space="preserve"/> </p> <div xml:id="echoid-div143" type="float" level="2" n="1"> <note position="left" xlink:label="note-076-02" xlink:href="note-076-02a" xml:space="preserve">Qũo intelli <lb/>ga@ur, cœlũ <lb/>aliquod ab <lb/>ortu in oc-<lb/>caſum, & <lb/>ab occaſu <lb/>ã<unsure/>n ortum <lb/>moueri.</note> </div> <p> <s xml:id="echoid-s2010" xml:space="preserve"><emph style="sc">Alter</emph> uero motus inferioribus octo ſphæris conuenit duntaxat, & </s> <s xml:id="echoid-s2011" xml:space="preserve"><lb/>nulla ratione primo mobili, eſtq́ue illi priori motui oppoſitus: </s> <s xml:id="echoid-s2012" xml:space="preserve">Mouentur e-<lb/>nim octo inferiores cœli ab occidente per meridiem in orientem, & </s> <s xml:id="echoid-s2013" xml:space="preserve">hinc per <lb/>mediam noctem in occidentem iterum dilabuntur. </s> <s xml:id="echoid-s2014" xml:space="preserve">Fortaſſis autem uocauit <lb/>hunc motum ſecundum auctor noſter per obliquum, quia nimirum non fit ſu-<lb/>per polos prioris motus, ſed ſuper polos alios diſtantes, ut ait, à polis motus <lb/>prioris 23. </s> <s xml:id="echoid-s2015" xml:space="preserve">gradibus, & </s> <s xml:id="echoid-s2016" xml:space="preserve">33. </s> <s xml:id="echoid-s2017" xml:space="preserve">minutis: </s> <s xml:id="echoid-s2018" xml:space="preserve">quæ di<unsure/>ſtantia obſeruata eſt ab Almeone, <lb/>quæ nunc minor eſt, nempe grad. </s> <s xml:id="echoid-s2019" xml:space="preserve">23. </s> <s xml:id="echoid-s2020" xml:space="preserve">& </s> <s xml:id="echoid-s2021" xml:space="preserve">Min. </s> <s xml:id="echoid-s2022" xml:space="preserve">30. </s> <s xml:id="echoid-s2023" xml:space="preserve">ferme, ut in 2. </s> <s xml:id="echoid-s2024" xml:space="preserve">cap. </s> <s xml:id="echoid-s2025" xml:space="preserve">dicemus. <lb/></s> <s xml:id="echoid-s2026" xml:space="preserve">Cæterum quid ſit gradus, dictum eſt ſupra, cũ de Zodiaco circulo loqueremur: </s> <s xml:id="echoid-s2027" xml:space="preserve"><lb/>Minutum uero eſt ſexageſima pars unius gradus. </s> <s xml:id="echoid-s2028" xml:space="preserve">Diuidunt etenim Aſtronomi <lb/>quemuis gradum in 60. </s> <s xml:id="echoid-s2029" xml:space="preserve">partes æquales, quæ Minuta dicuntur, de qua diuiſio-<lb/>ne plura habebis in 2. </s> <s xml:id="echoid-s2030" xml:space="preserve">cap. </s> <s xml:id="echoid-s2031" xml:space="preserve">quando de Zodiaco circulo longiorem ſermonem <lb/>habebimus. </s> <s xml:id="echoid-s2032" xml:space="preserve">Vel certe obliquus dicitur poſterior iſte motus, quoniam uidelicet <pb o="41" file="077" n="78" rhead="Ioan. de Sacro Boſco."/> fit ſecundũ circulum Zodiacum, qui oblique ſecat, ut ſupra eſt dictum, Aequino <lb/>ctiale m circulum, ſecundum quem prior motus cõficitur. </s> <s xml:id="echoid-s2033" xml:space="preserve">Hinc enim fit, ut hic <lb/>motu s poſterior obliquus quodammodo ſit, ſi cum priori comparetur.</s> <s xml:id="echoid-s2034" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s2035" xml:space="preserve"><emph style="sc">Sed</emph> primus omnes alias ſphæras ſecum impetu ſuo rapit intra <lb/> <anchor type="note" xlink:label="note-077-01a" xlink:href="note-077-01"/> diem, & </s> <s xml:id="echoid-s2036" xml:space="preserve">noctem circa terram ſemel; </s> <s xml:id="echoid-s2037" xml:space="preserve">Illis tamen contra nitentibus: </s> <s xml:id="echoid-s2038" xml:space="preserve">ut <lb/>octaua ſphæra in centum annis gradu uno. </s> <s xml:id="echoid-s2039" xml:space="preserve">Hunc ſiquidem motum ſe-<lb/>cundum diuidit per medium Zodiacus, ſub quo quilibet ſeptem planeta-<lb/>rum ſphæram habet propriam, in qua defertur motu proprio contra cœli <lb/>ultimi motum, & </s> <s xml:id="echoid-s2040" xml:space="preserve">in diuerſis ſpacijs temporum ipſum perficit. </s> <s xml:id="echoid-s2041" xml:space="preserve">ut Satur-<lb/> <anchor type="note" xlink:label="note-077-02a" xlink:href="note-077-02"/> nus in 30. </s> <s xml:id="echoid-s2042" xml:space="preserve">annis: </s> <s xml:id="echoid-s2043" xml:space="preserve">Iuppiter in 12. </s> <s xml:id="echoid-s2044" xml:space="preserve">Mars in duobus; </s> <s xml:id="echoid-s2045" xml:space="preserve">Sol in 365. </s> <s xml:id="echoid-s2046" xml:space="preserve">diebus, & </s> <s xml:id="echoid-s2047" xml:space="preserve"><lb/>ſex horis ferè; </s> <s xml:id="echoid-s2048" xml:space="preserve">Venus & </s> <s xml:id="echoid-s2049" xml:space="preserve">Mercurius ſimiliter ferè cum Sole; </s> <s xml:id="echoid-s2050" xml:space="preserve">Luna uero <lb/>in 27. </s> <s xml:id="echoid-s2051" xml:space="preserve">diebus, & </s> <s xml:id="echoid-s2052" xml:space="preserve">octo horis.</s> <s xml:id="echoid-s2053" xml:space="preserve"/> </p> <div xml:id="echoid-div144" type="float" level="2" n="2"> <note position="right" xlink:label="note-077-01" xlink:href="note-077-01a" xml:space="preserve">Cõparatio <lb/>duorũ mo-<lb/>tuũ ſphæra <lb/>rum cœle-<lb/>ſtium inter <lb/>ſe.</note> <note position="right" xlink:label="note-077-02" xlink:href="note-077-02a" xml:space="preserve">Periodimo <lb/>tuum Pla-<lb/>netarũ ab <lb/>occaſu in <lb/>orum.</note> </div> </div> <div xml:id="echoid-div146" type="section" level="1" n="53"> <head xml:id="echoid-head57" xml:space="preserve">COMMENTARIVS,</head> <p> <s xml:id="echoid-s2054" xml:space="preserve"><emph style="sc">Comparat</emph> hoc loco prædictos duos motus inter ſe, aſſignans <lb/>quoque tempora, ſeu peridos, quibus tales motus abſoluuntur. </s> <s xml:id="echoid-s2055" xml:space="preserve">Inquit igitur, <lb/>Primum motum, ſeu primum mobile, quod ſecundum ipſum eſt nonum cœlũ<unsure/>, <lb/>omnes alias ſphæras inferiores ſecũ impetu ſuo rapere intra diem & </s> <s xml:id="echoid-s2056" xml:space="preserve">noctem, <lb/>id eſt, intra ſpacium 24. </s> <s xml:id="echoid-s2057" xml:space="preserve">horarum, circa terram ſemel. </s> <s xml:id="echoid-s2058" xml:space="preserve">Vnde talis motus non <lb/>ſolum ab Aſtrologis, & </s> <s xml:id="echoid-s2059" xml:space="preserve">philoſophis, uerum etiam à vulgo Diurnus appellari <lb/>ſolet, quia uidelicet completur in die naturali, qui complectitur 24. </s> <s xml:id="echoid-s2060" xml:space="preserve">horas, ut <lb/> <anchor type="note" xlink:label="note-077-03a" xlink:href="note-077-03"/> copioſius in 3. </s> <s xml:id="echoid-s2061" xml:space="preserve">cap. </s> <s xml:id="echoid-s2062" xml:space="preserve">explanabitur.</s> <s xml:id="echoid-s2063" xml:space="preserve"/> </p> <div xml:id="echoid-div146" type="float" level="2" n="1"> <note position="right" xlink:label="note-077-03" xlink:href="note-077-03a" xml:space="preserve">Motus diur <lb/>nus.</note> </div> <p> <s xml:id="echoid-s2064" xml:space="preserve"><emph style="sc">Deinde</emph> aſſerit, Inferiores ſphęras omnes, quamuis, uti dictum eſt mo-<lb/>do, primo illo motu rapiantur ab oriente in occidentem, contra niti, hoc eſt, <lb/>in contrariam partem tendere, nempe ab occidente in orientem, diuerſis ta-<lb/>men temporibus. </s> <s xml:id="echoid-s2065" xml:space="preserve">Nam, ut ait, octaua ſphæra, ſeu cœlum ſtellatum in 100. </s> <s xml:id="echoid-s2066" xml:space="preserve">an-<lb/>nis unum gradum abſoluit ſuo motu; </s> <s xml:id="echoid-s2067" xml:space="preserve">quod quidem ex ſententia Ptolemæi di-<lb/>ctum eſt: </s> <s xml:id="echoid-s2068" xml:space="preserve">Ex quo efficitur, ut totus hic motus ſiniatur in ſpacio 36000. </s> <s xml:id="echoid-s2069" xml:space="preserve">anno-<lb/>rum: </s> <s xml:id="echoid-s2070" xml:space="preserve">Quem quidem motum Zodiacus circulus per medium diuidit, ſicut Ae-<lb/>quinoctialis illum primum. </s> <s xml:id="echoid-s2071" xml:space="preserve">Nam quemadmodum primus motus ſuper polos <lb/>mundi, & </s> <s xml:id="echoid-s2072" xml:space="preserve">per Aequinoctialem circulum efficitur, ita etiam ſecundus motus <lb/>ſuper polos Zodiaci, & </s> <s xml:id="echoid-s2073" xml:space="preserve">ſecundum Zodiacum circulum fieri ab Aſtronomis de-<lb/>prehenſus eſt.</s> <s xml:id="echoid-s2074" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2075" xml:space="preserve"><emph style="sc">Sve</emph> hoc poſtea Zodiaco quilibet planeta, ait, in ſua propria ſphæra defer-<lb/>tur proprio motu contra cœli ultimi motum, puta ab occidente in orientem <lb/>Quod non ita intelligas, quaſi ipſi planetæ per ſeſe ſub Zodiaco moueantur, <lb/>ſed quod cœli ipſi ſuper polos Zodiaci moueantur, atque hac ratione ſecum de <lb/>ferant planetas ſemper ſub Zodiaco exiſtentes; </s> <s xml:id="echoid-s2076" xml:space="preserve">& </s> <s xml:id="echoid-s2077" xml:space="preserve">hoc in diuerſis temporibus, <lb/>ut perſpicue ipſe exponit, & </s> <s xml:id="echoid-s2078" xml:space="preserve">nos uberibus paulo infra exponemus.</s> <s xml:id="echoid-s2079" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2080" xml:space="preserve"><emph style="sc">Qva</emph> in re licet hanc cęleſtium motuum harmoniam contemplari, ut quo <lb/> <anchor type="note" xlink:label="note-077-04a" xlink:href="note-077-04"/> ſphæra aliqua propinquior fuerit primo mobili, ſeu primo illi motui rapidiſſi <lb/>mo, eo minus ei contra nitatur, tardiuſque proprio ſuo motu ab occidente in <lb/>orientem feratur: </s> <s xml:id="echoid-s2081" xml:space="preserve">quo uero remotior, eo magis contra nitatur, uelociuſque <lb/>ſuũ motum abſoluat, quamuis nulla certa ſeruetur proportio in hac tardita <pb o="42" file="078" n="79" rhead="Comment. in I. Cap. Sphæræ"/> te, ac uelocitate, ut perſpicuum eſt ex peridos omnium motuum, quas auctor <lb/>retulit. </s> <s xml:id="echoid-s2082" xml:space="preserve">Vnde inter omnes octo ſphæras inferiores ſphæra ſtellarum fixarum, <lb/>quoniam propinquiſſima eſt primo mobili, tradiſſime ſuum curſum perficit: </s> <s xml:id="echoid-s2083" xml:space="preserve">In <lb/>ter ſeptem uero planetas, quia Saturnus eſt ſupremus, etiã proprio motu tar-<lb/>dius, quàm cæteri, incedit: </s> <s xml:id="echoid-s2084" xml:space="preserve">Luna denique, quoniam maximè à primo mobili re <lb/>cedit, celerrime ſuum motum abſoluit.</s> <s xml:id="echoid-s2085" xml:space="preserve"/> </p> <div xml:id="echoid-div147" type="float" level="2" n="2"> <note position="right" xlink:label="note-077-04" xlink:href="note-077-04a" xml:space="preserve">Harmonia <lb/>cœ@eſtium <lb/>motuum.</note> </div> <p> <s xml:id="echoid-s2086" xml:space="preserve"><emph style="sc">Sed</emph> quoniam auctor locutus eſt hic de numero orbium cœleſtium, motu <lb/>& </s> <s xml:id="echoid-s2087" xml:space="preserve">ordine eorundem, operæpretium me facturũ arbitror, ſi paulo uberius expli <lb/>cem, quotnam ſint cœli, & </s> <s xml:id="echoid-s2088" xml:space="preserve">quo artificio, induſtriaque eorũ numerus ab Aſtro-<lb/>nomis ſit repertus: </s> <s xml:id="echoid-s2089" xml:space="preserve">Deinde quot motibus moueantur, & </s> <s xml:id="echoid-s2090" xml:space="preserve">qua ratione ipſi mo-<lb/>tus ſint deprehenſi: </s> <s xml:id="echoid-s2091" xml:space="preserve">Poſtremo quiſnam ordo inter orbes cœleſtes ſtatuatur.</s> <s xml:id="echoid-s2092" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div149" type="section" level="1" n="54"> <head xml:id="echoid-head58" xml:space="preserve">DENVMERO ORBIVM CAELESTIVM.</head> <p> <s xml:id="echoid-s2093" xml:space="preserve"><emph style="sc">ANtiqvorvm</emph> philof<unsure/>ophorum nonnulli unicum duntaxat <lb/> <anchor type="note" xlink:label="note-078-01a" xlink:href="note-078-01"/> cœlum eſſe affirmabant, quos pauci admodum ex recentioribus <lb/>imitantur, hac unica perſuaſi ratione. </s> <s xml:id="echoid-s2094" xml:space="preserve">Omnis ſcientia noſtra ſe-<lb/>cundum philoſophorum dogmata, à ſenſu oritur. </s> <s xml:id="echoid-s2095" xml:space="preserve">Cũ igitur, quo-<lb/>tieſcun que ad cœlum oculos attollimus, non percipiamus uiſu <lb/>multitudinem cœlorum, (Sol enim, & </s> <s xml:id="echoid-s2096" xml:space="preserve">Luna, & </s> <s xml:id="echoid-s2097" xml:space="preserve">reliquæ omnes ſtellæ, in uno <lb/>eodemq́; </s> <s xml:id="echoid-s2098" xml:space="preserve">cœlo uidentur exiſtere) cœlumq́ue ipſum ſub nullum alium ſenſum, <lb/> <anchor type="note" xlink:label="note-078-02a" xlink:href="note-078-02"/> præter uiſum, cadere poſſit, non eſt, cur plures cœlos uno ponamus. </s> <s xml:id="echoid-s2099" xml:space="preserve">Verũ hæc <lb/>ſententia nulla ratione defendi poteſt. </s> <s xml:id="echoid-s2100" xml:space="preserve">Nullum enim corpus poteſt ſimul eodẽ <lb/>tẽpore moueri oppoſitis, & </s> <s xml:id="echoid-s2101" xml:space="preserve">contrarijs motibus; </s> <s xml:id="echoid-s2102" xml:space="preserve">Nam dum aſcendit, ſimul deſcẽ <lb/>dere nequit; </s> <s xml:id="echoid-s2103" xml:space="preserve">Et dum ex hoc loco in illum pergit, impoſſibile eſt, ut eodem tem <lb/>poris momento ex illo loco in hunc tendat, cum hæc inter ſe pugnent: </s> <s xml:id="echoid-s2104" xml:space="preserve">Atqui <lb/>in aſtris reperiuntur diuerſi motus, & </s> <s xml:id="echoid-s2105" xml:space="preserve">oppoſiti; </s> <s xml:id="echoid-s2106" xml:space="preserve">Cum ergo aſtra non per ſe mo-<lb/>ueãtur, ut piſces in aqua, uel aues in aere, ut Ariſtoteles vult cum philoſophis, <lb/>& </s> <s xml:id="echoid-s2107" xml:space="preserve">nos paulo poſt demonſtrabimus, ſed ad motum orbis, in quo ſunt, ſicuti no-<lb/>dus in tabula ad motum tabulę, uel clauus infixus in rota aliqua ad motũ rotæ; <lb/></s> <s xml:id="echoid-s2108" xml:space="preserve">oportebit concedere plures cęlos, quam unum, in quibus reponãtur aſtra illa, <lb/>quæ diuerſis lationibus ciẽtur. </s> <s xml:id="echoid-s2109" xml:space="preserve">Quòd uero diuerſi motus in aſtris reperiantur, <lb/>partim conſtat ex ijs, quæ auctor ſupra expoſuit de duplici motu corporũ cœle <lb/>ftium, ab oriente uidelicet in occidentẽ, & </s> <s xml:id="echoid-s2110" xml:space="preserve">contra, àb occidente in orientem; </s> <s xml:id="echoid-s2111" xml:space="preserve"><lb/>partim uero, & </s> <s xml:id="echoid-s2112" xml:space="preserve">multo dilucidius in ſequentibus eluceſcet, quando de cœlorũ <lb/>motibus diſputabimus, ubi ẽt oſtendemus, quanã induſtria ab Aſtronomis ſint <lb/>obſeruati. </s> <s xml:id="echoid-s2113" xml:space="preserve">Explẽodda igitur eſt, tanquã uana, & </s> <s xml:id="echoid-s2114" xml:space="preserve">inutilis hæc ſentẽtia. </s> <s xml:id="echoid-s2115" xml:space="preserve">Ad ratio <lb/>nem uero, quã auctores huius ſententiæ afferunt, reſpondendũ eſt, Verum qui-<lb/>dem eſſe, noſtram ſcientiã, dum in hac mortali uita ſumus, à ſenſibus oriri; </s> <s xml:id="echoid-s2116" xml:space="preserve">ſed <lb/>negandũ eſt, non plures cęlos ſenſu percipi. </s> <s xml:id="echoid-s2117" xml:space="preserve">Quamuis enim uiſu non cõprehen <lb/>damus cœlorũ multitudinem, immo ne unum quidem; </s> <s xml:id="echoid-s2118" xml:space="preserve">tamen uiſu percipimus <lb/>aſtra plurima, eaque diuerſis, & </s> <s xml:id="echoid-s2119" xml:space="preserve">oppoſitis motibus cõtinue cieri deprehẽdimus. </s> <s xml:id="echoid-s2120" xml:space="preserve"><lb/>Quare propter hãc motuum diuerſitatem plures orbes neceſſario ponẽdi ſunt.</s> <s xml:id="echoid-s2121" xml:space="preserve"/> </p> <div xml:id="echoid-div149" type="float" level="2" n="1"> <note position="left" xlink:label="note-078-01" xlink:href="note-078-01a" xml:space="preserve">Sententia <lb/>corum, qui <lb/>vnicum cę <lb/>lũ ponunt.</note> <note position="left" xlink:label="note-078-02" xlink:href="note-078-02a" xml:space="preserve">Cõfutatio <lb/>ſentẽtiæ eo <lb/>rũ qui uni-<lb/>cum cęlum <lb/>ponunt.</note> </div> <p> <s xml:id="echoid-s2122" xml:space="preserve"><emph style="sc">Alii</emph> igitur, ut fuere omnes fere Aegyptii, Chaldæi multum Aſtrologiæ <lb/>dediti, & </s> <s xml:id="echoid-s2123" xml:space="preserve">alii Aſtronomi ad tempora uſque Platonis, & </s> <s xml:id="echoid-s2124" xml:space="preserve">Ariſtotelis, octo ſaltẽ <lb/> <anchor type="note" xlink:label="note-078-03a" xlink:href="note-078-03"/> cœlos eſſe aſſeruerunt, propter octo diſtinctos motus, quos in ſideribus obſer-<lb/>uarunt. </s> <s xml:id="echoid-s2125" xml:space="preserve">Cum enim Solem, ac Lunam, nec non reliquas omnes ſtellas uiderent <lb/>continue moueri ab oriente uerſus occidentem, diuturna conſideratione, ac <pb o="43" file="079" n="80" rhead="Ioan. de Sacro Boſco."/> experimento didicerunt, ſtellas omnes non ſemper eſſe coniunctas, aut diſiun-<lb/>ctas eadem diſtantia, cum interdum iungerentur, interdum diſſociarentur, vt <lb/>luce clarius ſingulis menſibus in Sole, ac Luna experimur: </s> <s xml:id="echoid-s2126" xml:space="preserve">propterea quòd i@ <lb/>Noui lunijs coniuncti ſunt inuicem hi duo planetæ, in Pleniluniis autẽ inter <lb/>ſe oppoſiti per diametrum. </s> <s xml:id="echoid-s2127" xml:space="preserve">Qua ex re perſpicue collegerũt diuerſos motus in <lb/>aſtris. </s> <s xml:id="echoid-s2128" xml:space="preserve">Nam ſi unico duntaxat motu ueherentur, in eadem ſemper diſtantia, & </s> <s xml:id="echoid-s2129" xml:space="preserve"><lb/>propinquitate cernerentur. </s> <s xml:id="echoid-s2130" xml:space="preserve">Hinc plures cœlos eſſe coacti ſunt affirmare, ſaltẽ <lb/>tot, quot motus diuerſos in ſtellis deprehenderunt, quandoquidem ſtellæ non <lb/>per ſeſe, ſed una cum orbe, in quo ſunt infixæ, ceu nodus in tabula, circunfe-<lb/>runtur. </s> <s xml:id="echoid-s2131" xml:space="preserve">Quoniam uero diuturua obſeruatione cognouerunt, magnum nume-<lb/>rum ſtellarũ, quales ſunt omnes illæ, quas fixas uocamus, uniformiter ſemper <lb/>prog redi eadem diſtantia, & </s> <s xml:id="echoid-s2132" xml:space="preserve">eodem ſitu, atque ordine: </s> <s xml:id="echoid-s2133" xml:space="preserve">Exempli gratia, duæ po <lb/>ſtremæ ſtellæ plauſtri, quod in urſa maiore eſt, cum ſtella polari, quæ eſt in <lb/>extremitate caudæ urſæ minoris, & </s> <s xml:id="echoid-s2134" xml:space="preserve">ea ſtella, quæ in ſiniſtro pede Cephei exi-<lb/>ſtit; </s> <s xml:id="echoid-s2135" xml:space="preserve">conſtituunt ſemper lineam rectam: </s> <s xml:id="echoid-s2136" xml:space="preserve">Pari ratione ſtella illa lucida, quæ eſt <lb/>in lance Libræ occidentaliori, & </s> <s xml:id="echoid-s2137" xml:space="preserve">Arctophylax, ſeu Arcturus, & </s> <s xml:id="echoid-s2138" xml:space="preserve">ultima ſtella <lb/>caudæ vrſæ maioris, in recta etiam quaſi linea ſunt poſitæ ſemper: </s> <s xml:id="echoid-s2139" xml:space="preserve">Item Ca-<lb/>nis maior, canis minor, & </s> <s xml:id="echoid-s2140" xml:space="preserve">ſtella illa plauſtri, quæ propinquior eſt polo arcti-<lb/>co, ſecundum quoque rectam lineam ſunt collocate: </s> <s xml:id="echoid-s2141" xml:space="preserve">Item ſiniſter pes Orio-<lb/>nis, canis minor, & </s> <s xml:id="echoid-s2142" xml:space="preserve">cauda leonis efficiunt ſemper quaſi lineam rectam: </s> <s xml:id="echoid-s2143" xml:space="preserve">Idẽ ob-<lb/>ſeruatum eſt in oculo Tauri, humero ſiniſtro Orionis, & </s> <s xml:id="echoid-s2144" xml:space="preserve">cane maiore; </s> <s xml:id="echoid-s2145" xml:space="preserve">Item in <lb/>tribus ſtellis, quæ conſtituunt cingulum Orionis: </s> <s xml:id="echoid-s2146" xml:space="preserve">Rurſus in pede ſiniſtro Orio-<lb/>nis, oculo Tauri, & </s> <s xml:id="echoid-s2147" xml:space="preserve">lucida in capite Meduſæ. </s> <s xml:id="echoid-s2148" xml:space="preserve">Similiter ſpica uirginis, Arcto-<lb/>phylax, & </s> <s xml:id="echoid-s2149" xml:space="preserve">cauda leonis conſtituunt fere triangulum Iſoſcelem, cuius baſim ef <lb/>ficiunt Arctophylax, & </s> <s xml:id="echoid-s2150" xml:space="preserve">cauda leonis: </s> <s xml:id="echoid-s2151" xml:space="preserve">Item cor Leonis, canis minor, & </s> <s xml:id="echoid-s2152" xml:space="preserve">lucida <lb/>ftella Geminorum orientialior conſtituũt triangulum Iſoſcelem, cuius baſis <lb/>efficitur à cane min ore, & </s> <s xml:id="echoid-s2153" xml:space="preserve">ſtella illa Geminorum: </s> <s xml:id="echoid-s2154" xml:space="preserve">Idem denique in quam plu-<lb/>rimis alij ſtellis eſt obſeruatum; </s> <s xml:id="echoid-s2155" xml:space="preserve">De qua re lege Ptolemæum Dictione 7. </s> <s xml:id="echoid-s2156" xml:space="preserve">& </s> <s xml:id="echoid-s2157" xml:space="preserve">Epi <lb/>tomen Ioan. </s> <s xml:id="echoid-s2158" xml:space="preserve">Regiomontani in eadem Dictione, vbi complures obſeruationes <lb/>huiuſmodi in medium adducuntur; </s> <s xml:id="echoid-s2159" xml:space="preserve">Idcirco omnes illas in unico duntaxat or-<lb/>be cœleſti collocari affirmarunt, quẽ omnes Firmamentum appellarunt, ut ſu-<lb/>pra eſt dictum, ad cuius motum æquali ſemper remotione, ſitu ac diſtantia in-<lb/>ter ſeſe circunducerentur. </s> <s xml:id="echoid-s2160" xml:space="preserve">Obſeruarunt rurſus, inter omnia ſidera, ſeptem eſſe <lb/>ſtellas, quas erraticas dixere, quæ nec inter ſe eandem ſeruabant diſtantiã, nec <lb/>in eodem ſitu cum ſtellis fixis reperiebantur, concluſerunt eas nõ poſſe exiſte-<lb/>re in Firmamento, in quo ſunt ſtellæ fixæ; </s> <s xml:id="echoid-s2161" xml:space="preserve">ſic enim eandem diſtantiam ſemper <lb/>cum ipſis haberent, quemadmodum & </s> <s xml:id="echoid-s2162" xml:space="preserve">ipſæ inter ſe; </s> <s xml:id="echoid-s2163" xml:space="preserve">ſed nec omnes ſeptẽ ſimul <lb/>in aliquo alio cœlo eſſe repoſitas: </s> <s xml:id="echoid-s2164" xml:space="preserve">hac enim ratione eandẽ inter ſeſe ſeruarent <lb/>diſtantiam, ac ſitum, quamuis cum ſtellis fixis ordinem continuè uariarent. <lb/></s> <s xml:id="echoid-s2165" xml:space="preserve">Quamobrem firmiſſimo argumento collegerunt, ſub Firmamento eſſe ſeptem <lb/>alios orbes collocandos, quos Septem orbes ſeptem planetarum, ſeu ſtellarum <lb/>errantium nuncuparunt. </s> <s xml:id="echoid-s2166" xml:space="preserve">Et quoniam pręter hos octo motus omnino inter ſe <lb/>diſtinctos, & </s> <s xml:id="echoid-s2167" xml:space="preserve">diuerſos ſtellarum nullum alium cognouerunt, octonario cęlo-<lb/>rum numero contenti fuerunt, putaruntq́ue octauam ſphæram, id eſt, Firma-<lb/>mentum continens ſtelI<unsure/>as fixas eſſe primum mobile.</s> <s xml:id="echoid-s2168" xml:space="preserve"/> </p> <div xml:id="echoid-div150" type="float" level="2" n="2"> <note position="left" xlink:label="note-078-03" xlink:href="note-078-03a" xml:space="preserve">Sententia <lb/>corum, qui <lb/>octo co@los <lb/>ponunt.</note> </div> <note position="right" xml:space="preserve">Sententia <lb/>eorum, qui <lb/>no uem cæ-<lb/>los ponunt.</note> <p> <s xml:id="echoid-s2169" xml:space="preserve"><emph style="sc">CÆtervm</emph> poſt hos extiterunt alii Aſtronomi, inter quos fuere Ar <lb/>ſatilis, & </s> <s xml:id="echoid-s2170" xml:space="preserve">Timocharis, qui anno ante Chriſti Natiuitatem CCC. </s> <s xml:id="echoid-s2171" xml:space="preserve">XXX. </s> <s xml:id="echoid-s2172" xml:space="preserve">uel <lb/>circiter ſloruerunt, & </s> <s xml:id="echoid-s2173" xml:space="preserve">Alexandriæ ſiderum curſus obſeruantes deprehende- <pb o="44" file="080" n="81" rhead="Comment. in I. Cap. Sphæræ"/> runt, ſtellas Firmamenti, quod primum mobile antiquitas putauit, alio motu <lb/>tardiſſimo ab occidente in orientem ferri, & </s> <s xml:id="echoid-s2174" xml:space="preserve">non ſolum motu diurno ab ortu <lb/>in occaſum, ut antiqui exiſtimabant: </s> <s xml:id="echoid-s2175" xml:space="preserve">Sed quia nullas aliorum habebant obſer-<lb/>uatione, cum quibus ſuas conferre potuiſſent, effectum eſt, ut nihil fere certi <lb/>nobis de hoc motu reliquerint, ſed omnia ſub dubio, ob nimiam eius tardita-<lb/>tcm. </s> <s xml:id="echoid-s2176" xml:space="preserve">Hos tamen ſubſecutus eſt Abrachis, qui & </s> <s xml:id="echoid-s2177" xml:space="preserve">Hipparchus, 200. </s> <s xml:id="echoid-s2178" xml:space="preserve">fere annis <lb/>elapſis, qui ſuas obſeruationes cum illorum obſeruationibus conferens, mul-<lb/>to clarius, atque euidentius prædictum motum deprehendit. </s> <s xml:id="echoid-s2179" xml:space="preserve">Poſt annos dein-<lb/>de quaſi 170. </s> <s xml:id="echoid-s2180" xml:space="preserve">tranſactos Agrias in B@thynia, M@leus Geometra, qui & </s> <s xml:id="echoid-s2181" xml:space="preserve">Mene-<lb/>lus Romæ, & </s> <s xml:id="echoid-s2182" xml:space="preserve">poſt hos omnes Ptolemæus Aſtrologorum princeps anno Do-<lb/>mini C. </s> <s xml:id="echoid-s2183" xml:space="preserve">XXXI. </s> <s xml:id="echoid-s2184" xml:space="preserve">aut circiter, multo adhuc dilucidius iſtum motum ſtella-<lb/>rum fixarum ab occidente in orientem cognouerunt; </s> <s xml:id="echoid-s2185" xml:space="preserve">Qua autem id induſtria <lb/>deprehenderint, mox aperiemus, cum de cœlorum motibus egerimus. </s> <s xml:id="echoid-s2186" xml:space="preserve">Cum <lb/>igitur ſtellis fixis duplicem ineſſe motum nulli amplius ſit dubium, & </s> <s xml:id="echoid-s2187" xml:space="preserve">nullum <lb/>corpus ſimplex duobus poſſit ferri motibus, concludendum eſt, alterum ho-<lb/>rum proprium eſſe Firmamento, ad cuius motum ſtelle fixæ circumaguntur, <lb/>alterum uero, quem in eodem comperimus Firmamento, prouenire ab alio cæ <lb/>lo, quod nimirum ſupra Firmamentum collocandum erit, ut ſit nonum cœ-<lb/>lum, ac primum mobile. </s> <s xml:id="echoid-s2188" xml:space="preserve">Hac enim ratione mouebitur nonum cœlum ab ortu <lb/>in occaſum ſpatio 24. </s> <s xml:id="echoid-s2189" xml:space="preserve">horarum, ſecum que trahet ſphęram ſtellarum fixarum <lb/>eodem tempore, Ipſum uero Firmamentum proprio motu ab occaſu in or-<lb/>tum uoluetur, quamuis tardiſſime. </s> <s xml:id="echoid-s2190" xml:space="preserve">Ita igitur Aſtronomi nouem orbes cœle-<lb/>ſtes certiſſimis obſeruationibus collegerunt, propter motum diurnum ab or-<lb/>tu in occaſum, & </s> <s xml:id="echoid-s2191" xml:space="preserve">tardiſſimum illum ab occaſu in ortum, quorum uterque in <lb/>ſtellis fixis deprehenſus fuit. </s> <s xml:id="echoid-s2192" xml:space="preserve">Atque hunc numerum nouenarium orbium cœ-<lb/>leſtium ſequitur in hoc opuſculo loannes de Sacroboſco.</s> <s xml:id="echoid-s2193" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2194" xml:space="preserve"><emph style="sc">Post</emph> Ptolemæum denique annis interiectis M·<unsure/> C. </s> <s xml:id="echoid-s2195" xml:space="preserve">XL. </s> <s xml:id="echoid-s2196" xml:space="preserve">fere. </s> <s xml:id="echoid-s2197" xml:space="preserve">Tebith, <lb/> <anchor type="note" xlink:label="note-080-01a" xlink:href="note-080-01"/> Alphonſus Hiſpanorum rex anno Domini M. </s> <s xml:id="echoid-s2198" xml:space="preserve">CC. </s> <s xml:id="echoid-s2199" xml:space="preserve">L. </s> <s xml:id="echoid-s2200" xml:space="preserve">Georgius deinde Peur-<lb/>bachius, & </s> <s xml:id="echoid-s2201" xml:space="preserve">Ioannes de Regiomonte inſignes Aſtronomi, deprehenderunt qui-<lb/>dem in ſtellis fixis duos motus prædictos, ſed eas præterea obſeruarunt tertio <lb/>quodam motu, quẽ acceſſus, & </s> <s xml:id="echoid-s2202" xml:space="preserve">receſſus dixerunt, ut paulo poſt declarabitur, <lb/>agitari. </s> <s xml:id="echoid-s2203" xml:space="preserve">Quare cum corpus ſimplex vnico tantum motu ferri ſit aptum, ut uo-<lb/>lunt philoſophi, non poteſt nonum cœlum eſſe primum mobile, ſed ſupra ipsũ <lb/>erit decimum ſtatuendũ cœlũ, quod ſit primum mobile. </s> <s xml:id="echoid-s2204" xml:space="preserve">Ita enim fiet, ut deci-<lb/>mnm cœlũ motu diurno, quem habet proprium ab oriente in occidentem, ſecũ <lb/>trahat omnes cœlos inferiores, atque adeo F@rmamentum quoque cũ ſtellis fi <lb/>xis, ſpacio 24. </s> <s xml:id="echoid-s2205" xml:space="preserve">horarum: </s> <s xml:id="echoid-s2206" xml:space="preserve">Nonum deinde cœlum circumuehat ſuo proprio mo-<lb/>tu, quem obtinuit, ab occidente in orientem & </s> <s xml:id="echoid-s2207" xml:space="preserve">Firmamentum, & </s> <s xml:id="echoid-s2208" xml:space="preserve">reliquos om <lb/>nes cœlos infra ipſum: </s> <s xml:id="echoid-s2209" xml:space="preserve">Octauum denique cœlum, ſeu Firmamentum, in quo <lb/>ſtellę fixæ exiſtunt, moueatur tanquam proprio motu, acceſſu illo, & </s> <s xml:id="echoid-s2210" xml:space="preserve">receſſu, <lb/>quem præfati Aſtronomi repererunt. </s> <s xml:id="echoid-s2211" xml:space="preserve">Hic igitur denarius numerus orbium cę <lb/>leſtium in ſcholis Aſtronomorum celeberrimus hodie exiſtit; </s> <s xml:id="echoid-s2212" xml:space="preserve">quamuis non <lb/>deſint, qui, ne ab antiquis, maxime uero ab Ariſtotele diſcedere uideãtur, mor <lb/>dicus octo tantum eſſe cœlos defendere conantur. </s> <s xml:id="echoid-s2213" xml:space="preserve">Verum cum huiuſmodi au-<lb/>ctores nulla ratione defendere poſſint omnes motus, quos in cœleſtibus corpo <lb/>ribus uidemus, ut perſpicuum fiet, quando demotibus cœlorũ diſſeremus, me-<lb/>rito eorum ſententia ab Aſtronomis reijcitur. </s> <s xml:id="echoid-s2214" xml:space="preserve">Neque nos commouere debet <lb/>antiquorum, & </s> <s xml:id="echoid-s2215" xml:space="preserve">Ariſtotelis auctoritas: </s> <s xml:id="echoid-s2216" xml:space="preserve">Si enim alium motum pręter octo illos <pb o="45" file="081" n="82" rhead="Ioan. de Sacro Boſco."/> deprehendiſſent, haud dubie plure@ orbes admiſiſſent; </s> <s xml:id="echoid-s2217" xml:space="preserve">quandoquidem nulla <lb/>alia ratione octonarius numerus cœlorum, quàm ex numero motuũ, collectus <lb/>fuit ab ipſis. </s> <s xml:id="echoid-s2218" xml:space="preserve">Quare hac in parte magis Aſtrologis exercitariſſimis, qui decem <lb/>motus dictos obſeruauerunt, ſeptem nimirum interſe diſtinctos ſeptẽ planeta <lb/>rum, & </s> <s xml:id="echoid-s2219" xml:space="preserve">tres alios ſtellarum fixarum, eſt fides habenda, quàm Ariſtoteli, cum <lb/>ipſemet affirmet in 12. </s> <s xml:id="echoid-s2220" xml:space="preserve">Metaph. </s> <s xml:id="echoid-s2221" xml:space="preserve">Aſtr<unsure/>onomos in rebus Aſtronomicis eſſe con-<lb/>ſulendos. </s> <s xml:id="echoid-s2222" xml:space="preserve">Im mo uero hiijdem auctores, qui adeo addicti Ariſtoteli, & </s> <s xml:id="echoid-s2223" xml:space="preserve">antiquis <lb/>eſſe volunt, ut in numero orbium cæleſtium ab ipſis minime diſcedere uelint, <lb/>ab eiſdem in ordine eorundem orbium propter manifeſtiſſimas Aſtronomorũ <lb/>obſeruationes recedunt, nt poſtea perſpicuum fiet. </s> <s xml:id="echoid-s2224" xml:space="preserve">Quod ſi aliquis obijciat. <lb/></s> <s xml:id="echoid-s2225" xml:space="preserve">Omnis motus cęli, vt vult Ariſtoteles in 12. </s> <s xml:id="echoid-s2226" xml:space="preserve">Metaph. </s> <s xml:id="echoid-s2227" xml:space="preserve">cap. </s> <s xml:id="echoid-s2228" xml:space="preserve">8. </s> <s xml:id="echoid-s2229" xml:space="preserve">eſt propter mo-<lb/>tum aſtri; </s> <s xml:id="echoid-s2230" xml:space="preserve">cum igitur in nono cælo, ac decimo nullum exiſtat aſtrum, quoniam <lb/>ibi nullum apparet, fruſtra uidentur ſupra octo cælos, in quibus omnes ſtellæ <lb/>inhærent, duo alij mobiles nulla ſtella inſigniti collocari: </s> <s xml:id="echoid-s2231" xml:space="preserve">Reſpondendum eſt, <lb/>licet in cælo nono, & </s> <s xml:id="echoid-s2232" xml:space="preserve">decimo nullum exiftat aſtrum, motum tamen cuiuſque <lb/>illorum in motum aliquem aſtrorum, quæ in alijs exiſtunt cælis, re dundare. </s> <s xml:id="echoid-s2233" xml:space="preserve"><lb/>Nam ad motum decimi cæli, ſeu primi mobilis, mouentur omnia aſtra ab ortu <lb/>in occaſum; </s> <s xml:id="echoid-s2234" xml:space="preserve">Et ad motũ noni cæli eadẽ circumuehuntur aboccaſu in ortum, <lb/>quod quidem ſufficit, ut motus cæli ſit propter motum aſtri inſtitutus. </s> <s xml:id="echoid-s2235" xml:space="preserve">Dici-<lb/>quoque poteſt, Ariſtotelem locutum fuiſſe loco citato de motibus cælorum, <lb/>prout tuncco gniti fueraut, & </s> <s xml:id="echoid-s2236" xml:space="preserve">ſic motus cuinſlibet cæli ordinabatur in motum <lb/>aſtri in eo exiſtentis; </s> <s xml:id="echoid-s2237" xml:space="preserve">quod tamen non eſt neceſſarium, cum id nulla ratio ſua-<lb/>deat, & </s> <s xml:id="echoid-s2238" xml:space="preserve">experientia iam contrarium docuerit.</s> <s xml:id="echoid-s2239" xml:space="preserve"/> </p> <div xml:id="echoid-div151" type="float" level="2" n="3"> <note position="left" xlink:label="note-080-01" xlink:href="note-080-01a" xml:space="preserve">Sententia <lb/>eorum, qui <lb/>decẽ cęlos <lb/>ponunt.</note> </div> <p> <s xml:id="echoid-s2240" xml:space="preserve"><emph style="sc">Accedit</emph> etiam (ſi placet) auctoritas ſacrarum literarum, & </s> <s xml:id="echoid-s2241" xml:space="preserve">Theolo-<lb/>gorum ad confirmandum hunc numerum denarium cælorum, & </s> <s xml:id="echoid-s2242" xml:space="preserve">ad ponẽdum <lb/>faltem unum adhuc cælum ſupra Firmamentum. </s> <s xml:id="echoid-s2243" xml:space="preserve">Cum enim legamus in ſacra <lb/>Geneſi, Deum poſuiſſe Firmamẽtum diuidens aquas ab aquis. </s> <s xml:id="echoid-s2244" xml:space="preserve">Item in pſalmo <lb/>148. </s> <s xml:id="echoid-s2245" xml:space="preserve">Et aquæ omnes, quę ſuper cœlos ſunt, & </s> <s xml:id="echoid-s2246" xml:space="preserve">c. </s> <s xml:id="echoid-s2247" xml:space="preserve">nemo recto iudicio intelliget <lb/>eo loco aquas ſupra cælum octauum eſſeflux@biles, & </s> <s xml:id="echoid-s2248" xml:space="preserve">caducas, ſicut ſunt iſtæ <lb/>inferiores; </s> <s xml:id="echoid-s2249" xml:space="preserve">Sed nomine aquarum intelligendum erit, ut plurimi Theologorũ <lb/>explicant, Cęlum nonũ, uel portius aggregatũ ex nono, ac decimo cęlo; </s> <s xml:id="echoid-s2250" xml:space="preserve">quod <lb/>propter claritatem, & </s> <s xml:id="echoid-s2251" xml:space="preserve">perſpicuitatem, quam habet, cum ibi nullæ ſint partes <lb/>denſiores, ut in reliquis orbibus, cuiuſmodi ſunt aſtra, nomine aquarum opti-<lb/>mo iure appellari poteſt. </s> <s xml:id="echoid-s2252" xml:space="preserve">Quare a nonnullis Theologis dici ſolet cælum gla-<lb/>ciale, ſeu aqueum; </s> <s xml:id="echoid-s2253" xml:space="preserve">Et ab alijs Cryſtallinum.</s> <s xml:id="echoid-s2254" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">Cęlum Cry <lb/>ſtallinum. <lb/>Cęlum Em <lb/>pyreum.</note> <p> <s xml:id="echoid-s2255" xml:space="preserve"><emph style="sc">Svpra</emph> hos uero decem cœlos mobiles Theologi<unsure/>, ut Strabus, Venera-<lb/>bilis Beda, & </s> <s xml:id="echoid-s2256" xml:space="preserve">omnis iam Theologorum cœtus, aliud cœlum eſſe affirmant, im <lb/>mobile quidem, & </s> <s xml:id="echoid-s2257" xml:space="preserve">nulla præditum ſtella, ſed felicem angelorum, & </s> <s xml:id="echoid-s2258" xml:space="preserve">Beatorum <lb/>ſedem, ac patriam, quod uocant cælum Emphyreum, ab igne, quod mire ſit<unsure/> lu-<lb/>cidum, & </s> <s xml:id="echoid-s2259" xml:space="preserve">ingenti claritate præditum. </s> <s xml:id="echoid-s2260" xml:space="preserve">Hoc tamen cælum nullo modo ab Aſtro <lb/>nomis cogn@ſci poteſt, cum non moueatur.</s> <s xml:id="echoid-s2261" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2262" xml:space="preserve"><emph style="sc">Nihilominvs</emph> non deſunt, qui certis quibuſdam experientijs pro-<lb/>bare nituntur, ualde eſſe conueniens, undecimum illud cælum prorſus immo <lb/>bile ſupra omnes cælos exiſtere. </s> <s xml:id="echoid-s2263" xml:space="preserve">Nam, ut Plinius teſtatur lib. </s> <s xml:id="echoid-s2264" xml:space="preserve">8. </s> <s xml:id="echoid-s2265" xml:space="preserve">cap. </s> <s xml:id="echoid-s2266" xml:space="preserve">16. </s> <s xml:id="echoid-s2267" xml:space="preserve">In Eu-<lb/>ropa inter Acheloum, & </s> <s xml:id="echoid-s2268" xml:space="preserve">Neſtum amnes, procreantur leones lõge uiribus præ <lb/>ſtantiores ijs, quos Africa, aut Syria gignit. </s> <s xml:id="echoid-s2269" xml:space="preserve">Cum igitur hoc non fiat per totã <lb/>eam latitudinem, ſen tractum terræ ab oriente uerſus occidentẽ, in quo dicti <lb/>amnes ſunt ſiti, cauſa huius uarietatis erit, ut aſſerũt, influxus alicuius cæli in <pb o="46" file="082" n="83" rhead="Comment. in I. Cap. Sphæræ"/> moti ſuper illum tractum terræ exiſtentis. </s> <s xml:id="echoid-s2270" xml:space="preserve">Sienim cauſa eſſet influxus ſtell@-<lb/>rum, ſeu ſphærarum mobilium, deberent per totum illum terræ tractum ab <lb/>oriente uerſus occidentem, propter continuũ motum ſtellarum, tales leones <lb/>naſci, cuius oppoſitum uidemus. </s> <s xml:id="echoid-s2271" xml:space="preserve">Deinde quia in Hungaria ſub latitudine 47. <lb/></s> <s xml:id="echoid-s2272" xml:space="preserve">grad. </s> <s xml:id="echoid-s2273" xml:space="preserve">equi velociſſimi procreantur, & </s> <s xml:id="echoid-s2274" xml:space="preserve">validiſſimi, qui in alijs regionibus eiuſ-<lb/>dem latitudinis minime producũtur. </s> <s xml:id="echoid-s2275" xml:space="preserve">Denique in Mauritania innumeræ quaſi <lb/>ſimiæ generantur: </s> <s xml:id="echoid-s2276" xml:space="preserve">Et multa alia huiuſmodi experime nta adduci poſſent, vt à <lb/>vitibus, arboribus, fructibus, &</s> <s xml:id="echoid-s2277" xml:space="preserve">c. </s> <s xml:id="echoid-s2278" xml:space="preserve">qui omnes uarij effectus à cælo duntaxat <lb/>quieſcente produci uidentur. </s> <s xml:id="echoid-s2279" xml:space="preserve">Scio philoſophos reſpondere, hanc diuerſitatem <lb/>effectum in eodem climate pendere totam ex uaria diſpoſitione terræ:</s> <s xml:id="echoid-s2280" xml:space="preserve">ſed in-<lb/>ftant auctores prædicti, cum terra diſponatur varie à uarijs aſpectibus corpo-<lb/>rum ſuperiorum, non poterit reddi ſufficiens cauſa, cur in eodem climate ea-<lb/>dem non ſit diſpoſitio, quando quidem omnes partes eiuſdem climatis reſpe-<lb/>ctu cælorum mobilium eoſdem habeant aſpectus ſucceſſiue. </s> <s xml:id="echoid-s2281" xml:space="preserve">Verum enimue-<lb/>ro quidquid dicatur hacde re, hoc certum eſſe debet, ſine magna temeritate <lb/>non negari poſſe cælum Empyreum, quod eſt immobile, eo quod iam commu-<lb/>nis Theologorum ſchola illud admiſit.</s> <s xml:id="echoid-s2282" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2283" xml:space="preserve"><emph style="sc">Statvimvs</emph> ergo, in vniuerſum eſſe vndecim cælos, decem quidem, ſe-<lb/> <anchor type="note" xlink:label="note-082-01a" xlink:href="note-082-01"/> cundum Aſtronomos, mobiles, unum uero, ex ſententia Theologorum, immo-<lb/>bile prorſus. </s> <s xml:id="echoid-s2284" xml:space="preserve">Ratio autem, propter quam decẽ cælos mobiles admittimus, per-<lb/>ſpicua erit, quando pertractabimus, quanam induſtria inuenti fuerinr decẽ di-<lb/>ſtincti motus. </s> <s xml:id="echoid-s2285" xml:space="preserve">Quam ob rem nunc ad motus cælorum explicandos accedamus.</s> <s xml:id="echoid-s2286" xml:space="preserve"/> </p> <div xml:id="echoid-div152" type="float" level="2" n="4"> <note position="left" xlink:label="note-082-01" xlink:href="note-082-01a" xml:space="preserve">Vndecim <lb/>oęli ponen-<lb/>di funt.</note> </div> </div> <div xml:id="echoid-div154" type="section" level="1" n="55"> <head xml:id="echoid-head59" xml:space="preserve">DE MOTIBVS ORBIVM CÆLESTIVM.</head> <p> <s xml:id="echoid-s2287" xml:space="preserve"><emph style="sc">Avctores</emph>, qui unum duntaxat cælum eſſe credunt, omnem motum <lb/> <anchor type="note" xlink:label="note-082-02a" xlink:href="note-082-02"/> à cęleſti orbe excludunt, quamuis non eodem modo omnes. </s> <s xml:id="echoid-s2288" xml:space="preserve">Quidam enim nul <lb/>lum corpus cæleſte moueri aſſerunt, ſed in eodem loco ſemper permanere: </s> <s xml:id="echoid-s2289" xml:space="preserve">Vi <lb/>deri tamen nobis moueri ſtellas ab oriente in occidentem (hunc enim motũ <lb/>diurnũ, ſaltẽ apparentẽ, nulla ratione negare poſſunt, cum quotidie Solem, & </s> <s xml:id="echoid-s2290" xml:space="preserve"><lb/>reliqua ſidera oriri, & </s> <s xml:id="echoid-s2291" xml:space="preserve">occidere cernamus) propter motũ terrę, quem, ut aiunt, <lb/>habet ab occidẽte in orientẽ. </s> <s xml:id="echoid-s2292" xml:space="preserve">Nam quemadmodum ei, qui in flumine aliquo ce <lb/>leri nauis curſu defertur, uidẽtur arbores, domus, & </s> <s xml:id="echoid-s2293" xml:space="preserve">omnia in fluminis ripa po <lb/>ſita obuiam uenire, quaſi ipſe prorſus perſtaret immobilis, reliqua autem om-<lb/>nia mouerentur: </s> <s xml:id="echoid-s2294" xml:space="preserve">Ita etiam nobis in terra exiſtentibus cõtingit. </s> <s xml:id="echoid-s2295" xml:space="preserve">Quoniam enim <lb/>terra nobiſcum mouetur ab occaſu in ortum motu rapidiſſimo, uidemur nos <lb/>quieſcere, & </s> <s xml:id="echoid-s2296" xml:space="preserve">ſtellæ in contrariam partem, nempe ab ortu in occaſum, moueri, <lb/>cum tamen ipſę omnino ſint immobiles, nos autem moueamur, ut dictum eſt. <lb/></s> <s xml:id="echoid-s2297" xml:space="preserve">Verum hæc ſententia nullius prorſus eſt momenti, & </s> <s xml:id="echoid-s2298" xml:space="preserve">omnino ridicula exiſtit. </s> <s xml:id="echoid-s2299" xml:space="preserve"><lb/>Si enim uera eſſet, perpetuo inter aſtra idem ſitus, ordo, ac diſtantia cerneretur <lb/>quod eſt contra omnem experientiam: </s> <s xml:id="echoid-s2300" xml:space="preserve">Planetæ namque continuo inter ſe <lb/>uariant & </s> <s xml:id="echoid-s2301" xml:space="preserve">ſitum, & </s> <s xml:id="echoid-s2302" xml:space="preserve">ordinem, diſtantiamq́ue, ut luce clarius conſtat in Sole, <lb/>atque Luna, cum hi duo planetæ aliquando ſint quaſi coniuncti, aliquando ue <lb/> <anchor type="note" xlink:label="note-082-03a" xlink:href="note-082-03"/> ro per diametrum oppoſiti: </s> <s xml:id="echoid-s2303" xml:space="preserve">Idemq́ue de cæteris planetis iudicium habeto.</s> <s xml:id="echoid-s2304" xml:space="preserve"/> </p> <div xml:id="echoid-div154" type="float" level="2" n="1"> <note position="left" xlink:label="note-082-02" xlink:href="note-082-02a" xml:space="preserve">Sententia <lb/>corum, qui <lb/>omnẽ mo-<lb/>tũ à cœlis <lb/>abſtulerunt <lb/>eiuſq́ue cõ <lb/>ſutatio.</note> <note position="left" xlink:label="note-082-03" xlink:href="note-082-03a" xml:space="preserve">Sententia <lb/>@orum, qui <lb/>dicun@ coe-<lb/>lum quie-<lb/>ſcere, & ſtel <lb/>las per ſe <lb/>@@ue@i.</note> </div> <p> <s xml:id="echoid-s2305" xml:space="preserve"><emph style="sc">Qvidam</emph> vero aſſerunt, non ſolum cælum, uerum etiam terram quieſce <lb/>re, ſtellas uero per ſeſe moueri, ut aues in aere, ſeu piſces in mari, ab oriẽte in <lb/>occidentem Sed quoniam hac ratione non poſſent planetæ duobus ferri mo-<lb/>tibus, quod pugnat cum experiẽtia, cum nõ ſolum planetas uideamus ab ortu <pb o="47" file="083" n="84" rhead="Ioan. de Sacro Boſco."/> in occaſum moueri, ſed etiam ab occaſu in ortũ: </s> <s xml:id="echoid-s2306" xml:space="preserve">Idcirco alii cæIum moueri ab <lb/> <anchor type="note" xlink:label="note-083-01a" xlink:href="note-083-01"/> oriente in occidentem, ſecumq́ue ſtellas circumducere, ſingulas uero ſtellas, <lb/>fingulos etiam habere motus ab occidente in orientem, aſſirmant. </s> <s xml:id="echoid-s2307" xml:space="preserve">Quam ob <lb/>rem, inquiunt, efficitur, ut omnia aſtra eodem tempore uideantur motum diur <lb/>num abſolu ere; </s> <s xml:id="echoid-s2308" xml:space="preserve">In temporibus uero inæqualibus ea moueri ob occaſu in or-<lb/>@um depr ehendamus. </s> <s xml:id="echoid-s2309" xml:space="preserve">Cæterum neque hæc opinio admittenda eſt, quoniam, <lb/>ut in ſequentibus demonſtrabimus, impoſſibile eſt ſtellas per ſeſe moueri, ſi ue <lb/>ra ſunt ea, quę in motibus apparent, ſed neceſſe eſt, eas ad motum duntaxat or <lb/>bis, in quo ſunt, circumduci.</s> <s xml:id="echoid-s2310" xml:space="preserve"/> </p> <div xml:id="echoid-div155" type="float" level="2" n="2"> <note position="right" xlink:label="note-083-01" xlink:href="note-083-01a" xml:space="preserve">Sententia <lb/>eorum, qui <lb/>dicũt cęlũ <lb/>moueri ab <lb/>or@u in oc-<lb/>caſum, ſtel-<lb/>las uero per <lb/>ſe ab occa-<lb/>ſu in ortũ.</note> </div> <p> <s xml:id="echoid-s2311" xml:space="preserve"><emph style="sc">Neqve</emph> ueroij etiam, qui plures eſſe cælos exiſtimant, idem ſentiunt de <lb/> <anchor type="note" xlink:label="note-083-02a" xlink:href="note-083-02"/> motibus corporum cæleſtium. </s> <s xml:id="echoid-s2312" xml:space="preserve">Nam ut abijs, qui octo tantum eſſe credunt cæ-<lb/>@os, incipiamus: </s> <s xml:id="echoid-s2313" xml:space="preserve">Nonnulli arbitrantur, ſingulos orbes cæleſtes ſingulis ab occa-<lb/>ſu in ortum motibus cieri; </s> <s xml:id="echoid-s2314" xml:space="preserve">negare enim non poſſunt, diſtinctos eſſe motus 7. <lb/></s> <s xml:id="echoid-s2315" xml:space="preserve">planetarum & </s> <s xml:id="echoid-s2316" xml:space="preserve">inter ſeſe, & </s> <s xml:id="echoid-s2317" xml:space="preserve">facta quoque comparatione cum ſtellis fixis, cũ in <lb/>@erdum coniungantur planetæ inter ſe, & </s> <s xml:id="echoid-s2318" xml:space="preserve">cum ſtellis fixis, interdum uero diſſo <lb/>crentur ab eiſdem: </s> <s xml:id="echoid-s2319" xml:space="preserve">Motũ autem cælorum diurnum ab oriente in occidentem <lb/>omnino è medio tol@unt. </s> <s xml:id="echoid-s2320" xml:space="preserve">Neque enim fieri poteſt, (dicunt) ut unum idemq́ue <lb/>corpus motibus contrarijs, & </s> <s xml:id="echoid-s2321" xml:space="preserve">oppoſitis, cuiuſmodi ſunt motus ab oriente in oc <lb/>cidentem, & </s> <s xml:id="echoid-s2322" xml:space="preserve">motus ab occidente in orientem, ſimul poſſit eodem tempore mo <lb/>ueri. </s> <s xml:id="echoid-s2323" xml:space="preserve">At cum ſe uiderent cum experientia, & </s> <s xml:id="echoid-s2324" xml:space="preserve">ſenſu pugnare, (Videmus etenim <lb/>quotidie Solem, Lunam, ac reliquas ſtellas motu diurno ab oriente in occi-<lb/>dentem labi, cum modo oriantur ſupra Horizontem, modo ſub eodem deſcen <lb/>dant) commentati ſunt, apparere no bis cœlos cum aſtris moueri ab ortu in oc-<lb/>caſum, quoniam terra nobiſcum ab occaſu in ortum uelociori motu, quã Pla-<lb/>netæ, nempe ſpacio 24. </s> <s xml:id="echoid-s2325" xml:space="preserve">horarum, circumfertur. </s> <s xml:id="echoid-s2326" xml:space="preserve">Vnde nos quieſcere, ſtellas ve-<lb/>ro nobis obuiam procedere arbitramur, ueluti auctores primæ opinionis dice-<lb/>bant. </s> <s xml:id="echoid-s2327" xml:space="preserve">Sed neque ita de motibus cœleſtibus ſentiendum eſt, quoniam hac ratio-<lb/> <anchor type="note" xlink:label="note-083-03a" xlink:href="note-083-03"/> ne non omnes motus hactenus obſeruati defendi poſſunt, ut poſtea conſtabi@. <lb/></s> <s xml:id="echoid-s2328" xml:space="preserve">Huc accedit, minime terram tanta uelocitate ab occaſu in ortum ferri, ueluti <lb/>in ſequentibus etiam probabitur. </s> <s xml:id="echoid-s2329" xml:space="preserve">Adde quod hæc ſententia aſſumat, motum <lb/>cœlorum ab oriente in occidentem contrarium eſſe ei, quifit ab occidente in <lb/>orientem, quod falſum eſſe, mox explicabitur.</s> <s xml:id="echoid-s2330" xml:space="preserve"/> </p> <div xml:id="echoid-div156" type="float" level="2" n="3"> <note position="right" xlink:label="note-083-02" xlink:href="note-083-02a" xml:space="preserve">Prima ſen-<lb/>tentia de <lb/>motibus cę <lb/>lorũ, ſecũ-<lb/>dũ eos, qui <lb/>octo cęles <lb/>ſtatuu@t.</note> <note position="right" xlink:label="note-083-03" xlink:href="note-083-03a" xml:space="preserve">Confutatio <lb/>primæ ſen-<lb/>tentiæ.</note> </div> <p> <s xml:id="echoid-s2331" xml:space="preserve"><emph style="sc">Nonnvlli</emph> autem credentes quoque, prædictos duos motus inter <lb/> <anchor type="note" xlink:label="note-083-04a" xlink:href="note-083-04"/> ſe eſſe contrarios, aſſerunt, Cælos duntaxat moueri diurno motu ab oriente <lb/>in occidentem; </s> <s xml:id="echoid-s2332" xml:space="preserve">Immo hoc motu non ſolum orbes cœleſtes, uerum etiam om-<lb/>nia elementa moueri dicunt, quem quidem motum unica efficit intelligentia, <lb/>quàm animã mundi appellant; </s> <s xml:id="echoid-s2333" xml:space="preserve">Ita tamen, ut quò aliqua ſphæra animæ mundi <lb/>propinquior exiſtit, eò etiam uelocius abea moueatur; </s> <s xml:id="echoid-s2334" xml:space="preserve">& </s> <s xml:id="echoid-s2335" xml:space="preserve">quò remotior, eò <lb/>tardius: </s> <s xml:id="echoid-s2336" xml:space="preserve">quemadmodum in rotę alicuius motu cernimus. </s> <s xml:id="echoid-s2337" xml:space="preserve">Partes enim axi rotæ <lb/>propinquiores, ſeu centro ipſius, tardius mouentur; </s> <s xml:id="echoid-s2338" xml:space="preserve">partes uero eius circunfe-<lb/>rentiæ uiciniores, uelocius feruntur. </s> <s xml:id="echoid-s2339" xml:space="preserve">Vnde dicunt ſupremum cœlum uelociſſi <lb/>me omnium moueri, quoniã animæ mundi propinquiſſimum eſt; </s> <s xml:id="echoid-s2340" xml:space="preserve">terram autẽ <lb/>tardiſſime, adeo ut nõ percipiatur motus eius ob maximã tarditatẽ, quia lon-<lb/>giſſime ab anima mundi receſſit, & </s> <s xml:id="echoid-s2341" xml:space="preserve">propterea omnibus quieſcere uidetur, cum <lb/>tamen paulatim, & </s> <s xml:id="echoid-s2342" xml:space="preserve">quaſi inſenſibiliter ab oriente in occidentẽ rapiatur; </s> <s xml:id="echoid-s2343" xml:space="preserve">quod <lb/>hoc indicio perſuadere conantur. </s> <s xml:id="echoid-s2344" xml:space="preserve">Videmus, aiunt, terram in partibus occiden-<lb/>talibus continue, & </s> <s xml:id="echoid-s2345" xml:space="preserve">ſenſim ſub mare tendere, & </s> <s xml:id="echoid-s2346" xml:space="preserve">è cõtrario in partibus orienta-<lb/>@ous magis ac magis è mari emergere; </s> <s xml:id="echoid-s2347" xml:space="preserve">quod quidẽ euidẽter nobis demõſtrant <pb o="48" file="084" n="85" rhead="Comment. in I. Cap. Sphæræ"/> columnæ Herculis poſitæ in littore Oceani òccidentalis, & </s> <s xml:id="echoid-s2348" xml:space="preserve">columnæ eiuſdẽ <lb/>poſitæ in littore Oceani orientalis. </s> <s xml:id="echoid-s2349" xml:space="preserve">Illæ enim hac tempeſtate per multa millia <lb/>ria intra mare reperiuntur iuxta plagas occidentales; </s> <s xml:id="echoid-s2350" xml:space="preserve">Hæ vero cõtra per to-<lb/>tidem milliaria extra mare in partibus orientalibus conſpiciuntur. </s> <s xml:id="echoid-s2351" xml:space="preserve">Manifeſtũ <lb/>ergo ſignum eſt, terram paulatim ab oriente in occidentem ab anima illa mun <lb/>di deferri. </s> <s xml:id="echoid-s2352" xml:space="preserve">Quoniam vero præter hunc motum diurnum, planetæ moueri quo <lb/>que videntur ab occidente in orientem, quòd non ſemper ſint in eadẽ diſtan-<lb/>tia ad inuicem, neque ſub eiſdem ſemper exiſtant ſtellis fixis, ſed ab eis orientẽ <lb/>uerſus recedant, quod tamen ipſi negant; </s> <s xml:id="echoid-s2353" xml:space="preserve">Ideo cauſam eſſe hãc aſſerũt, cur ali-<lb/>qui cęli ab occidente in orientem ferri credantur, quamuis re ipſa ab oriente <lb/>tantũ in occidentẽ cieantur; </s> <s xml:id="echoid-s2354" xml:space="preserve">Quia nimirum ſphæræ inferiores, quo magis à ſu <lb/>premo cælo, & </s> <s xml:id="echoid-s2355" xml:space="preserve">ab anima illa mundi diſtant, eo minus, vt dictum eſt, efficaciter <lb/>mouentur; </s> <s xml:id="echoid-s2356" xml:space="preserve">qua de cauſa tard us circunferuntur, & </s> <s xml:id="echoid-s2357" xml:space="preserve">pedetentim uidentur retro-<lb/>cedere ab occidente in orientem. </s> <s xml:id="echoid-s2358" xml:space="preserve">Hinc quoque efficitur, ut Luna, quia inter <lb/>cæleſtes orbes maxime a ſupremo recedit, tardiſſime ab oriente in occidentẽ <lb/>moueatur, & </s> <s xml:id="echoid-s2359" xml:space="preserve">uelociſſime, nempe ſpacio vnius menſis, uideatur integrũ circui-<lb/>tum ab occidẽte in orientem peragere: </s> <s xml:id="echoid-s2360" xml:space="preserve">Reliquæ vero ſphæræ, quò ſuperiores, <lb/>eò quoque lentius appareant nobis ferri ab occaſu in ortũ. </s> <s xml:id="echoid-s2361" xml:space="preserve">Quæ omnia unico <lb/>hoc exemplo uolunt nobis ob oculos proponere. </s> <s xml:id="echoid-s2362" xml:space="preserve">Sint tres ordines homiuum <lb/>collaterales ſecundum lineas rectas diſpoſitorum, Incipiantq́ue ex eodẽ loco <lb/>ſimul ab oriente in occidentẽ progredi, hac tamen lege, vtij, qui in primo or-<lb/>dine reperiuntur, celerrimo greſſu incedant, tardius autem ij, qui in ſecũdo or <lb/>dine, & </s> <s xml:id="echoid-s2363" xml:space="preserve">lentiſſime ij, qui in tertio ordine exiſtunt. </s> <s xml:id="echoid-s2364" xml:space="preserve">Quo poſito, perſpicuum <lb/>eſt, Primum ordinẽ reliquos duos incitato illo curſu antecedere, magis tamẽ <lb/>tertium ordinẽ, quàm ſecundum. </s> <s xml:id="echoid-s2365" xml:space="preserve">Quare ſi quis procul dictos ordines intue-<lb/>retur, iudicaret ſecundum ordinem, & </s> <s xml:id="echoid-s2366" xml:space="preserve">tertiũ pederentim retrocedere, & </s> <s xml:id="echoid-s2367" xml:space="preserve">cita-<lb/>tiori motu tertium, quàm ſecundum; </s> <s xml:id="echoid-s2368" xml:space="preserve">cum tamẽ re ipſa ab oriente uerſus occi-<lb/>dentem, ceu primus ordo, duntaxat progrediantur. </s> <s xml:id="echoid-s2369" xml:space="preserve">Eadem igitur prorſus de <lb/>cauſa uidentur, aiunt, nobis planetæ ab occidente in orientem moueri. </s> <s xml:id="echoid-s2370" xml:space="preserve">Hanc <lb/>porro ſententiã eo libentius amplectuntur Alpetragius, & </s> <s xml:id="echoid-s2371" xml:space="preserve">Achilinus cum alijs <lb/>auctoribus, quòd nulla ratione imaginari queant vnũ, & </s> <s xml:id="echoid-s2372" xml:space="preserve">idem corpus cæleſte <lb/>duobus motibus ferri, nimirum ab oriente uerſus occidentem, & </s> <s xml:id="echoid-s2373" xml:space="preserve">rurſus ab oc-<lb/>cidente orientem uerſus; </s> <s xml:id="echoid-s2374" xml:space="preserve">Quoniam cum hi motus, ut aiunt, ſint contrarij, ne-<lb/>ceſſe eſt alterum eorum eſſe uiolentum, quod fieri nõ poteſt; </s> <s xml:id="echoid-s2375" xml:space="preserve">immo abſurdum <lb/>uidetur concedere uiolentiam in corporibus cęleſtibus; </s> <s xml:id="echoid-s2376" xml:space="preserve">tum quia nullum uio <lb/>lentum eſt perpetuum; </s> <s xml:id="echoid-s2377" xml:space="preserve">Motus autem cęli perpetuus eſt, ex Ariſtotelis ſenten-<lb/>tia; </s> <s xml:id="echoid-s2378" xml:space="preserve">tum etiam, quia omne uiolentum cõtinue magis, ac magis debilitatur; </s> <s xml:id="echoid-s2379" xml:space="preserve">Mo-<lb/>tus autem cæl@ſemper eadem celeritate abſque ulla defectione confici@ur. </s> <s xml:id="echoid-s2380" xml:space="preserve">Ac-<lb/>cedit etiã, aiunt, quod non eſt ponenda pluralitas motuũ abſque neceſſitate. <lb/></s> <s xml:id="echoid-s2381" xml:space="preserve">Cum igitur nulla nos heceſſitas cogat, ut fateamur planetas aboccidente in <lb/>orientem moueri; </s> <s xml:id="echoid-s2382" xml:space="preserve">quandoquidem obrationem iam dictã nobis ita moueri ui-<lb/>dentur, fruſtra & </s> <s xml:id="echoid-s2383" xml:space="preserve">temere inducitur hæc pluralitas motuũ ab Aſtronomis. </s> <s xml:id="echoid-s2384" xml:space="preserve">Ve-<lb/> <anchor type="note" xlink:label="note-084-01a" xlink:href="note-084-01"/> rum hæc ſententia uera eſſe nullo modo poteſt, cum non poſſit omnium, quæ <lb/>in motibus cęleſtibus apparent, reddere rationem. </s> <s xml:id="echoid-s2385" xml:space="preserve">Nam ſi orbes interiores nõ <lb/>haberent peculiares motus ab occidente in oriẽtem, ſed ſolum propter illam <lb/>quaſi repedationem, ſeu retardationem moueri ab occaſu in ortum exiſtima-<lb/>rentur, defectio illa inferiorum orbiũ per eandem lineam fieret, & </s> <s xml:id="echoid-s2386" xml:space="preserve">circa eoſdẽ <lb/>polos, puta per circulũ æquinoctialem, & </s> <s xml:id="echoid-s2387" xml:space="preserve">circa polos mundi, cum motus diur- <pb o="49" file="085" n="86" rhead="Ioan. de Sacro Boſco."/> @us rectà ſecundũ æquinoctialẽ circulum, & </s> <s xml:id="echoid-s2388" xml:space="preserve">ſuper mundi polos ab oriente <lb/>in occidentem tendat. </s> <s xml:id="echoid-s2389" xml:space="preserve">Ex quo effici deberet, ut omnes ſtellæ, & </s> <s xml:id="echoid-s2390" xml:space="preserve">planetæ mo <lb/>tu diurno eoſdẽ ſem per circulos parallelos citra, & </s> <s xml:id="echoid-s2391" xml:space="preserve">ultra æquinoctialem cõ-<lb/>tinue deſcriberent; </s> <s xml:id="echoid-s2392" xml:space="preserve">Stellæ autẽ, & </s> <s xml:id="echoid-s2393" xml:space="preserve">planetæ ſub æquinoctiali exiſtentes nun-<lb/>quã ab eo declinarent, ſed perpetuo ſub illo exiſterent; </s> <s xml:id="echoid-s2394" xml:space="preserve">Et quę ſunt citra vel <lb/>ultra ęquinoctialem, nunꝗ̃ magis uel minus accederent, vel recederent ab ip <lb/>ſo: </s> <s xml:id="echoid-s2395" xml:space="preserve">Quare neque Sol, neque Luna, ſicut neque<unsure/> ulla alia ſtella tam fixa, quàm <lb/>erratica, propius ad noſtri capitis uerticẽ appropinquaret, uel magis ab eo re <lb/>cederet uno tẽpore, quàm alio, quæ omnia apertiſſime cũ ſenſu, & </s> <s xml:id="echoid-s2396" xml:space="preserve">experien-<lb/>tia pugnãt. </s> <s xml:id="echoid-s2397" xml:space="preserve">Videmus enim Solem (ut interim alios planetas, ac ſtellas ſilẽtio <lb/>inuoluam) ipſi æquinoctiali circulo uarios parallelos circulos deſcribere, ut <lb/>in 3. </s> <s xml:id="echoid-s2398" xml:space="preserve">cap. </s> <s xml:id="echoid-s2399" xml:space="preserve">explicabit auctor, & </s> <s xml:id="echoid-s2400" xml:space="preserve">nõ ſemper eandem diſtantiã ad ęquinoctiali cir <lb/>culo obſeruare, cum bis in anno ſub ipſo reperiatur, & </s> <s xml:id="echoid-s2401" xml:space="preserve">modo ad auſtrum, mo <lb/>do ad ſeptentrionem ab eodem deflectat: </s> <s xml:id="echoid-s2402" xml:space="preserve">Vnde fit, ut in diuerſis punctis Hori <lb/>zontis, per anni circulum oriri, & </s> <s xml:id="echoid-s2403" xml:space="preserve">occidere cõſpiciatur. </s> <s xml:id="echoid-s2404" xml:space="preserve">Hinc etiam efficitur, <lb/>ut in æſtate exiſtẽs in principio Cancri proxime ad noſtrũ Zenith, ſeu punctũ <lb/>uerticale accedat; </s> <s xml:id="echoid-s2405" xml:space="preserve">In hyeme uero poſitus in principio C@pricorni ab eodẽ ma <lb/>xime recedat. </s> <s xml:id="echoid-s2406" xml:space="preserve">Et ſane mirum eſt, ſi omnes cæli moueantur tantũ ab oriente <lb/>in occidentẽ inferiores uero, quia tardius mouentur, repedent quodãmodo, <lb/>ſeu retardentur, ut ipſi autumant; </s> <s xml:id="echoid-s2407" xml:space="preserve">quòd nulla proportio in hac retardatione <lb/>cernatur. </s> <s xml:id="echoid-s2408" xml:space="preserve">Octaua enim ſphæra abſoluit, ſecundũ Ptolemæũ, ſuum circuitum <lb/>ſpatio 36000. </s> <s xml:id="echoid-s2409" xml:space="preserve">annorũ: </s> <s xml:id="echoid-s2410" xml:space="preserve">Saturnus 30. </s> <s xml:id="echoid-s2411" xml:space="preserve">annis: </s> <s xml:id="echoid-s2412" xml:space="preserve">Iuppiter 12. </s> <s xml:id="echoid-s2413" xml:space="preserve">Mars 2. </s> <s xml:id="echoid-s2414" xml:space="preserve">Sol uno anno, <lb/>Venus, ac Mercurius eodẽ fere tempore: </s> <s xml:id="echoid-s2415" xml:space="preserve">Luna denique 27. </s> <s xml:id="echoid-s2416" xml:space="preserve">diebus, & </s> <s xml:id="echoid-s2417" xml:space="preserve">8. </s> <s xml:id="echoid-s2418" xml:space="preserve">horis. <lb/></s> <s xml:id="echoid-s2419" xml:space="preserve">ubi manifeſte uides, nullam certam proportionem inueniri. </s> <s xml:id="echoid-s2420" xml:space="preserve">Non ergo cre-<lb/>dibile eſt, planetas carere proprijs motibus ab occidente in orientem, & </s> <s xml:id="echoid-s2421" xml:space="preserve">ſolũ <lb/>propter illam retardationem uideri nobis moueri ab occidente in oriẽtem. </s> <s xml:id="echoid-s2422" xml:space="preserve"><lb/>Quare ad primam rationem Alpetragij, & </s> <s xml:id="echoid-s2423" xml:space="preserve">Achillini reſpõdendum eſt, illos <lb/>motus non eſſe contrarios, vt infra manifeſtabitur, & </s> <s xml:id="echoid-s2424" xml:space="preserve">ob id neutrum eſſe vio <lb/>lentũ. </s> <s xml:id="echoid-s2425" xml:space="preserve">Adde, non ſequi, etiamſi concederemus, alterum illorum eſſe quodã-<lb/>modo uiolentũ, illum non fore perpetuum, atq. </s> <s xml:id="echoid-s2426" xml:space="preserve">debilitari poſſe, cum cauſa <lb/>eius motiua ſit perpetua, & </s> <s xml:id="echoid-s2427" xml:space="preserve">infatigabilis: </s> <s xml:id="echoid-s2428" xml:space="preserve">Illud enim uiolentũ ſolum dicitur <lb/>non poſſe eſſe perpetuum, quòd cauſam fatigabilem, & </s> <s xml:id="echoid-s2429" xml:space="preserve">non perpetuã habet: </s> <s xml:id="echoid-s2430" xml:space="preserve"><lb/>Hoc enim ſimpliciter, & </s> <s xml:id="echoid-s2431" xml:space="preserve">per ſe uio lentum dicitur. </s> <s xml:id="echoid-s2432" xml:space="preserve">Ad ſecundã uero dicendũ <lb/>eſt, pluralitatẽ motuum maxime eſſe neceſſariam ad reddendam cauſam om <lb/>nium illarũ apparentiarum, quas diximus, & </s> <s xml:id="echoid-s2433" xml:space="preserve">multarum aliarum huiuſmodi, <lb/>quas ipſi minime tueri poſſunt. </s> <s xml:id="echoid-s2434" xml:space="preserve">Ad illud deniq;</s> <s xml:id="echoid-s2435" xml:space="preserve">, quod de motu terrę aſſerũt, <lb/>reſpondemus, falſum eſſe, eam moueri; </s> <s xml:id="echoid-s2436" xml:space="preserve">neq. </s> <s xml:id="echoid-s2437" xml:space="preserve">hac in parte credẽdum eſſe fabu <lb/>lis de columnis Herculis: </s> <s xml:id="echoid-s2438" xml:space="preserve">Quod ſi aliquãdo fuit terra, ubi nunc eſt mare, & </s> <s xml:id="echoid-s2439" xml:space="preserve"><lb/>contra, illud nulla ratione prouenire ex motu terræ ab ortu in occaſum, ẽtſi <lb/>moueretur: </s> <s xml:id="echoid-s2440" xml:space="preserve">Cũ enim terra, & </s> <s xml:id="echoid-s2441" xml:space="preserve">aqua vnum efficiant globũ, vt poſtea oſtende-<lb/>mus, quis non uidet, eodem ſimul tꝑe terram, & </s> <s xml:id="echoid-s2442" xml:space="preserve">aquam moueri, & </s> <s xml:id="echoid-s2443" xml:space="preserve">rapi à pri <lb/>mo mobili? </s> <s xml:id="echoid-s2444" xml:space="preserve">Quòd ſi dicant, mare cum terra non efficere unicum globum, ſed <lb/>aquam eſſe altiorem, ut multi opinati ſunt; </s> <s xml:id="echoid-s2445" xml:space="preserve">t@c potius ſequi deberet, terram <lb/>tendere ſub mare ex parte orientis, quia illam operiret aqua continue, emer <lb/>gere uero e mari ex parte occidentis, quoniã illã aqua deſereret, quandoqui <lb/>dẽ iuxta illos corpora ſuperiora, & </s> <s xml:id="echoid-s2446" xml:space="preserve">propinquiora animę mundi, velocius mo <lb/>uentur ab ortu in occaſum. </s> <s xml:id="echoid-s2447" xml:space="preserve">Cauſam igitur huius rei cum Atiſt. </s> <s xml:id="echoid-s2448" xml:space="preserve">in 1. </s> <s xml:id="echoid-s2449" xml:space="preserve">Mereor, <lb/>hanc dicimus eſſe; </s> <s xml:id="echoid-s2450" xml:space="preserve">quoniam videlicet ob aſpectus ſuperiorum corporũ ma- <pb o="50" file="086" n="87" rhead="Comment. in I. Cap. Sphæræ"/> re conſumit terram in quibuſdam partibus, ob creſc@ntiã aquarũ, idcirco vbi <lb/>ante fuit terra, ibi nunc eſt mare: </s> <s xml:id="echoid-s2451" xml:space="preserve">Eodem modo ꝗain alijs partibus decreſc@@ <lb/>mare, ideo apparet nunc terra ubi antea fuit mare. </s> <s xml:id="echoid-s2452" xml:space="preserve">Cuius rei indiciũ efſe po-<lb/>teſt, quòd iſta permutatio maris cũ terra, & </s> <s xml:id="echoid-s2453" xml:space="preserve">terrę cum mari, non ſolum reperi <lb/>tur facta eſſe ab oriente in occidentem, quod tamen exillorũ ſentẽtia ſeque <lb/>retur, uerum etiam in ſeptentrione, & </s> <s xml:id="echoid-s2454" xml:space="preserve">auſtro, & </s> <s xml:id="echoid-s2455" xml:space="preserve">reliquis mundi partibus.</s> <s xml:id="echoid-s2456" xml:space="preserve"/> </p> <div xml:id="echoid-div157" type="float" level="2" n="4"> <note position="right" xlink:label="note-083-04" xlink:href="note-083-04a" xml:space="preserve">Secũda ſen <lb/>tẽtia de mo@ <lb/>tibus cœlo <lb/>rum, ſecun-<lb/>dũ eos, qui <lb/>octo cęlos <lb/>concedunt.</note> <note position="left" xlink:label="note-084-01" xlink:href="note-084-01a" xml:space="preserve">Cõfutatio <lb/>ſecũdæ ſen <lb/>tentiæ.</note> </div> <p> <s xml:id="echoid-s2457" xml:space="preserve"><emph style="sc">Alii</emph>, vt Auguſtinus Ricius, quem ſequitur Orontius, & </s> <s xml:id="echoid-s2458" xml:space="preserve">aliij nonnulli vi-<lb/> <anchor type="note" xlink:label="note-086-01a" xlink:href="note-086-01"/> dentes hac ratione nullo modo poſſe apparentias, & </s> <s xml:id="echoid-s2459" xml:space="preserve">φαινώμενα defendi, uo-<lb/>lentesq́, octonario orbium numero eſſe contenti, dixerunt, totum aggrega-<lb/>tum octo orbium habere unum communem motum ab oriẽte in occidentẽ, <lb/>ita, ut motus hic nulli particulari orbi, conueniat, tanquam uni, ſed omnibus <lb/>ſimul ſumptis: </s> <s xml:id="echoid-s2460" xml:space="preserve">Sicut nec motus progreſſiuus animalis conuenit huic, uel illi <lb/>mẽbro particulari, ſed toti animali. </s> <s xml:id="echoid-s2461" xml:space="preserve">Atq. </s> <s xml:id="echoid-s2462" xml:space="preserve">hic motus diutnus appellari ſolet. <lb/></s> <s xml:id="echoid-s2463" xml:space="preserve">Pręter hũc autem motum communem totius aggregati, vnuſquiſque orbis, <lb/>inquiunt, habet adhuc peculiarem, & </s> <s xml:id="echoid-s2464" xml:space="preserve">propriũ motum ab occidente in orien <lb/>tem, quem propria e<unsure/>fficit intelligentia cuilibet orbi aſſiſtens. </s> <s xml:id="echoid-s2465" xml:space="preserve">Neque hoc <lb/>mirum uideri debet, ut aſſerunt, cum etiam in animalibus uideamus ſingula <lb/>membra contrariũ poſſe habere motũ motui progreſſiuo totius animalis: </s> <s xml:id="echoid-s2466" xml:space="preserve">Po <lb/>teſt nam q. </s> <s xml:id="echoid-s2467" xml:space="preserve">fieri, ut totum animal progrediatur ab oriente occidentẽ uerſus, <lb/>& </s> <s xml:id="echoid-s2468" xml:space="preserve">nihil ominus manus uel caput, vel aliud membrũ interim moueatur ſimul <lb/>eodem tempore in contrariam partem, puta ab occidente uerſus orientem. </s> <s xml:id="echoid-s2469" xml:space="preserve"><lb/>Quod ſi obijcias, hac ratione nõ poſſe aſſignari primum mobile, cum octaua<unsure/> <lb/>quoq. </s> <s xml:id="echoid-s2470" xml:space="preserve">ſphæra ab occaſu in ortum uoluatur, quod tamen tota philoſophorũ <lb/>& </s> <s xml:id="echoid-s2471" xml:space="preserve">Aſtronomorum cohors unanimi conſenſu admittit. </s> <s xml:id="echoid-s2472" xml:space="preserve">Reſpõdet Auguſtinus <lb/>Ricius, Primũ mobile poſſe duplici fenſu intelligi. </s> <s xml:id="echoid-s2473" xml:space="preserve">Vno modo, ut ſignificet il <lb/>lud corpus, quod per ſe primò à motore primo uertitur, & </s> <s xml:id="echoid-s2474" xml:space="preserve">hoc modo nulla <lb/>ſphęra cæleſtis particularis primum mobile dici poteſt, cum nulla per ſe pri <lb/>mò moueatur à primo motore, ſed veluti pars ad motũ toti<emph style="sub">9</emph>. </s> <s xml:id="echoid-s2475" xml:space="preserve">Alio modo pri <lb/>mũ mobile ſumi poteſt pro eo corpore, quod inter cętera mobilia nobilitate, <lb/>& </s> <s xml:id="echoid-s2476" xml:space="preserve">ordine primum dicitur, & </s> <s xml:id="echoid-s2477" xml:space="preserve">in hoc ſenſu octaua ſphæra, etiam ſi ab occaſu in <lb/>ortum circumducatur, primum mobile poteſt appellari, eo quòd intelligen-<lb/>tijs, ſeu ſubſtantijs à corpore liberis ſit propinquior, & </s> <s xml:id="echoid-s2478" xml:space="preserve">uicinior.</s> <s xml:id="echoid-s2479" xml:space="preserve"/> </p> <div xml:id="echoid-div158" type="float" level="2" n="5"> <note position="left" xlink:label="note-086-01" xlink:href="note-086-01a" xml:space="preserve">Tertia ſen. <lb/>tẽtia demo <lb/>tibus cęlo-<lb/>rum, ſecun-<lb/>dũ eos, qui <lb/>octo tãtum <lb/>cælos 1<unsure/>0. <lb/>nunt.</note> </div> <p> <s xml:id="echoid-s2480" xml:space="preserve"><emph style="sc">Qvamvis</emph> vero hæc ſnĩa uideatur primo aſpectu ingenioſa ſatis, ac proba-<lb/> <anchor type="note" xlink:label="note-086-02a" xlink:href="note-086-02"/> bilis, nihilominus, ſi rem diligentius conſiderare uelimus, deprehendemus, <lb/>eam ueram eſſe non poſſe. </s> <s xml:id="echoid-s2481" xml:space="preserve">Primo, qm̃ impoſſibile eſt, totum aggregatum ab <lb/>una intelligentia moueri poſſe ab ortu in occaſum, & </s> <s xml:id="echoid-s2482" xml:space="preserve">ſingulos rurſus cælos, <lb/>nullo excepto, à proprijs intelligentijs in cõtrariã partem deferri. </s> <s xml:id="echoid-s2483" xml:space="preserve">Hoc enim <lb/>pacto totum aggregatũ & </s> <s xml:id="echoid-s2484" xml:space="preserve">ab ortu in occaſum, & </s> <s xml:id="echoid-s2485" xml:space="preserve">ab oco<unsure/>aſu in ortum eodem <lb/>tꝑe moueretur, quod nullo modo fieri poteſt, ut in exemplo ab auctoribus <lb/>huius opinionis adducto perſpicuum eſſe poteſt. </s> <s xml:id="echoid-s2486" xml:space="preserve">Nã licet, ſi animal ab ortu in <lb/>occaſum proprio motu progreſſiuo tendat, manus, uel aliquod aliud mẽbrũ <lb/>è contrario ab occaſu in ortum poſſit moueri, tamen naturæ repugnare uide <lb/>tur, ut omnes ſimul partes animalis, nulla dẽpta, hoc motu cõtrar@o cieri poſ <lb/>fint; </s> <s xml:id="echoid-s2487" xml:space="preserve">Sic enim totum animal ad partes contrarias, & </s> <s xml:id="echoid-s2488" xml:space="preserve">oppoſitas eodẽ tempore <lb/>pergeret, quod fieri nequaquam poteſt, ſed ne que cogitatione apprehendi. <lb/></s> <s xml:id="echoid-s2489" xml:space="preserve">Secundo, Si totum aggregatum cœlorum ab oriente in occidentem, deinde<unsure/> <lb/>ſinguli orbes peculiaribus motibus ab occidente in orientẽ ferrentur, ita ut <lb/>nullus orbis alterũ ſ@o motu trahat (ob hanc enim cauſam præcipuã nolun@ <pb o="51" file="087" n="88" rhead="Ioan. de Sacro Boſco."/> admittere ſupra Firmamentũ aliud cęlum, quod tamquam primũ mobile ſuo <lb/>motu inferiores orbes ab ortu in occaſum ſecũ rapiat) nõ poſſet unus, idẽq́; <lb/></s> <s xml:id="echoid-s2490" xml:space="preserve">o<unsure/>rbis plures motus hí<unsure/>e, quàm duos: </s> <s xml:id="echoid-s2491" xml:space="preserve">Vnũ uidelicet, quatenus eſt pars totius<unsure/> <lb/>aggregati, alterũ uero ſibi propriũ, & </s> <s xml:id="echoid-s2492" xml:space="preserve">peculiare; </s> <s xml:id="echoid-s2493" xml:space="preserve">Hoc aũt falſum eſt. </s> <s xml:id="echoid-s2494" xml:space="preserve">Nam in <lb/>cæleſtibus corporibus plures motus deprehenduntur. </s> <s xml:id="echoid-s2495" xml:space="preserve">Cęlũ. </s> <s xml:id="echoid-s2496" xml:space="preserve">n. </s> <s xml:id="echoid-s2497" xml:space="preserve">Lunæ totale <lb/>(relictis orbibus partialibus) mouetur ab ortu in occaſum, & </s> <s xml:id="echoid-s2498" xml:space="preserve">ab occaſu in or-<lb/>tũ, ut experientia docet, & </s> <s xml:id="echoid-s2499" xml:space="preserve">ipſi fateutur quo que. </s> <s xml:id="echoid-s2500" xml:space="preserve">Rurſus præter duos iſtos mo <lb/>tus mouetur alio diuerſo motu ab oriente in occidentẽ ſuper polos Zodia-<lb/>ci, ut ex theorica Lunæ cõſtat, quẽ quidẽ motũ nulla rõne tueri poſſunt, niſi <lb/>concedant motum raptus, ut mox declarabitur: </s> <s xml:id="echoid-s2501" xml:space="preserve">Hoc enim conceſſo, mouebi <lb/>tur cœlum Lunæ ab oriente in occidentẽ motu diurno ſuper polos mundi <lb/>ad motũ primi mobilis: </s> <s xml:id="echoid-s2502" xml:space="preserve">Ab occidente uero in orientem ſuper polos Zodia-<lb/>ci ad motum nonæ ſphæræ: </s> <s xml:id="echoid-s2503" xml:space="preserve">Ab oriente denique in occidentem ſuper polos <lb/>etiam Zodiaci proprio motu. </s> <s xml:id="echoid-s2504" xml:space="preserve">Tertio, ſi propterea totum aggregatum ab or <lb/>tu in occaſum mouetur, & </s> <s xml:id="echoid-s2505" xml:space="preserve">non ſinguli cęli, quia nimitum uidemus motũ iſtũ <lb/>communẽ eſſe omnibus cęlis, non uideo, cur non etiam eadem ratione aſſe-<lb/>rãt, omnes octo cœlos, tanquam unum totum, ab una intelligentia ab occa-<lb/>ſu in ortum circumduci, quandoquidem omnes octo cęli totales eodem tẽ-<lb/>pore, eadẽq́ue uelocitate ab occidenre in orientẽ feruntur: </s> <s xml:id="echoid-s2506" xml:space="preserve">(Diuerſitas enim <lb/>motus planetarũ, quã cernimus, non prouenit a cęlis totalibus, ſed a particu <lb/>laribus orbibus Eccentricis, in quibus planetæ, uel eorum Epicycli ſunt in-<lb/>fixi.) </s> <s xml:id="echoid-s2507" xml:space="preserve">immo multo maiori uniformitate, & </s> <s xml:id="echoid-s2508" xml:space="preserve">æqualitate, quám ab ortu in occa-<lb/>ſum; </s> <s xml:id="echoid-s2509" xml:space="preserve">quod tamen admittere nulla ratione uolũt. </s> <s xml:id="echoid-s2510" xml:space="preserve">Relinquẽda eſt ergo & </s> <s xml:id="echoid-s2511" xml:space="preserve">hæc <lb/>ſententia tanquam impoſſibilis, & </s> <s xml:id="echoid-s2512" xml:space="preserve">quæ non omnia phænomena tueri poſſit.</s> <s xml:id="echoid-s2513" xml:space="preserve"/> </p> <div xml:id="echoid-div159" type="float" level="2" n="6"> <note position="left" xlink:label="note-086-02" xlink:href="note-086-02a" xml:space="preserve">Confutatio <lb/>l<unsure/>ertię ſentẽ <lb/>t<unsure/>ię.</note> </div> <p> <s xml:id="echoid-s2514" xml:space="preserve"><emph style="sc">Qvapropter</emph> aliter cum Aſtronomis doctioribus de motibus cæ-<lb/> <anchor type="note" xlink:label="note-087-01a" xlink:href="note-087-01"/> lorũ dicendũ erit. </s> <s xml:id="echoid-s2515" xml:space="preserve">Dicimus igitur, duos præcipuos motus in genere, eosq́. </s> <s xml:id="echoid-s2516" xml:space="preserve">no <lb/>tiſſimos, in cęlis obſeruari, unũ uidelicet ab oriente in occidentẽ, alterũ ue-<lb/>ro ab occidente in orientẽ: </s> <s xml:id="echoid-s2517" xml:space="preserve">(De motu. </s> <s xml:id="echoid-s2518" xml:space="preserve">n. </s> <s xml:id="echoid-s2519" xml:space="preserve">illo acceſſus & </s> <s xml:id="echoid-s2520" xml:space="preserve">receſſus, qui obſerua <lb/>tus fuit in octaua ſphæra, quoniam non tam facile, & </s> <s xml:id="echoid-s2521" xml:space="preserve">uix à perit@ſſimis de-<lb/>preheuditur, nunc nihil dicimus, ſed eũ paulo poſt exponemus, cũ periodos <lb/>omniũ motuum aſſignabimus.) </s> <s xml:id="echoid-s2522" xml:space="preserve">Quorum prior proprius eſt, ac peculiaris pri <lb/>mo mobili, ſeu decimæ ſphæræ: </s> <s xml:id="echoid-s2523" xml:space="preserve">Vnde & </s> <s xml:id="echoid-s2524" xml:space="preserve">primus motus dici ſolet. </s> <s xml:id="echoid-s2525" xml:space="preserve">Mouetur. </s> <s xml:id="echoid-s2526" xml:space="preserve">n. <lb/></s> <s xml:id="echoid-s2527" xml:space="preserve">decima ſphæra, ſeu primum mobile ſimpliciſſimo tantum, ac regulariſſimo<unsure/> <lb/>motu ab oriente per meridiem in occidentem, & </s> <s xml:id="echoid-s2528" xml:space="preserve">hinc rurſus per mediam no <lb/>ctem in orientem; </s> <s xml:id="echoid-s2529" xml:space="preserve">Qui quidẽ motus cõficitur ſuper polos mundi, & </s> <s xml:id="echoid-s2530" xml:space="preserve">per cir-<lb/>culum æquinoctialem in die naturali, hoc eſt, ſpacio 24. </s> <s xml:id="echoid-s2531" xml:space="preserve">horarũ, circa terram <lb/>ſemel, propter quam cauſam motus diurnus uulgo appellari conſueuit: </s> <s xml:id="echoid-s2532" xml:space="preserve">Hoc <lb/>autem motu primum mobile, ſeu decima ſphæra omnes alias nouem inferio <lb/>res ſphæras ſecum rapit ab oriente in occidentẽ ſine ulla reſiſtentia, ſingulis <lb/>diebus circa terram ſemel: </s> <s xml:id="echoid-s2533" xml:space="preserve">qui quidẽ motus dicitur h@ſce inferioribus ſphæ <lb/>ris conuenite per accidens & </s> <s xml:id="echoid-s2534" xml:space="preserve">non per ſe, cum non ſit ipſarum proprius, ſed ab <lb/>extrinſeco ipſis adueniat: </s> <s xml:id="echoid-s2535" xml:space="preserve">Mouentur. </s> <s xml:id="echoid-s2536" xml:space="preserve">n. </s> <s xml:id="echoid-s2537" xml:space="preserve">raptu, ſeu motu primi mobilis: </s> <s xml:id="echoid-s2538" xml:space="preserve">nõ ſe-<lb/>cus, ac ij, qui in naui, aut curru ſedẽtes ad motũ nauis, ſeu currus rapiuntur, <lb/>ac deuehuntur. </s> <s xml:id="echoid-s2539" xml:space="preserve">Quod ſi a primo mobili non circunferrentur, nullo pacto <lb/>mouerentur ab oriente in occidentem: </s> <s xml:id="echoid-s2540" xml:space="preserve">quemadmodum nec illi, qui in na-<lb/>ui, ſiue curru ſedent, ſi non moueretur nauis, aut currus, deueherentur, ſed <lb/>immobi<unsure/>les permanerẽt. </s> <s xml:id="echoid-s2541" xml:space="preserve">Poſterior uero motus proprius eſt nouem infetiori-<lb/>bus ſphæris, & </s> <s xml:id="echoid-s2542" xml:space="preserve">nullo modo decimæ ſphæræ, ſiue primo mobili cõuenit. </s> <s xml:id="echoid-s2543" xml:space="preserve">Pri- <pb o="52" file="088" n="89" rhead="Comment. in I. Cap. Sphæræ"/> mo enim illi motui uidẽtur reluctari quodãmodo omnes inferiores ſphęræ <lb/>proprijs motibus ab occidentein oriẽtem; </s> <s xml:id="echoid-s2544" xml:space="preserve">Ita ut, etiãſi ab ortu in occaſum ra <lb/>piantur, cõtinue tñ ab occidente per meridiem in orientẽ, & </s> <s xml:id="echoid-s2545" xml:space="preserve">hinc rurſus per <lb/>mediã noctẽ in occidentẽ delabãtur quoque: </s> <s xml:id="echoid-s2546" xml:space="preserve">Qui quidẽ motus fit ſuper po-<lb/>los Zodiaci diſtantes à polis mundi iuxta recentiorũ obſeruationẽ, 23. </s> <s xml:id="echoid-s2547" xml:space="preserve">grad. <lb/></s> <s xml:id="echoid-s2548" xml:space="preserve">& </s> <s xml:id="echoid-s2549" xml:space="preserve">30. </s> <s xml:id="echoid-s2550" xml:space="preserve">min. </s> <s xml:id="echoid-s2551" xml:space="preserve">& </s> <s xml:id="echoid-s2552" xml:space="preserve">per circulum Zodiacum. </s> <s xml:id="echoid-s2553" xml:space="preserve">Hic autem motus per ſe conuenire dici <lb/>tur inferioribus ſphæris, & </s> <s xml:id="echoid-s2554" xml:space="preserve">non per accidens: </s> <s xml:id="echoid-s2555" xml:space="preserve">Quemadmodum, ſi quis in ali-<lb/>qua naui delatus ab oriente in occidẽtem ambularet proprio motu progreſ-<lb/>ſiuo ab occidente in orientem, proculdubio is, licet multo uelociori motu a <lb/>naui in occidentem moueretur, quàm motu proprio progreſſiuo in orientẽ, <lb/>diceretur tamen per accidẽs ad motum nauis tendere in occidentẽ, quia mo <lb/>tu alieno fertur; </s> <s xml:id="echoid-s2556" xml:space="preserve">per ſe uero in orientem, quia motu proprio incedit: </s> <s xml:id="echoid-s2557" xml:space="preserve">quo ẽt <lb/>moueretur, quamuis nauis immota permaneret. </s> <s xml:id="echoid-s2558" xml:space="preserve">Sic igitur iſte motus etiam <lb/>ab occidente in orientem inferiorum ſphærarum dicitur illis conuenire per <lb/>ſe, quia licet nullo pacto à primo mobili raperẽtur, adhuc tamen motu hoc <lb/>tenderent in orientem ab occidente.</s> <s xml:id="echoid-s2559" xml:space="preserve"/> </p> <div xml:id="echoid-div160" type="float" level="2" n="7"> <note position="right" xlink:label="note-087-01" xlink:href="note-087-01a" xml:space="preserve">Sentẽtia ue<unsure/> <lb/>rior de mo <lb/>tibus co@lo<unsure/> <lb/>tu@.</note> </div> <p> <s xml:id="echoid-s2560" xml:space="preserve"><emph style="sc">Qvoniam</emph> uero impoſsibile uidetur, unũ & </s> <s xml:id="echoid-s2561" xml:space="preserve">idem cœlum poſſe uno, <lb/>eodemq́; </s> <s xml:id="echoid-s2562" xml:space="preserve">tempore moueri ab oriente in occidentem, & </s> <s xml:id="echoid-s2563" xml:space="preserve">ab occidente in oriẽ <lb/>tẽ, cum oriens, & </s> <s xml:id="echoid-s2564" xml:space="preserve">occidens ſint termini oppoſiti, & </s> <s xml:id="echoid-s2565" xml:space="preserve">contrarij; </s> <s xml:id="echoid-s2566" xml:space="preserve">Reſpondent nõ-<lb/>nulli, hoc non eſſe incommodũ, quia hi duo motus contrarij fiunt ſuper di-<lb/>uerſos polos, & </s> <s xml:id="echoid-s2567" xml:space="preserve">per lineas diuerſas. </s> <s xml:id="echoid-s2568" xml:space="preserve">Mouentur enim ab oriente in occidentẽ <lb/>ſuper polos mundi, arcticũ ſcilicet, & </s> <s xml:id="echoid-s2569" xml:space="preserve">antarcticũ, & </s> <s xml:id="echoid-s2570" xml:space="preserve">per circulũ æquinoctialẽ; <lb/></s> <s xml:id="echoid-s2571" xml:space="preserve">At uero ab occidente in orientem mouentur ſuper alios polos, nimirum ſu-<lb/>per polos Zodiaci, & </s> <s xml:id="echoid-s2572" xml:space="preserve">per circulum Zodiacum. </s> <s xml:id="echoid-s2573" xml:space="preserve">Vetum hæc reſponſio non pla-<lb/>cet, quoniam in ea conceditur unum, & </s> <s xml:id="echoid-s2574" xml:space="preserve">idẽ mobile poſſe contraris motibus <lb/>ferri per diuerſas uias; </s> <s xml:id="echoid-s2575" xml:space="preserve">quod impoſsibile eſt omnino. </s> <s xml:id="echoid-s2576" xml:space="preserve">Si enim mouetur quip <lb/>piã ab oriente in occidentẽ, fieri non poteſt, ut eodem tempore ab occidente <lb/>in orientẽ moueatur. </s> <s xml:id="echoid-s2577" xml:space="preserve">Hac enim ratione accederet ad occidentem, & </s> <s xml:id="echoid-s2578" xml:space="preserve">ab eodẽ <lb/>recederet, quod nec per eandem lineam, nec per diuerſas lineas fieri poteſt, <lb/>cũ hæc duo maxime inter ſe pugnent. </s> <s xml:id="echoid-s2579" xml:space="preserve">Quamobrem dicendum eſt, nullo mo <lb/> <anchor type="note" xlink:label="note-088-01a" xlink:href="note-088-01"/> do prædictos duos motus inter ſe eſſe contrarios. </s> <s xml:id="echoid-s2580" xml:space="preserve">Omnes. </s> <s xml:id="echoid-s2581" xml:space="preserve">n. </s> <s xml:id="echoid-s2582" xml:space="preserve">cœli inferiores, <lb/>qui raptu primi mobilis mouentur, quamuis per accidens, & </s> <s xml:id="echoid-s2583" xml:space="preserve">præter @aturã <lb/>ſuã ab ortu in occaſum ferãtur, nẽpe motu alieno; </s> <s xml:id="echoid-s2584" xml:space="preserve">per ſe uero ab occaſu in <lb/>ortũ, puta proprio motu, & </s> <s xml:id="echoid-s2585" xml:space="preserve">ſecundum propriã naturam tendant: </s> <s xml:id="echoid-s2586" xml:space="preserve">Simpliciter <lb/>tamen ab oriente in occidentem mouẽtur omnes, & </s> <s xml:id="echoid-s2587" xml:space="preserve">nullũ ſimpliciter ab oc <lb/>cidente in orientem, ſed ſecundum quid, quia nimirũ ad ſigna orientalia mo <lb/>uentur, ut mox declarabitur, Quod ut intelligatur, duo ſunt Zodiaci in cor <lb/> <anchor type="note" xlink:label="note-088-02a" xlink:href="note-088-02"/> poribus cęleſtibus potiſſimũ concipiendi, Vnus quidẽ in primo mobili, ſeu <lb/>decimo cęlo, qui ſolus eſt uerus, ac proprius Zodiacus, quem Aſtronomi in-<lb/>telligunt, quando de Zodiaco abſolute loquuntur, conſtans duodecim parti-<lb/>bus æqualibus: </s> <s xml:id="echoid-s2588" xml:space="preserve">quæ ſigna cęleſtia uocantur, hoc ordine, Aries, Taurus, Gemi <lb/>ni, Cancer, Leo, Virgo, Libra, Scorpius, Sagittarius, Capricornus, Aquarius, <lb/>Piſces: </s> <s xml:id="echoid-s2589" xml:space="preserve">quæ his characteribus ab Aſtronomis exprimi ſolent. <lb/></s> <s xml:id="echoid-s2590" xml:space="preserve"> <anchor type="note" xlink:label="note-088-03a" xlink:href="note-088-03"/> <pb o="53" file="089" n="90" rhead="Ioan. de Sacro Boſco."/> Hi enim characteris ſignificant eodẽ ordine prædicta duo decim ſigna. </s> <s xml:id="echoid-s2591" xml:space="preserve">Quare <lb/>diligenter notandi erunt, memoriæq́; </s> <s xml:id="echoid-s2592" xml:space="preserve">mandandi, quoniam frequentiſſimis eo-<lb/>rum uſus exiſtit apud Aſtronomos, ſæpiſſimeq́ue in ſequentibus adducentur. <lb/></s> <s xml:id="echoid-s2593" xml:space="preserve">Sunt autem quælibet duo, ſuperius uidelicet, & </s> <s xml:id="echoid-s2594" xml:space="preserve">inferius, in cœlo per diame-<lb/>trum oppoſita, quod etiã notandum eſt; </s> <s xml:id="echoid-s2595" xml:space="preserve">Nam non raro fiet mentio ſignorum <lb/>oppoſitorum. </s> <s xml:id="echoid-s2596" xml:space="preserve">Alter uero Zodiacus concipiendum eſt in nona ſphæra priori Zo <lb/>diaco directè ſuppoſitus cum eiſdem duodecim ſignis. </s> <s xml:id="echoid-s2597" xml:space="preserve">Primus ille Zodiacus di <lb/>citur ab Aſtronomis immobilis & </s> <s xml:id="echoid-s2598" xml:space="preserve">fixus, non quòd non moueatur ad motũ ſui <lb/>orbis, in quo eſt, ſed quòd eius ſigna eodẽ ſemper modo ſe habeant ad Aequi-<lb/>noctialẽ, & </s> <s xml:id="echoid-s2599" xml:space="preserve">Coluros primi mobilis, ita ut ſemper principium ♈, ſit in Aequi-<lb/>noctiali circulo, ſimiliterq́; </s> <s xml:id="echoid-s2600" xml:space="preserve">principium ♎; </s> <s xml:id="echoid-s2601" xml:space="preserve">ubi nimirum Colurus æquinoctio <lb/>rum Æquinoctialẽ interſecat: </s> <s xml:id="echoid-s2602" xml:space="preserve">Rurſus principiũ ♋, reperiatur ſemper in Co-<lb/>luro ſolſti@iorum, ſimiliterq́; </s> <s xml:id="echoid-s2603" xml:space="preserve">principium ♑; </s> <s xml:id="echoid-s2604" xml:space="preserve">Idemq́; </s> <s xml:id="echoid-s2605" xml:space="preserve">de reliquis ſignis, & </s> <s xml:id="echoid-s2606" xml:space="preserve">pun-<lb/>ctis primarij illius Zodiaci proportione quadam dicendum erit. </s> <s xml:id="echoid-s2607" xml:space="preserve">Secundus au-<lb/>tẽ Zodiacus dicitur mobilis & </s> <s xml:id="echoid-s2608" xml:space="preserve">non fixus, non ea ſolum ratione, ꝙ ad motum <lb/>ſui orbis, in quo eſt, moueatur, hocetenim commune etiam eſt primo illi Zo-<lb/>diaco, qui tamen immobilis appellatur: </s> <s xml:id="echoid-s2609" xml:space="preserve">ſed quòd eius ſigna non ſemper eodẽ <lb/>modo ſeſe habeant ad Æquinoctialem, & </s> <s xml:id="echoid-s2610" xml:space="preserve">Coluros primi mobilis. </s> <s xml:id="echoid-s2611" xml:space="preserve">Non enim <lb/>principiũ ♈, & </s> <s xml:id="echoid-s2612" xml:space="preserve">♎, huius Zodiaci ſemper reperiuntur in æquinoctiali circulo, <lb/>ſiue Coluro æquinoctiorum primi mobilis: </s> <s xml:id="echoid-s2613" xml:space="preserve">neque principiũ ♋, & </s> <s xml:id="echoid-s2614" xml:space="preserve">♑, in Colu <lb/> <anchor type="note" xlink:label="note-089-01a" xlink:href="note-089-01"/> ro ſolſtitiorum. </s> <s xml:id="echoid-s2615" xml:space="preserve">Mouetur namque poſterior hic Zodiacus ſubillo priori pau-<lb/>latim uerſus ſigna orientalia prioris Zodiaci, hoc eſt, uerſus ſigna illa, quæ po-<lb/>ſterius oriuntur, aſcenduntve ſupra Horizontẽ. </s> <s xml:id="echoid-s2616" xml:space="preserve">Vt ſi exempli cauſa ſignum ♈, <lb/>noni cœli hoc momento tẽporis adæquate, & </s> <s xml:id="echoid-s2617" xml:space="preserve">directe ſuppoſitũ eſſet ſigno ♈, <lb/>primi mobilis, immediate poſt hoc in grederetur ſub ſignũ ♉, primi mobilis, & </s> <s xml:id="echoid-s2618" xml:space="preserve"><lb/>poſtquam præciſe, & </s> <s xml:id="echoid-s2619" xml:space="preserve">ad æquate fuerit ſub ſigno ♉, ſtatim ingrederetur ſub ſi-<lb/>gnũ ♊, & </s> <s xml:id="echoid-s2620" xml:space="preserve">ita deinceps ſubiret pedetentim alia, atq; </s> <s xml:id="echoid-s2621" xml:space="preserve">alia ſigna, quæ poſterius <lb/>oriuntur, donec iterũ directe ſigno ♈, primi mobilis ſupponeretur. </s> <s xml:id="echoid-s2622" xml:space="preserve">Cæterum <lb/>hac ratione Zodiacus noni cœli ſimpliciter mouetur ad motum primi mobi-<lb/>lis ab oriente in occidentẽ, quia nullũ datur tẽporis inſtãs poſt aliud, in quo <lb/>non magis ab oriẽte recedat, & </s> <s xml:id="echoid-s2623" xml:space="preserve">ad occidentẽ accedat, ut manifeſtè deprehen-<lb/>ditur in quauis ſtella: </s> <s xml:id="echoid-s2624" xml:space="preserve">Non autem ſimpliciter ab occidente in orientem, quo-<lb/>niã nunquam magis ab occidente recedit, aut ad orientem accedit, ſed potius <lb/>contrarium apparet, cũ perpetuo Solem ac Lunam, & </s> <s xml:id="echoid-s2625" xml:space="preserve">cęteras ſtellas, ab or-<lb/>tu in occaſum tendere cernamus. </s> <s xml:id="echoid-s2626" xml:space="preserve">Dicitur tñ ſecundum quid moueri quodam-<lb/>modo ab occidente in orientem, quoniam etiamſi occidentem nunquam de-<lb/>ſerat, & </s> <s xml:id="echoid-s2627" xml:space="preserve">orienti appropinquet, accedit tamen ad ſigna orientalia, ut dictum eſt. <lb/></s> <s xml:id="echoid-s2628" xml:space="preserve">Idem quoque prorſus dicendum eſt de alijs ſphæris, ut de cœlo octauo, & </s> <s xml:id="echoid-s2629" xml:space="preserve">or-<lb/>bibus ſeptem planetarum. </s> <s xml:id="echoid-s2630" xml:space="preserve">Quamuis enim continue trahantur à primo mobili <lb/>ab oriente in occidentẽ, ſenſim nihilominus ſub Zodiaco primi mobil s mo-<lb/>uentur, petẽdo ſigna orientalia, ſeu quæ poſterius oriuntur & </s> <s xml:id="echoid-s2631" xml:space="preserve">occidunt. </s> <s xml:id="echoid-s2632" xml:space="preserve">Ver-<lb/> <anchor type="note" xlink:label="note-089-02a" xlink:href="note-089-02"/> bi gratia, cum Sol ſubijt totum ſignum ♈, primi mobilis, incipit mox ex ♈, <lb/>ſub ſignum ♉, ſuccedere, & </s> <s xml:id="echoid-s2633" xml:space="preserve">ita deinceps, doneciterum ſubeat ſignum ♈.</s> <s xml:id="echoid-s2634" xml:space="preserve"/> </p> <div xml:id="echoid-div161" type="float" level="2" n="8"> <note position="left" xlink:label="note-088-01" xlink:href="note-088-01a" xml:space="preserve">Duo motus <lb/>cælorũ ab <lb/>ortu in oc-<lb/>c<unsure/>aſum, & <lb/>ab occaſu <lb/>in ortũ, nõ <lb/>ſunt con-<lb/>trarij.</note> <note position="left" xlink:label="note-088-02" xlink:href="note-088-02a" xml:space="preserve">Du plex Zo <lb/>diacus.</note> <note position="right" xlink:label="note-088-03" xlink:href="note-088-03a" xml:space="preserve"> <lb/>Aries # Taurus # Gemini # Cancer # Leo # Virgo <lb/>♈ # ♉ # ♊ # ♋ # ♌ # ♍ <lb/>Libra # Scorpius # Sagittarius # Capricornus # Aquarius # Piſces. <lb/>♎ # ♏ # ♐ # ♑ # ♒ # ♓ <lb/></note> <note position="right" xlink:label="note-089-01" xlink:href="note-089-01a" xml:space="preserve">Qua ratio-<lb/>ne Zodia-<lb/>cus nonæ <lb/>ſphæræ mo <lb/>ueri intelli <lb/>gatur ab oe <lb/>caſu in or-<lb/>tum.</note> <note position="right" xlink:label="note-089-02" xlink:href="note-089-02a" xml:space="preserve">Cœli infe-<lb/>riores mo-<lb/>uentur ſi@ <lb/>pliciter ab <lb/>ortu in oc-<lb/>caſum, ſe-<lb/>cũdum ꝗd <lb/>autem ab <lb/>occaſu in <lb/>ortum.</note> </div> <p> <s xml:id="echoid-s2635" xml:space="preserve"><emph style="sc">Hocigitvr</emph> pacto uerum eſt, cœlos omnes ſimpliciter moueri ab <lb/>oriente in occidentem, quia nullũ datur inſtans temporis, in quo quodlibet <lb/>punctum in illis aſſumptum non ſemper magis, ac magis ab oriente recedat, & </s> <s xml:id="echoid-s2636" xml:space="preserve"><lb/>accedat ad occidentem: </s> <s xml:id="echoid-s2637" xml:space="preserve">& </s> <s xml:id="echoid-s2638" xml:space="preserve">rurſus omnes orbes infra primũ mobile moaeri ab <lb/>o<unsure/>ccidente in orientem, ſecundum quid, id eſt, ad ſigna orientalia: </s> <s xml:id="echoid-s2639" xml:space="preserve">non autem <pb o="54" file="090" n="91" rhead="Comment. in I. Cap. Sphæræ"/> ſimpliciter, cum nullum detur inſtans, in quo ab occidente oriẽtem uerſus re-<lb/>cedant, ſed tantum ſub alijs ſignis orientalibus reperiantur, ut manifeſtò ſenſu <lb/>& </s> <s xml:id="echoid-s2640" xml:space="preserve">inſtrumentis percipimus. </s> <s xml:id="echoid-s2641" xml:space="preserve">Vt autẽ ſimpliciter aliquid ex uno loco in alium <lb/>dicatur moueri, neceſſe eſt, ut illum relinquat, & </s> <s xml:id="echoid-s2642" xml:space="preserve">ad aliam accedat. </s> <s xml:id="echoid-s2643" xml:space="preserve">Cum igitur <lb/>nunquam uideamus Solem, uel alias ftellas, occidentem deſerere, & </s> <s xml:id="echoid-s2644" xml:space="preserve">ad orien-<lb/>tem accedere, non poterimus dicere, cęlos ſimpliciter ab occidente in orien-<lb/>tem moueri, ſed tantum ſecundum quid, nempe ad ſigna orientalia, ut iam <lb/>expoſuimus. </s> <s xml:id="echoid-s2645" xml:space="preserve">Simpliciter autem moueri dicuntur ab oriente in occidentẽ, quo <lb/>niam nullum datur inſtans temporis, in quo non magis recedant ab oriente, <lb/>& </s> <s xml:id="echoid-s2646" xml:space="preserve">occidenti appropinquent, propter motum illum rapid@ſſimum primi mobi-<lb/>lis, à quo rapiuntur. </s> <s xml:id="echoid-s2647" xml:space="preserve">Quod ſi à primo mobili non raperentur, tunc ſimpliciter <lb/>ab occidente in orientem mouerentur, quia nullũ daretur inſtans, in quo non <lb/>magis ab occidente diſcederent, & </s> <s xml:id="echoid-s2648" xml:space="preserve">ad orientem accederent. </s> <s xml:id="echoid-s2649" xml:space="preserve">Item, ſi proprijs <lb/>motibus uelocius mouerentur ab occidente in orientem, quàm ad motũ pri-<lb/>mi mobilis ab oriente in occidentem, ſimpliciter quoque ferrentur ab occidẽ <lb/>te in orientem, & </s> <s xml:id="echoid-s2650" xml:space="preserve">ſecundum quid ab oriente in occidentem, ob rationem iam <lb/>dictam, quia nimirum hac ratione ſemper magis, magisq́ue ab occidente remo <lb/>uerentur, & </s> <s xml:id="echoid-s2651" xml:space="preserve">ad orientem accederent, non autem è contratio.</s> <s xml:id="echoid-s2652" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2653" xml:space="preserve"><emph style="sc">Haec</emph> autem omnia fieri poſſe, vno, aut altero exemplo perdiſces. </s> <s xml:id="echoid-s2654" xml:space="preserve">Mo-<lb/> <anchor type="note" xlink:label="note-090-01a" xlink:href="note-090-01"/> ueatur nauis aliqua ab oriente in occidentem maxima celeritate: </s> <s xml:id="echoid-s2655" xml:space="preserve">Naucle-<lb/>rus autem eodem tempore gradu admodũ tardo perambulet nauim à<unsure/> prora <lb/>in puppim. </s> <s xml:id="echoid-s2656" xml:space="preserve">Quo poſito, nonne uides, Nauclerum ſimpliciter quidem moueri <lb/>ab oriente in occidentem, eo quòd ad motũ nauis celerius multo, quàm pro-<lb/>prio motu in contratiã partẽ moueatur, & </s> <s xml:id="echoid-s2657" xml:space="preserve">ob id ſemper magis ab oriente rece<unsure/> <lb/>dat, occidenti uero appropinquet? </s> <s xml:id="echoid-s2658" xml:space="preserve">Simul tamen ſecundũ quid moueri ad oriẽ <lb/>tem, id eſt, ad partes orientales nauis, non autem ſimpliciter? </s> <s xml:id="echoid-s2659" xml:space="preserve">Nonne etiam ui-<lb/>des, ſi nauis immota conſiſteret, Naucleorum ſimpliciter tunc moueri ab occi-<lb/>dente in orientem, cum ſemper magis ad orientẽ accederet, & </s> <s xml:id="echoid-s2660" xml:space="preserve">ab occidente re <lb/>cederet? </s> <s xml:id="echoid-s2661" xml:space="preserve">Nonne denique idem contingere conſpicis, ſi Nauclerus citatiori mo <lb/>tu incederet, quàm nauis? </s> <s xml:id="echoid-s2662" xml:space="preserve">Ita igitur intelligendum eſt, cęlos inferiores moue-<lb/>ri ſub Zodiaco primi mobilis ab occidente in orientem. </s> <s xml:id="echoid-s2663" xml:space="preserve">Clarius autem fortaſ-<lb/>ſe res percipietur in formica, quæ lento gradu contra motum uelociſſimũ ali-<lb/>cuius rotæ, quæ ab oriente in occidẽtem moueatur, incedit. </s> <s xml:id="echoid-s2664" xml:space="preserve">Idem intelligi po<unsure/> <lb/>teſt in ſphærula aliqua uitrea lucente. </s> <s xml:id="echoid-s2665" xml:space="preserve">Si enim impleatur aqua limpida, quam <lb/>uerſus t<unsure/>e ſic agites, ut aqua paulatim aduerſus t<unsure/>e moueatur: </s> <s xml:id="echoid-s2666" xml:space="preserve">Deinde uitrea il <lb/>la ſphærula in oppoſitã partẽ celerrime circũuoluatur: </s> <s xml:id="echoid-s2667" xml:space="preserve">mox conſpicies aquam <lb/>in uitro contentã ad motũ ſphęrulæ pariter moueri, pariterq́ue contra niten-<lb/>do aduerſus te moueri. </s> <s xml:id="echoid-s2668" xml:space="preserve">Per ſphærulã igitur illã uitream lucentẽ primũ mobi-<lb/>le, & </s> <s xml:id="echoid-s2669" xml:space="preserve">per aquam in ea contentam inferiores ſphæræ primo mobili contra nitẽ-<lb/>tes animo concipiendi ſunt. </s> <s xml:id="echoid-s2670" xml:space="preserve">Hoc etiã cerni poteſt in pelui, ſi aqua impleatur.</s> <s xml:id="echoid-s2671" xml:space="preserve"/> </p> <div xml:id="echoid-div162" type="float" level="2" n="9"> <note position="left" xlink:label="note-090-01" xlink:href="note-090-01a" xml:space="preserve">Exempla, <lb/>quibus de-<lb/>@laratur mo <lb/>@@s cęlorũ <lb/>ab ortu in <lb/>occasũ ſi m-<lb/>pliciter, & <lb/>ab occaſu <lb/>in ortum <lb/>Secundum <lb/>@uid.</note> </div> <p> <s xml:id="echoid-s2672" xml:space="preserve"><emph style="sc">Exhac porro</emph> declaratione, & </s> <s xml:id="echoid-s2673" xml:space="preserve">exemplis adductis, perſpicuum re-<lb/> <anchor type="note" xlink:label="note-090-02a" xlink:href="note-090-02"/> linquitur, duos prædictos cœlorum motus, quorum unus eſt ab oriente in oc<unsure/> <lb/>cidentem, alter ab occidente in orientem, non eſſe contrarios, cum non ſimpli <lb/>citer ad terminos cõtrarios, puta ad orientẽ, & </s> <s xml:id="echoid-s2674" xml:space="preserve">ad occidentem fiant, ut expli-<lb/>cauimus. </s> <s xml:id="echoid-s2675" xml:space="preserve">Contrarij namque motus reſerri debent ad unum idemq́ue punctum <lb/>fixum, ut uidelicet uno motu ad illud punctum accedatur, & </s> <s xml:id="echoid-s2676" xml:space="preserve">alio ab eodem re <lb/>cedatur, quod in motibus cęlorum minime fieri diximus. </s> <s xml:id="echoid-s2677" xml:space="preserve">Dicuntur tamen iſti <lb/>duo motus, communi loquendi modo, contrarij, & </s> <s xml:id="echoid-s2678" xml:space="preserve">oppoſiti, ratione termino- <pb o="55" file="091" n="92" rhead="Ioan. de Sacro Boſco."/> rum contrariorum, puta orientis, & </s> <s xml:id="echoid-s2679" xml:space="preserve">occidentis. </s> <s xml:id="echoid-s2680" xml:space="preserve">Mouentur enim ſimpliciter ad <lb/> <anchor type="note" xlink:label="note-091-01a" xlink:href="note-091-01"/> vnum horum, nempe ad occidentem, ſecundum quid vero ad alterum, videli-<lb/>cet ad orientem, hoc eſt, ad partes orientales, vt dictum eſt. </s> <s xml:id="echoid-s2681" xml:space="preserve">Ex eiſdem quoque <lb/>exemplis liquido conſtat, cælos non modo ſuper diuerſos polos, & </s> <s xml:id="echoid-s2682" xml:space="preserve">diuerſam <lb/>viam poſſe moueri, vt re ipſa mouentur; </s> <s xml:id="echoid-s2683" xml:space="preserve">Verum etiam eos potuiſſe ſuper eoſdẽ <lb/>prorſus polos, & </s> <s xml:id="echoid-s2684" xml:space="preserve">per eandem viam reuerti ab occidente in orientem, per quam <lb/>ab orie<unsure/>nte in occidentem voluuntur. </s> <s xml:id="echoid-s2685" xml:space="preserve">Immo experientia didicerunt Aſtrono-<lb/>mi vnum & </s> <s xml:id="echoid-s2686" xml:space="preserve">idem corpus cæleſte moueri ab oriente in occidentẽ, & </s> <s xml:id="echoid-s2687" xml:space="preserve">ſuper eoſ-<lb/>dem polos ab occidente in orientcm. </s> <s xml:id="echoid-s2688" xml:space="preserve">Orbis enim ſphæræ Lunaris deferens ca-<lb/>put, & </s> <s xml:id="echoid-s2689" xml:space="preserve">caudam Draconis mouetur proprio motu (præter motum diurnũ, qui <lb/>fit ſuper polos mundi) ab oriente in occidentem ſuper polos Zodiaci, & </s> <s xml:id="echoid-s2690" xml:space="preserve">ſuper <lb/>eoſdem polos virtute cæli Mercurij ab occidente in orientem defertur, ut in <lb/>Theoricis planetarum declaratur. </s> <s xml:id="echoid-s2691" xml:space="preserve">Cauſa tamen, cur per aliam viam, uidelicet, <lb/>per circulum Zodiacum, & </s> <s xml:id="echoid-s2692" xml:space="preserve">non per eandem, nempe per Aequinoctialem circu <lb/>lum, hoc eſt, cur ſuper alios polos, nimirum Zodiaci, & </s> <s xml:id="echoid-s2693" xml:space="preserve">non ſuper eoſdem, pu-<lb/>ta mundi polos, (quod tamen optime fieri potuiſſet) ab occidente in orientẽ, <lb/>ad ſenſum iam expoſitum, inferiores ſphæræ reuoluantur, eſt ſecundum philo <lb/>ſophos gubernatio mundi; </s> <s xml:id="echoid-s2694" xml:space="preserve">ut uidelicet per acceſſum Solis, planetarumq́ue ſub <lb/>Zodiaco ad Boream, ſeu ſeptentrionem, & </s> <s xml:id="echoid-s2695" xml:space="preserve">ad Auſtrum, ſiue meridiem, diuerſa <lb/>contingant anni tempora ad uarias rerum generationes accomodata, vt inquit <lb/>Ariſtoteles lib. </s> <s xml:id="echoid-s2696" xml:space="preserve">2. </s> <s xml:id="echoid-s2697" xml:space="preserve">de Gener. </s> <s xml:id="echoid-s2698" xml:space="preserve">& </s> <s xml:id="echoid-s2699" xml:space="preserve">corrupt.</s> <s xml:id="echoid-s2700" xml:space="preserve"/> </p> <div xml:id="echoid-div163" type="float" level="2" n="10"> <note position="left" xlink:label="note-090-02" xlink:href="note-090-02a" xml:space="preserve">Cur<unsure/> motus <lb/>ab ortu in <lb/>occaſum, & <lb/>ab occaſu <lb/>in ortũ con-<lb/>trarij non <lb/>ſint, & ta-<lb/>men cõmu-<lb/>n<unsure/>iter cõtra <lb/>aij dicãtur.</note> <note position="right" xlink:label="note-091-01" xlink:href="note-091-01a" xml:space="preserve">Cęlos ſupe@ <lb/>eoſdem po-<lb/>los mouetĩ<unsure/> <lb/>poſſe ab oc-<lb/>caſu in or-<lb/>tum, ſuper <lb/>quos ab or-<lb/>tu in occa-<lb/>ſum mouẽ-<lb/>tur: & cut <lb/>nuncita nõ <lb/>moueãt@r.</note> </div> </div> <div xml:id="echoid-div165" type="section" level="1" n="56"> <head xml:id="echoid-head60" xml:space="preserve">DEPERIODIS MOTVVM CÆLESTIVM.</head> <p> <s xml:id="echoid-s2701" xml:space="preserve"><emph style="sc">Decimvm</emph> cælum, quod & </s> <s xml:id="echoid-s2702" xml:space="preserve">primum mobile nuncupatur, vniformi, re-<lb/>gulariq́;</s> <s xml:id="echoid-s2703" xml:space="preserve"><unsure/> motu, eoq́; </s> <s xml:id="echoid-s2704" xml:space="preserve">citatiſſimo, ſuper mundi polos, & </s> <s xml:id="echoid-s2705" xml:space="preserve">per circulum Aequino-<lb/> <anchor type="note" xlink:label="note-091-02a" xlink:href="note-091-02"/> ctialem, ut dictum eſt; </s> <s xml:id="echoid-s2706" xml:space="preserve">ſuam explet circuitionem ab oriente in occidentem, ho <lb/>ris 24. </s> <s xml:id="echoid-s2707" xml:space="preserve">æqualibus, quæ dicuntur horę Aequinoctiales; </s> <s xml:id="echoid-s2708" xml:space="preserve">hoc eſt, ſpatio vnius diei <lb/>naturalis: </s> <s xml:id="echoid-s2709" xml:space="preserve">Vnde & </s> <s xml:id="echoid-s2710" xml:space="preserve">eius motus Diurnus eſt appellatus. </s> <s xml:id="echoid-s2711" xml:space="preserve">Huius autẽ motus im-<lb/>petu omnes inferiores orbes, immo & </s> <s xml:id="echoid-s2712" xml:space="preserve">tota ſphæra ignis, & </s> <s xml:id="echoid-s2713" xml:space="preserve">magna pars aeris, & </s> <s xml:id="echoid-s2714" xml:space="preserve"><lb/>ſecundum quorundam ſententiam bona pars Oceani ab ortu ad occaſum ra-<lb/>piuntur. </s> <s xml:id="echoid-s2715" xml:space="preserve">Ex quo ſit, ut iſto motu diurno Sol, & </s> <s xml:id="echoid-s2716" xml:space="preserve">reliqua omnia aſtra, cæliq́; </s> <s xml:id="echoid-s2717" xml:space="preserve">pun <lb/>cta ſingula, quotidie parallelos circulos ad axem mundi rectos deſcribant cir-<lb/>ca polos mundi, eo quidem maiores, quo magis à polis recedunt, minores ue-<lb/>ro, quo magis ad polos accedunt: </s> <s xml:id="echoid-s2718" xml:space="preserve">Vnde Aequinoctialis circulus eſt omnium <lb/>parallelorum maximus, quoniã deſcribitur à punto maxime remoto ab utro-<lb/>que polo, nempe per 90. </s> <s xml:id="echoid-s2719" xml:space="preserve">gradus. </s> <s xml:id="echoid-s2720" xml:space="preserve">Porro inferiores orbes omnes eadem pror-<lb/>ſus, qua primum mobile, velocitate circunducerentur, niſi peculiaribus ſuis <lb/>motibus aliquantulum retrocederent. </s> <s xml:id="echoid-s2721" xml:space="preserve">Nullam enim reſiſtentiam reperit pri-<lb/>mum mobile in cælis inferioribus.</s> <s xml:id="echoid-s2722" xml:space="preserve"/> </p> <div xml:id="echoid-div165" type="float" level="2" n="1"> <note position="right" xlink:label="note-091-02" xlink:href="note-091-02a" xml:space="preserve">Periodiona <lb/>nium @o-<lb/>tuum cæle<unsure/>-<lb/>ſtium.</note> </div> <p> <s xml:id="echoid-s2723" xml:space="preserve"><emph style="sc">Nam nonvs</emph> orbis ſub primo mobili ſpacio 24. </s> <s xml:id="echoid-s2724" xml:space="preserve">horarum, hoceſt, <lb/>unius diei naturalis, ab occaſu in ortum progreditur, iuxta tabulas Alphonſi-<lb/>nas, quatuor particulis ſexagenarijs ex ijs, quæ ab Aſtronomis Tertia appellã-<lb/>tur, & </s> <s xml:id="echoid-s2725" xml:space="preserve">20. </s> <s xml:id="echoid-s2726" xml:space="preserve">Quartis; </s> <s xml:id="echoid-s2727" xml:space="preserve">ita ut ſingulis annis conficiat 26. </s> <s xml:id="echoid-s2728" xml:space="preserve">ſecunda, 25. </s> <s xml:id="echoid-s2729" xml:space="preserve">tertia, & </s> <s xml:id="echoid-s2730" xml:space="preserve">50. <lb/></s> <s xml:id="echoid-s2731" xml:space="preserve">quarta: </s> <s xml:id="echoid-s2732" xml:space="preserve">Ducentis uero annis 1. </s> <s xml:id="echoid-s2733" xml:space="preserve">grad. </s> <s xml:id="echoid-s2734" xml:space="preserve">28. </s> <s xml:id="echoid-s2735" xml:space="preserve">min. </s> <s xml:id="echoid-s2736" xml:space="preserve">9. </s> <s xml:id="echoid-s2737" xml:space="preserve">ſec. </s> <s xml:id="echoid-s2738" xml:space="preserve">47. </s> <s xml:id="echoid-s2739" xml:space="preserve">ter. </s> <s xml:id="echoid-s2740" xml:space="preserve">& </s> <s xml:id="echoid-s2741" xml:space="preserve">45. </s> <s xml:id="echoid-s2742" xml:space="preserve">quar. </s> <s xml:id="echoid-s2743" xml:space="preserve">Ex quo <lb/>efficitur, ut totum curſum per Zodiacum abſoluat quaſi in 49000. </s> <s xml:id="echoid-s2744" xml:space="preserve">annorum <lb/>ſpacio. </s> <s xml:id="echoid-s2745" xml:space="preserve">Nam ſi præciſe loqui uelimus, in tanto annorum ſpatio Nonus orbis <lb/>paulo plus conficit, ſecundum dictas tabulas, quàm integrum circulum: </s> <s xml:id="echoid-s2746" xml:space="preserve">conſi- <pb o="56" file="092" n="93" rhead="Comment. in I. Cap. Sphæræ"/> cit enim grad. </s> <s xml:id="echoid-s2747" xml:space="preserve">360. </s> <s xml:id="echoid-s2748" xml:space="preserve">tertia 5. </s> <s xml:id="echoid-s2749" xml:space="preserve">& </s> <s xml:id="echoid-s2750" xml:space="preserve">quarta 31. </s> <s xml:id="echoid-s2751" xml:space="preserve">Hoc autẽ ſpaciũ, ſeu tempus 49000. <lb/></s> <s xml:id="echoid-s2752" xml:space="preserve">annor<unsure/>ũ appellari ſolet à pleriſq; </s> <s xml:id="echoid-s2753" xml:space="preserve">annus Platonicus. </s> <s xml:id="echoid-s2754" xml:space="preserve">Hoc enim interuallo ſidc-<lb/> <anchor type="note" xlink:label="note-092-01a" xlink:href="note-092-01"/> ra omnia ad eundem ſitum redi<unsure/>tura autumant; </s> <s xml:id="echoid-s2755" xml:space="preserve">Immo quidam volunt, tunc <lb/>omnia quæcunque in mundo ſunt, eodem ordine eſſe reditura, quo nunc cer <lb/>nuntur. </s> <s xml:id="echoid-s2756" xml:space="preserve">Sed temerè hoc aſſerere videntur. </s> <s xml:id="echoid-s2757" xml:space="preserve">Cum enim ſecundũ pleroſque mo-<lb/>tus cælorum ſint inter ſe incommenſurabiles, fieri non poteſt, vt vnquam om-<lb/>nia ſidcra eundem ſitum & </s> <s xml:id="echoid-s2758" xml:space="preserve">ordinem, quem nunc habent, aut olim habuerunt, <lb/>obtinere poſſint. </s> <s xml:id="echoid-s2759" xml:space="preserve">Mouit aũt fortaſſis Alphonſum Regem, vt aſſereret periodũ <lb/>huius motus compleri in ſpacio 49000. </s> <s xml:id="echoid-s2760" xml:space="preserve">annorum, quoniam videbat ſuo tem-<lb/>pore Aequinoctia, & </s> <s xml:id="echoid-s2761" xml:space="preserve">ſolſtitia quotannis in Calendario retrocedere per Min. <lb/></s> <s xml:id="echoid-s2762" xml:space="preserve">10. </s> <s xml:id="echoid-s2763" xml:space="preserve">ſec. </s> <s xml:id="echoid-s2764" xml:space="preserve">44. </s> <s xml:id="echoid-s2765" xml:space="preserve">vnius horæ: </s> <s xml:id="echoid-s2766" xml:space="preserve">Et in annis 400. </s> <s xml:id="echoid-s2767" xml:space="preserve">per dies ferme 3. </s> <s xml:id="echoid-s2768" xml:space="preserve">Ita vt in dicto ſpacio <lb/>annorum 49000. </s> <s xml:id="echoid-s2769" xml:space="preserve">ad priſtinã quaſi ſedem redeant. </s> <s xml:id="echoid-s2770" xml:space="preserve">Ptolomęus autem aſſeuerat, <lb/>hunc motũ perfici in 36000. </s> <s xml:id="echoid-s2771" xml:space="preserve">annorum circulo, ita vt Nonus orbis vnũ gradum <lb/>percu@rat in 100. </s> <s xml:id="echoid-s2772" xml:space="preserve">annis. </s> <s xml:id="echoid-s2773" xml:space="preserve">Albategnius vero vult, iſtum motum abſolui ſpacio <lb/>23760. </s> <s xml:id="echoid-s2774" xml:space="preserve">annorum, ita vt peragret vnum gradum in 66. </s> <s xml:id="echoid-s2775" xml:space="preserve">annis. </s> <s xml:id="echoid-s2776" xml:space="preserve">Qua vero de cau-<lb/>ſa tam varie de periodo huius motus ſenſerint Aſtronomi mox declarabitur: </s> <s xml:id="echoid-s2777" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-092-02a" xlink:href="note-092-02"/> Nunc ratum ſit, & </s> <s xml:id="echoid-s2778" xml:space="preserve">certum, Nonum orbem motu iſto tardi<unsure/>ſſimo ab occidente <lb/>in orientem trahere ſecum 8. </s> <s xml:id="echoid-s2779" xml:space="preserve">inferiores ſphæras celeſtes, nullo vero<unsure/> pacto ſu-<lb/>premam ſphæram. </s> <s xml:id="echoid-s2780" xml:space="preserve">Iuxta enim ſententiam Aſtronomorum, qnicunque orbis ſu <lb/>perior ſuo motu circunfert inferiorem ſibi contiguum, & </s> <s xml:id="echoid-s2781" xml:space="preserve">concentricum, non <lb/>autem ſuperiorem.</s> <s xml:id="echoid-s2782" xml:space="preserve"/> </p> <div xml:id="echoid-div166" type="float" level="2" n="2"> <note position="left" xlink:label="note-092-01" xlink:href="note-092-01a" xml:space="preserve">Annus Pla-<lb/>@oni@@s.</note> <note position="left" xlink:label="note-092-02" xlink:href="note-092-02a" xml:space="preserve">Quilibet or <lb/>bis mouet <lb/>ſuo motu <lb/>inferiorem <lb/>ſibi conti-<lb/>guum.</note> </div> <p> <s xml:id="echoid-s2783" xml:space="preserve">OCTAVVS orbis præter duos iſtos motus prædictos ſibi ab alienis or-<lb/>bibus impreſſos, peculiarem adhuc, & </s> <s xml:id="echoid-s2784" xml:space="preserve">proprium motum habet, quem vocant <lb/>motum acce<unsure/>ſſus, & </s> <s xml:id="echoid-s2785" xml:space="preserve">receſſus, ſeu motum trepidationis, vt ſupra d@ximus. </s> <s xml:id="echoid-s2786" xml:space="preserve">Hic au <lb/>tem motus fit ſuper principia ♈, & </s> <s xml:id="echoid-s2787" xml:space="preserve">♎, nonæ ſphæræ, tanquã polos. </s> <s xml:id="echoid-s2788" xml:space="preserve">Principia <lb/> <anchor type="note" xlink:label="note-092-03a" xlink:href="note-092-03"/> enim ♈, & </s> <s xml:id="echoid-s2789" xml:space="preserve">♎, octauæ ſphæræ circa initia ♈, & </s> <s xml:id="echoid-s2790" xml:space="preserve">♎, nonæ ſphæræ, deſcribũt cir-<lb/>culos quoſdam paruos, quorum ſemidiametri continent 9. </s> <s xml:id="echoid-s2791" xml:space="preserve">grad. </s> <s xml:id="echoid-s2792" xml:space="preserve">Tantũ enim <lb/>diſt<unsure/>ãt initia ♈, & </s> <s xml:id="echoid-s2793" xml:space="preserve">♎, octauę ſphæræ à principijs ♈, & </s> <s xml:id="echoid-s2794" xml:space="preserve">♎, nonæ ſphæræ, iuxta <lb/>doctrinam Alphonſi Regis. </s> <s xml:id="echoid-s2795" xml:space="preserve">Ex hoc vero motu principiorum ♈, & </s> <s xml:id="echoid-s2796" xml:space="preserve">♎, octauæ <lb/>ſphæræ circa principia ♈, & </s> <s xml:id="echoid-s2797" xml:space="preserve">♎, nonæ ſphæræ conſequitur, nullum aliud pun-<lb/>ctum octaui cæli circulum perfectum abſoluere, ſed quodãmodo titubare, hoc <lb/>eſt, nunc accedere ad polum arcticũ, & </s> <s xml:id="echoid-s2798" xml:space="preserve">ab antatctico remoueri, nunc vero à po-<lb/>lo ar<unsure/>ctico diſcedere, & </s> <s xml:id="echoid-s2799" xml:space="preserve">ad antarcticum accedere. </s> <s xml:id="echoid-s2800" xml:space="preserve">Periodus iſtius motus cõple-<lb/>ctitur ſpacium 7000. </s> <s xml:id="echoid-s2801" xml:space="preserve">annorũ, ita vt ſi diuidantur circuli illi parui in 360. </s> <s xml:id="echoid-s2802" xml:space="preserve">grad. <lb/></s> <s xml:id="echoid-s2803" xml:space="preserve">in 20. </s> <s xml:id="echoid-s2804" xml:space="preserve">annis fere vnus gradus abſoluatur. </s> <s xml:id="echoid-s2805" xml:space="preserve">Hoc etiam motu orbes omnium pla-<lb/>netarum, mouentur, cum ſint cũ octaua ſphæra concentrici. </s> <s xml:id="echoid-s2806" xml:space="preserve">Sed vt verum fa-<lb/>i<unsure/>eamur, licet propter phænomena, ſeu apparentias, quas paulo poſt adduce-<lb/>mus, neceſſariò concedendus videatur huiuſmodi motus in octaua ſphæra, vel <lb/>aliquid ſimile, tamen valde incertum eſt, eum ita fieri, vt Alphonſini docent. </s> <s xml:id="echoid-s2807" xml:space="preserve"><lb/>Multa enim abſurda illum conſequi videntur, vt alibi docebimus.</s> <s xml:id="echoid-s2808" xml:space="preserve"/> </p> <div xml:id="echoid-div167" type="float" level="2" n="3"> <note position="left" xlink:label="note-092-03" xlink:href="note-092-03a" xml:space="preserve">Motus tre-<lb/>pidationis.</note> </div> <p> <s xml:id="echoid-s2809" xml:space="preserve">SATVRNI globus præter dictos tres motus, habet motum proprium, <lb/>quem conficit ab occidente in orientem annis 30. </s> <s xml:id="echoid-s2810" xml:space="preserve">fere. </s> <s xml:id="echoid-s2811" xml:space="preserve">Singulis namque die-<lb/>bus peragrat in Zodiaco minuta quaſi 2. </s> <s xml:id="echoid-s2812" xml:space="preserve">& </s> <s xml:id="echoid-s2813" xml:space="preserve">tertia 35.</s> <s xml:id="echoid-s2814" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2815" xml:space="preserve">IVPPITER ſuum circuitum explet 12. </s> <s xml:id="echoid-s2816" xml:space="preserve">fere annis. </s> <s xml:id="echoid-s2817" xml:space="preserve">Quolibet enim die <lb/>pertranſit min. </s> <s xml:id="echoid-s2818" xml:space="preserve">4. </s> <s xml:id="echoid-s2819" xml:space="preserve">ſec. </s> <s xml:id="echoid-s2820" xml:space="preserve">59. </s> <s xml:id="echoid-s2821" xml:space="preserve">ter. </s> <s xml:id="echoid-s2822" xml:space="preserve">15.</s> <s xml:id="echoid-s2823" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2824" xml:space="preserve">MARS abſoluit ſuum motum ab occaſu in ortum annis fere 2. </s> <s xml:id="echoid-s2825" xml:space="preserve">Percurrit <lb/>enim in Zodiaco quouis die min. </s> <s xml:id="echoid-s2826" xml:space="preserve">31. </s> <s xml:id="echoid-s2827" xml:space="preserve">ſec. </s> <s xml:id="echoid-s2828" xml:space="preserve">26. </s> <s xml:id="echoid-s2829" xml:space="preserve">ter. </s> <s xml:id="echoid-s2830" xml:space="preserve">38.</s> <s xml:id="echoid-s2831" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2832" xml:space="preserve">SOL conficit ſuum iter ab occidente in orientem diebus 365. </s> <s xml:id="echoid-s2833" xml:space="preserve">horis 5. </s> <s xml:id="echoid-s2834" xml:space="preserve">mi- <pb o="57" file="093" n="94" rhead="Ioan. de Sacro Boſco."/> nutis 49. </s> <s xml:id="echoid-s2835" xml:space="preserve">ſec. </s> <s xml:id="echoid-s2836" xml:space="preserve">16. </s> <s xml:id="echoid-s2837" xml:space="preserve">Quod ſpacium annus ſolaris appellari ſolet. </s> <s xml:id="echoid-s2838" xml:space="preserve">Ex quo patet, <lb/>Annum non præciſe continere 365. </s> <s xml:id="echoid-s2839" xml:space="preserve">dies, & </s> <s xml:id="echoid-s2840" xml:space="preserve">horas 6. </s> <s xml:id="echoid-s2841" xml:space="preserve">vt in Calendario Romano <lb/>ſupponitur. </s> <s xml:id="echoid-s2842" xml:space="preserve">Deſunt enim minuta fere 11. </s> <s xml:id="echoid-s2843" xml:space="preserve">vnius horæ. </s> <s xml:id="echoid-s2844" xml:space="preserve">Nam Sol ſingulis diebus <lb/>conſ@cit min, 59. </s> <s xml:id="echoid-s2845" xml:space="preserve">ſec. </s> <s xml:id="echoid-s2846" xml:space="preserve">8. </s> <s xml:id="echoid-s2847" xml:space="preserve">ter. </s> <s xml:id="echoid-s2848" xml:space="preserve">19. </s> <s xml:id="echoid-s2849" xml:space="preserve">quar. </s> <s xml:id="echoid-s2850" xml:space="preserve">37. </s> <s xml:id="echoid-s2851" xml:space="preserve">Quod dictum eſſe intelligas ſecundum <lb/>doctrinam Alphonſinorum. </s> <s xml:id="echoid-s2852" xml:space="preserve">Ptolomæus enim maiorem inuenit quantitatem <lb/>anni. </s> <s xml:id="echoid-s2853" xml:space="preserve">& </s> <s xml:id="echoid-s2854" xml:space="preserve">Albategnius minorem: </s> <s xml:id="echoid-s2855" xml:space="preserve">Copernicus autem annum iterum æqualem fe-<lb/>re deprehendit, hac tempeſtate, anno Ptolemaico; </s> <s xml:id="echoid-s2856" xml:space="preserve">Ita vt nunc receptum ſit ab <lb/>omnibus Aſtronomis, anni magnitudinem eſſe inęqualem. </s> <s xml:id="echoid-s2857" xml:space="preserve">Qua de re alio in <lb/>loco vberius diſputabitur.</s> <s xml:id="echoid-s2858" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2859" xml:space="preserve"><emph style="sc">Venvs</emph> totum ſuum circulum complet eodem quaſi tempo re cum Sole. <lb/></s> <s xml:id="echoid-s2860" xml:space="preserve">Progreditur namque quouis die min. </s> <s xml:id="echoid-s2861" xml:space="preserve">59. </s> <s xml:id="echoid-s2862" xml:space="preserve">ſec. </s> <s xml:id="echoid-s2863" xml:space="preserve">8. </s> <s xml:id="echoid-s2864" xml:space="preserve">ter. </s> <s xml:id="echoid-s2865" xml:space="preserve">19. </s> <s xml:id="echoid-s2866" xml:space="preserve">fere.</s> <s xml:id="echoid-s2867" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2868" xml:space="preserve"><emph style="sc">Mercvrivs</emph> tantundem fere omni die conficit. </s> <s xml:id="echoid-s2869" xml:space="preserve">Quamobrem totum <lb/>curſum abſoluet quaſi eodem tempore cum Venere.</s> <s xml:id="echoid-s2870" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2871" xml:space="preserve"><emph style="sc">Lvna</emph> denique totum Zodiacum percurrit 27. </s> <s xml:id="echoid-s2872" xml:space="preserve">diebus cum horis fere 8. <lb/></s> <s xml:id="echoid-s2873" xml:space="preserve">Deinde vero quaſi biduum conſumit, vt aſſequatur Solem. </s> <s xml:id="echoid-s2874" xml:space="preserve">Cum enim Sol in-<lb/>terim in 47. </s> <s xml:id="echoid-s2875" xml:space="preserve">diebus, & </s> <s xml:id="echoid-s2876" xml:space="preserve">horis 8. </s> <s xml:id="echoid-s2877" xml:space="preserve">percurrat fere 27. </s> <s xml:id="echoid-s2878" xml:space="preserve">gradus, quos Luna in biduo <lb/>quaſi abſoluit, neceſſe eſt, vt ab vna coniunctione Lunę cum Sole intercipian-<lb/>tur dies 29. </s> <s xml:id="echoid-s2879" xml:space="preserve">horæ 12. </s> <s xml:id="echoid-s2880" xml:space="preserve">fere. </s> <s xml:id="echoid-s2881" xml:space="preserve">Tale autem ſpacium menſis Lunaris appellari con-<lb/>ſueuit. </s> <s xml:id="echoid-s2882" xml:space="preserve">Verum hæc omnia accurratius, atque præciſius explicantur in Theo-<lb/>ricis Planetarum.</s> <s xml:id="echoid-s2883" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2884" xml:space="preserve"><emph style="sc">Caetervm</emph> periodi motuum Planetarũ intelligi debent non de orbi-<lb/> <anchor type="note" xlink:label="note-093-01a" xlink:href="note-093-01"/> bus, ſeu cęlis totalibus, ſed de proprijs orbibus planetas deferentibus, qui qui-<lb/>dem ſunt eccentrici in medio cælorum collocati. </s> <s xml:id="echoid-s2885" xml:space="preserve">In his namque planetæ, vel <lb/>eorum epicycli, infixi deferuntur temporibus prædictis. </s> <s xml:id="echoid-s2886" xml:space="preserve">Totales enim cęli pla <lb/>netarum mouentur ab occidente in orientem eadem prorſus tarditate, qua <lb/>nonum cęlum mouetur. </s> <s xml:id="echoid-s2887" xml:space="preserve">Rurſus mouentur motu trepidationis ad motũ octa-<lb/>uæ ſphæræ: </s> <s xml:id="echoid-s2888" xml:space="preserve">Nullus tamen planeta inferior mouetur ad motum proprium pla-<lb/>netæ ſuperioris, eo quòd non circa idem cẽtrum proprijs lationibus feruntur; <lb/></s> <s xml:id="echoid-s2889" xml:space="preserve">vt copioſius in theoricis Planetarum explicari ſolet.</s> <s xml:id="echoid-s2890" xml:space="preserve"/> </p> <div xml:id="echoid-div168" type="float" level="2" n="4"> <note position="right" xlink:label="note-093-01" xlink:href="note-093-01a" xml:space="preserve">Penes quos <lb/>orbes intel-<lb/>ligi debeãt <lb/>periodi mo <lb/>tuum Pla-<lb/>netarum.</note> </div> <p> <s xml:id="echoid-s2891" xml:space="preserve"><emph style="sc">Non</emph> eſt quoque prętereundum, hos nouem orbes infra primum mobile <lb/>eiſdem temporibus omnino curſus ſuos eſſe abſoluturos, quo n<unsure/>unc eos abſol-<lb/>unnt, & </s> <s xml:id="echoid-s2892" xml:space="preserve">non citius, etiamſi primum mobile quieſceret, vel eos ſecum non ra-<lb/>peret ab oriente in occidẽtem: </s> <s xml:id="echoid-s2893" xml:space="preserve">Sicut patet in Nauclero, qui motu proprio mo-<lb/>uetur contra motum nauis; </s> <s xml:id="echoid-s2894" xml:space="preserve">vel etiam in formica, quæ contra impetum rotæ <lb/>fertur: </s> <s xml:id="echoid-s2895" xml:space="preserve">Verum tunc ſimpliciter ab occidente in orientem deferrentur, quia<unsure/> <lb/>nullum tunc datetur inſtans poſt aliud, quo non magis ab occidente recede-<lb/>rent, & </s> <s xml:id="echoid-s2896" xml:space="preserve">ad orientem accederent; </s> <s xml:id="echoid-s2897" xml:space="preserve">Quemadmodum Nauclerus ille, manente na-<lb/>ui immobili, eodem rempore ad puppim perueniret, & </s> <s xml:id="echoid-s2898" xml:space="preserve">ſimpliciter ad oriẽtem <lb/>non autem ſolum ad partes nauis orientales, accederet.</s> <s xml:id="echoid-s2899" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div170" type="section" level="1" n="57"> <head xml:id="echoid-head61" style="it" xml:space="preserve">QVOMODO DEPREHENSVM SIT OMNES <lb/>cælos ſimpliciter ab ortu in occaſum moueri.</head> <p> <s xml:id="echoid-s2900" xml:space="preserve"><emph style="sc">Expositis</emph> tribus motibus cælorum in genere, quorum vnum dixi-<lb/>mus eſſe ab ortu in occaſum ſimpliciter alterum ab occaſu in ortum ſecũdum <lb/>quid, id eſt, à ſignis occidentalibus ad ſigna orientalia, tertium denique acceſ-<lb/>ſus, & </s> <s xml:id="echoid-s2901" xml:space="preserve">receſſus, quem motum trepidationis appellant; </s> <s xml:id="echoid-s2902" xml:space="preserve">Declarandum iam eſt, <lb/>quanam via, & </s> <s xml:id="echoid-s2903" xml:space="preserve">methodo triplicem hunc motum in corporibus cæleſtis de- <pb o="58" file="094" n="95" rhead="Comment. in I. Cap. Sphæræ"/> prehenderint Aſtronomi. </s> <s xml:id="echoid-s2904" xml:space="preserve">Omnes igitur cælos moueri ab oriente in occide@<emph style="sub">c</emph> <lb/> <anchor type="note" xlink:label="note-094-01a" xlink:href="note-094-01"/> tem, experientia quotidiana didicerunt: </s> <s xml:id="echoid-s2905" xml:space="preserve">Viderunt namque Solem, Lunam, a <lb/>reliquas ſtellas omnes, ex parte orientis paulatim aſcendere, & </s> <s xml:id="echoid-s2906" xml:space="preserve">eleuari ſupra <lb/>Horizontem, donec ad Meridianum peruenirent, atque hinc turſur declinare <lb/>in occidentem, donec iterum in oriente reperir<unsure/>entur. </s> <s xml:id="echoid-s2907" xml:space="preserve">Ex qua conſideratione <lb/>facile, & </s> <s xml:id="echoid-s2908" xml:space="preserve">non dubitanter concluſerunt motum omuium cęlorum ab oriente in <lb/>occidentem.</s> <s xml:id="echoid-s2909" xml:space="preserve"/> </p> <div xml:id="echoid-div170" type="float" level="2" n="1"> <note position="left" xlink:label="note-094-01" xlink:href="note-094-01a" xml:space="preserve">Motus ab <lb/>ortu in oc-<lb/>caſum quo <lb/>pacto depre <lb/>@enſus ſit.</note> </div> <p> <s xml:id="echoid-s2910" xml:space="preserve"><emph style="sc">Qvod</emph> autem motus iſte ſimpliciter fiat ab oriente, hoc eſt, ſemper ab <lb/>oriente recedat, & </s> <s xml:id="echoid-s2911" xml:space="preserve">occidenti appropinquet, multiplici via collegerunt. </s> <s xml:id="echoid-s2912" xml:space="preserve">Primũ <lb/>ex vmbra corporum. </s> <s xml:id="echoid-s2913" xml:space="preserve">Ab ortu enim Solis vſque ad meridiem umbræ omnes in <lb/>Horizontem proiectæ decreſcunt continue, ita vt in meridie vmbræ fiant mi-<lb/>nimæ, à meridie vero vſque ad Solis occaſum iterum augentur: </s> <s xml:id="echoid-s2914" xml:space="preserve">quod nulla ra-<lb/>tione fieri poſſet, niſi Sol continue laberetur ab ortu in occaſum. </s> <s xml:id="echoid-s2915" xml:space="preserve">Idem dice@ <lb/>de Luna, cuius vmbræ ſemper decreſcunt, dum ab ortu ad Meridianum moue-<lb/>tur, iterum vero augentur, dum à Meridiano ad occaſum vergit. </s> <s xml:id="echoid-s2916" xml:space="preserve">Secundo ex <lb/>altitudinibus ſtellarum, quæ ab ortu ipſarum ſemper maiores fiunt, donec ad <lb/>Meridianum circulum perueniant, vbi maximas obtinent nltitudines: </s> <s xml:id="echoid-s2917" xml:space="preserve">A Me-<lb/>ridiano vero circulo vſque ad occaſum earundem altitudinum decrementum <lb/>perpetuo ſuſcipiunt: </s> <s xml:id="echoid-s2918" xml:space="preserve">Quod quidem manifeſtum inditium eſt, eas ſimpliciter <lb/>ab oriente diſcedere, & </s> <s xml:id="echoid-s2919" xml:space="preserve">occidenti appropinquare.</s> <s xml:id="echoid-s2920" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div172" type="section" level="1" n="58"> <head xml:id="echoid-head62" style="it" xml:space="preserve">QVA RATIONE COLLECTVS SIT MOTVS <lb/>Cælorum ab occaſu in ortum.</head> <p> <s xml:id="echoid-s2921" xml:space="preserve"><emph style="sc">Etsi</emph> omnes cæli ſimpliciter ab ortu in occaſum feruntur, vt nuper oſtẽ-<lb/>dimus, deprehenſum tamen eſt, eos rurſus ab occaſu in ortum cieri, non qui-<lb/>dem ſimpliciter, cum ſimpliciter ſolum ab ortu in occaſum moueantur, vt iam <lb/>oſtenſum eſt, ſed ſecundum quid, petendo videlicet figna orientalia, ad ſenſum <lb/>ſuperius expoſitum. </s> <s xml:id="echoid-s2922" xml:space="preserve">Hoc autem prius deprehenderunt in 7. </s> <s xml:id="echoid-s2923" xml:space="preserve">Planetis, vt colli-<lb/>gitur à Ioanne de Regiomonte in Epitome Almageſti Ptolemęi lib. </s> <s xml:id="echoid-s2924" xml:space="preserve">1. </s> <s xml:id="echoid-s2925" xml:space="preserve">concl. <lb/></s> <s xml:id="echoid-s2926" xml:space="preserve">6. </s> <s xml:id="echoid-s2927" xml:space="preserve">hac ratione. </s> <s xml:id="echoid-s2928" xml:space="preserve">Obſeruarunt Aſtronomi, Solem & </s> <s xml:id="echoid-s2929" xml:space="preserve">Lunam, & </s> <s xml:id="echoid-s2930" xml:space="preserve">reliquos Plane-<lb/>tas, non habere ſemper eundem inter ſe ſitum & </s> <s xml:id="echoid-s2931" xml:space="preserve">diſtantiam; </s> <s xml:id="echoid-s2932" xml:space="preserve">ſed Lunam v.</s> <s xml:id="echoid-s2933" xml:space="preserve">g. </s> <s xml:id="echoid-s2934" xml:space="preserve"><lb/>vno die eſſe coniunctam cum Sole, alio vero ab eo receſſiſſe verſus partes oriẽ <lb/>tales: </s> <s xml:id="echoid-s2935" xml:space="preserve">non ſolum autem hanc diuerſitatem in vno planeta reſpectu alterius <lb/>inuenerunt, verum etiam in omnibus planetis reſpectu ſtellarum fixarum: </s> <s xml:id="echoid-s2936" xml:space="preserve">Cõ-<lb/>ſpexerunt enim hunc, vel illum planetam, vno die eſſe cum tali ſtella fixa con-<lb/>iunctum, aut in tali gradu alicuius ſigni exiſtere, alio vero die diſceſſiſſe ab illa <lb/>ſtella, ſeu gradu, verſus partes orientaliores, vt luce clarius nos etiam quoti-<lb/>die experimur. </s> <s xml:id="echoid-s2937" xml:space="preserve">Nulla igitur ratione dubitari poteſt, ſeptem orbes planetarum <lb/>præter motum diurnum ab oriente in occidentem, moueri quoque paulatim, <lb/>& </s> <s xml:id="echoid-s2938" xml:space="preserve">retrocedere quodammodo ab occiden te in orientem, hoc eſt, ad partes cæ-<lb/>li orientales, vt expoſuimus.</s> <s xml:id="echoid-s2939" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2940" xml:space="preserve"><emph style="sc">Neqve</emph> vero diuerſa via repererunt octauum etiam cælum ab occidente <lb/>in orientem moueri. </s> <s xml:id="echoid-s2941" xml:space="preserve">Quamuis enim antiqui fere omnes ante Ariſtotelem <lb/>crediderint, ſtellatum illud cælum vnico tantum illo motu cieri ab oriente <lb/>in occidentem, quoniam videlicet cernebant omnes ſtellas fixas eaſdem inter <lb/>ſe ſeruare diſtantias, locaq́; </s> <s xml:id="echoid-s2942" xml:space="preserve">ortuum, & </s> <s xml:id="echoid-s2943" xml:space="preserve">occaſuũ earundem in eodem Horizon-<lb/>te non variari, ſed ſemper in eiſdem locis eas oriri & </s> <s xml:id="echoid-s2944" xml:space="preserve">occidere, ob exiguum <pb o="59" file="095" n="96" rhead="Ioan. de Sacro Boſco."/> temporis interuallũ, in quo hæc obſeruabant: </s> <s xml:id="echoid-s2945" xml:space="preserve">Tamen poſt Ariſtotelem multò <lb/>ſecus rem ſeſe habere deprehenſum eſt. </s> <s xml:id="echoid-s2946" xml:space="preserve">Nam, ut ait Ptolemæus Dictione ſe-<lb/>ptima cap. </s> <s xml:id="echoid-s2947" xml:space="preserve">2. </s> <s xml:id="echoid-s2948" xml:space="preserve">& </s> <s xml:id="echoid-s2949" xml:space="preserve">Ioan. </s> <s xml:id="echoid-s2950" xml:space="preserve">Regiomont. </s> <s xml:id="echoid-s2951" xml:space="preserve">in Epitome eiuſdem Dictionis propoſ. </s> <s xml:id="echoid-s2952" xml:space="preserve">2. <lb/></s> <s xml:id="echoid-s2953" xml:space="preserve">Diſt antię ſtellarum fixarum à punctis Solſtitialibus & </s> <s xml:id="echoid-s2954" xml:space="preserve">Aequinoctialibus non <lb/>manent eędẽ ſemper, ſed creſcunt, & </s> <s xml:id="echoid-s2955" xml:space="preserve">augentur ſecundũ ſucceſſionem ſignorũ, <lb/>ideſt, uerſus orientales partes progrediendo, ita ut plurimæ ſtellę, quæ anti-<lb/>quo tempore fuerunt ante puncta ſolſtitialia, & </s> <s xml:id="echoid-s2956" xml:space="preserve">Aequinoctialia, modo repe-<lb/>riantur poſt ipſa puncta Solſtirialia & </s> <s xml:id="echoid-s2957" xml:space="preserve">Aequinoctialia, aliæ uero ſtellæ pro-<lb/>pius ad illa puucta acceſſerint, ut ex obſeruationibus antiquorum, & </s> <s xml:id="echoid-s2958" xml:space="preserve">recentio <lb/>rum liquido conſtat: </s> <s xml:id="echoid-s2959" xml:space="preserve">Et quo maius tempus inter conſiderationes antiquorum, <lb/>& </s> <s xml:id="echoid-s2960" xml:space="preserve">recentiorem intercedit, eo etiam magis inueniantur à ſedibus, locisq́ue <lb/>antiquis ſtellę ſecundum ſucceſſionem ſignorum elongatæ: </s> <s xml:id="echoid-s2961" xml:space="preserve">cuius rei plurima <lb/>exempla in medium adducũt Ptolemæus, & </s> <s xml:id="echoid-s2962" xml:space="preserve">Ioan. </s> <s xml:id="echoid-s2963" xml:space="preserve">Regiomon. </s> <s xml:id="echoid-s2964" xml:space="preserve">locis eitatis: </s> <s xml:id="echoid-s2965" xml:space="preserve">Nos <lb/>unum aut alterũ duntaxat afferemus. </s> <s xml:id="echoid-s2966" xml:space="preserve">Timocharis obſeruãs curſum ſtellarum, <lb/>reperit ſtellam Azimech, quã Latini ſpicã uirginis dicunt, ante punctũ Aequi <lb/>noctij autu mnalis, id eſt, ante principiũ ♎, primi mobilis, 8. </s> <s xml:id="echoid-s2967" xml:space="preserve">fere grad. </s> <s xml:id="echoid-s2968" xml:space="preserve">hoc eſt, <lb/>paulo poſt 22. </s> <s xml:id="echoid-s2969" xml:space="preserve">grad. </s> <s xml:id="echoid-s2970" xml:space="preserve">♍, fiue in principio 23. </s> <s xml:id="echoid-s2971" xml:space="preserve">grad. </s> <s xml:id="echoid-s2972" xml:space="preserve">♍. </s> <s xml:id="echoid-s2973" xml:space="preserve">Poſt hunc uero ducentis <lb/>fere annis elapſis, Abrachis, qui & </s> <s xml:id="echoid-s2974" xml:space="preserve">Hipparchus, eandem ſtellã reperit 6. </s> <s xml:id="echoid-s2975" xml:space="preserve">tantum <lb/>grad. </s> <s xml:id="echoid-s2976" xml:space="preserve">ante illud punctum, uidelicet in principio 25. </s> <s xml:id="echoid-s2977" xml:space="preserve">grad. </s> <s xml:id="echoid-s2978" xml:space="preserve">♍. </s> <s xml:id="echoid-s2979" xml:space="preserve">Et poſt hos Pt<unsure/>o-<lb/>lemæus eandem ſtellam plus acceſiſſe, ſecundum proportionem temporis in-<lb/>teriecti, ad principium ♎, inuenit. </s> <s xml:id="echoid-s2980" xml:space="preserve">Idemq́ue obſeruarunt Aſtronomi ipſum ſe <lb/>quentes, ut Albategnius, Aueneſra, Zachut, & </s> <s xml:id="echoid-s2981" xml:space="preserve">alij; </s> <s xml:id="echoid-s2982" xml:space="preserve">adeo ut hac noſtra tempe-<lb/>ſtate eadem ſtella exiſtat iam poſt principium ♎, nimirum in 17. </s> <s xml:id="echoid-s2983" xml:space="preserve">fere gradu <lb/>♎. </s> <s xml:id="echoid-s2984" xml:space="preserve">Rurſus Hipparchus inuenit ſtellam, quæ cor Leonis appellatur, in 50. </s> <s xml:id="echoid-s2985" xml:space="preserve"><lb/>min. </s> <s xml:id="echoid-s2986" xml:space="preserve">ultimi grad. </s> <s xml:id="echoid-s2987" xml:space="preserve">♋: </s> <s xml:id="echoid-s2988" xml:space="preserve">At poſt ipſum Ptolemæus eandem reperit exiſtere in <lb/>30. </s> <s xml:id="echoid-s2989" xml:space="preserve">min. </s> <s xml:id="echoid-s2990" xml:space="preserve">tertij gradus ♌: </s> <s xml:id="echoid-s2991" xml:space="preserve">Nunc uero eadem ſtella in 22. </s> <s xml:id="echoid-s2992" xml:space="preserve">fere gradu ♌. </s> <s xml:id="echoid-s2993" xml:space="preserve">exi-<lb/>ſtit. </s> <s xml:id="echoid-s2994" xml:space="preserve">Ex his igitur, & </s> <s xml:id="echoid-s2995" xml:space="preserve">plurimis alijs exemplis perſpicue colligitur, omnes orbes <lb/>cæleſtes infra primum mobile, præter diurnum motum, moueri quoque ſecũ-<lb/>dum ſucceſſionem ſignorum ab occidente in orientem, ſecundum quid tamẽ, <lb/>hoc eſt, uti explicuimus, ad partes orientales. </s> <s xml:id="echoid-s2996" xml:space="preserve">Sienim ſolum motu diurno mo-<lb/>uerentur, neceſſario æqualiter diſtarent ſtellæ omnes, & </s> <s xml:id="echoid-s2997" xml:space="preserve">planetæ, à quatuor il <lb/>lis punctis prædictis. </s> <s xml:id="echoid-s2998" xml:space="preserve">Cuius oppoſitum oſtendunt obſeruationes doctiſſimorũ <lb/>Aſtronomorum. </s> <s xml:id="echoid-s2999" xml:space="preserve">Neque uero quiſquam dubitare debet, recte ab Aſtronomis <lb/>prædictis loca ſtellarum inuenta eſſe. </s> <s xml:id="echoid-s3000" xml:space="preserve">Inter cętera enim inſtrumenta, quę plu-<lb/>rima ſunt pro ſtellarum locis explorandis excogitata ab artificibus, præſtan-<lb/>tiſſimum eſt illud, quod Armillam Ptolemæi dicun<unsure/>t cuius conſtructio doce-<lb/>tur in 5. </s> <s xml:id="echoid-s3001" xml:space="preserve">Dictione Almageſti.</s> <s xml:id="echoid-s3002" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div173" type="section" level="1" n="59"> <head xml:id="echoid-head63" style="it" xml:space="preserve">QVA INDVSTRIA CAELOS INFERIORES <lb/>ab Occaſu in Ortum ſuper diuerſos polos à polis mundi <lb/>moueri obſeruatum ſit.</head> <p> <s xml:id="echoid-s3003" xml:space="preserve"><emph style="sc">Divtvrna</emph> obſeruatione deprehenderunt Aſtronomi, cælos inferio-<lb/> <anchor type="note" xlink:label="note-095-01a" xlink:href="note-095-01"/> res non<unsure/> moueri ab occaſu in ortum ſuper polos mundi, & </s> <s xml:id="echoid-s3004" xml:space="preserve">per circulum æqui <lb/>noctialem, ſed ſuper polos diſtinctos, nempe ſuper polos Zodiaci, & </s> <s xml:id="echoid-s3005" xml:space="preserve">per circu <lb/>lum Zodiacum. </s> <s xml:id="echoid-s3006" xml:space="preserve">Planetę enim omnes uariant ſemper puncta ortus, & </s> <s xml:id="echoid-s3007" xml:space="preserve">occa-<lb/>ſus in Horizonte: </s> <s xml:id="echoid-s3008" xml:space="preserve">Quod luce Clarius in Sole deprehenditur. </s> <s xml:id="echoid-s3009" xml:space="preserve">Modo enim ori- <pb o="60" file="096" n="97" rhead="Comment. In I. Cap. Sphæræ"/> tur iuxta Aequinoctialem, modo ultra, modo denique citra; </s> <s xml:id="echoid-s3010" xml:space="preserve">quæ diuerſitas <lb/> <anchor type="note" xlink:label="note-096-01a" xlink:href="note-096-01"/> locum non haberet, ſi moueretur Sol ab occidente in orientem ſuper polos <lb/>mundi, & </s> <s xml:id="echoid-s3011" xml:space="preserve">per circulum ęquinoctialem: </s> <s xml:id="echoid-s3012" xml:space="preserve">Ita enim in eodem ſemper puncto Ho <lb/>rizontis oriretur, quemadmodum & </s> <s xml:id="echoid-s3013" xml:space="preserve">paralleli Aequatoris, in quorum uno ali-<lb/>quo Sol neceſſario fertur motu diurno, in eiſdem ſemper punctis Horizon-<lb/>tem interſecant: </s> <s xml:id="echoid-s3014" xml:space="preserve">Idemq́ue in alijs planetis obſeruatum fuit. </s> <s xml:id="echoid-s3015" xml:space="preserve">Rurſus non ſem-<lb/>per ſeruant eandem diſtantiam à polis mundi, ſed n@nc quidem accedunt ad <lb/>polum arcticum, nunc uer<unsure/>o ad antarcticum; </s> <s xml:id="echoid-s3016" xml:space="preserve">quod facile colligitur, eo quòd <lb/>non habent ſemper eandem altitudinem meridianam; </s> <s xml:id="echoid-s3017" xml:space="preserve">maximam ſiquidem al-<lb/>titudinem meridianam Sol deprehenditur habere in tropico ♋, minimam ve <lb/>ro in tropico ♑, ut perſpicuum eſſe poteſt ex umbra meridiana alicuius ſty-<lb/>li, quæ minima exiſtit, Sole commorante in ♋, longiſſima uero, eodem exi-<lb/>ſtente in ♑. </s> <s xml:id="echoid-s3018" xml:space="preserve">Vnde etiam fit, ut non ſemper eoſdem parallelos ad motum diur-<lb/>num deſcribant Planetæ. </s> <s xml:id="echoid-s3019" xml:space="preserve">Certiſſima igitur ratione concluditur, planetas ſu-<lb/>per diuerſos polos tendere ab occaſu in ortum. </s> <s xml:id="echoid-s3020" xml:space="preserve">Et quo niam animaduerterunt <lb/>Aſtronomi, hãc diuerſitatem motus Solis, cæterorumq́; </s> <s xml:id="echoid-s3021" xml:space="preserve">planetarũ, fere eiſdem <lb/>limitibus claudi, circumferriq́. </s> <s xml:id="echoid-s3022" xml:space="preserve">eos in circulo, cuius declinatio maxima ab ęqui <lb/>ctionali comprehendit grad. </s> <s xml:id="echoid-s3023" xml:space="preserve">23. </s> <s xml:id="echoid-s3024" xml:space="preserve">& </s> <s xml:id="echoid-s3025" xml:space="preserve">ſemis, & </s> <s xml:id="echoid-s3026" xml:space="preserve">cuius conſequenter poli totidem <lb/>gradibus à mundi polis diſtant, aſſeruerunt, hunc motum ſieri ſuper polos Zo <lb/>diaci, & </s> <s xml:id="echoid-s3027" xml:space="preserve">per circulum Zodiacum. </s> <s xml:id="echoid-s3028" xml:space="preserve">Quo poſito, facillime omnes diuerſitates <lb/>prædictæ locum habent, ut in ſphæra aliqua materiali perſpicue cerni poteſt.</s> <s xml:id="echoid-s3029" xml:space="preserve"/> </p> <div xml:id="echoid-div173" type="float" level="2" n="1"> <note position="right" xlink:label="note-095-01" xlink:href="note-095-01a" xml:space="preserve">Cœlos infe <lb/>riores mo-<lb/>neri ab oc-<lb/>c<unsure/>aſu in er-<lb/>tum ſupe@ <lb/>polos Ze.</note> <note position="left" xlink:label="note-096-01" xlink:href="note-096-01a" xml:space="preserve">diaci, qua <lb/>via ſitobſer <lb/>uatum.</note> </div> <p> <s xml:id="echoid-s3030" xml:space="preserve"><emph style="sc">Omnia</emph> uero hæc infallibili ratione in ſphæra quoque octaua deprehen-<lb/>ſa fuere. </s> <s xml:id="echoid-s3031" xml:space="preserve">Poſtquam enim diligentiſſimi illi ſtellarum obſeruatores intellexe-<lb/>runt, ſtellas fixas ſenſim ab occidente tenderein orientem, animaduerterunt <lb/>hunc motum fieri ſuper diſtinctos polos à polis mundi. </s> <s xml:id="echoid-s3032" xml:space="preserve">Nam non ſemper in <lb/>eiſdem locis ortę ſunt ſtellę, in quibus nũc oriuntur, reſpectu eiuſdẽ Horizon <lb/>tis: </s> <s xml:id="echoid-s3033" xml:space="preserve">Pari ratione altitudines meridianę ſtellarum fixarum diuerſę exiſtunt hoc <lb/>tempore ab ijs, quas antiqui Aſtronomi obſeruarunt. </s> <s xml:id="echoid-s3034" xml:space="preserve">Non igitur ſuper polos <lb/>mundi reuertuntur ab occideme in orientem ſtellæ fixæ. </s> <s xml:id="echoid-s3035" xml:space="preserve">Præterea ſtellę fixę, <lb/>ut Ptolemæus Dict. </s> <s xml:id="echoid-s3036" xml:space="preserve">7. </s> <s xml:id="echoid-s3037" xml:space="preserve">cap. </s> <s xml:id="echoid-s3038" xml:space="preserve">3. </s> <s xml:id="echoid-s3039" xml:space="preserve">& </s> <s xml:id="echoid-s3040" xml:space="preserve">Ioan. </s> <s xml:id="echoid-s3041" xml:space="preserve">de Regiom. </s> <s xml:id="echoid-s3042" xml:space="preserve">in Epitome eiuſdẽ Dictionis <lb/>aſſerunt, multisq́. </s> <s xml:id="echoid-s3043" xml:space="preserve">obſeruationibus comprobant, non ſemper æqualem diſtan-<lb/>tiam cum æquinoctiali circulo habent. </s> <s xml:id="echoid-s3044" xml:space="preserve">Declinationes etenim earum ab æqui <lb/>noctiali circulo uarię repertæ fuerunt, ita ut earum ſtellarum, quæ ſunt in me <lb/>dietate ſphærę, quę eſt à principio ♑, per ♈, ad principium ♋, uſque, decli-<lb/>nationes auſtrales quidẽ diminutæ, ſeptentrionales uero auctę fuerint. </s> <s xml:id="echoid-s3045" xml:space="preserve">E con-<lb/>trario uerò illarum ſtellatũ, quæ ſunt in reliqua medietate ſphęrę, quæ con-<lb/>tinetur à principio ♋, per ♎, uſq. </s> <s xml:id="echoid-s3046" xml:space="preserve">ad principiũ ♑, declinationes auſtrales qui <lb/>dem augeri, ſeptentrionales uero diminui repertæ ſint; </s> <s xml:id="echoid-s3047" xml:space="preserve">(Declinationem auſtra <lb/>lem dicimus habere illam ſtellam, quæ ab ęquinoctiali circulo uerſus polum <lb/>antarcticum declinat. </s> <s xml:id="echoid-s3048" xml:space="preserve">Septentrionalem uero eã ſtellam, quæ ab eodem circu-<lb/>lo ad arcticum polum uergit) Et quò propinquiores ſunt ſtellæ principio ♈, & </s> <s xml:id="echoid-s3049" xml:space="preserve"><lb/>♎, primi mobilis, eò maior diuer<unsure/>ſitas declinationis apparuerit; </s> <s xml:id="echoid-s3050" xml:space="preserve">Quò autem <lb/>propinquiores principio ♋, & </s> <s xml:id="echoid-s3051" xml:space="preserve">principio ♎, eò minorem uarietatẽ declina-<lb/>tionis ſuſceperint. </s> <s xml:id="echoid-s3052" xml:space="preserve">Quod ut melius intelligatur, adducam unum aut alterum <lb/>exemplum ex Ptolemęo, & </s> <s xml:id="echoid-s3053" xml:space="preserve">Ioan. </s> <s xml:id="echoid-s3054" xml:space="preserve">Regiom. </s> <s xml:id="echoid-s3055" xml:space="preserve">Stella, quæ uocatur a Latinis ocu-<lb/>lus ♉, tempore Timocharis declinabat ab Aequinoctiali uerſus ſeptentrionẽ <lb/>grad. </s> <s xml:id="echoid-s3056" xml:space="preserve">8. </s> <s xml:id="echoid-s3057" xml:space="preserve">& </s> <s xml:id="echoid-s3058" xml:space="preserve">ſemis, & </s> <s xml:id="echoid-s3059" xml:space="preserve">paulo amplius: </s> <s xml:id="echoid-s3060" xml:space="preserve">Tempore uero Abrachis, ſiue Hypparchi, <lb/>grad. </s> <s xml:id="echoid-s3061" xml:space="preserve">9. </s> <s xml:id="echoid-s3062" xml:space="preserve">min. </s> <s xml:id="echoid-s3063" xml:space="preserve">45. </s> <s xml:id="echoid-s3064" xml:space="preserve">Tempore deinde Ptolemæi grad. </s> <s xml:id="echoid-s3065" xml:space="preserve">11. </s> <s xml:id="echoid-s3066" xml:space="preserve">fere: </s> <s xml:id="echoid-s3067" xml:space="preserve">Noſtro deniq. </s> <s xml:id="echoid-s3068" xml:space="preserve">tẽpore <pb o="61" file="097" n="98" rhead="Ioan. de Sacro Boſco."/> grad. </s> <s xml:id="echoid-s3069" xml:space="preserve">quaſi 16. </s> <s xml:id="echoid-s3070" xml:space="preserve">Conſtat igitur huius ſtellæ declinationem ſeptentrionalẽ ſem <lb/>per incrementum ſuſcepiſſe, quoniam nimrum exiſtit in medietate ſphæræ, <lb/>quæ a principio ♑, per ♈, ad principium ♋, porrigitur. </s> <s xml:id="echoid-s3071" xml:space="preserve">Similiter Alhabor, <lb/>quæ ſtella dicit̃ canis maior, (eſt enim hæc ſtella in ore canis maioris, & </s> <s xml:id="echoid-s3072" xml:space="preserve">tem <lb/>pore antiquorum exiſtebat in eadem ſphæræ medietate) tẽpore Timocharis <lb/>habuit declinationem auſtralem ſiue meridionalem grad. </s> <s xml:id="echoid-s3073" xml:space="preserve">16. </s> <s xml:id="echoid-s3074" xml:space="preserve">min. </s> <s xml:id="echoid-s3075" xml:space="preserve">20. </s> <s xml:id="echoid-s3076" xml:space="preserve">Tempo <lb/>re deinde Abrachis ſiue Hipparchi grad. </s> <s xml:id="echoid-s3077" xml:space="preserve">16. </s> <s xml:id="echoid-s3078" xml:space="preserve">duntaxat: </s> <s xml:id="echoid-s3079" xml:space="preserve">Tempore deniq; </s> <s xml:id="echoid-s3080" xml:space="preserve">Pto-<lb/>lemæi grad. </s> <s xml:id="echoid-s3081" xml:space="preserve">15. </s> <s xml:id="echoid-s3082" xml:space="preserve">min. </s> <s xml:id="echoid-s3083" xml:space="preserve">35. </s> <s xml:id="echoid-s3084" xml:space="preserve">Vbi etiam perſpicuum eſt, ſemper decreuiſſe declina <lb/>tionem auſtralem: </s> <s xml:id="echoid-s3085" xml:space="preserve">At vero hac noſtra tempeſtate, quoniã eadem ſtella repe-<lb/>ritur in altera ſphæræ medietate, habet iterũ deelinationem auſtralẽ grad. <lb/></s> <s xml:id="echoid-s3086" xml:space="preserve">16. </s> <s xml:id="echoid-s3087" xml:space="preserve">fere. </s> <s xml:id="echoid-s3088" xml:space="preserve">Vbi manifeſte perſpicitur, eandem declinationem auſtralem iam ite-<lb/>rum creſcere. </s> <s xml:id="echoid-s3089" xml:space="preserve">Poſtremo (plura enim huiuſmodi exempla inuenies apud Pto-<lb/>lemæũ, & </s> <s xml:id="echoid-s3090" xml:space="preserve">Ioan. </s> <s xml:id="echoid-s3091" xml:space="preserve">de Regiom.) </s> <s xml:id="echoid-s3092" xml:space="preserve">Azimech, quæ ſtella appellatur ſpica ♍, habuit <lb/>apud Timocharẽ declinationẽ ſeptẽtrionalẽ. </s> <s xml:id="echoid-s3093" xml:space="preserve">gra. </s> <s xml:id="echoid-s3094" xml:space="preserve">1. </s> <s xml:id="echoid-s3095" xml:space="preserve">mi. </s> <s xml:id="echoid-s3096" xml:space="preserve">24. </s> <s xml:id="echoid-s3097" xml:space="preserve">Apud Abrachim, <lb/>ſiue Hipparchum, ſolum min. </s> <s xml:id="echoid-s3098" xml:space="preserve">36. </s> <s xml:id="echoid-s3099" xml:space="preserve">Apud Ptol. </s> <s xml:id="echoid-s3100" xml:space="preserve">vero habuit declinationem au-<lb/>ſtralem min. </s> <s xml:id="echoid-s3101" xml:space="preserve">40. </s> <s xml:id="echoid-s3102" xml:space="preserve">Nunc autem reperitur habere declinationem auſtralem gra. </s> <s xml:id="echoid-s3103" xml:space="preserve"><lb/>8. </s> <s xml:id="echoid-s3104" xml:space="preserve">min. </s> <s xml:id="echoid-s3105" xml:space="preserve">20. </s> <s xml:id="echoid-s3106" xml:space="preserve">fere; </s> <s xml:id="echoid-s3107" xml:space="preserve">Ex quo exemplo liquido conſtat, huius ſtellæ declinationem <lb/>ſeptentrionalem (quoniam nimirum exiſtit in ea ſphæræ medietate, quæ cõ <lb/>prehenditur inter ♋, & </s> <s xml:id="echoid-s3108" xml:space="preserve">♑, per ♎, procedendo) ſemper decreuiſſe, meridio-<lb/>nalem uero auctam fuiſſe. </s> <s xml:id="echoid-s3109" xml:space="preserve">In his omnibus porro exemplis perſpicue intueri <lb/>licet, maiorem uarietatem declinationum accidiſſe prope æquinoctialem cir <lb/>culum, quam apud tropicos. </s> <s xml:id="echoid-s3110" xml:space="preserve">Firmiſſima ergo demonſtratione collegerunt <lb/>Aſtronomi, ſtellas fixas proprio motu ab occidente in orientem ferri, non <lb/>quidem ſuper polos mundi, ſed ſuper alios diſtinctos polos; </s> <s xml:id="echoid-s3111" xml:space="preserve">aliàs enim habe-<lb/>rent ſemper eandem & </s> <s xml:id="echoid-s3112" xml:space="preserve">inuariabilem ab æquinoctiali circulo declinationẽ, <lb/>quod cum obſeruationibus Aſtronomorum pugnat.</s> <s xml:id="echoid-s3113" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3114" xml:space="preserve"><emph style="sc">Et</emph> quoniam cognouerunt ſtellas fixas, licet varient, ut dictum eſt, decli-<lb/>nationes ab æquinoctiali circulo, eandẽ tamen ſemper obtinere latitudinẽ, <lb/>hoc eſt, eandem diſtantiã ab ecliptica linea, quæ per medium Zodiacum tran <lb/>ſit, ut ex eorundem Aſtronomorũ obſeruationibus cõſtat. </s> <s xml:id="echoid-s3115" xml:space="preserve">Semper enim v.</s> <s xml:id="echoid-s3116" xml:space="preserve">g. <lb/></s> <s xml:id="echoid-s3117" xml:space="preserve">ſtella, q̃ uocatur Atctophylax, ſeu Arcturus, deprehẽſa eſt deflectere ab ecli-<lb/>ptica uerſus ſeptentrionẽ grad. </s> <s xml:id="echoid-s3118" xml:space="preserve">31. </s> <s xml:id="echoid-s3119" xml:space="preserve">min. </s> <s xml:id="echoid-s3120" xml:space="preserve">30. </s> <s xml:id="echoid-s3121" xml:space="preserve">idemq́; </s> <s xml:id="echoid-s3122" xml:space="preserve">proportione quadam in <lb/>alijs ſtellis fixis omnibus obſeruatũ fuit: </s> <s xml:id="echoid-s3123" xml:space="preserve">Neceſſaria ratiocinatione concludi-<lb/>tur, eas moueri præciſe ſuper polos Zodiaci, & </s> <s xml:id="echoid-s3124" xml:space="preserve">ſecundum circulum Zodiacũ; </s> <s xml:id="echoid-s3125" xml:space="preserve"><lb/>hoc enim poſito, deſcribent omnes ſtellæ ad motum ab occaſu in ortum cir <lb/>culos parallelos ipſi Zodiaco, æqualiterq́ue ſemper ab eodem diſtabunt.</s> <s xml:id="echoid-s3126" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">Duo argu-<lb/>menta ad-<lb/>uerſus mo <lb/>tum ſtella-<lb/>rum fixarũ <lb/>ab occaſu <lb/>in ortũ ſu-<lb/>per polos <lb/>Zodiaci, eo <lb/>ruinque ſo <lb/>lutio.</note> <p> <s xml:id="echoid-s3127" xml:space="preserve"><emph style="sc">Non</emph> poſſum hoc loco ſilentio præterire duo argumenta eruditiſſimi cu <lb/>iuſdam uiri, ac nobiliſſimi, qui nõ multis ab hinc annis floruit, quibus demõ-<lb/>ſtrare nititur in ſcriptis quibuſdã ad hanc rẽ confectis, quæ ego in cõgrega-<lb/>tione, quæ iuſſu ſummi Pontiſicis de Calẽdarij correctione Romæ nuper ha <lb/>bebatur, perlegi non indiligenter, fictitium omnino eſſe hunc motum ſtel-<lb/>larum fixarum ab occaſu in ortum ſuperpolos Zodiaci, ficta etiam eſſe om-<lb/>niailla phænomena, quibus Ptolemæus, alijq́ue Aſtronomi dictum motum <lb/>in ſcholas introducete conati ſunt. </s> <s xml:id="echoid-s3128" xml:space="preserve">Atgumenta enim hæc non parum nego <lb/>tij faceſſere poſſent cuiuis parum in ſtellarum cognitione uerſato, quæ ſunt <lb/>eiuſmodi. </s> <s xml:id="echoid-s3129" xml:space="preserve">Canopus, quæ ſtella lucidiſſima in temone argonauis exiſtit, in <lb/>Europa non cernitur, quòd ſit nimis auſtralis; </s> <s xml:id="echoid-s3130" xml:space="preserve">Alexandriæ autem, vt re-<lb/>fert Plinius lib. </s> <s xml:id="echoid-s3131" xml:space="preserve">primo Naturalis hiſtoriæ capit. </s> <s xml:id="echoid-s3132" xml:space="preserve">70. </s> <s xml:id="echoid-s3133" xml:space="preserve">quarta fere parte ſigni <pb o="62" file="098" n="99" rhead="Comment. in I. Cap. Sphæræ"/> vnius ſupra Horizontẽ eminebat tunc temporis in Meridiano circulo con-<lb/>ſtituta; </s> <s xml:id="echoid-s3134" xml:space="preserve">In inſula u<unsure/>ero Rhodo terram, ſeu Horizontem ſtringere quodammo <lb/>do uidebatur. </s> <s xml:id="echoid-s3135" xml:space="preserve">Cum ergo nunc, ut Mercatores referũt, eadem ſtella adhuc ra <lb/>dat quodammodo Horizontem eiuſdem inſulæ, quis non uidet, ſtellã illam <lb/>in eodem ſemper parallelo extitiſſe, atque adeo ſuper polos Zodiaci motũ <lb/>non fuiſſe? </s> <s xml:id="echoid-s3136" xml:space="preserve">Nã alias lata fuiſſet in circulo Eclipticæ Parallelo, qui oblique <lb/>interſecat parallelũ Aequatoris, atq; </s> <s xml:id="echoid-s3137" xml:space="preserve">adeo amplius non poſſet contingere i@ <lb/>lum Horizontem. </s> <s xml:id="echoid-s3138" xml:space="preserve">Præterea ſtella polaris in extremitate caudæ urſę minoris, <lb/>quæ abeſt à polo Zodiaci grad. </s> <s xml:id="echoid-s3139" xml:space="preserve">24. </s> <s xml:id="echoid-s3140" xml:space="preserve">& </s> <s xml:id="echoid-s3141" xml:space="preserve">prope polũ arcticũ exiſtit, ſi mouetur cir <lb/>ca polos Zodiaci, neceſſe eſt, ut aliqñ à polo mundi abfutura ſit gradibus fe-<lb/>re 47. </s> <s xml:id="echoid-s3142" xml:space="preserve">& </s> <s xml:id="echoid-s3143" xml:space="preserve">eo amplius, pro quãtitate nimitũ ſemidiametri illius paralleli, quẽ <lb/>circa polũ Zodiaci deſcribit, & </s> <s xml:id="echoid-s3144" xml:space="preserve">diſtãtiæ poli mũdi, à polo Zodiaci, ac ꝓinde <lb/>occaſura in Horizõte Romano, ubi polus arcticus grad. </s> <s xml:id="echoid-s3145" xml:space="preserve">42. </s> <s xml:id="echoid-s3146" xml:space="preserve">ferme ſupra Ho-<lb/>rizontẽ attollitur. </s> <s xml:id="echoid-s3147" xml:space="preserve">Cũ ergo ſtella polaris in tot ſeculis ſedẽ nõ videatur mu <lb/>taſſe reſpectu poli, veriſimile nõ eſt, eã motã eſſe ſuꝑ polos Zodiaci ab occa <lb/>ſu in ortum. </s> <s xml:id="echoid-s3148" xml:space="preserve">Quare fictitius omnino eſt motus ille, quem ſtellis fixis tribuũt <lb/>Aſtronomi: </s> <s xml:id="echoid-s3149" xml:space="preserve">alioquin ſtella polaris plus nũc diſtaret à polo mũdi, quàm olim: <lb/></s> <s xml:id="echoid-s3150" xml:space="preserve">quod falſum videtur. </s> <s xml:id="echoid-s3151" xml:space="preserve">Ad utrumque argumentũ ita reſpondemus. </s> <s xml:id="echoid-s3152" xml:space="preserve">Cum Cano <lb/>pus exiſtat circa Colurũ Solſtitiorũ, ita ut tempore Plinij paulo ante illum <lb/>extiterit, & </s> <s xml:id="echoid-s3153" xml:space="preserve">nunc paulo poſt eundẽ reperiatur, fit, ut parallelus Eclipticæ a <lb/>dicta ſtella ab occaſu in ortũ deſcriptus eo in loco fere coincidat cum paral-<lb/>lelo Aequatoris per eandẽ ſtellam ducto, ut in globo Aſtronomico appare-<lb/>re poteſt. </s> <s xml:id="echoid-s3154" xml:space="preserve">Vnde mirum non eſt, quod ſtella illa in 15. </s> <s xml:id="echoid-s3155" xml:space="preserve">gradibus, quos, ſecun-<lb/>dum Ptolemæi ſententiam, à tempore Plinij uſque ad noſtram æratem confe <lb/>cit ab occaſu in ortum, ſenſibiliter declinationem ab Aequatore non muta <lb/>uerit, ac proinde ſemper Horizontem Rhodi uiſa ſit radere; </s> <s xml:id="echoid-s3156" xml:space="preserve">quemadmodũ <lb/>& </s> <s xml:id="echoid-s3157" xml:space="preserve">Sol circa ſolſtitia in 23. </s> <s xml:id="echoid-s3158" xml:space="preserve">gradibus, quos in Ecliptica perambulat, (quorũ vn <lb/>decim ante, & </s> <s xml:id="echoid-s3159" xml:space="preserve">undecim poſt ſolſtitiũ utrumuis ſumuntur) uix dimidiato gra-<lb/>du declinationem mutat. </s> <s xml:id="echoid-s3160" xml:space="preserve">Futurum tamen erit, ut longo poſt tempore ſenſibi <lb/>liter ſtella illa declinationẽ mutet, atque adeo Horizontem Rhodi amplius <lb/>non tangat: </s> <s xml:id="echoid-s3161" xml:space="preserve">ſicuti & </s> <s xml:id="echoid-s3162" xml:space="preserve">aliarum ſtellarum declinationes mutatas eſſe videmus, <lb/>quia longius abſunt a Coluro ſolſtitiorum. </s> <s xml:id="echoid-s3163" xml:space="preserve">Quod uero attinet ad ſtellã po-<lb/>larem, reſpondemus, eam in taliloco cęli ſitam eſſe (ut ex globo Aſtronomi <lb/>co conſtat) ut ab Hipparcho, & </s> <s xml:id="echoid-s3164" xml:space="preserve">Prolemæo hucuſque motu illo ab occaſu in <lb/>ortum ſemper magis ac magis ad polum accedat. </s> <s xml:id="echoid-s3165" xml:space="preserve">Id quod re ipſa accidit. </s> <s xml:id="echoid-s3166" xml:space="preserve">Nã, <lb/>ut auctor eſt Ptolemæus lib. </s> <s xml:id="echoid-s3167" xml:space="preserve">1. </s> <s xml:id="echoid-s3168" xml:space="preserve">Geographiæ, cap. </s> <s xml:id="echoid-s3169" xml:space="preserve">7. </s> <s xml:id="echoid-s3170" xml:space="preserve">ſtella polaris tẽpore Hip-<lb/>parchi diſtabat à polo grad. </s> <s xml:id="echoid-s3171" xml:space="preserve">12. </s> <s xml:id="echoid-s3172" xml:space="preserve">min. </s> <s xml:id="echoid-s3173" xml:space="preserve">24. </s> <s xml:id="echoid-s3174" xml:space="preserve">nunc autem ſolum diſtat grad. </s> <s xml:id="echoid-s3175" xml:space="preserve">3. </s> <s xml:id="echoid-s3176" xml:space="preserve">& </s> <s xml:id="echoid-s3177" xml:space="preserve">ſe <lb/>mis, aut circiter. </s> <s xml:id="echoid-s3178" xml:space="preserve">Itaque ex hac mutatione potius confirmatur motus ſtellarũ <lb/>ab occaſu in ortum. </s> <s xml:id="echoid-s3179" xml:space="preserve">Succeſſu tamen temporis elongabitur eadem ſtella pola <lb/>ris a polo. </s> <s xml:id="echoid-s3180" xml:space="preserve">Ex his liquido cõſtare arbitror, duo illa argumenta non conclu-<lb/>dere, fictitium eſſe hunc motum ab occaſu in ortum in ſtellis fixis deprehen-<lb/>ſum. </s> <s xml:id="echoid-s3181" xml:space="preserve">Quare experientiis Aſtronomorum ſides habenda eft, donec in contra-<lb/>rium aliud quid afferatur, quo demonſtretur, vera nõ eſſe, quæ de motu ſtel-<lb/>larum ab occaſu in ortum ſuper polos Zodiaci traduntur ab Aſtronomis.</s> <s xml:id="echoid-s3182" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div175" type="section" level="1" n="60"> <head xml:id="echoid-head64" style="it" xml:space="preserve">PROPTER QV AE PHAENOMENA ASTROMI <lb/>motum trepidationis ſtellis fixis attribuerint.</head> <p> <s xml:id="echoid-s3183" xml:space="preserve"><emph style="sc">Qvoniam</emph> uero ſupra dictum eſt, ſtellas fixas non ſolum duplici iſto <pb o="63" file="099" n="100" rhead="Ioan. de Sacro Boſco"/> motu, quorũ unus eſt ab ortu in occaſum, alter uero ab occaſu in ortum, mo <lb/> <anchor type="note" xlink:label="note-099-01a" xlink:href="note-099-01"/> ueri, ſed habere etiam propriũ motũ acceſſus & </s> <s xml:id="echoid-s3184" xml:space="preserve">receſſus, quem trepidationis <lb/>dicunt: </s> <s xml:id="echoid-s3185" xml:space="preserve">oſtendendum nunc eſt, quæ phænomena, apparentiæve Aſtronomos <lb/>coegerint, ut hunc motum in cęlo ponerent. </s> <s xml:id="echoid-s3186" xml:space="preserve">Non paucienim motum hunc <lb/>omnino explodendum à ſcholis Aſtronomorũ, tanquam ridiculum, arbitrã <lb/>tur. </s> <s xml:id="echoid-s3187" xml:space="preserve">Primo ergo obſeruarũt, ſtellas fixas inæqualiter incedere ab occidẽte in <lb/>orientem: </s> <s xml:id="echoid-s3188" xml:space="preserve">Nunc enim velocius, nunc tardius, nunc nullo pacto moueri in Zo <lb/>diaco uidebantur, nunc uero retrocedere ab oriente in occidentem, p̃ter il-<lb/>lum motum diurnum, & </s> <s xml:id="echoid-s3189" xml:space="preserve">eandem nihilominus diſtantiam à centro mũdi ha <lb/>bere. </s> <s xml:id="echoid-s3190" xml:space="preserve">Quare dixerunt eas moueri à ſeptentrione in auſtum, & </s> <s xml:id="echoid-s3191" xml:space="preserve">contra, ut ſu-<lb/>pra declaratum fuit in motu illo acceſſus & </s> <s xml:id="echoid-s3192" xml:space="preserve">receſſus. </s> <s xml:id="echoid-s3193" xml:space="preserve">Propter hunc. </s> <s xml:id="echoid-s3194" xml:space="preserve">n. </s> <s xml:id="echoid-s3195" xml:space="preserve">motum <lb/>accidit tota iſta inæqualitas motus ſtellarum fixarum, ut facile intelligi po-<lb/>teſt ex aliquo inſtrumento materiali ad hanc rem fabricato. </s> <s xml:id="echoid-s3196" xml:space="preserve">Hanc quoque <lb/>Aſtronomi aſſerunt eſſe cãm, ꝙ tam uariæ opiniones exortæ ſint de quantita <lb/>te, ſiue periodo motus ſtellarum fixarum ab occidente in orientem. </s> <s xml:id="echoid-s3197" xml:space="preserve">Rurſus <lb/>animaduertunt, maximam ſolis declinationem uariam extitiſſe in diuerſis <lb/>temporibus, nunc. </s> <s xml:id="echoid-s3198" xml:space="preserve">ſ. </s> <s xml:id="echoid-s3199" xml:space="preserve">maiorem, nunc minorem; </s> <s xml:id="echoid-s3200" xml:space="preserve">ut in ſecundo capite dicemus. <lb/></s> <s xml:id="echoid-s3201" xml:space="preserve">Quamobrem coacti ſunt admittere hunc motum trepidationis, ut huius ua-<lb/>rietatis in maxima ſolis declinatione poſſent reddere cãm: </s> <s xml:id="echoid-s3202" xml:space="preserve">Poſito enim hoc <lb/>motu, ſequitur octauam ſphæram modo à ſeptentrione in auſtrum, modo ab <lb/>auſtro in ſeptentrionem declinare, & </s> <s xml:id="echoid-s3203" xml:space="preserve">ex conſequenti duos tropicos in orbe <lb/>Solari, aliquando propinquiores fieri æquinoctiali circulo, aliquando uero <lb/>magis ab eo diſtare, ut in theorica octauæ ſphæræ explicatur. </s> <s xml:id="echoid-s3204" xml:space="preserve">Poſtremo ob-<lb/>ſeruatum fuit ab illis, æquinoctia accidiſſe, antequam Sol ad ♈, primi mobi-<lb/>lis perueniret, aut ad ♎, immo poſtquam aliquando iam tranſiuerat princi-<lb/>pium ♈, aut ♎. </s> <s xml:id="echoid-s3205" xml:space="preserve">Pari ratione facta fuiſſe Solſtitia, etiamſi Sol non extiterit in <lb/>principio ♋, vel ♑. </s> <s xml:id="echoid-s3206" xml:space="preserve">Cum igitur Sol neceſſario reperiri debeat in Æquino-<lb/>ctiali circulo, ut fiat Æquinoctium. </s> <s xml:id="echoid-s3207" xml:space="preserve">Item in tropicis, ut contingant Solſtitia, <lb/>non potuit huius diuerſitatis alia cauſa aſſerri, præter motum trepidationis: </s> <s xml:id="echoid-s3208" xml:space="preserve"><lb/>Ad hũc enim motum facile conſequitut anticipatio illa Æquinoctiorum, & </s> <s xml:id="echoid-s3209" xml:space="preserve"><lb/>Solſtitiorum. </s> <s xml:id="echoid-s3210" xml:space="preserve">Hoc porro motu omnes quoque globi ſeptem planetarũ mo-<lb/>uentur, ita ut orbes omnium planetarum, concomitentur aſſidue Zodiacum <lb/>octauę ſphæræ. </s> <s xml:id="echoid-s3211" xml:space="preserve">Quemadmodum autem certum uidetur, ut uel motus trepi-<lb/>dationis, uel aliquid ſimile in octaua ſphæra concedatur, propter apparen-<lb/>tias dictas: </s> <s xml:id="echoid-s3212" xml:space="preserve">ita incertiſſimus eſt modus, quo eum Aſtronomi explicant: </s> <s xml:id="echoid-s3213" xml:space="preserve">ut ni-<lb/>mirum principia ♈, & </s> <s xml:id="echoid-s3214" xml:space="preserve">♎, octauæ ſphæræ deſcribant circulos circa initia ♈, <lb/>& </s> <s xml:id="echoid-s3215" xml:space="preserve">♎, nonæ ſphæræ, quorum ſemidametri contineant grad. </s> <s xml:id="echoid-s3216" xml:space="preserve">9. </s> <s xml:id="echoid-s3217" xml:space="preserve">cum ex hac po <lb/>fitione multa conſequantur, quæ cum experientia pugnare uidentur, ut in <lb/>theorica octauæ ſphæræ copioſe explicabimus.</s> <s xml:id="echoid-s3218" xml:space="preserve"/> </p> <div xml:id="echoid-div175" type="float" level="2" n="1"> <note position="right" xlink:label="note-099-01" xlink:href="note-099-01a" xml:space="preserve">Cur motus<unsure/> <lb/>trepidatio-<lb/>nis in cælo <lb/>ponatur ab <lb/>Aſtrono-<lb/>mis.</note> </div> </div> <div xml:id="echoid-div177" type="section" level="1" n="61"> <head xml:id="echoid-head65" xml:space="preserve">DE ORDINE SPÆRARVM CÆLESTIVM.</head> <p> <s xml:id="echoid-s3219" xml:space="preserve">Ex ijs, quę de motibus cælorũ dicta ſunt, perſpicuum relinquitur, cęlos <lb/>omnes unũ corpus continuũ minime efficere, propterea quòd cęli uarijs & </s> <s xml:id="echoid-s3220" xml:space="preserve"><lb/>diuerſis motibus quodammodo oppoſitis, ut dictum eſt, feruntur; </s> <s xml:id="echoid-s3221" xml:space="preserve">Nullũ au-<lb/>tem corpus cõtrarijs ſimul motibus ferri eſt aptũ. </s> <s xml:id="echoid-s3222" xml:space="preserve">Suntigitur omnes cęli ha <lb/>ctenus reperti concentrici cum mundo uniuerſo, atq. </s> <s xml:id="echoid-s3223" xml:space="preserve">contigui inter ſe, ita vt <lb/>inter quoslibet duos ꝓximos orbes nihil ſit intermediũ, quod ſit uel uacuũ, <pb o="64" file="100" n="101" rhead="Comment. in I. Cap. Sphæræ"/> uel corpus aliquod, ſed prorſus immediate ſeſe mutuo contingant, ut motus <lb/>ſuperioris orbis inferiori poſſit communicari. </s> <s xml:id="echoid-s3224" xml:space="preserve">Neque uero ualet argumẽtũ, <lb/>qd̃ communiter afferri ſolet ad probandum, cęlos non poſſe eſſe contiguos, <lb/>hoc modo. </s> <s xml:id="echoid-s3225" xml:space="preserve">Ducatur linea recta à centro mundi ad conuexũ v.</s> <s xml:id="echoid-s3226" xml:space="preserve">g. </s> <s xml:id="echoid-s3227" xml:space="preserve">decimi cęli, <lb/> <anchor type="note" xlink:label="note-100-01a" xlink:href="note-100-01"/> ſumaturq́; </s> <s xml:id="echoid-s3228" xml:space="preserve">punctum, quo lineailla tangit, ſeu ſecat conuexum noni orbis, <lb/>quod appelletur A; </s> <s xml:id="echoid-s3229" xml:space="preserve">capiatur pręterea punctum, quo eadem linea tangit, ſiue <lb/>interſecat concauum decimę ſphæræ, quod dicatur B. </s> <s xml:id="echoid-s3230" xml:space="preserve">Si igitur conuexũ no-<lb/>næ ſpheræ eſt immediatum, & </s> <s xml:id="echoid-s3231" xml:space="preserve">contiguum concauo decimę, erunt duo pũcta <lb/>A, & </s> <s xml:id="echoid-s3232" xml:space="preserve">B, in eadẽ linea exiſtentia inter ſeſe immediata, quod fieri nequit, vt pa <lb/>tet ex Ariſto. </s> <s xml:id="echoid-s3233" xml:space="preserve">6. </s> <s xml:id="echoid-s3234" xml:space="preserve">Phyſ. </s> <s xml:id="echoid-s3235" xml:space="preserve">Non igitur decimum cælum immediatum eſſe poteſt <lb/>nono cęlo: </s> <s xml:id="echoid-s3236" xml:space="preserve">ſimiliſq́ue eſt ratio de reliquis ſphæris cęleſtibus. </s> <s xml:id="echoid-s3237" xml:space="preserve">Non ualet, in-<lb/>quam, hoc argumentũ, quia unum & </s> <s xml:id="echoid-s3238" xml:space="preserve">idem punctum illius lineę tãgit conue <lb/>xum noni cęli & </s> <s xml:id="echoid-s3239" xml:space="preserve">concauum decimi: </s> <s xml:id="echoid-s3240" xml:space="preserve">quare illa duo puncta, quę concipiũtur <lb/>ibi, ſunt unum & </s> <s xml:id="echoid-s3241" xml:space="preserve">idem punctum, quoniam ſe inuicem tãgunt ſecundum ſe to <lb/>ta, cũ non habeant partes, & </s> <s xml:id="echoid-s3242" xml:space="preserve">idcirco in eodem exiſtũt loco, ſi tamen punctum <lb/>occupare locum dici poteſt. </s> <s xml:id="echoid-s3243" xml:space="preserve">Sunt igitur illa duo puncta duo quidẽ ratione, <lb/>unum aũt re ipſa, quoniam coincidunt, non ſecus, ac ſi duę lineę coniunge-<lb/>rentur per extrema earum puncta: </s> <s xml:id="echoid-s3244" xml:space="preserve">Coinciderent enim tunc prorſus duo illa <lb/>extrema puncta in vnũ. </s> <s xml:id="echoid-s3245" xml:space="preserve">Quod ſi argumentum aliquid concluderet, nulla duo <lb/>corpora poſſent unquã eſſe contigua, & </s> <s xml:id="echoid-s3246" xml:space="preserve">immediata, quod aperte falſum eſt, <lb/>vt perſpicuum eſt in globo aliquo poſito in aere; </s> <s xml:id="echoid-s3247" xml:space="preserve">Nihil enim intermediũ eſſe <lb/>poteſt inter globum & </s> <s xml:id="echoid-s3248" xml:space="preserve">aerem, aliàs daretur proceſſus in infinitũ & </s> <s xml:id="echoid-s3249" xml:space="preserve">tamen ſi <lb/>per centrum ipſius globi educeretur linea recta, tangeret utiq; </s> <s xml:id="echoid-s3250" xml:space="preserve">concauũ ae-<lb/>ris, & </s> <s xml:id="echoid-s3251" xml:space="preserve">conuexum globi. </s> <s xml:id="echoid-s3252" xml:space="preserve">Reſtat igitur cęlos eſſe à ſe inuicem ſeparatos, atque <lb/>contiguos, de quorum ordine nunc diſputandum eſt.</s> <s xml:id="echoid-s3253" xml:space="preserve"/> </p> <div xml:id="echoid-div177" type="float" level="2" n="1"> <note position="left" xlink:label="note-100-01" xlink:href="note-100-01a" xml:space="preserve">Cęols eſſe <lb/>immedia <lb/>@os interſe.</note> </div> <p> <s xml:id="echoid-s3254" xml:space="preserve"><emph style="sc">Ex</emph> <emph style="sc">Antiqvis</emph> igitur nonnulli, quorũ dux fuit Ariſtarchus Samius <lb/> <anchor type="note" xlink:label="note-100-02a" xlink:href="note-100-02"/> 400. </s> <s xml:id="echoid-s3255" xml:space="preserve">annis ante Ptolemęũ, quẽ ex recẽtioribus ſecutus eſt Nicolaus Coperni <lb/>cus in opere de reuolutionibus cęleſtibus, hunc ordinem inter corpora to-<lb/>tius Vniuerſi conſinxerunt: </s> <s xml:id="echoid-s3256" xml:space="preserve">ut Sol in centro, ſeu medio mundi immobilis ſit <lb/>collocatus; </s> <s xml:id="echoid-s3257" xml:space="preserve">circa quẽ orbis Mercurij; </s> <s xml:id="echoid-s3258" xml:space="preserve">deinde orbis Veneris; </s> <s xml:id="echoid-s3259" xml:space="preserve">circa hunc orbis <lb/>magnus, Terram una cum elementis, & </s> <s xml:id="echoid-s3260" xml:space="preserve">Luna continens; </s> <s xml:id="echoid-s3261" xml:space="preserve">circa quem orbis <lb/>Martis; </s> <s xml:id="echoid-s3262" xml:space="preserve">deinde cęlum Iouis; </s> <s xml:id="echoid-s3263" xml:space="preserve">poſtea globus Saturni; </s> <s xml:id="echoid-s3264" xml:space="preserve">vltimo tandem ſtellarum <lb/>ſixarum ſphæra ſequatur. </s> <s xml:id="echoid-s3265" xml:space="preserve">Verum hæc opinio multis experimentis refraga-<lb/>tur, & </s> <s xml:id="echoid-s3266" xml:space="preserve">communi omnium philoſophorum, Aſtrologorumq́; </s> <s xml:id="echoid-s3267" xml:space="preserve">ſentẽtiæ: </s> <s xml:id="echoid-s3268" xml:space="preserve">Debet <lb/>enim terra conſiſtere in medio totius mundi, ut poſtea demoſtrabimus pluri <lb/>mis experientijs, ac phænomenis.</s> <s xml:id="echoid-s3269" xml:space="preserve"/> </p> <div xml:id="echoid-div178" type="float" level="2" n="2"> <note position="left" xlink:label="note-100-02" xlink:href="note-100-02a" xml:space="preserve">Prima ſen-<lb/>tẽtia dior-<lb/>dine cęlo-<lb/>rum.</note> </div> <p> <s xml:id="echoid-s3270" xml:space="preserve"><emph style="sc">Vetvstissimi</emph> autem Ægyptij, Plato in Tymeo, Ariſt. </s> <s xml:id="echoid-s3271" xml:space="preserve">in 2. </s> <s xml:id="echoid-s3272" xml:space="preserve">de cœ-<lb/> <anchor type="note" xlink:label="note-100-03a" xlink:href="note-100-03"/> lo, cap. </s> <s xml:id="echoid-s3273" xml:space="preserve">12. </s> <s xml:id="echoid-s3274" xml:space="preserve">& </s> <s xml:id="echoid-s3275" xml:space="preserve">1. </s> <s xml:id="echoid-s3276" xml:space="preserve">Metereo. </s> <s xml:id="echoid-s3277" xml:space="preserve">cap. </s> <s xml:id="echoid-s3278" xml:space="preserve">4. </s> <s xml:id="echoid-s3279" xml:space="preserve">putarunt hunc eſſe ordinem in ſphæris cæle-<lb/>ſtibus, ut infimum locũ occuparet Luna; </s> <s xml:id="echoid-s3280" xml:space="preserve">hanc ſtatim ſubſequeretur Sol; </s> <s xml:id="echoid-s3281" xml:space="preserve">hunc <lb/>Mercurius; </s> <s xml:id="echoid-s3282" xml:space="preserve">deinde Venus; </s> <s xml:id="echoid-s3283" xml:space="preserve">quinto Mars; </s> <s xml:id="echoid-s3284" xml:space="preserve">ſexto Iuppiter; </s> <s xml:id="echoid-s3285" xml:space="preserve">ſeptimo Saturnus; <lb/></s> <s xml:id="echoid-s3286" xml:space="preserve">octauo deniq; </s> <s xml:id="echoid-s3287" xml:space="preserve">cælum ſtellatum, ſeu firmamentum. </s> <s xml:id="echoid-s3288" xml:space="preserve">Solus Ariſtoteles in libel-<lb/>lo de mundo ad Alexandrum (ſi tamen ipſius eſt) Venerem immediate ſupra <lb/>Solero, & </s> <s xml:id="echoid-s3289" xml:space="preserve">ſub Mercurio ſtatuit. </s> <s xml:id="echoid-s3290" xml:space="preserve">Sed talis quoq; </s> <s xml:id="echoid-s3291" xml:space="preserve">ordo planetarum, cęlorumve <lb/>iamdudum ab Aſtrologis eſt refutatus.</s> <s xml:id="echoid-s3292" xml:space="preserve"/> </p> <div xml:id="echoid-div179" type="float" level="2" n="3"> <note position="left" xlink:label="note-100-03" xlink:href="note-100-03a" xml:space="preserve">Secũda ſen <lb/>tẽtia di or-<lb/>dine cœlo-<lb/>rum.</note> </div> <p> <s xml:id="echoid-s3293" xml:space="preserve"><emph style="sc">Statvimvs</emph> igitur cum Ptolomæo, & </s> <s xml:id="echoid-s3294" xml:space="preserve">Ioan. </s> <s xml:id="echoid-s3295" xml:space="preserve">de Regiomon. </s> <s xml:id="echoid-s3296" xml:space="preserve">illum <lb/> <anchor type="note" xlink:label="note-100-04a" xlink:href="note-100-04"/> ordinem cælorum, quem auctor noſter ſupra recitauit, ita ut Luna primũ lo <lb/>cum occupet, ſeu infimũ, ſupra quam Mercurius collocetur, tertio loco Ve-<lb/>nus ſubſequatur, quarto Sol, quinto Mars, ſexto Iuppiter; </s> <s xml:id="echoid-s3297" xml:space="preserve">ſeptimo Saturn<emph style="sub">9</emph>, <pb o="65" file="101" n="102" rhead="Ioan. de Sacro Boſco."/> octauo & </s> <s xml:id="echoid-s3298" xml:space="preserve">poſtremo Firmamentum. </s> <s xml:id="echoid-s3299" xml:space="preserve">Vides igitur omnes opiniones in eo con-<lb/>uenire, vt cœlum ſtellarum fixarum ſupremo loco collocetur, & </s> <s xml:id="echoid-s3300" xml:space="preserve">ſub hoc Satur <lb/>nus, ſub quo Iuppiter, & </s> <s xml:id="echoid-s3301" xml:space="preserve">deinde Mars: </s> <s xml:id="echoid-s3302" xml:space="preserve">In alijs vero quatuor planetis totam di-<lb/>uerſitatem eſſe poſitam. </s> <s xml:id="echoid-s3303" xml:space="preserve">Quare breuiter ordinem iam recitatum confirmabi-<lb/>mus. </s> <s xml:id="echoid-s3304" xml:space="preserve">Primo quidem ex diuerſitate aſpectus. </s> <s xml:id="echoid-s3305" xml:space="preserve">Deinde ex velocitate & </s> <s xml:id="echoid-s3306" xml:space="preserve">tarditate <lb/>motus. </s> <s xml:id="echoid-s3307" xml:space="preserve">Tertio ex eclipſibus ſeu occultationibus planetarum. </s> <s xml:id="echoid-s3308" xml:space="preserve">Hoc enim triplici <lb/>medio potiſſimum ordo cœlorum ab aſtronomis confirmari ſolet.</s> <s xml:id="echoid-s3309" xml:space="preserve"/> </p> <div xml:id="echoid-div180" type="float" level="2" n="4"> <note position="left" xlink:label="note-100-04" xlink:href="note-100-04a" xml:space="preserve">Verior ſen <lb/>tẽtia di or-<lb/>dine cælo-<lb/>rum.</note> </div> <note position="right" xml:space="preserve">Ordo Pla-<lb/>netarum cõ <lb/>firmatur <lb/>ex diuerſitæ <lb/>te aſpectus.</note> <p> <s xml:id="echoid-s3310" xml:space="preserve"><emph style="sc">Qvod</emph> attinet ad diuerſitatem aſpectus, hoc modo argumentantur. </s> <s xml:id="echoid-s3311" xml:space="preserve">Illud <lb/>aſtrum eſt terræ uicinius, quod, cæteris paribus, maiorem habet diuerſitatem <lb/>aſpectus. </s> <s xml:id="echoid-s3312" xml:space="preserve">Atqui Luna maximam deprehenſa eſt pati aſpectus diuerſitatem, dein <lb/>de Mercurius, poſtea Venus, deinceps Sol. </s> <s xml:id="echoid-s3313" xml:space="preserve">Igitur conſtat primo loco collocan-<lb/>dam eſſe Lunam; </s> <s xml:id="echoid-s3314" xml:space="preserve">ſecundo Mercurium, tertio Venerem; </s> <s xml:id="echoid-s3315" xml:space="preserve">& </s> <s xml:id="echoid-s3316" xml:space="preserve">quarto Solem. </s> <s xml:id="echoid-s3317" xml:space="preserve">De <lb/> <anchor type="note" xlink:label="note-101-02a" xlink:href="note-101-02"/> reliquis vero planetis ex hac uia nihil ſtatui poteſt certi, cum propter nimiam <lb/>eorum aterra diſtantiam nullam habeant diuerſitatem aſpectus. </s> <s xml:id="echoid-s3318" xml:space="preserve">Quod ut ple-<lb/>nius intelligatur, dicenda erunt pauca de hac diuerſitate aſpectus. </s> <s xml:id="echoid-s3319" xml:space="preserve">Diuerſitas <lb/>igitur aſpectus, quam alij dicunt aſpectum diuerſitatis, eſt differentia ueri, uiſi-<lb/> <anchor type="note" xlink:label="note-101-03a" xlink:href="note-101-03"/> q́ue loci alicuius aſtri. </s> <s xml:id="echoid-s3320" xml:space="preserve">Verus porro locus aſtri dicitur punctũ illud circuli ma-<lb/>ximi per uerticem capitis, & </s> <s xml:id="echoid-s3321" xml:space="preserve">aſtrum tranſeuntis, ꝗ<unsure/> lineam rectam e centro terrę <lb/> <anchor type="note" xlink:label="note-101-04a" xlink:href="note-101-04"/> per centrum aſtri ad circulum illum maximum protractam terminat: </s> <s xml:id="echoid-s3322" xml:space="preserve">Viſus ue-<lb/>ro locus ſideris dicitur illud punctum eiuſdẽ circuli maximi, ꝗ<unsure/> lineam rectam <lb/>ab oculo noſtro per ſideris centrũ ad circulum illum maximũ eductã terminat. <lb/></s> <s xml:id="echoid-s3323" xml:space="preserve"> <anchor type="figure" xlink:label="fig-101-01a" xlink:href="fig-101-01"/> Exemplum. </s> <s xml:id="echoid-s3324" xml:space="preserve">Sit <lb/>cẽtrum terrę A; <lb/></s> <s xml:id="echoid-s3325" xml:space="preserve">Circulus maxi-<lb/>m<emph style="sub">9</emph> per uerticem <lb/>capitis D, & </s> <s xml:id="echoid-s3326" xml:space="preserve">ſtel-<lb/>lã trãſiẽs C D E. </s> <s xml:id="echoid-s3327" xml:space="preserve"><lb/>Locus terræ ver-<lb/>tici D, ſubiectus <lb/>ſit B; </s> <s xml:id="echoid-s3328" xml:space="preserve">aſtrũ quod <lb/>cunque ſit K, per <lb/>cuius centrum a <lb/>centro terræ du-<lb/>catur linea recta <lb/>A K S; </s> <s xml:id="echoid-s3329" xml:space="preserve">item per <lb/>eiuſdem ſtellæ cẽ <lb/>trum ducatur ex <lb/>B, loco terræ linea recta B K T. </s> <s xml:id="echoid-s3330" xml:space="preserve">Verus igitur locus aſtri K, eſt punctum S: </s> <s xml:id="echoid-s3331" xml:space="preserve">Vi-<lb/>ſus uero locus punctum T; </s> <s xml:id="echoid-s3332" xml:space="preserve">differentia autem ueri uiſiq́ue loci, arcus videlicet <lb/>S T, dicitur diuerſitas aſpectus aſtri K; </s> <s xml:id="echoid-s3333" xml:space="preserve">angulus uero, qui in centro ſtellæ effi-<lb/>citur ex duabus illis lineis rectis, qualis in dato exemplo eſt angulus A K B, <lb/>appellariſolet quantitas diuerſitatis aſpectus ab Aſtronomis: </s> <s xml:id="echoid-s3334" xml:space="preserve">ita ut ſi in duo-<lb/>bus aſtris efficiuntur tales anguli æquales, dicantur habere æqualem diuerſi-<lb/>tatem aſpectus; </s> <s xml:id="echoid-s3335" xml:space="preserve">in cuius uero centro maior continetur angulus, illud maio-<lb/>rem habeat aſpectus diuerſitatem.</s> <s xml:id="echoid-s3336" xml:space="preserve"/> </p> <div xml:id="echoid-div181" type="float" level="2" n="5"> <note position="right" xlink:label="note-101-02" xlink:href="note-101-02a" xml:space="preserve">Diuerſitas <lb/>aſpectus <lb/>quid.</note> <note position="right" xlink:label="note-101-03" xlink:href="note-101-03a" xml:space="preserve">Verus locus <lb/>aſtri quid.</note> <note position="right" xlink:label="note-101-04" xlink:href="note-101-04a" xml:space="preserve">Verus lo-<lb/>cus aſtri <lb/>quid.</note> <figure xlink:label="fig-101-01" xlink:href="fig-101-01a"> <image file="101-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/101-01"/> </figure> </div> <p> <s xml:id="echoid-s3337" xml:space="preserve">Ex quo perſpicuum fit, ſi duo aſtra in eodem cœlo exiſtentia eandem ha-<lb/>beant altitudinem ſupra Horizontem, cuiuſmodi ſunt aſtra H, & </s> <s xml:id="echoid-s3338" xml:space="preserve">O, æquali-<lb/>ter diſtantia a uertice M, ea eandem diuerſitatem aſpectus habere. </s> <s xml:id="echoid-s3339" xml:space="preserve">Sunt enim <pb o="66" file="102" n="103" rhead="Comment. in I. Cap. Sphæræ"/> duo latera H A, A B, trianguli A B H, æqualia duobus lateribus O A, A B, <lb/> <anchor type="note" xlink:label="note-102-01a" xlink:href="note-102-01"/> trianguli A B O, & </s> <s xml:id="echoid-s3340" xml:space="preserve">anguli dictis lateribus comprehenſi æquales, quòd arcus <lb/>O M, H M, æquales ſint, propter æqualitatem arcuum M H, M O, diſtantias di-<lb/> <anchor type="note" xlink:label="note-102-02a" xlink:href="note-102-02"/> ctorum aſtrorum a uertice M, metientium. </s> <s xml:id="echoid-s3341" xml:space="preserve">Quare & </s> <s xml:id="echoid-s3342" xml:space="preserve">baſes B H, B O, & </s> <s xml:id="echoid-s3343" xml:space="preserve">anguli <lb/>H, O, qui oſtendunt quantitatem diuerſitatis aſpectus, æquales erunt.</s> <s xml:id="echoid-s3344" xml:space="preserve"/> </p> <div xml:id="echoid-div182" type="float" level="2" n="6"> <note position="left" xlink:label="note-102-01" xlink:href="note-102-01a" xml:space="preserve">27. tertij.</note> <note position="left" xlink:label="note-102-02" xlink:href="note-102-02a" xml:space="preserve">4. primi.</note> </div> <p> <s xml:id="echoid-s3345" xml:space="preserve"><emph style="sc">Pari</emph> ratione ſequitur, aſtrum idem, quò propinquius fuerit Horizonti, <lb/>eo maiorem habere diuerſitatem aſpectus, adeo ut in Horizonte exiſtens maxi <lb/>mam habeat: </s> <s xml:id="echoid-s3346" xml:space="preserve">quò uerò remotius fuerit ab Horizonte, eo minorẽ habere, adeo <lb/>vt in uertice capitis exiſtens, vbi maxime ab Horizonte remouetur, nullã pror-<lb/>ſus habeat aſpectus diuerſitatem: </s> <s xml:id="echoid-s3347" xml:space="preserve">quæ omnia ordinatim demonſtrabimus. </s> <s xml:id="echoid-s3348" xml:space="preserve">Exi <lb/> <anchor type="note" xlink:label="note-102-03a" xlink:href="note-102-03"/> ſtat unum & </s> <s xml:id="echoid-s3349" xml:space="preserve">idem aſtrum modo in puncto M, id eſt, in uertice, modo in puncto <lb/>K, accedens ad Horizontem, modo in puncto H, quod uicinius eſt Horizonti, <lb/> <anchor type="figure" xlink:label="fig-102-01a" xlink:href="fig-102-01"/> modo deniq. </s> <s xml:id="echoid-s3350" xml:space="preserve">in <lb/>puncto F, id eſt, <lb/>in Horizonte, du <lb/>canturq́ue a cen-<lb/>tro terræ A, & </s> <s xml:id="echoid-s3351" xml:space="preserve"><lb/>ex oculo B, per <lb/>centrũ huius ſtel-<lb/>lę, vbicunque exi <lb/>ſtat, lineæ rectæ: <lb/></s> <s xml:id="echoid-s3352" xml:space="preserve">ſumatur quoque <lb/>arcus M O, æqua-<lb/>lis arcui M H, <lb/>ita ut duo aſtra <lb/>in punctis H, <lb/>& </s> <s xml:id="echoid-s3353" xml:space="preserve">O, exiſtentia, <lb/>& </s> <s xml:id="echoid-s3354" xml:space="preserve">ęqualiter a uertice M, remota, æquales habeant altitudines ſupra Horizon-<lb/>tem; </s> <s xml:id="echoid-s3355" xml:space="preserve">atq. </s> <s xml:id="echoid-s3356" xml:space="preserve">adeo, ut proxime demonſtratum eſt, aſpectus diuerſitatem eandem. </s> <s xml:id="echoid-s3357" xml:space="preserve"><lb/>Connectantur puncta K, & </s> <s xml:id="echoid-s3358" xml:space="preserve">O, linea recta K O. </s> <s xml:id="echoid-s3359" xml:space="preserve">Quoniam igitur B O, æqualis <lb/> <anchor type="note" xlink:label="note-102-04a" xlink:href="note-102-04"/> eſt ipſi B H, ut proxime demonſtratum eſt: </s> <s xml:id="echoid-s3360" xml:space="preserve">Eſt autem B H, maior quam B K; </s> <s xml:id="echoid-s3361" xml:space="preserve">e-<lb/> <anchor type="note" xlink:label="note-102-05a" xlink:href="note-102-05"/> rit quoq. </s> <s xml:id="echoid-s3362" xml:space="preserve">B O, maior quam B K; </s> <s xml:id="echoid-s3363" xml:space="preserve">& </s> <s xml:id="echoid-s3364" xml:space="preserve">ob id angulus B K O, maior angulo B O K; <lb/></s> <s xml:id="echoid-s3365" xml:space="preserve"> <anchor type="note" xlink:label="note-102-06a" xlink:href="note-102-06"/> Su nt autem anguli toti A K O, & </s> <s xml:id="echoid-s3366" xml:space="preserve">A O K, ęquales. </s> <s xml:id="echoid-s3367" xml:space="preserve">Reliquus igitur A O B, ma-<lb/>ior erit reliquo A K B, & </s> <s xml:id="echoid-s3368" xml:space="preserve">idcirco aſtrum in O, exiſtens, ac proinde & </s> <s xml:id="echoid-s3369" xml:space="preserve">in puncto <lb/>H, maiorẽ habebit diuerſitatẽ aſpectus, quã in puncto K. </s> <s xml:id="echoid-s3370" xml:space="preserve">Quare conſtat, aſtrum <lb/> <anchor type="note" xlink:label="note-102-07a" xlink:href="note-102-07"/> quodcunq;</s> <s xml:id="echoid-s3371" xml:space="preserve">, quo uicinius fuerit Horizonti, eo maiorẽ hẽre diuerſitatẽ aſpect<emph style="sub">9</emph>.</s> <s xml:id="echoid-s3372" xml:space="preserve"/> </p> <div xml:id="echoid-div183" type="float" level="2" n="7"> <note position="left" xlink:label="note-102-03" xlink:href="note-102-03a" xml:space="preserve">Aſtrũ, quõ <lb/>uicinius eſt <lb/>Morizonti, <lb/>eo maiorẽ <lb/>habet aſpe-<lb/>ctus diuerſi <lb/>tatem.</note> <figure xlink:label="fig-102-01" xlink:href="fig-102-01a"> <image file="102-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/102-01"/> </figure> <note position="left" xlink:label="note-102-04" xlink:href="note-102-04a" xml:space="preserve">7. tertij.</note> <note position="left" xlink:label="note-102-05" xlink:href="note-102-05a" xml:space="preserve">18. primi.</note> <note position="left" xlink:label="note-102-06" xlink:href="note-102-06a" xml:space="preserve">5. primi.</note> <note position="left" xlink:label="note-102-07" xlink:href="note-102-07a" xml:space="preserve">Aſtrum in <lb/>Horizonte <lb/>maximam <lb/>habetdiuer <lb/>ſitatẽ aſpe-<lb/>ctũs.</note> </div> <p> <s xml:id="echoid-s3373" xml:space="preserve"><emph style="sc">Rvrsvs</emph> exiſtat aliquod aſtrum in Horizonte, nempe in G, & </s> <s xml:id="echoid-s3374" xml:space="preserve">aliud in eo-<lb/>dem cælo in puncto L, ſupra Horizontem; </s> <s xml:id="echoid-s3375" xml:space="preserve">& </s> <s xml:id="echoid-s3376" xml:space="preserve">producatur Horizon G B, uſque <lb/>ad R, & </s> <s xml:id="echoid-s3377" xml:space="preserve">connectantur rectæ A G, A R, A L, B L, L R, eruntq́ue baſes B G, <lb/>B R, & </s> <s xml:id="echoid-s3378" xml:space="preserve">duo anguli A G B, A R B, ęquales: </s> <s xml:id="echoid-s3379" xml:space="preserve">Sed angulus A R B, maior eſt, an-<lb/> <anchor type="note" xlink:label="note-102-08a" xlink:href="note-102-08"/> gulo A L B, quod quidem eodem pacto demonſtrari poteſt, quemadmodum <lb/>oſtenſum fuit, angulum A O B, maiorem eſſe angulo A K B. </s> <s xml:id="echoid-s3380" xml:space="preserve">Igitur & </s> <s xml:id="echoid-s3381" xml:space="preserve">angu-<lb/> <anchor type="note" xlink:label="note-102-09a" xlink:href="note-102-09"/> lus A G B, maior erit eodem angulo A L B, & </s> <s xml:id="echoid-s3382" xml:space="preserve">propterea aſtrum in Horizonte <lb/>exiſtens maximam habebit diuerſitatem aſpectus. </s> <s xml:id="echoid-s3383" xml:space="preserve">Eadem enim ratione demon <lb/>ſtrabitur angulum A G B, maiorem eſſe quocunque alio. </s> <s xml:id="echoid-s3384" xml:space="preserve">Facile autem perſpi <lb/>cis, aſtrum in puncto M, exiſtens nullam habere diuerſitatem aſpectus, cum idẽ <lb/>ſit eius locus uiſus & </s> <s xml:id="echoid-s3385" xml:space="preserve">uerus.</s> <s xml:id="echoid-s3386" xml:space="preserve"/> </p> <div xml:id="echoid-div184" type="float" level="2" n="8"> <note position="left" xlink:label="note-102-08" xlink:href="note-102-08a" xml:space="preserve">4. primi.</note> <note position="left" xlink:label="note-102-09" xlink:href="note-102-09a" xml:space="preserve">Aſtrum in <lb/>uertice exi-<lb/>ſtens nullã <lb/>habet diuer <lb/>ſitatẽ aſpe-<lb/>ctus: Inter <lb/>duo uero <lb/>aſtra eũdẽ.</note> </div> <p> <s xml:id="echoid-s3387" xml:space="preserve"><emph style="sc">Rvrsvs</emph> ex eadem figura colligitur, inter duo aſtra, quę eundem uerum <pb o="67" file="103" n="104" rhead="Ioan. de Sacro Boſco."/> locum habent, uel uiſum, illud quod centro terræ propinquius extiterit, ma-<lb/> <anchor type="note" xlink:label="note-103-01a" xlink:href="note-103-01"/> iorem habere diuerſitatem aſpectus. </s> <s xml:id="echoid-s3388" xml:space="preserve">Nam aſtra F, & </s> <s xml:id="echoid-s3389" xml:space="preserve">G, ſiue R, & </s> <s xml:id="echoid-s3390" xml:space="preserve">Q, habent eun-<lb/>dem viſum locum S; </s> <s xml:id="echoid-s3391" xml:space="preserve">Verus autem locus aſtri F, uel Q, eſt T; </s> <s xml:id="echoid-s3392" xml:space="preserve">aſtri autem G, uel <lb/>R, eſt V; </s> <s xml:id="echoid-s3393" xml:space="preserve">ubi manifeſte cernitur S V, diuerſitatem aſpectus aſtri G, uel R, quo-<lb/>niam propinquius centro tcrrę exiſtit, maiorem eſſe arcu S T, nimirum diuerſi <lb/>tate aſpectus aſtri F, uel Q. </s> <s xml:id="echoid-s3394" xml:space="preserve">quod magis à centro terræ recedit. </s> <s xml:id="echoid-s3395" xml:space="preserve">Idem quoque <lb/>cernitur in aſtris P, & </s> <s xml:id="echoid-s3396" xml:space="preserve">O; </s> <s xml:id="echoid-s3397" xml:space="preserve">Item L, & </s> <s xml:id="echoid-s3398" xml:space="preserve">K; </s> <s xml:id="echoid-s3399" xml:space="preserve">Item I, & </s> <s xml:id="echoid-s3400" xml:space="preserve">H, quorum omnium uerus lo <lb/>cus oſtenditur per punctum S. </s> <s xml:id="echoid-s3401" xml:space="preserve">Ex his igitur ita declaratis perſpicue intelligi-<lb/>tur prima hæc uia deſumpta ex diuerſitate aſpectus.</s> <s xml:id="echoid-s3402" xml:space="preserve"/> </p> <div xml:id="echoid-div185" type="float" level="2" n="9"> <note position="right" xlink:label="note-103-01" xlink:href="note-103-01a" xml:space="preserve">locũ uiſum <lb/>au<unsure/>t uerum <lb/>habentia il <lb/>lud, quod <lb/>centro ter-<lb/>ræ propin-<lb/>quius eſt, <lb/>maiorẽ dt-<lb/>uerſitatem <lb/>aſpectus ha <lb/>bet.</note> </div> <p> <s xml:id="echoid-s3403" xml:space="preserve"><emph style="sc">Deinde</emph> ex uelocitate, & </s> <s xml:id="echoid-s3404" xml:space="preserve">tarditate motus hunc eundem ordinem cælo <lb/>rum colligunt Aſtronomi hac ratione. </s> <s xml:id="echoid-s3405" xml:space="preserve">Quò magis cœlum à natura, & </s> <s xml:id="echoid-s3406" xml:space="preserve">condi-<lb/>tione primi mobilis recedit, eo etiam in inferiori eſt loco ponendum: </s> <s xml:id="echoid-s3407" xml:space="preserve">At cum <lb/> <anchor type="note" xlink:label="note-103-02a" xlink:href="note-103-02"/> Lunainter omnes planetas celerrime ab occidente in orientem feratur, ut ſu-<lb/>pra diximus, maxime à motu, atque conditione primi mobilis videtur recede-<lb/>re, & </s> <s xml:id="echoid-s3408" xml:space="preserve">ob id primo cælo, ſeu primo mobili minus conformari. </s> <s xml:id="echoid-s3409" xml:space="preserve">Poſſidebit igitur <lb/>infimum locum. </s> <s xml:id="echoid-s3410" xml:space="preserve">Eadem ratione cęlum ſtellatum in ſupremo locum collocabit̃, <lb/>quoniam tardiſſime contra motum primi mobilis fertur: </s> <s xml:id="echoid-s3411" xml:space="preserve">Deinde ſuccedet ſphę <lb/>ra Saturni, poſtea Iouis, & </s> <s xml:id="echoid-s3412" xml:space="preserve">ſic de reliquis, ſtatuendo ſemper ordinem ſupra di-<lb/>ctum. </s> <s xml:id="echoid-s3413" xml:space="preserve">Cæterum ex hac uia nihil certi ſtatui poteſt de ordine Solis, Veneris, & </s> <s xml:id="echoid-s3414" xml:space="preserve"><lb/>Mercurij inter ſeſe. </s> <s xml:id="echoid-s3415" xml:space="preserve">Quamuis enim ex ea colligatur, quod hi tres planetæ <lb/>ſupra Lunam collocentur, quoniam uidelicet tardius ab oriente in occidentẽ <lb/>feruntur; </s> <s xml:id="echoid-s3416" xml:space="preserve">Et quod infra Firmamentum, Saturnum, Iouem, ac Martem ſint po-<lb/>ſiti, quod nimirum uelocius contra primum mobile ferantur: </s> <s xml:id="echoid-s3417" xml:space="preserve">tamen quiſnam <lb/>eorum ſupra alterum ſit conſtituendus, certo ſciri nequit, cum eodem fere tem <lb/>pore motus proprios ab occidente in orientem perficiant. </s> <s xml:id="echoid-s3418" xml:space="preserve">Immo Alpetragius, <lb/>vt teſtatur Ioan. </s> <s xml:id="echoid-s3419" xml:space="preserve">Regiom. </s> <s xml:id="echoid-s3420" xml:space="preserve">lib. </s> <s xml:id="echoid-s3421" xml:space="preserve">9. </s> <s xml:id="echoid-s3422" xml:space="preserve">Epitomes propoſ. </s> <s xml:id="echoid-s3423" xml:space="preserve">1. </s> <s xml:id="echoid-s3424" xml:space="preserve">ex hac ratione colligit, ſub <lb/>Marte poſitum eſſe cælum Veneris, & </s> <s xml:id="echoid-s3425" xml:space="preserve">ſub hoc cœlum Solis, Deinde Mercurij, <lb/>ac poſtremo Lunam; </s> <s xml:id="echoid-s3426" xml:space="preserve">propterea quòd Venus ratione epicycli tardius peragat <lb/>curſum ſuum, quàm Sol, & </s> <s xml:id="echoid-s3427" xml:space="preserve">Sol tard@us quàm Mercurius, Luna denique citiſſi-<lb/>me omnium periodum ſuam abſoluat.</s> <s xml:id="echoid-s3428" xml:space="preserve"/> </p> <div xml:id="echoid-div186" type="float" level="2" n="10"> <note position="right" xlink:label="note-103-02" xlink:href="note-103-02a" xml:space="preserve">Ordo cælo-<lb/>rum proba-<lb/>tur ex uelo <lb/>citate & tar <lb/>di<unsure/>rate mo-<lb/>tus.</note> </div> <note position="right" xml:space="preserve">Ordo cœlo-<lb/>rum confit <lb/>matur ex <lb/>eclipſibus.</note> <p> <s xml:id="echoid-s3429" xml:space="preserve"><emph style="sc">Tandem</emph> ex eclipſibus, ſiue occultationibus planetarum, ſtellarumq́ue <lb/>idem ordo cœlorum colligitur ab Aſtronomis. </s> <s xml:id="echoid-s3430" xml:space="preserve">Non enim dubium eſſe poteſt, <lb/>quin illud aſtrum ſit inferius, quod alterum nobis occultat. </s> <s xml:id="echoid-s3431" xml:space="preserve">Cum ergo Luna, <lb/>quando cum alijs planetis coniungitur, eos nobis interdum e uiſu eripiat, ne-<lb/>ceſſe eſt, ut ei infimum locum concedamus: </s> <s xml:id="echoid-s3432" xml:space="preserve">Pari ratione erit Mercurius ſub <lb/>Venere, & </s> <s xml:id="echoid-s3433" xml:space="preserve">Venus ſub Marte, & </s> <s xml:id="echoid-s3434" xml:space="preserve">ſic deinceps. </s> <s xml:id="echoid-s3435" xml:space="preserve">Hæ igitur ſunt rationes fere potiſ-<lb/>fimę, quibus Aſtronomi ordinem cœlorum, quem auctor explicauit, cõcludũt. <lb/></s> <s xml:id="echoid-s3436" xml:space="preserve">Quamuis. </s> <s xml:id="echoid-s3437" xml:space="preserve">n. </s> <s xml:id="echoid-s3438" xml:space="preserve">nulla earum ſufficienter hunc ordinem colligar, omnes tamen ſi-<lb/>mul ſumptę confirmant, cœlos eo ordine collocatos eſſe. </s> <s xml:id="echoid-s3439" xml:space="preserve">Nam ex diuerſitate <lb/>aſpectus infallibiliter colligitur ordo Lunę, Mercurii, Veneris, & </s> <s xml:id="echoid-s3440" xml:space="preserve">Solis. </s> <s xml:id="echoid-s3441" xml:space="preserve">Ex ue-<lb/>locitate uero & </s> <s xml:id="echoid-s3442" xml:space="preserve">tarditate motus conuenienter ſupra hos quatuor planetas col <lb/>locatur Mars, deinde Iupiter, poſtremo Saturnus, ſupra omnes uero planetas <lb/>Firmamentũ, ſiue octauũ cœlũ, quod ſequit̃ nona ſphæra ſub primo mobili con <lb/>ſtituta. </s> <s xml:id="echoid-s3443" xml:space="preserve">Ex eclipſibus deniq. </s> <s xml:id="echoid-s3444" xml:space="preserve">licet non oium planetarũ ordo firmiter poſſit colli-<lb/>gi@tñ Lunam cogimur infimo loco ponere, & </s> <s xml:id="echoid-s3445" xml:space="preserve">omnes ſub Firmamento.</s> <s xml:id="echoid-s3446" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3447" xml:space="preserve"><emph style="sc">Vt</emph> autem plenior cognitio huius ordinis habeatur, non abs re facturum <lb/>me arbitror, ſi rationes alias Aſtronomorum in medium adducam, ex quibus <lb/>conuenientia maxima huiuſce ordinis eluceſcet<unsure/>.</s> <s xml:id="echoid-s3448" xml:space="preserve"/> </p> <pb o="68" file="104" n="105" rhead="Comment. in I. Cap. Sphæræ"/> <p> <s xml:id="echoid-s3449" xml:space="preserve"><emph style="sc">Qvod</emph> igitur Luna inſimo in loco ſit poſita, hac ratione demonſtrari po-<lb/>teſt. </s> <s xml:id="echoid-s3450" xml:space="preserve">Corpus lucidum, quò altius & </s> <s xml:id="echoid-s3451" xml:space="preserve">remotius eſt a terra, cæteris paribus, eò um <lb/> <anchor type="note" xlink:label="note-104-01a" xlink:href="note-104-01"/> bræ corporum minores apparent in plano Horizontis, & </s> <s xml:id="echoid-s3452" xml:space="preserve">quò propinquius eſt <lb/>terræ corpus Luminoſum, eo longiores umbras corpora proijciunt; </s> <s xml:id="echoid-s3453" xml:space="preserve">ut uidere <lb/>licet in hac figura: </s> <s xml:id="echoid-s3454" xml:space="preserve">In qua utrumque aſtrum eandem habet altitudinem ſupra <lb/>Horizontem A B, reſpectu centri mundi, id eſt, obtinet eundem locum uerum <lb/>reſpectu Horizontis, quamuis in uiſo loco diſcrepent, & </s> <s xml:id="echoid-s3455" xml:space="preserve">tamen inferius aſtrum <lb/>longius proijcit umbram gnomonis C D, puta in punctum E, quàm ſuperius, ꝗ<unsure/> <lb/>umbram eiuſdem gnomonis tantum proijcit in punctum F: </s> <s xml:id="echoid-s3456" xml:space="preserve">Atqui umbra gno <lb/>monis erecti, ſplendente Sole, minor eſt, quam umbra eiuſdem gnomonis, Lu-<lb/>na lucente, cæteris omnibus paribus exiſtentibus, id eſt, æqualibus cum Sole <lb/> <anchor type="figure" xlink:label="fig-104-01a" xlink:href="fig-104-01"/> gradibus, diuerſo tamen tempore, ab <lb/>Horizonte diſtante; </s> <s xml:id="echoid-s3457" xml:space="preserve">quod facile quiuis <lb/>experiri poterit, ſi ſignetur tempore æqui <lb/>noctij altitudo Solis meridiana, Sole ui-<lb/>delicet tenẽte principiũ Aries, aut Libra, <lb/>quæ altitudo Romę eſt fere grad. </s> <s xml:id="echoid-s3458" xml:space="preserve">48. <lb/></s> <s xml:id="echoid-s3459" xml:space="preserve">noteturq́ue in aliquo plano gnomonis <lb/>umbra. </s> <s xml:id="echoid-s3460" xml:space="preserve">Poſtea idem fiat, Luna exiſtente <lb/>in eodem loco Zodiaci, in quo ante fuit <lb/>Sol, hoc eſt, ĩ prĩcipio Ariete, vel Libra, & </s> <s xml:id="echoid-s3461" xml:space="preserve"><lb/>tenẽte Meridianum circulum, carenteq́. </s> <s xml:id="echoid-s3462" xml:space="preserve">omni latitudine. </s> <s xml:id="echoid-s3463" xml:space="preserve">Deprehendetur nãq, <lb/>umbra gnomonis, ſplendente Luna, multo longior, quam lucente Sole, cum tñ <lb/>altitudo, ſeu diſtantia utriuſq. </s> <s xml:id="echoid-s3464" xml:space="preserve">planetæ ab Horizonte ſit eadem, nimirum grad. </s> <s xml:id="echoid-s3465" xml:space="preserve"><lb/>48. </s> <s xml:id="echoid-s3466" xml:space="preserve">reſpectu centri terræ. </s> <s xml:id="echoid-s3467" xml:space="preserve">Sequiturigitur, ſphęrã Solis longe eſſe ſuperiorem, ꝗ̃ <lb/>Lunæ. </s> <s xml:id="echoid-s3468" xml:space="preserve">Idẽ ꝙ de Luna reſpectu Solis diximus, accõmodari poteſt reſpectu alio-<lb/>rũ planetarum; </s> <s xml:id="echoid-s3469" xml:space="preserve">ꝗ̃ uis. </s> <s xml:id="echoid-s3470" xml:space="preserve">n. </s> <s xml:id="echoid-s3471" xml:space="preserve">alij planetę non ita ſplendeant, ut vmbras proijciant, ſci <lb/>ri tñ poteſt, quantum eorum radij per gnomonis uerticem proijciantur. </s> <s xml:id="echoid-s3472" xml:space="preserve">Quam <lb/>ob rem citra omnẽ controuerſiã cõſtat, Lunã omnibus eſſe planetis inferiorẽ.</s> <s xml:id="echoid-s3473" xml:space="preserve"/> </p> <div xml:id="echoid-div187" type="float" level="2" n="11"> <note position="left" xlink:label="note-104-01" xlink:href="note-104-01a" xml:space="preserve">Lunã poſi-<lb/>tam eſſe in <lb/>infimo lo-<lb/>co, proba-<lb/>@ut<unsure/> ex um-<lb/>bra.</note> <figure xlink:label="fig-104-01" xlink:href="fig-104-01a"> <image file="104-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/104-01"/> </figure> </div> <p> <s xml:id="echoid-s3474" xml:space="preserve"><emph style="sc">Qvam</emph> etiam conuenienter Sol ſupra Mercurium, & </s> <s xml:id="echoid-s3475" xml:space="preserve">Venerem, id eſt, in <lb/>medio planetarum ſtatuatur, hanc rationem Ioan. </s> <s xml:id="echoid-s3476" xml:space="preserve">de Regiom. </s> <s xml:id="echoid-s3477" xml:space="preserve">lib. </s> <s xml:id="echoid-s3478" xml:space="preserve">9. </s> <s xml:id="echoid-s3479" xml:space="preserve">Epitomes <lb/> <anchor type="note" xlink:label="note-104-02a" xlink:href="note-104-02"/> propoſ. </s> <s xml:id="echoid-s3480" xml:space="preserve">1. </s> <s xml:id="echoid-s3481" xml:space="preserve">affert. </s> <s xml:id="echoid-s3482" xml:space="preserve">Ptolemæus Dict. </s> <s xml:id="echoid-s3483" xml:space="preserve">5. </s> <s xml:id="echoid-s3484" xml:space="preserve">cap. </s> <s xml:id="echoid-s3485" xml:space="preserve">15. </s> <s xml:id="echoid-s3486" xml:space="preserve">a quo non diſſentit Albategnius ca-<lb/>50. </s> <s xml:id="echoid-s3487" xml:space="preserve">ſui operis, certis rationibus oſtendit, diſtantiam Solis a centro terræ, quan-<lb/>do minima eſt, id eſt, quando in Augis oppoſito exiſtit Sol, continere 1070. <lb/></s> <s xml:id="echoid-s3488" xml:space="preserve">terræ ſemidiametros; </s> <s xml:id="echoid-s3489" xml:space="preserve">diſtantiam uero Lunæ a centro terræ, quando ea maxi-<lb/>ma eſt, id eſt, quando Luna in Auge exiſtit, continere duntaxat 64. </s> <s xml:id="echoid-s3490" xml:space="preserve">ſemidiame-<lb/>tros terræ. </s> <s xml:id="echoid-s3491" xml:space="preserve">Vnde diſſerentia inter minimam Solis diſtãtiam, & </s> <s xml:id="echoid-s3492" xml:space="preserve">maximam Lunę <lb/>continebit terræ ſemidiametros 1006. </s> <s xml:id="echoid-s3493" xml:space="preserve">Tantum enim relinquitur, ſubtracta <lb/>maxima Lunæ diſtantia a minima Solis. </s> <s xml:id="echoid-s3494" xml:space="preserve">Cum igitur inter cœlum Lunæ, ac cœ-<lb/>lum Solis uacuum concedi non poſſit, cum a uacuo natura abhorreat, neque <lb/>rationi conſentaneum ſit, deferentes augium Solis & </s> <s xml:id="echoid-s3495" xml:space="preserve">Lunæ tanta eſſe mole <lb/>præditos, cum prorſus tanta moles eſſet inutilis & </s> <s xml:id="echoid-s3496" xml:space="preserve">ſuperuacanea, iure optimo <lb/>& </s> <s xml:id="echoid-s3497" xml:space="preserve">conueniẽtiſſime tantum ſpatium intermedium tribuetur orbibus Mercurij <lb/>ac Veneris: </s> <s xml:id="echoid-s3498" xml:space="preserve">Ac proinde Sol in medio Planetarum collocatus erit, nempe ſupra <lb/>Lunam, Mercurium, ac Venerem, atq. </s> <s xml:id="echoid-s3499" xml:space="preserve">infra Saturnum, Iouem, ac Martem.</s> <s xml:id="echoid-s3500" xml:space="preserve"/> </p> <div xml:id="echoid-div188" type="float" level="2" n="12"> <note position="left" xlink:label="note-104-02" xlink:href="note-104-02a" xml:space="preserve">Solem con-<lb/>uenienter <lb/>ſtatuiī<unsure/> me-<lb/>dio Planeta. <lb/>rum.</note> </div> <p> <s xml:id="echoid-s3501" xml:space="preserve"><emph style="sc">Accedit</emph> etiam, quod motus Solis eſt regula, & </s> <s xml:id="echoid-s3502" xml:space="preserve">menſura motuum alio <lb/>rum planetarum, alia tamen atq. </s> <s xml:id="echoid-s3503" xml:space="preserve">alia ratione. </s> <s xml:id="echoid-s3504" xml:space="preserve">Mars etenim, Iuppiter, & </s> <s xml:id="echoid-s3505" xml:space="preserve">Satur-<lb/>nus ratione epicycli cum Sole in motu conueniunt: </s> <s xml:id="echoid-s3506" xml:space="preserve">Luna uero, Mercurius, &</s> <s xml:id="echoid-s3507" xml:space="preserve"> <pb o="69" file="105" n="106" rhead="Ioan. de Sacro Boſco."/> Venus in deferentibus orbibus motui Solis conformantur, ut in Theoricis <lb/>planetarum explicatur. </s> <s xml:id="echoid-s3508" xml:space="preserve">Quare haud iniuria Sol in medio horum collocabi-<lb/>tur, ut ſuperiores tres planetas ab inferioribus tribus ſegreget, quandoqui-<lb/>dem non eadem ratione vniformitatem motus cum illo obſeruant.</s> <s xml:id="echoid-s3509" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3510" xml:space="preserve"><emph style="sc">His</emph> rationibus addi poteſt, quòd Sol eſt rex, & </s> <s xml:id="echoid-s3511" xml:space="preserve">quaſi cor omnium plane-<lb/>tarum; </s> <s xml:id="echoid-s3512" xml:space="preserve">quare non immerito in medio illorum conſtituetur, quemad modum <lb/>rex in medio regni, & </s> <s xml:id="echoid-s3513" xml:space="preserve">cor in medio animalis collocatur, ut omnibus inde mem <lb/>bris æqualiter poſſit ſuccurrere, ac prouidere. </s> <s xml:id="echoid-s3514" xml:space="preserve">Ita ut quodammodo (ut plerique <lb/>iocantur) Reſpublica ex 7. </s> <s xml:id="echoid-s3515" xml:space="preserve">planetis conſtituatur. </s> <s xml:id="echoid-s3516" xml:space="preserve">Eſt enim Sol omnium rex; </s> <s xml:id="echoid-s3517" xml:space="preserve">Sa-<lb/>turnus autem, ob ſenectutem, eius conſiliarius; </s> <s xml:id="echoid-s3518" xml:space="preserve">Iuppiter, ob magnanimitatẽ, iu-<lb/>dex omnium; </s> <s xml:id="echoid-s3519" xml:space="preserve">Mars dux milit<unsure/>iæ; </s> <s xml:id="echoid-s3520" xml:space="preserve">Venus, diſpenſatrix omnium bonorum, inſtar <lb/>matrisfamilias; </s> <s xml:id="echoid-s3521" xml:space="preserve">Mercurius eius ſcriba, ac cancellarius; </s> <s xml:id="echoid-s3522" xml:space="preserve">Luna denique nuntij of-<lb/>ficio fungitur. </s> <s xml:id="echoid-s3523" xml:space="preserve">Vnde & </s> <s xml:id="echoid-s3524" xml:space="preserve">velociſſimum motum habet ab occaſu in ortum, vt nimi <lb/>rum ſingulis menſibus ad quemlibet mandata regis perferat. </s> <s xml:id="echoid-s3525" xml:space="preserve">Præterea quoniã <lb/>ſecundũ Aſtronomos, & </s> <s xml:id="echoid-s3526" xml:space="preserve">philo ſophos, omnes ſtellæ, & </s> <s xml:id="echoid-s3527" xml:space="preserve">planetæ lumen ſuũ à So-<lb/>le recipiunt. </s> <s xml:id="echoid-s3528" xml:space="preserve">ſaltem perfectius, vt clare uidemus in eclipſi lunari, in qua Luna <lb/>ob ingreſſum in vmbrã terræ lumen ſuum amittit; </s> <s xml:id="echoid-s3529" xml:space="preserve">& </s> <s xml:id="echoid-s3530" xml:space="preserve">præterea diuerſis tempo-<lb/>ribus diuerſimode illuminatur à Sole: </s> <s xml:id="echoid-s3531" xml:space="preserve">Modo namq; </s> <s xml:id="echoid-s3532" xml:space="preserve">apparet corniculata, mo-<lb/>do media illuminata, modo uidetur plena, &</s> <s xml:id="echoid-s3533" xml:space="preserve">c. </s> <s xml:id="echoid-s3534" xml:space="preserve">quod non accideret, ſi lumen ex <lb/>ſe haberet. </s> <s xml:id="echoid-s3535" xml:space="preserve">Simile iudicium habeto de alijs ſtellis. </s> <s xml:id="echoid-s3536" xml:space="preserve">Sunt enim eiuſdem cum Lu-<lb/>na naturæ. </s> <s xml:id="echoid-s3537" xml:space="preserve">Quod etiam ex eo probari poteſt, quod uideamus planetas, qui ſunt <lb/>propinquiores Soli, uehementius illuminari, ut apparet in Marte, ac Venere. <lb/></s> <s xml:id="echoid-s3538" xml:space="preserve">Quapropter, ut æquabiliter Sol lumen ſuum omnibus planetis, ac ſtellis im-<lb/>pertiret, in medio illorum commodiſſime eſt collocatus.</s> <s xml:id="echoid-s3539" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3540" xml:space="preserve"><emph style="sc">Adivngit</emph> Albumaſar in ſuo magno introductorio, tractatu 3. </s> <s xml:id="echoid-s3541" xml:space="preserve">diffe-<lb/>rentia 3. </s> <s xml:id="echoid-s3542" xml:space="preserve">quod ob id Deus glorioſus Solem planetarum nobiliſſimum, atq; </s> <s xml:id="echoid-s3543" xml:space="preserve">ma-<lb/>xime actiuum in medio aliorum planetarum collocauit, quia ſi immediate cõ-<lb/>ſtitutus fuiſſet infra cęlum octauum, & </s> <s xml:id="echoid-s3544" xml:space="preserve">ſupra Saturnum, non poſſet propter ni-<lb/>miã diſtantiam à terra commode in hæc inferiora agere: </s> <s xml:id="echoid-s3545" xml:space="preserve">immo omnia hæc infe <lb/>riora frigeſcerent quodammodo; </s> <s xml:id="echoid-s3546" xml:space="preserve">ſi uero immediate ſupra Lunam poſitus fuiſ-<lb/>ſet, etiã non ſatis commode ſuo motu in hæc inferiora ageret, quia tunc nimis <lb/>tarde ab ortu in occaſum moueretur, propter diſtantiam nimiam à primo mo-<lb/>bili: </s> <s xml:id="echoid-s3547" xml:space="preserve">Quemad modum etiam in rota quauis partes illæ, quæ magis recedunt à <lb/>circunferentia, magisq́ue ad centrum, ſeu axem accedunt, remiſſius mouentur. <lb/></s> <s xml:id="echoid-s3548" xml:space="preserve">Adde quod tunc Sol propter nimiam uicinitatem ad terram omnia hæc infe-<lb/>riora combureret. </s> <s xml:id="echoid-s3549" xml:space="preserve">Quamobrem in medio planetarũ cõgrue ponitur, ut actio-<lb/>nem ſuam habeat temperatam, & </s> <s xml:id="echoid-s3550" xml:space="preserve">hiſce inferioribus magis accomodatam. </s> <s xml:id="echoid-s3551" xml:space="preserve">Vt <lb/>non temere apud Ouid. </s> <s xml:id="echoid-s3552" xml:space="preserve">2. </s> <s xml:id="echoid-s3553" xml:space="preserve">Metamorph. </s> <s xml:id="echoid-s3554" xml:space="preserve">Phœbus Phaetontem filium quadrigam <lb/>Solis temerarie conſcenſurum commonuerit, dicens.</s> <s xml:id="echoid-s3555" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s3556" xml:space="preserve">Altius egreßus cæleſtia ſigna cremabis:</s> <s xml:id="echoid-s3557" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s3558" xml:space="preserve">Inferius terras: </s> <s xml:id="echoid-s3559" xml:space="preserve">medio tutiſſimus ibis.</s> <s xml:id="echoid-s3560" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3561" xml:space="preserve">Voluit enim eo in loco ſignificare Ouidius, Solem in medio loco planeta-<lb/>rum habere actionem ſuam temperatam, non in alio, & </s> <s xml:id="echoid-s3562" xml:space="preserve">ideo ibidem eſſe pro-<lb/>prium eius locum.</s> <s xml:id="echoid-s3563" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">Mercuriu<unsure/> <lb/>conuenien-<lb/>ter ſtatui <lb/>ſupra Lunã <lb/>& infra Ve <lb/>nerem.</note> <p> <s xml:id="echoid-s3564" xml:space="preserve"><emph style="sc">Qvod</emph> autem Mercurius quoque conuenienter ſtatim ſupra Lunam, & </s> <s xml:id="echoid-s3565" xml:space="preserve"><lb/>ſub Venere collocetur, perſuadere nobis uidetur eius motus irregularis. </s> <s xml:id="echoid-s3566" xml:space="preserve">E ſt <lb/>enim Mercurius multo magis irregularis in ſuo motu, quàm Venus, propter <lb/>quod Aſtrologi tribuerunt Mercurio quinque orbes, & </s> <s xml:id="echoid-s3567" xml:space="preserve">epicyclum; </s> <s xml:id="echoid-s3568" xml:space="preserve">Veneri au- <pb o="70" file="106" n="107" rhead="Comment. in I. Cap. Sphæræ"/> tem tres tantum orbes, & </s> <s xml:id="echoid-s3569" xml:space="preserve">epicyclum, Conſentaneum igitur rationi eſſe vide-<lb/>tur, potius Mercurium ſupra Lunam conſtitui, quàm Venerem.</s> <s xml:id="echoid-s3570" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3571" xml:space="preserve"><emph style="sc">Ordinem</emph> porro planetarum, quem hactenus comprobauimus, uiden-<lb/> <anchor type="note" xlink:label="note-106-01a" xlink:href="note-106-01"/> tur omnes antiqui dierum hebdomadæ inſtitutores, atque denominatores con <lb/>firmare. </s> <s xml:id="echoid-s3572" xml:space="preserve">Impoſuerunt namque diebus nomina α<unsure/> planetis, quemlibet uidelicet <lb/>ab eo planeta, qui prima illius diei hora dominium obtinet, denominando. </s> <s xml:id="echoid-s3573" xml:space="preserve">Sin <lb/>guli enim planetæ ſingulis horis diei ſuo ordine præeſſe dicuntur ab Aſtrono-<lb/>mis; </s> <s xml:id="echoid-s3574" xml:space="preserve">quod quàm verum ſit, non eſt huius loci diſputare. </s> <s xml:id="echoid-s3575" xml:space="preserve">Vnde cum dies conti-<lb/>neat 24. </s> <s xml:id="echoid-s3576" xml:space="preserve">horas, neceſſe eſt, ut ſi die Sabbati prima hora dominatur Saturnus, à <lb/>quo denominatur dies Saturni, ſequenti die prima hora denominetur planeta <lb/>ordine retrogrado ſequens, duobus intermiſſis, nempe Sol, à<unsure/> quo denominatur <lb/>dies Solis. </s> <s xml:id="echoid-s3577" xml:space="preserve">Nam ſi prima hora denominatur Saturnus, ſecunda denominabitur <lb/>Iuppiter; </s> <s xml:id="echoid-s3578" xml:space="preserve">33. </s> <s xml:id="echoid-s3579" xml:space="preserve">Mars; </s> <s xml:id="echoid-s3580" xml:space="preserve">4. </s> <s xml:id="echoid-s3581" xml:space="preserve">Sol; </s> <s xml:id="echoid-s3582" xml:space="preserve">5. </s> <s xml:id="echoid-s3583" xml:space="preserve">Vẽnus; </s> <s xml:id="echoid-s3584" xml:space="preserve">6. </s> <s xml:id="echoid-s3585" xml:space="preserve">Mercurius; </s> <s xml:id="echoid-s3586" xml:space="preserve">7. </s> <s xml:id="echoid-s3587" xml:space="preserve">Luna; </s> <s xml:id="echoid-s3588" xml:space="preserve">8. </s> <s xml:id="echoid-s3589" xml:space="preserve">Saturnus; </s> <s xml:id="echoid-s3590" xml:space="preserve">9. </s> <s xml:id="echoid-s3591" xml:space="preserve">Iuppiter; <lb/></s> <s xml:id="echoid-s3592" xml:space="preserve">10. </s> <s xml:id="echoid-s3593" xml:space="preserve">Mars; </s> <s xml:id="echoid-s3594" xml:space="preserve">11. </s> <s xml:id="echoid-s3595" xml:space="preserve">Sol; </s> <s xml:id="echoid-s3596" xml:space="preserve">12. </s> <s xml:id="echoid-s3597" xml:space="preserve">Venus; </s> <s xml:id="echoid-s3598" xml:space="preserve">13. </s> <s xml:id="echoid-s3599" xml:space="preserve">Mercurius; </s> <s xml:id="echoid-s3600" xml:space="preserve">14. </s> <s xml:id="echoid-s3601" xml:space="preserve">Luna; </s> <s xml:id="echoid-s3602" xml:space="preserve">15. </s> <s xml:id="echoid-s3603" xml:space="preserve">Saturnus; </s> <s xml:id="echoid-s3604" xml:space="preserve">16. </s> <s xml:id="echoid-s3605" xml:space="preserve">Iuppiter; </s> <s xml:id="echoid-s3606" xml:space="preserve"><lb/>17. </s> <s xml:id="echoid-s3607" xml:space="preserve">Mars; </s> <s xml:id="echoid-s3608" xml:space="preserve">18. </s> <s xml:id="echoid-s3609" xml:space="preserve">Sol; </s> <s xml:id="echoid-s3610" xml:space="preserve">19. </s> <s xml:id="echoid-s3611" xml:space="preserve">Venus; </s> <s xml:id="echoid-s3612" xml:space="preserve">20. </s> <s xml:id="echoid-s3613" xml:space="preserve">Mercurius; </s> <s xml:id="echoid-s3614" xml:space="preserve">21. </s> <s xml:id="echoid-s3615" xml:space="preserve">Luna; </s> <s xml:id="echoid-s3616" xml:space="preserve">22. </s> <s xml:id="echoid-s3617" xml:space="preserve">Saturnus; </s> <s xml:id="echoid-s3618" xml:space="preserve">23. </s> <s xml:id="echoid-s3619" xml:space="preserve">Iuppiter; </s> <s xml:id="echoid-s3620" xml:space="preserve"><lb/>24. </s> <s xml:id="echoid-s3621" xml:space="preserve">Mars; </s> <s xml:id="echoid-s3622" xml:space="preserve">Deinde prima hora diei ſequentis Sol, at que ita deinceps. </s> <s xml:id="echoid-s3623" xml:space="preserve">Ex quo pa-<lb/>tet, cur non denominentur dies ſecundum ordinem planetarum immediate, <lb/>ſed ſemper ſecundum ordinem retrogradum, duobus intermiſſis, quia nimirum <lb/>hoc ordine præſunt horis diei, qui quidem ordo di<unsure/>erum talis minime eſſet, ni-<lb/>ſi planetæ eo ordine locarentur. </s> <s xml:id="echoid-s3624" xml:space="preserve">Hac de re extant duo carmina, ut ſciatur, qui-<lb/>bus horis diei quilibet planeta dominetur: </s> <s xml:id="echoid-s3625" xml:space="preserve">In quibus etiam apparet, quem o@ <lb/>dinem inter ſe habeant.</s> <s xml:id="echoid-s3626" xml:space="preserve"/> </p> <div xml:id="echoid-div189" type="float" level="2" n="13"> <note position="left" xlink:label="note-106-01" xlink:href="note-106-01a" xml:space="preserve">Ordo plane <lb/>tarũ confir <lb/>matur ex <lb/>dominio <lb/>Planetarũ, <lb/>& dier<unsure/>um <lb/>denomina-<lb/>tione.</note> </div> <p style="it"> <s xml:id="echoid-s3627" xml:space="preserve">cynthia, Mercurius, Venus, & </s> <s xml:id="echoid-s3628" xml:space="preserve">Sol, Mars, Ioue, Satur, <lb/>Ordine retrogrado ſibi quiuis uendicat horam.</s> <s xml:id="echoid-s3629" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3630" xml:space="preserve">Ioannes Xiphilinus ex lib. </s> <s xml:id="echoid-s3631" xml:space="preserve">36. </s> <s xml:id="echoid-s3632" xml:space="preserve">Dionis in Pompeio ſcribit, hunc ordinem dierum <lb/>inſtitutum eſſe ab Aegyptiis, quos dicit prædictum ordinem in Planetis conſti <lb/>tuiſſe. </s> <s xml:id="echoid-s3633" xml:space="preserve">Addit deinde aliam rationem huius denominationis dierum à conſonañ <lb/>tia Muſices, quæ διατεσσάρων dicitur, quæ ſecundum ueteres totius Muſicæ <lb/>fundamentum credebatur. </s> <s xml:id="echoid-s3634" xml:space="preserve">Propter hanc enim conſonantiam, atque harmo-<lb/>niam, ut dies muſica ratione quodammodo cum cœli ornatu cõuenirent, poſt-<lb/>quam dies unus ab uno Planeta fuit appellatus, dixerunt ſequentem diem à <lb/>quarto Planeta poſt illum, ordine tamen retrogrado: </s> <s xml:id="echoid-s3635" xml:space="preserve">ut poſt Saturnum ſequi-<lb/>tur quarto loco Sol, deinde Luna, deinde Mars, &</s> <s xml:id="echoid-s3636" xml:space="preserve">c.</s> <s xml:id="echoid-s3637" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3638" xml:space="preserve"><emph style="sc">Constat</emph> igitur ex omnibus ijs, quæ diximus, ordinem à noſtro auctore <lb/>præſcriptum inter planetas eſſe ueriorem, & </s> <s xml:id="echoid-s3639" xml:space="preserve">magis conformem Aſtronomis pe <lb/>ritis. </s> <s xml:id="echoid-s3640" xml:space="preserve">Explodenda ergo eſt opinio Metrodori & </s> <s xml:id="echoid-s3641" xml:space="preserve">Cratis, qui Solem, ac Lunam po <lb/>nebant ſupremos planetarum: </s> <s xml:id="echoid-s3642" xml:space="preserve">Reijcienda quoque eſt opinio Democriti, qui <lb/>Mercurium sole faciebant ſuperiorem: </s> <s xml:id="echoid-s3643" xml:space="preserve">Sententia item Alpetragij, qui Vene-<lb/>rem putabat Sole altiorem, nullius eſt momenti: </s> <s xml:id="echoid-s3644" xml:space="preserve">Opinio denique Platonis, & </s> <s xml:id="echoid-s3645" xml:space="preserve"><lb/>Ariſtotelis ualeat, qui Solem, ac Lunam infimo loco collocabant.</s> <s xml:id="echoid-s3646" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3647" xml:space="preserve"><emph style="sc">Vervm</emph> obijciunt nonnulli: </s> <s xml:id="echoid-s3648" xml:space="preserve">Solem nunquam eclipſim pati à Mercurio, <lb/>ac Venere, quare nullo modo Solem ſupra illos ſtatuendum eſſe: </s> <s xml:id="echoid-s3649" xml:space="preserve">Alias enim <lb/>interdum ab illis occultaretur, ſicut uidemus ipſum occultari à Luna, quoniam <lb/> <anchor type="note" xlink:label="note-106-02a" xlink:href="note-106-02"/> ſupra ipſum collocatur. </s> <s xml:id="echoid-s3650" xml:space="preserve">Attamen hæc obiectio nullum robur habet. </s> <s xml:id="echoid-s3651" xml:space="preserve">Vt enim <lb/>ait Ptolemæus Dict. </s> <s xml:id="echoid-s3652" xml:space="preserve">9. </s> <s xml:id="echoid-s3653" xml:space="preserve">ca. </s> <s xml:id="echoid-s3654" xml:space="preserve">1. </s> <s xml:id="echoid-s3655" xml:space="preserve">& </s> <s xml:id="echoid-s3656" xml:space="preserve">Ioan. </s> <s xml:id="echoid-s3657" xml:space="preserve">de Region. </s> <s xml:id="echoid-s3658" xml:space="preserve">lib. </s> <s xml:id="echoid-s3659" xml:space="preserve">9. </s> <s xml:id="echoid-s3660" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s3661" xml:space="preserve">1. </s> <s xml:id="echoid-s3662" xml:space="preserve">poſſunt duo pla-<lb/>netæ coniungi, id eſt, eſſe in eodem gradu Zodiaci, ita ut linea recta exiens ab <lb/>oculo, tranſiensq́ue per centrum unius, minime per centrum alterius tranſeat, <lb/>quod tamen requiritur ad eclipſim: </s> <s xml:id="echoid-s3663" xml:space="preserve">Hinc enim fit, vt uideamus ſæpiſſi<unsure/>me Lu- <pb o="71" file="107" n="108" rhead="Ioan. de Sacro Boſco."/> nam in Nouilunijs coniunctam cum Sole eum non occultare. </s> <s xml:id="echoid-s3664" xml:space="preserve">Præterea ſecun <lb/>dum Albategnium & </s> <s xml:id="echoid-s3665" xml:space="preserve">Tebith, & </s> <s xml:id="echoid-s3666" xml:space="preserve">alios Aſtronomos, diameter uiſualis Solis ad <lb/> <anchor type="note" xlink:label="note-107-01a" xlink:href="note-107-01"/> diametrum uiſualem Veneris (ſunt autem uiſuales diametri illorum circulo-<lb/>ru<unsure/>m, qui nobis apparent in aſtris) proportionem habet decuplam. </s> <s xml:id="echoid-s3667" xml:space="preserve">Vnde iuxta <lb/>demonſtrationes Geometricas, circulus viſualis Solis ad circulum uiſualem <lb/>Veneris proportionem habebit centuplam. </s> <s xml:id="echoid-s3668" xml:space="preserve">Nam cum circuli eam inter ſe <lb/>proportionem habeant, quam diametrorum quadrata, proportio autem qua-<lb/> <anchor type="note" xlink:label="note-107-02a" xlink:href="note-107-02"/> dratorum, quæ deſcribuntur ex diametris circulorum, duplicata ſit illius pro-<lb/> <anchor type="note" xlink:label="note-107-03a" xlink:href="note-107-03"/> portionis, quam habent diametri: </s> <s xml:id="echoid-s3669" xml:space="preserve">ſit, ut cum diametr<unsure/>i uiſuales circulorum So <lb/>lis, ac Veneris habeant proportionem decuplam, diametrorum quadrata, atque <lb/>adeo & </s> <s xml:id="echoid-s3670" xml:space="preserve">circulij uiſuales, proportionem habeant centuplam: </s> <s xml:id="echoid-s3671" xml:space="preserve">Hæc enim illius <lb/>duplicata eſt, ut in his numeris 1. </s> <s xml:id="echoid-s3672" xml:space="preserve">10. </s> <s xml:id="echoid-s3673" xml:space="preserve">100. </s> <s xml:id="echoid-s3674" xml:space="preserve">qui decuplam proportionem con-<lb/>tinuam habent, perſpicuum eſt. </s> <s xml:id="echoid-s3675" xml:space="preserve">Nam, ut ex defin. </s> <s xml:id="echoid-s3676" xml:space="preserve">10. </s> <s xml:id="echoid-s3677" xml:space="preserve">lib. </s> <s xml:id="echoid-s3678" xml:space="preserve">5. </s> <s xml:id="echoid-s3679" xml:space="preserve">Eucl. </s> <s xml:id="echoid-s3680" xml:space="preserve">conſtat, quando <lb/>ſunt tres magnitudines continue proportionales, dicitur tertia ad primam ha-<lb/>bere proportionem duplicatam illius proportionis, quam ſecunda habet ad pri <lb/>mam, vel tertia ad ſecundam. </s> <s xml:id="echoid-s3681" xml:space="preserve">Cum ergo dicti tres numeri 1. </s> <s xml:id="echoid-s3682" xml:space="preserve">10. </s> <s xml:id="echoid-s3683" xml:space="preserve">100. </s> <s xml:id="echoid-s3684" xml:space="preserve">conti-<lb/>nuè ſint proportionales in proportione decupla, erit proportio centupla, quã <lb/>tertius numerus 100. </s> <s xml:id="echoid-s3685" xml:space="preserve">ad primum 1. </s> <s xml:id="echoid-s3686" xml:space="preserve">hẽt, duplicata proportionis decuplæ, quã <lb/>hẽt ſecundus numerus 10. </s> <s xml:id="echoid-s3687" xml:space="preserve">ad primũ 1. </s> <s xml:id="echoid-s3688" xml:space="preserve">uel tertius 100. </s> <s xml:id="echoid-s3689" xml:space="preserve">ad ſecundum 10. </s> <s xml:id="echoid-s3690" xml:space="preserve">Ex quo <lb/>f<unsure/>it, circulum uiſualem Solis ad circulum uiſualem Veneris habere proportio-<lb/>nem centuplam, cum di<unsure/>ctorum circulorum diametri decuplam habeant pro-<lb/>portionem, & </s> <s xml:id="echoid-s3691" xml:space="preserve">circuli habeant proportionem duplicatam illius, quam diametri <lb/>habent, vt dictum eſt. </s> <s xml:id="echoid-s3692" xml:space="preserve">Eadem ratione, ſi duorum circulorum diametri habeant <lb/>proportionem duplam, habebunt ipſi circuli proportionem quadruplam. </s> <s xml:id="echoid-s3693" xml:space="preserve">Hæc <lb/>namque illius duplicata eſt, ut patet in his numeris 1. </s> <s xml:id="echoid-s3694" xml:space="preserve">2. </s> <s xml:id="echoid-s3695" xml:space="preserve">4. </s> <s xml:id="echoid-s3696" xml:space="preserve">continue proportio <lb/>nalibus in proportione dupla. </s> <s xml:id="echoid-s3697" xml:space="preserve">Sic etiam ſi diametri duorum circulorum ha-<lb/>beant proportionem centuplam, habebunt circuli ipſi proportionem, quam <lb/>10000. </s> <s xml:id="echoid-s3698" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s3699" xml:space="preserve">ut in tribus his numeris 1. </s> <s xml:id="echoid-s3700" xml:space="preserve">100. </s> <s xml:id="echoid-s3701" xml:space="preserve">10000. </s> <s xml:id="echoid-s3702" xml:space="preserve">continuam proportionem <lb/>centuplam habentibus manifeſtum eſt. </s> <s xml:id="echoid-s3703" xml:space="preserve">Hac arte quorumlibet circulorum pro-<lb/>portionem cognoſcemus, ſi proportio, quam eorum diametri habent, fuerit co-<lb/>gnita. </s> <s xml:id="echoid-s3704" xml:space="preserve">Vt autem facile ſciatur, quænam proportio dicatur alterius proportio <lb/>nis duplicata, multiplicandus erit denominator proportionis in ſeipſum: </s> <s xml:id="echoid-s3705" xml:space="preserve">pro-<lb/>ducetur enim denominator pro portionis duplicatæ: </s> <s xml:id="echoid-s3706" xml:space="preserve">Vt quoniam decuplæ pro <lb/>portionis denominator eſt 10. </s> <s xml:id="echoid-s3707" xml:space="preserve">ſi 10. </s> <s xml:id="echoid-s3708" xml:space="preserve">in 10. </s> <s xml:id="echoid-s3709" xml:space="preserve">multiplicentur, procreabuntur 100 <lb/>nempe denominator duplicatæ proportionis ipſius decuplæ. </s> <s xml:id="echoid-s3710" xml:space="preserve">Eadem ratione <lb/>duplicata proportio proportionis triplæ, erit noncupla, &</s> <s xml:id="echoid-s3711" xml:space="preserve">c. </s> <s xml:id="echoid-s3712" xml:space="preserve">qua de re lege ea, <lb/>quæ in defin. </s> <s xml:id="echoid-s3713" xml:space="preserve">10. </s> <s xml:id="echoid-s3714" xml:space="preserve">lib. </s> <s xml:id="echoid-s3715" xml:space="preserve">5. </s> <s xml:id="echoid-s3716" xml:space="preserve">Eucl. </s> <s xml:id="echoid-s3717" xml:space="preserve">ſcripſimus. </s> <s xml:id="echoid-s3718" xml:space="preserve">Hinc perſpicuum eſt, Venerem nullo <lb/>modo poſſe Solem obtegere, etiamſi interponatur inter noſtrum aſpectum, & </s> <s xml:id="echoid-s3719" xml:space="preserve"><lb/>Solem: </s> <s xml:id="echoid-s3720" xml:space="preserve">quoniam occultabit ſolum centeſimam,<unsure/> partem ipſius, quæ nullius eſt <lb/>momenti, & </s> <s xml:id="echoid-s3721" xml:space="preserve">uix animaduerti poteſt. </s> <s xml:id="echoid-s3722" xml:space="preserve">A fortiori igitur neque Mercurius id ef-<lb/>ficere poterit, cum eius diameter uiſualis ſit longe minor diametro uiſuali Ve-<lb/>neris. </s> <s xml:id="echoid-s3723" xml:space="preserve">Quòd ſi quis roget, cur igitur Luna e uiſu nobis Solem quandoque eri <lb/>pit, cum tamen mirum in modum minor ſit Luna ipſo Sole? </s> <s xml:id="echoid-s3724" xml:space="preserve">Reſpondendum <lb/> <anchor type="note" xlink:label="note-107-04a" xlink:href="note-107-04"/> eſt, id euenire ob nimiam vicinitatem Lunæ ad terram, & </s> <s xml:id="echoid-s3725" xml:space="preserve">maximam illius di-<lb/>ſtantiam à Sole. </s> <s xml:id="echoid-s3726" xml:space="preserve">Hinc enim efficitur, ut diameter uiſualis Lunæ appar<unsure/>eat no-<lb/>bis maior diametro<unsure/> uiſuali Solis, & </s> <s xml:id="echoid-s3727" xml:space="preserve">propterea tota Luna maior conſpiciatur. <lb/></s> <s xml:id="echoid-s3728" xml:space="preserve">quam Sol. </s> <s xml:id="echoid-s3729" xml:space="preserve">Vnde mirum non eſt, quod Luna Solem poſſit contegere aliquan-<lb/>do, ita ut cerni non poſſit.</s> <s xml:id="echoid-s3730" xml:space="preserve"/> </p> <div xml:id="echoid-div190" type="float" level="2" n="14"> <note position="left" xlink:label="note-106-02" xlink:href="note-106-02a" xml:space="preserve">Sol cur à <lb/>Mercurio, <lb/>& Venere, <lb/>cum inſra <lb/>ipſum ſint, <lb/>n<unsure/>on eclipſe <lb/>@ur.</note> <note position="right" xlink:label="note-107-01" xlink:href="note-107-01a" xml:space="preserve">Diametri<unsure/> <lb/>uiſuales a-<lb/>ſtrorum <lb/>guid.</note> <note position="right" xlink:label="note-107-02" xlink:href="note-107-02a" xml:space="preserve">2. duod.</note> <note position="right" xlink:label="note-107-03" xlink:href="note-107-03a" xml:space="preserve">20. ſexti.</note> <note position="right" xlink:label="note-107-04" xlink:href="note-107-04a" xml:space="preserve">Cur Luna <lb/>Solem in-<lb/>terdũ ecli-<lb/>pſet, cũ ta <lb/>mẽ multo <lb/>minor ipſo <lb/>ſit.</note> </div> <pb o="72" file="108" n="109" rhead="Comment. in I. Cap. Sphæræ"/> <p> <s xml:id="echoid-s3731" xml:space="preserve">Ex his omnibus colligitur & </s> <s xml:id="echoid-s3732" xml:space="preserve">numerus, & </s> <s xml:id="echoid-s3733" xml:space="preserve">ordo omnium corporum totius <lb/> <anchor type="note" xlink:label="note-108-01a" xlink:href="note-108-01"/> Vniuerſi. </s> <s xml:id="echoid-s3734" xml:space="preserve">Erunt enim in toto Vniuerſo quindecim corpora ſphærica totum <lb/>mundum integrantia, eo ordine poſita, ut partim in tractatu de elementis, <lb/>partim hic in tractatione de corporibus cæleſtibus oſtenſum eſt; </s> <s xml:id="echoid-s3735" xml:space="preserve">at que ſatis di-<lb/>lucide appoſita figura indicare uidetur, in qua totius Vniuerſi ordinem, ſitum-<lb/>q́ue conſpicis, una cum characteribus Planetarum, quibus Aſtronomi eos figu-<lb/>rare ſolent, ac depingere.</s> <s xml:id="echoid-s3736" xml:space="preserve"/> </p> <div xml:id="echoid-div191" type="float" level="2" n="15"> <note position="left" xlink:label="note-108-01" xlink:href="note-108-01a" xml:space="preserve">Numerus <lb/>& ordo om <lb/>nium cor-<lb/>porũ Vni-<lb/>uerſum cõ-<lb/>ponentiũ.</note> </div> <figure> <image file="108-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/108-01"/> </figure> <note position="left" xml:space="preserve">Extra mun <lb/>dum nihil <lb/>eſſe.</note> <p> <s xml:id="echoid-s3737" xml:space="preserve"><emph style="sc">EXTRA</emph> hunc uero mundum, ſeu extra cœlum Empyreum, nullum pror-<lb/>ſus corpus exiſtit, ſed eſt ſpatium quoddam infinitum, (ſi ita loqui fas ſit) in <lb/>quo etiam toto Deus exiſtit ſua eſſentia, in quo infinitos alios mundos, perſe-<lb/>ctiores etiam hoc, fabricare poſſet, ſi uellet, ut Theologi aſſerunt.</s> <s xml:id="echoid-s3738" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div193" type="section" level="1" n="62"> <head xml:id="echoid-head66" xml:space="preserve">COELVM MOVERI AB ORTV IN OCCASVM.</head> <note position="left" xml:space="preserve">Cœlũ mo-<lb/>ueri ab or-<lb/>tu in occa-<lb/>ſum, proba <lb/>tur ex ſtel-<lb/>lis orienti-<lb/>bus, occidẽ <lb/>tibusq́ue.</note> <p style="it"> <s xml:id="echoid-s3739" xml:space="preserve"><emph style="sc">QVod</emph> autem cœlum uoluatur ab oriente in occidentem, ſi-<lb/>gnum eſt. </s> <s xml:id="echoid-s3740" xml:space="preserve">Stellę, quæ oriuntur in oriente, ſemper eleuantur <lb/>paulatim, & </s> <s xml:id="echoid-s3741" xml:space="preserve">ſucceſſi<unsure/>ue, quouſque in medium cœli ueniant; </s> <s xml:id="echoid-s3742" xml:space="preserve">& </s> <s xml:id="echoid-s3743" xml:space="preserve"><lb/>ſunt ſemper in eadem propinquitate, & </s> <s xml:id="echoid-s3744" xml:space="preserve">remotione ad inuicem, <lb/>& </s> <s xml:id="echoid-s3745" xml:space="preserve">ita ſempe<unsure/>r ſe habentes, tendunt in occaſum continue, & </s> <s xml:id="echoid-s3746" xml:space="preserve">un<unsure/>iformiter.</s> <s xml:id="echoid-s3747" xml:space="preserve"/> </p> <pb o="73" file="109" n="110" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div194" type="section" level="1" n="63"> <head xml:id="echoid-head67" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s3748" xml:space="preserve"><emph style="sc">Haec</emph> eſt quarta, ac poſtrema pars huius primi capitis, in qua auctor ſex <lb/> <anchor type="note" xlink:label="note-109-01a" xlink:href="note-109-01"/> propoſitiones de æthera, acelementari regione oſtendit, quas quidem in pręce <lb/>denti parte, tanquam certas & </s> <s xml:id="echoid-s3749" xml:space="preserve">indubitatas aſſumere uiſus eſt. </s> <s xml:id="echoid-s3750" xml:space="preserve">Prima eſt, cęlum <lb/>moueri ab oriente in occidentem. </s> <s xml:id="echoid-s3751" xml:space="preserve">Secunda, cęlum eſſe rotundum. </s> <s xml:id="echoid-s3752" xml:space="preserve">Tertia, tam <lb/>terra, quàm aquam rotundam eſſe. </s> <s xml:id="echoid-s3753" xml:space="preserve">Quarta, terram eſſe centrum mundi: </s> <s xml:id="echoid-s3754" xml:space="preserve">Quin-<lb/>ta, terram eſſe immobilẽ. </s> <s xml:id="echoid-s3755" xml:space="preserve">Sexta, & </s> <s xml:id="echoid-s3756" xml:space="preserve">vltima, terrã habere quantitatem abſolutam <lb/>ac finitam, at que adeo cognitam, quamuis vulgo immenſa uideatur. </s> <s xml:id="echoid-s3757" xml:space="preserve">Neceſſc <lb/>enim eſt, Aſtronomo terræ magnitudinem exploratam eſſe, cum per eam ma-<lb/>gnitudines cęlorum, & </s> <s xml:id="echoid-s3758" xml:space="preserve">ſiderum cognoſcantur.</s> <s xml:id="echoid-s3759" xml:space="preserve"/> </p> <div xml:id="echoid-div194" type="float" level="2" n="1"> <note position="right" xlink:label="note-109-01" xlink:href="note-109-01a" xml:space="preserve">Quid in re-<lb/>liqua parte <lb/>huius cap. <lb/>agat<unsure/>ur.</note> </div> <p> <s xml:id="echoid-s3760" xml:space="preserve"><emph style="sc">Qvod</emph> igitur ad primam propoſitionem attinet, quoniam poſſet quis ne-<lb/>gare, cęlum moueri ab oriente in occidentem, ſed potius ſtellas per ſeſe moue-<lb/>ri, ceu piſces in mari, uel ut aues in aere, cęlum autem prorſus quieſcere, ut mul <lb/>ti auſi ſunt aſſerere, probat duplici argumento, hoc uerum non eſſe; </s> <s xml:id="echoid-s3761" xml:space="preserve">quorum <lb/>unum ſumitur ex ſtellis, quæ nobis oriuntur & </s> <s xml:id="echoid-s3762" xml:space="preserve">occidunt; </s> <s xml:id="echoid-s3763" xml:space="preserve">alterũ à ſtellis, quę <lb/>nunquam nobis oriuntur, occiduntve, ſed perpetuo apparent: </s> <s xml:id="echoid-s3764" xml:space="preserve">Quæ quidem ar <lb/>gumenta deſumpta ſunt ex Ptolemęo Dict. </s> <s xml:id="echoid-s3765" xml:space="preserve">1. </s> <s xml:id="echoid-s3766" xml:space="preserve">cap. </s> <s xml:id="echoid-s3767" xml:space="preserve">3. </s> <s xml:id="echoid-s3768" xml:space="preserve">& </s> <s xml:id="echoid-s3769" xml:space="preserve">Ioan. </s> <s xml:id="echoid-s3770" xml:space="preserve">de Regiom. </s> <s xml:id="echoid-s3771" xml:space="preserve">lib. </s> <s xml:id="echoid-s3772" xml:space="preserve">1. <lb/></s> <s xml:id="echoid-s3773" xml:space="preserve">concluſ. </s> <s xml:id="echoid-s3774" xml:space="preserve">1. </s> <s xml:id="echoid-s3775" xml:space="preserve">Eſt autem primum argumentũ huiuſmodi. </s> <s xml:id="echoid-s3776" xml:space="preserve">Omnes ſtellæ, quæ no-<lb/>bis oriuntur & </s> <s xml:id="echoid-s3777" xml:space="preserve">occidunt, in eadem ſemper diſtantia, codemq́ ſitu inter ſe mo-<lb/>uentur paulatim ab orcu per meridiem in occaſum. </s> <s xml:id="echoid-s3778" xml:space="preserve">Ergo ſtellæ infixę cęlo mo-<lb/>uentur ad motum cęli, tanquam clauus ad motum rotæ, uel nodus ad motum <lb/>tabulæ. </s> <s xml:id="echoid-s3779" xml:space="preserve">A ntecedens experientia quotidiana eſt manifeſtum: </s> <s xml:id="echoid-s3780" xml:space="preserve">Conſequentia pa-<lb/>tet, quia ſi mouerentur ſtellæ per ſe, non eſſent ſemper in eadem diſtantia, & </s> <s xml:id="echoid-s3781" xml:space="preserve"><lb/>ordine inter ſeſe, neque vniformiter ſemper procederent, ſed aliquando una <lb/>alteram præcederet, præſertim cum ipſæ inter ſe ſint inęquales, & </s> <s xml:id="echoid-s3782" xml:space="preserve">circulos inæ <lb/>quales deſcribant. </s> <s xml:id="echoid-s3783" xml:space="preserve">Temerè enim nidemur aſſerere, minores ſtellas eandem vim <lb/>motricem habere, quam maiores.</s> <s xml:id="echoid-s3784" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s3785" xml:space="preserve"><emph style="sc">Est</emph> & </s> <s xml:id="echoid-s3786" xml:space="preserve">aliud ſignum. </s> <s xml:id="echoid-s3787" xml:space="preserve">Stellæ, quæ ſunt iuxta polum arcticum, quæ <lb/> <anchor type="note" xlink:label="note-109-02a" xlink:href="note-109-02"/> nunquam nobis occidunt, mouentur continue, & </s> <s xml:id="echoid-s3788" xml:space="preserve">uniformiter circa polum <lb/>deſcribendo circulos ſuos, & </s> <s xml:id="echoid-s3789" xml:space="preserve">ſemper ſunt in æquali diſtantia ad inuicem, <lb/>& </s> <s xml:id="echoid-s3790" xml:space="preserve">propinquitate. </s> <s xml:id="echoid-s3791" xml:space="preserve">Vnde per iſtos duos motus continuos ſtellarum, tam <lb/>tendentium ad occaſum, quàm non, patet, quod Firmamentum mouet@r <lb/>ab oriente in occidentem.</s> <s xml:id="echoid-s3792" xml:space="preserve"/> </p> <div xml:id="echoid-div195" type="float" level="2" n="2"> <note position="right" xlink:label="note-109-02" xlink:href="note-109-02a" xml:space="preserve">Cęlũ moue <lb/>ri ab ortu <lb/>in occasũ, <lb/>ꝓbatur ex <lb/>ſtellis neq; <lb/>orientibus <lb/>neque occi-<lb/>dentibus.</note> </div> </div> <div xml:id="echoid-div197" type="section" level="1" n="64"> <head xml:id="echoid-head68" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s3793" xml:space="preserve"><emph style="sc">Proponit</emph> ſecundum argumentum in hunc fere ſenſum. </s> <s xml:id="echoid-s3794" xml:space="preserve">Stellæ exi-<lb/>ſ<unsure/>tentes iuxta polum arcticum, quæ nunquam nobis occidunt, deſcribunt ſuo <lb/>motu ſemper uniformi in eodem tempore diuerſos circulos, aliæ maiores, quę <lb/>nimirum remotiores ſunt à polo, alię minores, quę uidelicet propinquiores <lb/>polo exiſtunt, ſemperque in eadem propinquitate inter ſe conſpiciuntur. </s> <s xml:id="echoid-s3795" xml:space="preserve">Non <lb/>igitur per ſeſe, ſed ad motum orbis, cuius ſunt partes, mouentur. </s> <s xml:id="echoid-s3796" xml:space="preserve">Nam ſi pro-<lb/>prijs u<unsure/>iribus, ac per ſeſe in cęlo incederent, utique quę maiores circulos de-<lb/>ſcribunt, longiori tempore, quæ uero minores, breuiori tempore moueren-<lb/>tur; </s> <s xml:id="echoid-s3797" xml:space="preserve">immo ſtellæ inæquales in eodem circulo poſitę inæqualiter mouerentur; <lb/></s> <s xml:id="echoid-s3798" xml:space="preserve">quæ omnia ſenſui repugnant, & </s> <s xml:id="echoid-s3799" xml:space="preserve">experientiæ.</s> <s xml:id="echoid-s3800" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3801" xml:space="preserve"><emph style="sc">Non</emph> minorem uim habent ad perſuadendum, cęlum ab ortu in occaſum <pb o="74" file="110" n="111" rhead="Comment. in I. Cap. Sphæræ"/> moueri, ſuoq; </s> <s xml:id="echoid-s3802" xml:space="preserve">motu ſecum circumducere ſtellas omnes, duæ experientiæ, quas <lb/> <anchor type="note" xlink:label="note-110-01a" xlink:href="note-110-01"/> iam iam in medium depromã. </s> <s xml:id="echoid-s3803" xml:space="preserve">Altera ex uia lactea ſumitur, quę cum ſit uel in-<lb/>ſinita multitudo ſtellarum minimarum, vel quod magis probo, pars octaui cœ-<lb/>li denſior, & </s> <s xml:id="echoid-s3804" xml:space="preserve">continua, licet non uniformiter ſit denſa, qui fieri poteſt, ut to-<lb/>tus ille candor totum cęlum circundans tam regulariter ab ortu in occaſum <lb/>progrediatur, uiſi motu octauæ ſphæræ, in qua eſt, circunferatur? </s> <s xml:id="echoid-s3805" xml:space="preserve">Altera expe-<lb/>rientia conſiſtit in partibus cęli rarioribus, cuiuſmodi non paucæ cernuntur <lb/>(vt eruditus quidam vir, & </s> <s xml:id="echoid-s3806" xml:space="preserve">religioſus uitam degens in prouincia Peru, quæ po <lb/>lum antarcticum ſupra Horizontem habet eleuatum, teſtatur in libello, quem <lb/>de ſitu, & </s> <s xml:id="echoid-s3807" xml:space="preserve">natura Indiæ occidentalis inſcripſit.) </s> <s xml:id="echoid-s3808" xml:space="preserve">prope polum antarcticum; <lb/></s> <s xml:id="echoid-s3809" xml:space="preserve">ita ut nigror quidam pleris que in locis cęli appareat, ac ſi cęlum quodam-<lb/>modo eſſet perforatum. </s> <s xml:id="echoid-s3810" xml:space="preserve">Hæ ergo partes rariores cum vniformiter cum ſtel-<lb/>lis ab ortu in occaſum ſpatio 24. </s> <s xml:id="echoid-s3811" xml:space="preserve">horarum ſerantur, vt non ſemel ab habitan-<lb/>tibus in illo tractu terræ eſt obſeruatum, quis dixerit, illas per ſeſe moueri, & </s> <s xml:id="echoid-s3812" xml:space="preserve"><lb/>non potius ad motum cęli circumduci, cnm non ſint ſtellæ, ſed partes omnino <lb/>raræ, & </s> <s xml:id="echoid-s3813" xml:space="preserve">obſcuræ? </s> <s xml:id="echoid-s3814" xml:space="preserve">Quid enim partes illas impellet, ſi non unà cum cęlo circum-<lb/>ferantur? </s> <s xml:id="echoid-s3815" xml:space="preserve">Quæ cum ita ſint, ueriſimile eſt, totum cęlum ab ortu in occaſum <lb/>agitari, ſecumq́ue trahere & </s> <s xml:id="echoid-s3816" xml:space="preserve">ſtellas, & </s> <s xml:id="echoid-s3817" xml:space="preserve">partes alias denſiores, cuiuſmodi ſunt <lb/>illæ, quæ uiam lacteam efficiunt, & </s> <s xml:id="echoid-s3818" xml:space="preserve">partes rariores, ſiue obſcuras, de quibus <lb/>proxime diximus, & </s> <s xml:id="echoid-s3819" xml:space="preserve">quales etiam ſunt maculæ illæ, quæ in Luna cernuntur, & </s> <s xml:id="echoid-s3820" xml:space="preserve"><lb/>uniformiter cum Luna circumferuntur.</s> <s xml:id="echoid-s3821" xml:space="preserve"/> </p> <div xml:id="echoid-div197" type="float" level="2" n="1"> <note position="left" xlink:label="note-110-01" xlink:href="note-110-01a" xml:space="preserve">Ali<unsure/>æ duæ <lb/>experiẽtię, <lb/>quibus con <lb/>cluditur, cę <lb/>lum moue-<lb/>ri, & nõ ſtel <lb/>las ipſas.</note> </div> <p> <s xml:id="echoid-s3822" xml:space="preserve"><emph style="sc">Aristoteles</emph> lib. </s> <s xml:id="echoid-s3823" xml:space="preserve">2. </s> <s xml:id="echoid-s3824" xml:space="preserve">de cœlo probat quoque, ſtellas per ſeſe non <lb/> <anchor type="note" xlink:label="note-110-02a" xlink:href="note-110-02"/> moueri, hac ratione. </s> <s xml:id="echoid-s3825" xml:space="preserve">Aſtra, ſi per ſe mouentur, & </s> <s xml:id="echoid-s3826" xml:space="preserve">cœlum quieſcit, uel ſunt infi-<lb/>xa in cęlo, uel certe ſunt in ſuperficie extima cęli, concaua uidelicet uel con-<lb/>uexa, ita ut fit aliquid ſpatij interiectũ inter quoſlibet duos cælos, in quo mo-<lb/>ueri poſſint ſtellæ. </s> <s xml:id="echoid-s3827" xml:space="preserve">Si ſunt infixa cęló, dabitur ſciſſio cœli, ſiue penetratio cor-<lb/>porũ, quorum vtrumq; </s> <s xml:id="echoid-s3828" xml:space="preserve">eſt impoſſibile: </s> <s xml:id="echoid-s3829" xml:space="preserve">Si uero mouentur in ſuperficie extima <lb/>cœli, ſicut homo v.</s> <s xml:id="echoid-s3830" xml:space="preserve">g. </s> <s xml:id="echoid-s3831" xml:space="preserve">in pauimento, uel muſca, aut formica in laqueari aliquo, <lb/>erit ſpatiũ, in quo mouentur, uel uacuũ, quod iamdudũ remouit à rerum natu-<lb/>ra Ariſtor<unsure/>eles lib. </s> <s xml:id="echoid-s3832" xml:space="preserve">4. </s> <s xml:id="echoid-s3833" xml:space="preserve">Phyſ. </s> <s xml:id="echoid-s3834" xml:space="preserve">uel corpus, & </s> <s xml:id="echoid-s3835" xml:space="preserve">hoc uel cęleſte, & </s> <s xml:id="echoid-s3836" xml:space="preserve">ſic iterum ſequetur <lb/>primũ inconueniens; </s> <s xml:id="echoid-s3837" xml:space="preserve">aut elementare, quod extra locum ſuum naturalẽ perpe-<lb/>tuo eſſe non poteſt: </s> <s xml:id="echoid-s3838" xml:space="preserve">eſſet autem extra ſuum locum, ſi ibi eſſet. </s> <s xml:id="echoid-s3839" xml:space="preserve">Non igitur per <lb/>ſeſe mouentur ſtellæ. </s> <s xml:id="echoid-s3840" xml:space="preserve">Alias rationes loco citato affert Ariſtoteles, ſed illis re-<lb/>lictis, una ſola experientia, quæ meo iudicio maximũ robur habet, confirmare <lb/>poſſumus concluſionẽ hanc noſtri auctoris. </s> <s xml:id="echoid-s3841" xml:space="preserve">Sumatur quæuis ſtella, ſiue ſixa <lb/>ſit, ſiue erratica, quam aliquis dicat per ſeſe moueri. </s> <s xml:id="echoid-s3842" xml:space="preserve">Hæc ſtella mouetur moti <lb/> <anchor type="note" xlink:label="note-110-03a" xlink:href="note-110-03"/> bus quodammodo oppoſitis, ut ſupra diximus. </s> <s xml:id="echoid-s3843" xml:space="preserve">Mouetur enim ſimpliciter, & </s> <s xml:id="echoid-s3844" xml:space="preserve"><lb/>continue ab oriente in occidentem, & </s> <s xml:id="echoid-s3845" xml:space="preserve">ſimul eodem tempore ſecundum quid, <lb/>& </s> <s xml:id="echoid-s3846" xml:space="preserve">continue, ab occidente in orientem, quemadmodum ſupra expoſitum fuit, <lb/>atque demõſtratum. </s> <s xml:id="echoid-s3847" xml:space="preserve">At uero nullum corpus idem numero cieri poteſt diuerſis <lb/>motibus, atque adeo oppoſitis, eodem tempore: </s> <s xml:id="echoid-s3848" xml:space="preserve">Implicat enim contradictionẽ <lb/>unum & </s> <s xml:id="echoid-s3849" xml:space="preserve">idem corpus ſimul procedere ab oriente in occidentẽ, & </s> <s xml:id="echoid-s3850" xml:space="preserve">eodẽ inſtãti <lb/>ab occidẽte in orientẽ, ita ut neuter motus alterũ interrũpat, ſed uterque ſine <lb/>ulla intermis ſione uniformiter progrediatur, niſi altero motu moueatur tan-<lb/>quã ad uehiculũ alterius. </s> <s xml:id="echoid-s3851" xml:space="preserve">Non igitur ſtellæ liberæ, ac ſolutæ à corporibus cœ-<lb/>eſtibus mouẽtur, quia unico tantũ motu in eodem tẽpore poſſunt moueri; </s> <s xml:id="echoid-s3852" xml:space="preserve">(ut <lb/>aperte uidemus in animalibus, & </s> <s xml:id="echoid-s3853" xml:space="preserve">in aliis rebus, quas ab uno loco in alium im <lb/>pellimus. </s> <s xml:id="echoid-s3854" xml:space="preserve">Fieri enim non poteſt, ut eodem tempore ab alio in contrariã partẽ <pb o="75" file="111" n="112" rhead="Ioan. de Sacro Boſco."/> impellantur, niſi prior motus intermittatur, aut interrumpatur.) </s> <s xml:id="echoid-s3855" xml:space="preserve">ſed deuehun-<lb/>tur ad motũ orbiũ, in quibus ſunt@ita enim poteſt unum, idemq; </s> <s xml:id="echoid-s3856" xml:space="preserve">aſtrũ diuerſis <lb/>cieri lationibus, ut ſupra declaratum fuit, uarijs etiam adductis exemplis. </s> <s xml:id="echoid-s3857" xml:space="preserve">Con <lb/>firmatur hoc ipſum multo magis in planetis: </s> <s xml:id="echoid-s3858" xml:space="preserve">Mouentur enim adhuc pluribus <lb/>motibus, quam duobus illis ab ortu in occaſum, & </s> <s xml:id="echoid-s3859" xml:space="preserve">ab occaſu in ortum; </s> <s xml:id="echoid-s3860" xml:space="preserve">& </s> <s xml:id="echoid-s3861" xml:space="preserve">nunc <lb/>uelocius uidentur moueri ab occidente in orientem, nunc tardius: </s> <s xml:id="echoid-s3862" xml:space="preserve">Videntur <lb/>interdum ſtare, interdum retrocedere in occidentem, &</s> <s xml:id="echoid-s3863" xml:space="preserve">c. </s> <s xml:id="echoid-s3864" xml:space="preserve">vt in Theoricis pla-<lb/>netarum explicatur. </s> <s xml:id="echoid-s3865" xml:space="preserve">Si igitur ſtellæ per ſeſe mouerentur, non poſſet ſufficiens <lb/>ratio huiuſce uarietatis afferri: </s> <s xml:id="echoid-s3866" xml:space="preserve">Si autem ad motum cęli moueri dicãtur, facili <lb/>negotio omnes apparẽtiæ locũ habẽt. </s> <s xml:id="echoid-s3867" xml:space="preserve">ut in Theoricis planetarũ explicabitur.</s> <s xml:id="echoid-s3868" xml:space="preserve"/> </p> <div xml:id="echoid-div198" type="float" level="2" n="2"> <note position="left" xlink:label="note-110-02" xlink:href="note-110-02a" xml:space="preserve">Ratio Ari-<lb/>ſtotelis pro <lb/>bans ſtellas <lb/>non moue-<lb/>ri per ſeſe.</note> <note position="left" xlink:label="note-110-03" xlink:href="note-110-03a" xml:space="preserve">Ratio con-<lb/>uincẽs, ſtel-<lb/>las de facto <lb/>non moue-<lb/>ri per ſe, ſed <lb/>ad motum <lb/>cęli.</note> </div> <p> <s xml:id="echoid-s3869" xml:space="preserve"><emph style="sc">Videntes</emph> itaq; </s> <s xml:id="echoid-s3870" xml:space="preserve">nonnulli, hac ratione non poſſe dari multitudinem <lb/>motum in ſtellis, aliam rationem confinxerunt, quibus perſuadere conantur <lb/>ſtellas moueri per ſeſe, & </s> <s xml:id="echoid-s3871" xml:space="preserve">non infixas eſſe corporibus cœleſtibus. </s> <s xml:id="echoid-s3872" xml:space="preserve">Dicuntenim, <lb/> <anchor type="note" xlink:label="note-111-01a" xlink:href="note-111-01"/> unicum tantum eſſe cœlum, atque hoc ipſum unico motu moueri ab oriente <lb/>in occidẽtem, unà cum omnibus ſtellis; </s> <s xml:id="echoid-s3873" xml:space="preserve">Stellas uero proprijs motibus ab occi-<lb/>dente in orientẽ ferri, ut aiunt, ſolutas ab orbibus cœleſtibus: </s> <s xml:id="echoid-s3874" xml:space="preserve">non quidem tan <lb/>quam piſces in mari, uel aues in aere, ne detur penetratio corporum, aut ſciſſio <lb/>cęli, ſed per canales quoſdam. </s> <s xml:id="echoid-s3875" xml:space="preserve">Confinxerunt namq. </s> <s xml:id="echoid-s3876" xml:space="preserve">ſingulas ſtellas habere ſin-<lb/>gulos canales congruentes motibuspropriis, tantæ amplitudinis, quanta eſt <lb/>illarum magnitudo, ita ut quælibet ſtella repleat totum ſuum canalem. </s> <s xml:id="echoid-s3877" xml:space="preserve">In <lb/>his porro canalibus poſuerunt corpus quoddam fluxibile, ſicut eſt aer, quod <lb/>cedere poſſit ſtellis, quando ab occidente in orientem mouentur. </s> <s xml:id="echoid-s3878" xml:space="preserve">Itaq. </s> <s xml:id="echoid-s3879" xml:space="preserve">ſecun-<lb/>dũ hos auctores totum cęlũ erit refertũ iſtis canalibus, pro multitudine ſtella-<lb/>rũ, ad inſtar animalis, quod repletum eſt uariis, ac multiplicibus uenis. </s> <s xml:id="echoid-s3880" xml:space="preserve">Hanc ue <lb/>ro ſententiã eo libentius amplectuntur, quòd nolint concedere motum raptus. <lb/></s> <s xml:id="echoid-s3881" xml:space="preserve">Dicunt namque impoſſibile eſſe, ut unum cœlum alterum rapiat, quantumuis <lb/>ipſi contiguum. </s> <s xml:id="echoid-s3882" xml:space="preserve">Veruntamen hæc ſententia & </s> <s xml:id="echoid-s3883" xml:space="preserve">abſurda, & </s> <s xml:id="echoid-s3884" xml:space="preserve">infufficiens eſt: </s> <s xml:id="echoid-s3885" xml:space="preserve">Ab-<lb/>ſurda quidem, quoniam ſine ulla neceſſitate, aut ratione probabili, ponit cor-<lb/>pus cœleſte perforatum tot canalibus, & </s> <s xml:id="echoid-s3886" xml:space="preserve">refertum undique corpore illo fluxi-<lb/>bili, quod nemo ph@loſophorum hactenus cõcedere uiſus eſt: </s> <s xml:id="echoid-s3887" xml:space="preserve">Inſufficiens uero, <lb/>quia impoſſibile eſt defendere iuxta hanc ſententiam omnia Phænomena, quæ <lb/>Aſtronomi diligentiſſime obſeruarunt in motibus cœleſtibus. </s> <s xml:id="echoid-s3888" xml:space="preserve">Primo enim ve-<lb/>lint, nolint, uitare nequeunt motum raptus. </s> <s xml:id="echoid-s3889" xml:space="preserve">Cum enim ſtellæ ſint ſolutæ ac li-<lb/>beræ, ut ipſi dicunt, & </s> <s xml:id="echoid-s3890" xml:space="preserve">nullo modo cœlo inhæreant, moueanturque ad motum <lb/>cęli ab ortu in occaſum, neceſſe eſt, eas rapi à cœlo ſine ulla reſiſtentia, aut uio-<lb/>lentia, hanc ſolum ob cauſam, quòd contiguæ ſint canalibus, in quibus exi-<lb/>ſtunt. </s> <s xml:id="echoid-s3891" xml:space="preserve">Secundo quamuis hac ſententia duplex motus, ab oriente uidelicet in <lb/>occidentẽ, & </s> <s xml:id="echoid-s3892" xml:space="preserve">contra, ab occidente in orientem, utcunque defendi poſſit:</s> <s xml:id="echoid-s3893" xml:space="preserve">tamen <lb/>nullo modo plures motus, præter hos duos, ſtella quæuis habere poteſt, ob ra-<lb/>tionem, quam ſupra adduximus contra eos, qui aiebant ſtellas ex ſeſe moue-<lb/>ri. </s> <s xml:id="echoid-s3894" xml:space="preserve">Cum igitur in Luna plures ſint deprehenſi motus, nempe ſex, ut minimum. </s> <s xml:id="echoid-s3895" xml:space="preserve"><lb/>idemque de cæteris planetis ſit dicendum, immo & </s> <s xml:id="echoid-s3896" xml:space="preserve">ſtellę fixæ triplicẽ habeant <lb/>motum, ut ſupra oſtendimus, nullo modo hæc opinio uera eſſe poterit. </s> <s xml:id="echoid-s3897" xml:space="preserve">Tertio <lb/>planetæ, ut ex Theoricis planetarum liquet, non ſemper æqualiter diſtant à <lb/>centro terræ, ſed nunc propiores, nunc uero remotiores apparent, quod nul-<lb/>latenus fieri poſſet, ſi ſtellæ per ſeſe in dictis canalibus mouerentur, niſi dica-<lb/>tur illos canales eſſe eccentricos cum mundo, ita ut una pars magis recedat a <lb/>mundi centro, & </s> <s xml:id="echoid-s3898" xml:space="preserve">alia magis ad idem accedat: </s> <s xml:id="echoid-s3899" xml:space="preserve">quod dici non poteſt. </s> <s xml:id="echoid-s3900" xml:space="preserve">Nam cum <pb o="76" file="112" n="113" rhead="Comment. in I. Cap. Sphæræ"/> canales illi ſint infixi corpori cæleſti, neceſſario efficeretur, ut planeta qui-<lb/>cunque in eadẽ ſemper parte cęli maxime à terra diſtaret, &</s> <s xml:id="echoid-s3901" xml:space="preserve">c. </s> <s xml:id="echoid-s3902" xml:space="preserve">quod eſt falſisſi-<lb/>mũ; </s> <s xml:id="echoid-s3903" xml:space="preserve">Luna ſiquidẽ in omnibus punctis Zodiaci aliquãdo uiſa fuit remotiſſima @ <lb/>terra, item que propinquiſſima. </s> <s xml:id="echoid-s3904" xml:space="preserve">Omitto apparentias de uariatione latitudinum <lb/>omnium planetarum, uno Sole excepto, nec non de retrogradatione, &</s> <s xml:id="echoid-s3905" xml:space="preserve">c. </s> <s xml:id="echoid-s3906" xml:space="preserve">quas <lb/>nullo pacto prædicta opinio tueri poteſt, ut dilucidius explicari ſolet in pla-<lb/>netarum Theoricis. </s> <s xml:id="echoid-s3907" xml:space="preserve">Conſtat igitur ſtellas non per ſeſe moueri, ſed ad motum <lb/>cęlorum, in quibus ſunt infixę: </s> <s xml:id="echoid-s3908" xml:space="preserve">Ita enim cęli habere poſſunt plures motus, vnũ <lb/>quidem proprium, alios uero extrinſecos, nempe ad uehiculum aliorum, ut <lb/>ſupra declaratum fuit. </s> <s xml:id="echoid-s3909" xml:space="preserve">Vnde mirum non eſt, quòd tanta multitudo mor<unsure/>uum in <lb/>ſtellis cernatur.</s> <s xml:id="echoid-s3910" xml:space="preserve"/> </p> <div xml:id="echoid-div199" type="float" level="2" n="3"> <note position="right" xlink:label="note-111-01" xlink:href="note-111-01a" xml:space="preserve">Sententia <lb/>eorum, qu@ <lb/>dicunt ſtel-<lb/>las in cana-<lb/>libus moue <lb/>ri, eiusq. cõ-<lb/>fu@atio.</note> </div> <p> <s xml:id="echoid-s3911" xml:space="preserve"><emph style="sc">Ptolemaevs</emph> Dict. </s> <s xml:id="echoid-s3912" xml:space="preserve">1. </s> <s xml:id="echoid-s3913" xml:space="preserve">adducit opinionem quorundam, qui dicebant <lb/> <anchor type="note" xlink:label="note-112-01a" xlink:href="note-112-01"/> ſtellas moueri quidem ad motum cęli ab oriente in occidentem, ſed motu re-<lb/>cto in infinitum, non autem motu circulari. </s> <s xml:id="echoid-s3914" xml:space="preserve">Quæ quidem ſententia ridicula <lb/>prorſus exiſtit, & </s> <s xml:id="echoid-s3915" xml:space="preserve">propterea ab Aſtronomis reijcienda. </s> <s xml:id="echoid-s3916" xml:space="preserve">Primum, quia hac ratio-<lb/>ne una, eademque ſtella non apparet nobis in eadem propinquitate, ſed pro-<lb/>pius ad nos accederet in meridie, quàm in ortu, ſiue occaſu, quod falſum eſt. </s> <s xml:id="echoid-s3917" xml:space="preserve">De <lb/>inde, quia uidemus quotidie eaſdem ſtellas numero, poſtquam aliquandiu de-<lb/>lituere ſub terra, redire ad orientem: </s> <s xml:id="echoid-s3918" xml:space="preserve">Quod fieri nequaquam poſſet, ſi motu <lb/>recto veherentur. </s> <s xml:id="echoid-s3919" xml:space="preserve">Itaque ex his omnibus perſpicuum cuilibet eſſe poteſt, cęlos <lb/>ipſos moueri unà cum ſtellis ſibi infixis ab ortu in occaſum motu circulari; <lb/></s> <s xml:id="echoid-s3920" xml:space="preserve">idemq; </s> <s xml:id="echoid-s3921" xml:space="preserve">dicendũ eſt de motu ab occaſu in ortum, quẽ inferiores ſphęrę habẽt.</s> <s xml:id="echoid-s3922" xml:space="preserve"/> </p> <div xml:id="echoid-div200" type="float" level="2" n="4"> <note position="left" xlink:label="note-112-01" xlink:href="note-112-01a" xml:space="preserve">Sententia <lb/>antiquo-<lb/>rũ, qui ſtel-<lb/>las motu re <lb/>cto, non au-<lb/>tem circula <lb/>ti dicebant <lb/>moueri: <lb/>eiuſque cõ-<lb/>futatio.</note> </div> </div> <div xml:id="echoid-div202" type="section" level="1" n="65"> <head xml:id="echoid-head69" xml:space="preserve">COELVM ESSE FIGVRÆ SPHÆRICÆ.</head> <p style="it"> <s xml:id="echoid-s3923" xml:space="preserve"><emph style="sc">Qvod</emph> autem cœlum ſit rotundum, triplex eſt ratio. </s> <s xml:id="echoid-s3924" xml:space="preserve">Similitudo, <lb/>commoditas, & </s> <s xml:id="echoid-s3925" xml:space="preserve">neceſſitas. </s> <s xml:id="echoid-s3926" xml:space="preserve">Similitudo, quoniam mundus ſenſibilis factus <lb/> <anchor type="note" xlink:label="note-112-02a" xlink:href="note-112-02"/> eſt ad ſimilitudinem mundi archetypi, in quo nec eſt principium, nec fi-<lb/>nis. </s> <s xml:id="echoid-s3927" xml:space="preserve">Vnde ad huius ſimilitudinem factus mundus ſenſibilis habet formam <lb/>rotundam, in qua non eſt aſſignare principium, neque finem.</s> <s xml:id="echoid-s3928" xml:space="preserve"/> </p> <div xml:id="echoid-div202" type="float" level="2" n="1"> <note position="left" xlink:label="note-112-02" xlink:href="note-112-02a" xml:space="preserve">Cælum eſ-<lb/>ſe rotun-<lb/>dum, pro-<lb/>pter ſimili-<lb/>tudinẽ mũ-<lb/>di archety-<lb/>pi.</note> </div> </div> <div xml:id="echoid-div204" type="section" level="1" n="66"> <head xml:id="echoid-head70" xml:space="preserve">COMMENT ARIVS,</head> <p> <s xml:id="echoid-s3929" xml:space="preserve"><emph style="sc">Probat</emph> hoc loco auctor ſecundam concluſionem, nimirum cœlum eſſe <lb/>rotundum, tribus medijs, quorum primum deſumitur à ſimilitudine, ſecũdum <lb/>à commoditate, tertium à neceſſitate. </s> <s xml:id="echoid-s3930" xml:space="preserve">A ſimilitudine quidem ſic argumẽtatur. <lb/></s> <s xml:id="echoid-s3931" xml:space="preserve">tatur. </s> <s xml:id="echoid-s3932" xml:space="preserve">Mundus hic ſenſibilis fabricatus eſt ad ſimilitudinem mundi archetypi, <lb/>id eſt, Dei Opt. </s> <s xml:id="echoid-s3933" xml:space="preserve">Max. </s> <s xml:id="echoid-s3934" xml:space="preserve">in quo nec eſt princi pium nec finem aſſignare, cum ſit in-<lb/>finitus. </s> <s xml:id="echoid-s3935" xml:space="preserve">Debet igitur eſſe rotundus, ut nõ poſſit aſſignari in eo principiũ neque <lb/>finis: </s> <s xml:id="echoid-s3936" xml:space="preserve">Sic enim ſimilis erit quodammodo mundo illi archetypo, cum ſola figu-<lb/>ra rotunda inter omnes alias habeat quodammodo infinitatem.</s> <s xml:id="echoid-s3937" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3938" xml:space="preserve"><emph style="sc">Caetervm</emph> hæc ratio nihil prorſus uidetur concludere. </s> <s xml:id="echoid-s3939" xml:space="preserve">Eodem enim <lb/>pacto probaretur, hominem debuiſſe creari rotundum, ad ſimilitudinẽ mundi <lb/>archetypi: </s> <s xml:id="echoid-s3940" xml:space="preserve">Idem dices de cęteris creaturis. </s> <s xml:id="echoid-s3941" xml:space="preserve">Veruntamen dicendnm eſt cum B. <lb/></s> <s xml:id="echoid-s3942" xml:space="preserve">Aug. </s> <s xml:id="echoid-s3943" xml:space="preserve">Deum creaturas condidiſſe ad ſuæ bonitatis, perfectionisq́ue manifeſta-<lb/>tionem. </s> <s xml:id="echoid-s3944" xml:space="preserve">Cum igitnr una ſola creatura imperfectiſſime Dei perfectionem nobi<unsure/>s <lb/>oſtendat, potius uniuerſum mundum, in quo omnes creaturæ continentur, & </s> <s xml:id="echoid-s3945" xml:space="preserve"><lb/>qui efficacius, exactiuſque perfectionem, & </s> <s xml:id="echoid-s3946" xml:space="preserve">bonitatem Dei manifeſtat, ac decla <lb/>rat, rotundum effecit Deus, quàm ſingulas creaturas; </s> <s xml:id="echoid-s3947" xml:space="preserve">quamuis & </s> <s xml:id="echoid-s3948" xml:space="preserve">ſingulæ crea- <pb o="77" file="113" n="114" rhead="Ioan. de Sacro Boſco."/> turæ rotundam figuram, quo ad eius fieri poteſt, vbique imitãtur, ut in truncis <lb/>arborum, & </s> <s xml:id="echoid-s3949" xml:space="preserve">in ramis, & </s> <s xml:id="echoid-s3950" xml:space="preserve">in extremitatibus membrorum animalium, atq. </s> <s xml:id="echoid-s3951" xml:space="preserve">in fru-<lb/>ctibus apparet. </s> <s xml:id="echoid-s3952" xml:space="preserve">Omnia enim hæc rotunda quodammodo ſunt, non tamen om-<lb/>nino, ut eſſet maior pulchritudo & </s> <s xml:id="echoid-s3953" xml:space="preserve">ſplendor in tanta creaturarum varietate. </s> <s xml:id="echoid-s3954" xml:space="preserve">Ex <lb/>hac igitur reſponſione perſpicuum eſt, auctorem noſtrum præcipue probare, <lb/>mundum ſeu cælum eſſe rotundum, quantum ad ſuperficiem conuexam, quod <lb/>quidem ſufficit. </s> <s xml:id="echoid-s3955" xml:space="preserve">Ex conuexitate enim figuras corporum iudicare conſueuimus. <lb/></s> <s xml:id="echoid-s3956" xml:space="preserve">Nos tamen paulopoſt confirmabimus, omnes cœlos rotundos eſſe, tam ſecun-<lb/>dum concauum, quam ſecundum conuexum.</s> <s xml:id="echoid-s3957" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">Cælum eſſe <lb/>rotundum <lb/>propter cõ-<lb/>moditatẽ.</note> <p style="it"> <s xml:id="echoid-s3958" xml:space="preserve"><emph style="sc">Commoditas</emph>, quia omnium corporum iſoperimetrorum ſphæ-<lb/>ra maximum eſt omnium etiam formarum rotunda capaciſſima eſt. </s> <s xml:id="echoid-s3959" xml:space="preserve">Quo-<lb/>niam igitur maximum & </s> <s xml:id="echoid-s3960" xml:space="preserve">rotundum, ideo capaciſſimum; </s> <s xml:id="echoid-s3961" xml:space="preserve">Vnde cum mun <lb/>dus omnia contineat, talis forma fuit illi utilis & </s> <s xml:id="echoid-s3962" xml:space="preserve">commoda.</s> <s xml:id="echoid-s3963" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div205" type="section" level="1" n="67"> <head xml:id="echoid-head71" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s3964" xml:space="preserve"><emph style="sc">Ratio</emph> a commoditate deſ umpta talis fere eſt. </s> <s xml:id="echoid-s3965" xml:space="preserve">Mundus hic omnia intra ſe <lb/>continet: </s> <s xml:id="echoid-s3966" xml:space="preserve">Debuit igitur illi concedi figura maxime ad hoc utilis & </s> <s xml:id="echoid-s3967" xml:space="preserve">commoda, <lb/>quę uidelicet eſſet oĩum capaciſſima: </s> <s xml:id="echoid-s3968" xml:space="preserve">Natura etenim peccatum euitans commo <lb/>ditatem ꝗ̃ maxime affectat. </s> <s xml:id="echoid-s3969" xml:space="preserve">Atqui ſphæra inter oẽs figuras corporeas iſoperime <lb/>tras maxima eſt, & </s> <s xml:id="echoid-s3970" xml:space="preserve">capaciſſima. </s> <s xml:id="echoid-s3971" xml:space="preserve">Igitur @alis ei figura iure a natura conceſſa fuit.</s> <s xml:id="echoid-s3972" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3973" xml:space="preserve"><emph style="sc">Vervm</emph> & </s> <s xml:id="echoid-s3974" xml:space="preserve">hæcratio ſimpliciter nihil uidetur concludere. </s> <s xml:id="echoid-s3975" xml:space="preserve">Diceret enim <lb/>aliquis, quamuis inter iſoperimetra corpora ſphæra ſit maxime capax, ut uult <lb/>ratio, potuiſſe tamen Deum facere mundum alterius figuræ ampliorem, quam <lb/>nunc eſt, ut æque bene omnia intra ſe contineret, atque nunc continet. </s> <s xml:id="echoid-s3976" xml:space="preserve">Cæte-<lb/>rum cum Deus & </s> <s xml:id="echoid-s3977" xml:space="preserve">natura nihil fruſtra efficiant, & </s> <s xml:id="echoid-s3978" xml:space="preserve">ſemper id, quod melius eſt, p <lb/>ducant, conſentaneum rationi eſſe uidetur, mundum conditum fuiſſe rotundũ <lb/>a Deo, quandoquidem rotunda figura capaciſſima, atq. </s> <s xml:id="echoid-s3979" xml:space="preserve">nobiliſſima exiſtit, præ <lb/>ſertim cum exceſſus ille alterius figuræ amplioris ſuperfluus uideatur, & </s> <s xml:id="echoid-s3980" xml:space="preserve">ſine <lb/>ulla prorſus ratione, ſeu neceſſitate conſtitutus.</s> <s xml:id="echoid-s3981" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3982" xml:space="preserve"><emph style="sc">Possvmvs</emph> quoque aliam rationem ſubiungere a commoditate. </s> <s xml:id="echoid-s3983" xml:space="preserve">Cum <lb/> <anchor type="note" xlink:label="note-113-02a" xlink:href="note-113-02"/> enim Natura ſemper id, quod melius eſt, conetur efficere, iure optimo cœleſti <lb/>corpori, quod eſt omnium nobiliſſimum, figuram nobiliſſimam conceſſiſſe ui-<lb/>detur; </s> <s xml:id="echoid-s3984" xml:space="preserve">qualis eſt rotunda, ſiue ſphærica, multas ob cauſas. </s> <s xml:id="echoid-s3985" xml:space="preserve">Nam quemadmodum <lb/>inter planas figuras Circulus, ita inter ſolidas Sphæra principatum obtinet-<lb/>Sicut enim Circulus ſua ſimplicitate, partium ſimilitudine, æqualitate, identi-<lb/>tate loci, fortitudine, atque capacitate, cæteris omnibus planis figuris præcel-<lb/>lit, ita quoque de ſphæra dicendum eſt, ſi cum alijs figuris ſolidis comparetur. <lb/></s> <s xml:id="echoid-s3986" xml:space="preserve">Primo namque circulum unica linea, & </s> <s xml:id="echoid-s3987" xml:space="preserve">ſphæram unica ſuperficies concludit. </s> <s xml:id="echoid-s3988" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-113-03a" xlink:href="note-113-03"/> Secundo, ſicut in circulo ſunt arcus ſimiliter curui, ſic in Sphæra ſunt portio-<lb/>nes ſimiliter conuexæ. </s> <s xml:id="echoid-s3989" xml:space="preserve">Tertio, ut in circulo medium eſt ab extremis æquali-<lb/>ter remotum, unde & </s> <s xml:id="echoid-s3990" xml:space="preserve">ipſius longitudinem, latitudinemq́ue ęquales diametri <lb/>quoquo uerſus metiuntur, ita quoq. </s> <s xml:id="echoid-s3991" xml:space="preserve">res ſeſe habet in corpore ſphærico, cuius <lb/>longitudinem, latitudinem, profunditatemq́. </s> <s xml:id="echoid-s3992" xml:space="preserve">tres diametri æquales uerſus om <lb/>nem partem metiunt̃. </s> <s xml:id="echoid-s3993" xml:space="preserve">Quarto, quemadmodum in circulo, ita & </s> <s xml:id="echoid-s3994" xml:space="preserve">in ſphæra neq; <lb/></s> <s xml:id="echoid-s3995" xml:space="preserve">initium, neq. </s> <s xml:id="echoid-s3996" xml:space="preserve">finem adinuenire poſſumus. </s> <s xml:id="echoid-s3997" xml:space="preserve">Quinto, quemadmodum circulus, ſic <lb/>ẽt ſphæra circa centrum reuoluta eundem ſemper occupat locũ: </s> <s xml:id="echoid-s3998" xml:space="preserve">Vndetam cir- <pb o="78" file="114" n="115" rhead="Comment. in I. Cap. Sphæræ"/> culo, quam ſphæræ & </s> <s xml:id="echoid-s3999" xml:space="preserve">motus facilitas, & </s> <s xml:id="echoid-s4000" xml:space="preserve">partium firmitas, nullo obſtante ex-<lb/>crinſeco, maxima cõceditur. </s> <s xml:id="echoid-s4001" xml:space="preserve">Sexto & </s> <s xml:id="echoid-s4002" xml:space="preserve">ultimo utraq. </s> <s xml:id="echoid-s4003" xml:space="preserve">figura tam circularis, quàm <lb/>ſphærica inter figuras iſoperimetras, planas quidem, ſi de circulo loquamur, <lb/>ſolidas uero, ſi de ſphæra ſermo habeatur, capaciſſima exiſtit, ut infra oſtende-<lb/>mus. </s> <s xml:id="echoid-s4004" xml:space="preserve">Accedit ẽt, ꝙ circulus lineam rectam, & </s> <s xml:id="echoid-s4005" xml:space="preserve">ſphæra ſuperficiem planã in pun-<lb/>cto tantum unico contingit, quorum illud ex 2. </s> <s xml:id="echoid-s4006" xml:space="preserve">& </s> <s xml:id="echoid-s4007" xml:space="preserve">16. </s> <s xml:id="echoid-s4008" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s4009" xml:space="preserve">tertij lib. </s> <s xml:id="echoid-s4010" xml:space="preserve">Eucl. <lb/></s> <s xml:id="echoid-s4011" xml:space="preserve">euidenter colligitur, hoc autem a Theodoſio propoſ. </s> <s xml:id="echoid-s4012" xml:space="preserve">3. </s> <s xml:id="echoid-s4013" xml:space="preserve">primi lib. </s> <s xml:id="echoid-s4014" xml:space="preserve">ſphæricorum <lb/>elementorum clariſſime demonſtratur. </s> <s xml:id="echoid-s4015" xml:space="preserve">Cũ igitur ſphæricum corpus inter om-<lb/>nia alia tam nobile exiſtat, ob tam multas, tamque præclaras dignitates, ac ex-<lb/>cellentias, quis iam dubitare, aut hæſitare poterit, cœlum tali eſſe figura prædi-<lb/>tũ@ Præſertim cũ cœlum, ut d@ctum eſt in præcedenti concluſione, continue vol <lb/>uatur motu circulati, cui quidem motui corpus ſphæricum, inter reliqua, maxi <lb/>me eſt accommodatum, ob continuam, & </s> <s xml:id="echoid-s4016" xml:space="preserve">uniformem partium ſucceſſionem, <lb/>ita ut nihil extrinſecus eſſe poſſit impedimento, propterea quòd circa centrum <lb/>eiſdem ſemper loci limitibus cir cumagitatur; </s> <s xml:id="echoid-s4017" xml:space="preserve">Vnde & </s> <s xml:id="echoid-s4018" xml:space="preserve">facillime mouetur.</s> <s xml:id="echoid-s4019" xml:space="preserve"/> </p> <div xml:id="echoid-div205" type="float" level="2" n="1"> <note position="right" xlink:label="note-113-02" xlink:href="note-113-02a" xml:space="preserve">Alia ratio <lb/>a commodi <lb/>tate ꝓbans <lb/>cælum eſſe <lb/>rotundum.</note> <note position="right" xlink:label="note-113-03" xlink:href="note-113-03a" xml:space="preserve">Dignitates <lb/>variæ circu-<lb/>li, & ſphæ-<lb/>ræ.</note> </div> <p> <s xml:id="echoid-s4020" xml:space="preserve"><emph style="sc">Vt avtem</emph> ſecunda hæc auctoris ratio à commoditate deſumpta per-<lb/> <anchor type="note" xlink:label="note-114-01a" xlink:href="note-114-01"/> fectius intelligatur, pauca dicenda erunt de figuris iſoperimetris. </s> <s xml:id="echoid-s4021" xml:space="preserve">Figurę igitur <lb/>Iſoperimetrę appellantur illæ, quæ habent circunferentias, ſiue linearum am-<lb/>bitus æquales inter ſe. </s> <s xml:id="echoid-s4022" xml:space="preserve">Vt quadratum ſex palmos habens in ambitu dicitur iſo-<lb/>perimetrum triangulo, aut cuicunq. </s> <s xml:id="echoid-s4023" xml:space="preserve">alteri figuræ (ſiue rectilinea ea ſit, ſiue cur-<lb/>uilinea, ſiue ex his mixta,) habenti in circuitu ſex etiam palmos: </s> <s xml:id="echoid-s4024" xml:space="preserve">ita ut qua-<lb/>tuor lineæ rectæ quadrati ambitum conſtituentes in vnam, eandemq́ue rectam <lb/> <anchor type="note" xlink:label="note-114-02a" xlink:href="note-114-02"/> lineam coaptatę adęquentur ad amuſſim tribus lineis rectis trianguli, aut la-<lb/>teribus omnibus cuiuſcunque alterius figuræ in rectum quoque, atque conti-<lb/>nuum poſitis. </s> <s xml:id="echoid-s4025" xml:space="preserve">Quod idem intelligendum erit de corporibus quibuſcunque iſ@ <lb/>perimetris, ſumendo ſuperficies pro lineis.</s> <s xml:id="echoid-s4026" xml:space="preserve"/> </p> <div xml:id="echoid-div206" type="float" level="2" n="2"> <note position="left" xlink:label="note-114-01" xlink:href="note-114-01a" xml:space="preserve">Iſoperime-<lb/>træ figuræ <lb/>quæ.</note> <note position="left" xlink:label="note-114-02" xlink:href="note-114-02a" xml:space="preserve">Inter figu-<lb/>@as Iſoperi-<lb/>metras re-<lb/>cti lineas ca <lb/>pacior eſt, <lb/>quæ plures <lb/>angulos ha <lb/>bet; ac pro-<lb/>inde circu-<lb/>lus capaciſ-<lb/>ſimus.</note> </div> <p> <s xml:id="echoid-s4027" xml:space="preserve"><emph style="sc">Inter</emph> omnes autem figuras rectilineas iſoperimetsas ea, quę plures <lb/>continet an gulos, maior, capaciorq́ue exiſtit. </s> <s xml:id="echoid-s4028" xml:space="preserve">Quod breuiter, & </s> <s xml:id="echoid-s4029" xml:space="preserve">rudi quadam <lb/>mineua confirmabimus in triangulo æquilatero, ſiue Iſoſcele, & </s> <s xml:id="echoid-s4030" xml:space="preserve">figura altera <lb/>parte longiore. </s> <s xml:id="echoid-s4031" xml:space="preserve">Accuratius enim hoc ipſum mox in tractatione figurarum Iſo-<lb/>perimetrarum demonſtrabimus. </s> <s xml:id="echoid-s4032" xml:space="preserve">Sit triangulum ęquilaterum, uel Iſoſceles <lb/>A B C, cuius latus B C, diuidatur in partes ęquales in puncto D, & </s> <s xml:id="echoid-s4033" xml:space="preserve">ducatur li-<lb/>nea recta D A, quę perpendicularis erit ad B C. </s> <s xml:id="echoid-s4034" xml:space="preserve">Nam duo latera A D, D B, <lb/>trianguli A D B, ęqualia ſunt duobus lateribus A D, D C, trianguli A D C, <lb/>& </s> <s xml:id="echoid-s4035" xml:space="preserve">baſis A B, baſi A C, ęqualis ponitur. </s> <s xml:id="echoid-s4036" xml:space="preserve">Igitur duo anguli A D B, A D C, æ-<lb/> <anchor type="note" xlink:label="note-114-03a" xlink:href="note-114-03"/> <anchor type="figure" xlink:label="fig-114-01a" xlink:href="fig-114-01"/> quales erunt, & </s> <s xml:id="echoid-s4037" xml:space="preserve">ob id (per definitionem) <lb/>uterque rectus. </s> <s xml:id="echoid-s4038" xml:space="preserve">Perficiatur parallelogram <lb/>mum rectangulum A D C E. </s> <s xml:id="echoid-s4039" xml:space="preserve">Quoniam <lb/> <anchor type="note" xlink:label="note-114-04a" xlink:href="note-114-04"/> igitur triangulum A D B, triangulo <lb/>A D C, eſt æqualæ, eidemque triangu-<lb/>lo A D C, ęquale eſt triãgulum A C E, <lb/> <anchor type="note" xlink:label="note-114-05a" xlink:href="note-114-05"/> erunt (per communem ſententiam) trian <lb/>gula A D B, A C E, inter ſe æqualia. <lb/></s> <s xml:id="echoid-s4040" xml:space="preserve">Quare, addito cõmuni triangulo A D C, <lb/>erit parallelogrammum A D C E, ęqua-<lb/>le triangulo A B C. </s> <s xml:id="echoid-s4041" xml:space="preserve">Et quia duo latera <lb/>A E, D C, parallelogrammi, cum inter <lb/> <anchor type="note" xlink:label="note-114-06a" xlink:href="note-114-06"/> ſe ęqualia ſint, ſimul ſumpta æqualia ſunt lateri B C, trianguli A B B; </s> <s xml:id="echoid-s4042" xml:space="preserve">Reli- <pb o="79" file="115" n="116" rhead="Ioan. de Sacro Boſco."/> qua uero duo latera A D, C E, parallelogrammi A D C E, (propteree quòd <lb/>opponuntur minoribus angulis, nempe acutis, in triangulis A D B, A C E) <lb/> <anchor type="note" xlink:label="note-115-01a" xlink:href="note-115-01"/> minora ſunt reliquis duobus lateribus A B, A C, trianguli A B C, quòd hęc <lb/>in eiſdem triangulis opponantur maioribus angulis, nempe rectis: </s> <s xml:id="echoid-s4043" xml:space="preserve">erit ambi-<lb/>tus parallelogrammi A D C E, minor ambitu trianguli A B C. </s> <s xml:id="echoid-s4044" xml:space="preserve">Quamobrem, <lb/>ut ambitus parallelogrammi fiat æqualis ambitui trianguli, producenda e-<lb/>runt latera D A, C E, ad ęqualita@em laterum A B, A C. </s> <s xml:id="echoid-s4045" xml:space="preserve">Sit igitur recta <lb/>D A G, æqualis lateri A B, & </s> <s xml:id="echoid-s4046" xml:space="preserve">recta C E F, ęqualis lateri A C, dicaturq́ue re-<lb/>cta F G. </s> <s xml:id="echoid-s4047" xml:space="preserve">Ex quibus efficitur, parallelo grammum C F G D, & </s> <s xml:id="echoid-s4048" xml:space="preserve">triangulum <lb/>A B C, eſſe iſoperimetra. </s> <s xml:id="echoid-s4049" xml:space="preserve">Quoniam uero parallelogramum C F G D, ſu-<lb/>perat parallelo grammum A D C E, quantitate A E F G, oſtenſumq́ue eſt pa-<lb/>rallelo grammum A D C E, triangulo A B C, ęquale, maius quoque erit pa-<lb/>rallelo grammum idem C F G D, quam triangulum A B C, eadem quantita-<lb/>te A E F G. </s> <s xml:id="echoid-s4050" xml:space="preserve">Quapropter conſtat, figuram quadrilateram capaciorem eſſe fi-<lb/>gura triangulari ſibi iſoperimetra, quod erat oſtendendum. </s> <s xml:id="echoid-s4051" xml:space="preserve">Cum igitur ea-<lb/>dem eſſe uideatur ratio in alijs figuris rectilineis plurium laterum, iſoperi-<lb/>metris tamen; </s> <s xml:id="echoid-s4052" xml:space="preserve">Quo enim plures habet angulos figura, eo pluribus in locis <lb/>latera eius recedunt à centro, & </s> <s xml:id="echoid-s4053" xml:space="preserve">medio, ac propterea capacior exiſtit: </s> <s xml:id="echoid-s4054" xml:space="preserve">Perſpi-<lb/>cuum eſt circulum, quòd infinitos quodammodo includat angulos, & </s> <s xml:id="echoid-s4055" xml:space="preserve">latera, <lb/>omnibusq́ue punctis ęqualiter recedat à centro, omnium figurarum iſoperime <lb/>trarum eſſe capaciſſimum. </s> <s xml:id="echoid-s4056" xml:space="preserve">Idem quoque dicendum erit de ſphęra, ſi cum alijs <lb/>corporibus ſibi iſoperimetris comparetur.</s> <s xml:id="echoid-s4057" xml:space="preserve"/> </p> <div xml:id="echoid-div207" type="float" level="2" n="3"> <note position="left" xlink:label="note-114-03" xlink:href="note-114-03a" xml:space="preserve">8. primi.</note> <figure xlink:label="fig-114-01" xlink:href="fig-114-01a"> <image file="114-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/114-01"/> </figure> <note position="left" xlink:label="note-114-04" xlink:href="note-114-04a" xml:space="preserve">4. uel 38. <lb/>primi.</note> <note position="left" xlink:label="note-114-05" xlink:href="note-114-05a" xml:space="preserve">34. primi.</note> <note position="left" xlink:label="note-114-06" xlink:href="note-114-06a" xml:space="preserve">34. primi.</note> <note position="right" xlink:label="note-115-01" xlink:href="note-115-01a" xml:space="preserve">19. primi.</note> </div> <note position="right" xml:space="preserve">Inter figu-<lb/>ras Iſoperi-<lb/>metras ca--<lb/>pacior eſt, <lb/>quę æquila-<lb/>tera eſt, & <lb/>æquiangu@ -<lb/>la, poſito æ-<lb/>quali nume <lb/>ro laterum <lb/>in utraque, <lb/>ac proinde <lb/>circulus ca-<lb/>paciffimus <lb/>eſt.</note> <p> <s xml:id="echoid-s4058" xml:space="preserve"><emph style="sc">Rvrsvs</emph> Iſoperimetrarum figurarum rectilinearum latera numero ę-<lb/>qualia habentium, maior eſt illa, quę & </s> <s xml:id="echoid-s4059" xml:space="preserve">latera habet æqualia, & </s> <s xml:id="echoid-s4060" xml:space="preserve">angulos æ-<lb/>quales. </s> <s xml:id="echoid-s4061" xml:space="preserve">Eſto enim quadratum aliquod habens in quolibet latere 9. </s> <s xml:id="echoid-s4062" xml:space="preserve">ita ut to-<lb/>tus eius ambitus contineat 24. </s> <s xml:id="echoid-s4063" xml:space="preserve">Erit area huius quadrati, iuxta pręcepta A-<lb/>rithmeticorum, 36. </s> <s xml:id="echoid-s4064" xml:space="preserve">Ita enim uides, quadratum totum diuiſum eſſe in 36. </s> <s xml:id="echoid-s4065" xml:space="preserve">qua <lb/> <anchor type="figure" xlink:label="fig-115-01a" xlink:href="fig-115-01"/> drata paruula. </s> <s xml:id="echoid-s4066" xml:space="preserve">Eſto quoque aliquod parallelo grammum rectangulum habens <lb/>unumquodque duorum laterum oppoſitorum 10. </s> <s xml:id="echoid-s4067" xml:space="preserve">reliquorum uero duorum <lb/>quodlibet 2. </s> <s xml:id="echoid-s4068" xml:space="preserve">ut ſit ambitui illius ęqualis ambitus quadrati. </s> <s xml:id="echoid-s4069" xml:space="preserve">Quo poſito, area <lb/>huius parallelogrammi comprehendet tantummodo 20. </s> <s xml:id="echoid-s4070" xml:space="preserve">quadrata paruula ex <lb/>illis 36. </s> <s xml:id="echoid-s4071" xml:space="preserve">quę quadratum in ſe continet. </s> <s xml:id="echoid-s4072" xml:space="preserve">Hoc autem ideo euenit, quoniam pa-<lb/>rallelo grammum non eſt æquilaterum, ſed altera parte longius, quamuis æqui <pb o="80" file="116" n="117" rhead="Comment. in I. Cap. Sphæræ"/> angulum ſit, quadratum autem & </s> <s xml:id="echoid-s4073" xml:space="preserve">æquilaterum, & </s> <s xml:id="echoid-s4074" xml:space="preserve">æquiangulum eſt. </s> <s xml:id="echoid-s4075" xml:space="preserve">Sit præ-<lb/>terea aliud parallelogramum rectangulum, cuius unumquodque duorum <lb/>laterum oppoſitorum ſit 9. </s> <s xml:id="echoid-s4076" xml:space="preserve">aliorum uero duorum 3. </s> <s xml:id="echoid-s4077" xml:space="preserve">vt quadrati, & </s> <s xml:id="echoid-s4078" xml:space="preserve">parallelo-<lb/>grammi huius ambitus quoque ſint æquales. </s> <s xml:id="echoid-s4079" xml:space="preserve">Comprehendet igitur area hu-<lb/>i<unsure/>us parallelogrammi ſolum 27. </s> <s xml:id="echoid-s4080" xml:space="preserve">quadrata ex illis 36. </s> <s xml:id="echoid-s4081" xml:space="preserve">quæ in quadrato diximus <lb/>contineri. </s> <s xml:id="echoid-s4082" xml:space="preserve">Pari ratione, ſi parallelogrammi alicuius unumquodque duorum <lb/>laterum oppoſitorum eſſet 8. </s> <s xml:id="echoid-s4083" xml:space="preserve">& </s> <s xml:id="echoid-s4084" xml:space="preserve">aliorum duorum 4. </s> <s xml:id="echoid-s4085" xml:space="preserve">eſſet quidem ipſum qua-<lb/>drato iſoperimetrum, ſed eius area contineret duntaxat 32. </s> <s xml:id="echoid-s4086" xml:space="preserve">quadrata. </s> <s xml:id="echoid-s4087" xml:space="preserve">Item, <lb/>ſi duo latera alicuius parallelogrammi oppoſita, ſingula haberent 7. </s> <s xml:id="echoid-s4088" xml:space="preserve">alia ue-<lb/>ro duo ſingula 5. </s> <s xml:id="echoid-s4089" xml:space="preserve">eſſet etiam quadrato iſoperimetrum, area autem illius@ in-<lb/>cluderet tantum 35. </s> <s xml:id="echoid-s4090" xml:space="preserve">quadrata, &</s> <s xml:id="echoid-s4091" xml:space="preserve">c. </s> <s xml:id="echoid-s4092" xml:space="preserve">Vbi clare uides, quo magis figuræ iſoperi-<lb/>metrę accedunt ad æquilateram, cui ſunt iſoperimetræ, eo etiam maiorem <lb/>comprehendunt aream, & </s> <s xml:id="echoid-s4093" xml:space="preserve">minus differunt in capacitate a figura æquilatera. <lb/></s> <s xml:id="echoid-s4094" xml:space="preserve">Quod ſi aliquod parallelogrammum rectangulum altera parte longius eiuſ-<lb/>dem ſit capacitatis cum quadrato, illud maiorem ambitum continere neceſ-<lb/> <anchor type="figure" xlink:label="fig-116-01a" xlink:href="fig-116-01"/> ſe eſt. </s> <s xml:id="echoid-s4095" xml:space="preserve">Vt ſi paralle <lb/>logrammi alicuius <lb/>quodlibet duorum <lb/>oppoſitorum late-<lb/>rum contineat 12. <lb/></s> <s xml:id="echoid-s4096" xml:space="preserve">aliorum vero duo-<lb/>rum quodlibet 3. </s> <s xml:id="echoid-s4097" xml:space="preserve"><lb/>erit quidem area il <lb/>lius æqualis areæ <lb/>quadrati, cum con-<lb/>tineat 36. </s> <s xml:id="echoid-s4098" xml:space="preserve">quadratula: </s> <s xml:id="echoid-s4099" xml:space="preserve">At uero ambitus ipſius ſuperabit ambitum quadrati: </s> <s xml:id="echoid-s4100" xml:space="preserve">Ille <lb/>enim erit 30. </s> <s xml:id="echoid-s4101" xml:space="preserve">hic autem 24. </s> <s xml:id="echoid-s4102" xml:space="preserve">Quæ omnia perſpicua ſunt in appoſitis figuris.</s> <s xml:id="echoid-s4103" xml:space="preserve"/> </p> <div xml:id="echoid-div208" type="float" level="2" n="4"> <figure xlink:label="fig-115-01" xlink:href="fig-115-01a"> <image file="115-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/115-01"/> </figure> <figure xlink:label="fig-116-01" xlink:href="fig-116-01a"> <image file="116-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/116-01"/> </figure> </div> <p> <s xml:id="echoid-s4104" xml:space="preserve"><emph style="sc">Sit</emph> iam parallelogrammum inæqualium angulorum A B C D, & </s> <s xml:id="echoid-s4105" xml:space="preserve">a pun-<lb/>ctis C, D, educantur perpendiculares lineę C F, & </s> <s xml:id="echoid-s4106" xml:space="preserve">D E, ad rectam C D: </s> <s xml:id="echoid-s4107" xml:space="preserve">Pro <lb/>ducta igitur A B, vſque ad F, erit parallelogrammum A B C D, æquale paral-<lb/>lelogrammo C D E F, cum ſint hæc parallelogramma inter eaſdem paralle-<lb/> <anchor type="note" xlink:label="note-116-01a" xlink:href="note-116-01"/> las C D, A F, & </s> <s xml:id="echoid-s4108" xml:space="preserve">ſuper eandem baſim C D, conſtituta. </s> <s xml:id="echoid-s4109" xml:space="preserve">Et quoniam latera B C, <lb/>A D, maiora ſunt lateribus C F, D E, eſtq́ue latus A B, lateri E F, æquale, <lb/> <anchor type="note" xlink:label="note-116-02a" xlink:href="note-116-02"/> (quod utrumq. </s> <s xml:id="echoid-s4110" xml:space="preserve">lateri oppoſito C D, in parallelogrammis A B C D, C D E F, <lb/> <anchor type="note" xlink:label="note-116-03a" xlink:href="note-116-03"/> <anchor type="figure" xlink:label="fig-116-02a" xlink:href="fig-116-02"/> æquale ſit) & </s> <s xml:id="echoid-s4111" xml:space="preserve">latus C D, commune, erit <lb/>ambitus parallelogrammi C D E F, mi-<lb/>nor ambitu parallelogrammi A B C D. <lb/></s> <s xml:id="echoid-s4112" xml:space="preserve">Vnde ſi producantur C F, D E, ad G, & </s> <s xml:id="echoid-s4113" xml:space="preserve"><lb/>H, ita ut C G, æqualis ſit ipſi B C, & </s> <s xml:id="echoid-s4114" xml:space="preserve"><lb/>D H, ipſi A D, perficiaturq́ue parallelo-<lb/>grammum C D H G, (ducta uidelicet re-<lb/>cta G H,) erit parallelogramum C D <lb/>H G, iſoperimetrum parallelogrammo <lb/>A B C D. </s> <s xml:id="echoid-s4115" xml:space="preserve">Eſt autem parallelogrammum <lb/>C D H G, maius quam parallelogram-<lb/>mum C D E F, hoc eſt, quam parallelo-<lb/>grammum A B C D, quantitate E F G H. </s> <s xml:id="echoid-s4116" xml:space="preserve"><lb/>Conſtat igitur inter Iſoperimetras figuras rectilineas eam, quæ & </s> <s xml:id="echoid-s4117" xml:space="preserve">æquilate- <pb o="81" file="117" n="118" rhead="Ioan. de Sacro Boſco."/> ra, & </s> <s xml:id="echoid-s4118" xml:space="preserve">æquiangula exiſtit, omnium eſſe maximam: </s> <s xml:id="echoid-s4119" xml:space="preserve">Eadem enim eſt ratio haben-<lb/>da de figuris Iſoperimetris, quæ plura latera, pluresq́ue angulos continent. <lb/></s> <s xml:id="echoid-s4120" xml:space="preserve">Quamobrem, cum circulus infinita propemodum latera æqualia, infinitos <lb/>quoque angulos quodammodo æquales comprehendat, eo quòd eius circun-<lb/>ferentia ſemper curuetur æqualiter, efficitur, ut ſit inter omnes figuras Iſope-<lb/>rimetras capaciſſimus. </s> <s xml:id="echoid-s4121" xml:space="preserve">Atque hiſce potiſſimum rationibus nituntur nonnullĩ<unsure/> <lb/>auctores confirmare, circulum eſſe maxime capacem: </s> <s xml:id="echoid-s4122" xml:space="preserve">Ex quibus manifeſtum ar <lb/>bitror relinqui, quidnam ſibi uelit auctor noſter in ſecunda hac ratione de-<lb/>ſumpta à commoditate, in qua mentionem ſecit figurarum Iſoperimetrarum.</s> <s xml:id="echoid-s4123" xml:space="preserve"/> </p> <div xml:id="echoid-div209" type="float" level="2" n="5"> <note position="left" xlink:label="note-116-01" xlink:href="note-116-01a" xml:space="preserve">35. primi.</note> <note position="left" xlink:label="note-116-02" xlink:href="note-116-02a" xml:space="preserve">19. primi.</note> <note position="left" xlink:label="note-116-03" xlink:href="note-116-03a" xml:space="preserve">34. primi.</note> <figure xlink:label="fig-116-02" xlink:href="fig-116-02a"> <image file="116-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/116-02"/> </figure> </div> <p> <s xml:id="echoid-s4124" xml:space="preserve"><emph style="sc">Vervm</emph> quoniam prædictæ rationes coniecturæ potius, quàm demonſtra-<lb/>tiones ſunt appellandæ: </s> <s xml:id="echoid-s4125" xml:space="preserve">Neque enim circulus angulos ullos, aut latera conti <lb/>net, ex quibus componatur, quemadmodum in præfatis rationibus aſſumeba-<lb/>tur: </s> <s xml:id="echoid-s4126" xml:space="preserve">Immo vero, etiamſi & </s> <s xml:id="echoid-s4127" xml:space="preserve">angulos, & </s> <s xml:id="echoid-s4128" xml:space="preserve">latera haberet propemodum infinita, nõ <lb/>eſt tamen in uniuerſum demonſtratione confirmatum, eam ſemper figurã, quę <lb/>plures habet angulos, ſiue latera, atque adeo eam, quæ & </s> <s xml:id="echoid-s4129" xml:space="preserve">latera & </s> <s xml:id="echoid-s4130" xml:space="preserve">angulos ha-<lb/>bet æquales, inter iſoperimetras figuras eſſe capaciſſimam; </s> <s xml:id="echoid-s4131" xml:space="preserve">ſed hoc tantum oſtẽ <lb/>ſum eſt in triangulo Iſoſcele, vel Æquilatero, ſi cum parallelogrãmo confe-<lb/>ratur, & </s> <s xml:id="echoid-s4132" xml:space="preserve">in parallelogrammis; </s> <s xml:id="echoid-s4133" xml:space="preserve">non autem in figuris, quæ plura continent late-<lb/>ra. </s> <s xml:id="echoid-s4134" xml:space="preserve">Idcirco non abs re me facturum iudicaui, ſi hoc loco interponam tractatio <lb/>nem perbreuem de figuris Iſoperimetris, in qua euidentiſſime demonſtratur, <lb/>circulum inter figuras planas iſoperimetras eſſe capaciſſimum; </s> <s xml:id="echoid-s4135" xml:space="preserve">Itemq́; </s> <s xml:id="echoid-s4136" xml:space="preserve">ſphæ-<lb/>ram maiorem eſſe omnibus aliis figuris ſolidis ſibi iſoperimetris. </s> <s xml:id="echoid-s4137" xml:space="preserve">Quamuis. </s> <s xml:id="echoid-s4138" xml:space="preserve">n. <lb/></s> <s xml:id="echoid-s4139" xml:space="preserve">hæc omnia à Theone quoque in commentarijs, quos in Ptolemæi Almageſtũ <lb/>compoſuit, Geometrice ſint confir<unsure/>mata; </s> <s xml:id="echoid-s4140" xml:space="preserve">tamen quia non omnibus in promptu <lb/>habentur eius demonſtrationes, (Græcus enim tantum codex reperitur) & </s> <s xml:id="echoid-s4141" xml:space="preserve"><lb/>obſcure admodum, atque ſuccincte ab eo omnia demonſtrantur; </s> <s xml:id="echoid-s4142" xml:space="preserve">deo cona-<lb/>bor, quoad eius fieri poterit, aliquam lucem hiſce demonſtrationibus afferre, <lb/>vt uel illis ſatisfeciſſe videamur, qui plurimum demonſtrationibus Geometri-<lb/>cis delectantur. </s> <s xml:id="echoid-s4143" xml:space="preserve">Cæterum licet in hoctractatu ſolum demonſt@etur, ſphæram <lb/>eſſe maiorem corpore quolibet ſibi Iſoperimetro, in quo ſphæra aliqua deſcri-<lb/>bi poſſit, & </s> <s xml:id="echoid-s4144" xml:space="preserve">quod contineatur uel ſuperficiebus planis, uel conicis, ut ſuo loco <lb/>apparebit: </s> <s xml:id="echoid-s4145" xml:space="preserve">Pappus tamen idem de omnicorpore demonſtrauit 70. </s> <s xml:id="echoid-s4146" xml:space="preserve">propoſitio-<lb/>nibus, quas hoc loco apponere ſuperuacaneum duximus, cum breui, ut ſpero, <lb/>Pappus ipſe in latinam linguam conuerſus in lucem ſit proditurus.</s> <s xml:id="echoid-s4147" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div211" type="section" level="1" n="68"> <head xml:id="echoid-head72" xml:space="preserve">DE FIGVRIS ISOPERIMETRIS. <lb/>DEFINITIONES. <lb/>I.</head> <p style="it"> <s xml:id="echoid-s4148" xml:space="preserve"><emph style="sc">TSoperimetrae</emph> figurę ſunt, quæ æquales ambitus <lb/> <anchor type="note" xlink:label="note-117-01a" xlink:href="note-117-01"/> continent.</s> <s xml:id="echoid-s4149" xml:space="preserve"/> </p> <div xml:id="echoid-div211" type="float" level="2" n="1"> <note position="right" xlink:label="note-117-01" xlink:href="note-117-01a" xml:space="preserve">Definitio-<lb/>nes ad tra <lb/>ctationem-<lb/>Iſoperime-<lb/>trarum fi-<lb/>gurarũ per <lb/>tinentes.</note> </div> </div> <div xml:id="echoid-div213" type="section" level="1" n="69"> <head xml:id="echoid-head73" xml:space="preserve">II.</head> <p style="it"> <s xml:id="echoid-s4150" xml:space="preserve"><emph style="sc">Regvlaris</emph> figura dicitur ea, quæ & </s> <s xml:id="echoid-s4151" xml:space="preserve">æquilatera, & </s> <s xml:id="echoid-s4152" xml:space="preserve"><lb/>æquiangula eſt.</s> <s xml:id="echoid-s4153" xml:space="preserve"/> </p> <pb o="82" file="118" n="119" rhead="Comment. in I. Cap. Sphæræ"/> </div> <div xml:id="echoid-div214" type="section" level="1" n="70"> <head xml:id="echoid-head74" xml:space="preserve">III.</head> <p style="it"> <s xml:id="echoid-s4154" xml:space="preserve"><emph style="sc">Centrvm</emph> figuræregularis dicitur punctum illud, quod centrum <lb/>eſt circuli figuræi@ſcripti, uel circumſcripti.</s> <s xml:id="echoid-s4155" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div215" type="section" level="1" n="71"> <head xml:id="echoid-head75" xml:space="preserve">IIII.</head> <p style="it"> <s xml:id="echoid-s4156" xml:space="preserve"><emph style="sc">Area</emph> cuiuslibet figuræ dicitur capacitas, ſpatium, ſiue ſuperficies in-<lb/>tra lateraipſius comprehenſa.</s> <s xml:id="echoid-s4157" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div216" type="section" level="1" n="72"> <head xml:id="echoid-head76" xml:space="preserve">V.</head> <p style="it"> <s xml:id="echoid-s4158" xml:space="preserve"><emph style="sc">Omne</emph> ſolidum rectangulum (cuius nimirum baſes æquidiſtantes <lb/>ſunt, & </s> <s xml:id="echoid-s4159" xml:space="preserve">æquales, latera{q́ue} ad baſes recta, quale eſt Parallelepipedum) con-<lb/>tineri dicitur ſub altera baſium, ac perpendiculari ab illa baſi ad alteram <lb/>protracta.</s> <s xml:id="echoid-s4160" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4161" xml:space="preserve"><emph style="sc">Qvia</emph> nimirum altarutra baſium indicat longitudinem, ac Iatitudinem fi-<lb/>guræ, perpendicularis vero altitudinem, ſiue profonditatẽ eiuſdẽ demonſtrat.</s> <s xml:id="echoid-s4162" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div217" type="section" level="1" n="73"> <head xml:id="echoid-head77" style="it" xml:space="preserve">THEOR. 1. PROPOS. 1.</head> <p style="it"> <s xml:id="echoid-s4163" xml:space="preserve"><emph style="sc">ARea</emph> cuiuslibet trianguli æqualis eſt rectangulo comprehen-<lb/> <anchor type="note" xlink:label="note-118-01a" xlink:href="note-118-01"/> ſo ſub perpendiculari à uertice ad baſim protracta, & </s> <s xml:id="echoid-s4164" xml:space="preserve">dimidia <lb/>partes baſis.</s> <s xml:id="echoid-s4165" xml:space="preserve"/> </p> <div xml:id="echoid-div217" type="float" level="2" n="1"> <note position="left" xlink:label="note-118-01" xlink:href="note-118-01a" xml:space="preserve">Triangulũ <lb/>quodcun q; <lb/>eui rectan-<lb/>gulo ęqua-<lb/>@ ſ<unsure/>it.</note> </div> <p> <s xml:id="echoid-s4166" xml:space="preserve"><emph style="sc">Sit</emph> triangulum A B C, ex cuius uertice A, ad baſim B C, ducatur per-<lb/> <anchor type="figure" xlink:label="fig-118-01a" xlink:href="fig-118-01"/> pendicularis A D, diuidatq́ue primò baſim B C, bifariam, ut in prima figura. <lb/></s> <s xml:id="echoid-s4167" xml:space="preserve">Per A, ducatur E A F, in utramque partem æquidiſtans rectæ B C, complea- <pb o="83" file="119" n="120" rhead="Ioan. de Sacro Boſco."/> turq́ue rectangulum B E F C, quod erit duplum trianguli A B C; </s> <s xml:id="echoid-s4168" xml:space="preserve">Item duplũ <lb/> <anchor type="note" xlink:label="note-119-01a" xlink:href="note-119-01"/> rectanguli A D B E. </s> <s xml:id="echoid-s4169" xml:space="preserve">Quare rectangulum A D B E, quod nimirum continetur <lb/> <anchor type="note" xlink:label="note-119-02a" xlink:href="note-119-02"/> ſub perpendiculari A D, & </s> <s xml:id="echoid-s4170" xml:space="preserve">dimidio baſis B D, æquale eſt triangulo A B C. </s> <s xml:id="echoid-s4171" xml:space="preserve">Di <lb/>uidat ſecundo perpendicularis A D, baſim B C, non bifariam, uel etiam ca-<lb/>dat in baſim C B, protractam, ut in 2. </s> <s xml:id="echoid-s4172" xml:space="preserve">& </s> <s xml:id="echoid-s4173" xml:space="preserve">3. </s> <s xml:id="echoid-s4174" xml:space="preserve">figura; </s> <s xml:id="echoid-s4175" xml:space="preserve">Et per A, ducatur rurſus <lb/>A F, in utramque partem æquidiſtans rectæ B C, compleaturq́ue rectangulũ <lb/>A D C F. </s> <s xml:id="echoid-s4176" xml:space="preserve">Diuiſa deinde B C, bifariam in G, ducantur rectæ B E, G H, ipſi <lb/>A D, æquidiſtantes, eritq́ue G H, æqualis perpendiculari A D. </s> <s xml:id="echoid-s4177" xml:space="preserve">Quoniam igi-<lb/> <anchor type="note" xlink:label="note-119-03a" xlink:href="note-119-03"/> tur rectangulum B C E F, duplum eſt trianguli A B C; </s> <s xml:id="echoid-s4178" xml:space="preserve">Item duplum rectangu <lb/> <anchor type="note" xlink:label="note-119-04a" xlink:href="note-119-04"/> li B E H G; </s> <s xml:id="echoid-s4179" xml:space="preserve">erit rectangulum B E H G, quod continetur ſub perpendiculari <lb/> <anchor type="note" xlink:label="note-119-05a" xlink:href="note-119-05"/> G H, uel A D, & </s> <s xml:id="echoid-s4180" xml:space="preserve">dimidio baſis B G, æquale triangulo A B C. </s> <s xml:id="echoid-s4181" xml:space="preserve">Area igitur cu-<lb/>iuslibet trianguli æqualis eſt, &</s> <s xml:id="echoid-s4182" xml:space="preserve">c. </s> <s xml:id="echoid-s4183" xml:space="preserve">quod erat oſtendendum.</s> <s xml:id="echoid-s4184" xml:space="preserve"/> </p> <div xml:id="echoid-div218" type="float" level="2" n="2"> <figure xlink:label="fig-118-01" xlink:href="fig-118-01a"> <image file="118-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/118-01"/> </figure> <note position="right" xlink:label="note-119-01" xlink:href="note-119-01a" xml:space="preserve">41. primi.</note> <note position="right" xlink:label="note-119-02" xlink:href="note-119-02a" xml:space="preserve">36. primi.</note> <note position="right" xlink:label="note-119-03" xlink:href="note-119-03a" xml:space="preserve">34. primi.</note> <note position="right" xlink:label="note-119-04" xlink:href="note-119-04a" xml:space="preserve">41. primi.</note> <note position="right" xlink:label="note-119-05" xlink:href="note-119-05a" xml:space="preserve">36. primi.</note> </div> </div> <div xml:id="echoid-div220" type="section" level="1" n="74"> <head xml:id="echoid-head78" style="it" xml:space="preserve">THEOR. 2. PROPOS. 2.</head> <p style="it"> <s xml:id="echoid-s4185" xml:space="preserve"><emph style="sc">Area</emph> cuiuslibet figuræ regularis æqualis eſt rectangulo contento ſub <lb/> <anchor type="note" xlink:label="note-119-06a" xlink:href="note-119-06"/> perpendiculari à centro figurę ad unum latus ducta, & </s> <s xml:id="echoid-s4186" xml:space="preserve">ſub dimidiato ambi-<unsure/> <lb/>tu eiuſdem figuræ.</s> <s xml:id="echoid-s4187" xml:space="preserve"/> </p> <div xml:id="echoid-div220" type="float" level="2" n="1"> <note position="right" xlink:label="note-119-06" xlink:href="note-119-06a" xml:space="preserve">Regularis<unsure/> <lb/>figura quæ <lb/>cunque cui <lb/>rectangulo <lb/>ęqualis ſit.</note> </div> <p> <s xml:id="echoid-s4188" xml:space="preserve"><emph style="sc">Sit</emph> figura regularis quæcunque A B C D E F, & </s> <s xml:id="echoid-s4189" xml:space="preserve">centrum eius punctum <lb/>G, à quo ducatur G H, perpendicularis ad unum latus, nempe ad A B: </s> <s xml:id="echoid-s4190" xml:space="preserve">Sit <lb/> <anchor type="figure" xlink:label="fig-119-01a" xlink:href="fig-119-01"/> quoque rectãgulum I K-<lb/>L M, contentum ſub I K, <lb/>quæ æqualis ſit perpendi-<lb/>culari G H, & </s> <s xml:id="echoid-s4191" xml:space="preserve">ſub K L, re-<lb/>cta, quæ æqualis ponatur <lb/>dimidiæ parti ambitu fi-<lb/>guræ A B C D E F. </s> <s xml:id="echoid-s4192" xml:space="preserve">Dico <lb/>huic rectangulo æqualem <lb/>eſſe figuram regularẽ A <lb/>B C D E F. </s> <s xml:id="echoid-s4193" xml:space="preserve">Ducãtur em̃ <lb/>ex G, ad ſingulos angulos <lb/>lineæ rectæ, ut tota figura <lb/>in triangula reſoluatur, <lb/>quæ omnia æqualia inter <lb/>ſe erunt, ut in corollario <lb/>propoſ. </s> <s xml:id="echoid-s4194" xml:space="preserve">8. </s> <s xml:id="echoid-s4195" xml:space="preserve">lib. </s> <s xml:id="echoid-s4196" xml:space="preserve">1. </s> <s xml:id="echoid-s4197" xml:space="preserve">Eucl. </s> <s xml:id="echoid-s4198" xml:space="preserve">de-<lb/>monſtratum eſt à nobis; <lb/></s> <s xml:id="echoid-s4199" xml:space="preserve">propterea quòd omnia la-<lb/>tera triangulorum à pun-<lb/>cto G, exeuntia ſint inter <lb/>ſæ æqualia, habeantq́; </s> <s xml:id="echoid-s4200" xml:space="preserve">ba-<lb/>ſes æquales, nempe latera <lb/>figuræ regularis. </s> <s xml:id="echoid-s4201" xml:space="preserve">Hinc e-<lb/>nim efficitur, omnes angu <lb/>los ad G, æq uales eſſe, ac proinde, ex dicto corollario, triangula ipſa inter ſe <lb/> <anchor type="note" xlink:label="note-119-07a" xlink:href="note-119-07"/> quoque eſſe æqualia. </s> <s xml:id="echoid-s4202" xml:space="preserve">Quoniam igitur rectangulum cõtentum ſub G H, perpẽ- <pb o="84" file="120" n="121" rhead="Comment. in I. Cap. Sphæræ"/> diculari, & </s> <s xml:id="echoid-s4203" xml:space="preserve">medietate baſis A B, (ꝑ 1. </s> <s xml:id="echoid-s4204" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s4205" xml:space="preserve">huius) æquale eſt triangulo A B G; <lb/></s> <s xml:id="echoid-s4206" xml:space="preserve">ſi ſumantur tot huiuſmodi rectangula, in quot triangula diuiſa eſt figura regu-<lb/>laris, erunt omnia ſimul ſiguræ A B C D E F, æqualia; </s> <s xml:id="echoid-s4207" xml:space="preserve">propterea quòd omnia <lb/>triangula oſtenſa ſint æqualia triangulo A B G. </s> <s xml:id="echoid-s4208" xml:space="preserve">Cum igitur eadem ſimul æ-<lb/>qualia ſint rectangulo I K L M; </s> <s xml:id="echoid-s4209" xml:space="preserve">propterea quòd K L, æqualis ponitur dimidio <lb/>ambitus A B C D E F, hoc eſt, omnibus medietatibus baſium ſimul, & </s> <s xml:id="echoid-s4210" xml:space="preserve">recta <lb/>I K, perpendiculari G H; </s> <s xml:id="echoid-s4211" xml:space="preserve">erit figura regularis A B C D E F, æqualis rectangu <lb/>lo I K L M. </s> <s xml:id="echoid-s4212" xml:space="preserve">Area igitur cuiuslibet figuræ regularis æqualis eſt, &</s> <s xml:id="echoid-s4213" xml:space="preserve">c. </s> <s xml:id="echoid-s4214" xml:space="preserve">quod erat <lb/>demonſtrandum.</s> <s xml:id="echoid-s4215" xml:space="preserve"/> </p> <div xml:id="echoid-div221" type="float" level="2" n="2"> <figure xlink:label="fig-119-01" xlink:href="fig-119-01a"> <image file="119-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/119-01"/> </figure> <note position="right" xlink:label="note-119-07" xlink:href="note-119-07a" xml:space="preserve">8. primi.</note> </div> </div> <div xml:id="echoid-div223" type="section" level="1" n="75"> <head xml:id="echoid-head79" style="it" xml:space="preserve">THEOR. 3. PROPOS. 3.</head> <note position="left" xml:space="preserve">Regularis <lb/>figura quæ <lb/>cunque cui <lb/>triangulo <lb/>rectangulo <lb/>æqualis ſit.</note> <p style="it"> <s xml:id="echoid-s4216" xml:space="preserve"><emph style="sc">Area</emph> cuiuslibet figuræregularis æqualis eſt triangulo rectangulo, <lb/>cuius unum latus circa angulum rectum æquale eſt perpendiculari à centro <lb/>figuræ ad unum latus ductæ, alterum uero æquale ambitui eiuſdem figuræ.</s> <s xml:id="echoid-s4217" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4218" xml:space="preserve"><emph style="sc">Sit</emph> rurſus figura regularis A B C, cuius centrum D, à quo perpendicula-<lb/>ris ad latus A B, ducta ſit D E; </s> <s xml:id="echoid-s4219" xml:space="preserve">triangulum uero rectangulum D E F, habens <lb/> <anchor type="figure" xlink:label="fig-120-01a" xlink:href="fig-120-01"/> angulum E, rectum, & </s> <s xml:id="echoid-s4220" xml:space="preserve">latus D E, æquale perpendiculari D E, latus autẽ E F, <lb/>æquale ambitui figuræ A B C. </s> <s xml:id="echoid-s4221" xml:space="preserve">Dico triangulum D E F, figuræ A B C, æquale <lb/>eſſe. </s> <s xml:id="echoid-s4222" xml:space="preserve">Compleatur enim rectangulum D E F G; </s> <s xml:id="echoid-s4223" xml:space="preserve">& </s> <s xml:id="echoid-s4224" xml:space="preserve">diuiſa E F, bifa@iam in pun-<lb/>cto H, ducatur H I, æquidiſtans rectæ D E. </s> <s xml:id="echoid-s4225" xml:space="preserve">Erit igitur (per 2. </s> <s xml:id="echoid-s4226" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s4227" xml:space="preserve">huius) <lb/>rectangulum D E H I, contentum ſub D E, perpendiculari, & </s> <s xml:id="echoid-s4228" xml:space="preserve">ſub E H, dimi-<lb/>dio ambitus figuræ, æquale figuræ A B C: </s> <s xml:id="echoid-s4229" xml:space="preserve">At rectangulo D E H I, æquale eſt <lb/>triangulum D E F. </s> <s xml:id="echoid-s4230" xml:space="preserve">Nam rectangulum D E H I, eſt dimidium rectanguli <lb/>D E F G; </s> <s xml:id="echoid-s4231" xml:space="preserve">propterea quod æqualia ſunt rectangula D E H I, I H F G; </s> <s xml:id="echoid-s4232" xml:space="preserve">Triangu-<lb/> <anchor type="note" xlink:label="note-120-02a" xlink:href="note-120-02"/> lum quoque D E F, dimidium eſt eiuſdem rectanguli D E F G. </s> <s xml:id="echoid-s4233" xml:space="preserve">Igitur & </s> <s xml:id="echoid-s4234" xml:space="preserve">trian-<lb/> <anchor type="note" xlink:label="note-120-03a" xlink:href="note-120-03"/> gulum D E F, æquale erit figuræ A B C. </s> <s xml:id="echoid-s4235" xml:space="preserve">Area ergo cuiuslibet figuræ regula <lb/>ris æqualis eſt triangulo rectangulo, &</s> <s xml:id="echoid-s4236" xml:space="preserve">c. </s> <s xml:id="echoid-s4237" xml:space="preserve">quod demonſtrandum erat.</s> <s xml:id="echoid-s4238" xml:space="preserve"/> </p> <div xml:id="echoid-div223" type="float" level="2" n="1"> <figure xlink:label="fig-120-01" xlink:href="fig-120-01a"> <image file="120-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/120-01"/> </figure> <note position="left" xlink:label="note-120-02" xlink:href="note-120-02a" xml:space="preserve">38<unsure/>. primi.</note> <note position="left" xlink:label="note-120-03" xlink:href="note-120-03a" xml:space="preserve">41. primi.</note> </div> <pb o="85" file="121" n="122" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div225" type="section" level="1" n="76"> <head xml:id="echoid-head80" style="it" xml:space="preserve">THEOR. 4. PROPOS. 4.</head> <p style="it"> <s xml:id="echoid-s4239" xml:space="preserve"><emph style="sc">Area</emph> cuiuslibet circuli æqualis eſt rectangulo comprehenſo<unsure/> ſub ſe-<lb/> <anchor type="note" xlink:label="note-121-01a" xlink:href="note-121-01"/> midiametro, & </s> <s xml:id="echoid-s4240" xml:space="preserve">dimidiata circumferentia circuli.</s> <s xml:id="echoid-s4241" xml:space="preserve"/> </p> <div xml:id="echoid-div225" type="float" level="2" n="1"> <note position="right" xlink:label="note-121-01" xlink:href="note-121-01a" xml:space="preserve">Circulus <lb/>quicunque <lb/>cui rectan<unsure/>-<lb/>gulo æqua-<lb/>lis ſit.</note> </div> <p> <s xml:id="echoid-s4242" xml:space="preserve"><emph style="sc">Esto</emph> circulus A B C, cuius ſemidiameter D B: </s> <s xml:id="echoid-s4243" xml:space="preserve">Rectangulum autem <lb/> <anchor type="figure" xlink:label="fig-121-01a" xlink:href="fig-121-01"/> D B E F, comprehenſum ſub D B, ſemidiametro circuli, & </s> <s xml:id="echoid-s4244" xml:space="preserve">B E, recta, quæ <lb/>æqualis ſit dimidiatæ circunferentiæ circuli. </s> <s xml:id="echoid-s4245" xml:space="preserve">Dico aream circuli A B C, æqua <lb/>lem eſſe rectangulo D B E F. </s> <s xml:id="echoid-s4246" xml:space="preserve">Producatur enim B E, in continuum, ponatur-<lb/>q́ue E G, æqualis ipſi B E, ut ſit B G, recta æqualis toti circunferentiæ circu-<lb/>li. </s> <s xml:id="echoid-s4247" xml:space="preserve">Coniungantur denique puncta D, G, recta D G. </s> <s xml:id="echoid-s4248" xml:space="preserve">Quoniam igitur (per 1. <lb/></s> <s xml:id="echoid-s4249" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s4250" xml:space="preserve">Archimedis de Dimenſione circuli) circulus A B C, æqualis eſt trian <lb/>gulo D B G: </s> <s xml:id="echoid-s4251" xml:space="preserve">Eſt autem triangulum D B G, rectangulo D B E F, æquale, ut in <lb/>ſcholio propoſ. </s> <s xml:id="echoid-s4252" xml:space="preserve">41. </s> <s xml:id="echoid-s4253" xml:space="preserve">lib. </s> <s xml:id="echoid-s4254" xml:space="preserve">1. </s> <s xml:id="echoid-s4255" xml:space="preserve">Eucl. </s> <s xml:id="echoid-s4256" xml:space="preserve">demonſtrauimus, quòd baſis trianguli dupla ſit <lb/>baſis rectanguli, (Id quod etiam ex demonſtratione antecedentis propoſ. </s> <s xml:id="echoid-s4257" xml:space="preserve">li-<lb/>quet, ubi oſtendimus, triangulum D E F, æquale eſſe rectangulo D E H I:) </s> <s xml:id="echoid-s4258" xml:space="preserve"><lb/>erit quoque circulus A B C, rectangulo D B E F, æqualis. </s> <s xml:id="echoid-s4259" xml:space="preserve">Area ergo cuius-<lb/>libet circuli æqualis eſt rectangulo, &</s> <s xml:id="echoid-s4260" xml:space="preserve">c. </s> <s xml:id="echoid-s4261" xml:space="preserve">quod oſtendendum erat.</s> <s xml:id="echoid-s4262" xml:space="preserve"/> </p> <div xml:id="echoid-div226" type="float" level="2" n="2"> <figure xlink:label="fig-121-01" xlink:href="fig-121-01a"> <image file="121-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/121-01"/> </figure> </div> </div> <div xml:id="echoid-div228" type="section" level="1" n="77"> <head xml:id="echoid-head81" style="it" xml:space="preserve">THEOR. 5. PROPOS. 5.</head> <note position="right" xml:space="preserve">Proprietas <lb/>quædã triã-<lb/>guli rectan <lb/>guli.</note> <p style="it"> <s xml:id="echoid-s4263" xml:space="preserve"><emph style="sc">In</emph> omni triangulo rectangulo, ſi ab uno acutorum angul orum ut-<lb/>cunque ad latus oppoſitum linea recta ducatur, erit maior proportio <lb/>huius lateris ad eius ſegmentum, quod prope angulum rectum exi-<lb/>ſtit, quàm anguli acuti prędicti ad eius partem dicto ſegmento late-<lb/>ris oppoſitam.</s> <s xml:id="echoid-s4264" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4265" xml:space="preserve"><emph style="sc">Sit</emph> triangulum rectangulum A B C, cuius angulus C, ſit rectus; </s> <s xml:id="echoid-s4266" xml:space="preserve">duca- <pb o="86" file="122" n="123" rhead="Comment. in I. Cap. Sphæræ"/> turq́ue ab acu to angulo A, ad latus oppoſitum B C, recta A D, utcunque. </s> <s xml:id="echoid-s4267" xml:space="preserve">Di-<lb/>co maiore m eſſe proportionem rectæ B C, ad rectam C D, quàm anguli B A C, <lb/> <anchor type="figure" xlink:label="fig-122-01a" xlink:href="fig-122-01"/> ad angulum C A D. </s> <s xml:id="echoid-s4268" xml:space="preserve">Quoniam enim recta A D, <lb/>maior quidem eſt, quàm A C, minor uero, quã <lb/>A B, ſi centro A, interuallo autem A D, circu-<lb/>lus deſcribatur; </s> <s xml:id="echoid-s4269" xml:space="preserve">ſecabit is rectam A C, protractã <lb/> <anchor type="note" xlink:label="note-122-01a" xlink:href="note-122-01"/> infra punctum C, ut in E, at uero rectam A B, ſu <lb/>pra punctum B, ut in F. </s> <s xml:id="echoid-s4270" xml:space="preserve">Et quia maior eſt pro-<lb/>portio trianguli B A D, ad ſectorem F A D, quã <lb/>trianguli D A C, ad ſectorem D A E, (propterea <lb/>quòd ibi eſt proportio maioris inæqualitatis, hic <lb/>autem minoris inæqualitatis) erit quoque permu<unsure/> <lb/>tando maior proportio trianguli B A D, ad triã-<lb/> <anchor type="note" xlink:label="note-122-02a" xlink:href="note-122-02"/> gulum D A C, quàm ſectoris F A D, ad ſectorem <lb/>D A E. </s> <s xml:id="echoid-s4271" xml:space="preserve">Com ponendo igitur maior quoque erit proportio trianguli B A C, ad <lb/> <anchor type="note" xlink:label="note-122-03a" xlink:href="note-122-03"/> triangulum D A C, hoc eſt, rectæ B C, ad rectam C D, (habent enim trian-<lb/>gula B A C, D A C, eandem proportionem, quàm baſes B C, C D.) </s> <s xml:id="echoid-s4272" xml:space="preserve">quàm <lb/> <anchor type="note" xlink:label="note-122-04a" xlink:href="note-122-04"/> ſectoris F A E, ad ſectorem D A E, hoc eſt, quàm anguli B A C, ad angulum <lb/>C A D; </s> <s xml:id="echoid-s4273" xml:space="preserve">quòd ex coroll. </s> <s xml:id="echoid-s4274" xml:space="preserve">1. </s> <s xml:id="echoid-s4275" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s4276" xml:space="preserve">33. </s> <s xml:id="echoid-s4277" xml:space="preserve">lib. </s> <s xml:id="echoid-s4278" xml:space="preserve">6. </s> <s xml:id="echoid-s4279" xml:space="preserve">Eucl. </s> <s xml:id="echoid-s4280" xml:space="preserve">eandem habeant proportio-<lb/>n em ſectores, quàm anguli. </s> <s xml:id="echoid-s4281" xml:space="preserve">Quocirca in omni triangulo rectangulo, &</s> <s xml:id="echoid-s4282" xml:space="preserve">c. </s> <s xml:id="echoid-s4283" xml:space="preserve">quod <lb/>demonſtrandum erat.</s> <s xml:id="echoid-s4284" xml:space="preserve"/> </p> <div xml:id="echoid-div228" type="float" level="2" n="1"> <figure xlink:label="fig-122-01" xlink:href="fig-122-01a"> <image file="122-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/122-01"/> </figure> <note position="left" xlink:label="note-122-01" xlink:href="note-122-01a" xml:space="preserve">19. primi.</note> <note position="left" xlink:label="note-122-02" xlink:href="note-122-02a" xml:space="preserve">27. quinti.</note> <note position="left" xlink:label="note-122-03" xlink:href="note-122-03a" xml:space="preserve">28. quinti.</note> <note position="left" xlink:label="note-122-04" xlink:href="note-122-04a" xml:space="preserve">2. ſexti.</note> </div> </div> <div xml:id="echoid-div230" type="section" level="1" n="78"> <head xml:id="echoid-head82" style="it" xml:space="preserve">THEOR. 6. PROPOS. 6.</head> <note position="left" xml:space="preserve">Inter figu-<lb/>ras Iſoperi-<lb/>metras, quę <lb/>plures an-<lb/>gulos, ſeu <lb/>latera con-<lb/>@inet, illa <lb/>@aior eſt.</note> <p style="it"> <s xml:id="echoid-s4285" xml:space="preserve"><emph style="sc">Isoperimetrarvm</emph> figurarum regularium maior eſt il-<lb/>la, quæ plures continet angulos, plur areue latera.</s> <s xml:id="echoid-s4286" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4287" xml:space="preserve"><emph style="sc">Sint</emph> duæ figuræ regulares iſoperimetræ A B C, D E F, habeatq́; </s> <s xml:id="echoid-s4288" xml:space="preserve">plura <lb/>latera, ſiue angulos figura A B C, quàm D E F. </s> <s xml:id="echoid-s4289" xml:space="preserve">Dico A B C, maiorem eſſe, <lb/> <anchor type="figure" xlink:label="fig-122-02a" xlink:href="fig-122-02"/> quàm D E F. </s> <s xml:id="echoid-s4290" xml:space="preserve">Deſcribantur enim circa figuras circuli, à quorum centris G, H, <lb/>ducantur ad B C, E F, perpendiculares G I, H K, quæ diuident rectas B C, <lb/> <anchor type="note" xlink:label="note-122-06a" xlink:href="note-122-06"/> E F, bifariam. </s> <s xml:id="echoid-s4291" xml:space="preserve">Quo niam igitur figura A B C, plura habet latera, quàm D E F. <lb/></s> <s xml:id="echoid-s4292" xml:space="preserve">f<unsure/>bi iſoperimetra, efficitur, ut latus B C, ſæpius repetitum metiatur ambitum <pb o="87" file="123" n="124" rhead="Ioan. de Sacro Boſco."/> ſiguræ A B C, quam latus E F, ambitum figuræ D E F. </s> <s xml:id="echoid-s4293" xml:space="preserve">Quare latus B C, mi-<lb/>nus erit latere E F, ideoq, B I, medietas lateris B C, minor, quàm E K, medie <lb/>tas lateris E F. </s> <s xml:id="echoid-s4294" xml:space="preserve">Ponatur K L, æqualis ipſi B I, & </s> <s xml:id="echoid-s4295" xml:space="preserve">ducantur rectæ L H, H E, <lb/> <anchor type="note" xlink:label="note-123-01a" xlink:href="note-123-01"/> H F, G B, G C. </s> <s xml:id="echoid-s4296" xml:space="preserve">Et quia omnes arcus circuli D E F, ſunt æquales, quòd & </s> <s xml:id="echoid-s4297" xml:space="preserve">re-<lb/>ctæ ſubtenſæ æquales ponantur; </s> <s xml:id="echoid-s4298" xml:space="preserve">erit recta E F, ita ſubmultiplex ambitus ſigu-<lb/>ræ D E F, ut arcus E F, ſubmultiplex eſt circunferentiæ circuli D E F: </s> <s xml:id="echoid-s4299" xml:space="preserve">Ea-<lb/>demq́ue ratione ita multiplex ambitus figuræ A B C, rectæ B C, ficut multi-<lb/>plex eſt circunferentia A B C, arcus B C: </s> <s xml:id="echoid-s4300" xml:space="preserve">Vt autem arcus E F, ad circunferen <lb/>tiam circuli D E F, ita eſt (ex coroll. </s> <s xml:id="echoid-s4301" xml:space="preserve">2. </s> <s xml:id="echoid-s4302" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s4303" xml:space="preserve">33. </s> <s xml:id="echoid-s4304" xml:space="preserve">lib. </s> <s xml:id="echoid-s4305" xml:space="preserve">6. </s> <s xml:id="echoid-s4306" xml:space="preserve">Eucl.) </s> <s xml:id="echoid-s4307" xml:space="preserve">angulus E H F, <lb/>ad quatuor rectos. </s> <s xml:id="echoid-s4308" xml:space="preserve">Igitur erit quoque, ut recta E F, ad ambitum figuræ D E F, <lb/>hoc eſt, ad ambitum ſiguræ A B C, illi æqualem, ita angulus E H F, ad qua-<lb/>tuor rectos; </s> <s xml:id="echoid-s4309" xml:space="preserve">Vt autem ambitus figuræ A B C, ad rectam B C, ita eſt circunferẽ <lb/>tia circuli A B C, ad aroum B C, hoc eſt, ita quatuor recti (ex eodem coroll. <lb/></s> <s xml:id="echoid-s4310" xml:space="preserve">2. </s> <s xml:id="echoid-s4311" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s4312" xml:space="preserve">33. </s> <s xml:id="echoid-s4313" xml:space="preserve">lib. </s> <s xml:id="echoid-s4314" xml:space="preserve">6. </s> <s xml:id="echoid-s4315" xml:space="preserve">Eucl.) </s> <s xml:id="echoid-s4316" xml:space="preserve">ad angulum B G C. </s> <s xml:id="echoid-s4317" xml:space="preserve">Ex æquo igitur ut recta E F, ad <lb/>rectam B C, hoc eſt, ut recta E K, ad rectam B I, hoc eſt, ad rectam K L, ita an-<lb/>gulus E H F, ad angulum B G C, hoc eſt, ita angulus E H K, ad angulum <lb/> <anchor type="note" xlink:label="note-123-02a" xlink:href="note-123-02"/> B G I. </s> <s xml:id="echoid-s4318" xml:space="preserve">Eſ<unsure/>t autem maior proportio rectæ E K, ad rectam K L, (per 5. </s> <s xml:id="echoid-s4319" xml:space="preserve">propoſ. <lb/></s> <s xml:id="echoid-s4320" xml:space="preserve"> <anchor type="note" xlink:label="note-123-03a" xlink:href="note-123-03"/> huius) quàm anguli E H K, ad angulum K H L. </s> <s xml:id="echoid-s4321" xml:space="preserve">Quare maior erit proportio <lb/>quoque anguli E H K, ad angulum B G I, quàm eiuſdem anguli E H K, ad <lb/> <anchor type="note" xlink:label="note-123-04a" xlink:href="note-123-04"/> angulum K H L; </s> <s xml:id="echoid-s4322" xml:space="preserve">ideoq́ue maior erit angulus K H L, quàm angulus B G L. </s> <s xml:id="echoid-s4323" xml:space="preserve">Cũ <lb/> <anchor type="note" xlink:label="note-123-05a" xlink:href="note-123-05"/> igitur anguli H K L, G I B, ſint æquales, vtpote recti, erit reliquus an<unsure/>gulus <lb/>H L K, minor reliquo angulo G B I. </s> <s xml:id="echoid-s4324" xml:space="preserve">Fiat igitur angulus K L M, æqualis an-<lb/> <anchor type="note" xlink:label="note-123-06a" xlink:href="note-123-06"/> gulo G B I; </s> <s xml:id="echoid-s4325" xml:space="preserve">cadetq́ue L M, extra L H; </s> <s xml:id="echoid-s4326" xml:space="preserve">conuenietq́ue cum K H, producta ul-<lb/>tra H, in puncto M. </s> <s xml:id="echoid-s4327" xml:space="preserve">Quoniam igitur duo anguli B, I, trianguli G B I, æqua <lb/>les ſunt duobus angulis L, K, trianguli M L K, & </s> <s xml:id="echoid-s4328" xml:space="preserve">latera B I, L K, ęqualia, <lb/>erunt rectæ G I, M K, æquales. </s> <s xml:id="echoid-s4329" xml:space="preserve">Recta ergo G I, maior eſt, quàm recta H K. <lb/></s> <s xml:id="echoid-s4330" xml:space="preserve"> <anchor type="note" xlink:label="note-123-07a" xlink:href="note-123-07"/> Quamobrem rectangulum ſub G I, & </s> <s xml:id="echoid-s4331" xml:space="preserve">dimidio ambitu ſiguræ A B C, conten <lb/>tum maius erit rectangulo contento ſub H K, & </s> <s xml:id="echoid-s4332" xml:space="preserve">dimidio ambitu figuræ <lb/>D E C, qui æqualis ponitur dimidio ambitus figuræ A B C. </s> <s xml:id="echoid-s4333" xml:space="preserve">Quocirca cum <lb/>illud rectangulum oſtenſum ſit, in 2. </s> <s xml:id="echoid-s4334" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s4335" xml:space="preserve">huius, æquale figuræ A B C, <lb/>hoc autem figuræ D E F, æquale; </s> <s xml:id="echoid-s4336" xml:space="preserve">maior quoque erit figura A B C, quàm fi-<lb/>gura D E F. </s> <s xml:id="echoid-s4337" xml:space="preserve">Iſoperimetrarum ergo ſigurarum regularium maior eſt illa, &</s> <s xml:id="echoid-s4338" xml:space="preserve">c. <lb/></s> <s xml:id="echoid-s4339" xml:space="preserve">quod erat oſtendendum.</s> <s xml:id="echoid-s4340" xml:space="preserve"/> </p> <div xml:id="echoid-div230" type="float" level="2" n="1"> <figure xlink:label="fig-122-02" xlink:href="fig-122-02a"> <image file="122-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/122-02"/> </figure> <note position="left" xlink:label="note-122-06" xlink:href="note-122-06a" xml:space="preserve">@. tertij.</note> <note position="right" xlink:label="note-123-01" xlink:href="note-123-01a" xml:space="preserve">28. tertij.</note> <note position="right" xlink:label="note-123-02" xlink:href="note-123-02a" xml:space="preserve">15. quinti.</note> <note position="right" xlink:label="note-123-03" xlink:href="note-123-03a" xml:space="preserve">15. quinti.</note> <note position="right" xlink:label="note-123-04" xlink:href="note-123-04a" xml:space="preserve">13. quinti.</note> <note position="right" xlink:label="note-123-05" xlink:href="note-123-05a" xml:space="preserve">10. quinti.</note> <note position="right" xlink:label="note-123-06" xlink:href="note-123-06a" xml:space="preserve">32. primi.</note> <note position="right" xlink:label="note-123-07" xlink:href="note-123-07a" xml:space="preserve">26. primi.</note> </div> </div> <div xml:id="echoid-div232" type="section" level="1" n="79"> <head xml:id="echoid-head83" style="it" xml:space="preserve">THEOR. 1. PROPOS. 7.</head> <note position="right" xml:space="preserve">Qua arte <lb/>triangulũ <lb/>Iſoſceles cõ <lb/>ſtituatur <lb/>Iſoperime-<lb/>trũ cuiuis <lb/>triangulo <lb/>non Iſoſce-<lb/>li.</note> <p style="it"> <s xml:id="echoid-s4341" xml:space="preserve"><emph style="sc">Proposito</emph> triangulo, cuius duo latera ſint inæqualia, ſupra <lb/>reliquum latus triangulum priori Iſoperimetrum, ac duo habens latera <lb/>æqu alia, deſcribere.</s> <s xml:id="echoid-s4342" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4343" xml:space="preserve"><emph style="sc">Sit</emph> triangulum A B C, cuius duo latera A B, B C, ſint inæqualia, nempe <lb/>A B, maius, quàm B C; </s> <s xml:id="echoid-s4344" xml:space="preserve">oporreatq́ue ſupra A C, conſtruere triangulum Iſo-<lb/>ſceles, atque iſoperimetrum triangulo A B C. </s> <s xml:id="echoid-s4345" xml:space="preserve">Sumatur recta D E, æqualis <lb/>duobus lateribus A B, B C, ſimul, diuidaturq́ue bifariam in F. </s> <s xml:id="echoid-s4346" xml:space="preserve">Et quoniam <lb/> <anchor type="note" xlink:label="note-123-09a" xlink:href="note-123-09"/> latera A B, B C, ſimul maiora ſunt latere A G, erit quoque dimidium illo-<lb/>rum, nempe D F, vel F E, maius, quàm dimidium lateris A C: </s> <s xml:id="echoid-s4347" xml:space="preserve">Atque ob id <pb o="88" file="124" n="125" rhead="Comment. in I. Cap. Sphæræ"/> tres lin eę AC, DF, FE, ita ſeſe <lb/> <anchor type="figure" xlink:label="fig-124-01a" xlink:href="fig-124-01"/> habe bũt, vt quælibet duæ ſint <lb/>reliq ua maiores. </s> <s xml:id="echoid-s4348" xml:space="preserve">Si igitur ex <lb/>ipſis conficiatur triangulum <lb/>A G C, effectum erit, quod <lb/>proponitur. </s> <s xml:id="echoid-s4349" xml:space="preserve">Erunt enim late-<lb/> <anchor type="note" xlink:label="note-124-01a" xlink:href="note-124-01"/> ra AG, GC, & </s> <s xml:id="echoid-s4350" xml:space="preserve">inter ſe ęqualia, <lb/>& </s> <s xml:id="echoid-s4351" xml:space="preserve">ſimul ſumpta æqualia late-<lb/>ribus AB, BC, ſimul ſumptis: <lb/></s> <s xml:id="echoid-s4352" xml:space="preserve">addito igitur communi A C, <lb/>erunt triangula ABC, AGC, <lb/>iſoperimetra. </s> <s xml:id="echoid-s4353" xml:space="preserve">Propoſito igi-<lb/>tur triangulo, cuius duo latera ſint inæqualia, ſupra reliquum latus triangulũ, <lb/>&</s> <s xml:id="echoid-s4354" xml:space="preserve">c. </s> <s xml:id="echoid-s4355" xml:space="preserve">d eſcripſimus. </s> <s xml:id="echoid-s4356" xml:space="preserve">quod faciendum erat.</s> <s xml:id="echoid-s4357" xml:space="preserve"/> </p> <div xml:id="echoid-div232" type="float" level="2" n="1"> <note position="right" xlink:label="note-123-09" xlink:href="note-123-09a" xml:space="preserve">10. primi.</note> <figure xlink:label="fig-124-01" xlink:href="fig-124-01a"> <image file="124-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/124-01"/> </figure> <note position="left" xlink:label="note-124-01" xlink:href="note-124-01a" xml:space="preserve">22. primi.</note> </div> </div> <div xml:id="echoid-div234" type="section" level="1" n="80"> <head xml:id="echoid-head84" xml:space="preserve">SCHOLIVM.</head> <p style="it"> <s xml:id="echoid-s4358" xml:space="preserve"><emph style="sc">Cadet</emph> autem neceſſario punctum G, extra triangulum A B C: </s> <s xml:id="echoid-s4359" xml:space="preserve">Sinamque ca-<lb/> <anchor type="note" xlink:label="note-124-02a" xlink:href="note-124-02"/> deret in latus A B, ut ad punctum H, eßet ducta recta H C, minor quàm H B, B C, ſi-<lb/>mul, & </s> <s xml:id="echoid-s4360" xml:space="preserve">ob id triangulum A H C, non eſſet iſoperimetrum triangulo A B C, c{ui}us con <lb/>trarium ex conſtructione eſt demonſtratum. </s> <s xml:id="echoid-s4361" xml:space="preserve">Mu<unsure/>lto minus cadet punctum G, intra trian.</s> <s xml:id="echoid-s4362" xml:space="preserve"><unsure/> <lb/>gu lum A B C. </s> <s xml:id="echoid-s4363" xml:space="preserve">Quare extra cadet, quod eſt propoſitum.</s> <s xml:id="echoid-s4364" xml:space="preserve"/> </p> <div xml:id="echoid-div234" type="float" level="2" n="1"> <note position="left" xlink:label="note-124-02" xlink:href="note-124-02a" xml:space="preserve">20. primi.</note> </div> </div> <div xml:id="echoid-div236" type="section" level="1" n="81"> <head xml:id="echoid-head85" style="it" xml:space="preserve">THEOR. 7. PROPOS. 8.</head> <p style="it"> <s xml:id="echoid-s4365" xml:space="preserve"><emph style="sc">Dvorvm</emph> triangulorum iſoperimetrorum eandem habentium ba-<lb/> <anchor type="note" xlink:label="note-124-03a" xlink:href="note-124-03"/> ſim, quorum unius duo latera ſint æqualia, alterius uero inæqualia; </s> <s xml:id="echoid-s4366" xml:space="preserve">maius <lb/>erit i<unsure/>llud, cuius duo latera æqualia ſunt.</s> <s xml:id="echoid-s4367" xml:space="preserve"/> </p> <div xml:id="echoid-div236" type="float" level="2" n="1"> <note position="left" xlink:label="note-124-03" xlink:href="note-124-03a" xml:space="preserve">Iſoſeeles <lb/>triangulũ <lb/>maius eſt <lb/>triãgulo ſi <lb/>bi Iſoperi-<lb/>metro non <lb/>@ſoſcele.</note> </div> <p> <s xml:id="echoid-s4368" xml:space="preserve"><emph style="sc">Estg</emph> triangulum A B C, cuius latus A B, maius ſit latere B C, conſti-<lb/>tuaturq́ue ſuper baſim A C, (per præcedentẽ <lb/> <anchor type="figure" xlink:label="fig-124-02a" xlink:href="fig-124-02"/> propoſi.) </s> <s xml:id="echoid-s4369" xml:space="preserve">triangulo A B C, triangulum Iſo-<lb/>perimetrum A D C, habens latera A D, D C, <lb/>æqualia & </s> <s xml:id="echoid-s4370" xml:space="preserve">inter ſe, & </s> <s xml:id="echoid-s4371" xml:space="preserve">lateribus A B, B C, ſi-<lb/>mul ſumptis. </s> <s xml:id="echoid-s4372" xml:space="preserve">Dico triangulum A D C, maius <lb/>eſſe triangulo A B C. </s> <s xml:id="echoid-s4373" xml:space="preserve">Producatur enim A D, <lb/>ad partes D, ſitq́ue D E, æqualis ipſi A D, ſiue <lb/> <anchor type="note" xlink:label="note-124-04a" xlink:href="note-124-04"/> ipſi D C. </s> <s xml:id="echoid-s4374" xml:space="preserve">Ducantur quoque rectæ D B, B E. <lb/></s> <s xml:id="echoid-s4375" xml:space="preserve">Quoniam igitur A B, B E, maiores ſunt, quã <lb/>A E, hoc eſt, quàm A D, D C, ſimul hoc eſt, <lb/>quàm A B, B C, ſimul; </s> <s xml:id="echoid-s4376" xml:space="preserve">ablata communi A B, <lb/>erit B E, maior quam BC. </s> <s xml:id="echoid-s4377" xml:space="preserve">Et quia latera E D, <lb/>D B, trianguli E D B, æqualia ſunt lateribus <lb/>C D, D B, trianguli C D B. </s> <s xml:id="echoid-s4378" xml:space="preserve">Cum ergo baſis <lb/>B E, baſe B C, maior ſit, erit angulus E D B, <lb/>maior angulo C D B. </s> <s xml:id="echoid-s4379" xml:space="preserve">Quare angulus E D B, <lb/> <anchor type="note" xlink:label="note-124-05a" xlink:href="note-124-05"/> maior eſt, quàm dimidium anguli E D C: </s> <s xml:id="echoid-s4380" xml:space="preserve">Eſt <pb o="89" file="125" n="126" rhead="Ioan. de Sacro Boſco."/> au em augulus D A C, dimidiũ anguli E D C; </s> <s xml:id="echoid-s4381" xml:space="preserve">propterea quòd anguli D A C, <lb/> <anchor type="note" xlink:label="note-125-01a" xlink:href="note-125-01"/> D C A, æquales ſunt, & </s> <s xml:id="echoid-s4382" xml:space="preserve">his ſimul ſumptis æqualis quoque externus angulus <lb/> <anchor type="note" xlink:label="note-125-02a" xlink:href="note-125-02"/> E D C. </s> <s xml:id="echoid-s4383" xml:space="preserve">Maior igitur erit angulus E D B, angulo D A C. </s> <s xml:id="echoid-s4384" xml:space="preserve">Fiat angulus E D F, <lb/>æqualis angulo interno D A C; </s> <s xml:id="echoid-s4385" xml:space="preserve">cadetq́ue D F, recta ſupra rectam D B, æqui-<lb/>diſ<unsure/>tabit q́ue rectæ A C. </s> <s xml:id="echoid-s4386" xml:space="preserve">Producatur D F, donec cum A B protracta conueniat <lb/> <anchor type="note" xlink:label="note-125-03a" xlink:href="note-125-03"/> in F, du caturq́; </s> <s xml:id="echoid-s4387" xml:space="preserve">recta F C. </s> <s xml:id="echoid-s4388" xml:space="preserve">Quoniam igitur triangula A D C, A F C, æqualia <lb/>ſunt@tr i angulum autem A F C, maius eſt triangulo A B C; </s> <s xml:id="echoid-s4389" xml:space="preserve">maius quoque erit <lb/> <anchor type="note" xlink:label="note-125-04a" xlink:href="note-125-04"/> trian gulum A D C, triangulo A B C. </s> <s xml:id="echoid-s4390" xml:space="preserve">Quam ob rem duorum triangulorũ Iſo-<lb/>perim etorum eandem habentium baſim, &</s> <s xml:id="echoid-s4391" xml:space="preserve">c. </s> <s xml:id="echoid-s4392" xml:space="preserve">quod demonſtrandum erat.</s> <s xml:id="echoid-s4393" xml:space="preserve"/> </p> <div xml:id="echoid-div237" type="float" level="2" n="2"> <figure xlink:label="fig-124-02" xlink:href="fig-124-02a"> <image file="124-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/124-02"/> </figure> <note position="left" xlink:label="note-124-04" xlink:href="note-124-04a" xml:space="preserve">20. primi.</note> <note position="left" xlink:label="note-124-05" xlink:href="note-124-05a" xml:space="preserve">25. primi.</note> <note position="right" xlink:label="note-125-01" xlink:href="note-125-01a" xml:space="preserve">5. primi.</note> <note position="right" xlink:label="note-125-02" xlink:href="note-125-02a" xml:space="preserve">32. primi.</note> <note position="right" xlink:label="note-125-03" xlink:href="note-125-03a" xml:space="preserve">28. primi.</note> <note position="right" xlink:label="note-125-04" xlink:href="note-125-04a" xml:space="preserve">37. primi.</note> </div> </div> <div xml:id="echoid-div239" type="section" level="1" n="82"> <head xml:id="echoid-head86" style="it" xml:space="preserve">THEOR. 8. PROPOS. 9.</head> <p style="it"> <s xml:id="echoid-s4394" xml:space="preserve">IN ſimilibus triangulis rectangulis quadratum à lateribus, quæ an-<lb/> <anchor type="note" xlink:label="note-125-05a" xlink:href="note-125-05"/> gulis rectis ſubtenduntur, tanquam ab una linea, deſcriptum æquale eſt <lb/>quadratis duobus ſimul, quæ à reliquis homologis lateribus, tanquam ex <lb/>duabus lineis, ita ut quælibet duo latera homologa conficiant unam lineam <lb/>rectam, deſcribitur.</s> <s xml:id="echoid-s4395" xml:space="preserve"/> </p> <div xml:id="echoid-div239" type="float" level="2" n="1"> <note position="right" xlink:label="note-125-05" xlink:href="note-125-05a" xml:space="preserve">Proprieta <lb/>duorũ trian <lb/>gulorum re <lb/>ct angulorũ <lb/>ſimilium.</note> </div> <p> <s xml:id="echoid-s4396" xml:space="preserve"><emph style="sc">Sint</emph> triangula rectangula ſimilia A B C, D E F, ita ut anguli B, & </s> <s xml:id="echoid-s4397" xml:space="preserve">E, <lb/>ſint recti, anguli uero C, & </s> <s xml:id="echoid-s4398" xml:space="preserve">F, inter ſe æquales: </s> <s xml:id="echoid-s4399" xml:space="preserve">itemq́ue anguli A, & </s> <s xml:id="echoid-s4400" xml:space="preserve">D, inter ſe <lb/>æqua les: </s> <s xml:id="echoid-s4401" xml:space="preserve">homologaq́ue latera A B, D E; </s> <s xml:id="echoid-s4402" xml:space="preserve">Item <lb/>B C, E F, & </s> <s xml:id="echoid-s4403" xml:space="preserve">A C, D F. </s> <s xml:id="echoid-s4404" xml:space="preserve">Dico quadratum ex A C, <lb/> <anchor type="figure" xlink:label="fig-125-01a" xlink:href="fig-125-01"/> D F, tan quam ex linea una, deſcriptum æqua-<lb/>le eſſe duobus quadratis, quorũ unum ex A B, <lb/>D E, tanquam ex una linea, alterum uero ex <lb/>BC, E F, tanquam ex vna quoque linea, deſcri-<lb/>bitur. </s> <s xml:id="echoid-s4405" xml:space="preserve">Producta namque D E, ad partes E, ſu-<lb/>matur E G, æqualis rectæ A B, & </s> <s xml:id="echoid-s4406" xml:space="preserve">ducatur G H, <lb/>recta æquidiſtans rectę E F, donec cum D F, <lb/>producta conueniat in puncto H; </s> <s xml:id="echoid-s4407" xml:space="preserve">Deinde per <lb/>F, ducatur recta F I, æquidiſtans rectæ E G. <lb/></s> <s xml:id="echoid-s4408" xml:space="preserve">Erit igitur triangulum F I H, æquiangulum <lb/>triangulo D E F, hoc eſt, triangulo ABC: </s> <s xml:id="echoid-s4409" xml:space="preserve">Nam <lb/>angulus F I H, æqualis eſt angulo G, & </s> <s xml:id="echoid-s4410" xml:space="preserve">hic æ-<lb/> <anchor type="note" xlink:label="note-125-06a" xlink:href="note-125-06"/> qualis angulo D E F, hoc eſt, angulo B: </s> <s xml:id="echoid-s4411" xml:space="preserve">an-<lb/> <anchor type="note" xlink:label="note-125-07a" xlink:href="note-125-07"/> gulus uero H, æqualis eſt angulo D E F, hoc <lb/> <anchor type="note" xlink:label="note-125-08a" xlink:href="note-125-08"/> eſt, angulo C; </s> <s xml:id="echoid-s4412" xml:space="preserve">ac proinde & </s> <s xml:id="echoid-s4413" xml:space="preserve">angulus I F H, an <lb/>gulo A; </s> <s xml:id="echoid-s4414" xml:space="preserve">Sunt autem & </s> <s xml:id="echoid-s4415" xml:space="preserve">latera A B, F I, æqualia; <lb/></s> <s xml:id="echoid-s4416" xml:space="preserve">Nã recta F I, eſt æqualis rectæ E G, hæc autẽ <lb/> <anchor type="note" xlink:label="note-125-09a" xlink:href="note-125-09"/> rectæ A B, ſumpta fuit æqualis. </s> <s xml:id="echoid-s4417" xml:space="preserve">Igitur & </s> <s xml:id="echoid-s4418" xml:space="preserve">altera <lb/>B C, I H, item A C, F H, æqualia inter ſe e-<lb/> <anchor type="note" xlink:label="note-125-10a" xlink:href="note-125-10"/> runt. </s> <s xml:id="echoid-s4419" xml:space="preserve">Quare recta D H, compoſita erit ex A C, <lb/>D F; </s> <s xml:id="echoid-s4420" xml:space="preserve">Recta uero D G, ex A B, D E; </s> <s xml:id="echoid-s4421" xml:space="preserve">Recta deniq; </s> <s xml:id="echoid-s4422" xml:space="preserve">G H, ex B C, E F; </s> <s xml:id="echoid-s4423" xml:space="preserve">quòd G I, re-<lb/>cta æqualis ſit rectæ EF. </s> <s xml:id="echoid-s4424" xml:space="preserve">Et quoniam quadratũ rectæ D H, æquale eſt quadratis <lb/> <anchor type="note" xlink:label="note-125-11a" xlink:href="note-125-11"/> rectarum D G, G H, ſimul, conſtat verum eſſe, quod proponitur. </s> <s xml:id="echoid-s4425" xml:space="preserve">In ſimilibus <lb/>igitur triangulis rectangulis quadratum à<unsure/> lateribus, quæ angulis rectis ſubten-<lb/> <anchor type="note" xlink:label="note-125-12a" xlink:href="note-125-12"/> duntur, &</s> <s xml:id="echoid-s4426" xml:space="preserve">c. </s> <s xml:id="echoid-s4427" xml:space="preserve">quod erat demonſtrandum.</s> <s xml:id="echoid-s4428" xml:space="preserve"/> </p> <div xml:id="echoid-div240" type="float" level="2" n="2"> <figure xlink:label="fig-125-01" xlink:href="fig-125-01a"> <image file="125-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/125-01"/> </figure> <note position="right" xlink:label="note-125-06" xlink:href="note-125-06a" xml:space="preserve">29. primi.</note> <note position="right" xlink:label="note-125-07" xlink:href="note-125-07a" xml:space="preserve">29. primi.</note> <note position="right" xlink:label="note-125-08" xlink:href="note-125-08a" xml:space="preserve">32. primi.</note> <note position="right" xlink:label="note-125-09" xlink:href="note-125-09a" xml:space="preserve">34. primi.</note> <note position="right" xlink:label="note-125-10" xlink:href="note-125-10a" xml:space="preserve">26. primi.</note> <note position="right" xlink:label="note-125-11" xlink:href="note-125-11a" xml:space="preserve">34. primi.</note> <note position="right" xlink:label="note-125-12" xlink:href="note-125-12a" xml:space="preserve">47. primi.</note> </div> <pb o="90" file="126" n="127" rhead="Comment. in I. Cap. Spharæ"/> </div> <div xml:id="echoid-div242" type="section" level="1" n="83"> <head xml:id="echoid-head87" style="it" xml:space="preserve">PROBL. 2. PROPOS. 10.</head> <note position="left" xml:space="preserve">Qua arte <lb/>conſtituan <lb/>tur duo <lb/>triangula <lb/>Iſoſcelia ſi <lb/>milia qui-<lb/>dem inter <lb/>ſe, Iſoperi-<lb/>metra ue-<lb/>@o alijs duo <lb/>bus Iſoſce-<lb/>libus.</note> <p style="it"> <s xml:id="echoid-s4429" xml:space="preserve"><emph style="sc">Datis</emph> duobus triangulis Iſoſcelibus, quorum baſes inæquales e-<lb/>xiſtant, duoque lateraunius æqualia ſint duobus lateribus alterius; </s> <s xml:id="echoid-s4430" xml:space="preserve">Super <lb/>eiſdem baſibus duo alia triangula iſoſcelia iuter ſe quidem ſimilia, priori-<lb/>bus uero Iſoperimetra, conſtituere.</s> <s xml:id="echoid-s4431" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4432" xml:space="preserve"><emph style="sc">Sint</emph> ſuper baſes inæquales AB, CD, duo triangula Iſoſcelia AEB, C F D, <lb/>ſintq́. </s> <s xml:id="echoid-s4433" xml:space="preserve">quatuor lineæ A E, E B, C F, F D, inter ſe æquales; </s> <s xml:id="echoid-s4434" xml:space="preserve">maior autem ſit baſis <lb/>A B, baſe C D. </s> <s xml:id="echoid-s4435" xml:space="preserve">quibus poſitis, erit angulus E, maior angulo F, ideoque trian-<lb/> <anchor type="note" xlink:label="note-126-02a" xlink:href="note-126-02"/> <anchor type="figure" xlink:label="fig-126-01a" xlink:href="fig-126-01"/> gula nõ ſi <lb/>milia, cũ <lb/>nec æqui <lb/>angula. </s> <s xml:id="echoid-s4436" xml:space="preserve">O <lb/>porteat iã <lb/>ſuꝑ baſes <lb/>eaſdẽ A B, <lb/>C D, cõſti <lb/>tuere alia <lb/>duo trian <lb/>gula iſo-<lb/>ſcelia iter <lb/>fe quidem ſimilia, iſoperimetra uero ſimul ſumpta prioribus triangulis ſimul <lb/>ſumptis. </s> <s xml:id="echoid-s4437" xml:space="preserve">Ponatur recta G H, æqualis quatuor rectis A E, E B, C F, F D, diuidua <lb/>turq́ue in puncto K, ut eſſet rectacompoſita ex A B, & </s> <s xml:id="echoid-s4438" xml:space="preserve">C D, diuiſa in puncto B, <lb/> <anchor type="note" xlink:label="note-126-03a" xlink:href="note-126-03"/> hoc eſt, ſit ea proportio G L, ad K H, quę eſt A B, ad C D. </s> <s xml:id="echoid-s4439" xml:space="preserve">Et quia maior eſt re-<lb/>cta A B, quàm recta C D, maior quoque erit recta G K, quàm recta K H, cum <lb/>vtrobique ſit proportio maioris inæqualitatis. </s> <s xml:id="echoid-s4440" xml:space="preserve">Diuidatur utraque G K, K H, <lb/>bifariam in punctis L, & </s> <s xml:id="echoid-s4441" xml:space="preserve">M. </s> <s xml:id="echoid-s4442" xml:space="preserve">Itaque cum ſit vt G K, ad K H, ita A B, ad C D, <lb/>erit componendo, vt G H, ad K H, ita A B, C D, ſimul ad C D: </s> <s xml:id="echoid-s4443" xml:space="preserve">Eſt autem <lb/>G H, maior, quàm A B, C D, ſimul, quòd & </s> <s xml:id="echoid-s4444" xml:space="preserve">quatuor rectæ A E, E B, C F. <lb/></s> <s xml:id="echoid-s4445" xml:space="preserve">F D, quæ æquales ſunt rectæ G H, maiores ſint, quàm A B, C D. </s> <s xml:id="echoid-s4446" xml:space="preserve">Igitur & </s> <s xml:id="echoid-s4447" xml:space="preserve">K H, <lb/> <anchor type="note" xlink:label="note-126-04a" xlink:href="note-126-04"/> maior erit quàm C D: </s> <s xml:id="echoid-s4448" xml:space="preserve">Eademque ratione maior erit G K, quàm A B. </s> <s xml:id="echoid-s4449" xml:space="preserve">Quo-<lb/> <anchor type="note" xlink:label="note-126-05a" xlink:href="note-126-05"/> niam igitur trium rectarum A B, G L, L K, duæ reliqua ſunt maiores omni-<lb/>fariam ſumptæ; </s> <s xml:id="echoid-s4450" xml:space="preserve">(Duæ enim G L, L K, maiores ſunt, quàm A B, quod tota <lb/>G K, maior ſit, quàm A B, ut modo fuit oſtenſum; </s> <s xml:id="echoid-s4451" xml:space="preserve">Manifeſtum autem, eſt, <lb/>A B, G L, maiores eſſe reliqua L K; </s> <s xml:id="echoid-s4452" xml:space="preserve">Itemq́ue A B, L K, reliqua G L, eſſe ma-<lb/>iores, propterea quòd G K, diuiſa eſt bifariam in puncto L. </s> <s xml:id="echoid-s4453" xml:space="preserve">Idem quoque di-<lb/>ces de tribus rectis C D, K M, M H.) </s> <s xml:id="echoid-s4454" xml:space="preserve">conſtituatur ex tribus rectis AB, GL, <lb/> <anchor type="note" xlink:label="note-126-06a" xlink:href="note-126-06"/> L K, triangulum A N B, quod erit Iſoſceles, cadetq́ue punctum N, extra trian-<lb/>gulum A E B, cum A E, E B, ſimul dimidium conſtituant rectæ G H; </s> <s xml:id="echoid-s4455" xml:space="preserve">at vero, <lb/>A N, N B, ſimul maius efficiant, quàm dimidium rectæ G H. </s> <s xml:id="echoid-s4456" xml:space="preserve">Rurſus ex tri-<lb/>bus rectis C D, K M, M H, conſtituatur quoque triangulum C O D, quod <lb/>Iſoſceles erit, cadetq́ue punctum O, intra triangulum C F D, eo quòd CF, <lb/>FD, ſimul æquales ſint dimidio rectæ G H; </s> <s xml:id="echoid-s4457" xml:space="preserve">at C O, O D, ſimul minores ſint <lb/>dimidio rectæ GH. </s> <s xml:id="echoid-s4458" xml:space="preserve">Et quoniam quatuor latera A E, E B, C F, F D, ſimul <lb/>Item A N, N B, C O, O D, ſimul ęqualia ſunt rectæ G H, erunt priora qua- <pb o="91" file="127" n="128" rhead="Ioan. de Sacro Boſco."/> tuor ſimul, poſterioribus quatuor ſimul æqualia: </s> <s xml:id="echoid-s4459" xml:space="preserve">additis ergo communibus <lb/>A B, C D, fient ſex alte@a A E, E B, B A, C F, F D, D C, ſimul æqualia ſex late-<lb/>ribus A N, N B B A, C O, O D, D C, ſimul; </s> <s xml:id="echoid-s4460" xml:space="preserve">ideoq́uetriangula A N B, C O D, <lb/>ſimul iſoperimetra erunt triangulis A E B, C F D, ſimul. </s> <s xml:id="echoid-s4461" xml:space="preserve">Dico iam, quod & </s> <s xml:id="echoid-s4462" xml:space="preserve">ſi-<lb/>milia inter ſe ſunt triangula A N B, C O D. </s> <s xml:id="echoid-s4463" xml:space="preserve">Nam quoniam eſt, ut A B, ad O D, <lb/>ita G K, ad K H, hoc eſt, ita G L, ad K M, hoc eſt, ita A N, ad C O, & </s> <s xml:id="echoid-s4464" xml:space="preserve">N B, ad <lb/> <anchor type="note" xlink:label="note-127-01a" xlink:href="note-127-01"/> ad O D, erit permutando, vt A B, ad A N, ita C D, ad C O; </s> <s xml:id="echoid-s4465" xml:space="preserve">& </s> <s xml:id="echoid-s4466" xml:space="preserve">vt A N, ad N B, <lb/>ita C O; </s> <s xml:id="echoid-s4467" xml:space="preserve">ad O D. </s> <s xml:id="echoid-s4468" xml:space="preserve">Proportionalia ergo ſunt latera triangulorum A N B, COD; <lb/></s> <s xml:id="echoid-s4469" xml:space="preserve">ac proinde æquiangula inter ſe erunt, & </s> <s xml:id="echoid-s4470" xml:space="preserve">idcireo ſimilia. </s> <s xml:id="echoid-s4471" xml:space="preserve">Quare datis duobus <lb/>triangulis Iſoſcelibus, quorum baſes inæquales exiſtant. </s> <s xml:id="echoid-s4472" xml:space="preserve">&</s> <s xml:id="echoid-s4473" xml:space="preserve">c. </s> <s xml:id="echoid-s4474" xml:space="preserve">conſtituim us. </s> <s xml:id="echoid-s4475" xml:space="preserve">quod <lb/> <anchor type="note" xlink:label="note-127-02a" xlink:href="note-127-02"/> faciendum erat.</s> <s xml:id="echoid-s4476" xml:space="preserve"/> </p> <div xml:id="echoid-div242" type="float" level="2" n="1"> <note position="left" xlink:label="note-126-02" xlink:href="note-126-02a" xml:space="preserve">25. primi.</note> <figure xlink:label="fig-126-01" xlink:href="fig-126-01a"> <image file="126-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/126-01"/> </figure> <note position="left" xlink:label="note-126-03" xlink:href="note-126-03a" xml:space="preserve">10. ſexti.</note> <note position="left" xlink:label="note-126-04" xlink:href="note-126-04a" xml:space="preserve">29. primi.</note> <note position="left" xlink:label="note-126-05" xlink:href="note-126-05a" xml:space="preserve">14. quinti.</note> <note position="left" xlink:label="note-126-06" xlink:href="note-126-06a" xml:space="preserve">22. primi.</note> <note position="right" xlink:label="note-127-01" xlink:href="note-127-01a" xml:space="preserve">15. quinti</note> <note position="right" xlink:label="note-127-02" xlink:href="note-127-02a" xml:space="preserve">5. ſexti.</note> </div> </div> <div xml:id="echoid-div244" type="section" level="1" n="84"> <head xml:id="echoid-head88" style="it" xml:space="preserve">THEOR. 9. PROPOS. 11.</head> <p style="it"> <s xml:id="echoid-s4477" xml:space="preserve"><emph style="sc">Dvo</emph> triangula Iſoſcelia ſimilia ſuper inæqualibus baſibus conſtitu-<lb/> <anchor type="note" xlink:label="note-127-03a" xlink:href="note-127-03"/> ta, utraque ſimul maiora ſunt duobus triangulis Iſoſcelibus, utriuſque ſi-<lb/>mul, quę habeant eaſdem baſes cum prioribus, ſintq; </s> <s xml:id="echoid-s4478" xml:space="preserve">disſimila quidem <lb/>inter ſe. </s> <s xml:id="echoid-s4479" xml:space="preserve">at iſoperimetra prioribus duobus, nec non quatuor latera inter ſe <lb/>habeant æqualia.</s> <s xml:id="echoid-s4480" xml:space="preserve"/> </p> <div xml:id="echoid-div244" type="float" level="2" n="1"> <note position="right" xlink:label="note-127-03" xlink:href="note-127-03a" xml:space="preserve">Triangulæ<unsure/> <lb/>duo Iſoſce-<lb/>lia ſimilia <lb/>maiora sũt <lb/>duobus Iſo<unsure/> <lb/>ſcelibus nõ <lb/>ſimilibus, <lb/>quæ illis <lb/>ſint Iſope-<lb/>rimetta, ba-<lb/>ſesque ha-<lb/>beant eaſ-<lb/>dem.</note> </div> <p> <s xml:id="echoid-s4481" xml:space="preserve"><emph style="sc">Svper</emph> baſibus inæqualibus A C, C E, ſint duo triangula Iſoſcelia in-<lb/>ter ſe non ſimilia A B C, C D E, ita vt quatuor latera A B, B C, C D, D E, <lb/>inter ſe ſint æqualia. </s> <s xml:id="echoid-s4482" xml:space="preserve">At-<lb/> <anchor type="figure" xlink:label="fig-127-01a" xlink:href="fig-127-01"/> que ſuper eiſdem baſibus <lb/>A C, C E, (per præceden-<lb/>tem propoſ.) </s> <s xml:id="echoid-s4483" xml:space="preserve">conſtituan-<lb/>tur alia duo triãgula Iſo-<lb/>ſcelia A F C, C G E; </s> <s xml:id="echoid-s4484" xml:space="preserve">ſimi-<lb/>lia inter ſe, & </s> <s xml:id="echoid-s4485" xml:space="preserve">iſoperime-<lb/>tra ſimul prioribus trian-<lb/>gulis ſimul. </s> <s xml:id="echoid-s4486" xml:space="preserve">Dico duo triã <lb/>gula A F C, C G E, ſimul <lb/>maiora eſſe duobus trian <lb/>gulis A B C, C D E, ſi-<lb/>mul. </s> <s xml:id="echoid-s4487" xml:space="preserve">Ponantur enim A C, <lb/>C E, ſecundum lineam re <lb/>ctam vnam; </s> <s xml:id="echoid-s4488" xml:space="preserve">ſitq́; </s> <s xml:id="echoid-s4489" xml:space="preserve">A C, ba-<lb/>ſis maior baſe C E. </s> <s xml:id="echoid-s4490" xml:space="preserve">Dein-<lb/>de ex F, per B, ducatur <lb/>recta F B K, ſecans rectam <lb/>A C, in puncto K; </s> <s xml:id="echoid-s4491" xml:space="preserve">Item ex <lb/>D, per G, punctum duca <lb/>tur recta D C H, ſecans rectam C E, in H. </s> <s xml:id="echoid-s4492" xml:space="preserve">Et quia latera A F, F B, triangu-<lb/>li A F B, æqualia ſunt lateribus C F, F B, trianguli C F B, & </s> <s xml:id="echoid-s4493" xml:space="preserve">baſis A B, baſi <lb/>B C, æqualis, erit angulus A F B, angulo C F B, æqualis. </s> <s xml:id="echoid-s4494" xml:space="preserve">ſurſus quia late-<lb/>@a A F, F K, trianguli A F K, æqualia ſunt lateribus C F, F K, trianguli, <lb/> <anchor type="note" xlink:label="note-127-04a" xlink:href="note-127-04"/> <pb o="92" file="128" n="129" rhead="Comment. in I. Cap. Sphæræ"/> C F K, & </s> <s xml:id="echoid-s4495" xml:space="preserve">angulus A F K, angulo C F K, æqualis, vt probatum eſt, erunt ba-<lb/>ſes A K, K C, æquales, & </s> <s xml:id="echoid-s4496" xml:space="preserve">anguli ad K, æquales quoque, hoc eſt, recti. </s> <s xml:id="echoid-s4497" xml:space="preserve">Eadem <lb/> <anchor type="note" xlink:label="note-128-01a" xlink:href="note-128-01"/> ratiocinatione concludemus rectam C E, in puncto H, diuidi bifariam; </s> <s xml:id="echoid-s4498" xml:space="preserve">angu-<lb/>losq́ue ad H, eſſe rectos. </s> <s xml:id="echoid-s4499" xml:space="preserve">Producatur recta D H, ad partes H, ſumaturq́; </s> <s xml:id="echoid-s4500" xml:space="preserve">H L, <lb/>æqualis rectæ D H, & </s> <s xml:id="echoid-s4501" xml:space="preserve">extendatur à puncto L, per punctum C, recta L C N. <lb/></s> <s xml:id="echoid-s4502" xml:space="preserve">Quoniam uero latera D H, H C, trianguli D C H, æqualia ſunt lateribus <lb/>L H, H C, trianguli L C H, anguli ad H, æquales, vtpote recti, erunt baſes <lb/> <anchor type="note" xlink:label="note-128-02a" xlink:href="note-128-02"/> D C, L C, æquales, & </s> <s xml:id="echoid-s4503" xml:space="preserve">anguli D C H, L C H, æquales etiam: </s> <s xml:id="echoid-s4504" xml:space="preserve">At qui angulus <lb/>D C H, maior eſt angulo G C H, & </s> <s xml:id="echoid-s4505" xml:space="preserve">angulus G C H, æqualis eſt angulo F A K, <lb/>propter ſimilitudinem triangulorum G C E, & </s> <s xml:id="echoid-s4506" xml:space="preserve">F A C, hoc eſt, angulo F C A, <lb/>qui angulo F A C, æqualis eſt, Erit igitur angulus D C H, hoc eſt, angulus <lb/>L C H, qui illi oſtenſus eſt æqualis, hoc eſt angulus N C K, qui angulo L C H, <lb/> <anchor type="note" xlink:label="note-128-03a" xlink:href="note-128-03"/> ad uerticem eſt æqualis, maior etiam angulo F C A; </s> <s xml:id="echoid-s4507" xml:space="preserve">& </s> <s xml:id="echoid-s4508" xml:space="preserve">ob id C N, recta extra <lb/>rectam CF, cadet neceſſario; </s> <s xml:id="echoid-s4509" xml:space="preserve">& </s> <s xml:id="echoid-s4510" xml:space="preserve">rectæ L C, C B, propterea comprehendent ad <lb/> <anchor type="note" xlink:label="note-128-04a" xlink:href="note-128-04"/> partes K, angulum BCL. </s> <s xml:id="echoid-s4511" xml:space="preserve">Quare ſi ducatur recta B L, ſecabit ea lineam C K, <lb/>in aliquo puncto inter puncta C, & </s> <s xml:id="echoid-s4512" xml:space="preserve">K, quod ſit M. </s> <s xml:id="echoid-s4513" xml:space="preserve">Quoniam uero rectæ A B, <lb/>B C, C D, D E, ſimul æquales ſunt rectis A F, F C, C G, G E, ſimul, propter <lb/>triangula iſoperimetra, erunt quoque dimidia earum æqualia inter ſe, ni-<lb/>mirum rectæ B C, C D, hoc eſt, B C, C L, ſimul æquales ipſis F C, C G, ſi-<lb/>mul: </s> <s xml:id="echoid-s4514" xml:space="preserve">Sunt autem rectæ B C, C L, ſimul maiores recta B L. </s> <s xml:id="echoid-s4515" xml:space="preserve">Igitur & </s> <s xml:id="echoid-s4516" xml:space="preserve">F C, C G, <lb/> <anchor type="note" xlink:label="note-128-05a" xlink:href="note-128-05"/> ſimul maiores erunt eadem recta B L: </s> <s xml:id="echoid-s4517" xml:space="preserve">ideoq́ue quadratum ex F C, C G, tan-<lb/> <anchor type="figure" xlink:label="fig-128-01a" xlink:href="fig-128-01"/> quam ex una linea, de <lb/>ſcriptum maius erit <lb/>quadrato BL. </s> <s xml:id="echoid-s4518" xml:space="preserve">Quod <lb/>autem ex F C, C G, <lb/>tanquam ex una linea, <lb/>deſcribitur quadratum, <lb/>æquale eſt (per pro-<lb/>poſ. </s> <s xml:id="echoid-s4519" xml:space="preserve">9. </s> <s xml:id="echoid-s4520" xml:space="preserve">huius) quadrato <lb/>ex F K, G H, tan quam <lb/>ex una linea deſcripto, <lb/>vnà cum quadrato, <lb/>quod ex K C, C H, <lb/>tanquam ex una linea, <lb/>deſcribitur: </s> <s xml:id="echoid-s4521" xml:space="preserve">Quadratum <lb/>uero ex L B, deſcriptum <lb/>æquale eſt (per eandem <lb/>9. </s> <s xml:id="echoid-s4522" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s4523" xml:space="preserve">huius) qna-<lb/>drato ex B K, L H, <lb/>hoc eſt, ex B K, D H, <lb/>tanquam ex una linea, <lb/>deſcripto, unà cum qua-<lb/>drato, quod ex K M, M H, tanquam ex una linea, deſcribitur; </s> <s xml:id="echoid-s4524" xml:space="preserve">eò quòd trian-<lb/>gula rectangula B K M, L H M, ſint ſimilia inter ſe. </s> <s xml:id="echoid-s4525" xml:space="preserve">Sunt enim anguli M, ad <lb/> <anchor type="note" xlink:label="note-128-06a" xlink:href="note-128-06"/> uerticem æquales, & </s> <s xml:id="echoid-s4526" xml:space="preserve">anguli K, H, recti, ideoq́ue & </s> <s xml:id="echoid-s4527" xml:space="preserve">reliqui K B N, H L M, æ-<lb/> <anchor type="note" xlink:label="note-128-07a" xlink:href="note-128-07"/> quales. </s> <s xml:id="echoid-s4528" xml:space="preserve">Igitur quadratum ex F K, G H, tanquam ex una linea, deſcriptum, & </s> <s xml:id="echoid-s4529" xml:space="preserve"><lb/>quadratum ex K C, C H, tanquam ex una linea, deſcriptum, hoc eſt, quadra-<lb/>tum K H, utraque ſimul, maiora ſunt quadrato ex B K, D H, tanquam ex <pb o="93" file="129" n="130" rhead="Ioan. de Sacro Boſco."/> vna linea, deſcripto. </s> <s xml:id="echoid-s4530" xml:space="preserve">& </s> <s xml:id="echoid-s4531" xml:space="preserve">quadrato ex K M, M H, tanquam ex una linea deſcri-<lb/>pto, hoc eſt, quadrato K H, vtriuſque ſimul. </s> <s xml:id="echoid-s4532" xml:space="preserve">Ablato ergo communi quadrato <lb/>K H, erit quadratum ex F K, G H, tanquam ex una linea, deſcriptum maius <lb/>quadrato ex B K, D H, tanquam ex una linea, deſcripto; </s> <s xml:id="echoid-s4533" xml:space="preserve">ideòque maiores e-<lb/>runt rectæ linea F K, G H, ſimul rectis B K, D H, ſimnl: </s> <s xml:id="echoid-s4534" xml:space="preserve">Ac propterea, demptis <lb/>communibus B K, G H, erit F B, reliqua maior quàm reliqua D G. </s> <s xml:id="echoid-s4535" xml:space="preserve">Eſt autem <lb/>& </s> <s xml:id="echoid-s4536" xml:space="preserve">K C, maior quàm H C, eò quòd tota A C, cuius dimidium eſt K C, maior <lb/>ponitur, quam tota C E, <lb/> <anchor type="figure" xlink:label="fig-129-01a" xlink:href="fig-129-01"/> cuius dimidium eſt H C. <lb/></s> <s xml:id="echoid-s4537" xml:space="preserve">Qua propter rectangulũ <lb/>ſub F B, K C, contentum, <lb/>maius erit rectangulo <lb/>ſub D G, H C, contẽto. </s> <s xml:id="echoid-s4538" xml:space="preserve"><lb/>Et quoniam triangulum <lb/>F B C, dimidium eſt re, <lb/>ctanguli ſub F B, K C, con <lb/>tenti; </s> <s xml:id="echoid-s4539" xml:space="preserve">(Nam ſi ſuper F B, <lb/>conſtituatur rectangu--<lb/>lum altitudinem habens <lb/>K C, ita ut triangulum, <lb/>& </s> <s xml:id="echoid-s4540" xml:space="preserve">rectangulum inter eaſ-<lb/>dem ſint parallelas; </s> <s xml:id="echoid-s4541" xml:space="preserve">erit <lb/> <anchor type="note" xlink:label="note-129-01a" xlink:href="note-129-01"/> triangulum parallelo--<lb/>grammi dimidium. </s> <s xml:id="echoid-s4542" xml:space="preserve">quod <lb/>quidem parallelogram-<lb/>mum idem eſt, quod re-<lb/>ctangulum ſub F B, K C, <lb/>contentum, ut conſtat. <lb/></s> <s xml:id="echoid-s4543" xml:space="preserve">Triangulum uero D G C, dimidium eſt rectanguli contenti ſub, D G, H C; </s> <s xml:id="echoid-s4544" xml:space="preserve">(ſi <lb/>enim ſuper D G, conſtituatur rectangulum altitudinem habens H C, ita vt <lb/>triangulum, & </s> <s xml:id="echoid-s4545" xml:space="preserve">rectangulum inter eaſdem ſint parallelas; </s> <s xml:id="echoid-s4546" xml:space="preserve">erit triangulum pa-<lb/>rallelogrammi dimidium. </s> <s xml:id="echoid-s4547" xml:space="preserve">quod quidem parallelogrammum idem eſt, quod <lb/> <anchor type="note" xlink:label="note-129-02a" xlink:href="note-129-02"/> rectangulum ſub D H, H C, contentum, ut conſtat. </s> <s xml:id="echoid-s4548" xml:space="preserve">(erit quoque triangulum <lb/>FBC, maius triangulo D G C, ac propterea duplum trianguli F B C, nimirũ <lb/>rectilineum A F C B A, maius erit duplo trianguli D G C, ut pote rectilineo <lb/>erunt triangula A F C, C G E, utraque ſimul maiora triangulis A B C, C D E, <lb/>utriuſque ſimul. </s> <s xml:id="echoid-s4549" xml:space="preserve">Duo ergo triangula Iſoſcelia ſimilia ſuper inæqualibus baſi-<lb/>bus conſtituta, &</s> <s xml:id="echoid-s4550" xml:space="preserve">c. </s> <s xml:id="echoid-s4551" xml:space="preserve">quod oſtendendum erat.</s> <s xml:id="echoid-s4552" xml:space="preserve"/> </p> <div xml:id="echoid-div245" type="float" level="2" n="2"> <figure xlink:label="fig-127-01" xlink:href="fig-127-01a"> <image file="127-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/127-01"/> </figure> <note position="right" xlink:label="note-127-04" xlink:href="note-127-04a" xml:space="preserve">8. primi.</note> <note position="left" xlink:label="note-128-01" xlink:href="note-128-01a" xml:space="preserve">4. primi.</note> <note position="left" xlink:label="note-128-02" xlink:href="note-128-02a" xml:space="preserve">4. primi.</note> <note position="left" xlink:label="note-128-03" xlink:href="note-128-03a" xml:space="preserve">5. primi.</note> <note position="left" xlink:label="note-128-04" xlink:href="note-128-04a" xml:space="preserve">15. primi.</note> <note position="left" xlink:label="note-128-05" xlink:href="note-128-05a" xml:space="preserve">20. primi.</note> <figure xlink:label="fig-128-01" xlink:href="fig-128-01a"> <image file="128-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/128-01"/> </figure> <note position="left" xlink:label="note-128-06" xlink:href="note-128-06a" xml:space="preserve">15. primi.</note> <note position="left" xlink:label="note-128-07" xlink:href="note-128-07a" xml:space="preserve">32. primi.</note> <figure xlink:label="fig-129-01" xlink:href="fig-129-01a"> <image file="129-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/129-01"/> </figure> <note position="right" xlink:label="note-129-01" xlink:href="note-129-01a" xml:space="preserve">41. primi.</note> <note position="right" xlink:label="note-129-02" xlink:href="note-129-02a" xml:space="preserve">41. primi.</note> </div> </div> <div xml:id="echoid-div247" type="section" level="1" n="85"> <head xml:id="echoid-head89" style="it" xml:space="preserve">THEOR. 10. PROPOS. 52</head> <note position="right" xml:space="preserve">Inter Iſope-<lb/>rimetras fi-<lb/>guras ęqua-<lb/>lia numero <lb/>habentes la <lb/>tera maxi-<lb/>ma & æqui <lb/>latera eſt, <lb/>& æquian-<lb/>gula.</note> <p style="it"> <s xml:id="echoid-s4553" xml:space="preserve">ISOPERIMETR ARVM figur arum latera numero ęqualia ha-<lb/>bentium maxima & </s> <s xml:id="echoid-s4554" xml:space="preserve">æqualiter eſt, & </s> <s xml:id="echoid-s4555" xml:space="preserve">æquiangula.</s> <s xml:id="echoid-s4556" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4557" xml:space="preserve"><emph style="sc">Esto</emph> figura quotcunq; </s> <s xml:id="echoid-s4558" xml:space="preserve">laterum ABCDEF, maxima inter omnes totidem <lb/>laterum ſibi iſoperimetras; </s> <s xml:id="echoid-s4559" xml:space="preserve">ita ut maior dari non poſſit. </s> <s xml:id="echoid-s4560" xml:space="preserve">Dico eam eſſe æquila-<lb/>terã, & </s> <s xml:id="echoid-s4561" xml:space="preserve">æquiãgulã. </s> <s xml:id="echoid-s4562" xml:space="preserve">Sit enim, ſi fieri poteſt, primũ nõ æquilatera, ſed ſint latera <pb o="94" file="130" n="131" rhead="Comment. in I. Cap. Sphæræ"/> A B, B C, proxima inæqualia. </s> <s xml:id="echoid-s4563" xml:space="preserve">Ducta igitur recta A C, ſi conſtituatur ſuper <lb/>A C, (per 7. </s> <s xml:id="echoid-s4564" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s4565" xml:space="preserve">huius) triangulum Iſoſceles A G C, quod ſit iſoperime-<lb/> <anchor type="figure" xlink:label="fig-130-01a" xlink:href="fig-130-01"/> trum triangulo A B C, erit to-<lb/>ta figura A G C D E F, iſoperime <lb/>tra figuræ A B C D E F. </s> <s xml:id="echoid-s4566" xml:space="preserve">Ft quia <lb/>triangulum A G C, maius eſt <lb/>(per 8. </s> <s xml:id="echoid-s4567" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s4568" xml:space="preserve">huius) triangulo <lb/>A B C; </s> <s xml:id="echoid-s4569" xml:space="preserve">ſi addatur commune po-<lb/>lygonum A C D E F, erit figu-<lb/>ra A G C D E F, maior quàm <lb/>figura A B C D E F, quod eſt <lb/>contrarium hypotheſi. </s> <s xml:id="echoid-s4570" xml:space="preserve">Non er-<lb/>go inæqualia ſunt latera A B, <lb/>B C, ſed æqualia. </s> <s xml:id="echoid-s4571" xml:space="preserve">Eademq́ue ra-<lb/>tione oſtendemus, latera proxi-<lb/>ma B C, C D; </s> <s xml:id="echoid-s4572" xml:space="preserve">Itẽ proxima C D, <lb/>D E; </s> <s xml:id="echoid-s4573" xml:space="preserve">nec non & </s> <s xml:id="echoid-s4574" xml:space="preserve">reliqua proxi-<lb/>ma deinceps æqualia eſſe. </s> <s xml:id="echoid-s4575" xml:space="preserve">Ma-<lb/>xima igitur figura inter ſibi iſo-<lb/>perimetras æqualia numero lar<unsure/>e-<lb/>ra habentes æquilatera eſt, quod <lb/>eſt primum.</s> <s xml:id="echoid-s4576" xml:space="preserve"/> </p> <div xml:id="echoid-div247" type="float" level="2" n="1"> <figure xlink:label="fig-130-01" xlink:href="fig-130-01a"> <image file="130-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/130-01"/> </figure> </div> <p> <s xml:id="echoid-s4577" xml:space="preserve"><emph style="sc">Sit</emph> deinde, ſi fieri poteſt, figu <lb/>ra A B C D E F, æquilatera qui <lb/>dem, nt iam demonſtratum eſt, <lb/>at non æquiangula, ſed anguli <lb/>B, D, non proximi inæquales <lb/>ſint, maiorq́ue angulus B, quàm <lb/>angulus D. </s> <s xml:id="echoid-s4578" xml:space="preserve">Quoniã igitur demon <lb/>ſtratum eſt, figuram maximam eſ-<lb/>ſe æquilateram, erunt duo trian-<lb/>gula A B C, C D E, Iſoſcelia, ita ut duo latera A B, B C, æqualia ſint duo-<lb/>bus lateribus C D, D E; </s> <s xml:id="echoid-s4579" xml:space="preserve">Ponitur autem angulus B, maior angulo D, erit re-<lb/>cta A C, maior, quàm recta C E. </s> <s xml:id="echoid-s4580" xml:space="preserve">Si igitur conſtituantur ſuper baſes A C, C E, <lb/> <anchor type="note" xlink:label="note-130-01a" xlink:href="note-130-01"/> (per 10. </s> <s xml:id="echoid-s4581" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s4582" xml:space="preserve">huius) alia duo triangula Iſoſcelia A G C, C H E, ſimilia in <lb/>ter ſe, & </s> <s xml:id="echoid-s4583" xml:space="preserve">Iſoperimetra triangulis A B C, C D E, erunt triangula A G C, C H E, <lb/>utraq. </s> <s xml:id="echoid-s4584" xml:space="preserve">ſimnl (per præcedentẽ propoſ.) </s> <s xml:id="echoid-s4585" xml:space="preserve">maiora triangulis A B C, C D E, utriſq. </s> <s xml:id="echoid-s4586" xml:space="preserve">ſi <lb/>mul. </s> <s xml:id="echoid-s4587" xml:space="preserve">Si igitur addatur cõmune polygonũ A C EF, erit figura AGCHEF, maior <lb/>quàm figura ABCDEF, qđ cũ hypotheſi pugnat, quòd hæc omniũ maxima po-<lb/>natur. </s> <s xml:id="echoid-s4588" xml:space="preserve">Nõ ergo inæquales ſunt anguli B, D, ſed æquales. </s> <s xml:id="echoid-s4589" xml:space="preserve">Eadẽq́; </s> <s xml:id="echoid-s4590" xml:space="preserve">ratione oſten-<lb/>demus, angulos non proximos C, E, ęquales eſſe, & </s> <s xml:id="echoid-s4591" xml:space="preserve">binos alios quoſuis non <lb/>proximos. </s> <s xml:id="echoid-s4592" xml:space="preserve">Ex quo eſficitur, totam figutam æquiangulam eſſe, nempe proximos <lb/>etiam augulos inter ſe eſſe æquales. </s> <s xml:id="echoid-s4593" xml:space="preserve">Si enim v.</s> <s xml:id="echoid-s4594" xml:space="preserve">g. </s> <s xml:id="echoid-s4595" xml:space="preserve">angulus B, non dicatur æqua-<lb/>lis angulo C; </s> <s xml:id="echoid-s4596" xml:space="preserve">cum angulus C, æqualis ſit non proximo angulo E; </s> <s xml:id="echoid-s4597" xml:space="preserve">erit quo-<lb/>que angulus B, angulo E, non æqualis, quod abſurdum eſt. </s> <s xml:id="echoid-s4598" xml:space="preserve">Bini enim anguli <lb/>non proximi inte ſe æquales ſunt, ut oſtendimus. </s> <s xml:id="echoid-s4599" xml:space="preserve">Maxima ergo figura inter ſi <lb/>bi Iſoperimetras ęqualia numero latera habentes non ſolum æquilatera, <lb/>ſed & </s> <s xml:id="echoid-s4600" xml:space="preserve">æquiangula eſt. </s> <s xml:id="echoid-s4601" xml:space="preserve">Quocirca Iſoperimetrarum figurarum latera nume- <pb o="95" file="131" n="132" rhead="Ioan. de Sacro Boſco."/> @o æqualia habentium maxima & </s> <s xml:id="echoid-s4602" xml:space="preserve">æquilatera eſt, & </s> <s xml:id="echoid-s4603" xml:space="preserve">æquiangula. </s> <s xml:id="echoid-s4604" xml:space="preserve">quod demon-<lb/>ſtrandum erat.</s> <s xml:id="echoid-s4605" xml:space="preserve"/> </p> <div xml:id="echoid-div248" type="float" level="2" n="2"> <note position="left" xlink:label="note-130-01" xlink:href="note-130-01a" xml:space="preserve">24. primi.</note> </div> </div> <div xml:id="echoid-div250" type="section" level="1" n="86"> <head xml:id="echoid-head90" xml:space="preserve">SCHOLIVM.</head> <p style="it"> <s xml:id="echoid-s4606" xml:space="preserve"><emph style="sc">Circa</emph> demonſtrationem prioris partis huius propoſ. </s> <s xml:id="echoid-s4607" xml:space="preserve">obſeruandum efl, acci-<lb/> <anchor type="note" xlink:label="note-131-01a" xlink:href="note-131-01"/> pienda eſſe duo latrea inęqualia proxima inter ſe, ita vt angulum conſtituant, nul-<lb/>lumq́ue aliud inter ea interponatur, qualia ſunt latera accepta A B, B C, angulum <lb/>B, efficientia. </s> <s xml:id="echoid-s4608" xml:space="preserve">Hac enim ratione, ducta recta A C, factum erit triangulum A B C, <lb/>cuius duo latera A B, B C, inæquælia ſunt, vt in demonſtratione aſſumebatur. </s> <s xml:id="echoid-s4609" xml:space="preserve">Ne <lb/>que vero dubitare quis poterit, in figuranon æquilatera, qualis ponitur A B C <lb/>D E F, accipi poſſe duo latera proxima inæqualia. </s> <s xml:id="echoid-s4610" xml:space="preserve">Nam ſi quis dicat latera A <emph style="sc">B</emph>, <lb/>B C, eſſe æqualia, ſumemus latera A B, A F, quæ ſi dicantur etiam æqualia eſſe, <lb/>accipiemus A F, F E: </s> <s xml:id="echoid-s4611" xml:space="preserve">Et ſi hęc adhuc æqualia eſſe dicantur, capiemus E F, E D: </s> <s xml:id="echoid-s4612" xml:space="preserve">& </s> <s xml:id="echoid-s4613" xml:space="preserve">ſic de-<lb/>inceps progrediemur, donec ad duo latera proxima inæqualia ueniamus, quæ angulum <lb/>Conſtituant. </s> <s xml:id="echoid-s4614" xml:space="preserve">Neceſſarium autem ad duo huiuſmodi latera perueniemus: </s> <s xml:id="echoid-s4615" xml:space="preserve">aliàs figura eſ-<lb/>ſet æquilatera, quod non conceditur.</s> <s xml:id="echoid-s4616" xml:space="preserve"/> </p> <div xml:id="echoid-div250" type="float" level="2" n="1"> <note position="right" xlink:label="note-131-01" xlink:href="note-131-01a" xml:space="preserve">Quæ obſer-<lb/>uanda ſint <lb/>in demon-<lb/>ſtratiõe hu-<lb/>ius propoſ.</note> </div> <p style="it"> <s xml:id="echoid-s4617" xml:space="preserve"><emph style="sc">Qvod</emph> vero ad poſterioris partis demonſtrationem attinet, aduertendum eſt, <lb/>in figuris multilateris accipiendos eſſe duos angulos inæquales non proximos inter ſe <lb/>ita vt inter ipſos vnus vel plures anguli interponantur, quales ſunt anguli accepti <lb/>B, D, inter quos ponitur angulus C. </s> <s xml:id="echoid-s4618" xml:space="preserve">Hac enim ratione duæ rectæ A C, C E, dictos <lb/>augulos ſubtendentes ſe mutuo non interſecabunt, conſtituenturq́ue duæ figuræ A C-<lb/>C D E F, A G C H E F, ex additione communis figuræ A C E E, ad triangula ſu-<lb/>pra baſes AC, C E, conſiructa: </s> <s xml:id="echoid-s4619" xml:space="preserve">quod non contingeret, ſi duo anguli inæquales pro-<lb/>ximi inter ſe ſumerentur, vt conſtat. </s> <s xml:id="echoid-s4620" xml:space="preserve">Non eſt autem in dubinm vertendum, an ta-<lb/>les duo anguli poſſint accipi. </s> <s xml:id="echoid-s4621" xml:space="preserve">In omni enim figura multilatera non æquiangula ne-<lb/>ceſſario erunt aliqui duo anguli non proximi inter ſe inæquales. </s> <s xml:id="echoid-s4622" xml:space="preserve">Nam in propoſitæ<unsure/> <lb/>figura A B k D E F, comparabimus angulum B, cum omnibus non proximis angulis <lb/>D, E, F, qui neceſſario duo erunt in pentagono, in hexagono uero tres, & </s> <s xml:id="echoid-s4623" xml:space="preserve">ita dein-<lb/>ceps. </s> <s xml:id="echoid-s4624" xml:space="preserve">Quod ſi uni alicui eorum fuerit inæqualis, habebimus iam duos angulos non <lb/>proximos inter ſe inæquales, nempe angulum B, & </s> <s xml:id="echoid-s4625" xml:space="preserve">illum, cui inæqualis eſt: </s> <s xml:id="echoid-s4626" xml:space="preserve">Si vero <lb/>omnibus dicatur æqualis, erit tunc angulus B, ſaltem alteri proximorum inæqualis, <lb/>aliàs figura eßet æquiangula. </s> <s xml:id="echoid-s4627" xml:space="preserve">Si ergo inæqualis fuerit angulo A, erit angulus A, <lb/>tam angulo E, quàm angulo D, non proximo inæqualis, cum utriuis horum æqualis <lb/>ponatur angulus B: </s> <s xml:id="echoid-s4628" xml:space="preserve">Si uero inæqualis fuerit angulo C, erit angulus K, tam angule<unsure/> <lb/>E, quàm angulo F, non proximo inæqualis, quòd vtrius horum angulus B, ponatur <lb/>æqualis.</s> <s xml:id="echoid-s4629" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s4630" xml:space="preserve"><emph style="sc">Sed</emph> quoniam propoſitio hæc demonſtrata tantum eſt in figuris multilateris, vt <lb/>ex ijsconſiat, quæ proxi-<lb/> <anchor type="figure" xlink:label="fig-131-01a" xlink:href="fig-131-01"/> me de duobus angulis non <lb/>proximis inæqualibus di-<lb/>ximus: </s> <s xml:id="echoid-s4631" xml:space="preserve">In triangulis enim, <lb/>& </s> <s xml:id="echoid-s4632" xml:space="preserve">quadrilateris figuris <lb/>æquilateris anguli eiuſmo-<lb/>di reperiri non poſſunt, <lb/>cum in triangulis æquila-<lb/>teris omnes anguli ſint æ-<lb/>quales, vt ex coroll. </s> <s xml:id="echoid-s4633" xml:space="preserve">ꝓpoſ.</s> <s xml:id="echoid-s4634" xml:space="preserve"> <pb o="96" file="132" n="133" rhead="Comment. in I. Cap. Sphæræ"/> 5. </s> <s xml:id="echoid-s4635" xml:space="preserve">lib. </s> <s xml:id="echoid-s4636" xml:space="preserve">1. </s> <s xml:id="echoid-s4637" xml:space="preserve">Eucl. </s> <s xml:id="echoid-s4638" xml:space="preserve">patet: </s> <s xml:id="echoid-s4639" xml:space="preserve">in quadrilateris autem figuris omnia latcra habentibus æqualiæ <lb/>(quoniam neceſſario ſunt parallelogramma, vt in ſcholio propoſ. </s> <s xml:id="echoid-s4640" xml:space="preserve">34. </s> <s xml:id="echoid-s4641" xml:space="preserve">lib. </s> <s xml:id="echoid-s4642" xml:space="preserve">1. </s> <s xml:id="echoid-s4643" xml:space="preserve">Eucl. </s> <s xml:id="echoid-s4644" xml:space="preserve">@-<lb/> <anchor type="note" xlink:label="note-132-01a" xlink:href="note-132-01"/> ſtendimus) ſinguli oppoſiti inter ſe ſint æquales: </s> <s xml:id="echoid-s4645" xml:space="preserve">Idcirco totam hanc propoſitionem <lb/>in triangulis, & </s> <s xml:id="echoid-s4646" xml:space="preserve">quadrilateris figuris ita demonſtrabimus. </s> <s xml:id="echoid-s4647" xml:space="preserve">Sit primum triangulum <lb/>A B C, inter ſibi Iſoperimetra triangula maximum. </s> <s xml:id="echoid-s4648" xml:space="preserve">Dico illud æquilaterum eſſe & </s> <s xml:id="echoid-s4649" xml:space="preserve"><lb/> <anchor type="figure" xlink:label="fig-132-01a" xlink:href="fig-132-01"/> æquiangulum. </s> <s xml:id="echoid-s4650" xml:space="preserve">Si enim non <lb/>eſt æqui<unsure/>laterum, ſed latera <lb/>A B, B C, ſunt inæqualia: <lb/></s> <s xml:id="echoid-s4651" xml:space="preserve">ſi ſuper baſem A C, conſti-<lb/>tuatur, per propoſ. </s> <s xml:id="echoid-s4652" xml:space="preserve">7. </s> <s xml:id="echoid-s4653" xml:space="preserve">hu-<lb/>ius triangulum Iſoſceles <lb/>A D C, ita ut latera A D, <lb/>D C, ſimul æqualia ſint la-<lb/>teribus A B, B C, ſimul, <lb/>erunt triangula A B C, <lb/>A D C, Iſoperimetra, atque adeo per propoſ. </s> <s xml:id="echoid-s4654" xml:space="preserve">8. </s> <s xml:id="echoid-s4655" xml:space="preserve">huius, A D C, maius quàm A B C, quod <lb/>eſt contra hypotheſim. </s> <s xml:id="echoid-s4656" xml:space="preserve">Non ergo inæqualia ſunt latera A B, A C, ſed æqualia. </s> <s xml:id="echoid-s4657" xml:space="preserve">Eademq́<unsure/>. </s> <s xml:id="echoid-s4658" xml:space="preserve"><lb/>ratio eſt de cæteris. </s> <s xml:id="echoid-s4659" xml:space="preserve">A E quilaterum ergo eſt triangulum A B C. </s> <s xml:id="echoid-s4660" xml:space="preserve">Igitur, ex coroll. </s> <s xml:id="echoid-s4661" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s4662" xml:space="preserve"><lb/>5. </s> <s xml:id="echoid-s4663" xml:space="preserve">lib. </s> <s xml:id="echoid-s4664" xml:space="preserve">1. </s> <s xml:id="echoid-s4665" xml:space="preserve">Eucl. </s> <s xml:id="echoid-s4666" xml:space="preserve">& </s> <s xml:id="echoid-s4667" xml:space="preserve">æquiangulum eſt. </s> <s xml:id="echoid-s4668" xml:space="preserve">quod eſt, propoſitum.</s> <s xml:id="echoid-s4669" xml:space="preserve"/> </p> <div xml:id="echoid-div251" type="float" level="2" n="2"> <figure xlink:label="fig-131-01" xlink:href="fig-131-01a"> <image file="131-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/131-01"/> </figure> <note position="left" xlink:label="note-132-01" xlink:href="note-132-01a" xml:space="preserve">34. primi.</note> <figure xlink:label="fig-132-01" xlink:href="fig-132-01a"> <image file="132-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/132-01"/> </figure> </div> <p style="it"> <s xml:id="echoid-s4670" xml:space="preserve"><emph style="sc">Deinde</emph> ſit quadrilaterum A B C D, inter omnia ſibi Iſoperimetra maximum. <lb/></s> <s xml:id="echoid-s4671" xml:space="preserve">Dico illud eſſe & </s> <s xml:id="echoid-s4672" xml:space="preserve">æquilaterum & </s> <s xml:id="echoid-s4673" xml:space="preserve">æquiangulum. </s> <s xml:id="echoid-s4674" xml:space="preserve">Si enim non eſt æquilaterum, ſint late-<lb/>ra A B, B C, ſi fieri poteſt, inæqualia, ducaturq́ue recta A C. </s> <s xml:id="echoid-s4675" xml:space="preserve">Si igitur, per propoſ. </s> <s xml:id="echoid-s4676" xml:space="preserve">7. </s> <s xml:id="echoid-s4677" xml:space="preserve"><lb/>huius, ſuper A C, conſtituatur triangulum A E C, iſoperimetrum triangulo A B C, <lb/>erit, per propo<unsure/>ſ. </s> <s xml:id="echoid-s4678" xml:space="preserve">8. </s> <s xml:id="echoid-s4679" xml:space="preserve">huius, triangulum A E C, maius triangulo A B C, Addito, ergo con <lb/>muni triangulo A C D, erit quadrilaterum A E C D, maius quadrilatero A B C D. </s> <s xml:id="echoid-s4680" xml:space="preserve"><lb/>quod eſt contra hypotheſim cum A B C D, maximum ponatur. </s> <s xml:id="echoid-s4681" xml:space="preserve">Non ergo inæqualia ſunt <lb/>latera A B, B C, ſed ę<unsure/>qualia. </s> <s xml:id="echoid-s4682" xml:space="preserve">Eademq́. </s> <s xml:id="echoid-s4683" xml:space="preserve">ratio eſt de cæteris. </s> <s xml:id="echoid-s4684" xml:space="preserve">AEquilatera ergo eſt fi-<lb/>gura A B C D.</s> <s xml:id="echoid-s4685" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s4686" xml:space="preserve"><emph style="sc">Sit</emph> iam quadrilatera figura A B C D, omnium iſoperimetrarum maxima, æqui-<lb/>latera, vt oſtenſum eſt, at non æquiangula, ſed anguli B A D, C D A, inæquales ſint. <lb/></s> <s xml:id="echoid-s4687" xml:space="preserve">Quoniam igitur figura A B C D, cum ſit æquilatera parallelogrammum eſt vt in <lb/>ſcholio propoſ. </s> <s xml:id="echoid-s4688" xml:space="preserve">24. </s> <s xml:id="echoid-s4689" xml:space="preserve">lib. </s> <s xml:id="echoid-s4690" xml:space="preserve">1. </s> <s xml:id="echoid-s4691" xml:space="preserve">Eucl<unsure/>. </s> <s xml:id="echoid-s4692" xml:space="preserve">demonſtrauimus; </s> <s xml:id="echoid-s4693" xml:space="preserve">ſi educantur ex A, & </s> <s xml:id="echoid-s4694" xml:space="preserve">D, duœ linea <lb/>perpendiculares A H, D G, occurrentes lateri B C, in H, & </s> <s xml:id="echoid-s4695" xml:space="preserve">G, erit quoque <emph style="sc">AHGd</emph>, <lb/>parallelogrammum. </s> <s xml:id="echoid-s4696" xml:space="preserve">Quia uero latera A B, D C, maiora ſunt lateribus AH, D G, <lb/> <anchor type="note" xlink:label="note-132-02a" xlink:href="note-132-02"/> producantur hæc, ut fiant rectæ A E, D F, lateribus A B, D C, æquales, iungaturq́; <lb/></s> <s xml:id="echoid-s4697" xml:space="preserve">recta F F. </s> <s xml:id="echoid-s4698" xml:space="preserve">Quo facto, erit figura A E F D, iſoperimetra parallelogrammo A B C D, <lb/>cum latera A E, DF, lateribus A B, D C, ęqualia ſint, latus uero A D, commune, <lb/> <anchor type="note" xlink:label="note-132-03a" xlink:href="note-132-03"/> & </s> <s xml:id="echoid-s4699" xml:space="preserve">latus E F, lateri B C, æquale, quòd vtrumque æquale ſit lateri oppoſito A D. <lb/></s> <s xml:id="echoid-s4700" xml:space="preserve">Cum ergo figura A E F D, maior ſit parallelogrammo A H G D, hoc autem æquale <lb/>ſit parallelogrammo A B C D; </s> <s xml:id="echoid-s4701" xml:space="preserve">erit quoque figura A E F D, maior parallelogrammo <lb/> <anchor type="note" xlink:label="note-132-04a" xlink:href="note-132-04"/> A B C D. </s> <s xml:id="echoid-s4702" xml:space="preserve">Quare cum eidem ſit iſoperimetra, non erit A B C D, figura quadrilateræ <lb/>inter ſibi Iſoperimetras maximam. </s> <s xml:id="echoid-s4703" xml:space="preserve">quod eſt contra hypotheſim. </s> <s xml:id="echoid-s4704" xml:space="preserve">Non ergo inæquales <lb/>ſunt anguli B A D, C D A. </s> <s xml:id="echoid-s4705" xml:space="preserve">ſed æquales: </s> <s xml:id="echoid-s4706" xml:space="preserve">atque adeo cum A B C D, ſit parallelogram-<lb/>mum, erunt anguli oppoſiti B, C, angulis D, A, æquales, proptereaq́; </s> <s xml:id="echoid-s4707" xml:space="preserve">tota figura æ<unsure/>-<lb/> <anchor type="note" xlink:label="note-132-05a" xlink:href="note-132-05"/> quiangula erit. </s> <s xml:id="echoid-s4708" xml:space="preserve">quod eſt propoſitum.</s> <s xml:id="echoid-s4709" xml:space="preserve"/> </p> <div xml:id="echoid-div252" type="float" level="2" n="3"> <note position="left" xlink:label="note-132-02" xlink:href="note-132-02a" xml:space="preserve">19. primi.</note> <note position="left" xlink:label="note-132-03" xlink:href="note-132-03a" xml:space="preserve">34. primi.</note> <note position="left" xlink:label="note-132-04" xlink:href="note-132-04a" xml:space="preserve">35. primi.</note> <note position="left" xlink:label="note-132-05" xlink:href="note-132-05a" xml:space="preserve">34. primi.</note> </div> <pb o="97" file="133" n="134" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div254" type="section" level="1" n="87"> <head xml:id="echoid-head91" style="it" xml:space="preserve">THEOR. 11. PROPOS. 13.</head> <p style="it"> <s xml:id="echoid-s4710" xml:space="preserve"><emph style="sc">IRCVLVS</emph> omnibus figuris rectilineis regularibus ſibi iſoperime-<lb/> <anchor type="note" xlink:label="note-133-01a" xlink:href="note-133-01"/> tris eſt.</s> <s xml:id="echoid-s4711" xml:space="preserve"/> </p> <div xml:id="echoid-div254" type="float" level="2" n="1"> <note position="right" xlink:label="note-133-01" xlink:href="note-133-01a" xml:space="preserve">Circulus <lb/>omnium <lb/>figurarũ re <lb/>cti linearũ <lb/>regulariũ <lb/>ſibi iſoperi <lb/>metrarum <lb/>maximus <lb/>eſt.</note> </div> <p> <s xml:id="echoid-s4712" xml:space="preserve"><emph style="sc">Esto</emph> circulus A B C, figura autem regularis quotcunque laterum ei iſo-<lb/>perimetra D E F. </s> <s xml:id="echoid-s4713" xml:space="preserve">Dico circulum A B C, eſſe maiorem figura D E F. </s> <s xml:id="echoid-s4714" xml:space="preserve">Sit enim G, <lb/>centrum circuli A B C; </s> <s xml:id="echoid-s4715" xml:space="preserve">& </s> <s xml:id="echoid-s4716" xml:space="preserve">H, centrum figuræ D E F; </s> <s xml:id="echoid-s4717" xml:space="preserve">Deſcribaturq́. </s> <s xml:id="echoid-s4718" xml:space="preserve">circa cir-<lb/>culum A B C, figura B I K C, tot laterum, & </s> <s xml:id="echoid-s4719" xml:space="preserve">angulorum ęqualium, quot con-<lb/>tinet figura D E F, id eſt, ſimilis figurę D E F, per ea, quæ ex Campano docui-<lb/>mus in ſcholio 1. </s> <s xml:id="echoid-s4720" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s4721" xml:space="preserve">16. </s> <s xml:id="echoid-s4722" xml:space="preserve">lib. </s> <s xml:id="echoid-s4723" xml:space="preserve">4. </s> <s xml:id="echoid-s4724" xml:space="preserve">Eucl. </s> <s xml:id="echoid-s4725" xml:space="preserve">Deinde ex puncto contactus A, ad cen <lb/>trum G, ducatur recta A G, quæ perpendicularis erit ad I K. </s> <s xml:id="echoid-s4726" xml:space="preserve">Ducatur rur-<lb/> <anchor type="note" xlink:label="note-133-02a" xlink:href="note-133-02"/> ſus H D, ad L M, perpendicularis; </s> <s xml:id="echoid-s4727" xml:space="preserve">Diuidentq́. </s> <s xml:id="echoid-s4728" xml:space="preserve">rectæ G A, H D, rectas I K, L M, <lb/> <anchor type="note" xlink:label="note-133-03a" xlink:href="note-133-03"/> bifariam, ut conſtat, ſi figuris B I K C, D E F, circunſcribantur circuli. </s> <s xml:id="echoid-s4729" xml:space="preserve">Du-<lb/>cantur quoque recte G I, H L, quæ diuident angulos I, & </s> <s xml:id="echoid-s4730" xml:space="preserve">L, bifariam, ut ma-<lb/>nifeſtum eſt ex demonſtratione propoſ. </s> <s xml:id="echoid-s4731" xml:space="preserve">12. </s> <s xml:id="echoid-s4732" xml:space="preserve">lib. </s> <s xml:id="echoid-s4733" xml:space="preserve">4. </s> <s xml:id="echoid-s4734" xml:space="preserve">Eucl. </s> <s xml:id="echoid-s4735" xml:space="preserve">Quoniam igitur toti <lb/>anguli I, & </s> <s xml:id="echoid-s4736" xml:space="preserve">L, ſunt æquales, propter ſimilitudinem figurarum, erunt etia@ <lb/> <anchor type="figure" xlink:label="fig-133-01a" xlink:href="fig-133-01"/> ipſorum dimidia, uidelicet anguli A I G, D L H, ęqualia. </s> <s xml:id="echoid-s4737" xml:space="preserve">Cum ergo & </s> <s xml:id="echoid-s4738" xml:space="preserve">an-<lb/> <anchor type="note" xlink:label="note-133-04a" xlink:href="note-133-04"/> guli I A G, L D H, ſint ęquales, vtpote recti, erunt triangula A I G, D L H, <lb/>ęquiangula. </s> <s xml:id="echoid-s4739" xml:space="preserve">Quia uero ambitus figuræ B I K C, maior eſt (per 1. </s> <s xml:id="echoid-s4740" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s4741" xml:space="preserve">lib. </s> <s xml:id="echoid-s4742" xml:space="preserve">1. <lb/></s> <s xml:id="echoid-s4743" xml:space="preserve">Archimedis de ſphæra, & </s> <s xml:id="echoid-s4744" xml:space="preserve">cylindro) ambitu circuli A B C; </s> <s xml:id="echoid-s4745" xml:space="preserve">Ambitus autem cir-<lb/>culi æqualis ponitur ambitui figuræ D E F; </s> <s xml:id="echoid-s4746" xml:space="preserve">erit quoq. </s> <s xml:id="echoid-s4747" xml:space="preserve">ambitus figurę B I K C. </s> <s xml:id="echoid-s4748" xml:space="preserve"><lb/>maior ambitu figurę D E F. </s> <s xml:id="echoid-s4749" xml:space="preserve">Cum igitur figuræ ſint regulares, & </s> <s xml:id="echoid-s4750" xml:space="preserve">ſimiles, erit <lb/>etiam latus I K, latere L M, maius, & </s> <s xml:id="echoid-s4751" xml:space="preserve">ideo I A, dimidium lateris I K, maius, <lb/> <anchor type="note" xlink:label="note-133-05a" xlink:href="note-133-05"/> quàm L D, dimidium lateris L M. </s> <s xml:id="echoid-s4752" xml:space="preserve">Rurſus, quoniam eſt, vt I A, ad A G, ita L D, <lb/> <anchor type="note" xlink:label="note-133-06a" xlink:href="note-133-06"/> ad D H; </s> <s xml:id="echoid-s4753" xml:space="preserve">Et eſt I A, maior quàm L D, erit quoq. </s> <s xml:id="echoid-s4754" xml:space="preserve">A G, maior, quàm D H. </s> <s xml:id="echoid-s4755" xml:space="preserve">Quam <lb/>obrem rectangulum contentum ſub A G, & </s> <s xml:id="echoid-s4756" xml:space="preserve">dimidio ambitu circu li A B G, <lb/>quod (per 4. </s> <s xml:id="echoid-s4757" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s4758" xml:space="preserve">huius) circulo A B C, eſt æquale, maius eſt, quàm rectangu <lb/>lum contentum ſub D H, & </s> <s xml:id="echoid-s4759" xml:space="preserve">dimidio ambitu figurę D E F, hoc eſt, (per 2. </s> <s xml:id="echoid-s4760" xml:space="preserve">pro-<lb/>poſ. </s> <s xml:id="echoid-s4761" xml:space="preserve">huius) quàm area figurę D E F. </s> <s xml:id="echoid-s4762" xml:space="preserve">Circulus igitur omnibus figuris rectilineis <lb/>regularibus ſibi iſoperimetris maior eſt, quod oſtendendum erat.</s> <s xml:id="echoid-s4763" xml:space="preserve"/> </p> <div xml:id="echoid-div255" type="float" level="2" n="2"> <note position="right" xlink:label="note-133-02" xlink:href="note-133-02a" xml:space="preserve">18. tertij.</note> <note position="right" xlink:label="note-133-03" xlink:href="note-133-03a" xml:space="preserve">3. tertij.</note> <figure xlink:label="fig-133-01" xlink:href="fig-133-01a"> <image file="133-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/133-01"/> </figure> <note position="right" xlink:label="note-133-04" xlink:href="note-133-04a" xml:space="preserve">32. primi.</note> <note position="right" xlink:label="note-133-05" xlink:href="note-133-05a" xml:space="preserve">4. ſexti.</note> <note position="right" xlink:label="note-133-06" xlink:href="note-133-06a" xml:space="preserve">14. quinti.</note> </div> <pb o="98" file="134" n="135" rhead="Comment. in I. Cap. Sphæræ"/> </div> <div xml:id="echoid-div257" type="section" level="1" n="88"> <head xml:id="echoid-head92" xml:space="preserve">COROLLARIVM.</head> <p> <s xml:id="echoid-s4764" xml:space="preserve">Ex omnibusiis, quæ demonſtrata ſunt, perſpicuum eſt circu-<lb/> <anchor type="note" xlink:label="note-134-01a" xlink:href="note-134-01"/> lum abſolute omnium figurarum rectilinearum ſibi iſoperimetra-<lb/>rum maximum eſſe.</s> <s xml:id="echoid-s4765" xml:space="preserve"/> </p> <div xml:id="echoid-div257" type="float" level="2" n="1"> <note position="left" xlink:label="note-134-01" xlink:href="note-134-01a" xml:space="preserve">@Circul’ om <lb/>nibus figu-<lb/>@is rectili-<lb/>neis ſibi iſo <lb/>perimetris <lb/>maior eſt.</note> </div> <p style="it"> <s xml:id="echoid-s4766" xml:space="preserve"><emph style="sc">Qvoniam</emph> enim ex propoſitione 5. </s> <s xml:id="echoid-s4767" xml:space="preserve">habetur, regularium figurarum iſoperime-<lb/>trarum eam, quæ plura latera continet, eſſe maiorem: </s> <s xml:id="echoid-s4768" xml:space="preserve">Rurſus ex propoſitione 12. </s> <s xml:id="echoid-s4769" xml:space="preserve">conſtat, <lb/>inter omnes figuras iſoperimetras æqualia numero latera habentes, eam maximam eſ-<lb/>ſe, quę regularis eſt: </s> <s xml:id="echoid-s4770" xml:space="preserve">Ex hac denique 13. </s> <s xml:id="echoid-s4771" xml:space="preserve">propoſitioue perſpicuum eſt, circulum omnium <lb/>figurarum iſoperimet rarum regularium eſſe maximum: </s> <s xml:id="echoid-s4772" xml:space="preserve">Manifeſte concluditur, circu-<lb/>lum abſolute ac ſimpliciter omnium figurarum rectilinearum ſibi iſoperimetrarum ma-<lb/>ximum eſſe quod eſt propoſitum.</s> <s xml:id="echoid-s4773" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div259" type="section" level="1" n="89"> <head xml:id="echoid-head93" style="it" xml:space="preserve">THEOR. 12. PROPOS. 14.</head> <p style="it"> <s xml:id="echoid-s4774" xml:space="preserve"><emph style="sc">Area</emph> cuiuslibet pyramidis æqualis eſt ſolido rectangulo conten-<lb/> <anchor type="note" xlink:label="note-134-02a" xlink:href="note-134-02"/> to ſub perpendiculari à uertice ad baſim protracta, & </s> <s xml:id="echoid-s4775" xml:space="preserve">tertia parte <lb/>baſis.</s> <s xml:id="echoid-s4776" xml:space="preserve"/> </p> <div xml:id="echoid-div259" type="float" level="2" n="1"> <note position="left" xlink:label="note-134-02" xlink:href="note-134-02a" xml:space="preserve">Pyramis <lb/>quælibet <lb/>cui paralle-<lb/>lepipedo ſit <lb/>@qualis.</note> </div> <p> <s xml:id="echoid-s4777" xml:space="preserve"><emph style="sc">Sit</emph> pyramis, cuius baſis quotcu nque laterum A B C D E, & </s> <s xml:id="echoid-s4778" xml:space="preserve">uertex F. <lb/></s> <s xml:id="echoid-s4779" xml:space="preserve"> <anchor type="figure" xlink:label="fig-134-01a" xlink:href="fig-134-01"/> Solidum autem rectangulu<unsure/>m G N, cu-<lb/>ius baſis G H I K, æqualis ſit tertię par-<lb/>ti baſis A B C D E, altitudo uero, ſiue <lb/>perpendicularis G L, æqualis altitudini <lb/>pyramidis, ſiue perpendiculari à uerti-<lb/>ce pyramidis ad eius baſim productæ. <lb/></s> <s xml:id="echoid-s4780" xml:space="preserve">Dico ſolidum rectangulum G N, ęqua-<lb/>le eſſe pyramidi A B C D E F. </s> <s xml:id="echoid-s4781" xml:space="preserve">Ducan-<lb/>tur enim ab oibus angulis baſis G H I K, <lb/>ad aliquod punctum baſis oppoſitę, ni-<lb/>mirum ad L, lineę rectæ, ita ut conſti-<lb/>tuatur pyramis G H I K L, eandem ha-<lb/>bens baſim cum ſolido G N, eand emq́ue <lb/>altitudinem & </s> <s xml:id="echoid-s4782" xml:space="preserve">cum eodem ſolido G N, <lb/>& </s> <s xml:id="echoid-s4783" xml:space="preserve">cum pyramide A B C D E F. </s> <s xml:id="echoid-s4784" xml:space="preserve">Quo-<lb/>niam igitur pyramis A B C D E F, tri-<lb/>pla eſt pyramidis G H I K L, ut in ſcho-<lb/>lio propoſ. </s> <s xml:id="echoid-s4785" xml:space="preserve">6. </s> <s xml:id="echoid-s4786" xml:space="preserve">lib. </s> <s xml:id="echoid-s4787" xml:space="preserve">12. </s> <s xml:id="echoid-s4788" xml:space="preserve">Eucl. </s> <s xml:id="echoid-s4789" xml:space="preserve">demonſtraui-<lb/>mus: </s> <s xml:id="echoid-s4790" xml:space="preserve">Et ſolidum G N, triplum quoque <lb/>eſt, ex coroll. </s> <s xml:id="echoid-s4791" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s4792" xml:space="preserve">7. </s> <s xml:id="echoid-s4793" xml:space="preserve">lib. </s> <s xml:id="echoid-s4794" xml:space="preserve">12. </s> <s xml:id="echoid-s4795" xml:space="preserve">Eucl. </s> <s xml:id="echoid-s4796" xml:space="preserve"><lb/>eiuſdem pyramidis G H I K L; </s> <s xml:id="echoid-s4797" xml:space="preserve">erit ſo-<lb/>lidum G N, pyramidi A B C D E F, ęqua <lb/>le. </s> <s xml:id="echoid-s4798" xml:space="preserve">Quapropter area cuiuslibet pyrami-<lb/>dis ęqualis eſt ſolido rectãgulo, &</s> <s xml:id="echoid-s4799" xml:space="preserve">c. </s> <s xml:id="echoid-s4800" xml:space="preserve">quod <lb/>erat oſtendendum.</s> <s xml:id="echoid-s4801" xml:space="preserve"/> </p> <div xml:id="echoid-div260" type="float" level="2" n="2"> <figure xlink:label="fig-134-01" xlink:href="fig-134-01a"> <image file="134-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/134-01"/> </figure> </div> <pb o="99" file="135" n="136" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div262" type="section" level="1" n="90"> <head xml:id="echoid-head94" xml:space="preserve">THEOR. 13. PROPOS. 15.</head> <p style="it"> <s xml:id="echoid-s4802" xml:space="preserve"><emph style="sc">Area</emph> cuiuslibet corporis planis ſuper ficiebus contenti, & </s> <s xml:id="echoid-s4803" xml:space="preserve">circa ſphę <lb/> <anchor type="note" xlink:label="note-135-01a" xlink:href="note-135-01"/> ram aliquam circumſcriptibilis, hoc eſt, à cuius puncto aliquo medio omnes <lb/>perpendiculares ad baſes eius productæ ſunt æquales, æqualis eſt ſolido re-<lb/>ctangulo contento ſub una perpendicularium, & </s> <s xml:id="echoid-s4804" xml:space="preserve">tertia parte ambitus cor-<lb/>poris.</s> <s xml:id="echoid-s4805" xml:space="preserve"/> </p> <div xml:id="echoid-div262" type="float" level="2" n="1"> <note position="right" xlink:label="note-135-01" xlink:href="note-135-01a" xml:space="preserve">Corpus <lb/>quodlibet, <lb/>in qua ſphę <lb/>ra deſcribi <lb/>poteſt, cui <lb/>parallelepi-<lb/>pedo æqua-<lb/>le ſit.</note> </div> <p> <s xml:id="echoid-s4806" xml:space="preserve"><emph style="sc">Esto</emph> corpus planis ſupeificiebus contentum A B C D, circa ſphæram <lb/>E F G H, cuius centrum I, deſcriptum, in quo ducantur ex I, ad puncta con-<lb/>tactuum lineę rectæ I E, I F, I G, I H, quæ ad baſes ſolidi erunt perpendicula-<lb/>res. </s> <s xml:id="echoid-s4807" xml:space="preserve">Nam ſi v. </s> <s xml:id="echoid-s4808" xml:space="preserve">g. </s> <s xml:id="echoid-s4809" xml:space="preserve">per rectam I E, ducatur planum faciens in ſphæra, per propoſ. <lb/></s> <s xml:id="echoid-s4810" xml:space="preserve">1. </s> <s xml:id="echoid-s4811" xml:space="preserve">lib. </s> <s xml:id="echoid-s4812" xml:space="preserve">1. </s> <s xml:id="echoid-s4813" xml:space="preserve">Theod. </s> <s xml:id="echoid-s4814" xml:space="preserve">circulum E F G H, & </s> <s xml:id="echoid-s4815" xml:space="preserve">in baſi rectam A B, tanget circulus <lb/>E F G H, rectam A B, in puncto E, propterea quòd ſphæra baſim non ſecat, <lb/> <anchor type="note" xlink:label="note-135-02a" xlink:href="note-135-02"/> ſed tangit. </s> <s xml:id="echoid-s4816" xml:space="preserve">Igitur I E, ad rectam A B, perpendicularis erit. </s> <s xml:id="echoid-s4817" xml:space="preserve">Eadem ratione, ſi <lb/>per I E, ducatur aliud planum à priori dif-<lb/> <anchor type="figure" xlink:label="fig-135-01a" xlink:href="fig-135-01"/> <anchor type="note" xlink:label="note-135-03a" xlink:href="note-135-03"/> ferens, fiet alius circulus in ſphęra, & </s> <s xml:id="echoid-s4818" xml:space="preserve">alia li <lb/>nea recta in eadem baſi ſecans rectam A B, <lb/>in E, ad quã etiam I E, perpẽdicularis erit <lb/>Ac propterea I E, ad baſim ſolidi per illas <lb/>rectas ductam perpendicularis erit. </s> <s xml:id="echoid-s4819" xml:space="preserve">Nõ ali-<lb/>ter oſtendemus, rectas I F, I G, I H, ad <lb/> <anchor type="note" xlink:label="note-135-04a" xlink:href="note-135-04"/> alias baſes eſſe perpendiculares. </s> <s xml:id="echoid-s4820" xml:space="preserve">Sit quo-<lb/>que ſolidum rectangulum L R, cuius baſis <lb/>K L M N, ſit æqualis tertiæ parti ambitus <lb/>corporis A B C D; </s> <s xml:id="echoid-s4821" xml:space="preserve">altitudo uero, ſiue per <lb/>pendicularis L P, æqualis uni perpendicu-<lb/>lariũ ex centro I, ad baſes corporis ABCD, <lb/>cadentiũ; </s> <s xml:id="echoid-s4822" xml:space="preserve">quæ omnes inter ſe ęquales ſunt <lb/>ex defi. </s> <s xml:id="echoid-s4823" xml:space="preserve">ſphæræ. </s> <s xml:id="echoid-s4824" xml:space="preserve">Dico, ſolidum L R, corpori <lb/>A B C D, æquale eſſe. </s> <s xml:id="echoid-s4825" xml:space="preserve">Ducantur enim ex <lb/>centro I, ad oẽs angulos corporis ABCD, <lb/>rectę lineę, vt totum corpus in pyramides, <lb/>ex quibus componitur, diuidatur: </s> <s xml:id="echoid-s4826" xml:space="preserve">quarum <lb/>quidem pyramidum baſes e<unsure/>ędem ſunt, quę <lb/>corporis, vertex autem communis centrum I. </s> <s xml:id="echoid-s4827" xml:space="preserve">Quoniam igitur (per præceden <lb/>tem propoſ.) </s> <s xml:id="echoid-s4828" xml:space="preserve">quælibet harum pyramidum æqualis eſt ſolido rectangulo ſub <lb/>perpendiculari L P, quæ ſingulis perpendicularibus corporis A B C D, æqua-<lb/>lis ponitur, & </s> <s xml:id="echoid-s4829" xml:space="preserve">tertia parte ſuæ baſis contento; </s> <s xml:id="echoid-s4830" xml:space="preserve">Si fiant tot ſolida rectangula, <lb/>quot ſunt pyramides, erunt omnia hęc ſimul æqualia ſolido rectangulo L R. <lb/></s> <s xml:id="echoid-s4831" xml:space="preserve">(Si enim rectangulum K L M N, diuidatur in tot rectangula, quot baſes ſunt <lb/>in ſolido propoſito, ita ut primum æquale ſit tertię parti unius baſis, & </s> <s xml:id="echoid-s4832" xml:space="preserve">ſe-<lb/>cundum tertiæ parti alterius, & </s> <s xml:id="echoid-s4833" xml:space="preserve">ita deinceps, quandoquidem totum rectangu-<lb/>lum K L M N, æquale ponitur tertię parti totius ambitus ſolidi, intelligan-<lb/>tur autem ſuper illa rectangula conſtitui parallelepipeda; </s> <s xml:id="echoid-s4834" xml:space="preserve">erunt omnia ſimul <lb/>æqualia parallelepipedo L R.) </s> <s xml:id="echoid-s4835" xml:space="preserve">Cum ergo ſingula parallelepipeda ſingulis py-<lb/>ramidibus ſint ęqualia, per propoſ. </s> <s xml:id="echoid-s4836" xml:space="preserve">pręcedentem; </s> <s xml:id="echoid-s4837" xml:space="preserve">erunt quoque omnes pyrami <pb o="100" file="136" n="137" rhead="Comment. in I. Cap. Sphæræ"/> des (nempe corpus A B C D, ex illis compoſitum) æquales ſolido rectangu-<lb/>lo L R. </s> <s xml:id="echoid-s4838" xml:space="preserve">Quamobrem area cuiuſlibet corporis planis ſuperficiebus contenti, <lb/>&</s> <s xml:id="echoid-s4839" xml:space="preserve">c. </s> <s xml:id="echoid-s4840" xml:space="preserve">quod demonſtrandum erat.</s> <s xml:id="echoid-s4841" xml:space="preserve"/> </p> <div xml:id="echoid-div263" type="float" level="2" n="2"> <note position="right" xlink:label="note-135-02" xlink:href="note-135-02a" xml:space="preserve">3. undec.</note> <figure xlink:label="fig-135-01" xlink:href="fig-135-01a"> <image file="135-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/135-01"/> </figure> <note position="right" xlink:label="note-135-03" xlink:href="note-135-03a" xml:space="preserve">18. tertij.</note> <note position="right" xlink:label="note-135-04" xlink:href="note-135-04a" xml:space="preserve">4. vndec.</note> </div> </div> <div xml:id="echoid-div265" type="section" level="1" n="91"> <head xml:id="echoid-head95" style="it" xml:space="preserve">THEOR. 14. PROPOS. 16.</head> <p style="it"> <s xml:id="echoid-s4842" xml:space="preserve"><emph style="sc">Area</emph> cuiuslibet ſphærę æqualis eſt ſolido rectangulo comprehenſo <lb/> <anchor type="note" xlink:label="note-136-01a" xlink:href="note-136-01"/> ſub ſemidiametro ſphæræ, & </s> <s xml:id="echoid-s4843" xml:space="preserve">tertia parte ambitus ſphæræ.</s> <s xml:id="echoid-s4844" xml:space="preserve"/> </p> <div xml:id="echoid-div265" type="float" level="2" n="1"> <note position="left" xlink:label="note-136-01" xlink:href="note-136-01a" xml:space="preserve">Sphę ra q̃li <lb/>bet cui pa-<lb/>rallel epipe <lb/>do ſit ęqua <lb/>lis.</note> </div> <p> <s xml:id="echoid-s4845" xml:space="preserve"><emph style="sc">Esto</emph> ſphæra A B C, cuius centrum D, ſemidiameter A D: </s> <s xml:id="echoid-s4846" xml:space="preserve">Solidum au-<lb/>tem rectangulum E, contentum ſub ſemidiametro A D, & </s> <s xml:id="echoid-s4847" xml:space="preserve">tertia parte ambi-<lb/>tus ſpæræ A B C. </s> <s xml:id="echoid-s4848" xml:space="preserve">Dico corpus E, ſphæræ A B C, eſſe æquale. </s> <s xml:id="echoid-s4849" xml:space="preserve">Nam ſi non eſt <lb/>æquale; </s> <s xml:id="echoid-s4850" xml:space="preserve">ſit, ſi fieri poteſt, primum maius, ſitq́ue exceſfus corporis E, ſupra <lb/>ſphęram A B C, quantitas F. </s> <s xml:id="echoid-s4851" xml:space="preserve">Intelligatur circa ccntrum D, deſcripta ſphæ-<lb/>ra GHK, maior quàm ſphæra A B C, ita tamen, ut exceſſus ſphęrę G H K, <lb/>ſupra ſphęram A B C, non ſit maior quantitate F, ſed uel æqualis, uel mi-<lb/>nor, hoc eſt, vt ſphæra G H K, ſit uel ęqualis ſolido E, quando nimirum <lb/> <anchor type="figure" xlink:label="fig-136-01a" xlink:href="fig-136-01"/> ipſa excedit ſphæram A B C, præciſe <lb/>quantitate F; </s> <s xml:id="echoid-s4852" xml:space="preserve">uel minor, ſi nimirum <lb/>ipſa excedit ſphęram A B C, mino-<lb/>ri quantitate, quàm F. </s> <s xml:id="echoid-s4853" xml:space="preserve">Neceſlario <lb/>enim aliqua ſphæra erit, quæ uel <lb/>æqualis ſit magnitudini E, atque <lb/>adeo maior, quàm ſphæra A B C; <lb/></s> <s xml:id="echoid-s4854" xml:space="preserve">uel maior quidem quã ſphęra A B C, <lb/>minor vero quàm magnitudo E, quæ <lb/>maior ponitur, quàm ſphæra A B C. </s> <s xml:id="echoid-s4855" xml:space="preserve"><lb/>Inſcribatur deinde intra ſphæram <lb/>G H K, corpus, quod non tangat <lb/>ſphæram A B C, ita ut unaquæque <lb/> <anchor type="note" xlink:label="note-136-02a" xlink:href="note-136-02"/> perpendicularium ex centro D, ad <lb/>baſes iſtius corporis eductarum ma-<lb/>ior fit ſemidiametro A D. </s> <s xml:id="echoid-s4856" xml:space="preserve">Si igitur <lb/>à centro D, ad omnes angulos di-<lb/>cti corporis ducantur lineæ rectæ, <lb/>ut totum corpus in pyramides di-<lb/>uidatur, quarum baſes ſunt eædem, <lb/>quæ corporis G H K, uertex au-<lb/>tem communis centrum D; </s> <s xml:id="echoid-s4857" xml:space="preserve">erit quæ <lb/>libet pyramis (per 14. </s> <s xml:id="echoid-s4858" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s4859" xml:space="preserve">hu-<lb/>ius) æqualis ſolido rectangulo contento ſub eius perpendiculari, & </s> <s xml:id="echoid-s4860" xml:space="preserve">tertia <lb/>parte baſis; </s> <s xml:id="echoid-s4861" xml:space="preserve">A tque idcirco ſolidum rectangulum contentum ſub ſemidiame-<lb/>tro A D & </s> <s xml:id="echoid-s4862" xml:space="preserve">tertia parte baſis cuiuſlibet pyramidis, minus ipſa pyramide <lb/>erit. </s> <s xml:id="echoid-s4863" xml:space="preserve">Et quoniam omnia ſolida rectangula contenta ſub ſingulis perpendi-<lb/>cularibus ex centro D, ad baſes corporis dicti protractis, & </s> <s xml:id="echoid-s4864" xml:space="preserve">ſingulis ter-<lb/>tijs partibus baſium, ſimul ęqualia ſunt toti corpori, efficiunt autem om-<lb/>@es tertiæ partes baſium ſimul tertiam partem ambitus corporis, erit ſo@ <pb o="101" file="137" n="138" rhead="Ioan. de Sacro Boſco."/> lidum rectangulum contentum ſub ſemidiametro A D, & </s> <s xml:id="echoid-s4865" xml:space="preserve">tertia parte ambit@ <lb/>præfati corporis inſcripti intra ſphærã G H K, minus corpore inſcripto. </s> <s xml:id="echoid-s4866" xml:space="preserve">Quo-<lb/>niã vero ambitus corporis inſcripti maior eſt ambitu ſphæræ A B C, ut demon <lb/>ſtrat Archimedes lib. </s> <s xml:id="echoid-s4867" xml:space="preserve">1. </s> <s xml:id="echoid-s4868" xml:space="preserve">de ſphæra, & </s> <s xml:id="echoid-s4869" xml:space="preserve">cylindro propoſ. </s> <s xml:id="echoid-s4870" xml:space="preserve">27. </s> <s xml:id="echoid-s4871" xml:space="preserve">atque adeo & </s> <s xml:id="echoid-s4872" xml:space="preserve">tertia <lb/>pars ambitus dicti corporis maior tertia parte ambitus ſphęræ A B C, erit ſo-<lb/>lidum rectangulum contentum ſub ſemidiametro A D, & </s> <s xml:id="echoid-s4873" xml:space="preserve">tertia parte ambitus <lb/>ſphærę A B C, hoc eſt, ſolidum E, multo minus corpore inſcripto intra ſphærã <lb/>G H K: </s> <s xml:id="echoid-s4874" xml:space="preserve">Poſita eſt autem ſphæra G H K, uel æqualis ſolido E, vel minor. </s> <s xml:id="echoid-s4875" xml:space="preserve">Igitur <lb/>& </s> <s xml:id="echoid-s4876" xml:space="preserve">ſphęra G H K, minor erit corpore intra ipſam deſcripto, totum parte, quod <lb/>eſt abſurdum. </s> <s xml:id="echoid-s4877" xml:space="preserve">Quocirca ſolidum E, maius non erit ſphæra A B C.</s> <s xml:id="echoid-s4878" xml:space="preserve"/> </p> <div xml:id="echoid-div266" type="float" level="2" n="2"> <figure xlink:label="fig-136-01" xlink:href="fig-136-01a"> <image file="136-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/136-01"/> </figure> <note position="left" xlink:label="note-136-02" xlink:href="note-136-02a" xml:space="preserve">37. duod.</note> </div> <p> <s xml:id="echoid-s4879" xml:space="preserve"><emph style="sc">Sitdeinde</emph>, ſi fieri poteſt, ſolidum E, minus, quàm ſphæra A B C, <lb/>excedaturq́ue à ſphæra A B C, quantitate F. </s> <s xml:id="echoid-s4880" xml:space="preserve">Intelligatur circa centrum D, <lb/>ſphæra deſcripta L M N, minor, quàm ſphæia A B C, ita tamen, ut exceſſus, <lb/>quo ſphæra L M N, ſuperatur à ſphæra A B C, non ſit maior quantitate F, <lb/>ſed uel æqualis, uel minor, hoc eſt, ut ſphæra L M N, ſit uel ęqualis ſolido <lb/>E, ſi nimirum ipſa excedatur a ſphæra A B C, quantitate F, vel maior ſolido <lb/>E, ſi uidelicet ſphæra L M N, a ſphæra A B C, ſuperetur minori quantitate, <lb/>quam F. </s> <s xml:id="echoid-s4881" xml:space="preserve">Neceſſario enim aliqua ſphæra erit, quę uel æqualis ſit ſolido E, at-<lb/>que adeo minor, quàm ſphęra A B C; </s> <s xml:id="echoid-s4882" xml:space="preserve">uel minor quidem, quàm ſphęra A B C, <lb/>maior uerò, quàm magnitu<unsure/>do E, quæ minor ponitur, quàm ſphæra A B C. </s> <s xml:id="echoid-s4883" xml:space="preserve">De-<lb/>ſcribatur deinde intra ſphæram A B C, corpus, quod minime tangat ſphęram <lb/> <anchor type="note" xlink:label="note-137-01a" xlink:href="note-137-01"/> L M N; </s> <s xml:id="echoid-s4884" xml:space="preserve">ita ut unaquæque perpendicularium ex centro D, ad baſes huius cor-<lb/>poris inſcripti cadentium minor ſit ſemidiametro A D. </s> <s xml:id="echoid-s4885" xml:space="preserve">Si igitur à centro D, <lb/>ad omnes eius angulos lineæ extendantur, ut totum corpus in pyramides re-<lb/>ſoluatur, quarum baſes ſunt eędem, quæ corporis A B C, uertex autem com-<lb/>munis centrum D; </s> <s xml:id="echoid-s4886" xml:space="preserve">erit quælibet pyramis æqualis (per 14. </s> <s xml:id="echoid-s4887" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s4888" xml:space="preserve">huius) ſoli-<lb/>do rectangulo contento ſub eius perpendiculari, & </s> <s xml:id="echoid-s4889" xml:space="preserve">tertia parte baſis, Et ideo <lb/>ſolidum rectan gulum contentum ſub ſemidiametro A D, & </s> <s xml:id="echoid-s4890" xml:space="preserve">tertia baſis cuiuſ-<lb/>uis pyramidis, maius erit pyramide ipſa. </s> <s xml:id="echoid-s4891" xml:space="preserve">Et quoniam omnia ſolida rectangu-<lb/>la contenta ſub ſingulis perpendicularibus ex centro D, ad baſes corporis di-<lb/>cti protractis, & </s> <s xml:id="echoid-s4892" xml:space="preserve">ſingulis tertijs partibus baſium, ſimul ęqualia ſunt toti corpo-<lb/>ri, eſſiciunt autem omnes tertię partes baſium ſimul tertiam partem ambitus <lb/>corporis; </s> <s xml:id="echoid-s4893" xml:space="preserve">erit ſolidum rectangulum contentum ſub ſemidiametro A D, & </s> <s xml:id="echoid-s4894" xml:space="preserve">ter-<lb/>tia parte ambitus dicti corporis ſphærę A B C, inſcripti, maius corpore inſcri-<lb/>pto. </s> <s xml:id="echoid-s4895" xml:space="preserve">Cum igitur ambitus ſphærę A B C, maior ſit ambitu corporis ſibi in ſcripti <lb/>atque adeo & </s> <s xml:id="echoid-s4896" xml:space="preserve">tertia pars ambitus ſphæræ maior tertia parte ambitus dicti cor-<lb/>poris, erit ſolidum rectan gulum contentum ſub A D, ſemidiametro, & </s> <s xml:id="echoid-s4897" xml:space="preserve">tertia <lb/>parte ambitus ſphærę A B C, hoc eſt, ſolidum E, multo maius corpore inſcri-<lb/>pto intra ſphæram A B C: </s> <s xml:id="echoid-s4898" xml:space="preserve">Ponebatur autem ſphæra L M N, uel æqualis ſoli-<lb/>do E, uel maior. </s> <s xml:id="echoid-s4899" xml:space="preserve">Igitur & </s> <s xml:id="echoid-s4900" xml:space="preserve">ſphęra L M N, maior erit corpore intra ſphęram <lb/>A B C, deſcripto, pars toto, quod eſt abſurdum. </s> <s xml:id="echoid-s4901" xml:space="preserve">Non igitur ſolidum E, minus <lb/>erit ſphęra A B C. </s> <s xml:id="echoid-s4902" xml:space="preserve">Cum ergo neque maius ſit oſtenſum, ęquale omnino erit. <lb/></s> <s xml:id="echoid-s4903" xml:space="preserve">Ac propterea area cuiuslibet ſphæræ æqualis eſt ſolido rectangulo compre-<lb/>henſo ſub ſemidiametro ſphæræ, & </s> <s xml:id="echoid-s4904" xml:space="preserve">tertia parte ambitus ſphæræ, quod demon-<lb/>ſtrandum erat.</s> <s xml:id="echoid-s4905" xml:space="preserve"/> </p> <div xml:id="echoid-div267" type="float" level="2" n="3"> <note position="right" xlink:label="note-137-01" xlink:href="note-137-01a" xml:space="preserve">17. duod.</note> </div> <pb o="102" file="138" n="139" rhead="Comment. in I. Cap. Sphæræ"/> </div> <div xml:id="echoid-div269" type="section" level="1" n="92"> <head xml:id="echoid-head96" style="it" xml:space="preserve">THEOR. 15. PROPOS. 17.</head> <p style="it"> <s xml:id="echoid-s4906" xml:space="preserve"><emph style="sc">Sphaera</emph> omnibus corporibus ſibi iſoperimetris, planis ſuperficie-<lb/> <anchor type="note" xlink:label="note-138-01a" xlink:href="note-138-01"/> bus contineãtur; </s> <s xml:id="echoid-s4907" xml:space="preserve">circa{q́ue} alias ſphæras circumſcriptibilia ſint, hoc eſt, quorũ <lb/>omnes perpendiculares ad baſes productę ab aliquo puncto medio ſint equa <lb/>les, maior eſt.</s> <s xml:id="echoid-s4908" xml:space="preserve"/> </p> <div xml:id="echoid-div269" type="float" level="2" n="1"> <note position="left" xlink:label="note-138-01" xlink:href="note-138-01a" xml:space="preserve">Sphæra ma <lb/>ior eſt om-<lb/>nibus cor <lb/>poribus ſi-<lb/>bi Iſoperi-<lb/>metris, & <lb/>@irca alias <lb/>ſphæ as cir <lb/>cũſeriptibi-<lb/>libus, quæ <lb/>planis ſuꝑ <lb/>ficiebus co <lb/>tinentur.</note> </div> <p> <s xml:id="echoid-s4909" xml:space="preserve"><emph style="sc">Esto</emph> ſphęra A, cuius centrum A, & </s> <s xml:id="echoid-s4910" xml:space="preserve">ſemidiameter A B: </s> <s xml:id="echoid-s4911" xml:space="preserve">Solidum autem <lb/>circa aliquam ſphęram circum ſcriptibile ſibi iſoperimetrum C, cuius una per <lb/>pendicularium C D. </s> <s xml:id="echoid-s4912" xml:space="preserve">Dico ſphęram A, maiorem eſſe ſolido C. </s> <s xml:id="echoid-s4913" xml:space="preserve">Intelligatur <lb/>enim circa ſphæram A, corpus deſcriptum ſimile prorſus ſolido C, ita ut ſin-<lb/>gula quoque latera contingant ſphæram A, hoc eſt, eius perpendiculares, <lb/>quarum una ſit A B, ſint quoque æquales, nempe ſemidiametri ſphæræ A exi-<lb/>ſtentes. </s> <s xml:id="echoid-s4914" xml:space="preserve">Itaque quoniam ambitus corporis circa ſphęram A, maior eſt ambi-<lb/>tu ſphæræ A, (per ea, quę ab Archimede ſunt demonſtrata lib. </s> <s xml:id="echoid-s4915" xml:space="preserve">I. </s> <s xml:id="echoid-s4916" xml:space="preserve">de ſphæ-<lb/> <anchor type="figure" xlink:label="fig-138-01a" xlink:href="fig-138-01"/> ra, & </s> <s xml:id="echoid-s4917" xml:space="preserve">cylindro, propoſ. </s> <s xml:id="echoid-s4918" xml:space="preserve">27.) </s> <s xml:id="echoid-s4919" xml:space="preserve">e-<lb/>rit quoque eiuſdem corporis <lb/>ambitus maior ambitu corpo-<lb/>ris C. </s> <s xml:id="echoid-s4920" xml:space="preserve">Quare perpendicularis <lb/>A B, hoc eſt ſemidiametri ſphę <lb/>ræ A, maior erit perpendicula <lb/>ri C D. </s> <s xml:id="echoid-s4921" xml:space="preserve">Quamobrem rectangu <lb/>lum ſolidum contentum ſub <lb/>ſemidiametro A B, & </s> <s xml:id="echoid-s4922" xml:space="preserve">tertia <lb/>parte ambitus ſphęrę A, quod <lb/>(per præcedentẽ propoſ.) </s> <s xml:id="echoid-s4923" xml:space="preserve">ſphę <lb/>ræ A, æquale eſt, maius erit, <lb/>quàm rectangulum ſolidum <lb/>contentum ſub perpendicula-<lb/>ri C D, & </s> <s xml:id="echoid-s4924" xml:space="preserve">tertia parte ambitus <lb/>corporis C, hoc eſt, (per 15. </s> <s xml:id="echoid-s4925" xml:space="preserve">ꝓ-<lb/>poſ. </s> <s xml:id="echoid-s4926" xml:space="preserve">huius) quàm corpus C. <lb/></s> <s xml:id="echoid-s4927" xml:space="preserve">Sphæra igitur omnibus corpo <lb/>ribus ſibi Iſoperimetris, quæ <lb/>planis ſuperficiebus continean <lb/>tur, &</s> <s xml:id="echoid-s4928" xml:space="preserve">c. </s> <s xml:id="echoid-s4929" xml:space="preserve">maior eſt, quod erat de <lb/>@onſtr andum.</s> <s xml:id="echoid-s4930" xml:space="preserve"/> </p> <div xml:id="echoid-div270" type="float" level="2" n="2"> <figure xlink:label="fig-138-01" xlink:href="fig-138-01a"> <image file="138-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/138-01"/> </figure> </div> </div> <div xml:id="echoid-div272" type="section" level="1" n="93"> <head xml:id="echoid-head97" style="it" xml:space="preserve">THEOR. 16. PROPOS. 18.</head> <note position="left" xml:space="preserve">Sphæra ma <lb/>ior eſt om-<lb/>nibus cor-<lb/>poribus ſi <lb/>bi iſoperi <lb/>metris, & <lb/>circa alias <lb/>ſphæras cir <lb/>cunſcripti-<lb/>@ilibus.</note> <p style="it"> <s xml:id="echoid-s4931" xml:space="preserve"><emph style="sc">Sphaera</emph> omnibus corporibus ſibiiſoperimetris, & </s> <s xml:id="echoid-s4932" xml:space="preserve">circa alias ſphę <lb/>ras circumſcriptibilibus, quæ ſuperficiebus conicis contineantur, ita ut la-<lb/>tera omnia conica ſint æqualia, maior eſt.</s> <s xml:id="echoid-s4933" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4934" xml:space="preserve"><emph style="sc">Esto</emph> circulus A B C D, cui circumſcribatur figura regularis E F G H-<lb/>I K L M, ita ut numerus laterum à quaternario menſuretur, cuiuſmodi eſt qua <lb/>dratum, figura 8. </s> <s xml:id="echoid-s4935" xml:space="preserve">12. </s> <s xml:id="echoid-s4936" xml:space="preserve">16. </s> <s xml:id="echoid-s4937" xml:space="preserve">20. </s> <s xml:id="echoid-s4938" xml:space="preserve">24. </s> <s xml:id="echoid-s4939" xml:space="preserve">vel 28. </s> <s xml:id="echoid-s4940" xml:space="preserve">laterum, angulorumq́. </s> <s xml:id="echoid-s4941" xml:space="preserve">ęqualium, &</s> <s xml:id="echoid-s4942" xml:space="preserve">c.</s> <s xml:id="echoid-s4943" xml:space="preserve"> <pb o="103" file="139" n="140" rhead="Ioan. de Sacro Boſco."/> Ducaturq́. </s> <s xml:id="echoid-s4944" xml:space="preserve">ex angulo E, per centrum ad angulum I, recta E I. </s> <s xml:id="echoid-s4945" xml:space="preserve">Itaq; </s> <s xml:id="echoid-s4946" xml:space="preserve">ſi circa ma <lb/> <anchor type="note" xlink:label="note-139-01a" xlink:href="note-139-01"/> @entem rectam E I, immobilem circumuagatur planum, in quo eſt circulus <lb/>A B C D, & </s> <s xml:id="echoid-s4947" xml:space="preserve">figura E F G H I K L M, deſcribet circulus ſpheram, figura <lb/>uero corpus circa ſphæram conicis ſuperficiebus contentum, quarum ſuperfi-<lb/>cierum latera æqualia ſunt, nempe eadem, quæ figuræ, ut ab Archimede demõ <lb/>ſtratur propoſ. </s> <s xml:id="echoid-s4948" xml:space="preserve">22. </s> <s xml:id="echoid-s4949" xml:space="preserve">& </s> <s xml:id="echoid-s4950" xml:space="preserve">27. </s> <s xml:id="echoid-s4951" xml:space="preserve">lib. </s> <s xml:id="echoid-s4952" xml:space="preserve">1. </s> <s xml:id="echoid-s4953" xml:space="preserve">de ſphæra, & </s> <s xml:id="echoid-s4954" xml:space="preserve">cylindro. </s> <s xml:id="echoid-s4955" xml:space="preserve">Sitiam ſphæra N, iſo-<lb/>perimetra corpori E F G H I K L M, circa ſphęram A B C D, deſcripto. </s> <s xml:id="echoid-s4956" xml:space="preserve">Di-<lb/> <anchor type="figure" xlink:label="fig-139-01a" xlink:href="fig-139-01"/> co ſphæram N, dicto corpore eſſe maiorem. </s> <s xml:id="echoid-s4957" xml:space="preserve">Quoniam enim ambitus ſolidi <lb/>E F G H I K L M, maior eſt (per propoſ. </s> <s xml:id="echoid-s4958" xml:space="preserve">27. </s> <s xml:id="echoid-s4959" xml:space="preserve">lib. </s> <s xml:id="echoid-s4960" xml:space="preserve">1. </s> <s xml:id="echoid-s4961" xml:space="preserve">Archimedis de ſphæra & </s> <s xml:id="echoid-s4962" xml:space="preserve"><lb/>cylindro) ambitu ſphæræ A B C D, erit quoque ambitus ſphæræ N, maior am <lb/>bitu ſphæræ A B C D, ideoq́ue ſemidiameter ſphæræ N, maior erit ſemidiame <lb/>tro ſphæræ A B C D. </s> <s xml:id="echoid-s4963" xml:space="preserve">Et quia ſuperſicies ſphæræ quadrupla eſt (per propoſ. <lb/></s> <s xml:id="echoid-s4964" xml:space="preserve">31. </s> <s xml:id="echoid-s4965" xml:space="preserve">lib. </s> <s xml:id="echoid-s4966" xml:space="preserve">1. </s> <s xml:id="echoid-s4967" xml:space="preserve">Archimedis de ſphæra, & </s> <s xml:id="echoid-s4968" xml:space="preserve">cylindro) maximi circuli in ſphæra, ſi ſu-<lb/>matur circulus O P, quadruplus circuli maximi in ſphæra N, (quod quidem <lb/>facile fiet, ſi diameter O P, dupla ſumatur diametri circuli maximi in ſphæra <lb/>N. </s> <s xml:id="echoid-s4969" xml:space="preserve">Quoniam enim, ut circulus O P, ad circulum maximum in ſphæra N, ita <lb/>quadratum diametri O P, ad quadratum diametri circuli maximi in ſphæra <lb/> <anchor type="note" xlink:label="note-139-02a" xlink:href="note-139-02"/> N, Eſt autem quadrati ad quadratum proportio duplicata proporionis late-<lb/> <anchor type="note" xlink:label="note-139-03a" xlink:href="note-139-03"/> rum homologorum, erit quoque circulus O P, ad circulum maximũ in ſphæ <lb/>ra N, in proportione duplicata proportionis diametri O P, ad diametrum cir <lb/>culi maximi in ſphæra N. </s> <s xml:id="echoid-s4970" xml:space="preserve">Cum igitur diametri ponantur habere proportionẽ <lb/>duplam, habebunt circuli proportionem quadruplam: </s> <s xml:id="echoid-s4971" xml:space="preserve">quadrupla enim propor <lb/>tio duplicata eſt proportionis duplæ, ut in his numeris apparet. </s> <s xml:id="echoid-s4972" xml:space="preserve">1. </s> <s xml:id="echoid-s4973" xml:space="preserve">2. </s> <s xml:id="echoid-s4974" xml:space="preserve">4. </s> <s xml:id="echoid-s4975" xml:space="preserve">erit cir-<lb/>cul us O P, æqualis ſuperficiei ſphæræ N. </s> <s xml:id="echoid-s4976" xml:space="preserve">Accipiatur rurſus circulus S T, æqua <lb/>liscirculo O P. </s> <s xml:id="echoid-s4977" xml:space="preserve">Statuatur deinde ſupra circulum S T, conus rectus S T V, axẽ <pb o="104" file="140" n="141" rhead="Comment. in I. Cap. Sphæræ"/> V X, æqualem habens ſemidiametro ſphæræ N: </s> <s xml:id="echoid-s4978" xml:space="preserve">Item ſupra circulum O P, al-<lb/>ter conus O P Q, conſtruatur habens axem Q R, ęqualem ſemidiametro ſphæ <lb/>rę A B C D; </s> <s xml:id="echoid-s4979" xml:space="preserve">eritq́ue maior altitudo coni S T V, quàm coni O P Q; </s> <s xml:id="echoid-s4980" xml:space="preserve">at baſes ęqua <lb/>les erunt. </s> <s xml:id="echoid-s4981" xml:space="preserve">Quare conus S T V, maior erit cono O P Q, propterea quòd coni <lb/>æqualium baſium eam inter ſe habent proportionem, quàm altitudines, <lb/>Quoniam uero ſphæra N, quadrupla eſt eius coni, qui baſim habet æqualẽ ma <lb/> <anchor type="note" xlink:label="note-140-01a" xlink:href="note-140-01"/> ximo in ſphæra N, circulo, & </s> <s xml:id="echoid-s4982" xml:space="preserve">altitudinem æqualem ſemidiametro ſphæræ N, <lb/> <anchor type="figure" xlink:label="fig-140-01a" xlink:href="fig-140-01"/> ut demonſtrauit Archimedes lib. </s> <s xml:id="echoid-s4983" xml:space="preserve">1. </s> <s xml:id="echoid-s4984" xml:space="preserve">de ſphæra & </s> <s xml:id="echoid-s4985" xml:space="preserve">cylindro propoſ. </s> <s xml:id="echoid-s4986" xml:space="preserve">32. </s> <s xml:id="echoid-s4987" xml:space="preserve">Huius au <lb/>tem eiu ſdem coni quadruplus eſt conus S T V, eo quòd coni eandem haben-<lb/>tes alt itudinem proportionem habent, quam baſes; </s> <s xml:id="echoid-s4988" xml:space="preserve">erit conus S T V, ſphęræ <lb/> <anchor type="note" xlink:label="note-140-02a" xlink:href="note-140-02"/> N, æqualis. </s> <s xml:id="echoid-s4989" xml:space="preserve">Eodem pacto, quia baſis coni O P Q, æqualis eſt ambitui corporis <lb/>E F G H I K L M, quia & </s> <s xml:id="echoid-s4990" xml:space="preserve">ęqualis ſuperſiciei ſphæræ N, quæ corpori illi iſo-<lb/>perim etra eſt: </s> <s xml:id="echoid-s4991" xml:space="preserve">altitudo uero æqualis ſemidiametro ſphæræ A B C D, erit ſo-<lb/>lido E F G H I K L M, æqualis conus O P Q, per ea, quæ Archimedes libro <lb/>1. </s> <s xml:id="echoid-s4992" xml:space="preserve">de ſphæra, & </s> <s xml:id="echoid-s4993" xml:space="preserve">cylindro propoſ. </s> <s xml:id="echoid-s4994" xml:space="preserve">29. </s> <s xml:id="echoid-s4995" xml:space="preserve">demonſtrauit. </s> <s xml:id="echoid-s4996" xml:space="preserve">Quamobrem & </s> <s xml:id="echoid-s4997" xml:space="preserve">ſphæra N, <lb/>mai or erit ſolido E F G H I K L M, conicis ſuperficiebus contento. </s> <s xml:id="echoid-s4998" xml:space="preserve">Sphæra igi-<lb/>tur omnibus corporibus ſibi iſoperimetris, & </s> <s xml:id="echoid-s4999" xml:space="preserve">circa alias ſphæras circumſcripti <lb/>bilibus, &</s> <s xml:id="echoid-s5000" xml:space="preserve">c. </s> <s xml:id="echoid-s5001" xml:space="preserve">maior eſt, quod demonſtrandum erat.</s> <s xml:id="echoid-s5002" xml:space="preserve"/> </p> <div xml:id="echoid-div272" type="float" level="2" n="1"> <note position="right" xlink:label="note-139-01" xlink:href="note-139-01a" xml:space="preserve">quę conici@ <lb/>upe@ficie-<lb/>bus conti-<lb/>@entur.</note> <figure xlink:label="fig-139-01" xlink:href="fig-139-01a"> <image file="139-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/139-01"/> </figure> <note position="right" xlink:label="note-139-02" xlink:href="note-139-02a" xml:space="preserve">2. duod.</note> <note position="right" xlink:label="note-139-03" xlink:href="note-139-03a" xml:space="preserve">20. ſexti.</note> <note position="left" xlink:label="note-140-01" xlink:href="note-140-01a" xml:space="preserve">14. duod.</note> <figure xlink:label="fig-140-01" xlink:href="fig-140-01a"> <image file="140-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/140-01"/> </figure> <note position="left" xlink:label="note-140-02" xlink:href="note-140-02a" xml:space="preserve">11. duod.</note> </div> <p> <s xml:id="echoid-s5003" xml:space="preserve"><emph style="sc">Haec</emph> ſunt, quæ mihi dicenda uidebantur de figuris Iſoperimetris. </s> <s xml:id="echoid-s5004" xml:space="preserve">Copio-<lb/>ſiorem autem tractationem eadem de re, Deo volente, alio in loco edemus <lb/>Nunc ad propoſitam ſphærę expoſitionem reuertamur.</s> <s xml:id="echoid-s5005" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s5006" xml:space="preserve"><emph style="sc">Necessitas</emph>, quoniam ſi mundus eſset alterius formæ, quàm ro-<lb/> <anchor type="note" xlink:label="note-140-03a" xlink:href="note-140-03"/> tundæ, ſcilicet trilateræ, uel quadrilateræ, uel multilateræ, ſequerentur <lb/>duo impoſſibilia, ſcilicet quòd aliquis locus eſset uacuus, & </s> <s xml:id="echoid-s5007" xml:space="preserve">corpus ſine lo- <pb o="105" file="141" n="142" rhead="Ioan. de Sacro Boſco."/> co quorum utrumque eſt falſum, ſicut patet in angulis eleuatis & </s> <s xml:id="echoid-s5008" xml:space="preserve">circumu@ <lb/>lutis.</s> <s xml:id="echoid-s5009" xml:space="preserve"/> </p> <div xml:id="echoid-div273" type="float" level="2" n="2"> <note position="left" xlink:label="note-140-03" xlink:href="note-140-03a" xml:space="preserve">Cælum eſſe <lb/>ro tundum <lb/>pro batur à <lb/>neceſſitate.</note> </div> </div> <div xml:id="echoid-div275" type="section" level="1" n="94"> <head xml:id="echoid-head98" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s5010" xml:space="preserve"><emph style="sc">Anecessitate</emph> ita confirmat cœlum eſſe rotundum. </s> <s xml:id="echoid-s5011" xml:space="preserve">Cœlum, vt <lb/>oſtenſum eſt, mouetur; </s> <s xml:id="echoid-s5012" xml:space="preserve">ſi igitur non eſſet figuræ rotundæ, ſed multilateræ, tri-<lb/>laterę uidelicet, aut quadrilaterę, &</s> <s xml:id="echoid-s5013" xml:space="preserve">c. </s> <s xml:id="echoid-s5014" xml:space="preserve">(nomine trilateræ figurę intellige pyra-<lb/>mida lem, loco vero quadrilaterę cubicam) ſequerentur duo impoſſibilia: </s> <s xml:id="echoid-s5015" xml:space="preserve">unũ <lb/>quòd eſſet aliquis locus ſine corpore, alterum, quòd daretur corpus ſine loco, <lb/>quorum utrumque pugnat cum rerum natura. </s> <s xml:id="echoid-s5016" xml:space="preserve">Neceſſe eſt igitur cœlum eẽ ro <lb/>tundum. </s> <s xml:id="echoid-s5017" xml:space="preserve">Conſecutio manifeſta eſt ex eleuatione, & </s> <s xml:id="echoid-s5018" xml:space="preserve">depreſſione angulorum fi-<lb/>gurę cuiuſcunque multilateræ, ſi circa centrum moueretur.</s> <s xml:id="echoid-s5019" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5020" xml:space="preserve"><emph style="sc">Haec</emph> ratio ſolum concludit, cęlum eſſe aliquo modo rotundum, hoc eſt, <lb/>non angulare, propter illa inconuenientio, ad quæ deducit auctor, ſi eſſet figu <lb/>ræ angularis: </s> <s xml:id="echoid-s5021" xml:space="preserve">non tamen ſimpliciter ex c<unsure/>a colligitur, cælum eſſe ſphęricum. </s> <s xml:id="echoid-s5022" xml:space="preserve">Di <lb/>ceret enim quiſpiam, ipſum eſſe figurę oualis, ſeu lenticularis, conicę, uel cylin <lb/>dricæ. </s> <s xml:id="echoid-s5023" xml:space="preserve">Nam ſi ponatur cælum eſſe alicuius harum formarum, omnia illa abſur-<lb/>da facili negotio uitabuntur; </s> <s xml:id="echoid-s5024" xml:space="preserve">quoniam hoc conceſſo, poterit cælum ita circa <lb/>axem ſuum moueri, ut continue partes partibus in eiſdem ſuccedant locis, quẽ <lb/>admodum accidere uidemus in corpore ſphærico ſeu globoſo. </s> <s xml:id="echoid-s5025" xml:space="preserve">Attamen di-<lb/> <anchor type="note" xlink:label="note-141-01a" xlink:href="note-141-01"/> cendum eſt, rationem prædictam a neceſſitate concludere cęlum eſſe perfectiſ <lb/>ſime ſphæricum, & </s> <s xml:id="echoid-s5026" xml:space="preserve">nullo modo habere poſſe alteram figuram. </s> <s xml:id="echoid-s5027" xml:space="preserve">Cæli etenim in <lb/>feriores, ut ſupra fuit oſtenſum, mouentur motu oppoſito motui primi mobi-<lb/>lis ſuper diuerſos polos a polis primi mobilis: </s> <s xml:id="echoid-s5028" xml:space="preserve">non poſſent autem hoc motu <lb/>moueri, ſi ſphęrici non eſ@ent, niſi fieret penetratio corporum, uel ſciſſio cœlo-<lb/>rum, ut manifeſtum eſt rẽ accuratius conſideranti; </s> <s xml:id="echoid-s5029" xml:space="preserve">quorum vtrũq. </s> <s xml:id="echoid-s5030" xml:space="preserve">fieri nequit. <lb/></s> <s xml:id="echoid-s5031" xml:space="preserve">Item conſequerentur eadem abſurda allata ab auctore contra figuram angula-<lb/>rem. </s> <s xml:id="echoid-s5032" xml:space="preserve">Sit enim oualis, & </s> <s xml:id="echoid-s5033" xml:space="preserve">ſuperior or-<lb/> <anchor type="figure" xlink:label="fig-141-01a" xlink:href="fig-141-01"/> bis, ſi fieri poteſt, A B C, cuius axis <lb/>A D C, poli A, & </s> <s xml:id="echoid-s5034" xml:space="preserve">C, inferior uero <lb/>itidem oualis orbis ſit E H F G E, <lb/>qui quoniam cæli ſecundum omnes <lb/>philoſophos ſunt uniformes, quoad <lb/>craſſitiem & </s> <s xml:id="echoid-s5035" xml:space="preserve">ſpiſſitudinem, ſituabi-<lb/>tur ſecundum ſitum, & </s> <s xml:id="echoid-s5036" xml:space="preserve">lõgitudinem <lb/>ſuperioris orbis, ita ut longitudines <lb/>eorum habeant eandem diametrum, <lb/>vt hic uides. </s> <s xml:id="echoid-s5037" xml:space="preserve">Sit iam axis inferioris <lb/>orbis G D H, circa quem ab occaſu in ortum mouetur, iam manifeſtum eſt, ad <lb/>motum in ferioris orbis ſuper axe G D H, circumſtans corpus cæleſte diſcindi, <lb/>atque penetrari, traducetur enim pars E, circa polum G, in I, punctum, & </s> <s xml:id="echoid-s5038" xml:space="preserve">pars <lb/>F, circa polum H, in punctum K, quare relinquentur partes E, & </s> <s xml:id="echoid-s5039" xml:space="preserve">F, uacuæ, ut <lb/>in propoſita figura cernis.</s> <s xml:id="echoid-s5040" xml:space="preserve"/> </p> <div xml:id="echoid-div275" type="float" level="2" n="1"> <note position="right" xlink:label="note-141-01" xlink:href="note-141-01a" xml:space="preserve">Confirma -<lb/>tur ratio a <lb/>neceſſitate@.</note> <figure xlink:label="fig-141-01" xlink:href="fig-141-01a"> <image file="141-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/141-01"/> </figure> </div> <p> <s xml:id="echoid-s5041" xml:space="preserve"><emph style="sc">Possvmvs</emph> quoq. </s> <s xml:id="echoid-s5042" xml:space="preserve">cum Ptol. </s> <s xml:id="echoid-s5043" xml:space="preserve">in Dict. </s> <s xml:id="echoid-s5044" xml:space="preserve">1. </s> <s xml:id="echoid-s5045" xml:space="preserve">confirmare, cœlum eſſe ſphęri-<lb/> <anchor type="note" xlink:label="note-141-02a" xlink:href="note-141-02"/> cum, ex eo, quòd uidemus omnes ſtellas fixas ſemper in eadem diſtantia, & </s> <s xml:id="echoid-s5046" xml:space="preserve">pro <lb/>pinquitate ad nos moueri, & </s> <s xml:id="echoid-s5047" xml:space="preserve">eas, quæ ſunt propinquiores polis, deſcribere cir <lb/>culos minores, illas uero, quæ ſunt remotiores, proportionabiliter maiores:</s> <s xml:id="echoid-s5048" xml:space="preserve"> <pb o="106" file="142" n="143" rhead="Comment. in I. Cap. Sphæræ"/> quod quidem nullo pacto fieret, ſi cælum non eſſet rotundum, at que ſphæri-<lb/>cum. </s> <s xml:id="echoid-s5049" xml:space="preserve">Solum enim partes omnes corporis ſphærici à centro æqualiter remo-<lb/>uentur. </s> <s xml:id="echoid-s5050" xml:space="preserve">Vnde ſi cœlum eſſet alterius figuræ, quædam partes magis à nobis di <lb/>ftarent, quędam uero minus, proptereaq́ue non omnes ſtellæ in eadem a nobis <lb/>diſtantia cernerentur; </s> <s xml:id="echoid-s5051" xml:space="preserve">quod pugnat cum ſeuſu, & </s> <s xml:id="echoid-s5052" xml:space="preserve">experientia. </s> <s xml:id="echoid-s5053" xml:space="preserve">Rurſus omnia <lb/>inſtrumenta Aſtronomorum conueniunt cum motibus cæleſtium corporum, <lb/>non ſecus, ac ſi eſſent perſect ſſime ſphærica, quod quidem manifeſtiſſimũ eſt <lb/>in altitudinibus aſtrorum ſupra Horizontem, quę, antequam ad Meridianum <lb/>aſtra perueniunt, in ea proportione augentur, & </s> <s xml:id="echoid-s5054" xml:space="preserve">poſtquam Meridianum per-<lb/>tranſierunt, decreſcunt, quam in ſolo corpore ſphærico aſſignare poſſumus. <lb/></s> <s xml:id="echoid-s5055" xml:space="preserve">Idemq́ue oſtendunt omnes aliæ apparentiæ, maxime horologia ſolaria, quæ <lb/>conſtruuntur, poſito cœlo ſphærico. </s> <s xml:id="echoid-s5056" xml:space="preserve">Denique uidemus duas ſtellas in eodem <lb/>circulo longitudinis per polos mundi ducto exiſtentes, quò una auſtralior eſt, <lb/>eo etiam minorem habere altitudinem meridianam, ita ut tot gradibus altitu <lb/>dines meridianæ inter ſe differant, quot gradibus una ſtella ab altera diſtare <lb/>deprehenditur per inſtrumenta ad hanc rem confecta. </s> <s xml:id="echoid-s5057" xml:space="preserve">Atq. </s> <s xml:id="echoid-s5058" xml:space="preserve">hæc ratio apud me <lb/>magnum robur habet; </s> <s xml:id="echoid-s5059" xml:space="preserve">quandoquidem omnia inſtrumenta rotunda ſunt fabri-<lb/>cata, ut rotunditatem cęli quodammodo imitentur. </s> <s xml:id="echoid-s5060" xml:space="preserve">Vnde ſi cęlum non eſſet <lb/>ſphæricum, fieri non poſſet, ut ea inſtrumenta quoquo uerſus collocata appa-<lb/>rentijs cœleſtibus congruerent, quoad altitudines, & </s> <s xml:id="echoid-s5061" xml:space="preserve">diſtantias aſtrorum inter <lb/>ſe. </s> <s xml:id="echoid-s5062" xml:space="preserve">Cum ergo ea congruere cernamus, (id quod maxime in ſphæra materiali, <lb/>globo cæleſti, aſtrolabio, & </s> <s xml:id="echoid-s5063" xml:space="preserve">quadrante obſeruatum eſt) merito cælum eſſe per-<lb/>fecte ſphæricum colligemus: </s> <s xml:id="echoid-s5064" xml:space="preserve">aliàs neque inſtrumenta Aſtronomorum, nequ@ <lb/>apparentiæ locum haberent.</s> <s xml:id="echoid-s5065" xml:space="preserve"/> </p> <div xml:id="echoid-div276" type="float" level="2" n="2"> <note position="right" xlink:label="note-141-02" xlink:href="note-141-02a" xml:space="preserve">Alia ratio <lb/>probans cæ <lb/>lum eſſe ro <lb/>tundum, a@ <lb/>ſphęricum.</note> </div> <p style="it"> <s xml:id="echoid-s5066" xml:space="preserve"><emph style="sc">Item</emph> ſicut dicit Alphraganus, ſi cælum eßet planum, aliqua pars cæ <lb/> <anchor type="note" xlink:label="note-142-01a" xlink:href="note-142-01"/> li eſſet nobis propinquior alia, illa ſcilicet, quæ eſſet ſupra caput noſtrum. <lb/></s> <s xml:id="echoid-s5067" xml:space="preserve">Igitur ſtella ibi exiſtens eſſet nobis propinquior, quàm in ortu, uel occaſu, <lb/>ſed quæ nobis propinquiora ſunt, maiora uidentur, ergo Sol uel alia ſtella <lb/>exiſtens in medio cęli maior deberet uideri, quàm in ortu exiſtens, uel in oc-<lb/>caſu, cuius contrarium uidemus contingere. </s> <s xml:id="echoid-s5068" xml:space="preserve">Maior enim apparet Sol, uel <lb/>alia ſtella exiſtens in oriente, uel occidente, quàm in medio cęli.</s> <s xml:id="echoid-s5069" xml:space="preserve"/> </p> <div xml:id="echoid-div277" type="float" level="2" n="3"> <note position="left" xlink:label="note-142-01" xlink:href="note-142-01a" xml:space="preserve">Cælum nõ <lb/>eſſe planũ.</note> </div> </div> <div xml:id="echoid-div279" type="section" level="1" n="95"> <head xml:id="echoid-head99" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s5070" xml:space="preserve"><emph style="sc">Confirmat</emph> auctor hanc eandem conclufionem ratione Alphraga-<lb/>ni, quam ponit in differentia 2. </s> <s xml:id="echoid-s5071" xml:space="preserve">hoc modo. </s> <s xml:id="echoid-s5072" xml:space="preserve">Si cælum non eſſet rotundum, ſed <lb/>planum ſiue extenſum, tunc illa pars cæli, quæ capiti noſtro imminet, eſſet no <lb/>bis propinquior: </s> <s xml:id="echoid-s5073" xml:space="preserve">Quare Sol, uel ſtella aliqua ibi exiſtens maior nobis appare-<lb/>re, quàm alibi, cum propinquiora maiora cernantur, quàm remotiora: </s> <s xml:id="echoid-s5074" xml:space="preserve">cuius <lb/>tamen contrarium experimur. </s> <s xml:id="echoid-s5075" xml:space="preserve">Apparet namque Sol, & </s> <s xml:id="echoid-s5076" xml:space="preserve">Luna maior iuxta Ho-<lb/>rizontem, quàm ſupra uerticem capitis.</s> <s xml:id="echoid-s5077" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5078" xml:space="preserve"><emph style="sc">Caetervm</emph> hæc Alphragani ratio, ſi ſumatur, quemadmodum pro-<lb/>ponitur, nullius prorſus eſt momenti. </s> <s xml:id="echoid-s5079" xml:space="preserve">Cum enim, ut ſupra oſtenſum eſt, ſtellæ <lb/>non per ſeſe, ſed ad motum cæli, in quo exiſtunt, moueantur, quis non uidet, <pb o="107" file="143" n="144" rhead="Ioan. de Sacro Boſco."/> cuiuſcunq. </s> <s xml:id="echoid-s5080" xml:space="preserve">figurę ponatur cælum, quamlibet ſtellam ſemper ęquè appropin-<lb/>quare terrę, cum ad mot um cæli deſcribat circulum circa terram ab ea æqua-<lb/>liter remotum undiq;</s> <s xml:id="echoid-s5081" xml:space="preserve">? Quod in hac figura manifeſte perſpicitur, in qua cęlum <lb/>ponitur angularis figuræ: </s> <s xml:id="echoid-s5082" xml:space="preserve">Si enim cælum circa terram moueatur, de ſcribet quę <lb/>libet ſtella ſuum circulum circa ipſam, nempe ſtella A, circulum exteriorem, <lb/>& </s> <s xml:id="echoid-s5083" xml:space="preserve">ſtella B, circulum interiorem. </s> <s xml:id="echoid-s5084" xml:space="preserve">Quòd ſi cęlum quieſceret, ac ſtellæ per ſeſe <lb/>mouerentur, haberet maximum robur, & </s> <s xml:id="echoid-s5085" xml:space="preserve">uim argumentum, ut in eadem <lb/>figura cerni poteſt. </s> <s xml:id="echoid-s5086" xml:space="preserve">Veruntamen hoc idem <lb/> <anchor type="figure" xlink:label="fig-143-01a" xlink:href="fig-143-01"/> argumentũ poterit melius proponi in hũc <lb/>modũ. </s> <s xml:id="echoid-s5087" xml:space="preserve">Si cęlum eſſet planum, uel alterius <lb/>cuiuſcunq. </s> <s xml:id="echoid-s5088" xml:space="preserve">figuræ, quamuis quęlibet ſtella <lb/>circa terram propriũ deſcriberet circulũ, <lb/>& </s> <s xml:id="echoid-s5089" xml:space="preserve">idcirco ſemper ęqualiter diſtaret a terra, <lb/>tamẽ non omnes ſtellæ fixæ diſtantia æqua <lb/>li ab ea recederent, ſed quædã propinquio <lb/>res, quædam uero remotiores apparerent; <lb/></s> <s xml:id="echoid-s5090" xml:space="preserve">quemadmodum in ſupra poſita figura ſtel-<lb/>la A, conſtituta in angulo cæli maiorẽ hẽt <lb/>diſtantiam, quàm ſtella B, non in angulo cę <lb/>li collocata; </s> <s xml:id="echoid-s5091" xml:space="preserve">quod tamen eſt cõtra experiẽ-<lb/>tiã. </s> <s xml:id="echoid-s5092" xml:space="preserve">Præterea, ſi omnes cæli eſſent figuræ la <lb/>teratæ, & </s> <s xml:id="echoid-s5093" xml:space="preserve">non ſphęricæ, non poſſent inferiores cæli deferre planetas, & </s> <s xml:id="echoid-s5094" xml:space="preserve">ſtellas <lb/>fixas ab occidente in orientem ex uno ſigno in aliud, niſi detur ſciſſio, penetra <lb/>tioq́. </s> <s xml:id="echoid-s5095" xml:space="preserve">corporum cæleſtium; </s> <s xml:id="echoid-s5096" xml:space="preserve">Quod cum ſit abſurdum, concedendum erit, cęlum <lb/>eſſe ſphæricum. </s> <s xml:id="echoid-s5097" xml:space="preserve">Atque hæc ratio probat quoque, cælum non eſſe ouale, nec <lb/>lenticulare, &</s> <s xml:id="echoid-s5098" xml:space="preserve">c.</s> <s xml:id="echoid-s5099" xml:space="preserve">ut paulo ſupra etiam oſtendimus.</s> <s xml:id="echoid-s5100" xml:space="preserve"/> </p> <div xml:id="echoid-div279" type="float" level="2" n="1"> <figure xlink:label="fig-143-01" xlink:href="fig-143-01a"> <image file="143-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/143-01"/> </figure> </div> <p> <s xml:id="echoid-s5101" xml:space="preserve"><emph style="sc">Tametsi</emph> autem ſenſus noſter iudicat, & </s> <s xml:id="echoid-s5102" xml:space="preserve">ita communiter dici ſolet a <lb/> <anchor type="note" xlink:label="note-143-01a" xlink:href="note-143-01"/> philoſophis, & </s> <s xml:id="echoid-s5103" xml:space="preserve">Aſtronomis, cælum undiq. </s> <s xml:id="echoid-s5104" xml:space="preserve">æqualiter diſtare a nobis in ſuperfi-<lb/>cie terræ exiſtentibus; </s> <s xml:id="echoid-s5105" xml:space="preserve">ſi tamen diligentius rem introſpiciamus, deprehende-<lb/>mus ipſum duntaxat a centro terræ, & </s> <s xml:id="echoid-s5106" xml:space="preserve">non a quouis puncto in eius ſuperficie <lb/>aſſignato æqualiter recedere. </s> <s xml:id="echoid-s5107" xml:space="preserve">Pars enim orientalis, occidentalis, ſeptentriona-<lb/>lis, meridionalis, & </s> <s xml:id="echoid-s5108" xml:space="preserve">denique omnes partes prope Horizontem remotiores a no <lb/>bis ſunt, quàm pars ſupra uerticem noſtrum poſita, & </s> <s xml:id="echoid-s5109" xml:space="preserve">multo magis remota <lb/>erit ea pars cæli, quæ vertici noſtro opponitur. </s> <s xml:id="echoid-s5110" xml:space="preserve">Cauſa uero huius rei eſt, quia <lb/>inter nos & </s> <s xml:id="echoid-s5111" xml:space="preserve">uerticem capitis interijciuntur duntaxat duo elementa, aer uide <lb/>licet, & </s> <s xml:id="echoid-s5112" xml:space="preserve">ignis: </s> <s xml:id="echoid-s5113" xml:space="preserve">at inter nos, & </s> <s xml:id="echoid-s5114" xml:space="preserve">alias partes cæli iuxta Horizontem, præter hæc <lb/>duo elementa, eſt quoque intermedia ſemidiameter terræ: </s> <s xml:id="echoid-s5115" xml:space="preserve">atque inter nos & </s> <s xml:id="echoid-s5116" xml:space="preserve"><lb/>partem cæli uertici noſtro oppoſitam, præter eadem duo elementa, intercepta <lb/>eſt tota diameter terrę. </s> <s xml:id="echoid-s5117" xml:space="preserve">Si igitur Geometrice, & </s> <s xml:id="echoid-s5118" xml:space="preserve">præciſe loqui uelimus, non <lb/>æqualiter poſſumus diſtare ab omnibus partibus cæli. </s> <s xml:id="echoid-s5119" xml:space="preserve">Veruntamen quoniam <lb/>ſemidiameter terræ inſenſibilis eſt quantitatis reſpectu diſtantiæ cœli a cẽtro <lb/>terræ, non poteſt ſenſibiliter magis diſtare a nobis cælum iuxta Horizontẽ, <lb/>quàm iuxta uerticem capitis. </s> <s xml:id="echoid-s5120" xml:space="preserve">Quemadmodum ſi quis rem aliquam uideret 20. <lb/></s> <s xml:id="echoid-s5121" xml:space="preserve">aut 30. </s> <s xml:id="echoid-s5122" xml:space="preserve">milliarijs diſtantem, ſi propius accederet 6. </s> <s xml:id="echoid-s5123" xml:space="preserve">aut 8. </s> <s xml:id="echoid-s5124" xml:space="preserve">paſſibus eiuſdem ad-<lb/>huc quantitatis appareret ipſi eadem res, & </s> <s xml:id="echoid-s5125" xml:space="preserve">non maior, neq; </s> <s xml:id="echoid-s5126" xml:space="preserve">minor, quantum <lb/>ad ſenſum, eo quòd tam pauci paſſus inſenſibilem fere habent proportionem <lb/>ad 30000. </s> <s xml:id="echoid-s5127" xml:space="preserve">paſſum, cum tamen proportio hæc maior ſit, quàm proportio ſemi-<lb/>diametri terræ ad diſtantiam fitmamenti, quæ ſecundum Alphraganum, ut ad <pb o="108" file="144" n="145" rhead="Comment. in I. Cap. Sphæræ"/> finem huius cap. </s> <s xml:id="echoid-s5128" xml:space="preserve">dicemus, continet terræ ſemidiametros fere 45225. </s> <s xml:id="echoid-s5129" xml:space="preserve">Quare <lb/>Aſtronomi, ac philoſophi ſequentes iudicium uiſus merito aſſerunt, cælum ſe-<lb/>cundum omnes ſui partes æqualiter a nobis diſtare, quamuis ſecundum ratio-<lb/>nem, & </s> <s xml:id="echoid-s5130" xml:space="preserve">ueritatem res non ita ſe habeat. </s> <s xml:id="echoid-s5131" xml:space="preserve">Ex his manifeſtum eſt, unam, eandemq́. <lb/></s> <s xml:id="echoid-s5132" xml:space="preserve">ſtellam iuxta Horizontem tempore ſereno, ſecluſis omnibus uaporibus, & </s> <s xml:id="echoid-s5133" xml:space="preserve">ex-<lb/>halationibus, in eadem nobis magnitudine apparere, in qua iuxta meridiem à <lb/>nobis cernitur; </s> <s xml:id="echoid-s5134" xml:space="preserve">licet ibi magis à nobis diſtet, hic uero minus, quoniam uideli-<lb/>cet inter maiorem illam diſtantiam, & </s> <s xml:id="echoid-s5135" xml:space="preserve">hanc minorem non eſt tanta differen-<lb/>tia, quæ ſub ſenſum cadere poſſit. </s> <s xml:id="echoid-s5136" xml:space="preserve">Quod ſi quis obijciat, ſenſui primo aſpectu <lb/> <anchor type="note" xlink:label="note-144-01a" xlink:href="note-144-01"/> apparere, remotius eſſe cœlum iuxta Horizontem, quam ſupra uerticem capi-<lb/>tis, quare falſum eſſe, hanc diuerſitatem eſſe inſenſibilem: </s> <s xml:id="echoid-s5137" xml:space="preserve">Reſpondendum eſt, <lb/>uerum id quidem eſſe, ſed non ideo concludi, hanc diuerſitatem eſſe ſenſibi-<lb/>lem, ſiue notabilem. </s> <s xml:id="echoid-s5138" xml:space="preserve">Decipitur enim ſenſus, vt demonſtrant Per ſpectiui, qui per <lb/>interiacentia corpora interuallum quoduis iudicare, atque metiri ſolet; </s> <s xml:id="echoid-s5139" xml:space="preserve">at que <lb/>ita, quia inter nos, & </s> <s xml:id="echoid-s5140" xml:space="preserve">cælum ſupra uerticem nullum uidet interiectum corpus, <lb/>at ex parte quacunque Horizontis totam molem terrenam conſpicit porre-<lb/>ctam, iudicat illam diſtantiam maiorem eſſe multo, cum re ipſa tamen inſenſi-<lb/>biliter maior ſit, ita ut per inſtrumenta æqualiter iudicetur diſtare cœl um a no <lb/>bis. </s> <s xml:id="echoid-s5141" xml:space="preserve">Immo hanc ob cauſam iudicat quoque ſenſus, cælum iuxta Horizontem <lb/>contingere quodammodo ipſam terram, quia nimirum non percipit aliud cor <lb/>pus inter cœlum ac terram. </s> <s xml:id="echoid-s5142" xml:space="preserve">Idem accidere cernimus in cacuminibus montium. <lb/></s> <s xml:id="echoid-s5143" xml:space="preserve">Videntur enim quandoque duo cacumina montium eſſe omnino coniuncta, <lb/>eo quòd non uidemus alia corpora interiecta, cum tamen longiſſimo interual <lb/>lo inter ſe diſtent.</s> <s xml:id="echoid-s5144" xml:space="preserve"/> </p> <div xml:id="echoid-div280" type="float" level="2" n="2"> <note position="right" xlink:label="note-143-01" xlink:href="note-143-01a" xml:space="preserve">Cœlum à<unsure/> <lb/>centro ter-<lb/>ræ, non au-<lb/>tem à quo <lb/>uis puncto <lb/>in ſuperfi-<lb/>cie terræ aſ <lb/>ſignato æ-<lb/>qualiter di <lb/>ſtat, ſi Geo-<lb/>metrice lo <lb/>quamur, <lb/>ſed ſo lum, <lb/>quoad ſen-<lb/>ſum.</note> <note position="left" xlink:label="note-144-01" xlink:href="note-144-01a" xml:space="preserve">Cur cęlum <lb/>appareat lõ <lb/>gius diſtare <lb/>a nobis iux <lb/>ta Horizon <lb/>tem, quam <lb/>prope uerti <lb/>cem capitis</note> </div> <p style="it"> <s xml:id="echoid-s5145" xml:space="preserve"><emph style="sc">Sed</emph> cum rei ueritas ita non ſit, huius apparentiæ cauſa eſt, quòd in tem <lb/> <anchor type="note" xlink:label="note-144-02a" xlink:href="note-144-02"/> pore hyemali, uel pluuiali uapores quidam aſcendunt intra aſpectum no-<lb/>ſtrum, & </s> <s xml:id="echoid-s5146" xml:space="preserve">Solem, uel aliam ſtellam; </s> <s xml:id="echoid-s5147" xml:space="preserve">& </s> <s xml:id="echoid-s5148" xml:space="preserve">cum illi uapores ſint corpus diapha-<lb/>num, diſgregant radios noſtros uiſuales, ita quod non comprehendunt rem in <lb/>ſua naturali, & </s> <s xml:id="echoid-s5149" xml:space="preserve">uera quantitate, ſicut patet in denario proiecto in profundo <lb/>aquæ limpidæ, qui propter ſimilem diſgregationem radiorum apparet maio <lb/>ris, quàm ſuæ ueræ quantitatis.</s> <s xml:id="echoid-s5150" xml:space="preserve"/> </p> <div xml:id="echoid-div281" type="float" level="2" n="3"> <note position="left" xlink:label="note-144-02" xlink:href="note-144-02a" xml:space="preserve">Cur Sol & <lb/>ſtellæ maio <lb/>res appa-<lb/>reant iuxta <lb/>Horizontẽ, <lb/>quàm in <lb/>medio cęli.</note> </div> </div> <div xml:id="echoid-div283" type="section" level="1" n="96"> <head xml:id="echoid-head100" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s5151" xml:space="preserve"><emph style="sc">Dixerat</emph> in ratione Alphragani, Solem & </s> <s xml:id="echoid-s5152" xml:space="preserve">Lunam, aut quamcunque <lb/>aliam ſtellam maiorem apparere iuxta Horizontem, quàm ſupra uerticem ca-<lb/>pitis: </s> <s xml:id="echoid-s5153" xml:space="preserve">poſſet aliquis hinc inferre, cœlum non eſſe rotundum quandoquidem nõ <lb/>æqualiter à terra undique diſtat. </s> <s xml:id="echoid-s5154" xml:space="preserve">Vbi enim ſtella maior apparet, ibi cælum pro <lb/>pinquius exiſtet; </s> <s xml:id="echoid-s5155" xml:space="preserve">ubi uero minor, ibi remotius. </s> <s xml:id="echoid-s5156" xml:space="preserve">Idcirco occurrit tacitæ huic <lb/>obiectioni, dicens, cauſam cur Sol uel Luna, aut alia ſtella maior appareat <lb/>in ortu & </s> <s xml:id="echoid-s5157" xml:space="preserve">occaſu, quàm in medio cœli, ſeu uertice, non eſſe, quòd magis ibi, <lb/>quàm hic diſtet a nobis, ſaltem ſenſibiliter; </s> <s xml:id="echoid-s5158" xml:space="preserve">ſed eſſe uapores à terra eleuatos, <lb/>qui interponuntur inter Solem, uel quodlibet aliud aſtrum, & </s> <s xml:id="echoid-s5159" xml:space="preserve">uiſum noſtrum. <lb/></s> <s xml:id="echoid-s5160" xml:space="preserve">Vnde fit, ut uapores illi, cum ſint iuxta Horizontem ſpiſſiores, craſſioresq́ue, <lb/>uarient noſtros radios uiſuales, & </s> <s xml:id="echoid-s5161" xml:space="preserve">propterea minime cernamus rem in ſua pro <pb o="109" file="145" n="146" rhead="Ioan. de Sacro Boſco."/> pria quantitate. </s> <s xml:id="echoid-s5162" xml:space="preserve">Quod quidem euidenter pater, ut ait, in denario aliquo in fun <lb/>do aquæ perlucidæ, atque claræ.</s> <s xml:id="echoid-s5163" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5164" xml:space="preserve"><emph style="sc">Hanc</emph> eandem cauſam affert Alphraganus differt. </s> <s xml:id="echoid-s5165" xml:space="preserve">2. </s> <s xml:id="echoid-s5166" xml:space="preserve">eamq́. </s> <s xml:id="echoid-s5167" xml:space="preserve">demonſtrant <lb/>omnes Perſpectui. </s> <s xml:id="echoid-s5168" xml:space="preserve">Nam ex illa variatione radiorum uiſualium res quæuis pro <lb/>pinquior apparet, unde & </s> <s xml:id="echoid-s5169" xml:space="preserve">maior. </s> <s xml:id="echoid-s5170" xml:space="preserve">Eadem de cauſa contingit rem aliquam uide <lb/>ri per radios aliquando refractos, quæ alias per directos ad oculum noſtrum <lb/>peruenire nequaquam poteſt. </s> <s xml:id="echoid-s5171" xml:space="preserve">Exemplum clariſſimum habemus in denario ali-<lb/>quo proiecto in fundo alicuius uaſis uacui mediocris altitudinis. </s> <s xml:id="echoid-s5172" xml:space="preserve">Si enim eo vſ <lb/>que retrocedamus, donec denarium illum ob interiecta latera uaſis inter ipſum <lb/>& </s> <s xml:id="echoid-s5173" xml:space="preserve">noſtrum uiſum videre nequeamus; </s> <s xml:id="echoid-s5174" xml:space="preserve">deinde vero vas illud repleatur aqua lim <lb/>pida, ſubito apparebit denarius ille, atq. </s> <s xml:id="echoid-s5175" xml:space="preserve">conſpectui noſtro ſeſe offere@. </s> <s xml:id="echoid-s5176" xml:space="preserve">Hinc <lb/>deniq. </s> <s xml:id="echoid-s5177" xml:space="preserve">ſit, nonnunquam Solem, Lunam, & </s> <s xml:id="echoid-s5178" xml:space="preserve">reliquas ſtellas apparere nobis, an-<lb/>tequam ſupra Horizontem aſcenderint: </s> <s xml:id="echoid-s5179" xml:space="preserve">Vnde ortum habuit apud ſapientes <lb/>commune hoc dictum. </s> <s xml:id="echoid-s5180" xml:space="preserve">Quando Sol citiusſolito in Horizonte apparet, ſignum <lb/>eſt futuræ pluuiæ, quoniam uidelicet tunc interiiciuntur multi uapores, ac <lb/>craſſi inter aſpectum noſtrum & </s> <s xml:id="echoid-s5181" xml:space="preserve">Solem, ex quibus pluuia generatur.</s> <s xml:id="echoid-s5182" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5183" xml:space="preserve"><emph style="sc">Restat</emph> tandem quæſtiuncula breuis, an uidelicet omnes ſtellæ ſint figu <lb/>ræ etiam ſphæricæ, quandoquidem ex dictis perſpicuum relinquitur, cœlum <lb/>eſſe ſphæricum. </s> <s xml:id="echoid-s5184" xml:space="preserve">Qua in re non defuerunt nonnulli, qui putauerint, tot eſſe ua <lb/> <anchor type="note" xlink:label="note-145-01a" xlink:href="note-145-01"/> rias figuras in aſtris, quot ſunt in his inferioribus. </s> <s xml:id="echoid-s5185" xml:space="preserve">Verum quia temere iſtud ui-<lb/>dentur aſſeruiſſe abſque ulla ratione probabili, dicendum eſt cum omnibus <lb/>Aſtronomis, ac Philoſophis, ſtellas omnes eſſe figuræ rotundę, ac ſphæricæ. <lb/></s> <s xml:id="echoid-s5186" xml:space="preserve">Quod quidem manifeſte patet in Luna, quæ circulariter à Sole lumẽ recipit, <lb/>quod nullo modo fieri poſſet, niſi ipſa ſphærica eſſet. </s> <s xml:id="echoid-s5187" xml:space="preserve">Cum igitur de omnibus <lb/>aſtris eadem eſſe ratio videatur, concludendum eſt, omnia eſſe ſphærica. </s> <s xml:id="echoid-s5188" xml:space="preserve">Idem <lb/>confirmari poteſt ex eo, quod omnes ſtellæ in quacunque regione, & </s> <s xml:id="echoid-s5189" xml:space="preserve">ubicunq. </s> <s xml:id="echoid-s5190" xml:space="preserve"><lb/>in cœlo conſtitutæ fuerint, rotundæ nobis apparent, quod fieri non poſſet, niſi <lb/>rotundæ eſſent, ac ſphæricę. </s> <s xml:id="echoid-s5191" xml:space="preserve">Quod multo euidentius in planetis apparet. </s> <s xml:id="echoid-s5192" xml:space="preserve">Cum <lb/>enim iuxta communem ſententiam Aſtronomorum circunferantur in epicy-<lb/>@lis, non poterunt ſemper unum & </s> <s xml:id="echoid-s5193" xml:space="preserve">idem latus ad nos conuertere. </s> <s xml:id="echoid-s5194" xml:space="preserve">Quare cum <lb/>ſemper rotundi appareant, neceſſe eſt eos undiq́ue eſſe ſphæricos: </s> <s xml:id="echoid-s5195" xml:space="preserve">hæc nam-<lb/>que figura ſphęrica inter omnia corpora hoc habet priuilegium, ut omni <lb/>ex parte inſpecta circularis, atque rotunda uideatur. </s> <s xml:id="echoid-s5196" xml:space="preserve">Huc accedit, quòd <lb/>natura in his inſerioribus maxime rotun ditatem, quantũ potuit, affectauit: </s> <s xml:id="echoid-s5197" xml:space="preserve">Vt <lb/>videre eſt in animalium membris, arborum truncis, in fructibus & </s> <s xml:id="echoid-s5198" xml:space="preserve">reliquis hu <lb/>iuſmodi, quæ omnia ad rotundam figuram, quoad fieri poteſt, tendere <lb/>uidentur: </s> <s xml:id="echoid-s5199" xml:space="preserve">quoniam uidelicet, ut ſupra dictum fuit, figura rotunda <lb/>nobiliſſima exiſtit. </s> <s xml:id="echoid-s5200" xml:space="preserve">Quam ob rem non ſine cauſa corporibus <lb/>omnibus cœleſtibus, quæ omnia alia nobilitate ſuperant, <lb/>figuram nobiliſſimam, qualis eſt rotunda at q. </s> <s xml:id="echoid-s5201" xml:space="preserve">ſphæ-<lb/>rica, conceſſiſſe natura uidetur: </s> <s xml:id="echoid-s5202" xml:space="preserve">Hoc etiam <lb/>præſertim fine, ut æqualiter ex omni parte <lb/>ſuos radios poſſent diffundere, <lb/>ac plenius undique a So-<lb/>le illuſtrari.</s> <s xml:id="echoid-s5203" xml:space="preserve"/> </p> <div xml:id="echoid-div283" type="float" level="2" n="1"> <note position="right" xlink:label="note-145-01" xlink:href="note-145-01a" xml:space="preserve">Stellæ om-<lb/>nes ſphæri-<lb/>cam figurã <lb/>habent.</note> </div> <pb o="110" file="146" n="147" rhead="Comment. in I. Cap. Sphæræ"/> </div> <div xml:id="echoid-div285" type="section" level="1" n="97"> <head xml:id="echoid-head101" xml:space="preserve">TERRAM, ET AQVAM ESSE ROTVNDAS.</head> <p style="it"> <s xml:id="echoid-s5204" xml:space="preserve"><emph style="sc">Qvod</emph> etiam terraſit rotunda, patet ſic. </s> <s xml:id="echoid-s5205" xml:space="preserve">Signa & </s> <s xml:id="echoid-s5206" xml:space="preserve">ſtellæ non æ-<lb/> <anchor type="note" xlink:label="note-146-01a" xlink:href="note-146-01"/> qualiter oriuntur, & </s> <s xml:id="echoid-s5207" xml:space="preserve">occidunt omnibus hominibus ubique exi-<lb/>ſtentibus; </s> <s xml:id="echoid-s5208" xml:space="preserve">Sed prius oriuntur & </s> <s xml:id="echoid-s5209" xml:space="preserve">occiduntillis, qui ſunt uerſus <lb/>orientem, & </s> <s xml:id="echoid-s5210" xml:space="preserve">quod citius, uel tardius oriuntur, & </s> <s xml:id="echoid-s5211" xml:space="preserve">occidunt qui-<lb/>buſdam, cauſa eſt tumor terræ, quod bene patet per ea, quæ fiunt in ſublimi. <lb/></s> <s xml:id="echoid-s5212" xml:space="preserve">Vna enim & </s> <s xml:id="echoid-s5213" xml:space="preserve">eadem eclipſis Lunę numero, quæ apparet nobis in prima hora <lb/>noctis, apparet orientalibus circa horam noctis tertiam. </s> <s xml:id="echoid-s5214" xml:space="preserve">Vnde conſtat, quod <lb/>illis prius fuit nox, & </s> <s xml:id="echoid-s5215" xml:space="preserve">Sol prius eis occidit, quàm nobis, cuius reicauſa eſt <lb/>tantum tumor terræ.</s> <s xml:id="echoid-s5216" xml:space="preserve"/> </p> <div xml:id="echoid-div285" type="float" level="2" n="1"> <note position="left" xlink:label="note-146-01" xlink:href="note-146-01a" xml:space="preserve">Terram ro-<lb/>tundam eſ@ <lb/>ſe ab ortu <lb/>in occaſum</note> </div> </div> <div xml:id="echoid-div287" type="section" level="1" n="98"> <head xml:id="echoid-head102" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s5217" xml:space="preserve"><emph style="sc">Haec</emph> eſt tertia concluſio, Terram uidelicet, & </s> <s xml:id="echoid-s5218" xml:space="preserve">aquam rotundæ eſſe figu-<lb/>ræ; </s> <s xml:id="echoid-s5219" xml:space="preserve">quam quoniam duas continet partes, primo loco priorem eius partem, nem <lb/>pe terram eſſe rotundam, hac vnica ratione cofirmat. </s> <s xml:id="echoid-s5220" xml:space="preserve">Terra eſt rotunda ab <lb/>oriente in occidentem; </s> <s xml:id="echoid-s5221" xml:space="preserve">item à ſeptentrione in auſtrum. </s> <s xml:id="echoid-s5222" xml:space="preserve">Tota ergo terra rotun-<lb/>da exiſtit. </s> <s xml:id="echoid-s5223" xml:space="preserve">Conſecutio manifeſta eſt ex ſuffi cienti partium enumeratione: </s> <s xml:id="echoid-s5224" xml:space="preserve">Si <lb/>enim terra ab oriente in occidentem, ubicunque incipias, & </s> <s xml:id="echoid-s5225" xml:space="preserve">quocunque per-<lb/>gas, eſt rotunda, itemq́ue à ſeptentrione in auſtrum, verſus quamcumq. </s> <s xml:id="echoid-s5226" xml:space="preserve">etiam <lb/>tendas partem, nulla prorſus terræ particula relinquetur, quæ rotunditatis ſit <lb/>expers. </s> <s xml:id="echoid-s5227" xml:space="preserve">Antecedens antem probat dupliciter, primum quidem, quoniam duas <lb/>habet partes, priorem, quòd nimirum terra ſit rotunda ab oriente in occiden-<lb/>tem, oſtendit hac ratione. </s> <s xml:id="echoid-s5228" xml:space="preserve">Signa & </s> <s xml:id="echoid-s5229" xml:space="preserve">ſtellę prius orientalibus oriuntur, prius <lb/>ad medium cæli perueniunt, priuſq́ue occidunt, quàm occidentalibus, vt eui-<lb/>denter patet in eclypſi Lunari, in qua, quoniam uniuerſalis eſt toti mundo (fit <lb/> <anchor type="figure" xlink:label="fig-146-01a" xlink:href="fig-146-01"/> enim eclipſis Lunę propter <lb/>ingreſſum ipſius in vmbram <lb/>terræ, ut in 4. </s> <s xml:id="echoid-s5230" xml:space="preserve">cap. </s> <s xml:id="echoid-s5231" xml:space="preserve">explicabi-<lb/>mus) in eodem inſtanti tem-<lb/>poris Luna omnibus homi-<lb/>nibus, a quibus tunc uideri <lb/>poteſt, occultatur; </s> <s xml:id="echoid-s5232" xml:space="preserve">& </s> <s xml:id="echoid-s5233" xml:space="preserve">ta-<lb/>men, ſi nobis v. </s> <s xml:id="echoid-s5234" xml:space="preserve">g. </s> <s xml:id="echoid-s5235" xml:space="preserve">apparet in <lb/>prima hora noctis initiũ ecli <lb/>pſis, hæc eadem inchoaſſe ſci <lb/>tur ex libris hiſtoriarũ, ſiue <lb/>relatione aliorum, oriẽtalio <lb/>ribus populis circa tertiã v. <lb/></s> <s xml:id="echoid-s5236" xml:space="preserve">g. </s> <s xml:id="echoid-s5237" xml:space="preserve">horã noctis. </s> <s xml:id="echoid-s5238" xml:space="preserve">Ex quo clarũ <lb/>eſt, eos prius habuiſſe noctẽ, <lb/>& </s> <s xml:id="echoid-s5239" xml:space="preserve">ex cõſequẽti Solem ijſdẽ <lb/>citius exortum fuiſſe, & </s> <s xml:id="echoid-s5240" xml:space="preserve">occi <lb/>diſſe, duabus horis, quàm no <pb o="111" file="147" n="148" rhead="Ioan. de Sacro Boſco."/> bis: </s> <s xml:id="echoid-s5241" xml:space="preserve">Huiu sautem rei cauſa ſola eſt rotunditas terræ ab oriente in occidentem, <lb/>quia ſic efficiuntur diuerſi Horizontes ab oriente in occidentem: </s> <s xml:id="echoid-s5242" xml:space="preserve">quod non <lb/>contingeret, ſi terra rotunda non eſſet: </s> <s xml:id="echoid-s5243" xml:space="preserve">non ſecus, ac in monte aliquo accidit, <lb/>in quo quoniam rotundus eſt, & </s> <s xml:id="echoid-s5244" xml:space="preserve">gibboſus, multa fiunt ex una parte, & </s> <s xml:id="echoid-s5245" xml:space="preserve">coſpiciũ <lb/>tur, quę non videri poſſunt in altero montis latere, ob montis tumorem in-<lb/>teriectum, vt clariſſime in appoſita cernis figura: </s> <s xml:id="echoid-s5246" xml:space="preserve">In qua oriẽs ſit ex parte A; </s> <s xml:id="echoid-s5247" xml:space="preserve">oc-<lb/>cidens ex parte B. </s> <s xml:id="echoid-s5248" xml:space="preserve">Vides igitur duos Horizontes diuerſos A B, & </s> <s xml:id="echoid-s5249" xml:space="preserve">D E, ob rotun <lb/>ditatem terræ C. </s> <s xml:id="echoid-s5250" xml:space="preserve">Debet enim vertex cuiuſq; </s> <s xml:id="echoid-s5251" xml:space="preserve">habitantis in terra ad perpendi-<lb/>culum, ſeu ad angulos rectos inſiſtere ſuperficiei Horizontis, ac cæli. </s> <s xml:id="echoid-s5252" xml:space="preserve">Vides <lb/>rurſus Solem citius ortum fuiſſe, citius ad medium cęli, ſeu meridiem perueniſ <lb/>ſe, citius deniq. </s> <s xml:id="echoid-s5253" xml:space="preserve">occidiſſe illis hominibus, quorum Horizon eſt A B, quam ijs, <lb/>qui Horizontem habent D E. </s> <s xml:id="echoid-s5254" xml:space="preserve">Hinc igitur fit, ut ſi incipiat eclipſis Lunę exi-<lb/>ſtentis ſupra utrunq. </s> <s xml:id="echoid-s5255" xml:space="preserve">Horizontem, & </s> <s xml:id="echoid-s5256" xml:space="preserve">conſequenter Sole ſub utroque etiam <lb/>Horizonte depreſſo, plures ſint tranſactæ horæ poſt occaſum Solis, reſpectu <lb/>Horizontis A B, quàm reſpectu Horizontis D E: </s> <s xml:id="echoid-s5257" xml:space="preserve">Quod ut planius ad huc per-<lb/>cipiatur, ſciendum eſt: </s> <s xml:id="echoid-s5258" xml:space="preserve">Cum Æquinoctialis circulus diuiſus in 360 partes æ-<lb/>quales, quæ gradus uocantur, totus ſpatio 24. </s> <s xml:id="echoid-s5259" xml:space="preserve">horarum uniformi motu ele-<lb/>uetur ſupra Horizontem quemcunque, neceſſe eſſe, ut horis ſingulis quinde-<lb/>cim ipſius gradus eleuentur, Vnde quoniam regiones dicuntur magis orienta-<lb/>les, minuſue reſpectu Æquinoctialis, qui porrigitur ab oriente in occidentem <lb/>aut contra, perſpicuum reliquitur, omnibus regionibus, quę magis orientales <lb/>ſunt quindecim gradibus, quà<unsure/>m nos, prius oriri aſtra, & </s> <s xml:id="echoid-s5260" xml:space="preserve">occidere ſpatio unius <lb/>horæ, quę uero ſunt orientaliores triginta gradibus, prius illis oriri, & </s> <s xml:id="echoid-s5261" xml:space="preserve">occi-<lb/>dere aſtra ſpatio duarum horarum, & </s> <s xml:id="echoid-s5262" xml:space="preserve">ita deinceps, addendo, aut detrahendo, <lb/>ratione multitudinis graduum, quibus vna regio orientalior eſt, quàm altera; <lb/></s> <s xml:id="echoid-s5263" xml:space="preserve">hac tamen lege ac conditione, ut cuilibet gradui tribuantur quatuor minuta <lb/>horę Cum enim hora integra 60. </s> <s xml:id="echoid-s5264" xml:space="preserve">minuta complectatur, ſingulis gradibus qua <lb/>tuor huiuſmodi minuta reſpondebunt. </s> <s xml:id="echoid-s5265" xml:space="preserve">Hæc omnia intueri licet in figura ſu-<lb/>pra poſita, in qua cernis diuiſum eſſe circulum maiorem in 24. </s> <s xml:id="echoid-s5266" xml:space="preserve">horas ęquales, <lb/>init<unsure/>io ſumpto ab occaſu ſolis, ut in Italia fieri ſolet. </s> <s xml:id="echoid-s5267" xml:space="preserve">Gradus uero interiecti <lb/>inter quaſcunq; </s> <s xml:id="echoid-s5268" xml:space="preserve">duas ciuitates, quarum altera eſt oriẽtalis, altera occidentalis, <lb/>co gnoſcuntur per arcum Æquinoctialis circuli interceptum inter Meridianos <lb/>utriuſq. </s> <s xml:id="echoid-s5269" xml:space="preserve">ciuitatis: </s> <s xml:id="echoid-s5270" xml:space="preserve">Id quod facile ex deſcriptionibus orbis, quas mappas mundi <lb/>appellant, intelligi poteſt. </s> <s xml:id="echoid-s5271" xml:space="preserve">In his enim lineę procedentes ab uno polo ad alte-<lb/>rum Meridianos deſignant: </s> <s xml:id="echoid-s5272" xml:space="preserve">linea uero ab utroq. </s> <s xml:id="echoid-s5273" xml:space="preserve">polo æqualiter ſemota Æqui-<lb/>noctialem circulum demonſtrat. </s> <s xml:id="echoid-s5274" xml:space="preserve">V@de ſi ſumantur duo Meridiani per duas ci-<lb/>uitates incedentes, mox arcus Æequinoctialis circuli inter duos Meridianos <lb/>poſitus indicabit, quanto orientalior ſit una ciuitas, quam altera. </s> <s xml:id="echoid-s5275" xml:space="preserve">Verum hæc à <lb/>Coſmographis petantur.</s> <s xml:id="echoid-s5276" xml:space="preserve"/> </p> <div xml:id="echoid-div287" type="float" level="2" n="1"> <figure xlink:label="fig-146-01" xlink:href="fig-146-01a"> <image file="146-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/146-01"/> </figure> </div> <p> <s xml:id="echoid-s5277" xml:space="preserve"><emph style="sc">Porro</emph> quod auctor noſter dicit, orientalioribus populis duabus ho-<lb/>ris citius ortum fuiſſe Solẽ, atq. </s> <s xml:id="echoid-s5278" xml:space="preserve">occidiſſe, quàm minus orientalibus, ſi nimirũ <lb/>illi populi triginta gradibus orientaliores exiſtunt, intelligendũ eſt de duabus <lb/>ciuitatibus, quæ æqualiter ab Aequinoctiali circulo recedunt, id eſt, q̃ habent <lb/>eandem eleuationem poli. </s> <s xml:id="echoid-s5279" xml:space="preserve">Quando enim diuerſas eleuationes poli habent, & </s> <s xml:id="echoid-s5280" xml:space="preserve"><lb/>ex conſequenti non æqualiter ab Aequatore diſtant, non neceſſe eſt, ut illi ci-<lb/>uitati, quę orientalior eſt triginta gradibus, quàm altera, duabus horis citius <lb/>oriatur Sol atq. </s> <s xml:id="echoid-s5281" xml:space="preserve">occidat. </s> <s xml:id="echoid-s5282" xml:space="preserve">Poteſt namq. </s> <s xml:id="echoid-s5283" xml:space="preserve">fieri, nt illi ciuitati, quæ maiorem ha-<lb/>bet poli altitudinem, hoc eſt, quæ magis ad ſeptentrionem accedit, eodem mo <pb o="112" file="148" n="149" rhead="Comment. in I. Cap. Sphæræ"/> mento temporis oriatur Sol, quo illi ciuitati, quæ minorem habet altitudinem <lb/>poli, licet ſit orientalior. </s> <s xml:id="echoid-s5284" xml:space="preserve">Quod quidem accidit propter obliquitatem Hori-<lb/>zontis: </s> <s xml:id="echoid-s5285" xml:space="preserve">Hinc etenim efficitur, ut Sole exiſtente in ſignis Borealibus, in princi-<lb/>pio v.</s> <s xml:id="echoid-s5286" xml:space="preserve">g. </s> <s xml:id="echoid-s5287" xml:space="preserve">Cancer, ciuitas ſeptentrionalior longiorẽ habeat d@ẽ, quàm ciuitas mi-<lb/>nus ſeptentrionalis. </s> <s xml:id="echoid-s5288" xml:space="preserve">Vnde etiamſi tardius Sol ad meridiem illius ciuitatis, <lb/>quàm huius perueniat, quia nimirum hęc orientalior ponitur: </s> <s xml:id="echoid-s5289" xml:space="preserve">tamen, quoniã <lb/>tempus ab ortu Solis uſque ad meridiem illius ciuitatis maius eſt, quàm hu-<lb/>ius: </s> <s xml:id="echoid-s5290" xml:space="preserve">fieri poteſt, vt eodem tempore vtriq. </s> <s xml:id="echoid-s5291" xml:space="preserve">ciuitati Sol oriatur. </s> <s xml:id="echoid-s5292" xml:space="preserve">Exempli gratia. <lb/></s> <s xml:id="echoid-s5293" xml:space="preserve">Ponantur duæ ciuitates non eandem poli altitudinem habentes, quarum una <lb/>orientalior ſit, quàm altera, quindecim gradibus, ita ut orientaliori fiat meri-<lb/>dies una hora prius quàm alteri, orientalior autem habeat diem longiſſimum <lb/>horarum 14. </s> <s xml:id="echoid-s5294" xml:space="preserve">occidentalior autem horatum 16. </s> <s xml:id="echoid-s5295" xml:space="preserve">ita ut in illa ſeptem horæ ef-<lb/>fluant ab ortu Solis vſq; </s> <s xml:id="echoid-s5296" xml:space="preserve">ad meridiem, in hac uero octo. </s> <s xml:id="echoid-s5297" xml:space="preserve">Hoc poſito, quis non <lb/>videt, eodem momento temporis Solem utriq. </s> <s xml:id="echoid-s5298" xml:space="preserve">ciuitati oriri? </s> <s xml:id="echoid-s5299" xml:space="preserve">Nam cum prio-<lb/>ri eſt meridies, tranſactę erunt ab ortu horæ 7. </s> <s xml:id="echoid-s5300" xml:space="preserve">deeritq́. </s> <s xml:id="echoid-s5301" xml:space="preserve">poſteriori ciuitati una <lb/>hora ad meridiem uſque. </s> <s xml:id="echoid-s5302" xml:space="preserve">Cum ergo hæc ab ortu uſq. </s> <s xml:id="echoid-s5303" xml:space="preserve">ad meridiẽ habeat horas <lb/>8. </s> <s xml:id="echoid-s5304" xml:space="preserve">neceſſe eſt, vt tunc, cum priori ciuitati fit meridies, horæ 7. </s> <s xml:id="echoid-s5305" xml:space="preserve">etiam effluxerint <lb/>ab ortu. </s> <s xml:id="echoid-s5306" xml:space="preserve">Quare non citius illi, quàm huic ortus eſt Sol, quamuis illa orienta-<lb/>lior ſit, quam hæc. </s> <s xml:id="echoid-s5307" xml:space="preserve">Quòd ſi occidentalior & </s> <s xml:id="echoid-s5308" xml:space="preserve">ſeptentrionalior ciuitas habeat <lb/>diem longiſſimum horarum 17. </s> <s xml:id="echoid-s5309" xml:space="preserve">citius orietur Sol illi, quã ciuitati oriẽtaliori, <lb/>in qua longiſſimus dies horas continet 14. </s> <s xml:id="echoid-s5310" xml:space="preserve">vt patet. </s> <s xml:id="echoid-s5311" xml:space="preserve">E contrario ſi ſeptentriona <lb/>lior ciuitas ſit orientalior, fieri poterit, ut non citius illi, quàm occidentaliori, <lb/>atq. </s> <s xml:id="echoid-s5312" xml:space="preserve">auſtraliori ciuitati Sol occidat, ſed uel eodem tempore, uel tardius. </s> <s xml:id="echoid-s5313" xml:space="preserve">Immo <lb/>poſſunt eſſe duæ ciuitates, quar um neutra altera orientalior ſit, habentes inæ-<lb/>qualem altitudinem poli, quoniam uidelicet una magis ad ſeptentrionem ver <lb/>git, quàm altera, & </s> <s xml:id="echoid-s5314" xml:space="preserve">tamen non eodem tempore utrique Sol oritur & </s> <s xml:id="echoid-s5315" xml:space="preserve">occidit; </s> <s xml:id="echoid-s5316" xml:space="preserve"><lb/>quamuis in vtraque fiat meridies eodem tempore; </s> <s xml:id="echoid-s5317" xml:space="preserve">ſed multo citius ciuitati Bo <lb/>realiori orietur, & </s> <s xml:id="echoid-s5318" xml:space="preserve">tardius occidet, quàm minus Boreali: </s> <s xml:id="echoid-s5319" xml:space="preserve">propterea quòd illa <lb/>longiorem diem habet, quàm hæc. </s> <s xml:id="echoid-s5320" xml:space="preserve">Quòd ſi loquam<unsure/>ur de horis, quæ initium ſu <lb/>munt à meridie, verum erit dictum auctoris, & </s> <s xml:id="echoid-s5321" xml:space="preserve">Aſtronomorum, de quibuſcun-<lb/>que ciuitatibus, quarum una orientalior eſt, quàm altera, quamuis non ſub eo <lb/>dem parallelo ſitæ ſint, ſed ſub diuerſis, diuerſasq́. </s> <s xml:id="echoid-s5322" xml:space="preserve">habeant altitudines poli. </s> <s xml:id="echoid-s5323" xml:space="preserve">Sem <lb/>per enim ea ciuitas, quæ orientalior eſt v.</s> <s xml:id="echoid-s5324" xml:space="preserve">g. </s> <s xml:id="echoid-s5325" xml:space="preserve">triginta gradibus quàm altera, dua <lb/>bus horis citius meridiem habebit, quicquid ſit de anticipatione ortus, uel oc <lb/>caſus Solis. </s> <s xml:id="echoid-s5326" xml:space="preserve">Pari ratione duæ ciuitates, quarum neutra orientalior eſt altera, <lb/>quamuis ea, quæ borealior exiftit, longiorem habeat diem, & </s> <s xml:id="echoid-s5327" xml:space="preserve">idcirco citius il-<lb/>li Sol oriatur, tardiusq́. </s> <s xml:id="echoid-s5328" xml:space="preserve">occidat, eodem tamen temporis puncto meridiem, ob <lb/>tinebunt. </s> <s xml:id="echoid-s5329" xml:space="preserve">Vnde vtriq. </s> <s xml:id="echoid-s5330" xml:space="preserve">ciuitati eadem hora ante, uel poſt meridiem, initium ali <lb/>cuius eclypſis Lunę apparebit: </s> <s xml:id="echoid-s5331" xml:space="preserve">quod nequaquam contingere poteſt duabus ci-<lb/>uitatibus, quarum una orientalior eſt, ꝗ̃ altera, quoniam videlicet orientaliori <lb/>citius meridies efficitur, cũ eius Meridianus magis ad oriẽtales partes accedat.</s> <s xml:id="echoid-s5332" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s5333" xml:space="preserve"><emph style="sc">Qvod</emph> etiam terra habeat tumorem a ſeptentrione in auſtrum, & </s> <s xml:id="echoid-s5334" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-148-01a" xlink:href="note-148-01"/> contra, ſic patet. </s> <s xml:id="echoid-s5335" xml:space="preserve">Hominibus exiſtentibus uerſus ſeptentrionem quædam <lb/>ſtellæ ſunt ſempiternæ apparitionis, ſcilicet quæ propinquè accedunt ad po <lb/>lum arcticum: </s> <s xml:id="echoid-s5336" xml:space="preserve">aliæ uero ſunt ſempiternæ occultationis, ſicut illæ, quę ſunt <lb/>propinquæ polo antarctico. </s> <s xml:id="echoid-s5337" xml:space="preserve">Si igitur aliquis procederet a ſeptentrione uer- <pb o="113" file="149" n="150" rhead="Ioan. de Sacro Boſco."/> ſus auſtrum, in tantum poſſet procedere, quòd ſtellę, quæ prius erant ei <lb/>ſempiternæ apparitionis, ei iam tenderent in occaſum; </s> <s xml:id="echoid-s5338" xml:space="preserve">& </s> <s xml:id="echoid-s5339" xml:space="preserve">quanto magis <lb/>accederet ad auſtrum, tanto plus mouerentur in occaſum. </s> <s xml:id="echoid-s5340" xml:space="preserve">Ille iterum idem <lb/>homo poſſet uidere ſtellas, quæ prius fuerant eiſempiternæ occultationis: <lb/></s> <s xml:id="echoid-s5341" xml:space="preserve">& </s> <s xml:id="echoid-s5342" xml:space="preserve">e conuerſo contingeret alicui procedenti ab auſtro uerſus ſeptentrionem. </s> <s xml:id="echoid-s5343" xml:space="preserve"><lb/>Huius autem rei cauſa eſt tantum tumor terræ.</s> <s xml:id="echoid-s5344" xml:space="preserve"/> </p> <div xml:id="echoid-div288" type="float" level="2" n="2"> <note position="left" xlink:label="note-148-01" xlink:href="note-148-01a" xml:space="preserve">Terram eſ-<lb/>ſe rotundã <lb/>@ Sep tẽtrio <lb/>nein au-<lb/>ſt<unsure/>rum.</note> </div> </div> <div xml:id="echoid-div290" type="section" level="1" n="99"> <head xml:id="echoid-head103" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s5345" xml:space="preserve"><emph style="sc">Posteriorem</emph> hic partem antecedentis, quòd nimirum terra rotun <lb/>da etiam ſit a ſeptentrione in auſtrum, confirmat hac ratione. </s> <s xml:id="echoid-s5346" xml:space="preserve">Dubium no@ <lb/>eſt, quin aliquæ ſtellæ fixæ nobis in ſphæra obliqua, & </s> <s xml:id="echoid-s5347" xml:space="preserve">in partibus ſeptentrio-<lb/>nalibus degentibus ſemper appareant, illæ nimirum, quæ ſunt prope polum ar <lb/>cticum: </s> <s xml:id="echoid-s5348" xml:space="preserve">quædam uero ſemper deliteſcant, illæ videlicet, quæ prope polum an-<lb/>tarcti<unsure/>cum exiſtunt. </s> <s xml:id="echoid-s5349" xml:space="preserve">Rurſus compertum eſt, ſi aliquis a ſeptentione in auſtrum <lb/>procederet directe, hoc eſt, ſub eodem ſemper Meridiano, illæ ſtellæ, quæ illi <lb/>ſemper ante apparebant, occultari inciperent: </s> <s xml:id="echoid-s5350" xml:space="preserve">& </s> <s xml:id="echoid-s5351" xml:space="preserve">contra illæ, quas ante uidere <lb/>non poterat iuxta polum antarcticum, paulatim ſeſe ſupra Horizontẽ extolle <lb/>rent, atque ſub conſpectum uenirent: </s> <s xml:id="echoid-s5352" xml:space="preserve">Videmus enim in Germania, quæ eſt ſe-<lb/>ptentrionalior, plures ſtellas perpetuo apparere, quàm in Italia, quæ minus ſe-<lb/>ptentrionalis eſt: </s> <s xml:id="echoid-s5353" xml:space="preserve">contra autem in Italia plures ſſellas conſpici in parte auſtra-<lb/>li, quàm in Germania. </s> <s xml:id="echoid-s5354" xml:space="preserve">Signum ergo eſt manifeſtum, terram eſſe rotundam à ſe-<lb/>ptentrione in auſtrum; </s> <s xml:id="echoid-s5355" xml:space="preserve">quemad modum cauſa, cur, cum montem aliquem rotũ <lb/>dum conſcendimus, res, quas antea non uidebamus, incipimus uidere, & </s> <s xml:id="echoid-s5356" xml:space="preserve">quas <lb/>ante conſpiciebamus, amplius intueri non poſſumus, eſt tantum tumor montis.</s> <s xml:id="echoid-s5357" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5358" xml:space="preserve"><emph style="sc">Vervm</emph> ex his tantum colligi uidetur, terram a ſeptentrione in auſtrum <lb/> <anchor type="note" xlink:label="note-149-01a" xlink:href="note-149-01"/> eſſe rorundam aliquo modo, hoc eſt, minime planam exiſtere, non autem, quòd <lb/>ſit figuræ ſphæricæ. </s> <s xml:id="echoid-s5359" xml:space="preserve">Vnde idipſum hoc modo confirmandum erit<unsure/>. </s> <s xml:id="echoid-s5360" xml:space="preserve">Quando ali-<lb/>quis ſub eodem ſemper Meridiano exiſteu<unsure/>s a ſeptentrione in auſtrum pergit, <lb/>deprehendit continue eleuationem poli ſupra Horizontem decreſcere, hac ſer <lb/>uata proportione, ut ſi in uno loco altitudo poli eſt, v.</s> <s xml:id="echoid-s5361" xml:space="preserve">g. </s> <s xml:id="echoid-s5362" xml:space="preserve">grad. </s> <s xml:id="echoid-s5363" xml:space="preserve">40. </s> <s xml:id="echoid-s5364" xml:space="preserve">poſtquam con <lb/>fecerit uerſus auſtrum 62. </s> <s xml:id="echoid-s5365" xml:space="preserve">milliaria, reperiat polum eleuaritantum grad. </s> <s xml:id="echoid-s5366" xml:space="preserve">39. <lb/></s> <s xml:id="echoid-s5367" xml:space="preserve">& </s> <s xml:id="echoid-s5368" xml:space="preserve">ſic deinceps, quotieſcunque 62. </s> <s xml:id="echoid-s5369" xml:space="preserve">milliaria confecerit, inueniat altitudinem <lb/>poli decreuiſſe per unum gradum. </s> <s xml:id="echoid-s5370" xml:space="preserve">Neceſſe igitur eſt, terram eſſe ſphæricam <lb/>a ſeptentrione in auſtrum. </s> <s xml:id="echoid-s5371" xml:space="preserve">Hæc enim proportio decrementi altitudinis poli <lb/>figuræ duntaxat ſphæricæ conuenire poteſt, ut manifeſtum eſt apud Geome-<lb/>tras, & </s> <s xml:id="echoid-s5372" xml:space="preserve">Aſtronomos.</s> <s xml:id="echoid-s5373" xml:space="preserve"/> </p> <div xml:id="echoid-div290" type="float" level="2" n="1"> <note position="right" xlink:label="note-149-01" xlink:href="note-149-01a" xml:space="preserve">Rotundita <lb/>tem terræ <lb/>eſſe ſphæri-<lb/>cam.</note> </div> <p> <s xml:id="echoid-s5374" xml:space="preserve"><emph style="sc">Eodem</emph> pacto oſtendetur, terram ab ortu in occaſum non eſſe quocun-<lb/>que modo rotundam, ſed ſphæricam. </s> <s xml:id="echoid-s5375" xml:space="preserve">Nam illa anticipatio ortus, & </s> <s xml:id="echoid-s5376" xml:space="preserve">occaſus So <lb/>lis, nec non meridiei, proportionem ſupradictam (ut nimirum ciuitati illi, quę <lb/>altera orientalior cſt quindecim gradibus, una hora citius Sol oriatur, & </s> <s xml:id="echoid-s5377" xml:space="preserve">occi-<lb/>dat; </s> <s xml:id="echoid-s5378" xml:space="preserve">illi autem, quæ magis eſt orientalis triginta gradibus, duabus horis citius, <lb/>& </s> <s xml:id="echoid-s5379" xml:space="preserve">ſic de reliquis) minime ſeruare poteſt, niſi ſphæricam figuram terræ attribua <lb/>mus. </s> <s xml:id="echoid-s5380" xml:space="preserve">Quamobrem auctor noſter recte demonſtrauit, terram rotundam eſſe.</s> <s xml:id="echoid-s5381" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s5382" xml:space="preserve"><emph style="sc">Item</emph> ſi terra eſſet plana ab oriente in occidentem, tam cito ori-<lb/> <anchor type="note" xlink:label="note-149-02a" xlink:href="note-149-02"/> rentur ſtellæ occidentalibus, quàm orientalibus, quod patet eſſe fal<unsure/>ſum. <lb/></s> <s xml:id="echoid-s5383" xml:space="preserve">Item ſi terra eſſet plana a ſeptentrione in auſtrum, & </s> <s xml:id="echoid-s5384" xml:space="preserve">contra, ſiellæ, <pb o="114" file="150" n="151" rhead="Comment. in I. Cap. Sphæræ"/> quę eſſent alicui ſempiternæ apparitionis, ſemper apparerent eidem, quo-<lb/>cunque procederet: </s> <s xml:id="echoid-s5385" xml:space="preserve">quod falſum eſt. </s> <s xml:id="echoid-s5386" xml:space="preserve">Sed quod plana ſit, præ nimia eius <lb/>quantitate hominum uiſui apparet.</s> <s xml:id="echoid-s5387" xml:space="preserve"/> </p> <div xml:id="echoid-div291" type="float" level="2" n="2"> <note position="right" xlink:label="note-149-02" xlink:href="note-149-02a" xml:space="preserve">Terram nõ <lb/>eſſe planã.</note> </div> </div> <div xml:id="echoid-div293" type="section" level="1" n="100"> <head xml:id="echoid-head104" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s5388" xml:space="preserve"><emph style="sc">Probat</emph> iam idem antecedens, quoad vtramque eius partem, ab incon <lb/>uenienti, excludendo præſertim a terra ſiguram planã, qua uulgo prædita eſſe <lb/>creditur terra, hac ſcilicet ratione, quæ eſt explicatio, & </s> <s xml:id="echoid-s5389" xml:space="preserve">confirmatio quodam-<lb/>modo præceden is. </s> <s xml:id="echoid-s5390" xml:space="preserve">Si terra ab oriente in occidentem, uel contra, non eſſet ro-<lb/>tunda, ſed uerbi gratia plana, tam ci to orirẽtur ſtellæ regionibus occidentali-<lb/>bus, quam orientalibus, eodemq́ue tempore utriuſque occiderent;</s> <s xml:id="echoid-s5391" xml:space="preserve"><unsure/> quia omnes <lb/>haberent eundem Horizontem, planitiem uidelicet terræ. </s> <s xml:id="echoid-s5392" xml:space="preserve">Si uero a Septentrio <lb/>ne in auſtrum eſſet quoq; </s> <s xml:id="echoid-s5393" xml:space="preserve">plana, & </s> <s xml:id="echoid-s5394" xml:space="preserve">non potius rotunda, eadem de cauſa, ſi pro <lb/>cederet quis ſiue a ſeptentrione in auſtrum, ſiue contra, nunquam ſtellæ, quæ il <lb/>li perpetuo ſupra Horizontem apparebant, occultarentur, neque illæ, quæ per-<lb/>petuo illi occultabantur, aliquando inciperent apparere; </s> <s xml:id="echoid-s5395" xml:space="preserve">quoniam uidelicet <lb/>nunquam mutarẽt Horizontem, ſed ſemper in illa planitie terræ exiſterẽt: <lb/></s> <s xml:id="echoid-s5396" xml:space="preserve">Quorum utrumque eſt contra communem experientiam, ut ex præcedenti ra <lb/>tiocinatione conſtat; </s> <s xml:id="echoid-s5397" xml:space="preserve">quæ quidem, una cum hac, deſumpta eſt a Ptolemeo Dict. </s> <s xml:id="echoid-s5398" xml:space="preserve"><lb/>1. </s> <s xml:id="echoid-s5399" xml:space="preserve">cap. </s> <s xml:id="echoid-s5400" xml:space="preserve">4. </s> <s xml:id="echoid-s5401" xml:space="preserve">& </s> <s xml:id="echoid-s5402" xml:space="preserve">Ioan. </s> <s xml:id="echoid-s5403" xml:space="preserve">Regiomont. </s> <s xml:id="echoid-s5404" xml:space="preserve">lib. </s> <s xml:id="echoid-s5405" xml:space="preserve">1. </s> <s xml:id="echoid-s5406" xml:space="preserve">concluſio. </s> <s xml:id="echoid-s5407" xml:space="preserve">2. </s> <s xml:id="echoid-s5408" xml:space="preserve">& </s> <s xml:id="echoid-s5409" xml:space="preserve">Alphragano Diff. </s> <s xml:id="echoid-s5410" xml:space="preserve">3.</s> <s xml:id="echoid-s5411" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5412" xml:space="preserve"><emph style="sc">Ptoiem aevs</emph> loco prædicto aliam rationem adiungit, qua probat ter <lb/> <anchor type="note" xlink:label="note-150-01a" xlink:href="note-150-01"/> ram non poſſe eſſe cauam. </s> <s xml:id="echoid-s5413" xml:space="preserve">Nam, inquit, ſi caua exiſteret, citius orirentur ſtellæ <lb/>regionibus occidentalibus, quàm orientalibus, ut contingere uidemus in ualli <lb/>bus, in quibus partes occidentales citius a Sole illuſtrantur, quàm partes orien <lb/>tales. </s> <s xml:id="echoid-s5414" xml:space="preserve">Præterea, quò magis quis a ſeptentrione procederet in auſtrum eo plures <lb/>ſtellæ iuxta polum arcticum ei apparerent, & </s> <s xml:id="echoid-s5415" xml:space="preserve">plures ex parte oppoſita, meridio <lb/>nali nimirum, occultarentur: </s> <s xml:id="echoid-s5416" xml:space="preserve">Quæ omnia abſurda ſunt; </s> <s xml:id="echoid-s5417" xml:space="preserve">& </s> <s xml:id="echoid-s5418" xml:space="preserve">cum experimento <lb/>pugnant, ut dictum eſt.</s> <s xml:id="echoid-s5419" xml:space="preserve"/> </p> <div xml:id="echoid-div293" type="float" level="2" n="1"> <note position="left" xlink:label="note-150-01" xlink:href="note-150-01a" xml:space="preserve">Terram ca <lb/>m<unsure/>ã nõ eſſe.</note> </div> <p> <s xml:id="echoid-s5420" xml:space="preserve"><emph style="sc">Vnde</emph> cur terra uideatur uiſui noſtro plana, cauſam noſter auctor dicit <lb/> <anchor type="note" xlink:label="note-150-02a" xlink:href="note-150-02"/> eſſe nimiam eius quantitatem. </s> <s xml:id="echoid-s5421" xml:space="preserve">Quoniam uidelicet tam parum exiſtit id, quod <lb/>nobis de terra apparet, reſpectu totius ambitus terræ, ut mirum non ſit, quod <lb/>nobis planum id uideatur. </s> <s xml:id="echoid-s5422" xml:space="preserve">Quemad modum ſi quis ex circunferentia maximi <lb/>c<unsure/>uiuſpiam circuli minimam partem abſcinderet, haud dubie a quouis illa par-<lb/>ticula ſeorſim conſiderata recta linea eſſe iu dicaretur.</s> <s xml:id="echoid-s5423" xml:space="preserve"/> </p> <div xml:id="echoid-div294" type="float" level="2" n="2"> <note position="left" xlink:label="note-150-02" xlink:href="note-150-02a" xml:space="preserve">Terra cur <lb/>appar<unsure/>eat <lb/>plana.</note> </div> <p style="it"> <s xml:id="echoid-s5424" xml:space="preserve"><emph style="sc">Qvod</emph> autem aqua habeat tumorem, & </s> <s xml:id="echoid-s5425" xml:space="preserve">accedat ad rotunditatem, ſis<unsure/> <lb/> <anchor type="note" xlink:label="note-150-03a" xlink:href="note-150-03"/> patet. </s> <s xml:id="echoid-s5426" xml:space="preserve">Ponatur ſignum in litore maris, & </s> <s xml:id="echoid-s5427" xml:space="preserve">exeat nauis à portu, & </s> <s xml:id="echoid-s5428" xml:space="preserve">in tan-<lb/>tum elongetur, quòd oculus exiſtentis iuxta pedem mali non poſſit uidere <lb/>ſignum; </s> <s xml:id="echoid-s5429" xml:space="preserve">ſtante uero naui, oculus eiuſdem exiſtentis in ſummitate mali, be-<lb/>ne uidebit ſignum illud. </s> <s xml:id="echoid-s5430" xml:space="preserve">Sed oculus exiſtentis iuxta pedem mali melius de-<lb/>beret uidere ſignum, quàm qui eſt in ſummitate mali, ſicut patet per lineas <lb/>duct as ab utroque ad ſignum, & </s> <s xml:id="echoid-s5431" xml:space="preserve">nulla alia huius rei cauſa eſt, quàm tu-<lb/>mor aquæ. </s> <s xml:id="echoid-s5432" xml:space="preserve">Excludantur enim omnia alia impedimenta, ſicut nebulę & </s> <s xml:id="echoid-s5433" xml:space="preserve">ua <lb/>pores aſcendentes.</s> <s xml:id="echoid-s5434" xml:space="preserve"/> </p> <div xml:id="echoid-div295" type="float" level="2" n="3"> <note position="left" xlink:label="note-150-03" xlink:href="note-150-03a" xml:space="preserve">@quã eſſe <lb/>@tundam.</note> </div> <pb o="115" file="151" n="152" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div297" type="section" level="1" n="101"> <head xml:id="echoid-head105" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s5435" xml:space="preserve"><emph style="sc">Confirmat</emph> hoc loco poſteriorem partem propoſitæ tertiæ conclu-<lb/>ſionis; </s> <s xml:id="echoid-s5436" xml:space="preserve">aquam uidelicet eſſe quoque rotundam, duplici ratione. </s> <s xml:id="echoid-s5437" xml:space="preserve">Prima eſt. </s> <s xml:id="echoid-s5438" xml:space="preserve">Si <lb/>in litore maris ponatur aliquod ſignum notabile, nempe turris aliqua, aut do-<lb/>mus notetur, exeatq́ue a portu nauis, poſt aliquam diſtantiam nauis a litore, <lb/>illi, qui ſunt in naui i<unsure/>uxta pedem mali, non uide-<lb/> <anchor type="figure" xlink:label="fig-151-01a" xlink:href="fig-151-01"/> bunt amplius ſignũ illud notatũ; </s> <s xml:id="echoid-s5439" xml:space="preserve">ſi uero quiſpiam <lb/>e<unsure/>onſcendat tunc ſummitatem mali, illud adhuc <lb/>uidebit ſignum, atque hoc contingit, ſecluſis <lb/>e<unsure/>tiam omnibus aliis impedimentis, ut ſunt nebu-<lb/>læ, & </s> <s xml:id="echoid-s5440" xml:space="preserve">uapores. </s> <s xml:id="echoid-s5441" xml:space="preserve">Igitur manifeſte ſequitur, huiu-<lb/>ſee rei cauſam ſuiſſe tumorem duntaxat aquæ in-<lb/>@eriectum inter nauem, & </s> <s xml:id="echoid-s5442" xml:space="preserve">ſignum illud in litore. <lb/></s> <s xml:id="echoid-s5443" xml:space="preserve">Nam niſi tumor aquæ eſſet impedimento, nimirũ <lb/>ſi aqua plana exiſteret, melius deberent ſignum ui-<lb/>dere illi, qui ſunt ad pedem mali, quàm is, qui eſt in <lb/>ſummitate mali, cum illi ſint hoc propinquiores, ut patet per lineas rectas à ſi-<lb/>gno ad pedem mali, & </s> <s xml:id="echoid-s5444" xml:space="preserve">ad ſum mitatem eiuſdem ductas. </s> <s xml:id="echoid-s5445" xml:space="preserve">Eſſet enim illa, quæ du-<lb/>citur ad ſummitatem mali, longior ea, quæ ad pedem mali extenditur, cum <lb/>opponatur maiori angulo, ut in appoſita figura apparet.</s> <s xml:id="echoid-s5446" xml:space="preserve"/> </p> <div xml:id="echoid-div297" type="float" level="2" n="1"> <figure xlink:label="fig-151-01" xlink:href="fig-151-01a"> <image file="151-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/151-01"/> </figure> </div> <p> <s xml:id="echoid-s5447" xml:space="preserve"><emph style="sc">Qvamvis</emph> vero hæc ratio, quæ eſt omninm Aſtronomorum, optime de-<lb/>monſtret<unsure/>, aquam habere ſiguram rotundam, ſecluſis nebulis, & </s> <s xml:id="echoid-s5448" xml:space="preserve">vaporibus vis ũ <lb/> <anchor type="note" xlink:label="note-151-01a" xlink:href="note-151-01"/> noſtrum impedientibus: </s> <s xml:id="echoid-s5449" xml:space="preserve">tamen quoniam vix, aut nunquam tempus adeo ſere-<lb/>nũ exiſtit, vt nulliſint uapores eleuati ex mari; </s> <s xml:id="echoid-s5450" xml:space="preserve">immo ſolũ ex ea concluditur, <lb/>terrã eſſe aliquo modo rotundã, id eſt, non planã, nõ autem, eã eſſe ſphęricam; <lb/></s> <s xml:id="echoid-s5451" xml:space="preserve">idcirco melius, ac efficacius probare poterimus, aquam eſſe rotundã, ac ſphærĩ <lb/>cam, ijſdem medijs, quibus auctor collegitterræ rotunditatem, cõferendo ſcili <lb/>@et inſulas magis orientales cũ minus orientalibus, ſi nimirũ nauigetur ex Sy-<lb/>ria in Hiſpaniã, & </s> <s xml:id="echoid-s5452" xml:space="preserve">hinc verſus eã partẽ Hiſpaniæ nouæ, ſiue Americæ, quæ Flo <lb/>rida nuncupatur, vel contra. </s> <s xml:id="echoid-s5453" xml:space="preserve">Conferendo item inſulas ſeptentrionaliores cum <lb/>minus ſeptentrionalibus, ſi nimirum nauigatio inſtituatur ex Luſitania Flan-<lb/>driã uerſus, uel contra; </s> <s xml:id="echoid-s5454" xml:space="preserve">& </s> <s xml:id="echoid-s5455" xml:space="preserve">ex Luſitan a per Inſulas Fortunatas uerſus caput ui-<lb/>ride. </s> <s xml:id="echoid-s5456" xml:space="preserve">Omnes etenim experientię ſupra allatę ad comprobandam terrę rotun-<lb/>ditatem, anticipatio uidelicet ortus, & </s> <s xml:id="echoid-s5457" xml:space="preserve">occaſus ſtellarum, item variatio altitu-<lb/>dinis poli, eadem proportione cõpertæ ſunt à nautis in Oceano, & </s> <s xml:id="echoid-s5458" xml:space="preserve">mari. </s> <s xml:id="echoid-s5459" xml:space="preserve">Quare <lb/>neceſse eſt, aquam quoque rotundam eſse, ac ſphæricam.</s> <s xml:id="echoid-s5460" xml:space="preserve"/> </p> <div xml:id="echoid-div298" type="float" level="2" n="2"> <note position="right" xlink:label="note-151-01" xlink:href="note-151-01a" xml:space="preserve">19. primi</note> </div> <p style="it"> <s xml:id="echoid-s5461" xml:space="preserve"><emph style="sc">Item</emph> cum aqua ſit corpus homogeneum, totum cũ partibus eiuſdem <lb/>erit rationis: </s> <s xml:id="echoid-s5462" xml:space="preserve">ſed partes aquæ (ſicut in guttulis, & </s> <s xml:id="echoid-s5463" xml:space="preserve">roribus herbarũ accidit) <lb/>rotundam natur aliter appetunt formam. </s> <s xml:id="echoid-s5464" xml:space="preserve">ergo & </s> <s xml:id="echoid-s5465" xml:space="preserve">totum, cuius ſunt partes.</s> <s xml:id="echoid-s5466" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div300" type="section" level="1" n="102"> <head xml:id="echoid-head106" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s5467" xml:space="preserve"><emph style="sc">Secvnda</emph> ratio eſt. </s> <s xml:id="echoid-s5468" xml:space="preserve">Partes aquæ naturaliter appetunt figuram rotun-<lb/>dam, ut uidemus in guttulis, & </s> <s xml:id="echoid-s5469" xml:space="preserve">rore ſuper folia herbarũ: </s> <s xml:id="echoid-s5470" xml:space="preserve">cũ igitur aqua ſit cor-<lb/>pus homogeneũ, & </s> <s xml:id="echoid-s5471" xml:space="preserve">conſequenter totũ cum partibus eiuſdẽ ſit rationis, erit & </s> <s xml:id="echoid-s5472" xml:space="preserve"><lb/>tota aqua figuræ rotundæ. </s> <s xml:id="echoid-s5473" xml:space="preserve">Verũ hæc ratio non multũ efficax eſt. </s> <s xml:id="echoid-s5474" xml:space="preserve">Guttulæ enim <lb/>illæ fugiẽtes ſiccitatẽ ſibi inimicam, ex naturali, & </s> <s xml:id="echoid-s5475" xml:space="preserve">uniuerſali propenſione ada-<lb/>mant rotundam figurã, ut uidelicet diurius ſe cõſeruent. </s> <s xml:id="echoid-s5476" xml:space="preserve">Eſt enim figura ſphæ-<lb/>rica ad id commodiſſima, cum eius partes ſint magis unitæ, quàm aliarũ ſigu- <pb o="116" file="152" n="153" rhead="Comment. in I. Cap. Sphæræ"/> rarum. </s> <s xml:id="echoid-s5477" xml:space="preserve">Vnde uidemus guttulas aquarum, ſi amittant figuram ſphæricam, cito <lb/>ac facile corrumpi, atque exiccari.</s> <s xml:id="echoid-s5478" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">Ratio Ari-<lb/>ſtotelis pro <lb/>bans aquã <lb/>eſſe rotun <lb/>dam.</note> <p> <s xml:id="echoid-s5479" xml:space="preserve"><emph style="sc">Dvabvs</emph> his rationibus addere poſſumus aliam, quam etiam Ariſtoteles <lb/>affert lib. </s> <s xml:id="echoid-s5480" xml:space="preserve">2. </s> <s xml:id="echoid-s5481" xml:space="preserve">de cœlo, hoc modo. </s> <s xml:id="echoid-s5482" xml:space="preserve">Aqua ſuapte natura confluit ad loca decli-<lb/>uiora, utexperiẽtia didicimus quotidianatigitur ro <lb/> <anchor type="figure" xlink:label="fig-152-01a" xlink:href="fig-152-01"/> tunda exiſtit. </s> <s xml:id="echoid-s5483" xml:space="preserve">Nam alias non conflueret ad loca de-<lb/>cliuiora. </s> <s xml:id="echoid-s5484" xml:space="preserve">Sit enim aquæ ſuperficies, ſi fieri poteſt, <lb/>plana, uel alterius figuræ non circularis, expanſa ſu-<lb/>per terrã per lineã A D B, & </s> <s xml:id="echoid-s5485" xml:space="preserve">ex centro mundi C, de-<lb/>ſcribatur circulus E G F; </s> <s xml:id="echoid-s5486" xml:space="preserve">& </s> <s xml:id="echoid-s5487" xml:space="preserve">ex C, educatur C D, per <lb/>pendicularis ad A B; </s> <s xml:id="echoid-s5488" xml:space="preserve">cõnectanturq́; </s> <s xml:id="echoid-s5489" xml:space="preserve">rectæ A C, B C: <lb/></s> <s xml:id="echoid-s5490" xml:space="preserve">Et quoniã recta C D, minor eſt, quàm C A, vel C B, <lb/> <anchor type="note" xlink:label="note-152-02a" xlink:href="note-152-02"/> erit punctum D, in loco decliuiori, hoc eſt, propin-<lb/>quius centro, quã punctum A, uel B. </s> <s xml:id="echoid-s5491" xml:space="preserve">A qua igitur nõ <lb/>impedita non confluet ad loca decliuiora. </s> <s xml:id="echoid-s5492" xml:space="preserve">Quod cũ <lb/>pugnet cum experientia, neceſſe eſt, ut pars aquæ media, nempe D, attollatut <lb/>ad punctũ G, & </s> <s xml:id="echoid-s5493" xml:space="preserve">partes aquæ iuxta A, & </s> <s xml:id="echoid-s5494" xml:space="preserve">B, deſidant, perueniantq́ue ad puncta E, <lb/>& </s> <s xml:id="echoid-s5495" xml:space="preserve">F, ut tota aqua habe at tumorem E G F, æqualiterq́; </s> <s xml:id="echoid-s5496" xml:space="preserve">diſtet à centro mundi. <lb/></s> <s xml:id="echoid-s5497" xml:space="preserve">Hac enim ratione naturaliter quieſcet collibrata. </s> <s xml:id="echoid-s5498" xml:space="preserve">Ex qua quidem ratione pro-<lb/>babitur, nullam aliam figurã poſle habere aquã præter ſphæricam: </s> <s xml:id="echoid-s5499" xml:space="preserve">nã alias ſem <lb/>per haberet aliquas partes remotiores aterræ centro, (Sp hærica enim tantum <lb/>figura æqualiter undique propinquat centro) & </s> <s xml:id="echoid-s5500" xml:space="preserve">ex conſequenti non deflueret <lb/>ad loca decliuiora, quod pugnat cum natura aquæ. </s> <s xml:id="echoid-s5501" xml:space="preserve">Immoex hac ratione effi-<lb/>citur, quemlibet liquorem in aliquo uaſe contentum habere tumorem aliquẽ, <lb/>ſeu circuferentiam, cuius centrum idem eſt, quod centrum mundi.</s> <s xml:id="echoid-s5502" xml:space="preserve"/> </p> <div xml:id="echoid-div300" type="float" level="2" n="1"> <figure xlink:label="fig-152-01" xlink:href="fig-152-01a"> <image file="152-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/152-01"/> </figure> <note position="left" xlink:label="note-152-02" xlink:href="note-152-02a" xml:space="preserve">19. primi.</note> </div> <p> <s xml:id="echoid-s5503" xml:space="preserve"><emph style="sc">Sed</emph> omnium elegantiſſima eſt demonſtratio Archimedis in lib. </s> <s xml:id="echoid-s5504" xml:space="preserve">1. </s> <s xml:id="echoid-s5505" xml:space="preserve">de ijs. <lb/></s> <s xml:id="echoid-s5506" xml:space="preserve"> <anchor type="note" xlink:label="note-152-03a" xlink:href="note-152-03"/> quæ uehuntur in aqua, qua demonſtrat, non ſolum Oceanum, & </s> <s xml:id="echoid-s5507" xml:space="preserve">alia maria, ve <lb/>rũ etiam quemlibet humorem conſiſtentem, ac manentem, ſigurã habere ſphæ <lb/>ricam, cuius centrum ſit idem, quod centrum mundi, ad quod omnia grauia fe <lb/>funtur ſuapte natura. </s> <s xml:id="echoid-s5508" xml:space="preserve">Aſſ<unsure/>umit autem primum, humidieam eſſe naturam, ut par <lb/>tibus ipſius æqualiter iacentibus, & </s> <s xml:id="echoid-s5509" xml:space="preserve">continuatis interſeſe, minus preſſa a ma-<lb/>gis preſſa expellatur. </s> <s xml:id="echoid-s5510" xml:space="preserve">Vnamquam que uero partẽ eius premi humido ſupra ip-<lb/>ſam exiſtente ad perpendiculũ, ſi humidũ ſit deſcendens in aliquo, aut ab alio <lb/>aliquo preſſum. </s> <s xml:id="echoid-s5511" xml:space="preserve">Id quod experientia verũ eſſe didicimus: </s> <s xml:id="echoid-s5512" xml:space="preserve">quandocunque enim <lb/>liquorẽ aliqua in parte premimus uel manu, uel alio ſuperfuſo humore, cedũt <lb/>aliæ partes circunſtantes, atq; </s> <s xml:id="echoid-s5513" xml:space="preserve">expelluntur. </s> <s xml:id="echoid-s5514" xml:space="preserve">Deinde demonſtrat, ſi ſuperficies <lb/>aliqua plano ſecetur per idem ſemper punctum, ſitq́ ſectio circuli circunferem-<lb/>tia centrum habens punctum illud, per quod plano ſecatur, ſuperficiem illam <lb/>eſſe ſphæ icam, cuius centrum idem illud punctum ſit. </s> <s xml:id="echoid-s5515" xml:space="preserve">Demonſtratio huius rei <lb/>eruſmodi eſt. </s> <s xml:id="echoid-s5516" xml:space="preserve">Secetur ſuperficies aliqua plano per A, punctum ducto, ſitq́ue ſe-<lb/>ctio ſemper circuli circun ferentia centrum habens punctum A. </s> <s xml:id="echoid-s5517" xml:space="preserve">Dico eam ſu-<lb/>perficiem eſſe ſphæricam, cuius centrum A, hoc eſt, omnes lineas à puncto A, <lb/>ad illam ſuperficiem ductas inter ſe eſſe æquales. </s> <s xml:id="echoid-s5518" xml:space="preserve">Ducantur enim ex A, ad ſu-<lb/>perficiem duæ lineæ rectæ utcunque A B, A C, ut in prima figura: </s> <s xml:id="echoid-s5519" xml:space="preserve">per quas, <lb/>cum ſint in eodem plano, ducatur planum faciens in ſuperficie propoſita li-<lb/> <anchor type="note" xlink:label="note-152-04a" xlink:href="note-152-04"/> neam B C, quæ ex hypotheſi circunferentia circuli erit. </s> <s xml:id="echoid-s5520" xml:space="preserve">Recta igitur A C, <lb/>rectæ A B, per defin. </s> <s xml:id="echoid-s5521" xml:space="preserve">circuli, æqualis erit. </s> <s xml:id="echoid-s5522" xml:space="preserve">Eadem ratione oſtendemus, omnes <lb/>alias lineas rectas a puncto A, ad ſuperficiem propoſitam ductas rectæ A B, <pb o="117" file="153" n="154" rhead="Ioan. de Sacro Boſco."/> æquales eſſe, cum per <lb/> <anchor type="figure" xlink:label="fig-153-01a" xlink:href="fig-153-01"/> A B, & </s> <s xml:id="echoid-s5523" xml:space="preserve">quamcunque <lb/>aliam lineam rectam <lb/>ex A, ad datam ſuper-<lb/>ficiem ductã duci poſ <lb/>ſit planum faciens cir <lb/>culũ in ſuperficie pro <lb/>poſita. </s> <s xml:id="echoid-s5524" xml:space="preserve">Quamobrẽ om <lb/>nes rectæ inter ſe æ-<lb/>quales erunt, ac pro-<lb/>inde ſuperficies ſphæ-<lb/>rica erit, cuius centrum A.</s> <s xml:id="echoid-s5525" xml:space="preserve"/> </p> <div xml:id="echoid-div301" type="float" level="2" n="2"> <note position="left" xlink:label="note-152-03" xlink:href="note-152-03a" xml:space="preserve">Archime-<lb/>dis demon <lb/>ſtratio pro-<lb/>bans omne <lb/>liquorem <lb/>ſphæricam <lb/>figuram ha <lb/>bere.</note> <note position="left" xlink:label="note-152-04" xlink:href="note-152-04a" xml:space="preserve">2. vndec.</note> <figure xlink:label="fig-153-01" xlink:href="fig-153-01a"> <image file="153-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/153-01"/> </figure> </div> <p> <s xml:id="echoid-s5526" xml:space="preserve"><emph style="sc">Intelligatvr</emph> iã humor aliquis, ſiue liquor cõſiſtẽs, manensq́; </s> <s xml:id="echoid-s5527" xml:space="preserve">cu-<lb/>ius ſuperficies ſecetur plano per D, centrũ terræ ducto faciente lineã in ſuꝑficie <lb/>EFGH. </s> <s xml:id="echoid-s5528" xml:space="preserve">Dico lineã EFGH, circunferentiã circuli eſſe, cuius centrũ D. </s> <s xml:id="echoid-s5529" xml:space="preserve">Si. </s> <s xml:id="echoid-s5530" xml:space="preserve">n. </s> <s xml:id="echoid-s5531" xml:space="preserve">non <lb/>eſt, nõ erunt oẽs rectæ lineæ ductæ ex D, ad lineã EFGH, inter ſe æquales. </s> <s xml:id="echoid-s5532" xml:space="preserve">Sint <lb/>ergo DE, DG, inæquales, & </s> <s xml:id="echoid-s5533" xml:space="preserve">DG, maior, quã DE; </s> <s xml:id="echoid-s5534" xml:space="preserve">ducaturq́; </s> <s xml:id="echoid-s5535" xml:space="preserve">inter has recta DF, <lb/>maior quidẽ, quàm DE, minor uero, quàm DG. </s> <s xml:id="echoid-s5536" xml:space="preserve">Deſcripto aũt in plano ſecante <lb/>ex D, ad interuallũ DF, circulo IFKH, qui neceſſario rectã DE, ultra punctũ E, <lb/>in puncto I, & </s> <s xml:id="echoid-s5537" xml:space="preserve">rectã DG, infra punctũ G, in puncto K, ſecabit; </s> <s xml:id="echoid-s5538" xml:space="preserve">fiant in D, duo an <lb/>guli æquales FDI, FDG, deſcribaturq́; </s> <s xml:id="echoid-s5539" xml:space="preserve">in liquore, & </s> <s xml:id="echoid-s5540" xml:space="preserve">in plano circuli IFk H, cir-<lb/>culus LMN. </s> <s xml:id="echoid-s5541" xml:space="preserve">Partes ergo humoris prope circunferentiã LMN, æqualiter iacẽt, <lb/>& </s> <s xml:id="echoid-s5542" xml:space="preserve">continuatæ inter ſe, cũ æqualiter a centro D, diſtent, quarũ eæ, quæ ſunt iux <lb/>ta circunferentiã MN, magis premuntur à liquore prope FG, quàm illæ iuxta <lb/>circunferẽtiã LM, a liquore prope EF, cũ ille grauior ſit, quã hic, ut patet. </s> <s xml:id="echoid-s5543" xml:space="preserve">Qua-<lb/>re partes iuxta LM, a partibus iuxta MN, expellentur: </s> <s xml:id="echoid-s5544" xml:space="preserve">ac propterea humor non <lb/>conſiſter. </s> <s xml:id="echoid-s5545" xml:space="preserve">Ponebatur autem conſiſtens, & </s> <s xml:id="echoid-s5546" xml:space="preserve">manens. </s> <s xml:id="echoid-s5547" xml:space="preserve">quod eſt abſurdum. </s> <s xml:id="echoid-s5548" xml:space="preserve">Linea er-<lb/>go EFGH, circuli circunferentia eſt, cuius centrum D. </s> <s xml:id="echoid-s5549" xml:space="preserve">Similiter demonſtrabi-<lb/>tur, ſi quomodocunque aliter ſuperficies liquoris plano ſecta fuerit per D, cen <lb/>trũ terræ, ſectionem circunferentiam eſſe circuli, cuius centrũ D. </s> <s xml:id="echoid-s5550" xml:space="preserve">Igitur ut pau-<lb/>lo ante oſtendimus, ſuperficies ipſa ſphęrica erit, cuius centrum D, idem, quod <lb/>terræ: </s> <s xml:id="echoid-s5551" xml:space="preserve">quandoquidẽ eiuſmodi eſt, utſecta ſemper per centrũ terræ faciat circu <lb/>li circunferentiam centrũ habentis centrum terræ, quod erat demonſtrandum.</s> <s xml:id="echoid-s5552" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div303" type="section" level="1" n="103"> <head xml:id="echoid-head107" style="it" xml:space="preserve">AN EX TERRA, ET AQVA VNVS FIAT GLO-<lb/>bus, hoc eſt, an horum elementorum conuexæ ſuperficies <lb/>idem habeant centrum.</head> <p> <s xml:id="echoid-s5553" xml:space="preserve"><emph style="sc">QVamvis</emph> ab auctore recte ſit probatum, tam terrã, quàm aquam <lb/>eſſe rotundam, in dubium tamen à nonnullis uertitur, an hæc duo <lb/>elementa ita ſint rotunda, ac ſphærica, ut unicũ conſtituant globũ, <lb/>vel(quod idẽ eſt) unũ, & </s> <s xml:id="echoid-s5554" xml:space="preserve">idẽ habeant centrũ. </s> <s xml:id="echoid-s5555" xml:space="preserve"><emph style="sc">Q</emph>uidam enim aſſerũt, <lb/> <anchor type="note" xlink:label="note-153-01a" xlink:href="note-153-01"/> terram, & </s> <s xml:id="echoid-s5556" xml:space="preserve">aquã nullo modo idẽ habere centrũ, ſed duo diſtincta, ac <lb/>propterea non effici ex illis unam duntaxat ſphæram, ſed duas. </s> <s xml:id="echoid-s5557" xml:space="preserve">Dicunt nam-<lb/>que, in principio mundi terram, & </s> <s xml:id="echoid-s5558" xml:space="preserve">aquam rotundas quidem, atq; </s> <s xml:id="echoid-s5559" xml:space="preserve">concentricas, <lb/>circa centrum nimirum mundi, fuiſſe creatas: </s> <s xml:id="echoid-s5560" xml:space="preserve">Deinde receſſiſſe aquam ex una <lb/>parte, in oppoſitamq́ partem magno tumore congregatam fuiſſe, exiſtente in-<lb/>terim terra immobili in centro Vniuerſi, Itaque aiunt, ex illa ſegregatione a- <pb o="118" file="154" n="155" rhead="Comment. in I. Cap. Sphæræ"/> quæ à terra duos effectos eſſe globos inter ſe diſtinctos, diuerſosq́ue, unu@ <lb/>quidem terræ, alterum uero aquæ, quamuis nullus horum globorum totus, at-<lb/>que integer appareat, ſed ambo ſeſe mutuo interſecent. </s> <s xml:id="echoid-s5561" xml:space="preserve">Ex qua ſententia ſe-<lb/>quitur, duo ponenda eſſe centra, unum totius Vniuerſi, quod idem dicunt eſ-<lb/>ſe, quod centrum terræ, alterum ipſius aquæ. </s> <s xml:id="echoid-s5562" xml:space="preserve">Negare enim non poſſunt ratio-<lb/>nibus & </s> <s xml:id="echoid-s5563" xml:space="preserve">experientiis conuicti, tam terram, quàm aquam eſſe rotundam, atque <lb/>ſphæricam. </s> <s xml:id="echoid-s5564" xml:space="preserve">Quòd ſi illis obijcias, inde fieri, ut aqua uel uiolenter contineatur, <lb/>uel certe defluere poſſit, terramq́ue operite: </s> <s xml:id="echoid-s5565" xml:space="preserve">Reſpondent, aquam ſupernatu-<lb/>rali Dei beneficio, ac miraculo ibi contentam non poſſe terram operire; </s> <s xml:id="echoid-s5566" xml:space="preserve">ope-<lb/>riret uero maxime, ſi conditioni ſuæ naturæ, quæ ad decliuiora loca confluere <lb/>conatur, relinqueretur.</s> <s xml:id="echoid-s5567" xml:space="preserve"/> </p> <div xml:id="echoid-div303" type="float" level="2" n="1"> <note position="right" xlink:label="note-153-01" xlink:href="note-153-01a" xml:space="preserve">Sententi@ <lb/>corum, qui <lb/>duo contra <lb/>ponũt, u@@ <lb/>terræ, & a-<lb/>quę alter@.</note> </div> <p> <s xml:id="echoid-s5568" xml:space="preserve"><emph style="sc">Alii</emph> vero eoſdem duos globos ex terra, & </s> <s xml:id="echoid-s5569" xml:space="preserve">aqua cõſtituentes, nihil ſuper-<lb/> <anchor type="note" xlink:label="note-154-01a" xlink:href="note-154-01"/> naturale admittere uolunt, ſed autumant, iuſſu Dei non ſolum aquam, ueru@ <lb/>etiam terram a centro mundi receſſiſſe, neque iam ſupernaturaliter aquam cõ <lb/>tineri, ne fluat ad locum decliuiorem, terramq́ue operiat: </s> <s xml:id="echoid-s5570" xml:space="preserve">Vnde hi auctores <lb/>tria centra confingunt, unum totius Vniuerſi, alterum terræ, tertium denique <lb/>ipſius aquæ. </s> <s xml:id="echoid-s5571" xml:space="preserve">Cauſa uero, cur omnes prædicti auctores duos globos efficiant ex <lb/>terra, & </s> <s xml:id="echoid-s5572" xml:space="preserve">aqua, hæc eſſe uidetur, quia nimirum putant, aquam multo eſſe maio-<lb/>rem ipſa terra. </s> <s xml:id="echoid-s5573" xml:space="preserve">Vnde ſi aqua eſſet terræ concentrica, utique ipſam operiret. <lb/></s> <s xml:id="echoid-s5574" xml:space="preserve">Duo namque circuli ſeu globi inæquales concentrici eſſe nequeunt, quin m@ <lb/>ior totum minorem includat, ut ex Geometria manifeſtum eſt.</s> <s xml:id="echoid-s5575" xml:space="preserve"/> </p> <div xml:id="echoid-div304" type="float" level="2" n="2"> <note position="left" xlink:label="note-154-01" xlink:href="note-154-01a" xml:space="preserve">Sententia <lb/>corum, qui <lb/>tria centra <lb/>@tatuunt, <lb/>unũ terrę, <lb/>aquæ alte-<lb/>rum, & ter <lb/>tiũ totius <lb/>Vniuerſi.</note> </div> <p> <s xml:id="echoid-s5576" xml:space="preserve"><emph style="sc">Vervm</emph> utraque ſententia facile poteſt impugnari. </s> <s xml:id="echoid-s5577" xml:space="preserve">Prima quidem, quo-<lb/> <anchor type="note" xlink:label="note-154-02a" xlink:href="note-154-02"/> niam ſiue ulla neceſſitate confugit ad miracula: </s> <s xml:id="echoid-s5578" xml:space="preserve">Secunda uero, quia dum co-<lb/>natur defendere, omnia modo eſſe naturaliter conſtituta, efſugere non poteſt, <lb/>quin concedat, ſupernaturale eſſe, quod centrum mundi non ſit centrum te@ <lb/>ræ, cui naturaliter debetur ob ſummam ſui grauitatem, ut omnes philoſeph@ <lb/>fatentur. </s> <s xml:id="echoid-s5579" xml:space="preserve">Adde quod pugnat cum omni experientia, terram non eſſe in cen-<lb/>tro totius Vniuerſi collocatam unà cum aqua. </s> <s xml:id="echoid-s5580" xml:space="preserve">Vt enim paulo poſt demonſtra-<lb/>bimus, tam ſuperficies conuexa terræ, quàm aquæ, a centro mundi æquidiſtar, <lb/>quod utraque opinio negat.</s> <s xml:id="echoid-s5581" xml:space="preserve"/> </p> <div xml:id="echoid-div305" type="float" level="2" n="3"> <note position="left" xlink:label="note-154-02" xlink:href="note-154-02a" xml:space="preserve">Cõfutatio <lb/>@triuſque <lb/>ſententiæ <lb/>ſuperioris.</note> </div> <p> <s xml:id="echoid-s5582" xml:space="preserve"><emph style="sc">Deinde</emph>, quia cum auctores utriuſque ſententiæ admittant, aquã mul <lb/>to eſſe maiorem ipſa terra, concedere etiam neceſſario cogentur, plura ſtadia, <lb/>milliariaue cuilibet gradui ſuperficiei maris, ſeu aquæ correſpondere, quàm <lb/>cuilibet gradui terræ. </s> <s xml:id="echoid-s5583" xml:space="preserve">Nam in tot gradus diuiditur orbis terrenus, in quot glo <lb/>bus aqueus diſtribuitur, quemadmodum ſcilicet quilibet circulus cæleſtis diu@ <lb/>di ſolet. </s> <s xml:id="echoid-s5584" xml:space="preserve">Quare ſi aqua maior eſt, quàm terra, oportet gradus aquæ eſſe maio-<lb/>res gradibus terræ, ac proinde quiuis illorum plura ſtadia, milliariaue co@ti-<lb/>nebit, quàm quilibet horum. </s> <s xml:id="echoid-s5585" xml:space="preserve">Cuius oppoſitum omnes Nautę aſſerunt, qui ſe <lb/>expertos fuiſſe ſępenumero reſtantur, tot ſtadia, uel milliaria comprehendere <lb/>unum quemque gradum in ſuperficię t<unsure/>erræ, quot in ſuperficie maris.</s> <s xml:id="echoid-s5586" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5587" xml:space="preserve"><emph style="sc">Rvrsvs</emph> quoniam ſi uerę eſſent prędictæ ſententiæ, non poſſent ulli par-<lb/>ti terrę aſſignari antipodes; </s> <s xml:id="echoid-s5588" xml:space="preserve">quippe cum huic terrę parti habitatę oppoſita <lb/>pars maxima ſit aquarum proſunditate contecta, ut auctores earum fabulan-<lb/>tur: </s> <s xml:id="echoid-s5589" xml:space="preserve">Experientia autem quotidiana Luſitanorum, Hiſpanorumq́ue ſatis nos e-<lb/>docet, multis terrę partibus aſſignari antipodes, uel in cõtinenti, uel in inſulis: <lb/></s> <s xml:id="echoid-s5590" xml:space="preserve">Vt extremę parti prouincię Chinarum fere antipodes ſunt habitantes in ca-<lb/>pite Bonę ſpei. </s> <s xml:id="echoid-s5591" xml:space="preserve">Prouincię quoque Peru ferme opponitur pars illa Indię O-<lb/>rientalis, in qua emporium Calecut reperitur. </s> <s xml:id="echoid-s5592" xml:space="preserve">Item Malachæ in India Orien- <pb o="119" file="155" n="156" rhead="Ioan. de Sacro Boſco."/> tali per diametrum quaſi opponitur Breſilia in India Occidentali, & </s> <s xml:id="echoid-s5593" xml:space="preserve">c.</s> <s xml:id="echoid-s5594" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5595" xml:space="preserve"><emph style="sc">Praeterea</emph>, cum aqua ſecundum illos non ęqualiter diſtet a cen-<lb/>tro Vniuerſi, ſed eleuetur mirum in modum, ſequeretur, quod nauis exiens è <lb/>portu quocunque aſcenderet, & </s> <s xml:id="echoid-s5596" xml:space="preserve">accedens ad eundem portum deſcenderet, & </s> <s xml:id="echoid-s5597" xml:space="preserve"><lb/>ſic, ęquali exiſtente uento, uelocius ad portum deſcenderet, quàm à portu aſcẽ <lb/>deret, quod eſt contra experientiam: </s> <s xml:id="echoid-s5598" xml:space="preserve">immo nullo pacto conſiſtere poſſet nauis <lb/>extra portum conſtituta, quin ſua ſponte ad portum decurreret, cum omne <lb/>graue deorſum tendat; </s> <s xml:id="echoid-s5599" xml:space="preserve">quod tamen uerum non eſt.</s> <s xml:id="echoid-s5600" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5601" xml:space="preserve"><emph style="sc">Postremo</emph>, quoniam id, quod prima ſententia maxime uitare cu-<lb/>pit, nimirum aquam, ni ſupernaturali uirtute contineretur, uniuerſam terram <lb/>operturam eſſe, nullo modo uitat. </s> <s xml:id="echoid-s5602" xml:space="preserve">Cum enim ſint antipodes, ut quotidie naui <lb/>gantes hoc tempore experiuntur: </s> <s xml:id="echoid-s5603" xml:space="preserve">item totum mare Oceani pene infinitis ſit <lb/>inſulis reſperſum, ſi aqua ſuę naturali conditioni relicta deflueret, ut terrã hãc <lb/>habitabilem, ſecundum auctores illius <lb/> <anchor type="figure" xlink:label="fig-155-01a" xlink:href="fig-155-01"/> ſententię operiret, magis ſane, ac ma-<lb/>gis detegeretur illa pars, quam noſtri <lb/>antipodes inhabitant, quod idem dices <lb/>de inſulis. </s> <s xml:id="echoid-s5604" xml:space="preserve">Dum igitur auctores huius <lb/>opinionis oſtendere conantur, aquam <lb/>ſuę primę conditioni relictam poſſe ter <lb/>ram operire, aliam partem prorſus dete <lb/>gunt, quod ne quaquam illos conceſſu-<lb/>ros exiſtimo. </s> <s xml:id="echoid-s5605" xml:space="preserve">Hoc idem ſequitur in ſe-<lb/>cunda opinione, dummodo Deus iterũ <lb/>collocaret hęc duo elementa circa idẽ <lb/>centrum: </s> <s xml:id="echoid-s5606" xml:space="preserve">Nam tunc iuxta hanc ſenten <lb/>tiam terra operiretur aqua; </s> <s xml:id="echoid-s5607" xml:space="preserve">Quare mul <lb/>to magis detecta maneret pars illa, quã <lb/>incolunt modo noſtri antipodes. </s> <s xml:id="echoid-s5608" xml:space="preserve">Sed di <lb/>cent fortaſſe, (ut aliqui mihi cum il-<lb/>lis diſputanti reſponderunt) antipodes <lb/>noſtros, & </s> <s xml:id="echoid-s5609" xml:space="preserve">inſulas in eadem circunferentia cum tota terra contineri, & </s> <s xml:id="echoid-s5610" xml:space="preserve">mare <lb/>inter quaſcunque duas inſulas in tumorem, & </s> <s xml:id="echoid-s5611" xml:space="preserve">tumulum quendam attolli. </s> <s xml:id="echoid-s5612" xml:space="preserve">Vn-<lb/>de ſi deflueret, uniuerſam terram cooperiret, etiam illam, quę apud Antipodes <lb/>eſt, unà cum omnibus inſulis. </s> <s xml:id="echoid-s5613" xml:space="preserve">Verum hæc reſponſio abſurda eſt. </s> <s xml:id="echoid-s5614" xml:space="preserve">Primum, quia <lb/>ſi ita eſſet, non haberet tota aqua unicum centrum, ſed quilibet tumulus aquę <lb/>inter duas inſulas ſuum proprium, quod eſt contra communem omnium ſen-<lb/>tentiam, & </s> <s xml:id="echoid-s5615" xml:space="preserve">temere uidetur aſſertum. </s> <s xml:id="echoid-s5616" xml:space="preserve">Deinde ſequeretur, ſi aliquis eſſet in inſu <lb/>la quapiam conſtitutus, ex quauix alteram inſulam longius poſitam poſſet cõ-<lb/>ſpicere, ſi nauigaret continentem uerſus, recedendo uidelicet magis ab ea inſu <lb/>la, quam uix in portu exiſtens uidebat, melius, ac expeditius eam deberet con <lb/>ſpicere; </s> <s xml:id="echoid-s5617" xml:space="preserve">quandoquidem iuxta reſponſionem prędictam ex inſula illa diſcedẽs <lb/>montem quendam aquarum cõſcenderet: </s> <s xml:id="echoid-s5618" xml:space="preserve">quod aduerſatur omni experientię. <lb/></s> <s xml:id="echoid-s5619" xml:space="preserve">Si enim ex uno loco maris uix aliquid uideri poteſt, illud multo minus cerni-<lb/>tur ex alio, qui longius diſtat. </s> <s xml:id="echoid-s5620" xml:space="preserve">Omitto plurima alia huiuſmodi abſurda, quę <lb/>eam reſponſionem conſequuntur.</s> <s xml:id="echoid-s5621" xml:space="preserve"/> </p> <div xml:id="echoid-div306" type="float" level="2" n="4"> <figure xlink:label="fig-155-01" xlink:href="fig-155-01a"> <image file="155-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/155-01"/> </figure> </div> <p> <s xml:id="echoid-s5622" xml:space="preserve"><emph style="sc">Accedit</emph> tandem, quod iuxta utramque ſententiam terra non poſſit <lb/>eſſe ſphęrica, ſed potius oblonga, alteriusue figurę, cum re vera antipodes exi- <pb o="120" file="156" n="157" rhead="Comment. in I. Cap. Sphæræ"/> ſtant, & </s> <s xml:id="echoid-s5623" xml:space="preserve">innumeræ pene inſulæ in toto Oceano reperiantur. </s> <s xml:id="echoid-s5624" xml:space="preserve">Quæ omnia in <lb/>ſuprapoſita figura conſpicis.</s> <s xml:id="echoid-s5625" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5626" xml:space="preserve"><emph style="sc">Reiectis</emph> igitur hiſce opinionibus tanquam abſurdis, atq; </s> <s xml:id="echoid-s5627" xml:space="preserve">cum expe-<lb/> <anchor type="note" xlink:label="note-156-01a" xlink:href="note-156-01"/> rientia pugnantibus, dicendum eſt, Terram, & </s> <s xml:id="echoid-s5628" xml:space="preserve">aquam unum efficere globum, <lb/>vel (quod idem eſt) unum habere centrum commune, quod centrum eſt to-<lb/>tius Vniuerſi. </s> <s xml:id="echoid-s5629" xml:space="preserve">Eſt enim centrum totius Vniuerſi, cum ęqualiter ſit remotum vn-<lb/>dique à cœlo, & </s> <s xml:id="echoid-s5630" xml:space="preserve">conſequenter infimum in mundo locũ poſſideat, tali natura p̃-<lb/>ditum, ut ad illũ omnia grauia ſuapte natura deſcendant, niſi aliunde impedia <lb/>tur. </s> <s xml:id="echoid-s5631" xml:space="preserve">Vnde non immerito à philoſophis centrum grauitatis appellatur; </s> <s xml:id="echoid-s5632" xml:space="preserve">omnia <lb/>ſi quidem grauia ex natura ſua in loco inferiori quærunt eſſe, vt & </s> <s xml:id="echoid-s5633" xml:space="preserve">experientia <lb/>didicimus, & </s> <s xml:id="echoid-s5634" xml:space="preserve">ratione naturali: </s> <s xml:id="echoid-s5635" xml:space="preserve">Non enim eſt maior ratio, cur graue aliquod po-<lb/>tius hic extra centrum mundi, quã ibi, naturaliter uelit eſſe, cũ omnis pars re-<lb/>mota à centro propinquior cœlo exiſtat, & </s> <s xml:id="echoid-s5636" xml:space="preserve">propterea in ſuperioriloco. </s> <s xml:id="echoid-s5637" xml:space="preserve">Ex quo <lb/>ſequitur aquam, cum & </s> <s xml:id="echoid-s5638" xml:space="preserve">ipſa grauis ſit, ſuapte natura, ſi non impediatur, conflue <lb/>re ad loca decliuiora, vt poſſit centrum totius Vniuerſi æqualiter ambire, ne <lb/>una pars ſit in ſuperiori loco, quàm altera, quod eſſet contra ipſius naturam. </s> <s xml:id="echoid-s5639" xml:space="preserve">Id <lb/>quod ſupra Ariſtoteles quo que in ſua demonſtratione aſſumpſit, ut certiſſimis <lb/>experientijs comprobatum. </s> <s xml:id="echoid-s5640" xml:space="preserve">Ita igitur cum omnibus Aſtronomis, & </s> <s xml:id="echoid-s5641" xml:space="preserve">philoſophis <lb/>rectius ſentientibus dicimus, tam ſuperficiem conuexam terræ, quàm aquæ un <lb/>diq; </s> <s xml:id="echoid-s5642" xml:space="preserve">a centro totius mundi æqualiter diſtare; </s> <s xml:id="echoid-s5643" xml:space="preserve">atque idcirco unum & </s> <s xml:id="echoid-s5644" xml:space="preserve">idem eſſe <lb/>centrum horum duorum elementorum; </s> <s xml:id="echoid-s5645" xml:space="preserve">nempe centrum totius Vniuerſi: </s> <s xml:id="echoid-s5646" xml:space="preserve">ita ut <lb/>ſuperficies conuexa unius nullo modo ſuperficiem conuexã alterius interſe-<lb/>cet, ut uolebant ſuperiores opiniones, ſed ſuperficies cõuexa aquæ continuetur <lb/>cũ ſuperficie cõuexa terræ, efficiaturq́ue una ex utraque. </s> <s xml:id="echoid-s5647" xml:space="preserve">quod quidẽ licet facil <lb/>lime cuiuis recte grauitatem cuiuſque elementi ponderanti perſuaderi poſſit, <lb/>nonnullis tamen idipſum iam rationibus demonſtrabimus, quarum prima ſit.</s> <s xml:id="echoid-s5648" xml:space="preserve"/> </p> <div xml:id="echoid-div307" type="float" level="2" n="5"> <note position="left" xlink:label="note-156-01" xlink:href="note-156-01a" xml:space="preserve">Te@am & <lb/>aquã unũ <lb/>globum eſ-<lb/>ficerè<unsure/>.</note> </div> <note position="left" xml:space="preserve">@. ratio.</note> <p> <s xml:id="echoid-s5649" xml:space="preserve"><emph style="sc">In qvacvnqve</emph> orbis parte per eandem omnino aeris lineam <lb/>terra, & </s> <s xml:id="echoid-s5650" xml:space="preserve">aqua non impeditæ, ſed libere demiſſæ deſcendunt. </s> <s xml:id="echoid-s5651" xml:space="preserve">Petunt igitur idem <lb/>centrum pro@ſus, quod paulo ante diximus eſſe centrum totius Vniuerſi, & </s> <s xml:id="echoid-s5652" xml:space="preserve"><lb/>ex conſequenti unum globum conſtituunt. </s> <s xml:id="echoid-s5653" xml:space="preserve">Antecedens conſtat experimen-<lb/>to: </s> <s xml:id="echoid-s5654" xml:space="preserve">cõſecutio uero demõſtr atur a Mathematicis. </s> <s xml:id="echoid-s5655" xml:space="preserve">Ex oppoſito em<unsure/> conſequentis <lb/> <anchor type="figure" xlink:label="fig-156-01a" xlink:href="fig-156-01"/> infertur oppoſitum antecedentis. </s> <s xml:id="echoid-s5656" xml:space="preserve">Nã ſi <lb/>duo grauia ab aliquo puncto demiſſa in <lb/>quocunq; </s> <s xml:id="echoid-s5657" xml:space="preserve">mundi loco diuerſa centra pe <lb/>tunt, per diuerſas quoq; </s> <s xml:id="echoid-s5658" xml:space="preserve">lineas deſcen-<lb/>dant, neceſſe eſt. </s> <s xml:id="echoid-s5659" xml:space="preserve">Quamuis enim ex illo <lb/>loco, qui utrique centro per unam ean-<lb/>demq́ue lineam rectam reſpondet, de-<lb/>miſſa deſcenderent ſecundum eandem <lb/>lineam, ex omnibus tamẽ aliis locis de-<lb/>miſſa tenderent per diuerſas lineas ad il <lb/>la duo centra, ut luce clarius in hac fi-<lb/>gura apparet, in qua centrum terræ fit <lb/>B, centrum aquæ A. </s> <s xml:id="echoid-s5660" xml:space="preserve">Solum namque <lb/>ex puncto E, quod utriq; </s> <s xml:id="echoid-s5661" xml:space="preserve">centro per ean <lb/>dem lineam rectam E A, reſpondet, ten <lb/>det terra ad ſuum centrum B, & </s> <s xml:id="echoid-s5662" xml:space="preserve">aqua <lb/>ad ſuum centrum A, per eandem lineam E A. </s> <s xml:id="echoid-s5663" xml:space="preserve">Ex quouis autem alio puncto, <pb o="121" file="157" n="158" rhead="Ioan. de Sacro Boſco."/> vt ex O, per diuerſas lineas deſcendent, terra videlicet per lineam CB, & </s> <s xml:id="echoid-s5664" xml:space="preserve">aqua <lb/>per lineam C A. </s> <s xml:id="echoid-s5665" xml:space="preserve">Idemq́ue dices de puncto D: </s> <s xml:id="echoid-s5666" xml:space="preserve">Quod nõ contingeret, ſi vtrum-<lb/>que elementum ad centrum mundi F, ferretur. </s> <s xml:id="echoid-s5667" xml:space="preserve">Quare idem eſt centrum terræ, <lb/>aquæ, ac totius Vniuerſi, & </s> <s xml:id="echoid-s5668" xml:space="preserve">propterea una, eademq́ue ſphæra, ſiue globus ex ter <lb/>ra, & </s> <s xml:id="echoid-s5669" xml:space="preserve">a qua conſtituetur. </s> <s xml:id="echoid-s5670" xml:space="preserve">Si enim duos diuerſos globos conſtituerent, non poſ-<lb/>ſent idem continere centrum, cum tunc vnus globus alterum interſecaret; <lb/></s> <s xml:id="echoid-s5671" xml:space="preserve">quemadmodum neque duo circuli ſe mutuo interſecantes idem poſſunt cen-<lb/> <anchor type="note" xlink:label="note-157-01a" xlink:href="note-157-01"/> trum habere. </s> <s xml:id="echoid-s5672" xml:space="preserve">Sed reſpondẽt auctores contrariæ ſententiæ, ex hac ratione <lb/>ſolum colligi, centrum totius Vniuerſi eſſe quidem centrum grauitatis terræ <lb/>& </s> <s xml:id="echoid-s5673" xml:space="preserve">aquæ, ad quod nimirum naturaliter tendunt, non autem centrum magnitu-<lb/>dinis earum. </s> <s xml:id="echoid-s5674" xml:space="preserve">Poteſt enim vnum & </s> <s xml:id="echoid-s5675" xml:space="preserve">idem corpus habere centrum ſuæ magni-<lb/> <anchor type="note" xlink:label="note-157-02a" xlink:href="note-157-02"/> tudinis diuerſum à centro ſuæ grauitatis. </s> <s xml:id="echoid-s5676" xml:space="preserve">Quod ut intelligatur, ſciendum eſt <lb/>centrum grauitatis alicuius corporis eſſe punctum illud, quod ſemper ad per-<lb/>pendiculum tendit ad centrum totius Vniuerſi, quomodocunque, ac quo-<lb/>tieſcunque ſuſpendatur corpus, ita tamen vt libere pendeat. </s> <s xml:id="echoid-s5677" xml:space="preserve">Vel, vt Pappus <lb/>definit, punctum illud intra corpus poſitum, à quo ſi graue appenſum mente <lb/>concipiatur, dum fertur, quieſcit; </s> <s xml:id="echoid-s5678" xml:space="preserve">& </s> <s xml:id="echoid-s5679" xml:space="preserve">ſeruat eam, quàm in principio habebat, po <lb/>ſitionem, neque in ip ſa latione circumuertitur. </s> <s xml:id="echoid-s5680" xml:space="preserve">Qua ratione quoduis corpus <lb/>ſiue rotundum ſit, ſiue non, centrum grauitatis habet. </s> <s xml:id="echoid-s5681" xml:space="preserve">Centrum uero magni-<lb/> <anchor type="note" xlink:label="note-157-03a" xlink:href="note-157-03"/> tudinis. </s> <s xml:id="echoid-s5682" xml:space="preserve">eſſe punctum æqualiter remotum ab omnibus partibus extremis: </s> <s xml:id="echoid-s5683" xml:space="preserve">quod <lb/>quidem proprie in ſolo corpore ſphærico reperitur, in corporibus autem <lb/>regularibus improprie: </s> <s xml:id="echoid-s5684" xml:space="preserve">Punctum enim illud dicitur in quolibet eſſe centrum <lb/>magnitudinis, quod centrum eſt ſphærę, quæ illi circumſcribi poteſt, uel in-<lb/>ſcribi. </s> <s xml:id="echoid-s5685" xml:space="preserve">Hæc duo centra vnum, & </s> <s xml:id="echoid-s5686" xml:space="preserve">idem ſunt in corpore ſphærico, quod unifor-<lb/>me ſit in grauitate, ut uerbi gratia in ſphæra plumbea, ſiue ferrea, &</s> <s xml:id="echoid-s5687" xml:space="preserve">c. </s> <s xml:id="echoid-s5688" xml:space="preserve">at in cor-<lb/>pore ſphærico diſſormi in grauitate, ut in ſphæra partim lignea, partim lapi-<lb/>dea; </s> <s xml:id="echoid-s5689" xml:space="preserve">plumbea, ſeu ferrea, &</s> <s xml:id="echoid-s5690" xml:space="preserve">c. </s> <s xml:id="echoid-s5691" xml:space="preserve">aliud eſt centrum grauitatis, aliud magnitudinis. <lb/></s> <s xml:id="echoid-s5692" xml:space="preserve">Nam in medio illius globi erit centrum magnitudinis; </s> <s xml:id="echoid-s5693" xml:space="preserve">centrum uero grauita-<lb/>tis erit punctum in parte grauiori exiſtens, quod quidem cum centro totius <lb/>Vniuerſi coniungeretur, idemq́ue efficeretur, ſi corpus illud non impeditum <lb/> <anchor type="note" xlink:label="note-157-04a" xlink:href="note-157-04"/> ad ipſum ferretur. </s> <s xml:id="echoid-s5694" xml:space="preserve">Cognoſcitur autem centrum grauitatis cuiuſlibet corporis, <lb/>quantumuis etiam irregularis, ac difformis, hac ratione. </s> <s xml:id="echoid-s5695" xml:space="preserve">Suſpendatur libere <lb/>corpus, cuius centrum inueſtigatur, & </s> <s xml:id="echoid-s5696" xml:space="preserve">à ſuſpenſionis ſigno filum cum per-<lb/>pendiculo demittatur, noteturq́ue linea, quàm filum in corpore deſignat-<lb/>deinde rurſus ex alio puncto ſuſpendatur idem corpus, à quo rurſus filum <lb/>cum perpendiculo demittatur, notata quo-<lb/>que linea ipſius fili in corpore. </s> <s xml:id="echoid-s5697" xml:space="preserve">Quoniam <lb/> <anchor type="figure" xlink:label="fig-157-01a" xlink:href="fig-157-01"/> igitur, vtcunque corpus pendeat, cen-<lb/>trum grauitatis in linea illa perpendicula-<lb/>ri, quæ ad centrum mundi uergit, repe-<lb/>ritur, neceſſe eſt utramque perpendicu-<lb/>larem per grauitatis centrm tranſire. </s> <s xml:id="echoid-s5698" xml:space="preserve">Pun-<lb/>ctum igitur illud corporis, in quo ſe inter-<lb/>ſecant duæ illæ lineæ perpendiculares, cen-<lb/>trum grauitatis indicabit, vt in hoc ſchema-<lb/>te conſpicis; </s> <s xml:id="echoid-s5699" xml:space="preserve">in quo primum punctum ſuſpen <lb/>ſionis ſit A, linea uero perpendiculi in cor-<lb/>pore notata A B; </s> <s xml:id="echoid-s5700" xml:space="preserve">punctum ſecundum ſuſpen- <pb o="122" file="158" n="159" rhead="Comment. in I Cap. Sphæræ"/> ſionis ſit C, linea autẽ perpendiculi in eodẽ corpore notata CD, ſecãs priorem <lb/>A B, in puncto E, quod aſſerimus centrũ grauitatis indicare. </s> <s xml:id="echoid-s5701" xml:space="preserve">Sic igitur dicũt au <lb/>ctores illi centrũ totius Vniue@ſi eſſe centrũ grauitat@s terræ & </s> <s xml:id="echoid-s5702" xml:space="preserve">aquæ: </s> <s xml:id="echoid-s5703" xml:space="preserve">quando <lb/>quidẽ, ut experientia docet, ad illud tendũt, ſuntq́; </s> <s xml:id="echoid-s5704" xml:space="preserve">d@fformis grauitatis; </s> <s xml:id="echoid-s5705" xml:space="preserve">at cen-<lb/>trũ magnitudinis terræ aliud eſſe à centro magn@udinis aquæ, immo utrumq; <lb/></s> <s xml:id="echoid-s5706" xml:space="preserve">centrũ magnitudinis tã terræ, quã aquæ diuerſum eſſe poſſe à cẽtro totius mũ <lb/>di, quod eſt centrum grauitatis, ut uolebat ſecunda opinio, ponens tria centra.</s> <s xml:id="echoid-s5707" xml:space="preserve"/> </p> <div xml:id="echoid-div308" type="float" level="2" n="6"> <figure xlink:label="fig-156-01" xlink:href="fig-156-01a"> <image file="156-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/156-01"/> </figure> <note position="right" xlink:label="note-157-01" xlink:href="note-157-01a" xml:space="preserve">Reſponſi@ <lb/>auctorum <lb/>contratiæ <lb/>ſententiæ.</note> <note position="right" xlink:label="note-157-02" xlink:href="note-157-02a" xml:space="preserve">Centrũ gra <lb/>uitatis cu-<lb/>iuſque cor@ <lb/>poris quid.</note> <note position="right" xlink:label="note-157-03" xlink:href="note-157-03a" xml:space="preserve">Centrũ ma <lb/>gnitudinis <lb/>cuiuſq. cor-<lb/>poris quid.</note> <note position="right" xlink:label="note-157-04" xlink:href="note-157-04a" xml:space="preserve">Centrum <lb/>rauitatis <lb/>in quoli-<lb/>bet corpore <lb/>qũo cogno. <lb/>ſcatur.</note> <figure xlink:label="fig-157-01" xlink:href="fig-157-01a"> <image file="157-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/157-01"/> </figure> </div> <p> <s xml:id="echoid-s5708" xml:space="preserve"><emph style="sc">Vervm</emph> hæc reſponſio nulla eſt. </s> <s xml:id="echoid-s5709" xml:space="preserve">Nam tam in terra, quàm in aqua neceſ-<lb/> <anchor type="note" xlink:label="note-158-01a" xlink:href="note-158-01"/> ſario ponendum eſt idem centrum grauitatis, & </s> <s xml:id="echoid-s5710" xml:space="preserve">magnitudinis. </s> <s xml:id="echoid-s5711" xml:space="preserve">Cum igirur in <lb/>utro que elemento centrum totius Vniuerſi, ad quod nimirum ex omni loco <lb/>demiſſa feruntur, ut ex ratione probatum relinquitur, centrũ ſit grauitatis, per-<lb/>ſpicuum euadit, idem eſſe centrum magnitudinis, nempe centrum Vniuerſi, in <lb/>terra, & </s> <s xml:id="echoid-s5712" xml:space="preserve">aqua; </s> <s xml:id="echoid-s5713" xml:space="preserve">ac proinde duo hæc elementa unum globum conſtituere. </s> <s xml:id="echoid-s5714" xml:space="preserve">Quod <lb/> <anchor type="note" xlink:label="note-158-02a" xlink:href="note-158-02"/> uero idem ſit centrum grauitatis, & </s> <s xml:id="echoid-s5715" xml:space="preserve">magnitudinis in terra, ita demoſtrabimus. <lb/></s> <s xml:id="echoid-s5716" xml:space="preserve">Pondera, & </s> <s xml:id="echoid-s5717" xml:space="preserve">omnia grauia, quæ ex edito loco ad ſuperficiem terræ feruntur, ef <lb/>ſiciunt ſimiles, ac æquales angulos in ipſa, & </s> <s xml:id="echoid-s5718" xml:space="preserve">non ad æquidiſtantiam feruntur, <lb/>ut ſenſus iudicat, quandoquidem in centro Vniuerſi, quod eſt centrũ grauita-<lb/>tis, coeunt. </s> <s xml:id="echoid-s5719" xml:space="preserve">Igitur unum & </s> <s xml:id="echoid-s5720" xml:space="preserve">idem centrum eſt magnitudinis terræ, & </s> <s xml:id="echoid-s5721" xml:space="preserve">grauitatis <lb/>eiuſdẽ, ſeu Vniuerſi. </s> <s xml:id="echoid-s5722" xml:space="preserve">Antecedens communi experientia eſt comprobatũ, ut ui-<lb/>dere eſt in perpendiculis, quibus utuntur artifices in conſtru ctionibus ędificio <lb/>rum, quę nec in hanc, nec in illam @artem flectuntur, ſed ęqualibiter terrę ſu-<lb/>perficiei iuſiſtunt: </s> <s xml:id="echoid-s5723" xml:space="preserve">Ex quocunq. </s> <s xml:id="echoid-s5724" xml:space="preserve">enim loco demittantur in terram, ſimiles ſem-<lb/>per, & </s> <s xml:id="echoid-s5725" xml:space="preserve">ęquales angulos cum ea conſtituunt, ſuntq́ue ſemper fila illorum per-<lb/>pendiculorum in diametro cœli & </s> <s xml:id="echoid-s5726" xml:space="preserve">terrę; </s> <s xml:id="echoid-s5727" xml:space="preserve">Aliàs ędificia diu conſiſtere non poſ-<lb/>ſent. </s> <s xml:id="echoid-s5728" xml:space="preserve">Idem antecedens eſt Ariſtotelis in 2. </s> <s xml:id="echoid-s5729" xml:space="preserve">lib. </s> <s xml:id="echoid-s5730" xml:space="preserve">de cœlo. </s> <s xml:id="echoid-s5731" xml:space="preserve">Conſequentia uero cla-<lb/>riſſima eſt apud Geometras: </s> <s xml:id="echoid-s5732" xml:space="preserve">Ex oppoſito namque conſequentis infertur op-<lb/>poſitum antecedentis. </s> <s xml:id="echoid-s5733" xml:space="preserve">Sit enim, ſi fieri poteſt, centrum grauitatis, ſiue Vniuer-<lb/>ſi E, terrę uero centrum magnitudinis ſit aliud, nempe F, feraturq́; </s> <s xml:id="echoid-s5734" xml:space="preserve">è ſublimi <lb/>pondus aliquod ad centrum E, totius Vniuerſi per lineam B G E, non autem <lb/>ad centrũ terræ F. </s> <s xml:id="echoid-s5735" xml:space="preserve">Dico hoc pondus terrę incidens non efficere angulos ęqua <lb/>les, aut ſimiles cum ſuperficie terræ <lb/> <anchor type="figure" xlink:label="fig-158-01a" xlink:href="fig-158-01"/> ſed prorſus inęquales, diſſimileſue. <lb/></s> <s xml:id="echoid-s5736" xml:space="preserve">Ducta enim ſemidiametro terrę F G, <lb/>protractaque uſque ad H, erunt duo <lb/>anguli F G D, F G L, ęquales, cum <lb/>ſint ſemicirculorum ęqualium; </s> <s xml:id="echoid-s5737" xml:space="preserve">& </s> <s xml:id="echoid-s5738" xml:space="preserve">ex <lb/>conſequenti eadẽ ratione erunt duo <lb/>anguli exteriores D G H, L G Hęqua <lb/>les, ut patet, ſi unus angulus alteri ſu-<lb/>perponeretur. </s> <s xml:id="echoid-s5739" xml:space="preserve">Cõgrueret enim arcus <lb/>G D, arcui G L, & </s> <s xml:id="echoid-s5740" xml:space="preserve">communis eſſer re-<lb/>cta H F. </s> <s xml:id="echoid-s5741" xml:space="preserve">Cum igitur angulus D G B, <lb/>minor ſit angulo D G H, & </s> <s xml:id="echoid-s5742" xml:space="preserve">angulus <lb/>B G L maior angulo L G H; </s> <s xml:id="echoid-s5743" xml:space="preserve">erir an-<lb/>gulus D G B, multis partibus minor <lb/>angulo B G L. </s> <s xml:id="echoid-s5744" xml:space="preserve">Quocirca pondus per <lb/>lineam rectam B G E, demiſſu@m non feretur ad angulos ęquales, ſimilesue in <lb/>ſuperficiem terrę. </s> <s xml:id="echoid-s5745" xml:space="preserve">quod erat demonſtrandum. </s> <s xml:id="echoid-s5746" xml:space="preserve">Idem dices, ſi per lineam rectam <pb o="123" file="159" n="160" rhead="Ioan. de Sacro Boſco."/> @IE, graue aliquod deſcendat ad centrum Vniuerſi E. </s> <s xml:id="echoid-s5747" xml:space="preserve">Ducta enim ſemidiame-<lb/>tro terræ FIK, erit rurſus angulus B I D, in ſuperficie terræ minor angulo <lb/>BIL@ Sola illa pondera, quæ feruntur per lineam rectam, (quod pauciſſimis in <lb/>locis contingeret) quæ extenditur per centrum grauitatis, ſeu Vniuerſi, & </s> <s xml:id="echoid-s5748" xml:space="preserve">per <lb/>centrum magnitudinis terræ, nimirum per lineam A D F E, uel C L E E, ad an-<lb/>gulos æquales incidunt in terræ ſuperficiem, & </s> <s xml:id="echoid-s5749" xml:space="preserve">præter hæc nulla alia, vt demõ <lb/>ſtrauimus. </s> <s xml:id="echoid-s5750" xml:space="preserve">Quod cum pugnet cum experientia, & </s> <s xml:id="echoid-s5751" xml:space="preserve">Ariſtotele, dicendũ erit, cen-<lb/>trum magnitudiuis in terra idẽ eſſe, quod centrũ grauitatis, ſeu Vniuerſi; </s> <s xml:id="echoid-s5752" xml:space="preserve">adeo <lb/>vt è quocunque loco grauia demittantur, ad centrum terræ ferantur: </s> <s xml:id="echoid-s5753" xml:space="preserve">Hac enim <lb/>ſola ratione conſtituentur in ſuperficie anguli æquales, quos experientia do-<lb/>cet æquales debere eſſe. </s> <s xml:id="echoid-s5754" xml:space="preserve">Idem omnino iudicium habendum eſt de centro ma-<lb/>gnitudinis in aqua, eademq́; </s> <s xml:id="echoid-s5755" xml:space="preserve">adhiberi poteſt demonſtratio, dummodo circulis <lb/>DGL, referat globum aquæ, cuius centrum eſt F. </s> <s xml:id="echoid-s5756" xml:space="preserve">Quemadmodum enim perpen <lb/>dicula inſiſtunt ſuperficiei terræ ad angulos æquales, ita quoq; </s> <s xml:id="echoid-s5757" xml:space="preserve">eadem angulos <lb/>æquales efficiunt cum aquæ ſuperficie. </s> <s xml:id="echoid-s5758" xml:space="preserve">Propria tamen, ac peculiari ratione con <lb/>firmari poteſt, in aqua idem eſſe centrum grauitatis, & </s> <s xml:id="echoid-s5759" xml:space="preserve">magnitudinis. </s> <s xml:id="echoid-s5760" xml:space="preserve">Cũ enim <lb/>aqua nõ impedita ad loca decliuiora ſuapte natura ſemper confluat, vt experiẽ <lb/>tia oſtendit, neceſſe eſt, eius ſuperficiẽ conuexam æqualiter recedere à centro <lb/>grauitatis: </s> <s xml:id="echoid-s5761" xml:space="preserve">Atqui punctum illud, à quo omnes partes conuexæ diſtant æquali-<lb/>ter, eſt, per deſinitionem, centrum magnitudinis. </s> <s xml:id="echoid-s5762" xml:space="preserve">Nõ poteſt ergo diuerſum eſſe <lb/>centrũ grauitatis a cẽtro magnitudinis aquæ. </s> <s xml:id="echoid-s5763" xml:space="preserve">Probatur autẽ maior: </s> <s xml:id="echoid-s5764" xml:space="preserve">Si enim cõ-<lb/>uexa ſuperficies aquæ ex una parte magis recederet à cẽtro grauitatis, ſiue Vni <lb/>uerſi, quàm ex alia, pars illa magis à centro grauitatis remota non deflueret ad <lb/>locum decliuiorẽ, qui proculdubio eſt ille, qui pro pinquior exiſtit cẽtro grau@ <lb/>@atis, uel Vniuerſi, ut ex figura prima huius quæſtionis apparet, in qua centrum <lb/>magnitudinis terræ idẽ eſt, quod centrũ Mũdi; </s> <s xml:id="echoid-s5765" xml:space="preserve">centrũ autẽ magnitudinis aquæ <lb/>diſtinctũ. </s> <s xml:id="echoid-s5766" xml:space="preserve">Quod cum ſit abſurdum, & </s> <s xml:id="echoid-s5767" xml:space="preserve">cum aquæ natura pugnet, efficitur, idem <lb/>eſſe centrũ magnitudinis, & </s> <s xml:id="echoid-s5768" xml:space="preserve">grauitatis in aqua. </s> <s xml:id="echoid-s5769" xml:space="preserve">quod oſtendendum erat. </s> <s xml:id="echoid-s5770" xml:space="preserve">Quã <lb/>obrẽ concludendũ eſt, cũ terra, & </s> <s xml:id="echoid-s5771" xml:space="preserve">aqua idẽ habeant centrũ grauitatis, @empe to <lb/>tius Vniuerſi, ad quod naturaliter uergunt, quodq; </s> <s xml:id="echoid-s5772" xml:space="preserve">demonſtratum eſt non diſ-<lb/>ferre à centro magnitudinis utriuſq; </s> <s xml:id="echoid-s5773" xml:space="preserve">elementi, unam ſphæram, ſeu globum ex <lb/>utroq. </s> <s xml:id="echoid-s5774" xml:space="preserve">c<unsure/>lemento componi, & </s> <s xml:id="echoid-s5775" xml:space="preserve">nequaquam duos globos mutuo ſeſe interſecãtes</s> </p> <div xml:id="echoid-div309" type="float" level="2" n="7"> <note position="left" xlink:label="note-158-01" xlink:href="note-158-01a" xml:space="preserve">Confutatio <lb/>reſpõſionis <lb/>aucto@um <lb/>contrariæ <lb/>ſententiæ.</note> <note position="left" xlink:label="note-158-02" xlink:href="note-158-02a" xml:space="preserve">Idem eſſe <lb/>centrũ gra-<lb/>uitatis & <lb/>magnitudi <lb/>@is tam in <lb/>terra, quàm <lb/>in aqua.</note> <figure xlink:label="fig-158-01" xlink:href="fig-158-01a"> <image file="158-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/158-01"/> </figure> </div> <note position="right" xml:space="preserve">2. ratio.</note> <p> <s xml:id="echoid-s5776" xml:space="preserve"><emph style="sc">Secvndo</emph> demonftrabimus, terram & </s> <s xml:id="echoid-s5777" xml:space="preserve">aquam habere unam & </s> <s xml:id="echoid-s5778" xml:space="preserve">ean-<lb/>dem ſuperficiem conuexam, & </s> <s xml:id="echoid-s5779" xml:space="preserve">ex conſequentiidem centrum, multis experi-<lb/>mentis Aſtronomorum. </s> <s xml:id="echoid-s5780" xml:space="preserve">Sicut enim Sol, & </s> <s xml:id="echoid-s5781" xml:space="preserve">rellquæ ſtellæ ciuitati, quæ altera <lb/>orientalior eſt quindecim gradibus, ſpatio vnius horæ citius oriuntur, & </s> <s xml:id="echoid-s5782" xml:space="preserve">ad <lb/>medium cœli perueniunt, & </s> <s xml:id="echoid-s5783" xml:space="preserve">occidunt, quæ vero orientalior exiſtit triginta gra <lb/>dibus, ſpatio duarum horarum, &</s> <s xml:id="echoid-s5784" xml:space="preserve">c. </s> <s xml:id="echoid-s5785" xml:space="preserve">in quocunque tractu terræ ab ortu in occa-<lb/>ſum reperiantur illæ ciuitates, dummodo ſub eodem parallelo collocentur; </s> <s xml:id="echoid-s5786" xml:space="preserve">ſi@ <lb/>etiam nautæ peritiſſimi compertũ habent, idẽ accidere in mari, & </s> <s xml:id="echoid-s5787" xml:space="preserve">Oceano. </s> <s xml:id="echoid-s5788" xml:space="preserve">Na-<lb/>@igantes etenim ad occidẽtaliores plagas, ut ex Luſitania v.</s> <s xml:id="echoid-s5789" xml:space="preserve">g. </s> <s xml:id="echoid-s5790" xml:space="preserve">in Americam ſeu <lb/>Hiſpaniam nouam, præcipue ad illam pr@uinciam, quæ Florida nuncupatur, <lb/>poſtquam progreſſi ſunt quindecim gradibus, repererunt manifeſtiſſimis ſignis <lb/>maxime ex eclipſi Lunari, Solem ac reliquas ſtellas integ@a hora citius orir@ <lb/>in Luſitania, & </s> <s xml:id="echoid-s5791" xml:space="preserve">occidere@idemq́ue proportione eadem per totum Oceanum ab <lb/>ortu verſus occaſum contingere obſeruarunt. </s> <s xml:id="echoid-s5792" xml:space="preserve">Hoc autem nullo pacto fieri poſ-<lb/>@et, niſi ſuperficies conuexa maris uniformiter continuaretur cum conuexa <lb/>@uperficie terræ, ut omnibus Geometris notiſſimum eſt. </s> <s xml:id="echoid-s5793" xml:space="preserve">Si enim eleuaretur <pb o="124" file="160" n="161" rhead="Comment. in I. Cap. Sphæræ"/> paulatim mare in tumorem quendam, ac montem, vt co@trarium ſentientes fa-<lb/>bulantur, cuius illis, qui nauigant, poſtquam aliquot gradus confecerint, orire-<lb/>tur Sol, quàm quando exiſtebant in terra: </s> <s xml:id="echoid-s5794" xml:space="preserve">Pari ratione, ſi quis diceret, mare pe-<lb/>detentim deprimi, non poſſet ſeruari illa proportionalis uarietas exorientis So <lb/>lis, ac occidentis, reliquarumq. </s> <s xml:id="echoid-s5795" xml:space="preserve">ſtellarum. </s> <s xml:id="echoid-s5796" xml:space="preserve">Quod cum ſalſum ſit, perſpicuũ eſt, <lb/>terram & </s> <s xml:id="echoid-s5797" xml:space="preserve">aquam, vnum eandemq́ue ſuperficiem cõuexam obtinere à qua cun-<lb/>que parte orientis uerſus occidentem. </s> <s xml:id="echoid-s5798" xml:space="preserve">Præterea, quemad modum ſi aliquis pro <lb/>cederet in terra à ſeptentrione in auſtrum quoquo uerſus, poſtquam integrum <lb/>gradum perambulaſſet, reperiret polum arcticum magis depreſſum vno gradu; <lb/></s> <s xml:id="echoid-s5799" xml:space="preserve">ſi uero duos gradus in terra peregiſſet, duobus etiam gradibus depreſſum, atq; </s> <s xml:id="echoid-s5800" xml:space="preserve"><lb/>ita deinceps proportionaliter; </s> <s xml:id="echoid-s5801" xml:space="preserve">Ita quoque prorſus obſeruatum fuit in mari. </s> <s xml:id="echoid-s5802" xml:space="preserve"><lb/>Quando enim à ſeptentrione in auſtrum nauigatio inſtituitur, ut ex Luſitania <lb/>v.</s> <s xml:id="echoid-s5803" xml:space="preserve">g.</s> <s xml:id="echoid-s5804" xml:space="preserve">vbi eleuatio poli continet grad. </s> <s xml:id="echoid-s5805" xml:space="preserve">40. </s> <s xml:id="echoid-s5806" xml:space="preserve">uerſus inſulas Canarias ſeu Fortuna-<lb/>tas, poſtquam iter confectum eſt per integrum gradum, reperitur polus altitu-<lb/>dinem habere 39. </s> <s xml:id="echoid-s5807" xml:space="preserve">grad. </s> <s xml:id="echoid-s5808" xml:space="preserve">duntaxat, & </s> <s xml:id="echoid-s5809" xml:space="preserve">ſic deinceps proportionaliter. </s> <s xml:id="echoid-s5810" xml:space="preserve">Contrarium <lb/>vero obſeruatum fuit, quando à meridie in ſeptẽtrionem nauigatur, vt ex inſ@ <lb/>lis prædictis Luſitaniam uerſus, uel ex Luſitania in Britanniam. </s> <s xml:id="echoid-s5811" xml:space="preserve">Signum igi, <lb/>tur manifeſtiſſimum eſt, aquam eandem cum terra habere ſuperficiem conue-<lb/>xam à ſeptemtrione in auſtrum, ita ut neque terra, neque mare magis attolla-<lb/>tur, ſed utrumque elementum æquali diſtantia à centro mundi remoueantur: </s> <s xml:id="echoid-s5812" xml:space="preserve"><lb/>Aliàs enim dicta proportio in uariatione altitudinis poli conſlare minime poſ <lb/>ſet. </s> <s xml:id="echoid-s5813" xml:space="preserve">Cum igitur nulla in re diſcrepet conuexa ſuperficies aquæ à ſupe ficie con <lb/>uexa terræ, tam ab ortu in occaſum, quàm à ſeptentrione in auſtrum, nullus iã <lb/>dubitandi locus relinqultur, unum globum ex vtroque elemento conſtitui. </s> <s xml:id="echoid-s5814" xml:space="preserve"><lb/>Habuit hæc ratio tantum momentum apud quendam, qui contrariam ſenten-<lb/>tiam tuebatur, (quemadmodum à viris fide dignis, qui familiariter eo uteban-<lb/>tur, accepi.) </s> <s xml:id="echoid-s5815" xml:space="preserve">vt proprijs impenſis in diuerſas partes, aſſumptis ſecum uariis in-<lb/>ſtrumentis Mathematicis nauigarit periculum facturus, num hæc proportio, <lb/>quã in ortu, & </s> <s xml:id="echoid-s5816" xml:space="preserve">occaſu ſtellarum, & </s> <s xml:id="echoid-s5817" xml:space="preserve">in eleuatione poli ſeruari diximus, uera eſ-<lb/>ſet, an conficta ab Aſtronomis: </s> <s xml:id="echoid-s5818" xml:space="preserve">deinde vero cum deprehendiſſet eam ueriſſimã <lb/>eſſe, relicta priore ſua opinione erronea, ueram ſententiam amplexus ſit.</s> <s xml:id="echoid-s5819" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5820" xml:space="preserve"><emph style="sc">Tertio</emph> concludi poteſt hæc noſtra ſententia ex eclipſibus Lunaribus, <lb/> <anchor type="note" xlink:label="note-160-01a" xlink:href="note-160-01"/> hac ratione. </s> <s xml:id="echoid-s5821" xml:space="preserve">In omni eclipſi Lunæ umbra aggregati ex terra & </s> <s xml:id="echoid-s5822" xml:space="preserve">aqua rotunda <lb/>eſt, in quacunque cœli parte contingat eclipſis. </s> <s xml:id="echoid-s5823" xml:space="preserve">Igitur neceſſe eſt terram & </s> <s xml:id="echoid-s5824" xml:space="preserve">aquã <lb/>vnum componere globum. </s> <s xml:id="echoid-s5825" xml:space="preserve">Antecedens perſpicuum eſt in partibus Lunæ non-<lb/>dum eclypſatis: </s> <s xml:id="echoid-s5826" xml:space="preserve">Sunt etenim eæ corniculatæ, ſeu circulares, ut experientia no-<lb/>tum eſt omnibus Aſtronomis, & </s> <s xml:id="echoid-s5827" xml:space="preserve">ijs etiam, qui vel vnam Lunæ eclipſim conſpe-<lb/>xerunt. </s> <s xml:id="echoid-s5828" xml:space="preserve">Quare oportet vmbram eiuſdem eſſe figuræ, nempe circularis. </s> <s xml:id="echoid-s5829" xml:space="preserve">Si enim <lb/>eſſet quadrata, uel triangularis, uel alterius figuræ præter ſphæricam, non con <lb/>ſpiceretur Luna circulariter ingredi vmbram, ſed ad modum vmbræ non rotũ <lb/>dæ, quod cum experientia pugnat. </s> <s xml:id="echoid-s5830" xml:space="preserve">Conſecutio uero neceſſaria eſt. </s> <s xml:id="echoid-s5831" xml:space="preserve">Nã ut oſten <lb/>dunt Perſpectui, figura cuiuſque vmbræ imitatur figuram corporis opaci, quod <lb/>vmbram eſſicit; </s> <s xml:id="echoid-s5832" xml:space="preserve">vt ſi corpus opacum, ſeu vmbroſum extiterit rotundum, vm-<lb/>bra quoque rotunda proijciatur; </s> <s xml:id="echoid-s5833" xml:space="preserve">ſi figuræ lateratæ fuerit corpus vmbroſum, <lb/>eiuſdem figuræ cernatur umbra, & </s> <s xml:id="echoid-s5834" xml:space="preserve">ſic de cęteris, vt facillime quiuis experiri po <lb/>terit. </s> <s xml:id="echoid-s5835" xml:space="preserve">Cum igitur umbra in quauis eclipſi Lunari perfectiſſime rotunda appa-<lb/>reat, vt indicant partes nondum eclipſatę, neceſſario concludendum eſt, cor-<lb/>pus illam umbram efficiens, nempe compoſitum ex terra, & </s> <s xml:id="echoid-s5836" xml:space="preserve">aqua, rotundũ at- <pb o="125" file="161" n="162" rhead="Ioan. de Sacro Boſco."/> que ſphæricum eſſe. </s> <s xml:id="echoid-s5837" xml:space="preserve">Si enim aggregatum ex terra & </s> <s xml:id="echoid-s5838" xml:space="preserve">aqua eſſet alterius figuræ, <lb/>oblongæ nimirum quodammodo, & </s> <s xml:id="echoid-s5839" xml:space="preserve">diſſormis, vc oppoſita ſententia aſſerit, ta-<lb/>lem quo que figuram indueret vmbra in eclipſi, quod falſum eſt. </s> <s xml:id="echoid-s5840" xml:space="preserve">Quod ſi reſpõ-<lb/>deant contrarium ſentiens, etiam ſi totus Oceanus, & </s> <s xml:id="echoid-s5841" xml:space="preserve">mare in tumorem altiſ-<lb/>ſ<unsure/>imum erigatur ſupra terram, non tamen inde effici, vt vmbra in eclipſi Luna <lb/>ri rotunda minime appareat; </s> <s xml:id="echoid-s5842" xml:space="preserve">quoniam videlicet aqua nullum proijcit à ſe vm-<lb/>bram, ſed ſola terra, quæ rotunda exiſtit. </s> <s xml:id="echoid-s5843" xml:space="preserve">Dicendum eſt, hanc reſponſionem eſſe <lb/>valde abſudam. </s> <s xml:id="echoid-s5844" xml:space="preserve">Quoniam enim totus Oceanus, ac Mare reſperſum eſt infini-<lb/>tis pene inſulis, adeo vt verſus quamcunque partem nauigetur, ſi Nautis noſtri <lb/>temporis ſides eſt habenda, reperiantur ſemper vel continentes, vel inſulæ; <lb/></s> <s xml:id="echoid-s5845" xml:space="preserve">Quæ cum ſint continuatæ cum continente, (non enim eas ſupernatare aquis <lb/>quis dixerit) quis non videt, ſi talis eſſet horum duorum elementorum cõſtitu <lb/>tio, qualem ipſi confingunt, vmbram terræ vna cum vmbris inſularum omnium <lb/>mire fiactam, atq́; </s> <s xml:id="echoid-s5846" xml:space="preserve">difformem debere effici? </s> <s xml:id="echoid-s5847" xml:space="preserve">Quod cum aduerſetur experientiæ, <lb/>non erunt duo hęc elementa ita conſtituta, vt aduerſarij volunt, ſed vaum con <lb/>ficient globum, ne inſulæ in medio mari repertæ plus diſtent à centro mundi, <lb/>quàm continens, ſed æqualiter, vt vmbra in eclipſi rotunda efficiatur; </s> <s xml:id="echoid-s5848" xml:space="preserve">vt expe-<lb/>rientia docet. </s> <s xml:id="echoid-s5849" xml:space="preserve">Accedit etiam, quòd aqua haud dubie aliquam à ſe vmbrã proij-<lb/>ciat, vt experientia teſtatur, præſertim aqua maris, quæ denſior eſt, & </s> <s xml:id="echoid-s5850" xml:space="preserve">craſſior <lb/>ali<unsure/>js aquis. </s> <s xml:id="echoid-s5851" xml:space="preserve">Colligamus ergo, cum vmbra aggregati ſemper rotunda ſit, ipſum <lb/>quoque aggregatum rotundum eſſe, ac ſphæricum.</s> <s xml:id="echoid-s5852" xml:space="preserve"/> </p> <div xml:id="echoid-div310" type="float" level="2" n="8"> <note position="left" xlink:label="note-160-01" xlink:href="note-160-01a" xml:space="preserve">3. ratio</note> </div> <p> <s xml:id="echoid-s5853" xml:space="preserve"><emph style="sc">Confirmari</emph> poteſt eadem hæc veritas experientia quadam com-<lb/>muni, quàm etiam affert Ptolem. </s> <s xml:id="echoid-s5854" xml:space="preserve">Di<unsure/>ct. </s> <s xml:id="echoid-s5855" xml:space="preserve">1. </s> <s xml:id="echoid-s5856" xml:space="preserve">cap. </s> <s xml:id="echoid-s5857" xml:space="preserve">4. </s> <s xml:id="echoid-s5858" xml:space="preserve">& </s> <s xml:id="echoid-s5859" xml:space="preserve">Ioan. </s> <s xml:id="echoid-s5860" xml:space="preserve">Regiom. </s> <s xml:id="echoid-s5861" xml:space="preserve">lib. </s> <s xml:id="echoid-s5862" xml:space="preserve">1. </s> <s xml:id="echoid-s5863" xml:space="preserve">concl. </s> <s xml:id="echoid-s5864" xml:space="preserve">2. <lb/></s> <s xml:id="echoid-s5865" xml:space="preserve">quæ talis fere eſt. </s> <s xml:id="echoid-s5866" xml:space="preserve">Exiſtẽtes in medio mari nihil omnino præter cœlũ & </s> <s xml:id="echoid-s5867" xml:space="preserve">aquam <lb/>contuemur:</s> <s xml:id="echoid-s5868" xml:space="preserve"><unsure/> quando vero littora petimus, tunc primum montes, ſcopuli, arces <lb/>turres, & </s> <s xml:id="echoid-s5869" xml:space="preserve">huiuſmodi alia ſenſim exurgere cernũtur, quaſi ex aqua emergerent; </s> <s xml:id="echoid-s5870" xml:space="preserve"><lb/>Idq́; </s> <s xml:id="echoid-s5871" xml:space="preserve">ea proportione, vt prius cacumina montium, ſummitatesq́ue turrium, de-<lb/>inde mediæ partes, poſtremo infimæ iuxta litora appareant: </s> <s xml:id="echoid-s5872" xml:space="preserve">Quod minime, tam <lb/>ordinate accideret, ſi mare ſupra terram attolleretur, aut ſuperficies maris non <lb/>continuaretur cum terræ ſuperficie, ita vt vna ex vtraque conficeretur. </s> <s xml:id="echoid-s5873" xml:space="preserve">Nam ſi <lb/>mare in medio attolleretur, ita vt eius circunferentia cum terræ circunferen-<lb/>tia non continuaretur, poſtquam aliquis faſtigium tumoris, quem mare ſecun-<lb/>dum illos auctores eſficit, conſcendiſſet, continuò videret omnia, quæ in lito-<lb/>re ſunt poſita, quemad modum, ſi quis ad faſtigium montis peruenerit, ſtatim <lb/>omnia, quæ in ſubiecta planitie ſita ſunt, ſimul conſpicit. </s> <s xml:id="echoid-s5874" xml:space="preserve">quod abſurdum eſt. </s> <s xml:id="echoid-s5875" xml:space="preserve"><lb/>Prius en@m ea, quæ altiora ſunt in littore, deinde ea, quæ in inferiori loco ſunt <lb/>poſita, cern<unsure/>untur.</s> <s xml:id="echoid-s5876" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5877" xml:space="preserve"><emph style="sc">Accedit</emph> etiam, ſi terra, & </s> <s xml:id="echoid-s5878" xml:space="preserve">aqua non haberent vnam, eandemq́ue con-<lb/>tinuam ſuperficiem conuexã, ſed aqua paulatim eleuaretur, ſequeretur eũ qui <lb/>in aliqua naui e portu diſcedit, non poſſe non videre ſignum poſitum iuxta lit <lb/>tus, quoniam videlicet aſcenderet; </s> <s xml:id="echoid-s5879" xml:space="preserve">quod eſt contra experientiam. </s> <s xml:id="echoid-s5880" xml:space="preserve">His ad de, cum <lb/>aqua ſuapte natura ad loca decliuiora cõfluat, vt experientia demonſtrat, reci-<lb/>pietur vſ<unsure/>iq, in concauitat<unsure/>ibus terræ, donec eas expleat, redigaturq́ue ad æqua <lb/>litatem cum terra. </s> <s xml:id="echoid-s5881" xml:space="preserve">Hoc enim pacto æqualiter diſtabit à medio mundi, erit que <lb/>in æquilibrio poſita, ideoque cum terra vnam conficiet ſuperficiem ſphęricam.</s> <s xml:id="echoid-s5882" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5883" xml:space="preserve"><emph style="sc">Haec</emph> quoque ſententia d@lucidiſſime paulo poſt confirmatur, quan-<lb/>do videlicet vnam cum noſtro auctore demonſtrabimus, tam ſuperficiem ter-<lb/>tæ, quàm aquæ æqualiter centrum totius Vniuerſi ambire 5<unsure/> ex quo perſpicue <pb o="126" file="162" n="163" rhead="Comment. in I. Cap. Sphæræ"/> ſequitur, vnum, & </s> <s xml:id="echoid-s5884" xml:space="preserve">idem eſſe centrum vtriuſque elementi, atque propterea, <lb/> <anchor type="note" xlink:label="note-162-01a" xlink:href="note-162-01"/> vnum globum ex ipſis conſtitui.</s> <s xml:id="echoid-s5885" xml:space="preserve"/> </p> <div xml:id="echoid-div311" type="float" level="2" n="9"> <note position="left" xlink:label="note-162-01" xlink:href="note-162-01a" xml:space="preserve">Cur terra <lb/>ſola ceutrũ <lb/>mundi oc-<lb/>oupet, & nõ <lb/>ctiã aqua.</note> </div> <p> <s xml:id="echoid-s5886" xml:space="preserve"><emph style="sc">Sed</emph> quæret f<unsure/>ortaſſe aliquis, cum aqua, & </s> <s xml:id="echoid-s5887" xml:space="preserve">terra idem poſſideant centrum, <lb/>vt probatum eſt, ad quod per eandem lineam rectam deſcendunt non impedi-<lb/>tæ, qua de cauſa ſola terra centrum occupet, & </s> <s xml:id="echoid-s5888" xml:space="preserve">non etiam aqua; </s> <s xml:id="echoid-s5889" xml:space="preserve">videmus namq; <lb/></s> <s xml:id="echoid-s5890" xml:space="preserve">aquam ſupra terræ ſuperficiem extendi. </s> <s xml:id="echoid-s5891" xml:space="preserve">Huic reſpondendum eſt, hanc eſſe di-<lb/>ſtinctionem naturalem inter elementum terræ, & </s> <s xml:id="echoid-s5892" xml:space="preserve">elementum aquæ, vt terra <lb/>maiore ſui grauitate centrum occupet; </s> <s xml:id="echoid-s5893" xml:space="preserve">aqua vero, quoniam non ita grauis eſt, <lb/>naturaliter ſupra terram maneat, vt philoſophi aſſerunt adeo, vt ſi terra ita <lb/>rotunda exiſteret, vt politum aliquem globum efficeret, elementum aquæ to-<lb/>tam terram vndique contegeret: </s> <s xml:id="echoid-s5894" xml:space="preserve">quod etiam contingeret, ſi tanta eſſet copia <lb/>aquarum, vt omnes concauitates terræ expleret, & </s> <s xml:id="echoid-s5895" xml:space="preserve">montes tranſcenderet. </s> <s xml:id="echoid-s5896" xml:space="preserve">Sed <lb/>niam neq; </s> <s xml:id="echoid-s5897" xml:space="preserve">terra pefecte eſt ſphærica, propter montes, ſcopulos, concauitates <lb/>atque vales, neque tanta copia aquarum exiſtit, vt totam ſuperficiem terræ poſ <lb/>ſit contegere, effectum eſt, vt tota aqua in varijs terræ concauitatibus ſit rece-<lb/>pta, æqualiter tamen ſemper diſtans ſecundum eius ſuperficiem conuexam à<unsure/> <lb/>centro mundi, vt ſuperiores rationes oſtenderunt.</s> <s xml:id="echoid-s5898" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5899" xml:space="preserve"><emph style="sc">Caetervm</emph> quod diximus, vnum effici globum ex terra, & </s> <s xml:id="echoid-s5900" xml:space="preserve">aqua, il-<lb/> <anchor type="note" xlink:label="note-162-02a" xlink:href="note-162-02"/> lud non ita intelligendum eſt, vt perfectus globus, qualem Geometræ definiũt, <lb/>ex vtroque elemento reſultet. </s> <s xml:id="echoid-s5901" xml:space="preserve">Hoc enim falſum eſt, ſi Geometrice, & </s> <s xml:id="echoid-s5902" xml:space="preserve">proprie <lb/>loqui u<unsure/>elimus, tum quia lineæ rectæ egredientes à cẽtro huius globi ad ſum-<lb/>mitates montium altiſſimorũ longiores erunt haud dubie lineis rectis eductis <lb/>ad infimas partes vallium profundiſſimarum: </s> <s xml:id="echoid-s5903" xml:space="preserve">quare non omni ex parte conueni <lb/>re illi poterit definitio globi Geometrici: </s> <s xml:id="echoid-s5904" xml:space="preserve">tum etiã, quoniam ſuperficies conue <lb/>xa aquæ æquali diſtantia ſub terræ ſuperficie continetur, tanquam circulus mi <lb/>nor ſub maiori, qui idem centrum poſſidet; </s> <s xml:id="echoid-s5905" xml:space="preserve">adeo vt ſi circa centrum mundi per <lb/>ficeretur tota ſuperficies aquæ, item tota ſuperficies terræ, illa ſub hac æquali <lb/>ſemper diſtantia contineretur. </s> <s xml:id="echoid-s5906" xml:space="preserve">Verũ quia hæc difformitas, ſeu inæqualitas com-<lb/>parata cũ tota machina compoſita ex terra, & </s> <s xml:id="echoid-s5907" xml:space="preserve">aqua nullius fete eſt momẽti, ita <lb/>vt vix ſenſu percipiatur, effectum eſt, vt ſimpliciter aggregatum ex terra, & </s> <s xml:id="echoid-s5908" xml:space="preserve">aquæ <lb/>globus rotundus, ſiue ſphæricus ab Aſtronomis appelletur. </s> <s xml:id="echoid-s5909" xml:space="preserve">Quòd autem aquæ <lb/>ſuperficies contineatur ſub terræ ſuperficie æquali ſemper diſtantia, facile cui-<lb/>nis perſuaderi poteſt, facta hypotheſi, ab oriente in occidentem ſub Aequino-<lb/>ctionali circulo reperiri continentes, inſulas, peninſulas, &</s> <s xml:id="echoid-s5910" xml:space="preserve">c. </s> <s xml:id="echoid-s5911" xml:space="preserve">id, quod nauigatio <lb/>huius temporis, maxime Luſitanorũ, aperte docet, rem apud veteres ſatis inco-<lb/>gnitã. </s> <s xml:id="echoid-s5912" xml:space="preserve">Si namq; </s> <s xml:id="echoid-s5913" xml:space="preserve">deſcribatur circulus maximus in terra directe ſuppoſitus Ae-<lb/>quatori cœleſti incedens per inſulam D. </s> <s xml:id="echoid-s5914" xml:space="preserve">Thomæ, per Africam, per Taprobanẽ <lb/>in Indijs orientalibus, per inſulas Moluccas, per Americę, ſiue nouæ Hiſpaniæ <lb/>prouinciam, quæ Peru nominatur, quoſ iterũ abſoluatur in inſula D. </s> <s xml:id="echoid-s5915" xml:space="preserve">Tho-<lb/>mæ; </s> <s xml:id="echoid-s5916" xml:space="preserve">hic circulus, ſaltem prope littora, continebit ſub ſe ſuperficiẽ maris, quan <lb/>doquidem à terra ad mare ex omni parte deſcenditur, vt patet ex fluuiorum <lb/>decurſu. </s> <s xml:id="echoid-s5917" xml:space="preserve">Hinc iam ita colligemus inſtitutum Arcus deſcriptus in ſuperficie il-<lb/>lius maris, quod interijcitur inter Africam verbi gratia & </s> <s xml:id="echoid-s5918" xml:space="preserve">Taprobanem, æqua <lb/>li diſtantia eſt ſuppoſitus a, cui deſcripti circuli in terra, qui tranſit per Africã, <lb/>& </s> <s xml:id="echoid-s5919" xml:space="preserve">Taprobanem, &</s> <s xml:id="echoid-s5920" xml:space="preserve">c. </s> <s xml:id="echoid-s5921" xml:space="preserve">Atq. </s> <s xml:id="echoid-s5922" xml:space="preserve">idem dicendũ eſt de quouis arcu ſuperficiei maris in-<lb/>teriecti inter quaſcunq; </s> <s xml:id="echoid-s5923" xml:space="preserve">duas terras. </s> <s xml:id="echoid-s5924" xml:space="preserve">Ergo tota ſuperficies aquæ æquali diſtan-<lb/>tia cõtinetur ſub tota ſuperficie terræ. </s> <s xml:id="echoid-s5925" xml:space="preserve">Cõſecutio optima eſt ex ſufficienti par-<lb/>@um enumeratione: </s> <s xml:id="echoid-s5926" xml:space="preserve">Antecedens vero probatur; </s> <s xml:id="echoid-s5927" xml:space="preserve">nam ſi arcus ille deſcriptus <pb o="127" file="163" n="164" rhead="Ioan. de Sacro Boſco."/> in mari non eſſet æquidiſtans arcui terræ, ſed in medio magis attolleretur, vel <lb/>deprimeretur, vel etiam arcum terræ tranſcederet, eum ſecando, ſequeretur <lb/>vtrumque arcum non habere idem centrum, vt conſtat apud Geometras: <lb/></s> <s xml:id="echoid-s5928" xml:space="preserve">quod iam impugnauimus. </s> <s xml:id="echoid-s5929" xml:space="preserve">probatum enim eſt, idem eſſe centrum vtriuſque <lb/>elementi.</s> <s xml:id="echoid-s5930" xml:space="preserve"/> </p> <div xml:id="echoid-div312" type="float" level="2" n="10"> <note position="left" xlink:label="note-162-02" xlink:href="note-162-02a" xml:space="preserve">Quomodo <lb/>intelligen-<lb/>dum ſit, v-<lb/>nũ globum <lb/>ex terra & <lb/>aqua con-<lb/>ſ<unsure/>titui.</note> </div> <p> <s xml:id="echoid-s5931" xml:space="preserve"><emph style="sc">Svperest</emph>, vt nonnullas obiectiones, quæ contra noſtram ſenten-<lb/>tiam fie ri poſſent, in medium proferamus, easq́ue diſſoluamus. </s> <s xml:id="echoid-s5932" xml:space="preserve">Quamuis enim <lb/>ex perientiæ hactenus adductæ euidenter oſtendat, idem eſſe centrum terræ, & </s> <s xml:id="echoid-s5933" xml:space="preserve"><lb/>aquæ, atque adeo vnum ex illis globum conſtitui: </s> <s xml:id="echoid-s5934" xml:space="preserve">ſunt tamen nonnulla, quæ <lb/>difficultatem videntur facere, probareq́ue nulla ratione fieri poſſe, vt duo hæc <lb/>elementa vnicum globum conſiciant. </s> <s xml:id="echoid-s5935" xml:space="preserve">Primum igitur ſic poterit quis conari <lb/>probare, non eſſe idem centrum terræ, & </s> <s xml:id="echoid-s5936" xml:space="preserve">aquæ, ac propterea ex ipſis non com-<lb/> <anchor type="note" xlink:label="note-163-01a" xlink:href="note-163-01"/> poni vnum globum. </s> <s xml:id="echoid-s5937" xml:space="preserve">Terra & </s> <s xml:id="echoid-s5938" xml:space="preserve">aqua ſunt difformes in grauitate: </s> <s xml:id="echoid-s5939" xml:space="preserve">conſtat enim ter <lb/>ram eſſe grauiorem quàm aquam. </s> <s xml:id="echoid-s5940" xml:space="preserve">Igitur non poſſunt habere idem centrum gra <lb/>nitatis, & </s> <s xml:id="echoid-s5941" xml:space="preserve">magnitudinis, ſed terra grauitate ſua propellet aquam extra centrũ <lb/>totius Vuinerſi, quod ipſi debetur ob ſummam grauitatem: </s> <s xml:id="echoid-s5942" xml:space="preserve">Quemad modum <lb/>neque globus, qui partim ligneus, partim vero plumbeus exiſtit, idem ceutrum <lb/>grauitatis & </s> <s xml:id="echoid-s5943" xml:space="preserve">magnitudinis poſſidere poteſt, cum hoc ſit in medio ipſius, illud <lb/>vero in parte plumbea, tanquam grauiori, Ad hanc obiectionem dicendum eſt, <lb/> <anchor type="note" xlink:label="note-163-02a" xlink:href="note-163-02"/> e<unsure/>am ex falſa hypotheſi procedere: </s> <s xml:id="echoid-s5944" xml:space="preserve">putat enim, ex vna tantum parte eſſe terram, <lb/>& </s> <s xml:id="echoid-s5945" xml:space="preserve">ex oppoſita totum mare, quod faſſum eſt. </s> <s xml:id="echoid-s5946" xml:space="preserve">Nauigationibus enim huius no-<lb/>ſtræ tempeſtatis tam ſub polis, quàm ſub Aequinoctiali circulo, tam in oriente, <lb/>quàm in occidente, & </s> <s xml:id="echoid-s5947" xml:space="preserve">denique in toto orbe repertę ſunt vel continentes, vel <lb/>inſulæ, vel peninſulæ, ita vt per totum orbem fere permixtæ ſint terra, & </s> <s xml:id="echoid-s5948" xml:space="preserve">aqua. <lb/></s> <s xml:id="echoid-s5949" xml:space="preserve">Eſt enim mare innumeris pene inſulis conſperſum, adeo vt plus terræ, vel cer-<lb/>te non multo minus, extra mare appareat, quàm aquis ſit contectum, vt egre-<lb/>gie probat Alex. </s> <s xml:id="echoid-s5950" xml:space="preserve">Piccolomineus in libello de quantitate terræ, & </s> <s xml:id="echoid-s5951" xml:space="preserve">aquæ. </s> <s xml:id="echoid-s5952" xml:space="preserve">Vnde <lb/>dicimus hunc globum, quem confici aſſerimus ex terra, & </s> <s xml:id="echoid-s5953" xml:space="preserve">aqua, ita eſſe compa-<lb/>ratum, vt terra vndiqi emineat, aqua vero in partibus humilioribus deſidat. </s> <s xml:id="echoid-s5954" xml:space="preserve">Re <lb/>ſert itaque terra globi cuiuſdam lignei ſpeciem, in quo plurimæ ſint concaui-<lb/>tates, in quibus aqua poſſit tecipi: </s> <s xml:id="echoid-s5955" xml:space="preserve">Nam hac ratione ita eſt æqualitate ponderũ <lb/>hic globus collibratus, vt idem habeat centrum grauitatis, & </s> <s xml:id="echoid-s5956" xml:space="preserve">magnitudinis. </s> <s xml:id="echoid-s5957" xml:space="preserve">At <lb/>que hoc ipſum videtur ſentire Ariſto. </s> <s xml:id="echoid-s5958" xml:space="preserve">lib. </s> <s xml:id="echoid-s5959" xml:space="preserve">1. </s> <s xml:id="echoid-s5960" xml:space="preserve">Meteor. </s> <s xml:id="echoid-s5961" xml:space="preserve">vbi ait, [Terræ moles, quæ <lb/>toi<unsure/>am etiam aquæ copiam complexa eſt, nullius particulæ rationem ſubit ad ambientium <lb/>magnitudinem.</s> <s xml:id="echoid-s5962" xml:space="preserve">] Quibus verbis perſpicue aſſerere videtur, aquam in concauita <lb/>tibus terræ comprehendi, quandoquidem dicit, terram in ſe continere totam, <lb/>aquæ copiam: </s> <s xml:id="echoid-s5963" xml:space="preserve">immo hoc ipſum ratio naturalis ab experimento deſumpta per-<lb/>ſuadere videtur. </s> <s xml:id="echoid-s5964" xml:space="preserve">Deprehendimus enim aquas confluas, deciduasq́ue eſſe ad ter <lb/>ræ partes decliuiores, concauioresq́ue, ita vt intra eminentiora terræ loca non <lb/>aliter, quàm intra montes valles, contineatur, donec omnes partes collibren-<lb/>tur, ac ad amuſſim adæquentur, vt recte demonſtrauit Ariſt. </s> <s xml:id="echoid-s5965" xml:space="preserve">2. </s> <s xml:id="echoid-s5966" xml:space="preserve">lib. </s> <s xml:id="echoid-s5967" xml:space="preserve">de cœlo, cu-<lb/>ius rationem ſupra attullimus.</s> <s xml:id="echoid-s5968" xml:space="preserve"/> </p> <div xml:id="echoid-div313" type="float" level="2" n="11"> <note position="right" xlink:label="note-163-01" xlink:href="note-163-01a" xml:space="preserve">1. obiectio.</note> <note position="right" xlink:label="note-163-02" xlink:href="note-163-02a" xml:space="preserve">Solutio <lb/>obiectionis</note> </div> <p> <s xml:id="echoid-s5969" xml:space="preserve"><emph style="sc">Deinde</emph> obijciet aliquis hoc modo. </s> <s xml:id="echoid-s5970" xml:space="preserve">Partes terræ detectæ ſunt minus <lb/> <anchor type="note" xlink:label="note-163-03a" xlink:href="note-163-03"/> graues partibus tectis aqua maris, propter aerẽ incluſum in cauernis, & </s> <s xml:id="echoid-s5971" xml:space="preserve">calo-<lb/>rem Solis, qui eas continue exiccat. </s> <s xml:id="echoid-s5972" xml:space="preserve">Cum igitur centrum grauitatis in cor-<lb/>pore difformiter graui ſit in eius parte grauiori, erit centrum grauitatis terræ <lb/>magis propinquum illis partibus, quæ aquis ſunt contectæ, quàm illis, quæ ſunt <lb/>detectæ: </s> <s xml:id="echoid-s5973" xml:space="preserve">quare diuerſum erit centrum grauitatis terræ à centro magnitudin is <pb o="128" file="164" n="165" rhead="Comment. in I. Cap. Sphæræ"/> eiuſdem. </s> <s xml:id="echoid-s5974" xml:space="preserve">Cæterum & </s> <s xml:id="echoid-s5975" xml:space="preserve">hæc obiecto idem, quod prior, aſſumere videtur, nimi-<lb/>rum detectas terræ partes ad vnum hemiſphærium, rectas vero ad alterum ſpe-<lb/>ctare, quod uerum non eſt, vt diximus. </s> <s xml:id="echoid-s5976" xml:space="preserve">Reſpondemus igitur, partes detectas eſ-<lb/>ſe quidem minus graues ſimpliciter, propter cauſas dictas, quæ abſque dubio <lb/> <anchor type="note" xlink:label="note-164-01a" xlink:href="note-164-01"/> minuunt earum grauitatem; </s> <s xml:id="echoid-s5977" xml:space="preserve">at vero, quoniam aer incluſus, & </s> <s xml:id="echoid-s5978" xml:space="preserve">calor Solis in-<lb/>ſenſibilem fere partem illarum penetrant, ſi ea cum tota profunditat<unsure/>e terræ <lb/>cõparetur, (uix enim ad unum, aut alterum milliare ea penetratio pertingit, <lb/>cum tamen tota profunditas terræ complectatur miliaria 3579, & </s> <s xml:id="echoid-s5979" xml:space="preserve">amplius, vt <lb/>ad finem huius cap. </s> <s xml:id="echoid-s5980" xml:space="preserve">dicemus.) </s> <s xml:id="echoid-s5981" xml:space="preserve">extantq́ue in ipſis immenfi, & </s> <s xml:id="echoid-s5982" xml:space="preserve">plurimi montes, ac <lb/>rupes, item in partibus contectis innumeræ pene inſulæ reperi<unsure/>ũtur, quæ ſupra <lb/>mare eminent ſcopulis etiam altiſſimis præditæ, tota denique terra referta eſt <lb/>aquis, ut conſtat experientia, cum vbiuis locorum, effoſſa terra, aquæ reperian-<lb/>tur; </s> <s xml:id="echoid-s5983" xml:space="preserve">efficitur, vt partes detectæ, vnà cum contectis, addita etiam aqua maris, <lb/>quę ſupra partes contectas extenditur, ita librentur, & </s> <s xml:id="echoid-s5984" xml:space="preserve">quaſi compenſetur om-<lb/>nium partium grauitas, vt centrum grauitatis vtriuſque elementi, terræ uide-<lb/>licet, & </s> <s xml:id="echoid-s5985" xml:space="preserve">aquæ, ex æquo diſtet à ſuperficie ipſorum: </s> <s xml:id="echoid-s5986" xml:space="preserve">quemadmodum re ipſa di-<lb/>ſtat, vt ſupra pluribus experimentis demonſtrauimus. </s> <s xml:id="echoid-s5987" xml:space="preserve">Neque uero obſtat, quòd <lb/>ſuperficies terræ ſit aliquantò altior ſuperficie maris, ut ſupra diximus, quò <lb/>minus centrum grauitatis ab vtraque ſuperficie æquali diſtantia recedat. </s> <s xml:id="echoid-s5988" xml:space="preserve">Is <lb/>enim exceſſus perexiguus eſt comparatione tantæ magnitudinis, vt merito am-<lb/>bæ ſuperficies æqualiter diſtare à centro dici poſſint, ſi ſenſum conſulamus, qui <lb/>aquam eiuſdem eſſe altitudinis cum terra iudicat, licet præciſe, ac Geometrice <lb/>loquendo hoc verum non ſit. </s> <s xml:id="echoid-s5989" xml:space="preserve">Ex his quoque diſſoluitur argumentum illud, <lb/>quod ſupra contra auctores oppoſitam partem noſtræ ſententiæ defendentes af <lb/>ferebamus; </s> <s xml:id="echoid-s5990" xml:space="preserve">Nempe, ſecundum illos, plura debere milliaria vni gradui correſpõ <lb/>dere in mari, quàm in terra, quandoquidem altius illud, quàm terram, faciunt, <lb/>ac maius: </s> <s xml:id="echoid-s5991" xml:space="preserve">Poterat enim nunc idem argumentum in nos torqueri, quippe cum <lb/>terram nos altiorem ſtatuamus, quàm aquam; </s> <s xml:id="echoid-s5992" xml:space="preserve">ex quo eſſici videtur, plura mil-<lb/>liaria vni gradui terreſtri reſpondere, quàm marino. </s> <s xml:id="echoid-s5993" xml:space="preserve">Di<unsure/>ſſoluitur, inquam, hoc <lb/>argumentum in nos contortum, quoniam iſte exceſſus altitudinis terræ ſupra <lb/>altitudinem maris, quem ponimus, nullius eſt momenti, ſed omnino inſenſi-<lb/>bilis. </s> <s xml:id="echoid-s5994" xml:space="preserve">Vnde aduerſus nos nihil concludit: </s> <s xml:id="echoid-s5995" xml:space="preserve">At uero contra aduerſarios maximã <lb/>habet vim, cum ipſi ponant aquam multis partibus terra maiorem, nimirum in <lb/>deculpa proportione, Ex quo neceſſario conſequitur, plura eſſe milliaria in vno <lb/>gradu ſuperficiei maris, quàm in gradu terreno.</s> <s xml:id="echoid-s5996" xml:space="preserve"/> </p> <div xml:id="echoid-div314" type="float" level="2" n="12"> <note position="right" xlink:label="note-163-03" xlink:href="note-163-03a" xml:space="preserve">2. obiectio.</note> <note position="left" xlink:label="note-164-01" xlink:href="note-164-01a" xml:space="preserve">Solutio o-<lb/>biectionis.</note> </div> <p> <s xml:id="echoid-s5997" xml:space="preserve"><emph style="sc">TERTIO</emph> poterit quiſpiam iudicio ſenſus innixus in nos inſurgere, hac <lb/> <anchor type="note" xlink:label="note-164-02a" xlink:href="note-164-02"/> ratione. </s> <s xml:id="echoid-s5998" xml:space="preserve">Quonam modo fieri poteſt, vt vnus globus efficiatur, ex terra, & </s> <s xml:id="echoid-s5999" xml:space="preserve">aqua, <lb/>cum neque terra, neque aqua rotunda videatur eſſe? </s> <s xml:id="echoid-s6000" xml:space="preserve">Quando enim quis ſum-<lb/>mitatem alicuius montis conſcendit, vnde magnã terræ planitiem, marisq́; </s> <s xml:id="echoid-s6001" xml:space="preserve">ſu-<lb/>perficiem cõſpiciat, tam mare, quam terra plana a ſenſu iudicatur, & </s> <s xml:id="echoid-s6002" xml:space="preserve">nullo pa-<lb/>cto rotunda: </s> <s xml:id="echoid-s6003" xml:space="preserve">præcipueq́; </s> <s xml:id="echoid-s6004" xml:space="preserve">de terra di<unsure/>fficultas eſſe videtur, propter tot ingentis al <lb/>titudinis montes, & </s> <s xml:id="echoid-s6005" xml:space="preserve">miræ profunditatis valles. </s> <s xml:id="echoid-s6006" xml:space="preserve">Accedit etiam, quod Sol quan-<lb/>do oritur, uel occidit, videtur à ſuperficie terræ ſcindi ſecundum lineam recta: <lb/></s> <s xml:id="echoid-s6007" xml:space="preserve">igitur terra plana exiſtit. </s> <s xml:id="echoid-s6008" xml:space="preserve">Idemque dicendum eſt de mari. </s> <s xml:id="echoid-s6009" xml:space="preserve">Nam ſi terra, & </s> <s xml:id="echoid-s6010" xml:space="preserve">ma-<lb/>re eſſent rotunda, abſcinderent vtique à Sole exoriente, & </s> <s xml:id="echoid-s6011" xml:space="preserve">occidente partes <lb/>curuas, & </s> <s xml:id="echoid-s6012" xml:space="preserve">non rectas: </s> <s xml:id="echoid-s6013" xml:space="preserve">Quemadmodum videmus Lunam, quoniam rotunda eſt, <lb/>& </s> <s xml:id="echoid-s6014" xml:space="preserve">ſphærica, in eclipſi Solis, auferre ex Sole partes curuas, non autem rectas. </s> <s xml:id="echoid-s6015" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-164-03a" xlink:href="note-164-03"/> Huic tamen obiectioni occurrendum eſt. </s> <s xml:id="echoid-s6016" xml:space="preserve">Senſum noſtrum in hoc mitrum in mo <pb o="129" file="165" n="166" rhead="Ioan. de Sacro Boſco."/> dum falli. </s> <s xml:id="echoid-s6017" xml:space="preserve">Id enim, quod ſupra montem, licet editiſſimum conſtitutus quis de <lb/>ſuperficie terræ, marisq́ue contueri poteſt, tantillum eſt comparatione totius <lb/>terræ, & </s> <s xml:id="echoid-s6018" xml:space="preserve">aquæ magnitudinis, ut in eo nulla curuatura perpendi poſſit: </s> <s xml:id="echoid-s6019" xml:space="preserve">Non ſe-<lb/>cus, ac ſi de maximo aliquo circulo, qui ambitu ſuo cõplectitur 2000. </s> <s xml:id="echoid-s6020" xml:space="preserve">v. </s> <s xml:id="echoid-s6021" xml:space="preserve">g. <lb/></s> <s xml:id="echoid-s6022" xml:space="preserve">paſſuum, portio auferatur trium, quatuorue palmotũ. </s> <s xml:id="echoid-s6023" xml:space="preserve">Nam in linea ablata nul <lb/>lam prorſus cerneremus curuitatem; </s> <s xml:id="echoid-s6024" xml:space="preserve">ſed recta omnino appareret: </s> <s xml:id="echoid-s6025" xml:space="preserve">Similisq́; </s> <s xml:id="echoid-s6026" xml:space="preserve">ra-<lb/>tio eſt de ſphęra aliqua eiuſdem magnitudinis. </s> <s xml:id="echoid-s6027" xml:space="preserve">Mirum igitur uideri nõ debet, <lb/>cur uiſus noſter neque terræ, neq; </s> <s xml:id="echoid-s6028" xml:space="preserve">aquæ rotunditatem, ſuperficiemve conue-<lb/>xam animaduertere queat. </s> <s xml:id="echoid-s6029" xml:space="preserve">Quod uero ad montes, ac ualles in terra exiſtentes <lb/>attinet, dicendum eſt, Terram propter nimiam duritiem rupium, & </s> <s xml:id="echoid-s6030" xml:space="preserve">aliarũ par-<lb/>tium ſiccitatẽ, non potuiſſe ita perfecte, ac integre, uelut aqua, in globũ coire, <lb/>proptereaq́; </s> <s xml:id="echoid-s6031" xml:space="preserve">manſiſſe tã aſperam, plenamq́; </s> <s xml:id="echoid-s6032" xml:space="preserve">tot collibus, mõtibus, uallibusq́ue: </s> <s xml:id="echoid-s6033" xml:space="preserve"><lb/>qua in re conſ luiſſe uidetur natura quodãmodo plantis, ac animãtibus in ter <lb/>ra degentibus: </s> <s xml:id="echoid-s6034" xml:space="preserve">Plurimũ enim ipſis conducunt hu iuſmodi montes, & </s> <s xml:id="echoid-s6035" xml:space="preserve">ualles, ut <lb/>experientia docet. </s> <s xml:id="echoid-s6036" xml:space="preserve">Veruntamen iſtæ eminentiæ, & </s> <s xml:id="echoid-s6037" xml:space="preserve">concauitates terræ, quãuis <lb/>per ſe conſideratæ ingentes uideantur, collatione tamen facta cum toto globo <lb/>terreno, ita exiguæ ſunt, ut eius rotunditatem nihil fere impediunt, ut perſpi-<lb/>cue apparet in eclipſi Lunæ. </s> <s xml:id="echoid-s6038" xml:space="preserve">Quemadmodum ingens aliquis globus lapideus, <lb/>licet ruditer ſit elaboratus. </s> <s xml:id="echoid-s6039" xml:space="preserve">& </s> <s xml:id="echoid-s6040" xml:space="preserve">multis eminentiis aſper, & </s> <s xml:id="echoid-s6041" xml:space="preserve">concauitatibus, ro-<lb/>tundus tamen dicitur, & </s> <s xml:id="echoid-s6042" xml:space="preserve">eſt, ſic etiam deterra dicendum eſt, quamuis in ea ſint <lb/>hæ eminentiæ, & </s> <s xml:id="echoid-s6043" xml:space="preserve">concauitates. </s> <s xml:id="echoid-s6044" xml:space="preserve">Præterea ſicut, ſi in iſto lapideo globo mini-<lb/>mum quoddam animal reptaret, nihil aliud, quàm planitiem, montes, uallesq́; </s> <s xml:id="echoid-s6045" xml:space="preserve"><lb/>conſpiceret; </s> <s xml:id="echoid-s6046" xml:space="preserve">(Tantæ enim ei apparerent exiguæ illæ ſaxei globi aſperitates) <lb/>ſic etiam nobis, qui minimi, & </s> <s xml:id="echoid-s6047" xml:space="preserve">inſenſibilis quantitatis reſpectu ſphæræ terre-<lb/>ſtris ſumus, accidit in terra obambulantibus. </s> <s xml:id="echoid-s6048" xml:space="preserve">Denique ut in eodem globo aſpe-<lb/>ritates illæ non impediunt, quo minus umbra ipſius rotunda efficiatur, & </s> <s xml:id="echoid-s6049" xml:space="preserve">ap-<lb/>pareat; </s> <s xml:id="echoid-s6050" xml:space="preserve">ita pari ratione eminentiæ iſiæ terreſtres non poſſunt eſſe impedimen-<lb/>to, quo minus terræ umbra rotunda fiat, ut uidemus in eclipſi Lunari. </s> <s xml:id="echoid-s6051" xml:space="preserve">Quod <lb/>denique ad illud attinet, quod de Sole oriente, atque occidente afferebatur, re-<lb/>ſpondendum eſt, illud idcirco fieri, quoniam cum terra, in qua ſumus, ſenſui <lb/>multo maior appareat, quàm Sol, a quo lõ<unsure/>giſſime abſumus, uidetur a Sole ad-<lb/>modum parua portiuncula terræ intercipi in ortu, uel occaſu, quæ propter <lb/>quantitatem nimiam terræ recta uidetur, ut ſupra diximus de portiuncula cir <lb/>culi, qui ingentem ambitum habeat: </s> <s xml:id="echoid-s6052" xml:space="preserve">At uero quia Luna & </s> <s xml:id="echoid-s6053" xml:space="preserve">uiſui noſtro ſphæri-<lb/>ca apparet undique, & </s> <s xml:id="echoid-s6054" xml:space="preserve">fere æqualis magnitudinis cum Sole, efficitur, ut in ecli-<lb/>pſi Solis ipſa ex Sole auferat portiones circulares, & </s> <s xml:id="echoid-s6055" xml:space="preserve">non rectas.</s> <s xml:id="echoid-s6056" xml:space="preserve"/> </p> <div xml:id="echoid-div315" type="float" level="2" n="13"> <note position="left" xlink:label="note-164-02" xlink:href="note-164-02a" xml:space="preserve">3. Obiectio,</note> <note position="left" xlink:label="note-164-03" xlink:href="note-164-03a" xml:space="preserve">Solutio <lb/>obiectionis</note> </div> <p> <s xml:id="echoid-s6057" xml:space="preserve">Ex his, quæ de globo ex terra, & </s> <s xml:id="echoid-s6058" xml:space="preserve">aqua confecto diximus, facile colligitur, <lb/> <anchor type="note" xlink:label="note-165-01a" xlink:href="note-165-01"/> quantum ſenſus fallatur, qui cœlum terræ imminere, tanquam furnum exiſti-<lb/>mat. </s> <s xml:id="echoid-s6059" xml:space="preserve">Similiter Horizontis extremum contingere & </s> <s xml:id="echoid-s6060" xml:space="preserve">cœlum, & </s> <s xml:id="echoid-s6061" xml:space="preserve">terram, quaſi hęc <lb/>corpora contigua eſſent: </s> <s xml:id="echoid-s6062" xml:space="preserve">Pari ratione, Solem, quando oritur, ex Oceano emer-<lb/>gere, quando uero occidit, ſub eodem mergi, ut & </s> <s xml:id="echoid-s6063" xml:space="preserve">Poetæ fabulantur. </s> <s xml:id="echoid-s6064" xml:space="preserve">Cum. </s> <s xml:id="echoid-s6065" xml:space="preserve">n. <lb/></s> <s xml:id="echoid-s6066" xml:space="preserve">probatum ſit, terram, & </s> <s xml:id="echoid-s6067" xml:space="preserve">aquam concentricas eſſe cum cœlo, unumq́ue ex ipſis <lb/>globum conſtitui, neceſſe eſt, ut omni ex parte æqualiter a cœlo diſtent. </s> <s xml:id="echoid-s6068" xml:space="preserve">Quare <lb/>hallucinatur ſenſus, propterea quod non comprehendit ex parte Horizontis <lb/>ſpatium illud, quod inter cœlum, & </s> <s xml:id="echoid-s6069" xml:space="preserve">terram continetur.</s> <s xml:id="echoid-s6070" xml:space="preserve"/> </p> <div xml:id="echoid-div316" type="float" level="2" n="14"> <note position="right" xlink:label="note-165-01" xlink:href="note-165-01a" xml:space="preserve">Senſum ſal <lb/>li, quòd pu <lb/>tet cœlum <lb/>tei<unsure/>ræ immi <lb/>nere, ut fur <lb/>nũ & terrã <lb/>cœlũ ipsũ <lb/>continger<unsure/>e <lb/>ex parte Ho <lb/>rizõtis, &c.</note> </div> <p> <s xml:id="echoid-s6071" xml:space="preserve">Ex dictis quoq; </s> <s xml:id="echoid-s6072" xml:space="preserve">perſpicue colligi poteſt, quàm ſit abſurda ſententia quo-<lb/>rundam Peripateticorum, qui uolunt ſecundum Ariſtotelem, & </s> <s xml:id="echoid-s6073" xml:space="preserve">ueritatẽ, inter <lb/>elementa ſeruari proportionẽ decuplam, ita ut aqua ſit decies maior, quàm ter <pb o="130" file="166" n="167" rhead="Comment. in I. Cap. Sphæræ"/> ra, aer aquam ſuperet in decupla pro portione, ignis deniq; </s> <s xml:id="echoid-s6074" xml:space="preserve">decies maior aere <lb/> <anchor type="note" xlink:label="note-166-01a" xlink:href="note-166-01"/> exiſtat. </s> <s xml:id="echoid-s6075" xml:space="preserve">Cum enim eandem habeant ſuperficiem conuexam terra, & </s> <s xml:id="echoid-s6076" xml:space="preserve">aqua, ſitq; <lb/></s> <s xml:id="echoid-s6077" xml:space="preserve">uel maior pars terræ, uel certe non multò minor detecta, quàm aquis cõtecta, <lb/>ut diximus, dilucide perſpicitur falſitas illius ſententiæ. </s> <s xml:id="echoid-s6078" xml:space="preserve">Tantum enim abeſt, <lb/>ut hac ratione aqua decies terram ſuperet, ut potius contrario terra uincat a-<lb/>quam in magnitudine: </s> <s xml:id="echoid-s6079" xml:space="preserve">quandoquidem terræ profunditas ad centrum uſque <lb/>extenditur, complectiturq́ue milliaria 3500. </s> <s xml:id="echoid-s6080" xml:space="preserve">& </s> <s xml:id="echoid-s6081" xml:space="preserve">amplius, ut ad finem huius cap. </s> <s xml:id="echoid-s6082" xml:space="preserve"><lb/>dicemus: </s> <s xml:id="echoid-s6083" xml:space="preserve">maris autem profunditas uix ad duo, aut tria milliaria perueuiat, im-<lb/>mo, ut plurimum, ſemimilliarium non excedat, vt Nautæ noſtræ tempeſtatis <lb/>experti ſunt, qui in medio etiam Oceano bolide profunditatem maris inqui-<lb/>rentes ubique fundum reperiunt, & </s> <s xml:id="echoid-s6084" xml:space="preserve">non longe à ſuperficie maris. </s> <s xml:id="echoid-s6085" xml:space="preserve">Ex quibus <lb/>conſtat, multò minorem eſſe aquam terra.</s> <s xml:id="echoid-s6086" xml:space="preserve"/> </p> <div xml:id="echoid-div317" type="float" level="2" n="15"> <note position="left" xlink:label="note-166-01" xlink:href="note-166-01a" xml:space="preserve">Error quo-<lb/>rundam Pe <lb/>ripatetico-<lb/>rũ qui decu <lb/>plã propor-<lb/>tionẽ inter <lb/>elemẽra cõ <lb/>ſtituunt.</note> </div> <p> <s xml:id="echoid-s6087" xml:space="preserve"><emph style="sc">Vervm</emph> & </s> <s xml:id="echoid-s6088" xml:space="preserve">Geometrice talis ſententia impugnari poteſt. </s> <s xml:id="echoid-s6089" xml:space="preserve">Si enim elemẽ-<lb/>ta ſeruarent continuam proportionem decuplam, totum compoſitum ex ele-<lb/>mentis contineret terram duntaxat millies, centies & </s> <s xml:id="echoid-s6090" xml:space="preserve">undecies, ut patet in hac <lb/>continua proportione decupla. </s> <s xml:id="echoid-s6091" xml:space="preserve">1. </s> <s xml:id="echoid-s6092" xml:space="preserve">10. </s> <s xml:id="echoid-s6093" xml:space="preserve">100. </s> <s xml:id="echoid-s6094" xml:space="preserve">1000. </s> <s xml:id="echoid-s6095" xml:space="preserve">Omnes enim hi numeri in <lb/>unam collecti ſummam efficiunt 1111. </s> <s xml:id="echoid-s6096" xml:space="preserve">At vero hoc eſt prorſus falſum, & </s> <s xml:id="echoid-s6097" xml:space="preserve">te-<lb/>mere dictum. </s> <s xml:id="echoid-s6098" xml:space="preserve">Nam ſecundum Aſtronomos ſemidiameter totius regionis ele-<lb/>mentaris, ideſt, diſtantia a centro mundiuſque ad concauum Lunæ, continet <lb/>ſemidiametrum terræ trigeſies, & </s> <s xml:id="echoid-s6099" xml:space="preserve">ter, immo ſecundum aliquos hæc diſtãtia ma <lb/>ior eſt: </s> <s xml:id="echoid-s6100" xml:space="preserve">Quare & </s> <s xml:id="echoid-s6101" xml:space="preserve">tota diameter ſphæræ elementorum toties etiam diametrum <lb/>totam terræ continebit, cum eadem ſit proportio diametrorum, quæ ſemidia-<lb/> <anchor type="note" xlink:label="note-166-02a" xlink:href="note-166-02"/> metrorũ. </s> <s xml:id="echoid-s6102" xml:space="preserve">Qm̃ uero ſphæræ ſunt in triplicata diametrorum proportione, effici-<lb/> <anchor type="note" xlink:label="note-166-03a" xlink:href="note-166-03"/> tur ut tota ſphæra elementorũ contineat ſphærã terreſtrẽ trigeſies quinquies <lb/>millies, nongenties, trigeſies & </s> <s xml:id="echoid-s6103" xml:space="preserve">ſepties, utin iſtis cernis numeris 1. </s> <s xml:id="echoid-s6104" xml:space="preserve">33. </s> <s xml:id="echoid-s6105" xml:space="preserve">1089. <lb/></s> <s xml:id="echoid-s6106" xml:space="preserve">35937. </s> <s xml:id="echoid-s6107" xml:space="preserve">Adde, quòd ſecundum ipſorum opinionem diſtantia a centro mundi <lb/>uſque ad concauum Lunæ ſolum decies comprehenderet ſemidiametrum ter-<lb/>ræ, & </s> <s xml:id="echoid-s6108" xml:space="preserve">paulò plus, ut ſecundum legem triplicatæ proportionis ſphæra elemen-<lb/>torum ſphæram terræ comprehendat millies, centies, & </s> <s xml:id="echoid-s6109" xml:space="preserve">undecies, ut ipſi uo-<lb/>lunt. </s> <s xml:id="echoid-s6110" xml:space="preserve">Ex quo ſequeretur, oculum noſtrum nouem duntaxat ſemidiametris ter <lb/>ræ ab orbe Lunari diſtare, quod eſt contra omnium Aftrologorum experien-<lb/>tiam. </s> <s xml:id="echoid-s6111" xml:space="preserve">Quod ſi quis dicat, ut nonnulli ex ipſis uolunt, illam decuplam propor-<lb/>tionem debere intelligi de diametris ſeu ſemidiametris elementorum, & </s> <s xml:id="echoid-s6112" xml:space="preserve">non <lb/>de corporum quantitate ſeu mole, id multo abſurdius erit. </s> <s xml:id="echoid-s6113" xml:space="preserve">Primum, quia fal-<lb/>ſiſſimum eſt Lunæ diſtantiam à terra continere 1111. </s> <s xml:id="echoid-s6114" xml:space="preserve">ſemidiametros terræ, cũ <lb/>hoc pugnet cum omnibus Aſtronomis, & </s> <s xml:id="echoid-s6115" xml:space="preserve">uix Sol tanto interuallo a centro mũ <lb/>di remoueatur. </s> <s xml:id="echoid-s6116" xml:space="preserve">Deinde, quoniam ſphærę triplicatam proportionem diametro-<lb/> <anchor type="note" xlink:label="note-166-04a" xlink:href="note-166-04"/> rum habent, ſequeretur; </s> <s xml:id="echoid-s6117" xml:space="preserve">aquam eſſe millies maiorem terra, & </s> <s xml:id="echoid-s6118" xml:space="preserve">totam ſphæram <lb/>elementorum ad terrã habere proportionem, quã hic numerus 1000000000. <lb/></s> <s xml:id="echoid-s6119" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s6120" xml:space="preserve">ut manifeſtum eſt in his numeris. </s> <s xml:id="echoid-s6121" xml:space="preserve">1. </s> <s xml:id="echoid-s6122" xml:space="preserve">1000. </s> <s xml:id="echoid-s6123" xml:space="preserve">1000000. </s> <s xml:id="echoid-s6124" xml:space="preserve">1000000000. </s> <s xml:id="echoid-s6125" xml:space="preserve">quod <lb/>quidem ridiculum eſt, neque ullus unquam Aſtronomorum id aſſeruit. </s> <s xml:id="echoid-s6126" xml:space="preserve">Quis <lb/>enim dicat, aquam millies maiorem eſſe terra, cum e contrario terra multo ma <lb/>ior ſit, quàm aqua, propter modicam eius profunditatem, ut paulo ante dixi-<lb/>mus experimento nauigantium noſtri temporis compertum eſſe? </s> <s xml:id="echoid-s6127" xml:space="preserve">Relinquitur <lb/>igitur, ſententiam illorum Peripateticorum abſurdam eſſe.</s> <s xml:id="echoid-s6128" xml:space="preserve"/> </p> <div xml:id="echoid-div318" type="float" level="2" n="16"> <note position="left" xlink:label="note-166-02" xlink:href="note-166-02a" xml:space="preserve">@5. quinti.</note> <note position="left" xlink:label="note-166-03" xlink:href="note-166-03a" xml:space="preserve">38. duod.</note> <note position="left" xlink:label="note-166-04" xlink:href="note-166-04a" xml:space="preserve">18. duod.</note> </div> <p> <s xml:id="echoid-s6129" xml:space="preserve"><emph style="sc">Immo</emph> nõ ſolũ elemẽta hãc proportionẽ decuplam minime ſeruãt, ſed nec <lb/>ullã aliã continuã, ut recte probat Alex. </s> <s xml:id="echoid-s6130" xml:space="preserve">Picolom. </s> <s xml:id="echoid-s6131" xml:space="preserve">in opuſc. </s> <s xml:id="echoid-s6132" xml:space="preserve">de quantitabe ter-<lb/>tæ & </s> <s xml:id="echoid-s6133" xml:space="preserve">aquæ; </s> <s xml:id="echoid-s6134" xml:space="preserve">idemq́; </s> <s xml:id="echoid-s6135" xml:space="preserve">confirmat Fernelius Ambianas in ſua Coſmotheoria. </s> <s xml:id="echoid-s6136" xml:space="preserve">Neq;</s> <s xml:id="echoid-s6137" xml:space="preserve"> <pb o="131" file="167" n="168" rhead="Ioan. de Sacro Boſco."/> uero obſtat auctoritas Ariſtotelis, quam dicti Peripatetici in confirmationem <lb/>ſuæ ſententiæ adducunt, quando uidelicet dicit; </s> <s xml:id="echoid-s6138" xml:space="preserve">ex uno pugillo terræ decẽ pu <lb/>gillos aquæ generari, & </s> <s xml:id="echoid-s6139" xml:space="preserve">ex uno aquæ decem aeris, ex uno denique a eris decẽ <lb/>ignis. </s> <s xml:id="echoid-s6140" xml:space="preserve">Nam hoc Ariſt. </s> <s xml:id="echoid-s6141" xml:space="preserve">aſſeruit uel exempli gratia, uel ſi uere ita ſenſit, intelli-<lb/>gendum eſt, ſi ex tota quantitate terræ deberet generari aqua, eſſet aqua pro-<lb/>creata decuplo maior, quàm terra, & </s> <s xml:id="echoid-s6142" xml:space="preserve">ſic de cæteris: </s> <s xml:id="echoid-s6143" xml:space="preserve">non autem, quòd re ipſa ele <lb/>menta, quæ nunc extant, talem habeant proportionem: </s> <s xml:id="echoid-s6144" xml:space="preserve">ita enim deberet eſſe <lb/>æqualis materia in omnibus elementis: </s> <s xml:id="echoid-s6145" xml:space="preserve">quod tamen nuſquam Ariſtoteles af-<lb/>firmauit: </s> <s xml:id="echoid-s6146" xml:space="preserve">immo contra experientiam videtur eſſe. </s> <s xml:id="echoid-s6147" xml:space="preserve">Non ſolum. </s> <s xml:id="echoid-s6148" xml:space="preserve">n. </s> <s xml:id="echoid-s6149" xml:space="preserve">aqua minor <lb/>eſt, quàm terra, ut diximus, verum etiam aer multis partibus minor eſſe uide-<lb/>tur. </s> <s xml:id="echoid-s6150" xml:space="preserve">Nam cum ueriſimile ſit, aereã regionem eam eſſe tantummodo, in qua va-<lb/>pores ex terra, & </s> <s xml:id="echoid-s6151" xml:space="preserve">aqua extracti, eriam ſubtiliſſimi, domicilium habent: </s> <s xml:id="echoid-s6152" xml:space="preserve">cũ non <lb/>ſit maior ratio, cur in una magis parte aeris poſſint eſſe, quàm in altera, ſi qua <lb/>eſt: </s> <s xml:id="echoid-s6153" xml:space="preserve">ſit autem ſumma uaporum eleuatio ad 52. </s> <s xml:id="echoid-s6154" xml:space="preserve">milliaria, aut circiter, ut Geo-<lb/>metrice ab Alhazen lib. </s> <s xml:id="echoid-s6155" xml:space="preserve">7. </s> <s xml:id="echoid-s6156" xml:space="preserve">ſuæ Perſpectiuæ, à Vitellione lib. </s> <s xml:id="echoid-s6157" xml:space="preserve">10. </s> <s xml:id="echoid-s6158" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s6159" xml:space="preserve">60. </s> <s xml:id="echoid-s6160" xml:space="preserve">& </s> <s xml:id="echoid-s6161" xml:space="preserve">a <lb/>Petro Nonio in lib. </s> <s xml:id="echoid-s6162" xml:space="preserve">de crepuſculis demonſtratur: </s> <s xml:id="echoid-s6163" xml:space="preserve">dicendũ erit, altitudinẽ, pro-<lb/>funditatem ve aeris continere 52. </s> <s xml:id="echoid-s6164" xml:space="preserve">milliaria, aut circiter, & </s> <s xml:id="echoid-s6165" xml:space="preserve">non amplius, ita ut <lb/>in tanto interuallo à terra ſit confiniũ aeris & </s> <s xml:id="echoid-s6166" xml:space="preserve">ignis. </s> <s xml:id="echoid-s6167" xml:space="preserve">Alias altius adhuc aſcẽde-<lb/>re poſſent uapores, niſi ſiccitas, & </s> <s xml:id="echoid-s6168" xml:space="preserve">calor ignis obſiſteret. </s> <s xml:id="echoid-s6169" xml:space="preserve">quod a nemine hacte-<lb/>nus uiſum eft ſieri. </s> <s xml:id="echoid-s6170" xml:space="preserve">Quæ cũ ſint, ſacile reperiemus, quantò minor fit aer quàm <lb/>terra, & </s> <s xml:id="echoid-s6171" xml:space="preserve">ignis. </s> <s xml:id="echoid-s6172" xml:space="preserve">Cũ enim ſemidiameter terræ, ſecundum Ptolemæum, comple-<lb/> <anchor type="note" xlink:label="note-167-01a" xlink:href="note-167-01"/> ctatur milliaria ferme 3579. </s> <s xml:id="echoid-s6173" xml:space="preserve">comprehendet diſtantia à centro terræ vſq; </s> <s xml:id="echoid-s6174" xml:space="preserve">ad cõ <lb/>uexum aeris milliaria; </s> <s xml:id="echoid-s6175" xml:space="preserve">631. </s> <s xml:id="echoid-s6176" xml:space="preserve">& </s> <s xml:id="echoid-s6177" xml:space="preserve">tota diameter globi compoſiti ex terra, aqua, & </s> <s xml:id="echoid-s6178" xml:space="preserve"><lb/>aere, milliaria 7262. </s> <s xml:id="echoid-s6179" xml:space="preserve">Hinc per præcepta, quæ ad finem huius cap. </s> <s xml:id="echoid-s6180" xml:space="preserve">trademus, in-<lb/>ueniemus maximum circulum huius globi, & </s> <s xml:id="echoid-s6181" xml:space="preserve">totam ſuperficiem conuexam: </s> <s xml:id="echoid-s6182" xml:space="preserve">& </s> <s xml:id="echoid-s6183" xml:space="preserve"><lb/>@x hac rurſus ſoliditatem eiuſdem globi, quæ comple ctitur milliaria cubica <lb/>200610193776. </s> <s xml:id="echoid-s6184" xml:space="preserve">fere. </s> <s xml:id="echoid-s6185" xml:space="preserve">A quibus ſi detraha mus milliaria cubica 192138615000. <lb/></s> <s xml:id="echoid-s6186" xml:space="preserve">quæ globum ex terra & </s> <s xml:id="echoid-s6187" xml:space="preserve">aqua compoſitum conficiunt, relinquentur milliaria <lb/>cubica 8471578776. </s> <s xml:id="echoid-s6188" xml:space="preserve">pro ſoliditate & </s> <s xml:id="echoid-s6189" xml:space="preserve">quantitate aeris, ita ut proportio terræ <lb/>& </s> <s xml:id="echoid-s6190" xml:space="preserve">aquæ ſimul ad aerem ſit ferè, quæ 23. </s> <s xml:id="echoid-s6191" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s6192" xml:space="preserve">Quòd ſi globum conſectũ ex ter-<lb/>ra, aqua, & </s> <s xml:id="echoid-s6193" xml:space="preserve">aere rurſum detrahamus ex tota ſphæra omnium elementorũ, quę <lb/>cõplectit̃ fere 6904885407255000. </s> <s xml:id="echoid-s6194" xml:space="preserve">milliaria, remanebit ſoliditas ſolius ignis <lb/>milliarrorum 6904684797061224. </s> <s xml:id="echoid-s6195" xml:space="preserve">ita ut ignis ad terram proportionẽ fere ha <lb/>beat, quam 35437. </s> <s xml:id="echoid-s6196" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s6197" xml:space="preserve">ad aerem uero, quam 815041. </s> <s xml:id="echoid-s6198" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s6199" xml:space="preserve">Itaq; </s> <s xml:id="echoid-s6200" xml:space="preserve">ſi terra unà cũ <lb/>aqua ponatur 23. </s> <s xml:id="echoid-s6201" xml:space="preserve">erit aer fere ut 1. </s> <s xml:id="echoid-s6202" xml:space="preserve">& </s> <s xml:id="echoid-s6203" xml:space="preserve">ignis ut 815041. </s> <s xml:id="echoid-s6204" xml:space="preserve">Negligimus enim hic mi <lb/>nutias, quæ unitatẽ non conficiunt. </s> <s xml:id="echoid-s6205" xml:space="preserve">Hæc idcirco dixerim, ut appareat, quàm te-<lb/>mere nonnulli affirmare audeant, decuplam inter elementa proportionẽ eſſe-<lb/>Quòd ſi quis cõtendat, aerẽ ultra 52. </s> <s xml:id="echoid-s6206" xml:space="preserve">milliaria extendi, etiam ſi ulterius uapo-<lb/>res non aſcendant, ob nimiam ſiccitatem, & </s> <s xml:id="echoid-s6207" xml:space="preserve">calorẽ illius aeris, erit diſputatio <lb/>de nomine. </s> <s xml:id="echoid-s6208" xml:space="preserve">Illud enim ipſum, quod nimis ſiccum eſt, & </s> <s xml:id="echoid-s6209" xml:space="preserve">calidum ſupra aerem, <lb/>ignem appellamus. </s> <s xml:id="echoid-s6210" xml:space="preserve">quemadmodum & </s> <s xml:id="echoid-s6211" xml:space="preserve">Ariſtoteles lib. </s> <s xml:id="echoid-s6212" xml:space="preserve">1. </s> <s xml:id="echoid-s6213" xml:space="preserve">Meteor ſumma 1. </s> <s xml:id="echoid-s6214" xml:space="preserve">cap. </s> <s xml:id="echoid-s6215" xml:space="preserve">4. </s> <s xml:id="echoid-s6216" xml:space="preserve"><lb/>affirmat, ubi ait. </s> <s xml:id="echoid-s6217" xml:space="preserve">[Sed oportet intelligere dicti à nobis aeris, id quod eſt circa ter-<lb/>ram, uelut humidum & </s> <s xml:id="echoid-s6218" xml:space="preserve">calidum eſſe, propterea quod uaporet, & </s> <s xml:id="echoid-s6219" xml:space="preserve">exhalationem ha-<lb/>beat terræ: </s> <s xml:id="echoid-s6220" xml:space="preserve">quod autem ſuper hoc, calidum iam & </s> <s xml:id="echoid-s6221" xml:space="preserve">ſiccum. </s> <s xml:id="echoid-s6222" xml:space="preserve">Eſt enim uaporis natura, <lb/>humidum & </s> <s xml:id="echoid-s6223" xml:space="preserve">calidum: </s> <s xml:id="echoid-s6224" xml:space="preserve">exhalationis autem, calidum & </s> <s xml:id="echoid-s6225" xml:space="preserve">ſiccum.</s> <s xml:id="echoid-s6226" xml:space="preserve">] Item eodem lib. </s> <s xml:id="echoid-s6227" xml:space="preserve"><lb/>ſumma 2. </s> <s xml:id="echoid-s6228" xml:space="preserve">cap. </s> <s xml:id="echoid-s6229" xml:space="preserve">1. </s> <s xml:id="echoid-s6230" xml:space="preserve">ita ſcribens. </s> <s xml:id="echoid-s6231" xml:space="preserve">[Primo enim ſub circulari latione eſt calidum & </s> <s xml:id="echoid-s6232" xml:space="preserve">ſic-<lb/>cum, quod dicimus ignem. </s> <s xml:id="echoid-s6233" xml:space="preserve">Innominatum enim eſt, & </s> <s xml:id="echoid-s6234" xml:space="preserve">commune in omnifumoſa diſgre <lb/>gatione attamen, quia maxime natum eſt tale corpus exuri, ſic neceſſarium eſt uti no- <pb o="132" file="168" n="169" rhead="Comment. in I. Cap. Sphæræ"/> minibus ſub hac autem naturaaer.</s> <s xml:id="echoid-s6235" xml:space="preserve">] Immo idem Ariſtoteles aliis in locis ignem <lb/>ſub concauo Lunæ appellat exhalationem, ut eodẽ lib. </s> <s xml:id="echoid-s6236" xml:space="preserve">ſumma 2. </s> <s xml:id="echoid-s6237" xml:space="preserve">cap. </s> <s xml:id="echoid-s6238" xml:space="preserve">4. </s> <s xml:id="echoid-s6239" xml:space="preserve">in hanc <lb/>ſententiam ſcribens. </s> <s xml:id="echoid-s6240" xml:space="preserve">[Supponitur enim nobis mundi eius, qui circa terram, quan-<lb/>tum ſub circulari eſt latione, eſse primam partem exhalationem ſiccam, & </s> <s xml:id="echoid-s6241" xml:space="preserve">calida<unsure/>m. </s> <s xml:id="echoid-s6242" xml:space="preserve">Ip-<lb/>ſa autem, & </s> <s xml:id="echoid-s6243" xml:space="preserve">continui ſub ipſa aeris adhuc multum, ſimul circunducitur circa terram <lb/>à latione, & </s> <s xml:id="echoid-s6244" xml:space="preserve">motu circulari.</s> <s xml:id="echoid-s6245" xml:space="preserve">] Ex his omnibus locis perſpicuũ eſſe uidetur, Ari-<lb/>ſtotelem eam ſolum partem ſub concauo Lunæ appellare aerem, in quo uapo-<lb/>res exiſtunt, reliquam autem Ignem. </s> <s xml:id="echoid-s6246" xml:space="preserve">Vana ergo omnino eſt, ac reijcienda ſen-<lb/>tentia eorum, qui decuplam proportionem inter elementa ponunt, cum nec <lb/>ulla continua proportio inter illa ſit, immo tam aqua, quàm aer, minor ſit, <lb/>quàm terra, ut ex ijs, quæ diximus, perſpicue apparet.</s> <s xml:id="echoid-s6247" xml:space="preserve"/> </p> <div xml:id="echoid-div319" type="float" level="2" n="17"> <note position="right" xlink:label="note-167-01" xlink:href="note-167-01a" xml:space="preserve">Quãto mi-<lb/>nor ſit aer. <lb/>quàm terra <lb/>& ignis. Itẽ <lb/>quanto ma <lb/>ior ſit ignis <lb/>quàm ter-<lb/>ra.</note> </div> <p> <s xml:id="echoid-s6248" xml:space="preserve"><emph style="sc">Colligitvr</emph> rurſus ex eo, quod diximus, omnia grauia tendere ad <lb/>centrum totius Vniuerſi, quod & </s> <s xml:id="echoid-s6249" xml:space="preserve">centrũ eſt aquæ & </s> <s xml:id="echoid-s6250" xml:space="preserve">ter-<lb/> <anchor type="note" xlink:label="note-168-01a" xlink:href="note-168-01"/> <anchor type="figure" xlink:label="fig-168-01a" xlink:href="fig-168-01"/> ræ; </s> <s xml:id="echoid-s6251" xml:space="preserve">omnia perpendicula & </s> <s xml:id="echoid-s6252" xml:space="preserve">grauia ex diuerſis locis libere <lb/>demiſſa ſibi inuicẽ appropinquare, adeo ut in cẽtro ter-<lb/>ræ, ſeu Vniuerſi, ſi eo peruenirent, in unum punctum coi <lb/>rent, ut in figura appoſita conſpicis. </s> <s xml:id="echoid-s6253" xml:space="preserve">Quoniam uero tota <lb/>diſtantia ad centrum uſq; </s> <s xml:id="echoid-s6254" xml:space="preserve">per ſe conſiderata admodũ mæ <lb/>gna eſt, fit, ut in paruo ſpatio iſte perpẽdiculorum acceſ-<lb/>ſus percipi nequeat. </s> <s xml:id="echoid-s6255" xml:space="preserve">Si enim duo perpendicula inter ſe <lb/>decẽ palmis, aut cẽtum, aut etiam pluribus diſtent, quia <lb/>admodum exigua eſt hæc diſtantia comparatione ſemi-<lb/>diametri terræ, & </s> <s xml:id="echoid-s6256" xml:space="preserve">ex conſequenti in centro mundi angu <lb/>lus concurſus minimus efficitur, uidebuntur prorſus in-<lb/>ter ſe æquidiſtare. </s> <s xml:id="echoid-s6257" xml:space="preserve">Atq; </s> <s xml:id="echoid-s6258" xml:space="preserve">hęc eſt cauſa, cur ædificia ad per-<lb/>pendiculũ conſtructa uideantur æquidiſtantia, ſeu paral <lb/>lela, cũ tamẽ re ipſa in loco inferiori fint magis propin-<lb/>qua inter ſe, in ſuperiori uero magis unũ ab altero ſeiun <lb/>gatur. </s> <s xml:id="echoid-s6259" xml:space="preserve">Idemq́; </s> <s xml:id="echoid-s6260" xml:space="preserve">dices de duobus quibuſcunque parietibus <lb/>ſeu muris, Itaq; </s> <s xml:id="echoid-s6261" xml:space="preserve">ſi puteus conſtrueretur ad perpendiculum uſque ad mundi cen <lb/>trum, eius latera continuo in anguſtum tenderent, licet in ſenſibiliter, donec <lb/>in centro conuenientia pyramidis figuram abſoluerent, cuius baſis eſſet os pu <lb/>tei, uertex autem centrum totius Vniuerſi. </s> <s xml:id="echoid-s6262" xml:space="preserve">Similiter ſi turris tantæ celſitudi-<lb/>nis, quanta eſt terræ profunditas, ad perpendiculum conſtrueretur, mirum in <lb/>modum eius latera in ſummitate ab inuicem diſtarent. </s> <s xml:id="echoid-s6263" xml:space="preserve">Ex quibus efficitur, om-<lb/>nes muros ad perpendiculum conſtru ctos ita rectà tendere ad centrum, ſicut <lb/>quæuis rectæ lineæ circuli a centro exeuntes in centro cõueniunt. </s> <s xml:id="echoid-s6264" xml:space="preserve">Quod niſi <lb/>obſeruaretur ab artificibus, ædificia nulla ratione conſiſtere poſſent.</s> <s xml:id="echoid-s6265" xml:space="preserve"/> </p> <div xml:id="echoid-div320" type="float" level="2" n="18"> <note position="left" xlink:label="note-168-01" xlink:href="note-168-01a" xml:space="preserve">Aedificia <lb/>ad perpen-<lb/>diculũ con <lb/>ſtruct a non <lb/>eſſe paralle <lb/>la, ſed in cẽ <lb/>tro mundi <lb/>coitura eſ-<lb/>ſe, ſi produ-<lb/>caniur.</note> <figure xlink:label="fig-168-01" xlink:href="fig-168-01a"> <image file="168-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/168-01"/> </figure> </div> <note position="left" xml:space="preserve">Fauiment@ <lb/>ad libellã <lb/>ſeu perpen <lb/>diculũ con <lb/>ftructũ nẽ <lb/>eſſe plan@, <lb/>ſed portio-<lb/>nẽ eſſe ſphę <lb/>ræ cuius cẽ <lb/>trũ fit idẽ <lb/>quod terrę.</note> <p> <s xml:id="echoid-s6266" xml:space="preserve"><emph style="sc">Exhis</emph> rurſus infertur, nullum pauimentum ad libellam, ſeu perpendi-<lb/>culum extructum planum eſſe, ſed iacere librarum, id eſt, omnibus partibus æ-<lb/>qualiter a centro remotum, eſſeq́; </s> <s xml:id="echoid-s6267" xml:space="preserve">portionem cuiuſdã ſphæræ, cuius centrum <lb/>ſit centrũ mundi, ſeu terræ; </s> <s xml:id="echoid-s6268" xml:space="preserve">ſiquidẽ perpendicula ad centrũ ſemper uergentia <lb/>paulatim coarctantur, ut diximus, pauimentumq́; </s> <s xml:id="echoid-s6269" xml:space="preserve">rotundum cogunt eſſe. </s> <s xml:id="echoid-s6270" xml:space="preserve">Ve-<lb/>rum hæc rotunditas in modico ſpatio percipi non poteſt, ſicut nec rotunditas <lb/>terræ uel aquæ: </s> <s xml:id="echoid-s6271" xml:space="preserve">Ingens uero aliquod pauimentũ 3000 v.</s> <s xml:id="echoid-s6272" xml:space="preserve">g. </s> <s xml:id="echoid-s6273" xml:space="preserve">vel 4000. </s> <s xml:id="echoid-s6274" xml:space="preserve">paſſuũ ad <lb/>libellã ſaòricatũ omnino aliquẽ præ ſe ferret tumorẽ. </s> <s xml:id="echoid-s6275" xml:space="preserve">Vnde fit, ut immenſum <lb/>aliquod pauimentum rectilineum, ſecun dum uidelicet rect@m lineam conſti-<lb/>tutum, minime dici poſſi@ libratum. </s> <s xml:id="echoid-s6276" xml:space="preserve">Ea etenim proprie librata dicuntur, quæ <pb o="133" file="169" n="170" rhead="Ioan. de Sacro Boſco."/> æqualiter à mundi centro remouentur, qualis eſt ſuperficies extima aquę ubi <lb/>cunq. </s> <s xml:id="echoid-s6277" xml:space="preserve">collocetur, cuiuſmodi non poteſt eſſe ſuperficies rectilinea, ſeu plan@. <lb/></s> <s xml:id="echoid-s6278" xml:space="preserve">Si enim à cen-<lb/> <anchor type="figure" xlink:label="fig-169-01a" xlink:href="fig-169-01"/> tro mundi pluri <lb/>mę lineæ rectæ <lb/>ad ipſam proten <lb/>dãtur, omnium <lb/>minima erit ea, <lb/>quæ perpendicu <lb/>laris exiſtit ad <lb/>ſuperficiem: </s> <s xml:id="echoid-s6279" xml:space="preserve">reli <lb/>quę vero, quo a perpendiculari remotiores fuerint, eo quoq. </s> <s xml:id="echoid-s6280" xml:space="preserve">longiores erunt, <lb/>ut in hac figura cernis, facileq́. </s> <s xml:id="echoid-s6281" xml:space="preserve">probari poteſt ex propoſ. </s> <s xml:id="echoid-s6282" xml:space="preserve">19. </s> <s xml:id="echoid-s6283" xml:space="preserve">lib. </s> <s xml:id="echoid-s6284" xml:space="preserve">1. </s> <s xml:id="echoid-s6285" xml:space="preserve">Eucl. </s> <s xml:id="echoid-s6286" xml:space="preserve">Quam-<lb/>obrem punctum illud in plano, in quod perpendicularis cadit, centro erit pro-<lb/>ximum, ac proinde infimum: </s> <s xml:id="echoid-s6287" xml:space="preserve">Reliqua uero puncta plani à centro erunt remo <lb/>tiora, ac propterea altiora, ita ut extrema plani ſint altiſſima, cœloq. </s> <s xml:id="echoid-s6288" xml:space="preserve">uiciniſſi-<lb/>ma. </s> <s xml:id="echoid-s6289" xml:space="preserve">Quocirca ſi aliquis in illo plano incederet circa punctum centro proximũ <lb/>putaret ſe omnino deambulare in librato, quippe cum nihil ſentiret accliuit@ <lb/>ti@ in tam paruo ſpatio, cum tamen uere modo aſcenderet, modo deſcenderet, <lb/>adeo ut quo magis inde receſſerit, eo accliuius aſcenderet, donec tandem ere <lb/>ctio ei negaret aſcenſum, ut luce clarius in propoſita figura deprehendi poteſt. <lb/></s> <s xml:id="echoid-s6290" xml:space="preserve">Hinc etiam fit, ut ſi quiſpiam in pauimento aliquo librato, qualis eſt ſuperſi-<lb/>cies terræ, uel aquę, obambulet, caput illius uelocius feratur, quam medię cor <lb/>poris partes; </s> <s xml:id="echoid-s6291" xml:space="preserve">quoniam nimirum eodem tempore tam caput, quàm mediæ cor-<lb/>poris partes, portionem circuli deſcribunt, cuius centrum idem eſt, quod terrę: </s> <s xml:id="echoid-s6292" xml:space="preserve"><lb/>Clarum autem eft, caput maiorem circulum deſcribere, cum magis à centro <lb/>diſter, quam medias corporis partes, cum uiciniores centro exiftant.</s> <s xml:id="echoid-s6293" xml:space="preserve"/> </p> <div xml:id="echoid-div321" type="float" level="2" n="19"> <figure xlink:label="fig-169-01" xlink:href="fig-169-01a"> <image file="169-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/169-01"/> </figure> </div> <note position="right" xml:space="preserve">Plus aquæ <lb/>contine@i <lb/>in uaſe ad <lb/>radices mõ <lb/>tis, quami@ <lb/>cacumine.</note> <p> <s xml:id="echoid-s6294" xml:space="preserve"><emph style="sc">Manifestvm</emph> quoq. <lb/></s> <s xml:id="echoid-s6295" xml:space="preserve"> <anchor type="figure" xlink:label="fig-169-02a" xlink:href="fig-169-02"/> ex dictis relinquitur, uas <lb/>quodcunque plus aquę reci <lb/>pere in loco inferiori poſi-<lb/>tũ, quàm in ſuperiori, ut v. <lb/></s> <s xml:id="echoid-s6296" xml:space="preserve">g. </s> <s xml:id="echoid-s6297" xml:space="preserve">ad radices montis altiſſi-<lb/>mi, quàm in cacumine. </s> <s xml:id="echoid-s6298" xml:space="preserve">Cũ <lb/>enim, ut ſupra oſtendimus, <lb/>quælibet pars aquæ quieſcẽ <lb/>tis, in quocunq. </s> <s xml:id="echoid-s6299" xml:space="preserve">loco conti-<lb/>neatur, iaceat librata, pro-<lb/>pterea quòd ſuapte natura <lb/>ad decliuiora loca confluat, <lb/>efficiatq́. </s> <s xml:id="echoid-s6300" xml:space="preserve">ſphęricam ſuperſi-<lb/>ciẽ, cuius centrum eſt cẽtrũ <lb/>mũdi, luce clarius eſt, ſuper-<lb/>ficiẽ aquæ, quo uicinior cen <lb/>tro fuerit, eò minorẽ effice-<lb/>re ſphæram, cũ minorẽ poſ-<lb/>ſideat diametrum. </s> <s xml:id="echoid-s6301" xml:space="preserve">Quoniã <lb/>uero una eademq́. </s> <s xml:id="echoid-s6302" xml:space="preserve">linea re- <pb o="134" file="170" n="171" rhead="Comment. in I. Cap. Sphæræ"/> cta ex minori circulo, ſeu ſphæra maiorem tumorem aufert, ſit, ut idem uas <lb/>maiorem partem à minori ſphæra auferat, quàm à maiore, & </s> <s xml:id="echoid-s6303" xml:space="preserve">idcirco maiorem <lb/>copiam aquę in loco inferiori recipiat, quàm in ſuperiori, ut cernis in propoſi <lb/>ta figura. </s> <s xml:id="echoid-s6304" xml:space="preserve">At quoniam tam exiguum interuallum, quale eſt à radice montis <lb/>etiam altiſſimi, ad eiuſdem cacumen, nullius eſt momenti, ſi cum tota terrę <lb/>ſemidiametro conferatur, efficitur, ut uix ſentiatur hæc diuerſitas. </s> <s xml:id="echoid-s6305" xml:space="preserve">Si tamea <lb/>ad centrum uſq. </s> <s xml:id="echoid-s6306" xml:space="preserve">pateret aditus, ibi plane oculis intueremur, atq. </s> <s xml:id="echoid-s6307" xml:space="preserve">animaduer <lb/>teremus aquæ cumulum, ſeu tumorẽ ſphæricũ uaſi pleno inſiſtere. </s> <s xml:id="echoid-s6308" xml:space="preserve">Quo enim <lb/>aqua magis ad centrum accedit, eo magis ẽt ſenſibiliter rotunditatem acqui-<lb/>rit: </s> <s xml:id="echoid-s6309" xml:space="preserve">Adeo ut ſi terra a mundi centro diſcederet, pateretq́; </s> <s xml:id="echoid-s6310" xml:space="preserve">aditus ipſi aquæ, con-<lb/>tinuò tota aquæ multitudo ad mediũ mundi conflueret, ac primo impetu huc <lb/>illucq́. </s> <s xml:id="echoid-s6311" xml:space="preserve">fluctuaret, donec ſenſim, remiſſo motus impetu, in perfectiſſimũ coiret <lb/>globũ, ambiretq́. </s> <s xml:id="echoid-s6312" xml:space="preserve">æqualiter totius mundi centrũ. </s> <s xml:id="echoid-s6313" xml:space="preserve">Multa alia his ſimilia colligi <lb/>poſsũt ex ijs, quæ dicta ſunt, quibus breuitatis cauſa ſuperſedẽdum eſſe cẽſeo.</s> <s xml:id="echoid-s6314" xml:space="preserve"/> </p> <div xml:id="echoid-div322" type="float" level="2" n="20"> <figure xlink:label="fig-169-02" xlink:href="fig-169-02a"> <image file="169-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/169-02"/> </figure> </div> <p> <s xml:id="echoid-s6315" xml:space="preserve"><emph style="sc">Postremo</emph> ut nonnihil etiam de figuris reliquorum duorũ elemento-<lb/>rum, aeris ſcilicet & </s> <s xml:id="echoid-s6316" xml:space="preserve">ignis, dicamus, ſatis perſpicue uidetur concludi poſſe, ea <lb/> <anchor type="note" xlink:label="note-170-01a" xlink:href="note-170-01"/> eſſe figuræ ſphęricæ. </s> <s xml:id="echoid-s6317" xml:space="preserve">In primis namq. </s> <s xml:id="echoid-s6318" xml:space="preserve">aer, quantum ad ſuperficiem eius conca <lb/>uam, rotundus eſt, quoniam circundat, & </s> <s xml:id="echoid-s6319" xml:space="preserve">ambit globum rotundum, quem di-<lb/>ximus conſtitui ex aqua & </s> <s xml:id="echoid-s6320" xml:space="preserve">terra: </s> <s xml:id="echoid-s6321" xml:space="preserve">Pari ratione Ignis quo ad ſuperficiem eius <lb/>conuexam, neceſſario rotundus exiſtit, cum ſit ſub concauo Lunæ. </s> <s xml:id="echoid-s6322" xml:space="preserve">Et quia <lb/>tam ignis, quàm aer, æqualiter uidetur à centro recedere propter leuitatem, <lb/>non ſecus ac grauia ad centrum tendunt ob grauitatem, fit, ut, & </s> <s xml:id="echoid-s6323" xml:space="preserve">aer ſecũdum <lb/>conuexum, & </s> <s xml:id="echoid-s6324" xml:space="preserve">ignis ſecundum concauum ſphęricæ quoq. </s> <s xml:id="echoid-s6325" xml:space="preserve">fit figuræ: </s> <s xml:id="echoid-s6326" xml:space="preserve">Alias par@ <lb/>illa aeris, uel ignis: </s> <s xml:id="echoid-s6327" xml:space="preserve">quę magis centro mundi propinquaret, non quæreret ſur-<lb/>ſum aſcendere, quod eſt contra utriuſq. </s> <s xml:id="echoid-s6328" xml:space="preserve">elementi inclinationem naturalem. <lb/></s> <s xml:id="echoid-s6329" xml:space="preserve">Veriſimile tamen eſt, neq. </s> <s xml:id="echoid-s6330" xml:space="preserve">ignis concauum, neq. </s> <s xml:id="echoid-s6331" xml:space="preserve">aeris conuexũ eſſe ſphæricum, <lb/>cum plus ignis uideatur generari ſub Zona torrida, hoc eſt, ſub Aequatore, vel <lb/>prope, ubi nimirum continue uerſatnr Sol, cęlumq́ne ſumma uelocitate con-<lb/>uertitur, plus uero aeris ſub Zonis frigidis, id eſt, ſub polis, aut prope, propter <lb/>nimiam diſtantiam Solis, frigiditatem & </s> <s xml:id="echoid-s6332" xml:space="preserve">tarditatem motus.</s> <s xml:id="echoid-s6333" xml:space="preserve"/> </p> <div xml:id="echoid-div323" type="float" level="2" n="21"> <note position="left" xlink:label="note-170-01" xlink:href="note-170-01a" xml:space="preserve">Figura ae-<lb/>@is, & Ignis <lb/>quę.</note> </div> <p> <s xml:id="echoid-s6334" xml:space="preserve"><emph style="sc">Neqve</emph> uero hocloco prætereundem eſt, Platonem in Tymæo attribue <lb/>re cęlo, & </s> <s xml:id="echoid-s6335" xml:space="preserve">quatuor elementis, figuras quinque corporum regularium, de qui-<lb/> <anchor type="note" xlink:label="note-170-02a" xlink:href="note-170-02"/> bus agitur lib. </s> <s xml:id="echoid-s6336" xml:space="preserve">13. </s> <s xml:id="echoid-s6337" xml:space="preserve">14. </s> <s xml:id="echoid-s6338" xml:space="preserve">15. </s> <s xml:id="echoid-s6339" xml:space="preserve">& </s> <s xml:id="echoid-s6340" xml:space="preserve">16. </s> <s xml:id="echoid-s6341" xml:space="preserve">Eucl. </s> <s xml:id="echoid-s6342" xml:space="preserve">ob ſimilitudines quaſdam. </s> <s xml:id="echoid-s6343" xml:space="preserve">Igni enim pro-<lb/>pter acumẽ ſuæ flammę attribuit pyramidem, ſeu tetraedron; </s> <s xml:id="echoid-s6344" xml:space="preserve">Aſcendit namq-<lb/>quælibet particula ignis ad modũ pyramidis. </s> <s xml:id="echoid-s6345" xml:space="preserve">Aeri uero octaedron: </s> <s xml:id="echoid-s6346" xml:space="preserve">Sicut enim <lb/>aer proxime ad ignem accedit, ſic etiam octaedron maximam ſimilitudinem cũ <lb/>Tetraedro obtinet, cũ conſtet ex duabus pyramidibus. </s> <s xml:id="echoid-s6347" xml:space="preserve">Aquæ deinde concedit <lb/>Icoſaedron, propter nimiam mobilitatem, ac fluxibilitatem. </s> <s xml:id="echoid-s6348" xml:space="preserve">Cubum autem, ſi-<lb/>ue Hexaedron tribuit terræ ob ſuam immobilitatem, ac ſtabilitatem: </s> <s xml:id="echoid-s6349" xml:space="preserve">Iuter oĩa <lb/>enim corpora regularia cubus motui ineptiſſimus eſt. </s> <s xml:id="echoid-s6350" xml:space="preserve">Cælo denique adſcribit <lb/>Dodecaedron: </s> <s xml:id="echoid-s6351" xml:space="preserve">Nam quemadmodum cęlum in toto ambitu 12. </s> <s xml:id="echoid-s6352" xml:space="preserve">ęqualia ſigna <lb/>complectitur, ita quoq. </s> <s xml:id="echoid-s6353" xml:space="preserve">dodecaedron 12. </s> <s xml:id="echoid-s6354" xml:space="preserve">æqualibus ſuperficiebus continetur. <lb/></s> <s xml:id="echoid-s6355" xml:space="preserve">Omitto alias cauſas, proprietateſve, propter quas Plato figuras quinq. </s> <s xml:id="echoid-s6356" xml:space="preserve">corpo <lb/>rum ſimplicium mundum componẽtium corporibus regularibus aſſimilauit. </s> <s xml:id="echoid-s6357" xml:space="preserve"><lb/>Has enim copioſius pertractatas reperies apud Platonicos. </s> <s xml:id="echoid-s6358" xml:space="preserve">Non eſt tamẽ ullo <lb/>modo exiſtimandum, ut multi falſo arbitrantur, Platonem philoſophum inſi <lb/>gnem putaſſe, Cælum & </s> <s xml:id="echoid-s6359" xml:space="preserve">quatuor elemẽta vere talibus eſſe figuris prædita. </s> <s xml:id="echoid-s6360" xml:space="preserve">Ait <lb/>enim in eodem Tymæo, Mundum cum omnibus partibus præcipuis, cuiuſmo- <pb o="135" file="171" n="172" rhead="Ioan. de Sacro Boſco."/> di ſunt corpora cæleſtia, & </s> <s xml:id="echoid-s6361" xml:space="preserve">elementa, factum eſſe rotundum, ita ut rotundius <lb/>nil excogitari poſſit: </s> <s xml:id="echoid-s6362" xml:space="preserve">Similitudine tamen quadam propter multas proprietates <lb/>cælo, elementisq́ue, cum corporibus regularibus communes, huiuſmodi illis <lb/>figuras attribuit, ut facilius explicaret, & </s> <s xml:id="echoid-s6363" xml:space="preserve">eorum naturam, & </s> <s xml:id="echoid-s6364" xml:space="preserve">mutuam ex uno <lb/>in alterum traſmutationem: </s> <s xml:id="echoid-s6365" xml:space="preserve">Maxime uero, quoniam ſicut impoſſibile eſt pror <lb/>ſus dari plura corpora regularia, præter illa quinque enumerata, ut clariſſime <lb/>à nobis demonſtratum eſt ad finem lib. </s> <s xml:id="echoid-s6366" xml:space="preserve">13. </s> <s xml:id="echoid-s6367" xml:space="preserve">Eucl. </s> <s xml:id="echoid-s6368" xml:space="preserve">ita quoque quinque tantum-<lb/>modo corpora illa ſimplicia in toto Vniuerſo reperiuntur, ut ex lib. </s> <s xml:id="echoid-s6369" xml:space="preserve">1. </s> <s xml:id="echoid-s6370" xml:space="preserve">de cælo <lb/>conſtat. </s> <s xml:id="echoid-s6371" xml:space="preserve">Quocirca Plato ſolum uultin Tymæo, quinque corpora ſimplicia <lb/>mundum uniuerſum componentia proportione quadam reſpondere quinque <lb/>illis corporibus regularibus.</s> <s xml:id="echoid-s6372" xml:space="preserve"/> </p> <div xml:id="echoid-div324" type="float" level="2" n="22"> <note position="left" xlink:label="note-170-02" xlink:href="note-170-02a" xml:space="preserve">Plato quo <lb/>pacto qua-<lb/>tuor elemẽ <lb/>tis, & cælo <lb/>tribuerit fi-<lb/>guras quin <lb/>que corpo <lb/>rum regula <lb/>rium.</note> </div> </div> <div xml:id="echoid-div326" type="section" level="1" n="104"> <head xml:id="echoid-head108" xml:space="preserve">TERRAM ESSE CENTRVM MVNDI.</head> <p style="it"> <s xml:id="echoid-s6373" xml:space="preserve"><emph style="sc">QVod</emph> autem terra ſit in medio Firmamenti ſita, ſic patet. </s> <s xml:id="echoid-s6374" xml:space="preserve">Exi <lb/> <anchor type="note" xlink:label="note-171-01a" xlink:href="note-171-01"/> ſtentibus in ſuperficie terræ, ſtellæ apparent eiuſdem quantita-<lb/>tis, ſiue ſint in medio cæli, ſiue iuxta ortum ſiue iuxta occa-<lb/>ſum: </s> <s xml:id="echoid-s6375" xml:space="preserve">& </s> <s xml:id="echoid-s6376" xml:space="preserve">hoc ideo, quia æqualiter terra diſtat ab eis.</s> <s xml:id="echoid-s6377" xml:space="preserve"/> </p> <div xml:id="echoid-div326" type="float" level="2" n="1"> <note position="right" xlink:label="note-171-01" xlink:href="note-171-01a" xml:space="preserve">Terram in <lb/>centro mũ-<lb/>di eſſe ſitã.</note> </div> </div> <div xml:id="echoid-div328" type="section" level="1" n="105"> <head xml:id="echoid-head109" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s6378" xml:space="preserve"><emph style="sc">Avctor</emph> hoc loco demonſtrat quartam concluſionem, nimrum, Ter-<lb/>ram eſſe centrum mundi: </s> <s xml:id="echoid-s6379" xml:space="preserve">Intellige terram ſimul cum aqua. </s> <s xml:id="echoid-s6380" xml:space="preserve">Quamuis enim au <lb/>@tor de terra ſolum hic loquatur expreſſe, rationes tamen eædem uim habent <lb/>in toto aggregato ex terra & </s> <s xml:id="echoid-s6381" xml:space="preserve">aqua. </s> <s xml:id="echoid-s6382" xml:space="preserve">Quoniã uero centrũ alicuius ſphæræ duas <lb/>debet habere conditiones, unam quidẽ, ut ſit in medio illius æqualiter ab om-<lb/>nibus extremitatibus remotum, alteram uero, ut ſit punctum, & </s> <s xml:id="echoid-s6383" xml:space="preserve">omnino inſen <lb/>ſibile reſpectu illius, cuius centrum dicitur. </s> <s xml:id="echoid-s6384" xml:space="preserve">Idcirco utramq. </s> <s xml:id="echoid-s6385" xml:space="preserve">conditionem ter-<lb/>ræ ineſſe reſpectu cæli auctor oſtendit hoc loco. </s> <s xml:id="echoid-s6386" xml:space="preserve">Quòd enim terra ſit in medio <lb/>cæli, ſeu totius mundi, duabus ſuadet rationibus, quarum prima eſt. </s> <s xml:id="echoid-s6387" xml:space="preserve">Exiſtenti-<lb/>bus nobis in ſuperficie terræ, & </s> <s xml:id="echoid-s6388" xml:space="preserve">in quacunq. </s> <s xml:id="echoid-s6389" xml:space="preserve">regione, apparent ſtellæ eiuſdem <lb/>ſemper magnitudinis tam in ortu, & </s> <s xml:id="echoid-s6390" xml:space="preserve">occaſu, quam in medio cęli, ſecluſis omni <lb/>bus uaporibus, nebulis, & </s> <s xml:id="echoid-s6391" xml:space="preserve">exhalationibus, quæ uiſum noſtrum poſſent impedi-<lb/>re. </s> <s xml:id="echoid-s6392" xml:space="preserve">Igitur ęqualiter diſtamus ab omnibus cæli partibus, ac propterea terra, in <lb/>qua ſumus, erit in medio mundi, ſeu, quod idem eſt, in centro mundi. </s> <s xml:id="echoid-s6393" xml:space="preserve">Antece-<lb/>dens experimento eſt comprobatum, conſecutio uero facile probari poteſt. <lb/></s> <s xml:id="echoid-s6394" xml:space="preserve">Si enim non diſtaremus æqualiter à cælo, ſed ex una parte propius ad id acce-<lb/>deremus, quàm ex alia, cum ea, quę propinquiora ſunt, maiora uideantur, appa <lb/>rerent nobis ſtellæ maioris quantitatis in parte terræ propinquiori exiſtenti-<lb/>bus, quàm in remotiori, quod eſt contra experientiam.</s> <s xml:id="echoid-s6395" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6396" xml:space="preserve"><emph style="sc">Svmpta</emph> eſt hæc ratio ex Alphragano Differt. </s> <s xml:id="echoid-s6397" xml:space="preserve">4. </s> <s xml:id="echoid-s6398" xml:space="preserve">quę non concludit, ſi præ <lb/>ciſe, & </s> <s xml:id="echoid-s6399" xml:space="preserve">Geometrice loquamur, hominem in eodem loco æqualiter diſtare ab <lb/>omnibus cæli partibus. </s> <s xml:id="echoid-s6400" xml:space="preserve">Hoc enim falſum efſe ſupra diximus, cum cælum a no-<lb/>bis ex parte Horizontis plus diſtet, ob ſemidiametrũ terræ interpoſitã: </s> <s xml:id="echoid-s6401" xml:space="preserve">ſed ſo-<lb/>lum colligit nos æquidiſtare a quacunq; </s> <s xml:id="echoid-s6402" xml:space="preserve">parte cæli, ſm iudicium ſenſus. </s> <s xml:id="echoid-s6403" xml:space="preserve">Tam <lb/>paruus enim exceſſus, ut ẽt ſupra dictum eſt, efficere non poteſt, ut ex parte Ho <lb/>rizontis minores appareant ſtellæ ſereno tempore, quàm in medio cæli. </s> <s xml:id="echoid-s6404" xml:space="preserve">Qua-<lb/>re recte poterũt dici ſtellæ, quòd ad ſenſum attinet, à quocũq loco teræ ęqua-<lb/>liter diſtare. </s> <s xml:id="echoid-s6405" xml:space="preserve">Optime tamẽ ratio probat, centrũ terræ ęqualiter à cęlo diſtare, <lb/>id eſt, eſſe idem, ꝙ centrum mundi. </s> <s xml:id="echoid-s6406" xml:space="preserve">Alias enim aliquæ partes ſuperficiei terræ <lb/>ſenſibiliter recederent a centro mundi, atq. </s> <s xml:id="echoid-s6407" xml:space="preserve">adeo ſenſibiliter quoq. </s> <s xml:id="echoid-s6408" xml:space="preserve">in eiſdem <pb o="136" file="172" n="173" rhead="Comment. in I. Cap. Sphæræ"/> partibus ſtellæ eædem maiores, vel minores apparerent, quod falſum eſt.</s> <s xml:id="echoid-s6409" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6410" xml:space="preserve"><emph style="sc">Porro</emph> quoniam in ortu, & </s> <s xml:id="echoid-s6411" xml:space="preserve">occaſu exiſtunt quaſi ſemper uapores, exhala <lb/>tionesve impedientes uerum iudicium ſenſus, non ſatis firmiter uidetur ex <lb/>prędicta ratione colligi poſſe, hominem quemcunque ęqualiter à cęlo diſtare. <lb/></s> <s xml:id="echoid-s6412" xml:space="preserve">Quare melius eadẽ rõ ex magnitudine ſtellarum ſumpta proponetur in hunc <lb/>modũ. </s> <s xml:id="echoid-s6413" xml:space="preserve">Eidẽ homini exiſtenti nunc ſub eo Meridiano, in quo eſt Sol, cum nobis <lb/>oritur; </s> <s xml:id="echoid-s6414" xml:space="preserve">Nunc ſub eo, ſub quo nos ſumus, nunc uero ſub eo, in quo eſt Sol, cum <lb/>nobis occidit, & </s> <s xml:id="echoid-s6415" xml:space="preserve">deniq. </s> <s xml:id="echoid-s6416" xml:space="preserve">ſub quocunq; </s> <s xml:id="echoid-s6417" xml:space="preserve">Meridiano, uidentur ſtellæ eædem eſſe <lb/>eiuſdem quantitatis, quando ad Meridianum perueniunt, ubi nulli exiſtunt <lb/>vapores tempore ſereno. </s> <s xml:id="echoid-s6418" xml:space="preserve">Quamobrem terræ ſuperficies æqualit<unsure/>er a ſtellis di-<lb/>ſtat ſecundum omnes illas partes prædictis Meridianis ſubiectas. </s> <s xml:id="echoid-s6419" xml:space="preserve">Quæ quid <lb/>ratio ſiue hoc poſteriori modo, ſiue illo priori proponatur, ſimiles uires ha-<lb/>bet in aqua. </s> <s xml:id="echoid-s6420" xml:space="preserve">Eadem nam que apparentia locum habet etiam in Mari.</s> <s xml:id="echoid-s6421" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6422" xml:space="preserve">Ex quo euidenter colligitur id, quod ſupra probauimus, Terram nimirum <lb/>& </s> <s xml:id="echoid-s6423" xml:space="preserve">aquam idem habere centrum cum centro totius Vniuerſi, quandoquidem <lb/>ſuperficies conuexa vtriuſque æquidiſtat a centro mundi, ut ex hac ratione, <lb/>quæ ab experimento ſumpta eſt, colligitur.</s> <s xml:id="echoid-s6424" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s6425" xml:space="preserve"><emph style="sc">Si</emph> enim terra magis accederet ad Firmamentum in una parte, quàm <lb/> <anchor type="note" xlink:label="note-172-01a" xlink:href="note-172-01"/> in alia, ſequeretur, quòd aliquis exiſtens in illa parte ſuperficiei terræ, quæ <lb/>magis accederet ad Firmamentum, non uideret cæli medietatem: </s> <s xml:id="echoid-s6426" xml:space="preserve">Sed hoc <lb/>eſt contra Ptolemæum, & </s> <s xml:id="echoid-s6427" xml:space="preserve">omnes philoſophos dicentes, quòd ubicunque <lb/>homo exiſtat, ſex ſigna ei oriuntur, & </s> <s xml:id="echoid-s6428" xml:space="preserve">ſex occidunt, & </s> <s xml:id="echoid-s6429" xml:space="preserve">medietas cæli ſem-<lb/>per apparet ei, medietas uero occultatur.</s> <s xml:id="echoid-s6430" xml:space="preserve"/> </p> <div xml:id="echoid-div328" type="float" level="2" n="1"> <note position="left" xlink:label="note-172-01" xlink:href="note-172-01a" xml:space="preserve">Alia ratio <lb/>probans ter <lb/>ram eſſe in <lb/>@entro mũ-<lb/>@i.</note> </div> </div> <div xml:id="echoid-div330" type="section" level="1" n="106"> <head xml:id="echoid-head110" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s6431" xml:space="preserve"><emph style="sc">Secvnda</emph> ratio eſt hæc fere. </s> <s xml:id="echoid-s6432" xml:space="preserve">Vbicunq. </s> <s xml:id="echoid-s6433" xml:space="preserve">homo exiſtat, ſex ei ſemper ſi-<lb/>gna oriuntur, ſex occidunt; </s> <s xml:id="echoid-s6434" xml:space="preserve">medietasq́. </s> <s xml:id="echoid-s6435" xml:space="preserve">una cæli ſemper ei apparet, medietas <lb/>uero altera ei occultatur. </s> <s xml:id="echoid-s6436" xml:space="preserve">Igitur terra in medio eſt Firmamẽti. </s> <s xml:id="echoid-s6437" xml:space="preserve">Antecedens eſt <lb/>Ptolemęi dict. </s> <s xml:id="echoid-s6438" xml:space="preserve">1. </s> <s xml:id="echoid-s6439" xml:space="preserve">c. </s> <s xml:id="echoid-s6440" xml:space="preserve">5. </s> <s xml:id="echoid-s6441" xml:space="preserve">& </s> <s xml:id="echoid-s6442" xml:space="preserve">6. </s> <s xml:id="echoid-s6443" xml:space="preserve">Alphragani Differt. </s> <s xml:id="echoid-s6444" xml:space="preserve">4. </s> <s xml:id="echoid-s6445" xml:space="preserve">omniumq́. </s> <s xml:id="echoid-s6446" xml:space="preserve">aliorum Aſtrologo-<lb/>rum, philoſophorumq́ue, qui experientia docti uno omnes ore fatentur, nos <lb/>ubiuis locorum medietatem cæli conſpicere, &</s> <s xml:id="echoid-s6447" xml:space="preserve">c. </s> <s xml:id="echoid-s6448" xml:space="preserve">Conſequentia uero neceſſa-<lb/>ria eſt. </s> <s xml:id="echoid-s6449" xml:space="preserve">Nam ſi terra non eſſet in medio cęli, ſed magis appropinquaret uni par <lb/>ti, quàm alteri, tunc is, qui exiſter et in parte cęlo propinquiori, nõ uideret cęli <lb/>medietatem, ſed minorem partẽ, qui uero in altera parte remotiori exiſteret, <lb/>plus conſpiceret ꝗ̃ medietatem, quia non omnis Horizon ſeparans partem cęli <lb/>uiſam à non uiſa tranſiret per centrum mundi, & </s> <s xml:id="echoid-s6450" xml:space="preserve">ex conſequenti non eſſet cir <lb/>culus maior, quare nec diuideret cęlum in duas partes æquales. </s> <s xml:id="echoid-s6451" xml:space="preserve">quod cum ſit <lb/>falſum, & </s> <s xml:id="echoid-s6452" xml:space="preserve">contra experientiam, falſum erit quoq. </s> <s xml:id="echoid-s6453" xml:space="preserve">terram nõ eſſe in medio cæli.</s> <s xml:id="echoid-s6454" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">Quomodo <lb/>u<unsure/>erum ſit, <lb/>hominem <lb/>medietatẽ <lb/>@ęli uidere.</note> <p> <s xml:id="echoid-s6455" xml:space="preserve"><emph style="sc">Reperitvr</emph> hæc ratio apud Alphraganum, & </s> <s xml:id="echoid-s6456" xml:space="preserve">Ptolemęum locis ci <lb/>tatis, in qua ſolum hoc obiter notandum eſt, fieri non poſſe, ut aliquis homo in <lb/>terræ ſuperficie conſtitutus præciſe medietatem cæli videat. </s> <s xml:id="echoid-s6457" xml:space="preserve">Concipitur enim <lb/>Horizon, qui uiſum noſtrum terminat, eſſe quædam plana ſuperficies circula-<lb/>ris ſuperincumbens terræ, eò quòd nos in aliqua magna campi planitie con-<lb/>ſtituti putemus partem terræ uiſam eſſe planam, atq. </s> <s xml:id="echoid-s6458" xml:space="preserve">ibidem cælum contingere <lb/>Quo fit, ut Horizon illi diuidere non poſſit cęlũ in duo æqualia, Deerit enim <lb/>illa pars cæli, quæ intercipitur inter illam ſuperficiem contingentem terram. <lb/></s> <s xml:id="echoid-s6459" xml:space="preserve">ſeu illi incumbentem, & </s> <s xml:id="echoid-s6460" xml:space="preserve">illam, quæ tranſit per cẽtrum terræ priori æquidiſtãs, <pb o="137" file="173" n="174" rhead="Ioan. de Sacro Boſco."/> Hæc namque ſola cęlum in duas partes æquales diuidet, ex propoſ. </s> <s xml:id="echoid-s6461" xml:space="preserve">11. </s> <s xml:id="echoid-s6462" xml:space="preserve">lib. </s> <s xml:id="echoid-s6463" xml:space="preserve">1. <lb/></s> <s xml:id="echoid-s6464" xml:space="preserve">Thæodoſij, & </s> <s xml:id="echoid-s6465" xml:space="preserve">conſpicuũ <lb/> <anchor type="figure" xlink:label="fig-173-01a" xlink:href="fig-173-01"/> quoque eſſe poteſt in ap-<lb/>poſita figura. </s> <s xml:id="echoid-s6466" xml:space="preserve">Verum <lb/>iſtud, quod inter vtram-<lb/>que ſuperficiem interij-<lb/>citur, nullius eſt momen <lb/>ti, ſeu quãtitatis fere re-<lb/>ſpectu totius machinæ <lb/>cæli. </s> <s xml:id="echoid-s6467" xml:space="preserve">Cum enim mirum <lb/>in modum diſtet à nobis <lb/>cœlum, ut poſtea dice-<lb/>mus, efficitur, ut ſi a no-<lb/>ſtro oculo, & </s> <s xml:id="echoid-s6468" xml:space="preserve">centro ter-<lb/>ræ duæ lineæ æquidiſtan <lb/>tes producerentur vſque <lb/>ad Firmamentum, uiſus <lb/>prorſus iudicaret illas <lb/>ibi coir<unsure/>e propter nimiam <lb/>diſtantiam a nobis, & </s> <s xml:id="echoid-s6469" xml:space="preserve">ex <lb/>conſequenti nullũ pror-<lb/>ſus ſpacium cõſpiceret fere interceptum inter illas: </s> <s xml:id="echoid-s6470" xml:space="preserve">Quemadmodum etiam in <lb/>aliquo longo ędificio, cuius parietes interiores ſunt æquidiſtantes, uidentur <lb/>nobis propinquiores eſſe inter ſe eius parietes in fine, quàm in principio, ex <lb/>quo parietes intuemur, propter illã diſtantiã. </s> <s xml:id="echoid-s6471" xml:space="preserve">Multo igitur magis hoc accidet <lb/>in cælo, cum ſine comparatione multo longius diſtet. </s> <s xml:id="echoid-s6472" xml:space="preserve">Vnde quo ad iudicium <lb/>ſenſus optime dici poterit, nos in loco terræ, ſecluſis impedimentis montium <lb/>ac ualium, conſpicere cęli medietatem. </s> <s xml:id="echoid-s6473" xml:space="preserve">Quod quidem perſpicue declarãt phę-<lb/>nomena, ſeu apparẽtię cęleſtes. </s> <s xml:id="echoid-s6474" xml:space="preserve">Cernimus enim duo luminaria, Solem nimirũ, <lb/>atq. </s> <s xml:id="echoid-s6475" xml:space="preserve">Lunam, quando opponuntur per diametrum, eodem ferè tempore ſupra <lb/>Horizontẽ, alterum quidem in oriente, alterum uero in occidente: </s> <s xml:id="echoid-s6476" xml:space="preserve">Vel certe, <lb/>quando alterum occidit, alterum ſtatim exoriri, quod fieri nõ poſſet, ſi portio <lb/>@æli intercepta inter utramque prędictam ſuperficiem eſſet alicuius notabilis <lb/>quantitatis. </s> <s xml:id="echoid-s6477" xml:space="preserve">Idem etiam clariſſime ex eo apparet, quòd ubique, ſecluſis impe-<lb/>dimentis, ſupra Horizontem ſex ſigna apparent, & </s> <s xml:id="echoid-s6478" xml:space="preserve">ſe infra, quæ quidem oc-<lb/>cupant medietatem cęli. </s> <s xml:id="echoid-s6479" xml:space="preserve">Immo auctore Plinio lib. </s> <s xml:id="echoid-s6480" xml:space="preserve">2. </s> <s xml:id="echoid-s6481" xml:space="preserve">cap. </s> <s xml:id="echoid-s6482" xml:space="preserve">13. </s> <s xml:id="echoid-s6483" xml:space="preserve">Luna aliquando vi <lb/>ſa eſt eclipſari in puncto orientis, exiſtente Sole adhuc quodammodo ſupra <lb/>Horizontem in puncto occidentis, & </s> <s xml:id="echoid-s6484" xml:space="preserve">tamen tune per diametrum opponeban-<lb/>tur duo illa luminaria.</s> <s xml:id="echoid-s6485" xml:space="preserve"/> </p> <div xml:id="echoid-div330" type="float" level="2" n="1"> <figure xlink:label="fig-173-01" xlink:href="fig-173-01a"> <image file="173-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/173-01"/> </figure> </div> <p> <s xml:id="echoid-s6486" xml:space="preserve"><emph style="sc">Dvabvs</emph> dictis rationibus poſſumus alias adiungere idem propoſitum <lb/>concludentes; </s> <s xml:id="echoid-s6487" xml:space="preserve">Terram videlicer eſſe in medio Firmamenti, ſeu totius Vniuerſi. <lb/></s> <s xml:id="echoid-s6488" xml:space="preserve">Quarum prima deſumpta ex Ptolem. </s> <s xml:id="echoid-s6489" xml:space="preserve">Dict. </s> <s xml:id="echoid-s6490" xml:space="preserve">1. </s> <s xml:id="echoid-s6491" xml:space="preserve">cap. </s> <s xml:id="echoid-s6492" xml:space="preserve">5. </s> <s xml:id="echoid-s6493" xml:space="preserve">ſit hæc.</s> <s xml:id="echoid-s6494" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6495" xml:space="preserve"><emph style="sc">Si</emph> terra non eſt in medio Firmamenti, ſiue totius Vniuerſi ſita, obtinebit <lb/> <anchor type="note" xlink:label="note-173-01a" xlink:href="note-173-01"/> neceſſario aliquem horum ſituum. </s> <s xml:id="echoid-s6496" xml:space="preserve">Aut erit in plano circuli Aequinoctialis ex <lb/>tra mundi axem: </s> <s xml:id="echoid-s6497" xml:space="preserve">(Nam ſi eſſet in axe mundi, & </s> <s xml:id="echoid-s6498" xml:space="preserve">in plano Æquatoris, exiſteret <lb/>in centro mundi.) </s> <s xml:id="echoid-s6499" xml:space="preserve">Aut in axe mundi, & </s> <s xml:id="echoid-s6500" xml:space="preserve">in planum Æquinoctialis circuli: </s> <s xml:id="echoid-s6501" xml:space="preserve">Aut <lb/>deniq. </s> <s xml:id="echoid-s6502" xml:space="preserve">neque in plano circuli Aequinoctialis, neque in axe mundi collocabi <lb/>tur: </s> <s xml:id="echoid-s6503" xml:space="preserve">quos omnes ſitus plurima abſurda conſequuntur. </s> <s xml:id="echoid-s6504" xml:space="preserve">Nam ſi in plano Aequa <pb o="138" file="174" n="175" rhead="Comment. in I. cap. Sphæræ"/> toris exiſteret extra axem mundi, efficeretur primum, In ſphæra recta nunqu@ <lb/> <anchor type="note" xlink:label="note-174-01a" xlink:href="note-174-01"/> fieri æquinoctium, niſi in eo in Horizonte, qui per centrum mundi tranſit. </s> <s xml:id="echoid-s6505" xml:space="preserve">Sit <lb/> <anchor type="figure" xlink:label="fig-174-01a" xlink:href="fig-174-01"/> .</s> <s xml:id="echoid-s6506" xml:space="preserve">n. </s> <s xml:id="echoid-s6507" xml:space="preserve">ſphæra B D C E, cu <lb/>ius centrum A; </s> <s xml:id="echoid-s6508" xml:space="preserve">Æqua <lb/>tor D E; </s> <s xml:id="echoid-s6509" xml:space="preserve">axis mundi <lb/>B C; </s> <s xml:id="echoid-s6510" xml:space="preserve">& </s> <s xml:id="echoid-s6511" xml:space="preserve">terra in F, ſi-<lb/>ue ſupra axem mun-<lb/>di, fiue infra; </s> <s xml:id="echoid-s6512" xml:space="preserve">Hori-<lb/>zon rectus H G, non <lb/>per centrum mundi <lb/>A, tranſiens, qui pa-<lb/>rallelus erit axi B C, <lb/>cum Aequator ad re-<lb/>ctos inſiſtat angulos <lb/>Horizonti recto. </s> <s xml:id="echoid-s6513" xml:space="preserve">Per-<lb/>ſpicuum igitur eſt, tã <lb/>Aequatorẽ, quàm re-<lb/>liquos parallelos So-<lb/>lis inęqualiter ab Ho-<lb/>rizonte recto diuidi, <lb/>cum non tranſeat per <lb/>centrum, aut polos <lb/>mundi: </s> <s xml:id="echoid-s6514" xml:space="preserve">Quare perpe-<lb/>tuo fient dies inæqua-<lb/>les noctibus, quod <lb/>eſt contra omnem experientiam, cũ in ſphæra recta perpetuũ ſit æquinoctium.</s> <s xml:id="echoid-s6515" xml:space="preserve"/> </p> <div xml:id="echoid-div331" type="float" level="2" n="2"> <note position="right" xlink:label="note-173-01" xlink:href="note-173-01a" xml:space="preserve">Ratio Ptole <lb/>mæi pro-<lb/>bãs terram <lb/>in medio <lb/>mũ di eſſ@.</note> <note position="left" xlink:label="note-174-01" xlink:href="note-174-01a" xml:space="preserve">Terram nõ <lb/>eſſe in pla-<lb/>no Aequa-<lb/>toris extra <lb/>axem mu@ <lb/>di.</note> <figure xlink:label="fig-174-01" xlink:href="fig-174-01a"> <image file="174-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/174-01"/> </figure> </div> <p> <s xml:id="echoid-s6516" xml:space="preserve"><emph style="sc">Deinde</emph>. </s> <s xml:id="echoid-s6517" xml:space="preserve">Nullus in eadem ſphæra recta uideret medietatem cęli, ſed par <lb/>tem minorem, vel maiorem medietate, ut eadem figura indicat; </s> <s xml:id="echoid-s6518" xml:space="preserve">quod ſenſui <lb/>aduerſatur. </s> <s xml:id="echoid-s6519" xml:space="preserve">Semper etenim ſunt ſex ſigna ſupra Horizontem, & </s> <s xml:id="echoid-s6520" xml:space="preserve">ſex infra. </s> <s xml:id="echoid-s6521" xml:space="preserve">So-<lb/>lum in eo Horizonte, qui per mundi cẽtrum ducitur, medietas cæli uideretur</s> </p> <p> <s xml:id="echoid-s6522" xml:space="preserve"><emph style="sc">Tertio</emph>. </s> <s xml:id="echoid-s6523" xml:space="preserve">Eædem ſtellæ tempore ſereno non apparerent ſemper eiuſdem <lb/>magnitudinis. </s> <s xml:id="echoid-s6524" xml:space="preserve">Si enim terra eſt in Aequinoctialis circuli plano, & </s> <s xml:id="echoid-s6525" xml:space="preserve">extra axem <lb/>mundi uerſus meridiem, hoc eſt, verſus Zenith, apparebunt ſtellę eædem maio <lb/>res in Meridiano circulo conſtitutæ, quàm in oriente, uel occidente, cum ibi <lb/>propinquiores exiſtant: </s> <s xml:id="echoid-s6526" xml:space="preserve">Si uero vergit ad mediam noctem, hoc eſt, uerſus Na-<lb/>dir, maiores conſpicientur in oriente, uel occidente collocatæ, quàm in Meri-<lb/>diano circulo: </s> <s xml:id="echoid-s6527" xml:space="preserve">Si autem ſita eſt uerſus ortum, uel occaſum, maiores uidebũtur <lb/>poſitę in oriẽte quoque, uel occidente. </s> <s xml:id="echoid-s6528" xml:space="preserve">Quæ omnia pugnant cum experiẽtia. <lb/></s> <s xml:id="echoid-s6529" xml:space="preserve">Accedit etiam, quod hoc poſteriori modo tempus antemeridianum minime <lb/>æquale erit pomeridiano; </s> <s xml:id="echoid-s6530" xml:space="preserve">propterea quod Meridianus circulus per uerticem <lb/>capitis incedit qui hac ratione eſſe non poteſt in medio Hemiſphærij, ſed uel <lb/>magis ad ortũ accedit, uel ad occaſum, ut manifeſte conſtat ex ſphæra materia-<lb/>li. </s> <s xml:id="echoid-s6531" xml:space="preserve">Solum igitur Phænomena locum habebunt in ſphæra recta, quando Terra <lb/>in medio mundi collocabitur, ut in puncto A, Horizonte exiſtente recta B C.</s> <s xml:id="echoid-s6532" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6533" xml:space="preserve"><emph style="sc">Qvarto</emph>. </s> <s xml:id="echoid-s6534" xml:space="preserve">In ſphæra obliqua aut nullum omnino fieret æquinoctium, <lb/>aut certe, ſi alicubi fieret, hoc non in medio loco inter ſolſtitium æſtiuum, atq; <lb/></s> <s xml:id="echoid-s6535" xml:space="preserve">hybernum contingeret; </s> <s xml:id="echoid-s6536" xml:space="preserve">quod uidemus communi experientiæ repugnare. </s> <s xml:id="echoid-s6537" xml:space="preserve">Eſto <lb/>enim rurſus ſphæra A B C D, cuius centrum F; </s> <s xml:id="echoid-s6538" xml:space="preserve">Aequator B D; </s> <s xml:id="echoid-s6539" xml:space="preserve">Duo tropici, <pb o="139" file="175" n="176" rhead="Ioan. de Sacro Boſco."/> I L, X H; </s> <s xml:id="echoid-s6540" xml:space="preserve">Axis mundi A C. </s> <s xml:id="echoid-s6541" xml:space="preserve">Si igitur terra in plano Aequin octialis circuli ex-<lb/>tra axem iacet, ut in F, ſit primum Horizon obliquus Z F Y’ſecans omnes pa-<lb/>rallelos in partes inæquales, & </s> <s xml:id="echoid-s6542" xml:space="preserve">axem in φ, extra parallelos. </s> <s xml:id="echoid-s6543" xml:space="preserve">Manifeſtum igi-<lb/> <anchor type="figure" xlink:label="fig-175-01a" xlink:href="fig-175-01"/> tur eſt, in dicto Ho-<lb/>rizonte nullum cõ-<lb/>tingere ęquinoctiũ, <lb/>cum Horizon eum <lb/>ſolum parallelũ bi-<lb/>fariam ſecet, qui ꝑ <lb/>φ, deſcribitur, quẽ <lb/>tamẽ nunquam Sol <lb/>attingere põt, quip <lb/>pe cum ultra tropi-<lb/>cum X H, non re-<lb/>cedat ab Aequato-<lb/>re. </s> <s xml:id="echoid-s6544" xml:space="preserve">Sit deinde a lius <lb/>Horizon obliquus <lb/>O F M, ſecans axem <lb/>A C, intra paralle-<lb/>los in N. </s> <s xml:id="echoid-s6545" xml:space="preserve">Perſpicuũ <lb/>iam eſt, fieri ęquino <lb/>ctiũ in prędicto Ho <lb/>rizõte, dum Sol pa-<lb/>rallelum per N, de-<lb/>ſcribit, quoniã hic <lb/>parallelus bifatiam <lb/>ab Horizonte diui-<lb/>ditur: </s> <s xml:id="echoid-s6546" xml:space="preserve">Verum nequaquam hoc contingere poteſt in tempore medio inter duo <lb/>ſolſtitia, cum ſolus Aequator B D, ab utroq. </s> <s xml:id="echoid-s6547" xml:space="preserve">Solſtitio æqualiter remouea-<lb/>tur. </s> <s xml:id="echoid-s6548" xml:space="preserve">Manifeſtum autem eſt, Sole exiſtente in Aequatore B D, non poſſe eſ-<lb/>ſe æquinoctium, ſed uel ante, uel poſt, quòd ſane abſurdum, & </s> <s xml:id="echoid-s6549" xml:space="preserve">inconueniens <lb/>eſt.</s> <s xml:id="echoid-s6550" xml:space="preserve"/> </p> <div xml:id="echoid-div332" type="float" level="2" n="3"> <figure xlink:label="fig-175-01" xlink:href="fig-175-01a"> <image file="175-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/175-01"/> </figure> </div> <p> <s xml:id="echoid-s6551" xml:space="preserve"><emph style="sc">Qvinto</emph>. </s> <s xml:id="echoid-s6552" xml:space="preserve">Nullus Horizon diuideret cælum in duas partes ęquales, præ <lb/>ter eum, qui cum circulo ęquinoctiali coincidit, cuiuſmodi eſt B C. </s> <s xml:id="echoid-s6553" xml:space="preserve">Quare ij <lb/>ſolum, qui ſub polis degunt, medietatem cæli conſpicerent.</s> <s xml:id="echoid-s6554" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6555" xml:space="preserve"><emph style="sc">Sexto</emph>. </s> <s xml:id="echoid-s6556" xml:space="preserve">Exceſſus maxime diei ſupra diem ęquinoctialem non eſſet ęqua-<lb/>lis defectui breuiſſimę diei, quo à die æquinoctiali ſuperatur, quod quotidia-<lb/>nę experientię aduerſatur. </s> <s xml:id="echoid-s6557" xml:space="preserve">Vt ſi A, eſt polus arcticus, erit P G, exceſſus maxi-<lb/>mæ diei X P, ſupra X G, diem æquinoctialem: </s> <s xml:id="echoid-s6558" xml:space="preserve">At K Q, defectus, quo breuiſſi-<lb/>ma dies I Q, ſuperatur ab eodem die ęquinoctiali I K. </s> <s xml:id="echoid-s6559" xml:space="preserve">Omnia autem hæc ab-<lb/>ſurda uitantur, ſi terra in centro E, ponatur. </s> <s xml:id="echoid-s6560" xml:space="preserve">Nam tunc in quouis obliquo Ho-<lb/>rizonte, nempe S R, fiet ęquinoctium, Sole exiſtẽte in Aequatore: </s> <s xml:id="echoid-s6561" xml:space="preserve">Diuidetur <lb/>cælum per æqualia; </s> <s xml:id="echoid-s6562" xml:space="preserve">eritq́; </s> <s xml:id="echoid-s6563" xml:space="preserve">T G, exceſſus longiſſimę diei, ęqualis defectui K V, <lb/>breuiſſimæ dici, & </s> <s xml:id="echoid-s6564" xml:space="preserve">c.</s> <s xml:id="echoid-s6565" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6566" xml:space="preserve"><emph style="sc">Si vero</emph> terra collocaretur in axe mundi extra planum Aeq<unsure/>uatoris, <lb/> <anchor type="note" xlink:label="note-175-01a" xlink:href="note-175-01"/> nimirum in puncto φ, conſequerentur hæc omnia inconuenientia. </s> <s xml:id="echoid-s6567" xml:space="preserve">Primum. <lb/></s> <s xml:id="echoid-s6568" xml:space="preserve">Nullus Horizon, præter rectum, ſecaret cœlum in duas partes ęquales, quare <lb/>neque Zodiacum; </s> <s xml:id="echoid-s6569" xml:space="preserve">ꝙ cum apparentijs pugnat. </s> <s xml:id="echoid-s6570" xml:space="preserve">Semper enim medietas Zodiaci <pb o="140" file="176" n="177" rhead="Comment. in I. Cap. Sphæræ"/> diaci eſt ſupra Horizontem quemcunque, & </s> <s xml:id="echoid-s6571" xml:space="preserve">medietas infra, eo quòd ſemper <lb/>ſex ſigna ſupra Horizontem exiſtant.</s> <s xml:id="echoid-s6572" xml:space="preserve"/> </p> <div xml:id="echoid-div333" type="float" level="2" n="4"> <note position="right" xlink:label="note-175-01" xlink:href="note-175-01a" xml:space="preserve">Terram nõ <lb/>eſſc in axe <lb/>mundi ex-<lb/>tra planum <lb/>Aequatoris</note> </div> <p> <s xml:id="echoid-s6573" xml:space="preserve"><emph style="sc">Deinde</emph>. </s> <s xml:id="echoid-s6574" xml:space="preserve">Solum in ſphæra recta fieret æquinoctium, quoniam ſolus Ho-<lb/>rizon rectus bifariam diuideret Æquatorem, ut ex ſuperiori figura conſtat, in <lb/>qua Æquator eſt B D; </s> <s xml:id="echoid-s6575" xml:space="preserve">Horizon rectus, A C; </s> <s xml:id="echoid-s6576" xml:space="preserve">obliquus, Y Z, ſecans Aequato-<lb/>rem in F, in partes inæquales. </s> <s xml:id="echoid-s6577" xml:space="preserve">Quòd in aliquo Horizonte obliquo continge <lb/>ret fieri æquinoctium, illud minime accideret in tempore medio inter utrum-<lb/>que Solſtitium, ſed multo propinquius eſſet æquinoctium uni ſolſtitiorum <lb/>quàm alteri. </s> <s xml:id="echoid-s6578" xml:space="preserve">Vt ſi terra conſtitueretur in N, inter tropicum X H, & </s> <s xml:id="echoid-s6579" xml:space="preserve">Æquato-<lb/>rem B D, fieret ęquinoctium, quando Sol parallelum percurrit, qui per N, de-<lb/>ſcribitur; </s> <s xml:id="echoid-s6580" xml:space="preserve">quod quidẽ ęquinoctium lõge uicinius exiſtit ſolſtitio ęſtiuo, quàm <lb/>hyberno. </s> <s xml:id="echoid-s6581" xml:space="preserve">Quòd ſi terra ſita eſſet in G, contingeret ęquinoctium in ipſo die Sol <lb/>@titij æſtiui, quæ quidem omnia abſurdiſſima ſunt.</s> <s xml:id="echoid-s6582" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6583" xml:space="preserve"><emph style="sc">Tertio</emph>, Vni <lb/> <anchor type="figure" xlink:label="fig-176-01a" xlink:href="fig-176-01"/> uerſa ſeries, atq. </s> <s xml:id="echoid-s6584" xml:space="preserve">pro <lb/>portio incrementi, <lb/>& </s> <s xml:id="echoid-s6585" xml:space="preserve">decrementi die-<lb/>rum, ac noctium cõ <lb/>funderet̃, quę ubiq-<lb/>extra rectam ſphæ-<lb/>ram apparet ante & </s> <s xml:id="echoid-s6586" xml:space="preserve"><lb/>poſt ęquinoctium; <lb/></s> <s xml:id="echoid-s6587" xml:space="preserve">quæ talis eſt, ut bis <lb/>in anno dies adę-<lb/>quentur noctibus, <lb/>in tempore uideli-<lb/>cet medio inter diẽ <lb/>longiſſimam, ac bre <lb/>uiſſimam: </s> <s xml:id="echoid-s6588" xml:space="preserve">Dies lon <lb/>giſſima ſit æqualis <lb/>nocti longiſſimæ: </s> <s xml:id="echoid-s6589" xml:space="preserve">& </s> <s xml:id="echoid-s6590" xml:space="preserve"><lb/>dies breuiſſima no-<lb/>ctibreuiſſimæ. </s> <s xml:id="echoid-s6591" xml:space="preserve">Ex-<lb/>ceſſus diei longiſſi-<lb/>mæ ſupra diem æꝗ-<lb/>noctij tantus ſit, ꝗ̃-<lb/>tus eſt defectus minimæ diei ab eodem die æquinoctij: </s> <s xml:id="echoid-s6592" xml:space="preserve">Quod idem dicẽdum <lb/>eſt de duobus diebus quibuſcunq. </s> <s xml:id="echoid-s6593" xml:space="preserve">a die ęquinoctij æque remotis, quorum u-<lb/>nus ſit ante, alter vero poſt æquinoctium: </s> <s xml:id="echoid-s6594" xml:space="preserve">& </s> <s xml:id="echoid-s6595" xml:space="preserve">alia huiuſmodi. </s> <s xml:id="echoid-s6596" xml:space="preserve">Quæ quidem per <lb/>petua ſeries, ac proportio conſtare duntaxat, & </s> <s xml:id="echoid-s6597" xml:space="preserve">conſeruari poterit, ſi terra in <lb/>centro E, collocetur: </s> <s xml:id="echoid-s6598" xml:space="preserve">Hac enim ratione Horizõ obliquus quilibet, nempe S R, <lb/>diuidet Æquatorem B D, in partes æquales, ut tãta portio eius extet ſupra Ho <lb/>rizontem, ꝗ̃ta infra Horizontem later, ac proinde tanta erit dies, quanta nox. </s> <s xml:id="echoid-s6599" xml:space="preserve"><lb/>Pari ratione ſecabuntur tropici X H, & </s> <s xml:id="echoid-s6600" xml:space="preserve">I L, in partes inæquales, ita tamen, ut <lb/>alterna ſegmenta æqualia exiſtant, nempe T X, & </s> <s xml:id="echoid-s6601" xml:space="preserve">V L; </s> <s xml:id="echoid-s6602" xml:space="preserve">Item T H, & </s> <s xml:id="echoid-s6603" xml:space="preserve">V I, ut <lb/>demonſtrat Theodoſius lib. </s> <s xml:id="echoid-s6604" xml:space="preserve">2. </s> <s xml:id="echoid-s6605" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s6606" xml:space="preserve">19. </s> <s xml:id="echoid-s6607" xml:space="preserve">Ex quo fit, diem longiſſimam X T, <lb/>æqualem eſſe nocti longiſſimæ I. </s> <s xml:id="echoid-s6608" xml:space="preserve">V; </s> <s xml:id="echoid-s6609" xml:space="preserve">& </s> <s xml:id="echoid-s6610" xml:space="preserve">diem breuiſſimam I V, nocti breuiſſimæ <lb/>H T. </s> <s xml:id="echoid-s6611" xml:space="preserve">Denique T G, exceſſus maximæ diei X T, ſupra diem ęquinoctij X G, <pb o="141" file="177" n="178" rhead="Ioan. de Sacro Boſco."/> æqualis erit K V, defectui minimæ diei I V, à die æquinoctij I K, propter ſimi-<lb/>litudinem, æqualiratemq; </s> <s xml:id="echoid-s6612" xml:space="preserve">triangulorum T E G, & </s> <s xml:id="echoid-s6613" xml:space="preserve">V E K. </s> <s xml:id="echoid-s6614" xml:space="preserve">Si vero terra in axe-<lb/>extra centrum E, ſtatuatur, ut in φ, extra omnes parallelos, nullum fieri pote-<lb/>rit in ſphæra obliqua æquinoctium, vt dictum eſt; </s> <s xml:id="echoid-s6615" xml:space="preserve">ſemperq́; </s> <s xml:id="echoid-s6616" xml:space="preserve">erunt dies noctibus <lb/>longiores, vel noctes diebus. </s> <s xml:id="echoid-s6617" xml:space="preserve">Quod ſi terra ponatur iu G, puncto, per quod ex-<lb/>tremus parallelus incedit, vnicum fieret æquinoctium in ſphæra obliqua, nem <lb/>pe in altero Solſtitiorũ; </s> <s xml:id="echoid-s6618" xml:space="preserve">Reliquo anni tempore omnes dies eſſent noctibus vel <lb/>maiores, vel minores. </s> <s xml:id="echoid-s6619" xml:space="preserve">At vero ſi terra conſiſtat intra parallelos in puncto N, <lb/>fieret quidem æquinoctium bis in anno, & </s> <s xml:id="echoid-s6620" xml:space="preserve">vtrinque creſcerent, ac decreſcerent <lb/>dierum, noctiumq; </s> <s xml:id="echoid-s6621" xml:space="preserve">ſpacia; </s> <s xml:id="echoid-s6622" xml:space="preserve">tamen hæc dierum incrementa, ac decremẽta nec nu <lb/>mero, nec magnitudine eſſent æqualia decrementis, incrementisq́; </s> <s xml:id="echoid-s6623" xml:space="preserve">noctium: </s> <s xml:id="echoid-s6624" xml:space="preserve">id <lb/>quod vel oculi facillime iudicare poſſant, collatis inter ſe duobus triangulis <lb/>PNG, & </s> <s xml:id="echoid-s6625" xml:space="preserve">QNK; </s> <s xml:id="echoid-s6626" xml:space="preserve">quoniam & </s> <s xml:id="echoid-s6627" xml:space="preserve">plura, & </s> <s xml:id="echoid-s6628" xml:space="preserve">maiora ſegmenta parallelorum compre-<lb/>henduntur in triangullo QNK, quàm in triangulo P N G.</s> <s xml:id="echoid-s6629" xml:space="preserve"/> </p> <div xml:id="echoid-div334" type="float" level="2" n="5"> <figure xlink:label="fig-176-01" xlink:href="fig-176-01a"> <image file="176-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/176-01"/> </figure> </div> <p> <s xml:id="echoid-s6630" xml:space="preserve"><emph style="sc">Qvarto</emph>. </s> <s xml:id="echoid-s6631" xml:space="preserve">Vmbræ gnomonum, qui cum Horizonte angulos rectos eſ-<lb/>ficiunt, tempore æquinoctiorum non per vnam, eandemq́; </s> <s xml:id="echoid-s6632" xml:space="preserve">lineam rectã ab oriẽ <lb/>te in occidentem proijcerentur, Sole exiſtente præciſe in ortu, atq; </s> <s xml:id="echoid-s6633" xml:space="preserve">in occaſu, <lb/>ſi terra inæqualiter ab vtroque polo remoueretur, eiusq́ue centrum non idem <lb/>eſſet, quod centrum mundi. </s> <s xml:id="echoid-s6634" xml:space="preserve">Sit namque <lb/>ptimum terra A, ſita in plano Aequino-<lb/> <anchor type="figure" xlink:label="fig-177-01a" xlink:href="fig-177-01"/> ctialis circuli, quod nobis repræſentet li-<lb/>nea B C; </s> <s xml:id="echoid-s6635" xml:space="preserve">ſitq́ue Gn@mon ſupra pl<unsure/>anũ Ho-<lb/>rizontis erectus, quod nobis referat cir-<lb/>culus BC. </s> <s xml:id="echoid-s6636" xml:space="preserve">Perſpicue iam cernis, Sole exo-<lb/>riente in B, vmbram ſtyli A D, proijci in <lb/>lineam rectam A C: </s> <s xml:id="echoid-s6637" xml:space="preserve">Similiter, Sole occi-<lb/>dente in B, eandem vmbram proiici in li-<lb/>neam rectam A B, quæ cum priori A C, <lb/>lineam vnam rectam, atque continuan@ ef-<lb/>ficit: </s> <s xml:id="echoid-s6638" xml:space="preserve">Quod quidem clariſſime nobis oſten-<lb/>dunt apparentiæ Aſtronomorum, & </s> <s xml:id="echoid-s6639" xml:space="preserve">huius <lb/>rei cauſa eſt hæc duntaxat: </s> <s xml:id="echoid-s6640" xml:space="preserve">quia nimirum <lb/>terra eſt in plano Aequatoris ſita, Si enim extra ipſum foret collocata, in <lb/>axe tamen mundi, vel etiam quamcunq; </s> <s xml:id="echoid-s6641" xml:space="preserve">partem verſus, uempe in E; </s> <s xml:id="echoid-s6642" xml:space="preserve">ſi erige-<lb/>retur ſtyllus ſupra Horizontem rectus, qualis eſt E F, quis non videt, Sole in B, <lb/>oriente tempore æquinoctij, vmbram extendi ſecundum rectam E G, oc@iden <lb/>te vero Sole in C, eandem vmbram extendi ſecundum rectam E H, quæ nequa <lb/>quam cum priori E G, lineam conſtituit rectam, ſed ambæ ſe mutuo interſecãt <lb/>in puncto E, quippe cum productæ peruenirẽt ad puncta B, & </s> <s xml:id="echoid-s6643" xml:space="preserve">C? </s> <s xml:id="echoid-s6644" xml:space="preserve">Huius autem <lb/>contrarium experientia nos docet.</s> <s xml:id="echoid-s6645" xml:space="preserve"/> </p> <div xml:id="echoid-div335" type="float" level="2" n="6"> <figure xlink:label="fig-177-01" xlink:href="fig-177-01a"> <image file="177-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/177-01"/> </figure> </div> <p> <s xml:id="echoid-s6646" xml:space="preserve"><emph style="sc">Qvinto</emph>. </s> <s xml:id="echoid-s6647" xml:space="preserve">Nunquã per dioptram cernerentur duo ſigna Zodiaci per dia <lb/>metrũ oppoſita, quod eſt cõtra experientiã, quæ teſtatur, ortũ & </s> <s xml:id="echoid-s6648" xml:space="preserve">occaſum So-<lb/>lis in æquinoctus per dioptrã ſecundum unã rectam lineã cõſpici: </s> <s xml:id="echoid-s6649" xml:space="preserve">Pari ratione <lb/>ortũ in ſolſtitio æſtiuo, & </s> <s xml:id="echoid-s6650" xml:space="preserve">occaſum in ſolſtitio hyemali: </s> <s xml:id="echoid-s6651" xml:space="preserve">Item ortũ in ſolſtitio <lb/>hyemali, & </s> <s xml:id="echoid-s6652" xml:space="preserve">occaſum in Solſtitio æſtiuo, per dioptrã ſecundum lineã rectam ſibi <lb/>correſpondere in quolibet Horizonte. </s> <s xml:id="echoid-s6653" xml:space="preserve">Quod fieri minime poſſet, niſi terra in <lb/>plano Aequinoctialis circuli, & </s> <s xml:id="echoid-s6654" xml:space="preserve">in eins cẽtro eſſet collocata. </s> <s xml:id="echoid-s6655" xml:space="preserve">Sit enim Horizon <lb/>BDCE; </s> <s xml:id="echoid-s6656" xml:space="preserve">Aequator BC; </s> <s xml:id="echoid-s6657" xml:space="preserve">axis mundi D E; </s> <s xml:id="echoid-s6658" xml:space="preserve">tropicus cancri FG; </s> <s xml:id="echoid-s6659" xml:space="preserve">tropicus Capricor- <pb o="142" file="178" n="179" rhead="Comment. in I. Cap. Sphæræ"/> ni HI: </s> <s xml:id="echoid-s6660" xml:space="preserve">ponaturq; </s> <s xml:id="echoid-s6661" xml:space="preserve">primũ terra in cẽtro A. </s> <s xml:id="echoid-s6662" xml:space="preserve">Perſpicue igitur uides, ortũ æquino-<lb/>ctialẽ B, & </s> <s xml:id="echoid-s6663" xml:space="preserve">occaſum C, per lineã rectam B C; </s> <s xml:id="echoid-s6664" xml:space="preserve">ortũ uero æſtiuum F, & </s> <s xml:id="echoid-s6665" xml:space="preserve">occaſum <lb/>hyemalẽ I, ſecundum rectam lineam F I; </s> <s xml:id="echoid-s6666" xml:space="preserve">ortum deniq. </s> <s xml:id="echoid-s6667" xml:space="preserve">hyemalem H, & </s> <s xml:id="echoid-s6668" xml:space="preserve">occa-<lb/>ſum æſtiuum G, per lineam rectã GH, <lb/> <anchor type="figure" xlink:label="fig-178-01a" xlink:href="fig-178-01"/> ſibi mutuo reſpondere; </s> <s xml:id="echoid-s6669" xml:space="preserve">vt res poſtulat. <lb/></s> <s xml:id="echoid-s6670" xml:space="preserve">Quod quidẽ phænomena Aſtronomo-<lb/>rũ teſtantur, aſſumiturq. </s> <s xml:id="echoid-s6671" xml:space="preserve">ab Euclide in <lb/>principio φαινομένων vt certiſſimũ, aſ-<lb/>ſeriturque à Plinio lib. </s> <s xml:id="echoid-s6672" xml:space="preserve">2. </s> <s xml:id="echoid-s6673" xml:space="preserve">c. </s> <s xml:id="echoid-s6674" xml:space="preserve">71. </s> <s xml:id="echoid-s6675" xml:space="preserve">ex ſentẽ<unsure/> <lb/>tia omniũ Aſtrologorũ. </s> <s xml:id="echoid-s6676" xml:space="preserve">Collocetur de <lb/>inde terra in axe mũdi extra Aequato-<lb/>rẽ, nẽpe in K. </s> <s xml:id="echoid-s6677" xml:space="preserve">Quo poſito, luce clarius <lb/>cõftat, totũ oppoſitũ accidere. </s> <s xml:id="echoid-s6678" xml:space="preserve">Occaſus <lb/>enim hyemalis I<unsure/>; </s> <s xml:id="echoid-s6679" xml:space="preserve">per lineam rectã, quæ <lb/>per terrã extenditur, nõ amplius reſpõ-<lb/>debit ortui æſtiuo F, ſed puncto L: </s> <s xml:id="echoid-s6680" xml:space="preserve">Simi <lb/>liter occaſus æſtiuus G, puncto M, non <lb/>antem ortui hyemali H, reſpondebit.</s> <s xml:id="echoid-s6681" xml:space="preserve"/> </p> <div xml:id="echoid-div336" type="float" level="2" n="7"> <figure xlink:label="fig-178-01" xlink:href="fig-178-01a"> <image file="178-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/178-01"/> </figure> </div> <p> <s xml:id="echoid-s6682" xml:space="preserve"><emph style="sc">Si deniqve</emph> terra nec in plano Aequinoctialis circuli, nec in a@e-<lb/>mundi eſſet poſita, ſed alibi, in omnia prædicta abſurda incideremus, vt facile <lb/>quiuis ex ijs, quæ dicta ſunt, deducere poteſt. </s> <s xml:id="echoid-s6683" xml:space="preserve">In ſphæra enim recta nullum fie-<lb/>ret æquinoctium, & </s> <s xml:id="echoid-s6684" xml:space="preserve">in ſphæra obliqua ille tantum Horizon ſecaret ſphæram <lb/>per æqualia, qui tranſiret per centrum mundi; </s> <s xml:id="echoid-s6685" xml:space="preserve">Confundereturq́ue vniuerſa ſe <lb/>ries in decrementis dierum, ac noctium, &</s> <s xml:id="echoid-s6686" xml:space="preserve">c.</s> <s xml:id="echoid-s6687" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6688" xml:space="preserve"><emph style="sc">Secvnda</emph> ratio deſumpta etiam ex Ptolemæo loco citato, qua quoq. <lb/></s> <s xml:id="echoid-s6689" xml:space="preserve"> <anchor type="note" xlink:label="note-178-01a" xlink:href="note-178-01"/> vtitur Auerrores lib. </s> <s xml:id="echoid-s6690" xml:space="preserve">2. </s> <s xml:id="echoid-s6691" xml:space="preserve">de cœlo, eſt talis. </s> <s xml:id="echoid-s6692" xml:space="preserve">Si terra uon eſſet in medio mundi ſita, <lb/>non fierent eclipſes Lunæ ſemper, quando duo luminaria per diametrũ oppo-<lb/>nuntur, ſed plerunq. </s> <s xml:id="echoid-s6693" xml:space="preserve">contingerent, <lb/> <anchor type="figure" xlink:label="fig-178-02a" xlink:href="fig-178-02"/> quando nõ exiſtunt in locis Zodiaci <lb/>oppoſitis, quod falſum eſt. </s> <s xml:id="echoid-s6694" xml:space="preserve">Teſtatur <lb/>ſiquidem experientiæ Aſtronomorũ, <lb/>tum demũ fieri eclipſim Lunæ & </s> <s xml:id="echoid-s6695" xml:space="preserve">ſem <lb/>per, quando Luna Soli opponitur, <lb/>aliàs nunquam. </s> <s xml:id="echoid-s6696" xml:space="preserve">Sit enim centrum <lb/>mundi A, in quo ſi ponatur terra, <lb/>manifeſtum eſt eclipſim fieri, quan-<lb/>do luminaria per diametrum oppo-<lb/>nuntur, quia nimirum tunc ipſa ter-<lb/>ra interponitur inter vtr<unsure/>ũque; </s> <s xml:id="echoid-s6697" xml:space="preserve">Quã-<lb/>do uero non ſunt per diametrum <lb/>oppoſita, nullam poſſe eſſe eclipſim. <lb/></s> <s xml:id="echoid-s6698" xml:space="preserve">Nam terra non poteſt tunc eſſe im-<lb/>pedimento, quò minus Luna à Sole illuſtretur. </s> <s xml:id="echoid-s6699" xml:space="preserve">Quòd ſi terra extra centrum <lb/>ſedem habeat, vt in B, poterunt duo luminaria in punctis Zodiaci oppoſitis <lb/>exiſtere, & </s> <s xml:id="echoid-s6700" xml:space="preserve">tamen nulla fieri eclipſis, quòd terra non reperiatur in illa mundi <lb/>diametro, ſecundum quàm opponuntur. </s> <s xml:id="echoid-s6701" xml:space="preserve">Immo Luna patietur eclipſim, vt plu-<lb/>rimum, quando minus à Sole diſtat, quàm ſemicirculo. </s> <s xml:id="echoid-s6702" xml:space="preserve">Ac breuiter, Lunæ de-<lb/>ſectus tunc demum in oppoſitis per ſemicirculum locis fieri poteſt, quando <pb o="143" file="179" n="180" rhead="Ioan. de Sacro Boſco."/> diameter oppoſitionis per centrum terræ, ac Vniuerſi tranſierit. </s> <s xml:id="echoid-s6703" xml:space="preserve">Quæ omnia <lb/>cum phænomenis pugnant.</s> <s xml:id="echoid-s6704" xml:space="preserve"/> </p> <div xml:id="echoid-div337" type="float" level="2" n="8"> <note position="left" xlink:label="note-178-01" xlink:href="note-178-01a" xml:space="preserve">Alia ratio <lb/>Ptolemæi <lb/>probãs ter-<lb/>ram in me-<lb/>dio mundi <lb/>eſſe.</note> <figure xlink:label="fig-178-02" xlink:href="fig-178-02a"> <image file="178-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/178-02"/> </figure> </div> <p> <s xml:id="echoid-s6705" xml:space="preserve">EX <emph style="sc">Hac</emph> rurſus ratione ſic licebit quoq. </s> <s xml:id="echoid-s6706" xml:space="preserve">propoſitum noſtrum conclu-<lb/>dere, Accipiantur duæ eclipſes Lunares, <lb/> <anchor type="figure" xlink:label="fig-179-01a" xlink:href="fig-179-01"/> quæ cõtigerint in diuerſis Zodiaci locis. </s> <s xml:id="echoid-s6707" xml:space="preserve">Et <lb/>quoniam vtraque eclipſis facta eſt, quando <lb/>Luna Soli per diametrũ obijciebatur, vt & </s> <s xml:id="echoid-s6708" xml:space="preserve"><lb/>experientia, & </s> <s xml:id="echoid-s6709" xml:space="preserve">ſupputatio Aſtronomica do-<lb/>cuit: </s> <s xml:id="echoid-s6710" xml:space="preserve">efficitur, terram neceſſario in vtraq. </s> <s xml:id="echoid-s6711" xml:space="preserve">il-<lb/>la diametro exiſtere, atq. </s> <s xml:id="echoid-s6712" xml:space="preserve">adeo in communi <lb/>earum ſectione. </s> <s xml:id="echoid-s6713" xml:space="preserve">Cumigitur omnes diametri <lb/>mundi ſeſe in centro mundi interſecent, ne-<lb/>ceſſe eſt, terram in medio mundi eſſe collo-<lb/> <anchor type="note" xlink:label="note-179-01a" xlink:href="note-179-01"/> catam, vt in propoſita figura apparet.</s> <s xml:id="echoid-s6714" xml:space="preserve"/> </p> <div xml:id="echoid-div338" type="float" level="2" n="9"> <figure xlink:label="fig-179-01" xlink:href="fig-179-01a"> <image file="179-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/179-01"/> </figure> <note position="right" xlink:label="note-179-01" xlink:href="note-179-01a" xml:space="preserve">Ratio Ioa@ <lb/>Region.</note> </div> <p> <s xml:id="echoid-s6715" xml:space="preserve"><emph style="sc">Tertia</emph> ratio eſt Ioan. </s> <s xml:id="echoid-s6716" xml:space="preserve">Region in Epi-<lb/>tom. </s> <s xml:id="echoid-s6717" xml:space="preserve">lib. </s> <s xml:id="echoid-s6718" xml:space="preserve">1. </s> <s xml:id="echoid-s6719" xml:space="preserve">concl. </s> <s xml:id="echoid-s6720" xml:space="preserve">3. </s> <s xml:id="echoid-s6721" xml:space="preserve">quam ſumſipſſe videtur <lb/>ex Ariſtorele lib. </s> <s xml:id="echoid-s6722" xml:space="preserve">2. </s> <s xml:id="echoid-s6723" xml:space="preserve">de cœlo. </s> <s xml:id="echoid-s6724" xml:space="preserve">Omnia grauia libere ſecundum mundi diametrũ <lb/>deſcendẽtia ſuperficiei terræ ad angulos æquales occurrũt, in quacunq. </s> <s xml:id="echoid-s6725" xml:space="preserve">orbis <lb/>parte deſcendant. </s> <s xml:id="echoid-s6726" xml:space="preserve">igitur omnia tendunt ad terræ centrum, aliàs non inciderẽt <lb/>ſuperficiei terræ ad angulos æquales, vt ſuperius demonſtrauimus: </s> <s xml:id="echoid-s6727" xml:space="preserve">Et quia <lb/>diametri mundi, ſecundum quas grauia feruntur, tranſeunt per centrum Vni-<lb/>uerſi ibidem ſe interſecantes; </s> <s xml:id="echoid-s6728" xml:space="preserve">efficitur, idem eſſe terræ, & </s> <s xml:id="echoid-s6729" xml:space="preserve">mundi centrum.</s> <s xml:id="echoid-s6730" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">Ratio Ari-<lb/>ſtotelis.</note> <p> <s xml:id="echoid-s6731" xml:space="preserve"><emph style="sc">Qvarta</emph> ratio ſit Ariſtor<unsure/>elis. </s> <s xml:id="echoid-s6732" xml:space="preserve">Cum terra ſit grauiſſima, tende@ vtique <lb/>ad infimum locum, nempe ad punctum remotiſſimum à cœlo, quod eſt cen-<lb/>trum mundi. </s> <s xml:id="echoid-s6733" xml:space="preserve">Naturaliter igitur ibidem conſiſter, tanquam in propria ſede, ali <lb/>bi vero violenter.</s> <s xml:id="echoid-s6734" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">Alia ratio <lb/>probãs ter-<lb/>ram eſſe in <lb/>medio mũ-<lb/>di.</note> <p> <s xml:id="echoid-s6735" xml:space="preserve"><emph style="sc">Accedit</emph> etiam, quod ſi hæc grauis terræ moles in quotuis æquales <lb/>partes eiuſdem figuræ inter ſe, eluſdemq́ue magnitudinis, ac ponderis eſſet ſe <lb/>cta, quæ in diuerſis locis ſub concauo Lunæ collocarentur, indeq́. </s> <s xml:id="echoid-s6736" xml:space="preserve">libere de-<lb/>mittentur, proculdubio omnes partes, cum ſint eiuſdem naturæ, ponderis, <lb/>magnitudinis, ac figuræ, æquali motu, eodemq́ue tempore ad eundem locum <lb/>deſcenderent, quod nullo pacto fieri poſſer, niſi in centro mundi conuenirẽt. <lb/></s> <s xml:id="echoid-s6737" xml:space="preserve">Ac proſecto Natura iure optimo terram in medio mundi collocaſſe videtur, vt <lb/>tam vile, ac rude corpus ab omnibus partibus cœli, quod eſt corpus præſtantiſ-<lb/>fimum, æqualiter ſemoueretur, ne ulla pars conqueri poſſer, cur ſibi magis ru-<lb/>dis iſta moles appropinquaret, quàm alteri parti.</s> <s xml:id="echoid-s6738" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">Terram eſ-<lb/>ſe inſtarpũ-<lb/>cti reſpectu <lb/>Firmamen<unsure/> <lb/>ti.</note> <p style="it"> <s xml:id="echoid-s6739" xml:space="preserve"><emph style="sc">Illvd</emph> item eſt ſignum, quod terra ſit tanquam centrum, & </s> <s xml:id="echoid-s6740" xml:space="preserve">pun-<lb/>ctum reſpectu Firmamenti: </s> <s xml:id="echoid-s6741" xml:space="preserve">Quia ſi terra eßet alicuius quantitatis reſpe-<lb/>ctu Firmamenti, non contingeret medietatem cæli uideri.</s> <s xml:id="echoid-s6742" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div340" type="section" level="1" n="107"> <head xml:id="echoid-head111" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s6743" xml:space="preserve"><emph style="sc">Tribvs</emph> nunc medijs Ioannes de Sacro Boſco cõfirmat, alteram quoque <lb/>conditionem centri (quòd videlicet ſit inſenſibile quippiam, & </s> <s xml:id="echoid-s6744" xml:space="preserve">inſtar pũcti in-<lb/>diuiſibilis.) </s> <s xml:id="echoid-s6745" xml:space="preserve">ineſſe terræ reſpectu machinæ cœleſtis; </s> <s xml:id="echoid-s6746" xml:space="preserve">quorum primũ eſt. </s> <s xml:id="echoid-s6747" xml:space="preserve">Si terra <lb/>re ſpectu Firmamenti haberet ſenſibilem, ac notabilem quantitatem, & </s> <s xml:id="echoid-s6748" xml:space="preserve">nõ po <lb/>rius inſtar puncti omnino indiuiſibilis exiſteret, non poſſe@us uidere cęli me-<lb/>dietatem: </s> <s xml:id="echoid-s6749" xml:space="preserve">quod eſt contra experientiam, & </s> <s xml:id="echoid-s6750" xml:space="preserve">omnes Aſtrologos, ut ſupra di- <pb o="144" file="180" n="181" rhead="Comment. in I. Cap. Sphæræ"/> ctum eſt. </s> <s xml:id="echoid-s6751" xml:space="preserve">Sequela confirmatur. </s> <s xml:id="echoid-s6752" xml:space="preserve">Nam ſi terra collata cum cœleſti corpore eſſet <lb/>alicuius magnitudinis, quæ ſub ſenſum caderet, haud dubie ſupeificies quoq; <lb/></s> <s xml:id="echoid-s6753" xml:space="preserve">terræ notabiliter à centro mundi, quod idem <lb/> <anchor type="figure" xlink:label="fig-180-01a" xlink:href="fig-180-01"/> iam probauimus eſſe, quod centrum terræ re <lb/>cederet. </s> <s xml:id="echoid-s6754" xml:space="preserve">Quocirca Hor@on incumbens ter-<lb/>rę ſuperficiei, notabiliter cœlum in duas par-<lb/>tes inæquales ſecaret; </s> <s xml:id="echoid-s6755" xml:space="preserve">vt luce clarius in figura <lb/>propoſita cernis.</s> <s xml:id="echoid-s6756" xml:space="preserve"/> </p> <div xml:id="echoid-div340" type="float" level="2" n="1"> <figure xlink:label="fig-180-01" xlink:href="fig-180-01a"> <image file="180-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/180-01"/> </figure> </div> <p> <s xml:id="echoid-s6757" xml:space="preserve"><emph style="sc">Invenies</emph> hanc candem ratione@ <lb/>apud Ptolemæum Dict. </s> <s xml:id="echoid-s6758" xml:space="preserve">1. </s> <s xml:id="echoid-s6759" xml:space="preserve">cap. </s> <s xml:id="echoid-s6760" xml:space="preserve">6. </s> <s xml:id="echoid-s6761" xml:space="preserve">& </s> <s xml:id="echoid-s6762" xml:space="preserve">apud Al-<lb/>phraganum Differ. </s> <s xml:id="echoid-s6763" xml:space="preserve">4. </s> <s xml:id="echoid-s6764" xml:space="preserve">eſtq́; </s> <s xml:id="echoid-s6765" xml:space="preserve">omnium aliorum <lb/>Aſtronomorum: </s> <s xml:id="echoid-s6766" xml:space="preserve">quam quidem vides eaſdem <lb/>habere vires in mari. </s> <s xml:id="echoid-s6767" xml:space="preserve">Si enim mare eſſet mul-<lb/>to maius, & </s> <s xml:id="echoid-s6768" xml:space="preserve">altius quàm terra, vt nonnulli <lb/>fabulantur, non poſſemus in medio mari con <lb/>ſtituti medietatem cęli videre, aut certe non @que bene, ac in terra; </s> <s xml:id="echoid-s6769" xml:space="preserve">cuius op-<lb/>poſitum experientia quotidiana nos docet.</s> <s xml:id="echoid-s6770" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s6771" xml:space="preserve"><emph style="sc">Item</emph> ſi intelligatur ſuperficies plana ſuper centrum terræ diuidens <lb/> <anchor type="note" xlink:label="note-180-01a" xlink:href="note-180-01"/> eam in duo æqualia, & </s> <s xml:id="echoid-s6772" xml:space="preserve">ipſum per conſequens Firmamentum, oculus exi-<lb/>ſtens in terræ centro uider@t medietatem cœli; </s> <s xml:id="echoid-s6773" xml:space="preserve">Sed idem exiſtens in ſuperficie <lb/>terræ uidet eandem medietatem. </s> <s xml:id="echoid-s6774" xml:space="preserve">Igitur patei, quod inſenſibilis eſt quantitas <lb/>terræ, quæ eſt à ſuperficie ad centrum, & </s> <s xml:id="echoid-s6775" xml:space="preserve">per conſequens quantitas totius <lb/>terræ inſenſibilis eſt reſpectu Firmamenti.</s> <s xml:id="echoid-s6776" xml:space="preserve"/> </p> <div xml:id="echoid-div341" type="float" level="2" n="2"> <note position="left" xlink:label="note-180-01" xlink:href="note-180-01a" xml:space="preserve">Con@rma-<lb/>tio antece-<lb/>dentis @a-<lb/>tionis.</note> </div> </div> <div xml:id="echoid-div343" type="section" level="1" n="108"> <head xml:id="echoid-head112" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s6777" xml:space="preserve"><emph style="sc">Sicv ndvm</emph> medium explicans quodammodo, ac conſirmans pri-<lb/>mum, hoc eſt. </s> <s xml:id="echoid-s6778" xml:space="preserve">Si imagi-<lb/>naremur ſuperficiem pla <lb/> <anchor type="figure" xlink:label="fig-180-02a" xlink:href="fig-180-02"/> nam circularem ingen-<lb/>tis magnitudinis t@ãſire <lb/>per centrum mundi, ſeu <lb/>terræ, diuideret hæc vti-<lb/>que & </s> <s xml:id="echoid-s6779" xml:space="preserve">terram, & </s> <s xml:id="echoid-s6780" xml:space="preserve">Firma-<lb/>mentũ in ſegmẽta ęqua-<lb/>lia, & </s> <s xml:id="echoid-s6781" xml:space="preserve">ex conſequenti <lb/>oculus aliquis exiſtens <lb/>in centro mundi ſuper <lb/>illã ſuper<unsure/>ficiem medie-<lb/>tatem cœli præcisè con-<lb/>ſpiceret, niſi à denſitate <lb/>terræ impediretur: </s> <s xml:id="echoid-s6782" xml:space="preserve">At-<lb/>qui idem oculus conſtitu <lb/>tus in ſuperficie terræ, <lb/>eandem, quoad iudici@ <lb/>ſenſus, medietatem cer-<lb/>nit, ut vult Ptolemæus, <pb o="145" file="181" n="182" rhead="Ioan. de Sacro Boſco."/> & </s> <s xml:id="echoid-s6783" xml:space="preserve">omnes Aſtronomi, eſtq́; </s> <s xml:id="echoid-s6784" xml:space="preserve">experientia quotidiana compertum, ut ſupra dixi-<lb/>mus, Igitur tota ea terra, quæ interijcitur inter centrum tertæ, & </s> <s xml:id="echoid-s6785" xml:space="preserve">ſuperficiem <lb/>eiuſdem, nullius eſt momenti reſpectu Firmamenti; </s> <s xml:id="echoid-s6786" xml:space="preserve">quandoquidem duo radij <lb/>uiſuales (hoc eſt, lineæ rectæ) inter ſe æquidiſtantes, quorũ unus à centro mun <lb/>di, ſiue terrę, alter uero ex ſuperficie terræ conuexa uſque ad cęlum excurrit, <lb/>nullam omnino quantitatẽ, quæ ſit alicuius momenti, in Firmamento interci-<lb/>piant, ſed uideantur prorſus in eodem puncto conuenire. </s> <s xml:id="echoid-s6787" xml:space="preserve">Quod quidem nulla <lb/>ratione contingeret, ſi hęc portio terræ haberet molem aliquam notabilẽ col <lb/>lata cum magnitudine Firmamenti. </s> <s xml:id="echoid-s6788" xml:space="preserve">Ex quo perſpicuũ eſt, totam terram eſſe <lb/>ueluti punctum, ſi cum Firmamento comparetur. </s> <s xml:id="echoid-s6789" xml:space="preserve">Vt autem planius fiat, quonã <lb/> <anchor type="note" xlink:label="note-181-01a" xlink:href="note-181-01"/> modo duo illi radij uiſuales inſenſibile quid ex Firmamento auferant, explicã <lb/>dum breuiter erit, quantum ſit illud, quod inter duos illos radios in Firmamẽ <lb/>to intercipitur quod hac ralione fiet. </s> <s xml:id="echoid-s6790" xml:space="preserve">Quoniam ſecundum Alphraganum di-<lb/>ftantia à centro terræ vſq. </s> <s xml:id="echoid-s6791" xml:space="preserve">ad concauum Firmamenti continet ſemidiametros <lb/>terræ 22612. </s> <s xml:id="echoid-s6792" xml:space="preserve">& </s> <s xml:id="echoid-s6793" xml:space="preserve">ſemis; </s> <s xml:id="echoid-s6794" xml:space="preserve">ita ut proportio ſemidiametri Firmamẽti ad ſemidiame <lb/>trum terræ eadẽ ſit, quæ 23612 {1/2}. </s> <s xml:id="echoid-s6795" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s6796" xml:space="preserve">fit, ut ſi ſemidiameter Firmamẽti po-<lb/>natur ſinus totus partium 100000. </s> <s xml:id="echoid-s6797" xml:space="preserve">ſemidiameter terræ cõprehendat ex dictis <lb/>particulis 4 {1/2}. </s> <s xml:id="echoid-s6798" xml:space="preserve">Cũ ergo ſemidiameter terrę ſit ſinus rectus illius arcus Firma-<lb/>menti, qui inter illos duos radios intercipitur, ut cõſtat ex proxima figura, & </s> <s xml:id="echoid-s6799" xml:space="preserve"><lb/>ex definitione ſinus recti; </s> <s xml:id="echoid-s6800" xml:space="preserve">reſpõdeat autem ſinui recto partiũ 4. </s> <s xml:id="echoid-s6801" xml:space="preserve">& </s> <s xml:id="echoid-s6802" xml:space="preserve">ſemis, arcus <lb/>continens Grad. </s> <s xml:id="echoid-s6803" xml:space="preserve">0. </s> <s xml:id="echoid-s6804" xml:space="preserve">Min. </s> <s xml:id="echoid-s6805" xml:space="preserve">0 Sec. </s> <s xml:id="echoid-s6806" xml:space="preserve">9. </s> <s xml:id="echoid-s6807" xml:space="preserve">& </s> <s xml:id="echoid-s6808" xml:space="preserve">paulo amplius; </s> <s xml:id="echoid-s6809" xml:space="preserve">intercipietur in Firmamẽto <lb/>inter illos duos radios arcus Grad. </s> <s xml:id="echoid-s6810" xml:space="preserve">0. </s> <s xml:id="echoid-s6811" xml:space="preserve">Min. </s> <s xml:id="echoid-s6812" xml:space="preserve">0. </s> <s xml:id="echoid-s6813" xml:space="preserve">Sec. </s> <s xml:id="echoid-s6814" xml:space="preserve">9. </s> <s xml:id="echoid-s6815" xml:space="preserve">& </s> <s xml:id="echoid-s6816" xml:space="preserve">paulo amplius. </s> <s xml:id="echoid-s6817" xml:space="preserve">Tantil-<lb/>lum eſt illud, quod ſemidiameter terræ ex concauo Firmamenti aufert@: </s> <s xml:id="echoid-s6818" xml:space="preserve">quod <lb/>inſenſibile eſt reſpectu totius ambitus Firmamenti, cum totus. </s> <s xml:id="echoid-s6819" xml:space="preserve">ambitus Fir-<lb/>mamenti complectatur 1296000. </s> <s xml:id="echoid-s6820" xml:space="preserve">Secunda; </s> <s xml:id="echoid-s6821" xml:space="preserve">ita ut arcus ille 9. </s> <s xml:id="echoid-s6822" xml:space="preserve">Secundorum ſit <lb/>{1/144000}. </s> <s xml:id="echoid-s6823" xml:space="preserve">totius ambitus; </s> <s xml:id="echoid-s6824" xml:space="preserve">uel {1/400}. </s> <s xml:id="echoid-s6825" xml:space="preserve">unius Gradus. </s> <s xml:id="echoid-s6826" xml:space="preserve">Et quoniam dia-<lb/>meter Solis occupat dimidium unius gradus, fit ut arcus ille ſit {1/200}. </s> <s xml:id="echoid-s6827" xml:space="preserve">dia-<lb/>metri Solis: </s> <s xml:id="echoid-s6828" xml:space="preserve">quæ quantitas imperceptibilis eſt cum toto ambitu cęli collata, <lb/>ut patet. </s> <s xml:id="echoid-s6829" xml:space="preserve">Atque hic arcus Firmamenti aufertur à ſemidiametro terræ, ſi radius <lb/>ab oculo egrediens æquidiſtans ponatur radio illi, qui a centro terræ egredi-<lb/>tur. </s> <s xml:id="echoid-s6830" xml:space="preserve">Sed quoniam radius ab oculo emiſſus non ęquidiſtat illi alteri, ſed potius <lb/>ei appropinquat eò magis, ac magis, quò longius producitur, cum ſuperficiem <lb/>terræ tangat in alio duncto, quàm in eo, quo uertici capitis ſupponitur; </s> <s xml:id="echoid-s6831" xml:space="preserve">fit, <lb/>ut multo minor arcus Firmamenti intercipiatur inter duos illos radios, quà m <lb/>{1/200}. </s> <s xml:id="echoid-s6832" xml:space="preserve">diametri Solis. </s> <s xml:id="echoid-s6833" xml:space="preserve">Immo fieri fortaſſe poteſt, ut oculus in monte edito <lb/>conſtitutus plus aliquanto uideat, quàm medietatẽ cæli, propter illã inclina-<lb/>tionem lineæ rcctæ ab oculo egredientis ad lineam à centro terræ eductam.</s> <s xml:id="echoid-s6834" xml:space="preserve"/> </p> <div xml:id="echoid-div343" type="float" level="2" n="1"> <figure xlink:label="fig-180-02" xlink:href="fig-180-02a"> <image file="180-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/180-02"/> </figure> <note position="right" xlink:label="note-181-01" xlink:href="note-181-01a" xml:space="preserve">Quãtus ſit <lb/>arcus Firma <lb/>mẽti inter-<lb/>ceptusintes <lb/>duos radios <lb/>viſuales æ-<unsure/> <lb/>qui diſtãtes <lb/>quorũ vnus <lb/>à centro ter <lb/>ræ egredi-<lb/>tur, alter v@ <lb/>ro terrã @@-<lb/>tingit.</note> </div> <p> <s xml:id="echoid-s6835" xml:space="preserve"><emph style="sc">Placet</emph> hiſce duabus rationibus nonnullas alias ex Phænomenis, ap-<lb/> <anchor type="note" xlink:label="note-181-02a" xlink:href="note-181-02"/> parentij ve deprompta adiungere, quibus euidentiſſime concluditur, to<unsure/>tum <lb/>hunc globum, qui ex terra, & </s> <s xml:id="echoid-s6836" xml:space="preserve">aqua conficitur, ad uniuerſi cæli complexũ in <lb/>ſtar puncti obtinere. </s> <s xml:id="echoid-s6837" xml:space="preserve">Prima eſt Pcolemæi Dict. </s> <s xml:id="echoid-s6838" xml:space="preserve">1. </s> <s xml:id="echoid-s6839" xml:space="preserve">cap. </s> <s xml:id="echoid-s6840" xml:space="preserve">6. </s> <s xml:id="echoid-s6841" xml:space="preserve">in hunc fere modum. <lb/></s> <s xml:id="echoid-s6842" xml:space="preserve">Cernimus quotidie extremas umbras gnomonum in horologij, aliorumq́ue <lb/>corporũ ſiue in planis Horizõtis æquidiſtãtibus poſitorũ, ſiue in ſuper@@ciebus <lb/>quibuſcunque, ita uniformiter, atq; </s> <s xml:id="echoid-s6843" xml:space="preserve">regulariter incedere, motuiq́; </s> <s xml:id="echoid-s6844" xml:space="preserve">Solis con-<lb/>formari, ac ſi in centro terræ extremitates gnomonum illorũ, ſiue corporũ eſ-<lb/>ſent collocatæ. </s> <s xml:id="echoid-s6845" xml:space="preserve">Indicium igitur eſt certiſſimum, gnomonẽ, ſeu ſtylum quem-<lb/>cunque in ſuperficie terræ poſitum non diſcrepare à centro mundi ſenſibil@ter, <lb/>quandoquidem Sol & </s> <s xml:id="echoid-s6846" xml:space="preserve">circa mundi centrum, & </s> <s xml:id="echoid-s6847" xml:space="preserve">circa huiuſmodi ſtylum vnifor- <pb o="146" file="182" n="183" rhead="Comment. in I. Cap. Sphæræ"/> mi motu incedit. </s> <s xml:id="echoid-s6848" xml:space="preserve">Hoc enim neutiquã ſieri poſſet, ſi notabiliterſtylus à centro <lb/>mundi diſtaret. </s> <s xml:id="echoid-s6849" xml:space="preserve">Nam impoſſibile eſt Solẽ circa duo centra inter ſe diſtincta re@ <lb/>gulariter poſſe moueri, ut in Theorica Mercurij demõſtratur ab Eraſmo Rein <lb/>holdo. </s> <s xml:id="echoid-s6850" xml:space="preserve">Perſpicuũ igitur eſt, hanc molẽ terræ, quæ inter eius centrum, ſuperfi-<lb/>ciemq́; </s> <s xml:id="echoid-s6851" xml:space="preserve">conuexã intercipitur, nullius eſſe fere quantitatis reſpectu cęli Solis, <lb/>ideoq́; </s> <s xml:id="echoid-s6852" xml:space="preserve">multo magis reſpectu Firmamenri, tanquam punctum, iudicanda erit.</s> <s xml:id="echoid-s6853" xml:space="preserve"/> </p> <div xml:id="echoid-div344" type="float" level="2" n="2"> <note position="right" xlink:label="note-181-02" xlink:href="note-181-02a" xml:space="preserve">Aliæ rõnes <lb/>probantes <lb/>terrã inſtat <lb/>centri eſſe <lb/>reſpectu Fi@ <lb/>mamenti.</note> </div> <p> <s xml:id="echoid-s6854" xml:space="preserve"><emph style="sc">Secvnda</emph> ratio præcedentem quodammodo magis declarans ſit hæc. <lb/></s> <s xml:id="echoid-s6855" xml:space="preserve">Inſtrumentis Mathematicorũ, quale eſt Aſtrolabium; </s> <s xml:id="echoid-s6856" xml:space="preserve">Quadrans, Annulus, &</s> <s xml:id="echoid-s6857" xml:space="preserve">c. </s> <s xml:id="echoid-s6858" xml:space="preserve"><lb/>obſeruamus conſtituti in ſuperficie terrę ueras altitudines ſtellarũ, & </s> <s xml:id="echoid-s6859" xml:space="preserve">Planeta <lb/>rum, excludendo tamen inſeriores tres planetas, ut Lunã, Mercuriũ, ac Vene-<lb/>rem, motusq́; </s> <s xml:id="echoid-s6860" xml:space="preserve">earundem ſtellarũ, atq; </s> <s xml:id="echoid-s6861" xml:space="preserve">loca, nõ aliter, quàm ſi hęc omnia in cẽ-<lb/>tro terræ exiſtentes obſeruaremus, ita ut nullũ in hac re errorem, qui ſub ſen-<lb/>ſum cadere poſl<unsure/>it, cõmittamus. </s> <s xml:id="echoid-s6862" xml:space="preserve">Videmus enim per Mediclinium, ſiue Dioptr@ <lb/>duo aſtra è diametro oppoſita, quaſi Dioptra perf@ctam nobis mundi diame-<lb/>trũ indicet; </s> <s xml:id="echoid-s6863" xml:space="preserve">ide<unsure/>mq; </s> <s xml:id="echoid-s6864" xml:space="preserve">iudiciũ de reliquis obſeruationibus habeto. </s> <s xml:id="echoid-s6865" xml:space="preserve">Manifeſte igi-<lb/>tur concluditur, @olẽ terræ nullius eſſe momentireſpectu machinæ cęleſtis, <lb/>fiquidẽ centra dictorum inſtrumentorũ in terræ ſuperficie conſiſtentiũ coin-<lb/>cidunt prorſus, ſi ſenſuum iudicium conſulamus, cum centro terræ. </s> <s xml:id="echoid-s6866" xml:space="preserve">Quod ſi <lb/>ſenſibiliter diſtarent huiuſmodi inſtrumenta à terrę medio, mirum in modum <lb/>Aſtronomi in ſuis obſeruationibus deciperẽtur, nullumq́; </s> <s xml:id="echoid-s6867" xml:space="preserve">horologium Solare <lb/>recte horas indicare poſſet: </s> <s xml:id="echoid-s6868" xml:space="preserve">quæ omnia experientia quotidianæ repugnant.</s> <s xml:id="echoid-s6869" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6870" xml:space="preserve"><emph style="sc">Tertia</emph> ratio eſt quoque Ptolemæi loco citato, nempe hæc. </s> <s xml:id="echoid-s6871" xml:space="preserve">In omnibus <lb/>t<unsure/>erræ partibus, mundiq́; </s> <s xml:id="echoid-s6872" xml:space="preserve">climatibus, eodem tempore à uarijs Aſtronomis ma-<lb/>gnitudo, & </s> <s xml:id="echoid-s6873" xml:space="preserve">diſtan tia unius eiuſdemq́; </s> <s xml:id="echoid-s6874" xml:space="preserve">ſtxllæ, Martis uidelicet, eadem eſt depre <lb/>henſa, idemq́; </s> <s xml:id="echoid-s6875" xml:space="preserve">compertũ habemus in omnibus alijs obſeruationibus, quæ in di <lb/>uerſis Climatibus ſunt factæ, ita ut ſenſibiliter inter ſe non diſcrepent. </s> <s xml:id="echoid-s6876" xml:space="preserve">Quam-<lb/>obrem merito terra, ut punctum indiuiſibile, cenſebitur, quãdoquidem nullus <lb/>terræ locus ab alio reſpectu unius, eiuſdemq; </s> <s xml:id="echoid-s6877" xml:space="preserve">pũcti cæleſtis differt ſenſibiliter.</s> <s xml:id="echoid-s6878" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6879" xml:space="preserve"><emph style="sc">Qvarta</emph> ratio hæc eſſe poterit. </s> <s xml:id="echoid-s6880" xml:space="preserve">Si terra eſſet alicuius notabilis magni-<lb/>@udinis collata cum Firmamento, uel etiam cũ cælo Solis, omnia illa abſurda <lb/>conſequeremur, quæ paulo antea infere<unsure/>bamus, ſi terra non eſſet in medio mũ-<lb/> <anchor type="figure" xlink:label="fig-182-01a" xlink:href="fig-182-01"/> di poſita; </s> <s xml:id="echoid-s6881" xml:space="preserve">propterea quòd, ſi terra non <lb/>eſſet inſtar puncti, minime nosin eius <lb/>ſu perficie degentes in medio, ſeu cen-<lb/>tro mundi eſſemus conſtituti. </s> <s xml:id="echoid-s6882" xml:space="preserve">Vnde ef-<lb/>ficeretur primo, Nullum Horizontem <lb/>diuidere cœlum in duas partes æqua-<lb/>les. </s> <s xml:id="echoid-s6883" xml:space="preserve">Quare nullibi medietas cœli conſpi-<lb/>ceretur, neque unquam æquinoctium <lb/>poſſet fieri, ſed perpetuo dies tempore <lb/>æquinoct@j minor eſſet nocte, cum ar-<lb/>cus nocturnus notabiliter maior exi-<lb/>ſteret arcu diurno. </s> <s xml:id="echoid-s6884" xml:space="preserve">Deinde, Eædem ſtel-<lb/>læ ſereno tempore minores appare-<lb/>rent iuxta Horizontem poſitæ, quàm <lb/>in medio cœli, eò quòd iuxta Horizon-<lb/>lem notabiliter remotiores à nobis eſſent: </s> <s xml:id="echoid-s6885" xml:space="preserve">quod tamen falſum eſt. </s> <s xml:id="echoid-s6886" xml:space="preserve">Tertio, um-<lb/>bræ gnome<unsure/>num in ſuperſiciebus quibuslibet nullo modo tempore æquine- <pb o="147" file="183" n="184" rhead="Ioan. de Sacro Boſco."/> ctiorum proijcerentur ſecundum lineam rectam, (ut demonſtratiue concludi <lb/>poſſet, niſi id negotij ad ſcientiam de Horologiorum deſcriptionibus ſpecta-<lb/>ret) ſi uertex gnomonis non concedatur eſſe idem, quo ad iudicium ſenſus, <lb/>quod centrum terræ: </s> <s xml:id="echoid-s6887" xml:space="preserve">Hoc autem clariſſime experientiæ repugnat. </s> <s xml:id="echoid-s6888" xml:space="preserve">Si enim <lb/>tempore æquinoctiorum in quocunque plano ſtylus affigatur, notenturq́ue <lb/>uarijs horis diei extremitates umbræ in plano illo punctis quibuſdam, depre-<lb/>hendentur omnia hæc puncta in una linea recta iacere: </s> <s xml:id="echoid-s6889" xml:space="preserve">Quod quidem ſolum <lb/>ea de cauſa contingit, quia nimirum uertex ſtyli aſſumitur tanquam mundi <lb/>centrum, ut clariſſime in noſtra Gnomonica demonſtrauimus. </s> <s xml:id="echoid-s6890" xml:space="preserve">Quarto, Neque <lb/>ortus Solſtitij æſtiui reſpõderet per lineam rectam occaſui Brumalis Solſtitij: <lb/></s> <s xml:id="echoid-s6891" xml:space="preserve">Neque ortus Solſtitij Brumalis occaſui Solſtitij æſtiui. </s> <s xml:id="echoid-s6892" xml:space="preserve">Quinto, Confundc<unsure/>-<lb/>rentur uniuerſa proportio, quam nunc cernimus in augmento, decrementoq́<unsure/>; </s> <s xml:id="echoid-s6893" xml:space="preserve"><lb/>dierum ante & </s> <s xml:id="echoid-s6894" xml:space="preserve">poſt æquinoctium utrumque. </s> <s xml:id="echoid-s6895" xml:space="preserve">Quæ cum omnia abſurda ſint & </s> <s xml:id="echoid-s6896" xml:space="preserve"><lb/>quotidianæ aduerſentur experientiæ, omnibusq́. </s> <s xml:id="echoid-s6897" xml:space="preserve">Aſtronomorum peritorum <lb/>obſeruationibus, concludendum erit, Terram eſſe ueluti punctum inſenſibile, <lb/>ſi cum cæleſti corpore conferatur.</s> <s xml:id="echoid-s6898" xml:space="preserve"/> </p> <div xml:id="echoid-div345" type="float" level="2" n="3"> <figure xlink:label="fig-182-01" xlink:href="fig-182-01a"> <image file="182-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/182-01"/> </figure> </div> <p> <s xml:id="echoid-s6899" xml:space="preserve"><emph style="sc">Qvinta</emph>, ac poſtrema ratio hæc ſit. </s> <s xml:id="echoid-s6900" xml:space="preserve">Secundum cõem Aſtronomorum <lb/>ſententiam ſemidiamet<unsure/>er Firmamenti, quo ad concauam eius ſuperficiẽ, terrę <lb/>ſemidiametrũ continet uicies & </s> <s xml:id="echoid-s6901" xml:space="preserve">bis millies, ſexcenties, & </s> <s xml:id="echoid-s6902" xml:space="preserve">duodecies, & </s> <s xml:id="echoid-s6903" xml:space="preserve">eo am-<lb/>plius, ita ut ſit talis proportio totius ſemidiametri Firmamenti ad ſemidiame-<lb/>trum globi, qui cõſtat ex terra, & </s> <s xml:id="echoid-s6904" xml:space="preserve">aqua, qualis eſt huius numeri 22612. </s> <s xml:id="echoid-s6905" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s6906" xml:space="preserve">ad 1. <lb/></s> <s xml:id="echoid-s6907" xml:space="preserve">Tanta. </s> <s xml:id="echoid-s6908" xml:space="preserve">n. </s> <s xml:id="echoid-s6909" xml:space="preserve">diſtantia Firmamenti à centro terræ eſt deprehenſa, ut ad finẽ huius <lb/>c. </s> <s xml:id="echoid-s6910" xml:space="preserve">dicemus: </s> <s xml:id="echoid-s6911" xml:space="preserve">ut nimirum à terra uſq. </s> <s xml:id="echoid-s6912" xml:space="preserve">ad Firmamentũ contineantur terræ ſemidia <lb/> <anchor type="note" xlink:label="note-183-01a" xlink:href="note-183-01"/> metri 22612 {1/2}. </s> <s xml:id="echoid-s6913" xml:space="preserve">Ac propterea, cum eadem ſit proportio diametrorum, quæ ſe-<lb/>midiametrorum, continebit quoq. </s> <s xml:id="echoid-s6914" xml:space="preserve">toties tota diameter Firmamenti totam ter <lb/>ræ diametrum. </s> <s xml:id="echoid-s6915" xml:space="preserve">Cum ergo ſphęrarum proportio triplicata ſit eius proportioni@ <lb/> <anchor type="note" xlink:label="note-183-02a" xlink:href="note-183-02"/> quam habent diametri, habebit totus mundus intra concauum Firmamenti <lb/>contentus ad globum terrę proportionem eandem, quã 11562340095703 {1/8}. <lb/></s> <s xml:id="echoid-s6916" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s6917" xml:space="preserve">ut in his numeris continue proportionalibus apparet. </s> <s xml:id="echoid-s6918" xml:space="preserve">1. </s> <s xml:id="echoid-s6919" xml:space="preserve">22612 {1/4}. </s> <s xml:id="echoid-s6920" xml:space="preserve"><lb/>511325156 {1/4}. </s> <s xml:id="echoid-s6921" xml:space="preserve">11562340095703 {1/8}. </s> <s xml:id="echoid-s6922" xml:space="preserve">Quæ cum ita ſint, non immerito dicetur <lb/>terra inſenſibilem quantitatem habere, ſi cũ Firmamento conferatur: </s> <s xml:id="echoid-s6923" xml:space="preserve">cũ uni-<lb/>tas nihil fere ſit reſpectu tanti numeri. </s> <s xml:id="echoid-s6924" xml:space="preserve">Atq. </s> <s xml:id="echoid-s6925" xml:space="preserve">ut planius adhuc percipiatur, totã <lb/>terram eſſe inſtar puncti reſpectu Firmamenti, accipiemus ſphærulam, cuius <lb/>diameter ad pedem Geometricum antiquum proportionem fere habeat quam <lb/>1. </s> <s xml:id="echoid-s6926" xml:space="preserve">ad 44. </s> <s xml:id="echoid-s6927" xml:space="preserve">qualis eſt ſphærula in hac ſigura appoſita. </s> <s xml:id="echoid-s6928" xml:space="preserve">Nam ſi aliam ſphæram acci-<lb/>piamus, cuius diameter contineat 400. </s> <s xml:id="echoid-s6929" xml:space="preserve">pedes, ita ut proportio huius diametri <lb/>ad diametrum illius ſphærulæ ſit, quæ 17600. </s> <s xml:id="echoid-s6930" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s6931" xml:space="preserve">quis dubita-<lb/> <anchor type="figure" xlink:label="fig-183-01a" xlink:href="fig-183-01"/> <anchor type="note" xlink:label="note-183-03a" xlink:href="note-183-03"/> bit, ſphærulam illam eſſe inſtar punct: </s> <s xml:id="echoid-s6932" xml:space="preserve">ferè indiuiſibilis reſpectu <lb/>huius ſphæræ? </s> <s xml:id="echoid-s6933" xml:space="preserve">Cum ergo terra reſpectu Firmamenti ſit multo <lb/>minor, quàm ſphærula illa reſpectu huius ſphæræ, (poſita nãq; <lb/></s> <s xml:id="echoid-s6934" xml:space="preserve">terra, ut 1. </s> <s xml:id="echoid-s6935" xml:space="preserve">tota ſphæra mundi uſque ad concauum Firmamenti <lb/>eſt, vt 11562340095703. </s> <s xml:id="echoid-s6936" xml:space="preserve">& </s> <s xml:id="echoid-s6937" xml:space="preserve">paulo amplius, ut diximus. </s> <s xml:id="echoid-s6938" xml:space="preserve">Poſita <lb/>autem ſphęrula prædicta, ut 1. </s> <s xml:id="echoid-s6939" xml:space="preserve">ſphæra illa alia erit cantummodo, <lb/>@t 545177600000. </s> <s xml:id="echoid-s6940" xml:space="preserve">Hic enim numerus ad unitatem proportio-<lb/>nem habet triplicatam eius, quam habet diameter ſphæræ illius <lb/>ad diametrum ſphærulæ prædictæ, ut in his numeris apparet. </s> <s xml:id="echoid-s6941" xml:space="preserve">1. </s> <s xml:id="echoid-s6942" xml:space="preserve">1760@. </s> <s xml:id="echoid-s6943" xml:space="preserve"><lb/>309760000. </s> <s xml:id="echoid-s6944" xml:space="preserve">5451776000000.) </s> <s xml:id="echoid-s6945" xml:space="preserve">multo magis punctum dicemus eſſe terram re <lb/>ſpectu Firmamenti, quàm ſphærulam illam reſpectu alterius ſphæræ.</s> <s xml:id="echoid-s6946" xml:space="preserve"/> </p> <div xml:id="echoid-div346" type="float" level="2" n="4"> <note position="right" xlink:label="note-183-01" xlink:href="note-183-01a" xml:space="preserve">15. quinto.</note> <note position="right" xlink:label="note-183-02" xlink:href="note-183-02a" xml:space="preserve">18. duod.</note> <figure xlink:label="fig-183-01" xlink:href="fig-183-01a"> <image file="183-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/183-01"/> </figure> <note position="right" xlink:label="note-183-03" xlink:href="note-183-03a" xml:space="preserve">Confirma-<lb/>tio huius <lb/>quintæ @@-<lb/>tionis.</note> </div> <pb o="148" file="184" n="185" rhead="Comment. In I. Cap. Sphæræ"/> <p style="it"> <s xml:id="echoid-s6947" xml:space="preserve">DICIT etiam Alphraganus, quod minima ſtellarum fixarum uiſu <lb/> <anchor type="note" xlink:label="note-184-01a" xlink:href="note-184-01"/> notabilium maior eſt tota terra: </s> <s xml:id="echoid-s6948" xml:space="preserve">Sed ipſa ſtella reſpectu totius Firmamenti <lb/>eſt ſicut punctus, & </s> <s xml:id="echoid-s6949" xml:space="preserve">centrum: </s> <s xml:id="echoid-s6950" xml:space="preserve">Multo igitur fortius terra eſt punctus re-<lb/>ſp@ctu Firmamenti, cum ſit minor ea.</s> <s xml:id="echoid-s6951" xml:space="preserve"/> </p> <div xml:id="echoid-div347" type="float" level="2" n="5"> <note position="left" xlink:label="note-184-01" xlink:href="note-184-01a" xml:space="preserve">Alia ratio <lb/>probans ter <lb/>ram @ſſe ve <lb/>luti punctũ <lb/>reſpectu Fir <lb/>mamen@@.</note> </div> </div> <div xml:id="echoid-div349" type="section" level="1" n="109"> <head xml:id="echoid-head113" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s6952" xml:space="preserve"><emph style="sc">Confirmat</emph> tertio medio, quod auctoritati Alphraganiinnititur, <lb/>terram eſſe ueluti punctum, ut perſpicuum eſt in ipſa litera. </s> <s xml:id="echoid-s6953" xml:space="preserve">Non autem ſolus <lb/>Alphraganus dicit, minimam ſtellarum, quæ viſu percipiuntur, maiorem eſſe <lb/>terra, uerum etiam idipſum omnes fere Aſtronomi aſſerunt.</s> <s xml:id="echoid-s6954" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6955" xml:space="preserve"><emph style="sc">Vt</emph> autem intelligatur, de quibuſnam ſtellis minimis auctor noſter ex ſen <lb/>tentia Alphragani, & </s> <s xml:id="echoid-s6956" xml:space="preserve">aliorum Aſtronomorum locutus ſit, pauca mihi uidẽtur <lb/>dicenda de ſtellis in vniuerſum; </s> <s xml:id="echoid-s6957" xml:space="preserve">quot uidelicet numero obſeruatæ ſint ab A-<lb/>ſtronomis, & </s> <s xml:id="echoid-s6958" xml:space="preserve">quã proportionem earum magnitudines habeant ad magnitudi-<lb/>nem terræ. </s> <s xml:id="echoid-s6959" xml:space="preserve">Aſtronomi igitur omnes ſtellas fixas in Firmamento uiſu percepti-<lb/>biles, hoc eſt, quæ ſemper, cum cælum ſerenum eſt, commode uideri poſſunt, <lb/>diligenter obſeruantes deprehenderunt, eas eſſe numero 1022. </s> <s xml:id="echoid-s6960" xml:space="preserve">Sunt quidem <lb/>plurimæ aliæ ſtellæ minimæ, (Hoc enim nunquam negabo) quas, quia non di <lb/>ſtincte, & </s> <s xml:id="echoid-s6961" xml:space="preserve">clare ſeſe obtutui oſl<unsure/>erunt, uel quia non quolibet tempore anni, pro <lb/>pter earum paruitatem uidentur, conſulto Aſtronomi prætermittunt, & </s> <s xml:id="echoid-s6962" xml:space="preserve">ſolũ <lb/>de ijs, quas oculi ad cælum ſublati commode comprehendere poſſunt, ſermo-<lb/>nem habent. </s> <s xml:id="echoid-s6963" xml:space="preserve">Sed quoniam vulgo incredibile uidetur, eſſe tantummodo 1022. <lb/></s> <s xml:id="echoid-s6964" xml:space="preserve">ſtellas in Firmamento commode uiſibiles, propterea ꝙ uiſus eas nocte ſerena <lb/>confuſe intuens, ſine ullo ordine, putat eſſe propemodũ innumeras@ Viſum eſt, <lb/>omnes 1022. </s> <s xml:id="echoid-s6965" xml:space="preserve">ſtellas ab Aſtronomis obſeruatas eo ordine hic recenſere, quo in <lb/>globo cæleſti depingi ſolent. </s> <s xml:id="echoid-s6966" xml:space="preserve">Ita enim fiet, vt ſi quis diligenter nocte ſerena <lb/>ſtellas obſeruans conferat globum cum ſtellis uiſis, nulla aliam, præter eas, quę <lb/>in globo notatæ ſunt, reperiat; </s> <s xml:id="echoid-s6967" xml:space="preserve">immo uix minimas quaſdam ibidem notatas <lb/>uiſu percipere poſſit. </s> <s xml:id="echoid-s6968" xml:space="preserve">Vnde mirum ei uideri non poterit, non plures in Firma-<lb/>mento ſtellas lucidas exiſtere, quam 1022.</s> <s xml:id="echoid-s6969" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6970" xml:space="preserve"><emph style="sc">Hvnc</emph> autem numerum hac arte inueſtigarunt. </s> <s xml:id="echoid-s6971" xml:space="preserve">Ex omnibus ſtellis, quæ <lb/> <anchor type="note" xlink:label="note-184-02a" xlink:href="note-184-02"/> u<unsure/>iſu commode percipiuntur, animaduerterunt Aſtronomi 48. </s> <s xml:id="echoid-s6972" xml:space="preserve">conſtellationes, <lb/>Aſteriſmos, ſeu imagines (Eſt autem conſtellatio, Aſteriſmus, ſiue imago, mul-<lb/>titudo quædã ſtellarum formã alicuius animalis, aut alterius cuiuſuis rei effi-<lb/>giem ſuo ſitu, ac ordine referentiũ) conſtitu<unsure/>i. </s> <s xml:id="echoid-s6973" xml:space="preserve">Vnde facile comprehendere po-<lb/>tuerunt numerũ ſtellarum cuiuslibet cõſtellationis per ſeſe conſideratæ. </s> <s xml:id="echoid-s6974" xml:space="preserve">Neq; <lb/></s> <s xml:id="echoid-s6975" xml:space="preserve">enim aliam ob cauſam vetuſtiſſimi illi, & </s> <s xml:id="echoid-s6976" xml:space="preserve">diligentiſſimi ſtellarum obſeruatotes <lb/>videntur huiuſmodi imaginibus ſtellas formaſſe, ut teſtatur Theon iunior in <lb/>expoſitione Aratæa, niſi ut tanta earũ multitudo per partes diſtinctas diſcerne <lb/>retur, & </s> <s xml:id="echoid-s6977" xml:space="preserve">oẽs ſtellæ ordine quodam poſſent deſignari. </s> <s xml:id="echoid-s6978" xml:space="preserve">Quod quidem ante mul-<lb/>ta ſecula factum eſſe conſtat, cum ẽt in libro Iob ſacræ literæ nominent Orio-<lb/>na, Arcturũ, Hyadas, atq; </s> <s xml:id="echoid-s6979" xml:space="preserve">pleiades, multarumq́; </s> <s xml:id="echoid-s6980" xml:space="preserve">aliarum conſtellationum nomi <lb/> <anchor type="note" xlink:label="note-184-03a" xlink:href="note-184-03"/> na apud Homerum, atque Heſiodum, uetuſt@ſſimos Poetas, legan<unsure/>tur. </s> <s xml:id="echoid-s6981" xml:space="preserve">Præte-<lb/>rea obſeruarunt quaſdam ſtellas alijs multo ſplendidiores, ita ut ſex omnino <lb/>gradus in ſtellis, quantum ad magnitudinem, & </s> <s xml:id="echoid-s6982" xml:space="preserve">maiorem, uel minorẽ ſplendo <lb/>rem, deprehenderit: </s> <s xml:id="echoid-s6983" xml:space="preserve">quos gradus Aſtronomi differentias magnitudinum ap-<lb/>pellarũt. </s> <s xml:id="echoid-s6984" xml:space="preserve">Ex quo admodum facile potuerunt numerum ſtellarum cuiuſcunq; <lb/></s> <s xml:id="echoid-s6985" xml:space="preserve">differentiæ longo uſu percipere. </s> <s xml:id="echoid-s6986" xml:space="preserve">Ita enim deprehenderunt in prima differen- <pb o="149" file="185" n="186" rhead="Ioan. de Sacro Boſco."/> @ia contineri ſtellas 15. </s> <s xml:id="echoid-s6987" xml:space="preserve">maximas, easq́; </s> <s xml:id="echoid-s6988" xml:space="preserve">lucidisſimas, quę primę magnitudinis <lb/>dicuntur. </s> <s xml:id="echoid-s6989" xml:space="preserve">In 2. </s> <s xml:id="echoid-s6990" xml:space="preserve">differentia inuenerũt ſtellas minores, ac minus lucidas 45. </s> <s xml:id="echoid-s6991" xml:space="preserve">quas <lb/>ſecundę magnitudinis dixerunt. </s> <s xml:id="echoid-s6992" xml:space="preserve">In 3. </s> <s xml:id="echoid-s6993" xml:space="preserve">differentia repererunt ſtellas 208. </s> <s xml:id="echoid-s6994" xml:space="preserve">ad huc <lb/>minores, easq́; </s> <s xml:id="echoid-s6995" xml:space="preserve">tertię magnitudinis nominarunt. </s> <s xml:id="echoid-s6996" xml:space="preserve">In 4. </s> <s xml:id="echoid-s6997" xml:space="preserve">differentia, ſeu magnitu-<lb/>dine obſeruarũt ſtellas m@nores adhuc 474. </s> <s xml:id="echoid-s6998" xml:space="preserve">In 5. </s> <s xml:id="echoid-s6999" xml:space="preserve">differẽtia, magnitudineue nu <lb/>merarũtad huc minores ſtellas 217. </s> <s xml:id="echoid-s7000" xml:space="preserve">In 6. </s> <s xml:id="echoid-s7001" xml:space="preserve">denique <lb/> <anchor type="note" xlink:label="note-185-01a" xlink:href="note-185-01"/> differẽtia, ſeu magnitudine annotarũt ſtellas 49. <lb/></s> <s xml:id="echoid-s7002" xml:space="preserve">quę omnium minimę ſunt. </s> <s xml:id="echoid-s7003" xml:space="preserve">Pręter has autem om <lb/>nes ſtellas reperiũtur alię quinq; </s> <s xml:id="echoid-s7004" xml:space="preserve">dictę nebuloſę, <lb/>& </s> <s xml:id="echoid-s7005" xml:space="preserve">nouem obſcuriores, quę vix ſeſe noſtris ſenſi-<lb/>busingerunt: </s> <s xml:id="echoid-s7006" xml:space="preserve">ob idq; </s> <s xml:id="echoid-s7007" xml:space="preserve">non referuntur in aliquam <lb/>dictarum magnitudinum, quoniam earum quãti <lb/>tates notari minime potuerunt propter earũ ob-<lb/>ſcuritatẽ. </s> <s xml:id="echoid-s7008" xml:space="preserve">Si igitur omnes has ſtellas in unã ſum <lb/>mam colligas, inueniens p̃ciſe numero 1022. </s> <s xml:id="echoid-s7009" xml:space="preserve">ut <lb/>in appoſita formula conſpicis.</s> <s xml:id="echoid-s7010" xml:space="preserve"/> </p> <div xml:id="echoid-div349" type="float" level="2" n="1"> <note position="left" xlink:label="note-184-02" xlink:href="note-184-02a" xml:space="preserve">Quomodo <lb/>Aftronomi <lb/>numerum <lb/>ſtellarũ in <lb/>ueſtigar<unsure/>int</note> <note position="left" xlink:label="note-184-03" xlink:href="note-184-03a" xml:space="preserve">Sex differẽ-<lb/>@iæ magni-<lb/>tudinũ ſtel-<lb/>larum, & <lb/>quot i<unsure/> qua <lb/>habet diſſe-<lb/>rentia con-<lb/>tineantur.</note> <note position="right" xlink:label="note-185-01" xlink:href="note-185-01a" xml:space="preserve"> <lb/>Magnitudo. Num. # ſtell. <lb/>1 # 15 <lb/>2 # 45 <lb/>3 # 208 <lb/>4 # 474 <lb/>5 # 217 <lb/>6 # 49 <lb/>Nebuloſæ # 5 <lb/>Obſcuriores # 9 <lb/>Omnes ſimul # 1022 <lb/></note> </div> <p> <s xml:id="echoid-s7011" xml:space="preserve"><emph style="sc">Qvod</emph> autem in hyeme nocte ſerena infini <lb/>ta propemodum multitudo ſtellarum appareat, (vt opinioni communi vulgi-<lb/>reſpondeamus.) </s> <s xml:id="echoid-s7012" xml:space="preserve">maxime uerſus polum arcticum, id ex altera duarum cauſa-<lb/>rum arbitror euenire. </s> <s xml:id="echoid-s7013" xml:space="preserve">Vel quia, cum tunc aer magis purgatus ſit, quàm in æſta <lb/>te, fit, vt posſint etiã uideri ſtellę minimæ, quę in ſex dictis differentiis propte-<lb/> <anchor type="note" xlink:label="note-185-02a" xlink:href="note-185-02"/> rea non ſunt notatæ, quòd non ſemper appareant. </s> <s xml:id="echoid-s7014" xml:space="preserve">Vel quia, cum tunc ſtellæ <lb/>ualde admodũ micare ſoleãt, fit, ut uiſus hallucinetur, putetq́. </s> <s xml:id="echoid-s7015" xml:space="preserve">ſe plures ſtel <lb/>las uiſu percipere, cũ tamẽ re ipſa ſtellas nõ uideat, ſed apparẽtias quaſdã ſtel-<lb/>larum propter illã uehementem micationẽ, ſeu ſcintillationẽ generatas. </s> <s xml:id="echoid-s7016" xml:space="preserve">Cu-<lb/>ius rei ſignum eſt, quòd ſi quis oculorum aciem uelit in una illarũ ſtellarum fi-<lb/>gere, eam uel omnino perdat, uel certe uacillare deprehẽdat, ita ut nõ in eo-<lb/>dem loco maneat. </s> <s xml:id="echoid-s7017" xml:space="preserve">quod in aliis ſtellis nõ accidit. </s> <s xml:id="echoid-s7018" xml:space="preserve">Et procul dubio, ſi tãta eſſet <lb/>multitudo ſtellarum, quãta tunc uiſui apparet, mirum eſſet, eas ab Aſtronomis <lb/>non fuiſſe notatas, cum tamen multo minores notarint, immo etiã illas, quę <lb/>extra imagines, ſeu conſtellationes reperiuntur, ut ex ſequenti<unsure/> tabula appa-<lb/>rebit, & </s> <s xml:id="echoid-s7019" xml:space="preserve">quarũ nullus omnino uſus eſt apud Aſtronomos. </s> <s xml:id="echoid-s7020" xml:space="preserve">Illud etiã, quod ſcri <lb/>pturæ ſacrę referunt, Denm Abrahamo dixiſſe cap. </s> <s xml:id="echoid-s7021" xml:space="preserve">12. </s> <s xml:id="echoid-s7022" xml:space="preserve">Geneſ. </s> <s xml:id="echoid-s7023" xml:space="preserve">[Suſpice cælum, <lb/>& </s> <s xml:id="echoid-s7024" xml:space="preserve">numera ſtellas, ſi potes.</s> <s xml:id="echoid-s7025" xml:space="preserve">] Et dixiſſe ei. </s> <s xml:id="echoid-s7026" xml:space="preserve">[Sic erit ſemen tuum] Item cap. </s> <s xml:id="echoid-s7027" xml:space="preserve">22. </s> <s xml:id="echoid-s7028" xml:space="preserve">[Be-<lb/>nedicam tibi, & </s> <s xml:id="echoid-s7029" xml:space="preserve">multiplicabo ſemen tuum, ſicut ſtellas cæli, & </s> <s xml:id="echoid-s7030" xml:space="preserve">uelut arenam, quæ <lb/>eſt in littore maris.</s> <s xml:id="echoid-s7031" xml:space="preserve">] Item cap. </s> <s xml:id="echoid-s7032" xml:space="preserve">26. </s> <s xml:id="echoid-s7033" xml:space="preserve">[Et multiplicabo ſemen tuum, ſicut ſtellas cæli.</s> <s xml:id="echoid-s7034" xml:space="preserve">] <lb/>Intelligndum eſt ſecundum communem ſententiam uulgi exiſtimantis, in-<lb/>finitam eſſe multitudinẽ ſtellarum, dum eas nocte ſerena confuſe intuetur, ac <lb/>ſine ordine, non autẽ, quod re uera tanta ſit multitudo ſtellarũ, quanta eſſet <lb/>futura multitudo filiorũ Iſrael, qui ex Abrahamo ortum duxerũt. </s> <s xml:id="echoid-s7035" xml:space="preserve">Nam c@m <lb/>ſint 48 imagines, in quibus omnes ſtellæ 1022. </s> <s xml:id="echoid-s7036" xml:space="preserve">collocantur, licet nõnullæ ex-<lb/>tra illas poſitæ ſint, nemo ſane affirmabit, in ſingulis conſtellationibus eſſe <lb/>10000. </s> <s xml:id="echoid-s7037" xml:space="preserve">ſtellas, cum nec 100. </s> <s xml:id="echoid-s7038" xml:space="preserve">videantur, etiã in maxima cõſtellatione. </s> <s xml:id="echoid-s7039" xml:space="preserve">Et certe <lb/>mirũ eſſet, Aſtronomos in numeratione ſtellarũ in qualibet cõſtellatione er <lb/>raſſe hoc tãto numero 10000. </s> <s xml:id="echoid-s7040" xml:space="preserve">ferè. </s> <s xml:id="echoid-s7041" xml:space="preserve">Nã ſi ita eſſet, ꝗ fieri poſſet, ut illæ ſtellæ, <lb/>quas in conſtellationibus notarũt, in tãta multitudine diſcernerẽtur? </s> <s xml:id="echoid-s7042" xml:space="preserve">Immo <lb/>etiã ſi concedamus, in ſingulis cõſtellationib. </s> <s xml:id="echoid-s7043" xml:space="preserve">eſſe 10000. </s> <s xml:id="echoid-s7044" xml:space="preserve">ſtellas, nõ tñ intelli <lb/>gẽda erũt uerba ſcripturæ, ut ſonãt, nẽpe tot eſſe ſtellas, quot filii Iſrael futu- <pb o="150" file="186" n="187" rhead="Comment. in I. cap. Sphæræ."/> ri eſsẽt. </s> <s xml:id="echoid-s7045" xml:space="preserve">Nã hac rõne erũt in toto cęlo ſtellæ tm̃modo 480000. </s> <s xml:id="echoid-s7046" xml:space="preserve">ꝗs ãt dixerit, nõ <lb/>fuiſſe multò plures filios Iſrael? </s> <s xml:id="echoid-s7047" xml:space="preserve">Non ſunt ergo accipienda uerba illa ſcripturę <lb/>in hoc ſenſu, ut di camus infinitas ſtellas eſſe. </s> <s xml:id="echoid-s7048" xml:space="preserve">Dici etiam poteſt. </s> <s xml:id="echoid-s7049" xml:space="preserve">Scripturam lo <lb/>qui de omnibus ſtellis, quæ in cœlo ſunt, etiã de illis, quæ minores ſunt, quàm <lb/>quæ in ſex differentijs continẽtur, quæ fortaſſe innumerabiles ſunt: </s> <s xml:id="echoid-s7050" xml:space="preserve">Deum au <lb/>tẽ tunc ita intendiſſe aciem oculorum Abrahamo, ut eas omnes in cœlo aſpi-<lb/>ceret. </s> <s xml:id="echoid-s7051" xml:space="preserve">Quòd ſi quis omnino contendere uelit, plures eſſe ſtellas, ei per me lice <lb/>bit, quod uult, opinari; </s> <s xml:id="echoid-s7052" xml:space="preserve">mihi certe facile perſuadeo, nõ eſſe plures in ſex dictis <lb/>differentijs cõtentas, quam 1022. </s> <s xml:id="echoid-s7053" xml:space="preserve">propterea quòd in conſtellationibus per ſe <lb/>cõſideratis non reperio plures, quà<unsure/>m ab Aſtronomis ſunt notatæ: </s> <s xml:id="echoid-s7054" xml:space="preserve">excepto tem <lb/>pore hyemali, ubi aliqñ plures, præſertim iuxta polũ arcticũ, uidentur appare-<lb/>re propter cauſas paulo ante dictas, præſertim propter uiſus hallucinationem. <lb/></s> <s xml:id="echoid-s7055" xml:space="preserve">Itaq; </s> <s xml:id="echoid-s7056" xml:space="preserve">ex omnibus 1022. </s> <s xml:id="echoid-s7057" xml:space="preserve">ſtellis conſtituerunt Mathematici cura & </s> <s xml:id="echoid-s7058" xml:space="preserve">ſolertia mi-<lb/>rabili, ut dictũ eſt. </s> <s xml:id="echoid-s7059" xml:space="preserve">48. </s> <s xml:id="echoid-s7060" xml:space="preserve">Imagines, conſtellationesve, quatũ nomina, & </s> <s xml:id="echoid-s7061" xml:space="preserve">ordinem <lb/>in tabula infra poſita expoſuimus, iuxta obſeruationes fere Nicolai Coperni <lb/>ci. </s> <s xml:id="echoid-s7062" xml:space="preserve">Mutatæ. </s> <s xml:id="echoid-s7063" xml:space="preserve">n. </s> <s xml:id="echoid-s7064" xml:space="preserve">iam reperiuntur omniũ ſtellarũ ſedes, ſiue longitudines, à tempo <lb/>ribus Ptolemæi, ad noſtrã uſq; </s> <s xml:id="echoid-s7065" xml:space="preserve">ætatem, ꝑꝑ motum illum tardiſſimum, quo eas <lb/>moueri diximus ab occidente in orientẽ; </s> <s xml:id="echoid-s7066" xml:space="preserve">adeo ut hoc tẽpore aliæ ſint ſtellarũ <lb/>longitudines, quàm quæ poſitæ ſunt in tabulis Almageſti à Ptolemæo, quam-<lb/>uis earundẽ latitudines eædẽ ſemper inuentę fuerint, ut doctiſſimorum Aſtro <lb/>nomorũ obſeruationes teſtantur. </s> <s xml:id="echoid-s7067" xml:space="preserve">Itaq; </s> <s xml:id="echoid-s7068" xml:space="preserve">in tabula ſubſequenti differũt quidem <lb/>longitudines a longitudinibus Ptolemæi: </s> <s xml:id="echoid-s7069" xml:space="preserve">At latitudines nulla rõne di<unsure/>ſcrepãt <lb/>à latitudinibus, quas Ptolemæus in Almageſto explicauit. </s> <s xml:id="echoid-s7070" xml:space="preserve">Immo ex hac perpe <lb/>tua latitudinũ conſtãtia firmiſſime colligi ſupra aſſeruimus, ſtellas ab occiden <lb/>te in orientẽ moueri ſuper polos Zodiaci, quemadmodũ ex continua illa lon-<lb/>gitudinũ mutatione deprehenſum fuit, eas ſenſim moueri ab occaſu in ortũ. </s> <s xml:id="echoid-s7071" xml:space="preserve">Ap <lb/>pellamus longitudinẽ cuiuſq; </s> <s xml:id="echoid-s7072" xml:space="preserve">ſtellæ, diſtantiã eius à principio ♈, uerſus ſigna<unsure/> <lb/>oriẽtalia, hoc eſt, uerſus ♉. </s> <s xml:id="echoid-s7073" xml:space="preserve">♊. </s> <s xml:id="echoid-s7074" xml:space="preserve">♋. </s> <s xml:id="echoid-s7075" xml:space="preserve">♌. </s> <s xml:id="echoid-s7076" xml:space="preserve">&</s> <s xml:id="echoid-s7077" xml:space="preserve">c. </s> <s xml:id="echoid-s7078" xml:space="preserve">progrediendo. </s> <s xml:id="echoid-s7079" xml:space="preserve">Latitudinẽ uero eiuſ-<lb/>dẽ diſtantiã ab Ecliptica ſiue in Boreã, ſiue in auſtrũ. </s> <s xml:id="echoid-s7080" xml:space="preserve">Plura tñ de longitudini <lb/>bus, latitudinibusq́; </s> <s xml:id="echoid-s7081" xml:space="preserve">ſtellarũ reperies in 2. </s> <s xml:id="echoid-s7082" xml:space="preserve">cap. </s> <s xml:id="echoid-s7083" xml:space="preserve">qñ de Zodiaco diſſeremus. </s> <s xml:id="echoid-s7084" xml:space="preserve">Cor-<lb/>reximus autem multarũ ſtellarum longitudines, latitudinesq́ue, partim ex an <lb/>tiquo Almageſto manu ſcripto, partim etiam ex obſeruationibus Ptolemæi, <lb/>aliorumq́; </s> <s xml:id="echoid-s7085" xml:space="preserve">Aſtronomorum. </s> <s xml:id="echoid-s7086" xml:space="preserve">Quando enim obſeruatum eſt, tres aliquas ſtellas <lb/>v.</s> <s xml:id="echoid-s7087" xml:space="preserve">g. </s> <s xml:id="echoid-s7088" xml:space="preserve">in cœlo lineã quaſi rectam conſtituere, ſi id non ſeruetur in globo cęleſti, <lb/>fi ſtellæ ſecundum longitudines, latitudineſq́; </s> <s xml:id="echoid-s7089" xml:space="preserve">in tabulis notatas deſcribantur, <lb/>argumento eſt, longitudines, latitudinesve illas ſtellarũ ueras non eſſe. </s> <s xml:id="echoid-s7090" xml:space="preserve">Vnde <lb/>emendandæ ſunt, ita tamen, ut ſtellæ illum ſitum in conſtellationibus reti-<lb/>neant, qui ab Aſtronomis obſeruatus eſt. </s> <s xml:id="echoid-s7091" xml:space="preserve">Id quod in noſtra cotrectione obſer-<lb/>uauimus. </s> <s xml:id="echoid-s7092" xml:space="preserve">Cæterum ut ſtellas illas, quarum longitudines, latitudinesve corre-<lb/>ximus, ab alijs diſtingueremus, appoſuimus illis aſteriſmum hoc modo *. </s> <s xml:id="echoid-s7093" xml:space="preserve">Rur <lb/>ſus aliquæ ſtellæ dicebantur aliquando in tabulis eſſe v.</s> <s xml:id="echoid-s7094" xml:space="preserve">g. </s> <s xml:id="echoid-s7095" xml:space="preserve">in manu ſiniſtra, uel <lb/>in alia parte, cum tamen ſint in dextra, uel alibi, ut picturę poſtulant. </s> <s xml:id="echoid-s7096" xml:space="preserve">Has igi-<lb/>tur etiam emendauimus, eiſq́ue eundem aſteriſmum appoſuimus. </s> <s xml:id="echoid-s7097" xml:space="preserve">Sed iam præ <lb/>dictam tabulam oculis ſubijciamus, cuius uſum poft ipſius ſ<unsure/>inem exponemus. </s> <s xml:id="echoid-s7098" xml:space="preserve"><lb/>Eſt autem tabula uniuerſa in tres partes diſtributa. </s> <s xml:id="echoid-s7099" xml:space="preserve">in quarum prima continen <lb/>tur omnes ſtellæ, quæ à Zodiaco in Boream uergunt. </s> <s xml:id="echoid-s7100" xml:space="preserve">Secunda omnes ſtellas <lb/>complectitur, quæ in Zodiaco reperiuntur: </s> <s xml:id="echoid-s7101" xml:space="preserve">In tertia denique omnia aſtra re-<lb/>ponuntur, quæ à Zodiaco in Auſtrum deflectunt.</s> <s xml:id="echoid-s7102" xml:space="preserve"/> </p> <div xml:id="echoid-div350" type="float" level="2" n="2"> <note position="right" xlink:label="note-185-02" xlink:href="note-185-02a" xml:space="preserve">Cur in hye-<lb/>me plures <lb/>ſtellę uideã <lb/>tur, quàm <lb/>in æſtate.</note> </div> <pb o="151" file="187" n="188" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve">Vrſa min@@</note> <note position="right" xml:space="preserve"> <lb/>########## TABVL AE PRIMA PARS COMPLECTENS \\ nomina omnium conſtellationum, quæ à Zodiaco ad eius po- \\ lum Boreum ue<unsure/>rgunt, unà cum numero, ordine, \\ longitudinibus, latitudinibus, atque \\ magnitudinibus ſtellarum. <lb/>## FORMÆ STELLARVM ### Longit. ### Latit. ## Magni- \\ tudo. <lb/># # # G. # M. # # G. # M. <lb/>########## VRSA MINOR, SIVE CYNOSVRA <lb/> ########## Conſtellatio I. 1 # Stella, quæ in extremo caudæ, Polaris # 53 # 30 # # 66 # 0 # # 3 2 # Sequens in cauda # 55 # 50 # # 70 # 0 # # 4 3 # In eductione caudæ # 69 # 30 # # 74 # 0 # # 4 4 # In latere quadrãgulari p̃cedẽte, Auſtralior # 83 # 0 # # 75 # 20 # # 4 5 # Eiuſdem lateris Borealior # 87 # 0 # # 77 # 40 # # 4 6 # Earum quæ in latere ſequente, Auſtralior # 100 # 30 # # 72 # 40 # # 2 7 # Eiuſdem lateris Borealior # 109 # 30 # # 74 # 50 # # 2 ########## Omnes ſtellæ 7. Secundæ magnit. 2. Tertiæ 1. Quartæ 4. 1 # Eſt quoq; circa Cynoſuram alia ſtella infor \\ mis, quæ uidelicet extra formam vrſæ repe- \\ ritur, eſtq́ue in latere ſequenti ad rectam li- \\ neam, maxime Auſtralis # 0 # 0 # # 0 # 0 # # 0 # # * # # 0 # 0 # # 0 # 0 # # 0 # # 0 # 0 # # 0 # 0 # # 0 # # 96 # 20 # # 71 # 10 # # 4</note> <note position="right" xml:space="preserve">Vrſa maibr@</note> <note position="right" xml:space="preserve"> ########## VRSA MAIOR, QVAM HELICEN VOCANT. ########## Conſtellatio II. 1 # Stella, quæ in roſtro # 78 # 40 # # 39 # 50 # # 4 2 # In binis oculis præcedens # 79 # 10 # # 43 # 0 # # 5 3 # Sequens hanc # 79 # 40 # # 43 # 0 # # 5 4 # In fronte duarum præcedens # 79 # 30 # # 47 # 10 # # 5 5 # Sequens in fronte # 81 # 0 # # 47 # 0 # # 5 6 # Quæ in ſiniſtra auricula præcedente # 81 # 30 # # 50 # 30 # # 5 # # * 7 # Duarum in collo antecedens # 85 # 50 # # 43 # 50 # # 4 8 # Sequens # 92 # 50 # # 44 # 20 # # 4 9 # In pectore duarum Borealior # 94 # 20 # # 44 # 0 # # 4 10 # Auſtralior # 93 # 20 # # 42 # 0 # # 4 11 # In genu ſi niſtro anteriori # 93 # 0 # # 35 # 0 # # 3 # # * 12 # Duarum in pede ſiniſtro priori Borealior # 89 # 50 # # 29 # 0 # # 3 13 # Quæ magis ad Auſtrum # 88 # 40 # # 28 # 30 # # 3 14 # In genu dextro priori # 89 # 0 # # 36 # 0 # # 4 15 # Quæ ſub ipſo genu # 89 # 10 # # 33 # 30 # # 4 # # * 16 # Quæ in dorſo # 104 # 0 # # 49 # 0 # # 2 # # * 11 # Quæ in ilibus # 105 # 30 # # 44 # 30 # # 2 18 # Quæ in eductione caudæ # 116 # 30 # # 51 # 0 # # 3 19 # In ſiniſtra coxa poſteriore # 117 # 20 # # 46 # 30 # # 2 20 # Duarũ pręcedens in pede ſiniſtro poſteriore # 106 # 0 # # 29 # 30 # # 2 # # * </note> <pb o="152" file="188" n="189" rhead="Comment. in I. cap. Sphæræ."/> <note position="left" xml:space="preserve">D@@@</note> <note position="right" xml:space="preserve"> <lb/>## FORMÆ STELLARVM ### Longit. ### Latit. ## Magni- \\ tudo. <lb/># # # G. # M. # # G. # M. <lb/>21 # Sequens hanc # 107 # 30 # # 28 # @@ # # 3 <lb/>22 # Quæ in ſiniſtra cauitate (realior # 115 # 0 # # 35 # 15 # # 4 <lb/>23 # Duarũ, quæ in pede dextro poſteriore, Bo # 123 # 10 # # 25 # 50 # # 3 <lb/>24 # Quæ magis ad Auſtrum # 123 # 40 # # 25 # 0 # # 3 <lb/>25 # Prima trium in cauda poſt eductionem # 125 # 30 # # 53 # 30 # # 2 <lb/>26 # Media earum # 131 # 20 # # 55 # 40 # # 2 <lb/>27 # Vltima, & in extrema cauda # 143 # 10 # # 54 # 0 # # 2 <lb/>########## Omnes ſtellæ numero 27. Secundæ magnit. 6. Tertiæ 8. \\ Quartæ 8. Quintæ 5. <lb/>########## INFORMES CIRCA HELICEN. <lb/># 1 # Quæ à cauda in Auſtrum # 141 # 10 # # 39 # 45 # # 3 <lb/># 2 # Ante<unsure/>cedens hanc obſcurior # 133 # 30 # # 41 # 20 # # 5 <lb/># 3 # Inter vrſæ pedes priores, & caput ♌ # 98 # 20 # # 17 # 15 # # 4 <lb/># 4 # Quæ magis ab hac in Boream # 96 # 40 # # 19 # 10 # # 4 <lb/># 5 # Vltima trium obſcurarum # 99 # 30 # # 20 # 0 # # obſc. <lb/># 6 # Antecedens hanc # 95 # 30 # # 22 # 45 # # obſc. <lb/># 7 # Quæ magis antecedit # 94 # 30 # # 23 # 15 # # obſc. <lb/># 8 # Quæ intra priores pedes, & ♊ # 80 # 20 # # 22 # 15 # # obſc. <lb/>* ########## Informes numero 8. Tertiæ magnit. 1. Quartæ 2. \\ Quintæ 1. obſcuræ 4. <lb/>########## DRACO. Conſtellatio III. <lb/> # 1 # Quæ in lingua # 200 # 0 # # 76 # 30 # # 4 # 2 # In ore # 115 # 10 # # 78 # 30 # # 4 * # 3 # Supra oculum # 216 # 30 # # 75 # 40 # # 3 # 4 # In gena # 229 # 40 # # 80 # 20 # # 4 # 5 # Supra cap@t # 233 # 30 # # 75 # 30 # # 3 # 6 # In prima colli inſlexione, Borealis # 258 # 40 # # 82 # 20 # # 4 * # 7 # Auſtralis ipſarum # 266 # 40 # # 78 # 15 # # 4 # 8 # Media earundem # 262 # 10 # # 80 # 20 # # 4 # 9 # Quæ ſequitur has ab ortu in flexione ſcđa # 282 # 50 # # 81 # 10 # # 4 # 10 # Auſtrina lateris præcedentis quadrila@eris # 331 # 20 # # 81 # 40 # # 4 # 11 # Borea eiuſdem lateris # 343 # 50 # # 83 # 0 # # 4 # 12 # Borea lateris ſequentis # 1 # 0 # # 78 # 58 # # 4 # 13 # Auſtralis eiuſdem lateris # 346 # 10 # # 77 # 57 # # 4 # 14 # In flexione tertia Auſtralis trianguli # 4 # 0 # # 80 # 30 # # 5 # 15 # Reliquarum trianguli præcedens # 15 # 0 # # 81 # 40 # # 5 # 16 # Quæ ſequitur # 19 # 30 # # 80 # 15 # # 5 # 17 # In triangulo antecedente trium ſequens # 66 # 20 # # 84 # 30 # # 4 # 18 # Reliquarum eiuſdem trianguli Auſtralis # 43 # 40 # # 83 # 30 # # 4 # 19 # Quæ Borealior ſuperioribus duabus # 35 # 10 # # 84 # 50 # # 4 # 20 # Duarum paruarum à triangulo ſequens # 200 # 0 # # 87 # 30 # # 6 # 21 # Antecedens earum # 19@ # 0 # # 86 # 50 # # 0 </note> <pb o="153" file="189" n="190" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve">Geplieus.</note> <note position="right" xml:space="preserve"> <lb/>## FORMÆ STELLARVM ### Longit. ### Latit. ## Magni- \\ tudo <lb/># # # G. # M. # # G. # M. <lb/># 22 # Trium, quæ in rectum ſequuntur, Auſtralis # 152 # 30 # # 81 # 15 # # 5 <lb/># 23 # Media trium # 152 # 30 # # 83 # 0 # # 5 <lb/># 24 # Quæ magis in Boream ipſarum # 151 # 0 # # 84 # 50 # # 3 <lb/># 25 # Poſthæc ad occasũ duarũ, q̃ magis in Boreã # 153 # 20 # # 78 # 0 # # 3 <lb/># 26 # Magis ad Auſtrum # 156 # 30 # # 74 # 40 # # 4 <lb/># 27 # Hinc ad occaſum in conuerſione caudę # 156 # 0 # # 70 # 0 # # 3 <lb/># 28 # Duarum plurimum diſtantium pręcedens # 220 # 40 # # 64 # 40 # # 4 <lb/># 29 # Quę ſequitur ipſam # 124 # 30 # # 65 # 30 # # 3 <lb/># 30 # Sequens in cauda # 102 # 30 # # 61 # 15 # # 3 # # * <lb/># 31 # In extrema cauda # 96 # 30 # # 56 # 15 # # 3 # # * <lb/>########## Omnes ſtellæ 31. Tertiæ magnit. 8. Quartæ 16. Quintæ 5. Sextæ 2. <lb/>########## CEPHEVS. Conſtellatio II II. <lb/> 1 # In pede dextro # 28 # 40 # # 75 # 40 # # 4 2 # In ſiniſtro pede # 26 # 20 # # 64 # 15 # # 4 3 # In latere dextro ſub cingulo # 0 # 40 # # 71 # 10 # # 4 4 # Quę ſupra dextrum humerum attingit # 340 # 0 # # 69 # 0 # # 3 5 # Quæ dextrum cubitum coxæ contingit # 332 # 40 # # 72 # 0 # # 4 6 # Quæ ſequitur eandem coxam attingens # 333 # 20 # # 74 # 0 # # 4 # # * 7 # Quę in pectore # 352 # 0 # # 65 # 30 # # 5 8 # In brachio ſiniſtro # 1 # 0 # # 62 # 30 # # 4 9 # Trium in tiara Auſtralis # 339 # 40 # # 60 # 15 # # 5 10 # Media ipſarum # 340 # 40 # # 61 # 15 # # 4 11 # Borea trium # 342 # 20 # # 61 # 30 # # 5 ########## Omnes ſtellæ 11. Tertiæ magnit. 1. Q@artæ 7. Quintæ 3. 1 # Informium duarum, quæ præcedit tiaram # 337 # 0 # # 64 # 0 # # 5 2 # Quæ ſequitur ipſam # 344 # 40 # # 59 # 30 # # 4</note> <note position="right" xml:space="preserve">Bootes ſiue <lb/>Arctophy-<lb/>lax.</note> <note position="right" xml:space="preserve"> ########## BOOTES, SIVE ARC TOPHYLAX. ########## Conſlellatio V. 1 # In manu ſiniſtra trium præcedens # 145 # 40 # # 58 # 40 # # 5 2 # Media trium Auſtralior # 147 # 30 # # 58 # 20 # # 5 3 # Sequens trium # 149 # 0 # # 60 # 10 # # 5 4 # Quæ in vlna ſiniſtra coxæ # 153 # 0 # # 54 # 40 # # 5 5 # In ſiniſtro humero # 163 # 0 # # 49 # 0 # # 3 6 # In capite # 170 # 0 # # 53 # 50 # # 4 7 # In dextro humero # 179 # 0 # # 48 # 40 # # 4 8 # In colorobo duarum Auſtralior # 179 # 0 # # 53 # 15 # # 4 9 # Quæ magis in Boreã in extremo colorobo # 178 # 20 # # 57 # 30 # # 4 10 # Duarũ ſub humero in uenabulo Borealis # 181 # 0 # # 46 # 10 # # 4 11 # Auſtralior ipſarum # 181 # 50 # # 45 # 30 # # 5 12 # In dextræ manus extremo # 181 # 35 # # 41 # 30 # # 5 13 # Duarum in uola præcedens # 180 # 0 # # 41 # 40 # # 5 </note> <pb o="154" file="190" n="191" rhead="Comment. in I. Cap. Sphæræ"/> <note position="left" xml:space="preserve">@orona Bo <lb/>@ealis.</note> <note position="right" xml:space="preserve"> <lb/>## FORMÆ STELLARVM ### Longit. ### Latit. ## Magni- \\ tudo. <lb/># # # # G. # M. # # G. # M. <lb/># 14 # Quæ ſequitur ipſam # 180 # 20 # # 42 # 30 # # 5 <lb/># 15 # In extremo colorobi manubrio # 182 # 0 # # 40 # 20 # # 5 <lb/># 16 # In dextro latere # 173 # 20 # # 40 # 15 # # 3 <lb/># 17 # Duarum in cingulo, quæ ſequitur # 169 # 0 # # 41 # 40 # # 4 <lb/># 18 # Quæ antecedit # 168 # 20 # # 42 # 10 # # 4 <lb/>* # 19 # In crure dextro # 178 # 40 # # 28 # 0 # # 3 <lb/># 20 # In ſiniſtro crure Borea trium # 164 # 40 # # 28 # 0 # # 3 <lb/># 21 # Media trium # 163 # 50 # # 26 # 30 # # 4 <lb/># 22 # Auſtralior ipſarum # 164 # 50 # # 25 # 0 # # 4 <lb/>########## Omnes ſtellæ 22. Tertiæ magnit. 4. Quartæ 9. Quintæ 9. <lb/># 1 # Informis inter crura, quã Arcturũ uocant. # 170 # 20 # # 31 # 30 # # 1 <lb/>########## CORONA BOREA. <lb/> ########## Conſtellatio VI. # 1 # Lucens in corona. Ariadne # 188 # 0 # # 44 # 30 # # 1 # 2 # Præcedens omnium # 185 # 0 # # 46 # 20 # # 4 # 3 # Sequens in Boream # 185 # 20 # # 48 # 0 # # 5 # 4 # Sequens magis in Boream # 193 # 0 # # 50 # 30 # # 6 # 5 # Quæ ſequitur lucentem ab Auſtro # 191 # 30 # # 44 # 45 # # 4 # 6 # Quæ proxime ſequitur # 190 # 30 # # 44 # 50 # # 4 # 7 # Poſt has longius ſequens # 194 # 40 # # 46 # 10 # # 4 # 8 # Quæ ſequitur omnes in corona # 195 # 0 # # 49 # 20 # # 4 ########## Omnes ſtellæ 8. Secundæ magnit. 1. Quartæ 5. \\ Quintæ 1. Sextæ 1.</note> <note position="left" xml:space="preserve">Hercules.</note> <note position="left" xml:space="preserve"> ########## ENGONASIS, QVI ET HERCVLES. ########## Conſtellatio VII. # 1 # In capite # 221 # 0 # # 37 # 30 # # 3 # 2 # In axilla dextra # 207 # 0 # # 43 # 0 # # 3 # 3 # In dextro brachio # 205 # 0 # # 40 # 10 # # 3 * # 4 # In dextro cubito # 201 # 20 # # 37 # 10 # # 4 # 5 # In ſiniſtro humero # 220 # 0 # # 48 # 0 # # 3 # 6 # In ſiniſtro brachio # 225 # 30 # # 49 # 30 # # 4 * # 7 # In ſiniſtro cubito # 231 # 0 # # 52 # 0 # # 4 # 8 # Trium in ſiniſtra uola # 238 # 50 # # 52 # 50 # # 4 # 9 # Borea duarum reliquarum # 235 # 0 # # 54 # 0 # # 4 # 10 # Auſtralior # 234 # 50 # # 53 # 0 # # 4 # 11 # In dextro latere # 207 # 10 # # 56 # 10 # # 3 # 12 # In ſiniſtro latere # 213 # 30 # # 53 # 30 # # 4 * # 13 # In uertebra ſiniſtræ coxæ # 213 # 20 # # 56 # 10 # # 5 * # 14 # In eductione eiuſdem coxę # 214 # 30 # # 58 # 30 # # 5 * # 15 # In coxa ſiniſtra trium pręcedens # 217 # 20 # # 59 # 50 # # 4 # 16 # Sequens hanc # 218 # 40 # # 60 # 20 # # 3 </note> <pb o="155" file="191" n="192" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve">Iyra.</note> <note position="right" xml:space="preserve"> <lb/>## FORMÆ STELLARVM ## Longit. ### Latit. ### Magni- \\ tudo. <lb/># # G. # M. # # G. # M. <lb/>17 # Tertia ſequens # 219 # 40 # # 61 # 15 # # 4 <lb/>18 # In ſiniſtro genu # 234 # 10 # # 61 # 0 # # 4 # # * <lb/>19 # In ſiniſtra tibia # 225 # 30 # # 69 # 20 # # 4 # # * <lb/>20 # In pede ſiniſtro trium præcedens # 218 # 40 # # 70 # 15 # # 6 # # * <lb/>21 # Madia earum # 220 # 10 # # 71 # 15 # # 6 <lb/>22 # Sequens trium # 223 # 0 # # 72 # 0 # # 6 <lb/>23 # In eductione dextræ coxæ # 204 # 0 # # 60 # 15 # # 4 # # * <lb/>24 # Eiuſdem coxæ Borealior # 198 # 50 # # 63 # 0 # # 4 # # * <lb/>25 # In dextro genu # 189 # 0 # # 65 # 30 # # 4 <lb/>26 # Sub eodem genu duarum Auſtralior # 186 # 40 # # 63 # 40 # # 4 <lb/>27 # Quæ magis in Boream # 183 # 30 # # 64 # 15 # # 4 <lb/>28 # In tibia dextra # 184 # 30 # # 60 # 0 # # 4 <lb/>29 # In extremo dextri pedis eadem, quæ in ex \\ tremo colorobo Bootis # 0 # 0 # # 0 # 0 # # 0 <lb/># # 178 # 20 # # 57 # 30 # # 4 <lb/>########## Omnes ſtellę pręter ultimam. 28. Tertiæ magnit. 6. \\ Quartæ 17. Quintæ 2. Sextæ 3. <lb/>1 # Informis à dextro brachio Auſtralior # 206 # 0 # # 38 # 10 # # 5 <lb/>########## LYRA, SEV SEVVLTVR CADENS. <lb/> ########## Conſtellatio VIII. 1 # Lucida, quæ Lyra, ſiue Fidicula uocatur # 250 # 40 # # 62 # 0 # # 1 2 # Duarum adiacentium Borea # 253 # 40 # # 62 # 40 # # 4 3 # Quę magis in Auſtrum # 253 # 40 # # 61 # 0 # # 4 4 # In medio eductionis cornuum # 256 # 0 # # 60 # 0 # # 4 # # * 5 # Duarum cõtinuarum ad ortum in Boream # 265 # 20 # # 61 # 10 # # 4 6 # Quæ magis in Auſtrum # 265 # 0 # # 60 # 20 # # 4 7 # Pręcedẽtium in iunctura duarũ Borealior # 264 # 20 # # 56 # 10 # # 3 8 # Auſtralior # 253 # 10 # # 55 # 0 # # 4 9 # Sequentiũ duarũ in eodem iugo Borealior # 257 # 30 # # 55 # 20 # # 3 10 # Quæ magis in Auſtrum # 257 # 20 # # 54 # 45 # # 4 # # * ########## Omnes ſtellæ 10. Primæ magnit. 1. Tertiæ 2. \\ Quartæ 7.</note> <note position="right" xml:space="preserve">Cyguns</note> <note position="right" xml:space="preserve"> ########## OLOR, SIVE CYGNVS, QVI ETIAM ########## Auis, ſeu Gallina dicitur. \\ Conſtellatio IX. 1 # Quæ in ore Roſtrum Gallinæ # 267 # 50 # # 49 # 20 # # 3 2 # In capite # 272 # 20 # # 50 # 30 # # 5 3 # In medio collo # 279 # 20 # # 54 # 30 # # 4 4 # In pectore # 291 # 50 # # 56 # 20 # # 3 5 # In cauda lucens # 302 # 30 # # 60 # 0 # # 2 6 # In ancone dextrę alæ # 282 # 40 # # 64 # 40 # # 3 7 # Trium in dextra ala Auftralior # 285 # 50 # # 69 # 40 # # 4 </note> <pb o="156" file="192" n="193" rhead="Comment. in I. Cap. Sphæræ"/> <note position="left" xml:space="preserve">Caſſiopeia.</note> <note position="right" xml:space="preserve"> <lb/># ## FORMÆ STELLARVM ## Longit. ### Latit. ### Magni- \\ tudo. <lb/># # # G. # M. # G. # M. <lb/>* # 8 # Media # 284 # 30 # # 71 # 30 # # 4 <lb/># 9 # Vltima trium, & in extrema ala # 280 # 0 # # 74 # 0 # # 4 <lb/># 10 # In ancone ſiniſtræ alę # 294 # 10 # # 49 # 30 # # 3 <lb/>* # 11 # In medio ipſius alę, & Borealior # 298 # 10 # # 52 # 10 # # 4 <lb/># 12 # In eiuſdem extremo # 300 # 0 # # 44 # 0 # # 3 <lb/># 13 # In pede ſiniſtro # 303 # 20 # # 55 # 10 # # 4 <lb/>* # 14 # In ſiniſtro genu # 307 # 50 # # 57 # 0 # # 4 <lb/># 15 # In dextro pede duarum pręcedcns # 294 # 30 # # 64 # 0 # # 4 <lb/># 16 # Quę ſequitur # 296 # 0 # # 64 # 30 # # 4 <lb/># 17 # n ſiniſtro genu # 305 # 30 # # 63 # 45 # # 5 <lb/># ########## Omnes ſtellæ 17. Secundę magnit. 1. Tertiæ 5. \\ Quartę 9. Quintæ 2. <lb/>* # 1 # Informiũ ea, q̃ ſub dextra aladuarũ Auſtra # 306 # 0 # # 49 # 40 # # 4 <lb/># 2 # Quę magis in Boream (lior # 307 # 10 # # 51 # 40 # # 4 <lb/># ########## CASSIOPEIA. <lb/> # ########## Conſtellatio X. # 1 # In capite # 1 # 10 # # 45 # 20 # # 4 # 2 # In pectore # 4 # 10 # # 46 # 45 # # 3 # 3 # In cingulo # 6 # 20 # # 47 # 50 # # 4 # 4 # Super cathedra ad cox as # 10 # 0 # # 49 # 0 # # 3 # 5 # Ad genua # 13 # 40 # # 45 # 30 # # 3 # 6 # In crure # 12 # 20 # # 45 # 30 # # 4 * # 7 # In extremo pedis # 25 # 0 # # 47 # 20 # # 4 # 8 # In ſiniſtro brachio # 8 # 0 # # 44 # 20 # # 4 *9 # In ſiniſtro cubito # 20 # 40 # # 45 # 0 # # 5 # 10 # In dextro cubito # 457 # 40 # # 50 # 0 # # 6 # 11 # In ſedis pede # 8 # 20 # # 32 # 40 # # 4 # 12 # In aſcenſu medio # 1 # 10 # # 51 # 40 # # 3 * # 13 # In extremo # 356 # 0 # # 51 # 40 # # 7 # ########## Omnes ſtellæ 13. Tertiæ magnit. 4. Quartæ 6. \\ Quintæ 1. Sextæ 2.</note> <note position="left" xml:space="preserve">Perſeus.</note> <note position="left" xml:space="preserve"> # ########## PERSEVS. Conſtellatio XI. # 1 # In extremo dextrę manus # 21 # 0 # # 40 # 30 # # 4 # 2 # In dex tro cubito # 24 # 30 # # 37 # 30 # # 4 # 3 # In humero dextro # 26 # 0 # # 34 # 30 # # 4 # 4 # In ſiniſtro humero # 20 # 50 # # 32 # 20 # # 4 # 5 # In capite, ſiue nebula # 24 # 0 # # 34 # 30 # # 4 # 6 # In ſcapulis # 24 # 50 # # 31 # 10 # # 4 # 7 # In dextro latere fulgens # 28 # 20 # # 30 # 0 # # 2 # 8 # In eodem latere trium præcedens # 28 # 40 # # 27 # 30 # # 4 # 9 # Media # 30 # 20 # # 27 # 40 # # 4 </note> <pb o="157" file="193" n="194" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve">Erichto-<lb/>nius, ſiue <lb/>Auriga.</note> <note position="right" xml:space="preserve"> <lb/>## FORMÆ STELLARVM ## Longit. ### Latit. ### Magni- \\ tudo. <lb/># # G. # M. # # G. # M. <lb/>10 # Reliqua trium # 31 # 0 # # 27 # 30 # # 3 <lb/>11 # In cubito ſiniſtro # 24 # 0 # # 27 # 0 # # 4 <lb/>12 # In ſiniſtra manu, & capite Meduſæ, lucens # 23 # 0 # # 23 # 0 # # 2 <lb/>13 # Eiuſdem capitis ſequens # 22 # 30 # # 21 # 0 # # 4 <lb/>14 # Quæ præit in eodem capite # 21 # 0 # # 21 # 0 # # 4 <lb/>15 # Præcedens etiam hanc # 20 # 10 # # 22 # 15 # # 4 <lb/>16 # In dextro genu # 38 # 10 # # 28 # 15 # # 4 <lb/>17 # Præcedens hanc in genu # 37 # 10 # # 28 # 10 # # 4 <lb/>18 # In poplite duarum præcedens # 35 # 40 # # 25 # 10 # # 4 # # * <lb/>19 # Sequens # 37 # 20 # # 26 # 15 # # 4 # # * <lb/>20 # In dextro crure # 37 # 30 # # 24 # 30 # # 5 # # * <lb/>21 # In dextro pede # 39 # 40 # # 18 # 45 # # 5 # # * <lb/>22 # In ſiniſtra coxa # 30 # 10 # # 21 # 40 # # 4 <lb/>23 # In ſiniſtro genu # 32 # 0 # # 19 # 50 # # 3 <lb/>24 # In ſiniſtro crure # 31 # 40 # # 13 # 45 # # 3 <lb/>25 # In ſiniſtro calcaneo # 27 # 30 # # 12 # 0 # # 3 <lb/>26 # In ſummo pedis ſiniſtra parte # 29 # 40 # # 11 # 0 # # 3 # # * <lb/>########## Omnes ſtellæ num. 26. Secundæ magnit. 2. Tertiæ 5. \\ Quartæ 16. Quintæ 2. Nebuloſa 1. <lb/>########## INFORMES CIRCA PERSEA. <lb/>1 # Quæ ad ortum à ſiniſtro genu # 34 # 10 # # 18 # 0 # # 5 # # * <lb/>2 # In Boream à dextro genu # 38 # 20 # # 31 # 0 # # 5 <lb/>3 # Antecedens a capite Meduſæ # 18 # 0 # # 20 # 40 # # # obſc. <lb/>########## AVRIGA, QVI ET HENIOCHVS, SEV \\ ERICHTONIVS. <lb/> ########## Conſtellatio XII. 1 # Duarum in capite Auſtralior # 55 # 50 # # 30 # 0 # # 4 2 # Quæ magis in Boream (Hircus # 55 # 40 # # 30 # 50 # # 4 3 # In ſiniſtro humero fulgens. Capella ſeu # 48 # 20 # # 22 # 30 # # 1 4 # In dextro humero # 56 # 10 # # 20 # 0 # # 2 # # * 5 # In dextro cubito # 54 # 30 # # 15 # 15 # # 4 6 # In dextra vola # 56 # 10 # # 13 # 30 # # 4 7 # In ſiniſtro cubito # 45 # 20 # # 20 # 40 # # 4 8 # Antecedens hædorum # 45 # 30 # # 18 # 0 # # 4 9 # In ſiniſtra vola hædorum ſequens # 46 # 0 # # 18 # 0 # # 4 10 # In ſiniſtro talo # 43 # 10 # # 10 # 10 # # 3 # # * 11 # In dextro pede, & extremo cornu ♉ Boreo # 49 # 0 # # 5 # 0 # # 3 # # * 12 # In dextra ſura # 49 # 20 # # 8 # 30 # # 5 # # * 13 # In clune # 49 # 40 # # 12 # 20 # # 5 14 # In ſiniſtro pede exigua # 44 # 0 # # 10 # 20 # # 6 # # * </note> <pb o="158" file="194" n="195" rhead="Comment. in I. Cap. Sphæræ"/> <note position="left" xml:space="preserve">Ophiu chus</note> <note position="right" xml:space="preserve"> <lb/># ## FORMÆ STELLARVM ## Longit. ## Latit. ## Magni- \\ tudo. <lb/># # # G. # M. # # G. # M. <lb/># ########## Omnes ſtellæ 14. Primæ magnit. 1. Secundæ 1. Tertiæ 2. Quartæ 7. \\ Quintæ 2. Sextæ 1. <lb/># ########## OPHIVCHVS, SEV SERPENTARIVS. <lb/> # ########## Conſtellatio XIII. # 1 # In capite # 228 # 10 # 36 # 0 # 3 # 2 # In dextro humero duarum præcedens # 231 # 20 # 27 # 15 # 4 # 3 # Sequens # 232 # 20 # 26 # 45 # 4 # 4 # In ſiniſtro humero duarum præcedens # 216 # 40 # 33 # 0 # 4 # 5 # Quæ ſequitur # 218 # 0 # 31 # 50 # 4 * # 6 # In ancone ſiniſtro # 211 # 40 # 24 # 30 # 4 # 7 # In ſiniſtra manu duarum præcedens # 208 # 20 # 17 # 0 # 4 * # 8 # Sequens # 209 # 20 # 16 # 30 # 3 * # 9 # In dextro ancone # 230 # 0 # 15 # 0 # 4 * # 10 # In dextra manu præcedens # 235 # 40 # 13 # 40 # 4 * # 11 # Sequens # 236 # 40 # 14 # 20 # 4 * # 12 # In dextro genu # 224 # 30 # 7 # 30 # 3 # 13 # In dextra tibia # 227 # 0 # 2 # 15 # 3 # 14 # In pede dextro ex quatuor præcedens # 226 # 20 # 2 # 15 # 4 # Auſt. # 15 # Sequens # 227 # 40 # 1 # 30 # 4 # Auſt. # 16 # Tertia ſequens # 228 # 20 # 0 # 20 # 4 # Auſt. * # 17 # Reliqua ſequens # 229 # 10 # 0 # 45 # 5 # Auſt. # 18 # Quæ calcaneum contingit # 229 # 30 # 1 # 0 # 5 # Auſt. # 19 # In ſiniſtro genu # 215 # 30 # 11 # 50 # 3 # Bor. # 20 # In crure ſiniſtro trium ad rectã lineam Borealior # 215 # 0 # 5 # 20 # 5 # Bor. # 21 # Media earum # 214 # 0 # 3 # 10 # 5 # Bor. # 22 # Auſtralior trium # 213 # 10 # 1 # 40 # 5 # Bor. # 23 # In ſiniſtro calcaneo # 215 # 40 # 0 # 40 # 5 # Bor. # 24 # Plantam ſiniſtri pedis attingens # 214 # 0 # 0 # 45 # 4 # Auſt. # ######## Omnes ſtellæ 24. Tertiæ magnit. 5. Quartæ 13. \\ Quintæ 6. # ######## INFORMES CIRCA OPHIVCHVM. # 1 # Ab ortu in dextrum humerũ maxime Borea trium # 235 # 20 # 28 # 10 # 4 # 2 # Media trium # 236 # 0 # 26 # 20 # 4 # 3 # Auſtralis trium # 233 # 40 # 25 # 0 # 4 # 4 # Adhuc ſequens tres # 237 # 0 # 27 # 0 # 4 # 5 # Separata a quatuor in Septentriones # 238 # 0 # 33 # 0 # 4 # ######## Omnes ſtellæ 5. magnitudinis Quartæ.</note> <note position="left" xml:space="preserve">Serpens <lb/>Ophiuchi.</note> <note position="left" xml:space="preserve"> # ######## SERPENS OPHIVCHI. # ######## Conſtellatio XIIII. # 1 # In quadrilatero quæ in gena # 192 # 10 # 38 # 0 # 4 # 2 # Quæ nares attingit # 295 # 0 # 40 # 0 # 4 </note> <pb o="159" file="195" n="196" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve">Sagitta.</note> <note position="right" xml:space="preserve"> <lb/>## FORMÆ STELLARVM ### Longit. ### Latit. ## Magni- \\ tudo <lb/># # G. # M. # # G. # M. <lb/>3 # In tempore # 197 # 40 # # 35 # 0 # # 3 <lb/>4 # In edactione colli # 195 # 20 # # 34 # 15 # # 3 <lb/>5 # Media quadrilateri, & in ore # 194 # 40 # # 37 # 15 # # 4 <lb/>6 # A capite in Septentriones # 196 # 30 # # 42 # 30 # # 4 # # * <lb/>7 # In prima colli conuerſi@@e # 195 # 0 # # 29 # 15 <lb/>8 # Sequentium trium Borea # 198 # 10 # # 26 # 30 # # 4 <lb/>9 # Media earum # 197 # 40 # # 25 # 20 # # 3 <lb/>10 # Auſtralior trium # 199 # 40 # # 24 # 0 # # 3 <lb/>11 # Duarum præcedens ſiniſtrã manũ Serpẽtarij # 202 # 0 # # 16 # 30 # # 4 <lb/>12 # Quæ ſequitur eandem manum # 211 # 30 # # 16 # 15 # # 5 # # * <lb/>13 # Quæ poſt coxam dextram # 227 # 0 # # 10 # 30 # # 4 # # * <lb/>14 # Sequentium duarum Auſtrina # 230 # 20 # # 8 # 30 # # 4 <lb/>15 # Quæ Borea # 231 # 10 # # 10 # 30 # # 4 <lb/>16 # Poſt dextram manum in inflexione caudæ # 237 # 0 # # 20 # 0 # # 4 <lb/>17 # Sequens in cauda # 244 # 0 # # 21 # 10 # # 4 <lb/>18 # In extrema cauda # 251 # 40 # # 27 # 0 # # 4 <lb/>########## Omnesſtellæ 18. Tertiæ magnit. 5. Quartæ 12. Quintæ 1. <lb/>########## SAGITTA, SP<unsure/>VE TELVM. Conſtellatio XV. <lb/> 1 # In cuſpide # 273 # 30 # # 39 # 20 # # 4 2 # In arundine trium ſequens # 270 # 0 # # 39 # 10 # # 6 3 # Media ipſarum # 269 # 10 # # 39 # 50 # # 5 4 # Antecedens trium # 268 # 0 # # 39 # 0 # # 5 5 # In Glyphide # 266 # 40 # # 38 # 45 # # 5 ########## Omnes ſtellæ 5. Quartæ magnit. 1. Quintæ 3. Sextæ 1.</note> <note position="right" xml:space="preserve">Aguila.</note> <note position="right" xml:space="preserve"> ########## AQVILA, SEV VVLTVR VOLANS. ########## Conſtellatio XVI. 1 # In medio capite # 270 # 30 # # 26 # 50 # # 4 2 # In collo # 268 # 10 # # 27 # 10 # # 3 3 # In ſcapulis lucida, quam dicunt Aquilam # 267 # 10 # # 29 # 10 # # 2 4 # Proxima huic magis in Boream # 268 # 0 # # 30 # 0 # # 3 5 # In ſiniſtro humero præcedens # 266 # 30 # # 31 # 30 # # 3 6 # Quæ ſequitur # 269 # 20 # # 31 # 30 # # 5 7 # In dextro humero antecedens # 263 # 0 # # 28 # 40 # # 5 8 # Quæ ſequitur # 264 # 30 # # 26 # 40 # # 5 9 # In cauda Lacteum circulum attingens # 255 # 30 # # 36 # 20 # # 3 # # * ########## Omnes ſtellæ 9. Secundæ magnit. 1. Tertiæ 4. Quartæ 1. Quintæ 3. ########## INFORMES CIRCA AQVILAM, QVÆ ########## conſtituunt Antinoum. 1 # A capite in Auſtrum præcedens # 272 # 0 # # 21 # 40 # # 3 2 # Quæ ſequitur # 272 # 20 # # 59 # 10 # # 3 # # * 3 # In humero dextro uerſus Aſricum # 259 # 20 # # 25 # 0 # # 4 </note> <pb o="160" file="196" n="197" rhead="Comment. in I. Cap. Sphæræ"/> <note position="left" xml:space="preserve">Delphinus.</note> <note position="right" xml:space="preserve"> <lb/># ## FORMÆ STELLARVM ## Longit. ## Latit. ## Magni- \\ tudo. <lb/># # # G. # M. # G. # M. <lb/># 4 # Ad Auſtrum # 261 # 30 # 20 # 0 # 3 <lb/># 5 # Magis ad Auſtrum # 263 # 0 # 15 # 30 # 5 <lb/># 6 # Quæ pręcedit omnes # 254 # 30 # 18 # 10 # 3 <lb/>######### Omnes ſtellę 6. Tertiæ magnit. 4. Quartæ 1. \\ Quintæ 1. <lb/> ######### DELPHINVS. \\ Conſtellario XVII. # 1 # In cauda trium præcedens # 281 # 0 # 29 # 10 # 3 # 2 # Reliquarum duarum magis Borea # 282 # 0 # 29 # 0 # 4 # 3 # Auſtralior # 282 # 0 # 26 # 40 # 4 # 4 # In Romboide præcedentis lateris Auſtralior # 281 # 50 # 32 # 0 # 3 # 5 # Eiuſdem lateris Borea # 283 # 30 # 33 # 50 # 3 # 6 # Sequentis lateris Auſtrina # 284 # 40 # 32 # 0 # 3 # 7 # Eiuſdem lateris Borea # 286 # 50 # 33 # 10 # 3 * # 8 # Inter caudam & rhombum trium Septẽtrionalior # 280 # 50 # 34 # 15 # 6 * # 9 # Cæterarum duarum in auſtrum præcedens # 280 # 50 # 31 # 50 # 6 # 10 # Quæ ſequitur # 282 # 20 # 31 # 30 # 6 ######### Omnes ſtellæ 10. Tertiæ magnit 5. Quartę 2. Sextæ 3.</note> <note position="left" xml:space="preserve">@quiculus.</note> <note position="left" xml:space="preserve"> ######### EQVISECTIO, SIVE EQVICVLVS. \\ Conſtellatio XVIII. # 1 # In capite duarum præcedens # 289 # 40 # 20 # 30 # obſc. * # 2 # Sequens # 281 # 20 # 20 # 40 # obſc. # 3 # in ore duarum præcedens # 289 # 40 # 25 # 30 # obſc. # 4 # Quæ ſequitur # 191 # 0 # 25 # 0 # obſc. ######### Omnes ſtellæ 4. & obſcuræ.</note> <note position="left" xml:space="preserve">@egaſus.</note> <note position="left" xml:space="preserve"> ######### EQVS ALATVS, SEV PEGASVS. \\ Conſtellatio XIX. # 1 # In vmbilico, quæ & in capite Andromedæ # 341 # 10 # 26 # 0 # 2 # 2 # In extrema ala # 335 # 30 # 12 # 30 # 2 # 3 # In dextro humero, & cruris eductione # 325 # 30 # 31 # 0 # 2 # 4 # In ſcapulis, & armo alæ # 320 # 0 # 19 # 40 # 2 # 5 # In corpore duarum ſub ala, quæ Borea # 327 # 50 # 25 # 40 # 4 # 6 # Quæ Auſtralior # 328 # 20 # 25 # 0 # 4 # 7 # In dextro genu duarum Borea # 322 # 10 # 35 # # 3 * # 8 # In auſtrum magis # 311 # 50 # 34 # 30 # 5 # 9 # In pectore duarum propinquarum præcedens # 319 # 30 # 29 # 0 # 4 * # 10 # Sequens # 320 # 20 # 29 # 30 # 4 # 11 # In ceruice duarum præcedens # 312 # 10 # 18 # 0 # 3 # 12 # Sequens # 313 # 50 # 19 # 0 # 5 # 13 # In iuba duarum Auſtralior # 314 # 40 # 15 # 0 # 5 # 14 # Quæ magis in Boream # 313 # 50 # 15 # 0 # 5 </note> <pb o="161" file="197" n="198" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve">Androme-<lb/>da.</note> <note position="right" xml:space="preserve"> <lb/>### FORMÆ STELLARVM ## Longit. ### Latit. ## Magni- \\ tudo. <lb/># # # G. # M. # # G. # M. <lb/>15 # In capite duarum propinquarum Borea # 302 # 40 # # 16 # 50 # # 3 <lb/>16 # Quę magis in Auſtrum # 301 # 20 # # 16 # 0 # # 4 <lb/>17 # In rictu # 298 # 40 # # 21 # 30 # # 3 <lb/>18 # In dextra ſuffragine # 317 # 0 # # 41 # 10 # # 4 <lb/>19 # In ſiniſtro genu # 311 # 0 # # 34 # 15 # # 4 <lb/>20 # In ſiniſtra ſuffragine # 305 # 40 # # 36 # 30 # # 4 <lb/>########## Omnes ſtellæ 20. Secundæ magnit. 4. Tertiæ 4. \\ Quartæ 9. Quintæ 3. <lb/>########## ANDROMEDA. Conſtellatio XX. <lb/> 1 # Quę in capite, & etiam in umbilico Pegaſi # 341 # 10 # # 26 # 0 # # 2 2 # Quæ in ſcapulis # 348 # 40 # # 24 # 30 # # 3 3 # In dextro humero # 349 # 40 # # 27 # 0 # # 4 4 # In ſiniſtro humero # 347 # 40 # # 23 # 0 # # 4 5 # In dextro Brachio trium Auſtralior # 347 # 0 # # 32 # 0 # # 4 6 # Quę magis in Boream # 348 # 0 # # 33 # 30 # # 4 7 # Media trium # 348 # 20 # # 32 # 20 # # 5 8 # In ſumma manu dextra trium Auſtralior # 343 # 0 # # 41 # 0 # # 4 9 # Media earum # 344 # 0 # # 42 # 0 # # 4 10 # Borea trium # 345 # 30 # # 44 # 0 # # 4 11 # In ſiniſtro brachio # 347 # 30 # # 17 # 30 # # 4 12 # In ſiniſtro cubito # 349 # 0 # # 15 # 50 # # 3 13 # In cingulo trium Auſtralis # 357 # 10 # # 25 # 20 # # 3 14 # Media # 355 # 10 # # 30 # 0 # # 3 15 # Septentrionalis trium # 355 # 20 # # 32 # 30 # # 3 16 # In pede ſiniſtro # 10 # 10 # # 23 # 0 # # 3 17 # In dextro pede # 10 # 30 # # 37 # 20 # # 4 18 # Auſtralior ab hac # 9 # 30 # # 35 # 20 # # 4 # * 19 # Sub poplite ſiniſtro duarum Borea # 5 # 40 # # 29 # 0 # # 4 # * 20 # Auſtrina # 5 # 20 # # 28 # 0 # # 4 21 # In dextro genu # 3 # 30 # # 35 # 30 # # 5 # * 22 # In ſyrmate, ſiue tractu duarum Borea # 6 # 0 # # 34 # 30 # # 5 23 # Auſtrina # 7 # 30 # # 32 # 30 # # 5 24 # A dextra manu excedens, & informis # 335 # 0 # # 44 # 0 # 3 # * ########## Omnes ſtellæ præter primam, 23. Tertiæ magnit. 7. \\ Quartæ 12. Quintæ 4.</note> <note position="right" xml:space="preserve">T@iangulũ.</note> <note position="right" xml:space="preserve"> ########## TRIANGVLVM, SIVE DELTOTON. \\ Conſtellatio XXI. 1 # In apice trianguli # 4 # 20 # # 16 # 30 # # 3 2 # In baſi pręcedens trium # 9 # 20 # # 20 # 40 # # 3 3 # Media # 9 # 30 # # 19 # 40 # # 4 4 # Sequens trium # 10 # 10 # # 19 # 0 # # 3 ########## Omnes ſtellę 4. Tertiæ magnitud. 3. Quartæ 1. </note> <pb o="162" file="198" n="199" rhead="Comment. in I. Cap. Sphæræ"/> <note position="left" xml:space="preserve">Ares.</note> <note position="right" xml:space="preserve"> <lb/>########## IGITVR In plaga Septentrionali ſtellæ omnes 360. Primæ magnit. 3. <lb/>Secundæ 18. Tertiæ 84. Quartæ 174. Quintæ 58. Sextæ 13. Nebuloſa 1. Ob-<lb/>ſcuræ 9. <lb/>########## TABVLÆ SECVNDA PARS COMPLECTENS <lb/>nomina omnium conſtellationum, quæ in Zodiaco reperiuntur, <lb/>unà cum numero, ordine, longitudinibus, lati-<lb/>tudinibus, atque magnitudini-<lb/>bus ſtellarum. <lb/># ## FORMÆ STELLARVM ## Longit. ### Latit. ### Magni- \\ tudo. <lb/># # # G. # M. # G. # ## M. <lb/>########## ARIES. Conſtellatio XXII. <lb/> # 1 # In cor@u duarũ p̃cedens, & prima omnium # 0 # 0 # # 7 # 20 # # 3 # Bor. # 2 # Sequens in cornu # 1 # 0 # # 8 # 10 # # 3 # Bor. # 3 # In rictu duarum Borea # 4 # 20 # # 7 # 40 # # 5 # Bor. * # 4 # Quę magis in auſtrum # 4 # 50 # # 6 # 0 # # 5 # Bor. # 5 # In ceruice # 259 # 50 # # 5 # 30 # # 5 # Bor. # 6 # In renibus # 10 # 50 # # 6 # 0 # # 6 # Bor. # 7 # Quę in eductione caudæ # 14 # 40 # # 4 # 50 # # 5 # Bor. # 8 # In cauda trium præcedens # 17 # 10 # # 1 # 40 # # 4 # Bor. # 9 # Media # 18 # 40 # # 2 # 30 # # 4 # Bor. # 10 # Sequens trium # 20 # 20 # # 1 # 50 # # 4 # Bor. # 11 # In coxendice # 13 # 0 # # 1 # 10 # # 5 # Bor. # 12 # In poplite # 11 # 20 # # 1 # 30 # # 5 # Bor. * # 13 # In extremo pede poſteriore # 8 # 20 # # 5 # 15 # # 4 # Bor. ########## Omnes ſtellæ 13. Tertiæ magnit. 2. Quartæ 4. \\ Quintæ 6. Sextæ 1. ########## INFORMES CIRCA ARIETEM. * # 1 # Quę ſupra caput # 3 # 45 # # 10 # 0 # # 3 # Bor. # 2 # Supra dorſum # 15 # 0 # # 10 # 10 # # 4 # Bor. # 3 # Reliquarum trium paruarum Borea # 14 # 40 # # 12 # 40 # # 5 # Bor. # 4 # Media # 13 # 0 # # 10 # 40 # # 5 # Bor. # 5 # Auſtralis earum # 12 # 30 # # 10 # 40 # # 5 # Bor. ########## Omnes ſtellæ 5. Tertiæ magnit. 1. Quartę 1. Quintæ 4.</note> <note position="left" xml:space="preserve">Taurus.</note> <note position="left" xml:space="preserve"> ########## TAVRVS Conſtellatio XXIII. # 1 # In ſectione ex quatuor maxime Borea # 19 # 40 # # 6 # 0 # # 4 # Auſt. # 2 # Altera poſt ipſam # 19 # 20 # # 7 # 15 # # 4 # Auſt. # 3 # Tertia # 18 # 0 # # 8 # 30 # # 4 # Auſt. # 4 # Quarta maxima Auſtrina # 17 # 50 # # 9 # 15 # # 4 # Auſt. # 5 # In dextro armo # 23 # 0 # # 9 # 30 # # 5 # Auſt. # 6 # In pectore # 27 # 0 # # 8 # 0 # # 3 # Auſt. </note> <pb o="163" file="199" n="200" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve"> <lb/>## FORMÆ STELLARVM ### Longit. ### Latit. ## Magni- \\ tudo. <lb/># # G. # M. # # G. # ## M. <lb/>7 # In dextro genu # 30 # 0 # # 12 # 40 # # 4 # Auſt. <lb/>8 # In ſuffragine dextra # 26 # 20 # # 14 # 50 # # 4 # Auſt. <lb/>9 # In ſiniſtro genu # 35 # 30 # # 10 # 0 # # 4 # Auſt. <lb/>10 # In ſiniſtra ſuffragino # 36 # 20 # # 12 # 30 # # 4 # Auſt. <lb/>11 # In facie quinq; quæ Succulæ uocãtur, quæ # 32 # 0 # # 5 # 45 # # 3 # Auſt. <lb/>12 # Inter hanc & Boreum oculum (in narib. # 33 # 40 # # 4 # 15 # # 3 # Auſt. <lb/>13 # Inter eandem, & oculum Auſtralem # 34 # 10 # # 5 # 50 # # 3 # Auſt. # * <lb/>14 # In ipſo oculo lucẽs ſubruffa, dicta oculus. ♉ # 36 # 0 # # 5 # 10 # # 1 # Auſt. <lb/>15 # In oculo Boreo # 35 # 10 # # 3 # 0 # # 3 # Auſt. <lb/>16 # Quæ inter originẽ Auſtralis cornu, & aurẽ # 40 # 30 # # 4 # 0 # # 4 # Auſt. <lb/>17 # In eodem cornu duarum Auſtralior # 43 # 40 # # 5 # 0 # # 4 # Auſt. <lb/>18 # Quæ magis in Boream # 43 # 20 # # 3 # 30 # # 5 # Auſt. <lb/>19 # In extremo eiuſdem # 50 # 30 # # 2 # 30 # # 3 # Auſt. <lb/>20 # In origine cornu Septentrionalis # 40 # 0 # # 4 # 0 # # 4 # Bor. # * <lb/>21 # In extremo eiuſdem, quæq́; in dextro pede # 49 # 0 # # 5 # 0 # # 5 # Bor. <lb/>22 # In aure Borea, duarum Borea (Erichtonij # 35 # 20 # # 4 # 30 # # 5 # Bor. <lb/>23 # Auſtralis earum # 35 # 0 # # 4 # 0 # # 5 # Bor. <lb/>24 # In ceruice duarum exiguarum præcedens # 30 # 20 # # 0 # 40 # # 5 # Bor. <lb/>25 # Quæ ſequitur # 32 # 20 # # 1 # 0 # # 6 # Bor. <lb/>26 # In collo quadrilateri pręcedentiũ Auſtrina # 31 # 20 # # 5 # 0 # # 5 # Bor. <lb/>27 # Eiuſdem lateris Borea # 32 # 0 # # 7 # 10 # # 5 # Bor. <lb/>28 # Sequentis lateris Auſtralis # 35 # 20 # # 3 # 0 # # 5 # Bor. <lb/>29 # Huius lateris Borea # 35 # 0 # # 5 # 0 # # 5 # Bor. <lb/>30 # Pleiadũ p̃cedentis lateris Boreus terminus # 25 # 30 # # 4 # 30 # # 5 # Bor. <lb/>31 # Eiuſdem lateris Auſtralis terminus # 25 # 50 # # 3 # 40 # # 5 # Bor. # * <lb/>32 # Pleiadum ſequens anguſtiſſimus terminus # 27 # 0 # # 3 # 20 # # 5 # Bor. # * <lb/>33 # Exigua Pleiadum, & ab extremis ſecta # 26 # 0 # # 5 # 0 # # 5 # Bor. # * <lb/>########## Omnes ſtellæ præter eam, quæ in extremo cornu Boreo, 32. Primæ \\ magnit. 1. Tertiæ 6. quartæ 11. Quintæ 13. Sextæ 1. <lb/>########## INFORMES CIRCA TAVRVM. <lb/>1 # Infra pedem, & armum dextrum # 18 # 40 # # 17 # 30 # # 4 # Auſt. <lb/>2 # Circa Auſtrinum cornu præcedens trium # 43 # 20 # # 2 # 0 # # 5 # Auſt. # * <lb/>3 # Media trium # 47 # 20 # # 1 # 45 # # 5 # Auſt. <lb/>4 # Sequens trium # 49 # 20 # # 2 # 0 # # 5 # Auſt. <lb/>5 # Sub extremo eiuſdẽ cornu duarum Borea # 52 # 20 # # 6 # 20 # # 5 # Auſt. <lb/>6 # Auſtrina # 52 # 20 # # 7 # 40 # # 5 # Auſt. <lb/>7 # Sub Boreo cornu, quinque præcedens # 50 # 20 # # 2 # 40 # # 5 # Bor. <lb/>8 # Altera ſequens # 52 # 20 # # 1 # 0 # # 5 # Bor. <lb/>9 # Tertia ſequens # 54 # 20 # # 1 # 20 # # 5 # Bor. <lb/>10 # Reliquarum duarum, quæ Borea # 55 # 40 # # 3 # 20 # # 5 # Bor. <lb/>11 # Quæ Auſtralis # 56 # 40 # # 1 # 15 # # 5 # Bor. <lb/></note> <pb o="164" file="200" n="201" rhead="Comment. in I. Cap. Sphæræ"/> <note position="left" xml:space="preserve">@emini</note> <note position="right" xml:space="preserve"> <lb/># ## FORMÆ STELLARVM ### Longit. ### Latit. ## Magni- \\ tudo. <lb/># # # G. # M. # # G. # M. <lb/>########## Omnes ſtellæ 11. Quartæ magnit. 1. Quintæ 10. <lb/>########## GEMINI. Conſtellatio XXIIII. <lb/> # 1 # In capite Gemini præcedentis. Caſtoris # 76 # 40 # # 9 # 30 # # 2 # Bor. # 2 # In capite Gemini ſequẽtis ſubflaua. Pollucis # 79 # 50 # # 6 # 15 # # 2 # Bor. # 3 # In ſiniſtro cubito Gemini præcedentis # 70 # 0 # # 10 # 0 # # 4 # Bor. # 4 # In eodem brachio # 72 # 0 # # 7 # 20 # # 4 # Bor. # 5 # In ſcapulis eiuſdem Gemini # 75 # 20 # # 5 # 30 # # 4 # Bor. # 6 # In dextro humero eiuſdem # 77 # 20 # # 4 # 50 # # 4 # Bor. # 7 # In ſiniſtro humero ſequentis Gemini # 80 # 0 # # 2 # 40 # # 4 # Bor. # 8 # In dextro latere antecedentis Gemini # 75 # 0 # # 2 # 40 # # 5 # Bor. # 9 # In ſiniſtro latere ſequentis Gemini # 76 # 30 # # 3 # 0 # # 5 # Bor. # 10 # In ſiniſtro genu præcedentis Gemini # 66 # 30 # # 1 # 30 # # 3 # Bor. # 11 # In ſiniſtro genu ſequentis # 71 # 40 # # 2 # 30 # # 3 # Auſt. # 12 # In ſiniſtro bubone eiuſdem # 75 # 0 # # 0 # 30 # # 3 # Auſt. * # 13 # In cauitate dextra eiuſdem # 74 # 40 # # 6 # 40 # # 3 # Auſt. # 14 # In pede præcedentis Gemini, præcedens # 60 # 0 # # 1 # 30 # # 4 # Auſt. # 15 # In eodem pede ſequens # 61 # 30 # # 1 # 15 # # 4 # Auſt. # 16 # In extremo præcedentis Gemini. Propus # 63 # 30 # # 3 # 30 # # 4 # Auſt. * # 17 # In ſummo pede ſiniſtro ſe quentis Gemini # 65 # 20 # # 7 # 30 # # 3 # Auſt. * # 18 # In inſimo pedis dextri eiuſdem Gemini # 68 # 0 # # 10 # 30 # # 4 # Auſt. ########## Omnes ſtellæ 18. Secundæ magnit. 2. Tertiæ 5. \\ Quartæ 9. Quintæ 2. ########## INFORMES CIRCA GEMINOS. # 1 # Pręcedens ad ſummum pedem Gemini prę # 57 # 30 # # 0 # 40 # # 4 # Auſt. * # 2 # Quæ ante genu eiuſdem lucet (cedentis # 59 # 50 # # 5 # 50 # # 4 # Bor. # 3 # Antecedens genu ſiniſtrũ ſequentis Gemini # 68 # 30 # # 2 # 15 # # 5 # Auſt. # 4 # Sequentium dextrã manum Gemini ſequẽ # 81 # 40 # # 1 # 20 # # 5 # Auſt. # 5 # Media (tis trium Borea # 79 # 40 # # 3 # 20 # # 5 # Auſt. # 6 # Auſtralis trium # 79 # 20 # # 4 # 30 # # 5 # Auſt. # 7 # Lucida ſequens tres # 84 # 0 # # 2 # 40 # # 4 # Auſt. ########## Omnes ſtellæ 7. Quartæ magnit. 3. Quintæ 4.</note> <note position="left" xml:space="preserve">Gen@@@.</note> <note position="left" xml:space="preserve"> ########## CANCER. Conſtellatio XXV. # 1 # In pectore nebuloſa media, q̃ præſepe vocat̃ # 93 # 40 # # 0 # 40 # ## neb. # Bor. # 2 # Quadrilateri duarum præcedentium Borea # 91 # 0 # # 1 # 15 # # 4 # Bor. * # 3 # Auſtrina # 91 # 20 # # 1 # 10 # # 4 # Auſt. # 4 # Sequentiũ duarũ, quæ uocãtur Aſini, Borea # 93 # 40 # # 2 # 40 # # 4 # Bor. # 5 # Auſtralis aſinus # 94 # 40 # # 0 # 10 # # 4 # Auſt. # 6 # In Chele, ſeu brachio Auſtrino # 99 # 50 # # 5 # 30 # # 4 # Auſt. # 7 # In brachio ſeptentrionali # 91 # 40 # # 11 # 50 # # 4 # Bor. # 8 # In extremo pedis Borei # 86 # 0 # # 1 # 0 # # 5 # Bor. # 9 # In extremo pedis Auſtrini # 90 # 30 # # 7 # 30 # # 4 # Auſt. </note> <pb o="165" file="201" n="202" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve">Leo.</note> <note position="right" xml:space="preserve"> <lb/>## FORMÆ STELLARVM ## Longit. ### Latit. ### Magni- \\ tudo. <lb/># # # G. # M. # G. # M. <lb/>########## Omnes ſtellæ 9. Quartæ magnit. 7. Quintæ 1. Nebuloſa 1. <lb/>########## INFORMES CIRCA CANCRVM. <lb/>1 # Supra cubitum Auſtralis Cheles # 103 # 0 # 2 # 40 # 4 # Auſt. <lb/>2 # Sequens ab extremo eiuſdem Cheles # 105 # 0 # 5 # 40 # 4 # Auſt. <lb/>3 # Supra nubeculam duarum præcedens # 97 # 20 # 4 # 50 # 5 # Bor. <lb/>4 # Sequens hanc # 100 # 20 # 7 # 15 # 5 # Bor. <lb/>########## Omnes ſtellæ 4. Quartæ magnit. 2. Quintæ 2. <lb/>########## LEO. Conſtellatio XXVI. <lb/> 1 # In naribus # 101 # 40 # 10 # 0 # 4 # Bor. 2 # In hiatu # 104 # 30 # 7 # 30 # # Bor. 3 # In capite duarum Borea # 107 # 40 # 12 # 0 # # Bor. 4 # Auſtralis # 107 # 30 # 9 # 30 # 3 # Bor. 5 # In ceruice trium Borea # 113 # 30 # 11 # 0 # 3 # Bor. 6 # Media # 115 # 30 # 8 # 30 # 2 # Bor. 7 # Auſtralis trium # 114 # 0 # 4 # 30 # 3 # Bor. 8 # In corde. Baſiliſcus, ſeu Regulus. Cor ♌ # 115 # 50 # 0 # 10 # 1 # Bor. 9 # In pectore duarum Auſtrina # 116 # 50 # 1 # 50 # 4 # Auſt. 10 # Antecedens parum eam, quæ in corde # 113 # 20 # 0 # 15 # 5 # Auſt. 11 # In genu dextro priori # 110 # 40 # 0 # 0 # 5 # Auſt. 12 # In drace dextra priori # 107 # 30 # 3 # 40 # 6 # Auſt. 13 # In drace ſiniſtra priori # 110 # 50 # 4 # 10 # 4 # Auſt. # * 14 # In genu ſiniſtro priori # 115 # 30 # 4 # 15 # 4 # Auſt. # * 15 # In ſiniſtra axilla # 122 # 30 # 0 # 10 # 4 # Auſt. 16 # In uentre trium antecedens # 120 # 20 # 4 # 0 # 6 # Bor. 17 # Sequentium duarum Borea # 126 # 20 # 5 # 20 # 6 # Bor. 18 # Quæ Auſtralis # 125 # 40 # 2 # 20 # 6 # Bor. 19 # In lumbis duarum, quæ præit # 124 # 40 # 12 # 15 # 5 # Bor. 20 # Quæ ſequitur # 127 # 30 # 13 # 40 # 2 # Bor. 21 # In clune duarum Borea # 127 # 40 # 11 # 30 # 5 # Bor. # * 22 # Auſtrina # 129 # 40 # 9 # 40 # 3 # Bor. 23 # In poſteriori coxa # 133 # 40 # 5 # 50 # 3 # Bor. 24 # In cauitate # 135 # 0 # 1 # 15 # 4 # Bor. 25 # In poſteriori cubito # 135 # 0 # 0 # 50 # 4 # Auſt. 26 # In pede poſteriori # 140 # 0 # 3 # 0 # 4 # Auſt. 27 # In extremo caudæ # 137 # 50 # 11 # 50 # 1 # Bor. ########## Omnes ſtellæ 27. Primæ magnit. 2. Secundæ 2. Tertiæ 6. ########## Quartæ 8. Quintæ 5. Sextæ 4. ########## INFORMES CIRCA LEONEM. 1 # Supra dorſum duarum præcedens # 119 # 20 # 13 # 20 # 5 # Bor. 2 # Quæ ſequitur # 121 # 30 # 15 # 30 # 5 # Bor. 3 # Sub uentre trium Borea # 129 # 50 # 1 # 10 # 4 # Bor. 4 # Media # 130 # 30 # 0 # 30 # 5 # Auſt. </note> <pb o="166" file="202" n="203" rhead="Comment. in I. Cap. Sphæræ"/> <note position="left" xml:space="preserve">Virgo.</note> <note position="right" xml:space="preserve"> <lb/>## FORMÆ STELLARVM ### Longit. ### Latir. ## Magni- \\ tudo <lb/># # G. # M. # # G. # M. <lb/>* # 5 # Auſtralis trium # 131 # 20 # 2 # 40 # 0 # Auſt. <lb/># 6 # Inter extrema Leonis, & vrſę nebulo ſę in \\ uolutionis quã vocãt Beronices crines \\ quæ maxime Borea # 0 # 0 # 0 # 0 # 0 <lb/># # 0 # 0 # 0 # 0 # 5 <lb/># # 138 # 10 # 30 # 0 # Lumi. <lb/># 7 # Auſtralium duarum præcedens # 137 # 50 # 25 # 0 # obſcu. <lb/>* # 8 # Quæ ſequitur in figura folij hederæ # 141 # 50 # 25 # 30 # obſcu. <lb/>########## Omnes ſtellæ 8. Quartæ magnit. 1. Quintæ 4. \\ luminoſa 1. obſcuræ 2. <lb/>########## VIRGO. Conſtellatio XXVII. <lb/> # 1 # In ſummo capite duarum p̃edẽs Auſtrina # 139 # 40 # 4 # 15 # 5 # Bor. # 2 # Sequens ſeptentrionalior # 140 # 20 # 5 # 40 # 5 # Bor. # 3 # In vultu duarum Borea # 144 # 0 # 8 # 0 # 5 # Bor. # 4 # Auſtralis # 143 # 30 # 5 # 30 # 5 # Bor. * # 5 # In extremo alæ ſiniſtræ, & Auſtrinæ # 142 # 20 # 0 # 9 # 3 # Bor. # 6 # Earũ, q̃ in ſiniſtra ala, quatuor præcedens # 151 # 30 # 1 # 10 # 3 # Bor. # 7 # Altera ſequens # 156 # 30 # 2 # 50 # 3 # Bor. # 8 # Tertia # 160 # 30 # 2 # 50 # 5 # Bor. # 9 # Vltima quatuor ſequens # 164 # 20 # 1 # 40 # 4 # Bor. # 10 # In dextro latere ſub cingulo # 157 # 40 # 8 # 30 # 3 # Bor. # 11 # In dextra, & Borea ala trium præcedens # 151 # 30 # 13 # 50 # 5 # Bor. # 12 # Reliquarum duarum Auſtrina # 153 # 30 # 11 # 40 # 6 # Bor. # 13 # Ipſarum Borea uocata uindemiator # 155 # 30 # 15 # 10 # 5 # Bor. # 14 # In ſiniſtra manu, quæ ſpica ♍ uocatur # 170 # 0 # 2 # 0 # 1 # Auſt. # 15 # Sub perizomate, & in clune dextra # 168 # 10 # 8 # 40 # 3 # Bor. # 16 # In ſiniſtra coxa quadrifateri, præcedentiũ \\ (Borea # 169 # 40 # 2 # 20 # 5 # Bor. # 17 # Auſtralis # 170 # 20 # 0 # 10 # 6 # Bor. # 18 # Sequentium duarum Borea # 173 # 20 # 1 # 30 # 4 # Bor. # 19 # Auſtrina # 171 # 20 # 0 # 20 # 5 # Bor. # 20 # In genu ſiniſtro # 175 # 0 # 1 # 30 # 5 # Bor. # 21 # In poſtremo coxæ dextræ # 171 # 20 # 8 # 80 # 5 # Bor. # 22 # In ſyrmate, quæ media # 180 # 0 # 7 # 30 # 4 # Bor. # 23 # Quæ Auſtrina # 180 # 40 # 2 # 40 # 4 # Bor. # 24 # Quæ Borea # 181 # 40 # 11 # 40 # 4 # Bor. # 25 # In ſiniſtro, & Auſtrino pede # 183 # 20 # 0 # 30 # 4 # Bor. # 26 # In dextro & Boreo pede # 186 # 0 # 9 # 50 # 3 # Bor. ########## Omnes ſtellæ 26. Primæ magnit. 1. Tertiæ 6. Quartæ 6. \\ Quintæ 11. Sextæ 2. ########## INFORMES CIRCA VIRGINEM. # 1 # Sub brachio ſiniſtro in directũ triũ p̃cedẽs # 158 # 0 # 3 # 30 # 5 # Auſt. # 2 # Media # 162 # 20 # 3 # 30 # 5 # Auſt. # 3 # Sequens (præcedens # 165 # 40 # 3 # 30 # 5 # Auſt. # 4 # Sub ſpica tanquam in lineam rectam triũ # 170 # 30 # 7 # 20 # 6 # Auſt. </note> <pb o="167" file="203" n="204" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve">Libra<unsure/>.</note> <note position="right" xml:space="preserve"> <lb/>## FORMÆ STELLARVM ## Longit. ### Latit. ### Magni- \\ tudo. <lb/># # G. # M. # # G. # M. <lb/>5 # Media earum, quę & dupla # 171 # 30 # 8 # 20 # 5 # Auſt. <lb/>6 # Sequens ex tribus # 173 # 20 # 7 # 50 # 6 # Auſt. <lb/>########## Omnes ſtellę 6. Quintę magnit. 4. Sextæ 2. <lb/>########## LIBRA. Conſtellatio XXVIII. <lb/> 1 # In extrema Auſtrina Chele duarum lucẽs # 191 # 20 # 0 # 40 # 2 # Bor. 2 # Cbſcurior in Borea m # 190 # 20 # 2 # 20 # 5 # Bor. 3 # In extrema Borea C hele duarum lucens # 195 # 30 # 8 # 30 # 2 # Bor. 4 # Obſcurior præcedens hanc # 191 # 0 # 8 # 30 # 5 # Bor. 5 # In medio Cheles Auſtriuę # 197 # 20 # 1 # 40 # 4 # Bor. 6 # In eadem, quę pręit # 194 # 50 # 1 # 15 # 4 # Bor. 7 # In media Chela Borea # 200 # 50 # 3 # 45 # 4 # Bor. 8 # In eadem, quæ ſequitur # 206 # 0 # 4 # 30 # 4 # Bor. ########## Omnes ſtellę 8. Secundæ magnit. 2. Quartę 4. Quintæ 2. ########## INFORMES CIRCA LIBRAM. 1 # In boream à Chele Borea trium pręcedens # 199 # 30 # 9 # 0 # 5 # Bor. 2 # Sequentium duarum Auſtralis # 207 # 0 # 6 # 40 # 4 # Bor. 3 # Borea ipſatum # 207 # 40 # 9 # 15 # 4 # Bor. 4 # Inter Chelas ex tribus, quæ ſequitur # 205 # 50 # 5 # 30 # 6 # Bor. 5 # Reliquarum duarum pręcedentium Borea # 203 # 40 # 2 # 0 # 4 # Bor. 6 # Quæ Auſtralis # 204 # 30 # 1 # 30 # 5 # Bor. 7 # Sub Auſtrina Chele trium pręceden # 196 # 20 # 7 # 30 # 3 # Bor. 8 # Reliquarum ſequentium duarum Borea # 204 # 30 # 8 # 10 # 4 # Auſt. 9 # Auſtralis # 205 # 10 # 9 # 40 # 4 # Auſt. ########## Omnes ſtellæ 9. Tertię magnit. 1. quartæ 5. Quintę 2. Sextæ 1.</note> <note position="right" xml:space="preserve">Scorpius.</note> <note position="right" xml:space="preserve"> ########## SCORPIVS. Conſtellatio XXIX. 1 # In fronte lucentium trium Borea # 209 # 40 # 1 # 20 # 3 # Bor. 2 # Media # 209 # 0 # 1 # 40 # 3 # Auſt. 3 # Auſtralis trium # 209 # 0 # 5 # 0 # 3 # Auſt. 4 # Quæ magis ad auſtrum, & in pede # 209 # 20 # 7 # 50 # 3 # Bor. 5 # Duarum coniunctarum fulgens Borea # 210 # 20 # 1 # 40 # 4 # Bor. 6 # Auſtralis # 210 # 40 # 0 # 30 # 4 # Auſt. 7 # In corpore trium lucidarum præcedens # 214 # 0 # 3 # 40 # 3 # Auſt. 8 # Media Rutilans. Antares uocata. Cor ♍. # 216 # 0 # 4 # 0 # 2 # Auſt. 9 # Sequens trium # 217 # 50 # 5 # 30 # 3 # Auſt. 10 # In ultimo acetabulo duarum præcedens # 212 # 40 # 6 # 10 # 5 # Auſt. 11 # Sequens # 213 # 50 # 6 # 40 # 5 # Auſt. 12 # In primo corporis ſpondylo # 221 # 50 # 11 # 0 # 3 # Auſt. 13 # In ſecundo ſpondylo # 222 # 10 # 15 # 0 # 4 # Auſt. 14 # In tertio duplicis Auſtrina # 223 # 20 # 18 # 40 # 4 # Auſt. # * 15 # Borea duplicis # 223 # 30 # 18 # 0 # 3 # Auſt. # * 16 # In quarto ſpondylo # 226 # 30 # 19 # 30 # 3 # Auſt. </note> <pb o="168" file="204" n="205" rhead="Comment. in I. Cap. Sphæræ"/> <note position="left" xml:space="preserve">Sagittarius.</note> <note position="right" xml:space="preserve"> <lb/>### FORMÆ STELLARVM ## Longit. ### Latit. ## Magni- \\ tudo. <lb/># # # G. # M. # G. # M. <lb/># 17 # In quinto # 231 # 30 # 18 # 50 # 3 # Auſt. <lb/># 18 # In ſexto ſpondylo # 233 # 50 # 16 # 40 # 3 # Auſt. <lb/># 19 # In ſeptimo, quæ proxima aculeo # 232 # 20 # 15 # 20 # 3 # Auſt. <lb/># 20 # In ipſo aculeo duarum ſequens # 230 # 50 # 13 # 50 # 3 # Auſt. <lb/># 21 # Antecedens # 230 # 20 # 13 # 20 # 4 # Auſt. <lb/>########## Omnes ſtellæ 21. Secundæ magnit. 1. Tertię 13. Quartæ 5. Quintę 2. <lb/>########## INFORMES CIRCA SCORPIVM <lb/># 1 # Nebuloſa ſequens aculeum # 234 # 30 # 13 # 15 # ## neb. Auſt. <lb/># 2 # Ab aculeo in Boream duarum ſequens # 228 # 50 # 6 # 10 # 5 # Auſt. <lb/># 3 # Quæ ſequitur # 232 # 50 # 4 # 10 # 5 # Auſt. <lb/>########## SAGITARIVS. Conſtellatio XXX: <lb/> # 1 # In cuſpide ſagittę # 237 # 50 # 6 # 30 # 3 # Auſt. # 2 # In manubrio ſiniſtræ manus # 241 # 0 # 6 # 30 # 3 # Auſt. # 3 # In Auſtrali parte arcus # 241 # 20 # 10 # 50 # 3 # Auſt. # 4 # In ſeptentrionali duarum Auſtralior # 242 # 20 # 1 # 30 # 3 # Auſt. # 5 # Magis in Boream in extremitate arcus # 240 # 0 # 2 # 50 # 4 # Bor. # 6 # In humero ſiniſtro # 248 # 40 # 3 # 10 # 3 # Auſt. # 7 # Antecedens hanc in iaculo # 246 # 20 # 3 # 50 # 4 # Auſt. # 8 # In oculo nebuloſa duplex # 248 # 30 # 0 # 45 # ## neb. Bor. # 9 # In capite trium, quę anteit # 249 # 0 # 2 # 10 # 4 # Bor. # 10 # Media # 251 # 0 # 1 # 30 # 4 # Bor. # 11 # Sequens # 252 # 30 # 2 # 0 # 4 # Bor. # 12 # In boreo contactu trium Auſtralior # 254 # 40 # 2 # 50 # 4 # Bor. # 13 # Media # 255 # 40 # 4 # 30 # 4 # Bor. # 14 # Borea trium # 256 # 10 # 6 # 30 # 4 # Bor. # 15 # Sequens tres obſcura # 259 # 0 # 5 # 30 # 6 # Bor. # 16 # In Auſtrali contactu duarum Borea # 262 # 50 # 5 # 0 # 5 # Bor. # 17 # Auſtralis # 261 # 0 # 2 # 0 # 5 # Bor. # 18 # In humero dextro # 255 # 40 # 1 # 50 # 5 # Auſt. # 19 # In dextro cubito # 258 # 10 # 2 # 50 # 5 # Auſt. # 20 # In ſcapulis # 253 # 20 # 2 # 30 # 5 # Auſt. # 21 # In armo # 251 # 0 # 4 # 30 # 4 # Auſt. # 22 # Sub axilla # 249 # 40 # 6 # 45 # 3 # Auſt. # 23 # In ſuffragine finiſtra priori # 251 # 0 # 23 # 0 # 2 # Auſt. # 24 # In genu eiuſdem cruris # 250 # 20 # 18 # 0 # 2 # Auſt. # 25 # In priori dextra ſuffragine # 240 # 0 # 13 # 0 # 3 # Auſt. # 26 # In ſiniſtra ſcapula # 160 # 40 # 13 # 30 # 3 # Anſt. * # 27 # In poſteriori @extro genu (pręcedens # 260 # 0 # 20 # 10 # 3 # Auſt. # 28 # In eductione caudę quatuor Borei lateris # 261 # 0 # 4 # 50 # 5 # Auſt. * # 29 # Sequens eiuſdem lateris # 261 # 50 # 4 # 50 # 5 # Auſt. * # 30 # Auſtrini lateris præcedens # 261 # 50 # 5 # 50 # 5 # Auſt. # 31 # Sequens eiuſdem lateris # 262 # 50 # 6 # 30 # 5 # Auſt. </note> <pb o="169" file="205" n="206" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve">Capricor-<lb/>nus.</note> <note position="right" xml:space="preserve"> <lb/>### FORMÆ STELLARVM ## Longit. ### Latit. ## Magni- \\ tudo. <lb/># # # G. # M. # G. # M. <lb/>########## Omnes ſtellæ 31. Secundæ magnit. 2. Tertiæ 9. Quartæ 9. <lb/>########## Quintæ 8. Sextæ 2. Nebuloſa 1. <lb/>########## CAPRICORNVS <lb/> ########## Conſtellatio XXXI. 1 # In pręcedenti cornu trium Borea # 270 # 40 # 7 # 30 # 3 # Bor. 2 # Media # 271 # 0 # 6 # 40 # 6 # Bor. 3 # Auſtralis trium # 270 # 40 # 5 # 0 # 3 # Bor. 4 # In extremo ſequentis cornu # 272 # 20 # 8 # 0 # 6 # Bor. 5 # In rictu trium Auſtralis # 272 # 20 # 0 # 45 # 6 # Bor. 6 # Reliquarum duarum præcedens # 272 # 0 # 1 # 45 # 6 # Bor. 7 # Sequens # 272 # 10 # 1 # 30 # 6 # Bor. 8 # Super oculum dextrum # 270 # 30 # 0 # 40 # 5 # Bor. # * 9 # In ceruice duarum Borea # 275 # 0 # 4 # 50 # 6 # Bor. 10 # Auſtralis # 275 # 10 # 0 # 50 # 5 # Auſt. 11 # In dextro genu # 275 # 0 # 6 # 30 # 4 # Auſt. # * 12 # In ſiniſtro genu ſubfracto # 274 # 10 # 8 # 40 # 4 # Auſt. # * 13 # In ſiniſtro humero # 280 # 0 # 7 # 40 # 4 # Auſt. 14 # Sub aluo duarum contiguarum pręcedens # 283 # 30 # 6 # 50 # 4 # Auſt. 15 # Sequens # 283 # 40 # 6 # 0 # 5 # Auſt. 16 # In medio corpore trium ſequens # 282 # 0 # 4 # 15 # 5 # Auſt. 17 # Reliquarum pręcedentium Auſtralis # 280 # 0 # 4 # 0 # 5 # Auſt. 18 # Septentrionalis earum # 280 # 0 # 2 # 50 # 5 # Auſt. 19 # In dorſo duarum, quæ anteit # 280 # 0 # 0 # 0 # 4 # Ecli. 20 # Sequens # 284 # 20 # 0 # 50 # 4 # Auſt. 21 # In Auſtrali ſpina antecedens duarum # 286 # 40 # 4 # 45 # 4 # Auſt. 22 # Sequens # 288 # 20 # 4 # 30 # 4 # Auſt. 23 # In eductione caudæ duarum præcedens # 288 # 40 # 2 # 10 # 3 # Auſt. 24 # Sequens # 289 # 40 # 2 # 0 # 3 # Auſt. # * 25 # In Borea parte caudæ quatuor præcedens # 290 # 10 # 2 # 20 # 4 # Bor. # * 26 # Reliquarum trium Auſtralis # 292 # 0 # 5 # 0 # 5 # Bor. # * 27 # Media # 291 # 0 # 2 # 50 # 5 # Bor. 28 # Borea, quæ in extremo caudæ # 292 # 0 # 4 # 20 # 5 # Bor. ########## Omnes ſtellæ 28. Tertiæ magnit. 4. Quartæ 9. Quintæ 9. \\ Sextæ 6.</note> <note position="right" xml:space="preserve">Aquatius.</note> <note position="right" xml:space="preserve"> ########## AQVARIVS. Conſtellatio XXXII. 1 # In capite # 293 # 40 # 15 # 45 # 5 # Bor. 2 # In humero dextro quæ clarior # 299 # 40 # 11 # 0 # 3 # Bor. 3 # Quæ obſcurior # 298 # 30 # 9 # 40 # 5 # Bor. # * 4 # In humero ſiniſtro # 290 # 0 # 8 # 50 # 3 # Bor. 5 # Sub axilla # 290 # 40 # 6 # 15 # 5 # Bor. 6 # Sub ſiniſtra manu in veſte ſequens trium # 280 # 0 # 5 # 30 # 3 # Bor. 7 # Media # 279 # 30 # 8 # 0 # 4 # Bor. </note> <pb o="170" file="206" n="207" rhead="Comment. in I. Cap Sphæræ"/> <note position="right" xml:space="preserve"> <lb/># ## FORMÆ STELLARVM. # ## Longit. # ## Latit. # ## Magni- \\ tudo. <lb/># # # G. # M. # G. # M. <lb/># 8 # Antecedens trium # 278 # 0 # 8 # 30 # 3 # Bor. <lb/>* # 9 # In brachio dextro # 302 # 50 # 8 # 45 # 3 # Bor. <lb/># 10 # In dextra manu, quæ Borea # 303 # 0 # 10 # 45 # 3 # Bor. <lb/># 11 # Reliquarum duarum Auſtr. præcedens # 305 # 20 # 9 # 0 # 3 # Bor. <lb/>* # 12 # Quæ ſequitur # 306 # 40 # 8 # 30 # 3 # Bor. <lb/># 13 # In vaſe duarum propinquarum præcedens # 299 # 30 # 3 # 0 # 4 # Bor. <lb/># 14 # Sequens # 300 # 20 # 2 # 10 # 5 # Bor. <lb/># 15 # In dextro clune # 302 # 0 # 0 # 50 # 4 # Auſt. <lb/># 16 # In ſiniſtro clune duarum Auſtralis # 295 # 0 # 1 # 40 # 4 # Auſt. <lb/># 17 # Septentrionalior # 295 # 30 # 4 # 0 # 6 # Auſt. <lb/># 18 # In dextra tibia Auſtralis # 305 # 0 # 7 # 30 # 3 # Auſt. <lb/># 19 # Borea # 304 # 40 # 5 # 0 # 4 # Auſt. <lb/># 20 # In ſiniſtra coxa # 301 # 0 # 5 # 40 # 5 # Auſt. <lb/># 21 # In ſiniſtra tibia duarum Auſtralis # 300 # 40 # 10 # 0 # 5 # Auſt. <lb/># 22 # Septentrionalis ſub genu # 302 # 10 # 9 # 0 # 5 # Auſt. <lb/># 23 # In profuſione aque à manu prima # 308 # 20 # 2 # 0 # 4 # Bor. <lb/>* # 24 # Sequens<unsure/> Auſtralior # 308 # 10 # 0 # 10 # 4 # Auſt. <lb/># 25 # Quæ ſequitur in primo flexu aquæ # 311 # 0 # 1 # 10 # 4 # Auſt. <lb/># 26 # Sequens hanc # 313 # 20 # 0 # 30 # 4 # Auſt. <lb/># 27 # In altero flexu Auſtralis # 313 # 50 # 1 # 40 # 4 # Auſt. <lb/># 28 # Sequentinm duarum Borea # 312 # 30 # 3 # 30 # 4 # Auſt. <lb/># 29 # Auſtralis # 312 # 50 # 4 # 10 # 4 # Auſt. <lb/># 30 # In Auſtrum auulſa # 314 # 10 # 8 # 15 # 5 # Auſt. <lb/># 31 # Poſt hanc duarum coniunctarũ præcedẽs # 316 # 0 # 11 # 0 # 5 # Auſt. <lb/># 32 # Sequens # 316 # 30 # 10 # 50 # 5 # Auſt. <lb/># 33 # In tertio aquæ flexu Borea trium # 315 # 0 # 14 # 0 # 5 # Auſt. <lb/># 34 # Media # 316 # 0 # 14 # 45 # 5 # Auſt. <lb/># 35 # Sequens trium # 316 # 30 # 15 # 40 # 5 # Auſt. <lb/># 36 # Sequentium exemplo ſimili trium Borea # 310 # 20 # 14 # 10 # 4 # Auſt. <lb/># 37 # Media # 310 # 50 # 15 # 0 # 4 # Auſt. <lb/># 38 # Auſtralis trium # 311 # 40 # 15 # 45 # 4 # Auſt. <lb/># 39 # In ultima inflexione trium præcedens # 305 # 10 # 14 # 50 # 4 # Auſt. <lb/># 40 # Sequentium duarum Auſtralis # 306 # 0 # 15 # 20 # 4 # Auſt. <lb/># 41 # Borea # 306 # 30 # 14 # 0 # 4 # Auſt. <lb/># 42 # Vltima aquę, & in ore piſcis Auſtrini # 300 # 20 # 13 # 0 # 1 # Auſt. <lb/>########### Omnes ſtellę 42. Primę magnit. 1. Tertię 9. Quartę 18. <lb/>########### Quintę 13. Sextę 1. <lb/>########### INFORMES CIRCA AQVARIVM. <lb/># 1 # Sequentium flexum aquę trium pręcedẽs # 320 # 0 # 15 # 30 # 4 # Auſt. <lb/># 2 # Reliquarum duarum Borea # 323 # 0 # 14 # 20 # 4 # Auſt. <lb/># 3 # Auſtralis earum # 322 # 20 # 18 # 15 # 4 # Auſt. <lb/></note> <pb o="171" file="207" n="208" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve">Piſces.</note> <note position="right" xml:space="preserve"> <lb/>## FORMÆ STELLARVM ### Longit. ### Latit. ## Magni- \\ tudo. <lb/># # G. # M. # G. # M. <lb/>########### PISCES. Conſtellatio XXXIII. <lb/> 1 # In ore piſcis antecedentis # 315 # 0 # 9 # 15 # 4 # Bor. 2 # In occipite duarum Auſtral is # 317 # 30 # 7 # 30 # 4 # Bor. 3 # Borea # 319 # 20 # 9 # 20 # 4 # Bor. 4 # In dorſo duarum, quæ præit # 321 # 30 # 9 # 30 # 4 # Bor. 5 # Quæ ſequitur # 324 # 0 # 7 # 30 # 4 # Bor. 6 # In aliud præcedens # 319 # 20 # 4 # 30 # 4 # Bor. 7 # Sequens # 323 # 0 # 2 # 30 # 4 # Bor. 8 # In cauda eiuſdem piſcis # 329 # 20 # 6 # 20 # 4 # Bor. 9 # In lino eius prima à cauda # 334 # 20 # 5 # 45 # 6 # Bor. 10 # Quæ ſequitur # 336 # 20 # 2 # 45 # 6 # Bor. 11 # Poſt hanc trium lucidarum præcedens # 340 # 30 # 2 # 15 # 4 # Bor. 12 # Media # 343 # 50 # 1 # 10 # 4 # Bor. 13 # Sequens # 346 # 20 # 1 # 20 # 4 # Auſt. 14 # In flexura duarum exiguarum Borea # 345 # 40 # 2 # 0 # 6 # Auſt. 15 # Auftralis # 346 # 20 # 5 # 0 # 6 # Auſt. 16 # Poſt inflexionem trium præcedens # 350 # 20 # 2 # 20 # 4 # Auſt. 17 # Media # 352 # 0 # 4 # 40 # 4 # Auſt. 18 # Sequens # 354 # 0 # 7 # 45 # 4 # Auſt. 19 # In nexu amborum linorum # 356 # 0 # 8 # 30 # 3 # Auſt. 20 # In Boreo lino à connexu præcedens # 354 # 0 # 4 # 20 # 4 # Bor. 21 # Poſt hanc trium Auſtralis # 353 # 30 # 1 # 30 # 5 # Bor. 22 # Media # 353 # 40 # 5 # 20 # 3 # Bor. 23 # Borea trium, & eſt in extremitate caudæ # 353 # 50 # 9 # 0 # 4 # Bor. # * 24 # In ore piſcis ſequentis duarum Borea # 355 # 20 # 21 # 45 # 5 # Bor. 25 # Auſtralis # 355 # 0 # 21 # 30 # 5 # Bor. 26 # In capite trium paruarum, quæ ſequitur # 352 # 0 # 20 # 0 # 6 # Bor. 27 # Media # 351 # 0 # 19 # 50 # 6 # Bor. 28 # Quæ præit ex tribus # 350 # 20 # 23 # 0 # 6 # Bor. 29 # In auſtrali ſpina trium præcedens prope cu # 349 # 0 # 14 # 20 # 4 # Bor. 30 # Media # (bitũ Andromedes ſiniſtrũ # 349 # 40 # 13 # 0 # 4 # Bor. 31 # Sequens trium # 351 # 0 # 12 # 0 # 4 # Bor. 32 # In aluo duarum, quæ Borea # 355 # 30 # 17 # 0 # 4 # Bor. 33 # Quæ magis in auſtrum # 352 # 40 # 15 # 20 # 4 # Bor. 34 # In ſpina ſequente prope caudam # 353 # 20 # 11 # 40 # 4 # Bor. ########### Omnes ſtellæ 34. Tertiæ magnit. 2. Quartæ 22. ########### Quintæ 3. Sextæ 7. ########### INFORMES CIRCA PISCES. 1 # In quadrilatero ſub piſce præcedente Borei # 324 # 30 # 2 # 40 # 4 # Auſt. 2 # Quæ ſequitur # (lateris, quæ præit # 325 # 45 # 2 # 30 # 4 # Auſt. 3 # Auſtralis lateris antecedens # 324 # 0 # 5 # 50 # 4 # Auſt. 4 # Sequens # 325 # 40 # 5 # 20 # 4 # Auſt. </note> <pb o="172" file="208" n="209" rhead="Comment. in I. Cap. Sphæræ"/> </div> <div xml:id="echoid-div352" type="section" level="1" n="110"> <head xml:id="echoid-head114" xml:space="preserve">Omnes ſtellæ 4. magnit. Quartæ.</head> <p> <s xml:id="echoid-s7103" xml:space="preserve"><emph style="sc">Itaqve</emph> in Zodiaco ſtellæ omnes 346. </s> <s xml:id="echoid-s7104" xml:space="preserve">Primæ magnitud. </s> <s xml:id="echoid-s7105" xml:space="preserve">5. </s> <s xml:id="echoid-s7106" xml:space="preserve">Secundæ 9. <lb/></s> <s xml:id="echoid-s7107" xml:space="preserve">Tertiæ 64. </s> <s xml:id="echoid-s7108" xml:space="preserve">Quartæ 132. </s> <s xml:id="echoid-s7109" xml:space="preserve">Quintæ 106. </s> <s xml:id="echoid-s7110" xml:space="preserve">Sextæ 27. </s> <s xml:id="echoid-s7111" xml:space="preserve">Nebuloſæ 3. </s> <s xml:id="echoid-s7112" xml:space="preserve">Et coma, quam ſu <lb/>perius Beronices crines diximus appellari. </s> <s xml:id="echoid-s7113" xml:space="preserve">Luminoſa 1. </s> <s xml:id="echoid-s7114" xml:space="preserve">obſcuræ 2. </s> <s xml:id="echoid-s7115" xml:space="preserve">extra nume-<lb/>rum à Conone Mathematico.</s> <s xml:id="echoid-s7116" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s7117" xml:space="preserve">TABVLAE TERTIA PARS COMPLECTENS <lb/>nomina omnium conſtellationum, quæ à Zodiaco ad eius polum <lb/>Auſtralem uergunt, unà cum numero, ordine, lon-<lb/>gitudinibus, latitudinibus, atque ma-<lb/>gnitudinibus ſtellarum</s> </p> <note position="left" xml:space="preserve">Cetus.</note> <note position="right" xml:space="preserve"> <lb/># ## FORMÆ STELLARVM ### Longit. ### Latit. ## Magni- \\ tudo. <lb/># # # G. # M. # G. # M. <lb/>########### CETVS. Conſtellatio XXXIIII. <lb/> # 1 # In extremitate naris # 11 # 0 # 7 # 45 # 4 # 2 # In mandibula trium # 11 # 0 # 11 # 20 # 3 # 3 # Media in ore medio # 6 # 0 # 11 # 30 # 3 # 4 # Præcedens trium in genu # 3 # 50 # 14 # 0 # 3 # 5 # In oculo # 4 # 0 # 8 # 10 # 4 # 6 # In capillamento Borea # 5 # 30 # 6 # 20 # 4 # 7 # In iuba præcedens # 1 # 0 # 4 # 10 # 4 # 8 # In pectore quatuor præcedentium Borea # 355 # 20 # 24 # 30 # 4 # 9 # Auſtralis # 356 # 40 # 28 # 0 # 4 # 10 # Sequentium Borea # 0 # 0 # 25 # 10 # 4 # 11 # Auſtralis # 0 # 20 # 27 # 30 # 3 # 12 # In corpore trium, quæ media # 345 # 20 # 25 # 20 # 3 # 13 # Auſtralis # 346 # 20 # 30 # 30 # 4 # 14 # Borea trium # 348 # 20 # 20 # 30 # 3 # 15 # Ad caudam duarum ſequens # 343 # 0 # 15 # 20 # 3 # 16 # Præcedens # 338 # 20 # 15 # 40 # 3 # 17 # In cauda quadrilateri ſequentium Borea # 335 # 0 # 11 # 40 # 5 # 18 # Auſtralis # 334 # 0 # 13 # 40 # 5 # 19 # Antecedentium reliquarum Borea # 332 # 40 # 13 # 0 # 5 # 20 # Auſtralis # 332 # 20 # 14 # 0 # 5 # 21 # In extremitate ſeptentrionali caudæ # 327 # 40 # 9 # 30 # 3 # 22 # In extremitate Auſtrali caudæ # 329 # 0 # 20 # 20 # 3 ########### Omnes ſtellæ 22. Tertiæ magnit. 10. Quartæ 8. Quintæ 4.</note> <note position="left" xml:space="preserve">Orion.</note> <note position="right" xml:space="preserve"> ########### ORION. Conſtellatio XXXV. # 1 # In capite nebuloſa # 50 # 20 # 16 # 30 # # Neb. # 2 # In humero dextro lucida rubeſcens # 55 # 20 # 17 # 0 # 1 * # 3 # In humero ſiniſtro # 46 # 40 # 17 # 30 # 2 # 4 # Quæ ſequitur hanc # 48 # 20 # 18 # 0 # 4 # 5 # In dextro cubito # 57 # 40 # 14 # 30 # 4 # 6 # In vlna dextra # 59 # 40 # 11 # 50 # 6 # 7 # In manu dextra quatuor Auſtralium ſequẽs # 59 # 50 # 10 # 40 # 4 </note> <pb o="173" file="209" n="210" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve">Eridanus.</note> <note position="right" xml:space="preserve"> <lb/>## FORMÆ STELLARVM ### Longit. ### Latit. ## Magni- \\ tudo. <lb/># # # G. # M. # G. # M. <lb/>8 # Præcedens # 59 # 20 # 9 # 45 # 4 <lb/>9 # Borei lateris ſequens # 60 # 40 # 8 # 15 # 6 <lb/>10 # Præcedens eiuſdem lateris # 60 # 0 # 8 # 15 # 6 # # * <lb/>11 # In colorobo duarum præcedens # 55 # 0 # 3 # 45 # 5 <lb/>12 # Sequens # 57 # 40 # 3 # 15 # 5 <lb/>13 # In dorſo quatuor ad lineam rectam, q̃ ſequit̃ # 50 # 50 # 19 # 40 # 4 <lb/>14 # Secunda præcedens # 49 # 40 # 20 # 0 # 6 <lb/>15 # Tertio præcedens # 48 # 40 # 20 # 20 # 6 <lb/>16 # Quarto loco præcedens # 47 # 30 # 20 # 40 # 5 # # * <lb/>17 # In clypeo maxime Borea ex nouem # 43 # 50 # 8 # 0 # 4 <lb/>18 # Secunda # 42 # 50 # 8 # 10 # 4 <lb/>19 # Tertia # 41 # 20 # 10 # 15 # 4 <lb/>20 # Quarta # 39 # 40 # 12 # 50 # 4 <lb/>21 # Quinta # 38 # 30 # 14 # 15 # 4 <lb/>22 # Sexta # 37 # 50 # 15 # 50 # 3 <lb/>23 # Septima # 38 # 10 # 17 # 10 # 3 <lb/>24 # Octaua # 38 # 40 # 20 # 20 # 3 # # * <lb/>25 # Reliqua ex his maxime Auſtralis # 39 # 40 # 21 # 30 # 3 <lb/>26 # In baltheo ſulgentium trium præcedens # 48 # 40 # 24 # 10 # 2 <lb/>27 # Media # 50 # 40 # 24 # 50 # 2 <lb/>28 # Sequens trium ad lineam rectam # 51 # 40 # 25 # 30 # 2 # # * <lb/>29 # In manubrio enſis # 47 # 10 # 25 # 50 # 3 <lb/>30 # In enſe trium Borea # 50 # 10 # 28 # 40 # 4 <lb/>31 # Media # 50 # 0 # 29 # 30 # 3 <lb/>32 # Auſtralis # 50 # 20 # 29 # 50 # 3 <lb/>33 # In extremo enfis duarum ſequens # 51 # 0 # 30 # 30 # 4 # # * <lb/>34 # Præcedens # 48 # 20 # 30 # 50 # 4 <lb/>35 # In ſiniſtro pede clara, & fluuio communis # 42 # 30 # 31 # 30 # 1 <lb/>36 # In tibia ſiniſtra # 44 # 20 # 30 # 15 # 4 <lb/>37 # In ſiniſtro calcaneo # 46 # 40 # 31 # 10 # 4 <lb/>38 # In dextro genu # 53 # 30 # 33 # 30 # 3 <lb/>########### Omnes ſtellæ 38. Primæ magnit. 2. Secundæ 4. Tertiæ 8. Quartæ 15. <lb/>########### Quintæ 3. Sextæ 5. Nebuloſa 1. <lb/>########### FLVVIVS, SIVE ERIDANVS, VEL NILVS. \\ Conſtellatio XXXVI. <lb/> 1 # Quę à ſinittro pede Orionis ĩ prĩcipio fluuij # 41 # 40 # 31 # 50 # 4 2 # In flexura ad crus Orionis maxime Borea # 42 # 10 # 28 # 15 # 4 3 # Poſt hanc duarum ſequens # 41 # 20 # 29 # 50 # 4 4 # Quæ præit # 38 # 0 # 28 # 15 # 4 5 # Deinde duarum quæ ſequitur # 36 # 30 # 25 # 50 # 4 6 # Quæ præcedit # 33 # 30 # 25 # 20 # 4 # # * 7 # Poſt hæc ſequens trium # 29 # 40 # 26 # 0 # 4 </note> <pb o="174" file="210" n="211" rhead="Comment. in I. Cap. Sphæræ"/> <note position="left" xml:space="preserve">Lep@s<unsure/>.</note> <note position="right" xml:space="preserve"> <lb/># ## FORMÆ STELLARVM ## Longit. ### Latit. ### Magni- \\ tudo. <lb/># # # G. # M. # G. # M. <lb/># 8 # Media # 29 # 0 # 27 # 0 # 4 <lb/># 9 # Antecedens trium # 26 # 10 # 27 # 50 # 4 <lb/># 10 # Poſt interuallum ſequens ex quatuor # 20 # 20 # 32 # 50 # 3 <lb/># 11 # Quæ præit hanc # 18 # 0 # 31 # 0 # 4 <lb/># 12 # Tertio præcedens # 17 # 30 # 28 # 50 # 3 <lb/># 13 # Antecedens omnes quatuor # 15 # 30 # 28 # 0 # 3 <lb/># 14 # Rurſus ſimili modo, q̃ ſequitur ex quatuor # 10 # 30 # 25 # 30 # 3 <lb/># 15 # Antecedens hanc # 8 # 10 # 23 # 50 # 4 <lb/># 16 # Præcedens hanc etiam # 5 # 30 # 23 # 10 # 3 <lb/># 17 # Quæ antecedit has quatuor # (tingit # 3 # 50 # 23 # 5 # 4 <lb/># 18 # Quæ in conucrſione fluuij pectus Ceti con # 358 # 30 # 32 # 10 # 4 <lb/># 19 # Quæ ſequitur hanc # 359 # 20 # 34 # 50 # 4 <lb/># 20 # Sequentium trium præcedens # 2 # 10 # 38 # 30 # 4 <lb/># 21 # Media # 7 # 10 # 38 # 10 # 4 <lb/># 22 # Sequens trium # 10 # 50 # 30 # 0 # 5 <lb/># 23 # In quadrilatero præcedentium duarũ Borea # 14 # 40 # 41 # 30 # 4 <lb/># 24 # Auſtrina # 14 # 50 # 42 # 30 # 4 <lb/># 25 # Sequentis lateris antecedens # 15 # 30 # 43 # 20 # 4 <lb/># 26 # Sequens earum quatuor # 18 # 0 # 43 # 20 # 4 <lb/># 27 # Verſus ortum coniunctarum duarum Borea # 27 # 30 # 50 # 20 # 4 <lb/># 28 # Magis in Auſtrum # 28 # 20 # 51 # 45 # 4 <lb/># 29 # In reflexione, duarum ſequens # 21 # 30 # 53 # 50 # 4 <lb/># 30 # Præcedens # 19 # 10 # 53 # 10 # 4 <lb/># 31 # In reliqua diſtantia trium ſequens # 11 # 10 # 53 # 0 # 4 <lb/># 32 # Media # 8 # 10 # 53 # 30 # 4 <lb/># 33 # Præcedens trium # 5 # 10 # 52 # 0 # 4 <lb/># 34 # In extremo fluminis # 353 # 30 # 53 # 30 # 1 <lb/>########### Omnes ſtellæ 34. Primæ magnit. 1. Tertiæ 5. <lb/>########### Quartæ 27. Quintæ 1. <lb/>########### LEPVS. Conſtellatio XXXVII. <lb/> # 1 # In auribus quadrilateri præcedentiũ Borea # 43 # 0 # 35 # 0 # 5 # 2 # Auſtralis # 43 # 10 # 36 # 30 # 5 # 3 # Sequentis lateris Borealis # 44 # 40 # 35 # 40 # 5 # 4 # Auſtralis # 44 # 40 # 36 # 40 # 5 * # 5 # In mento # 42 # 20 # 39 # 40 # 4 # 6 # In excremo pedis ſiniſtri prioris # 39 # 30 # 45 # 15 # 4 # 7 # In medio corpore # 48 # 50 # 41 # 30 # 3 # 8 # Sub aluo # 48 # 10 # 44 # 20 # 3 # 9 # In poſterioribus pedibus duarum Borealior # 53 # 20 # 44 # 0 # 4 # 10 # Quæ magis in Auſtrum # 52 # 20 # 45 # 50 # 4 # 11 # In lumbo # 53 # 20 # 38 # 20 # 4 # 12 # In extrema cauda # 56 # 0 # 38 # 10 # 4 </note> </div> <div xml:id="echoid-div353" type="section" level="1" n="111"> <head xml:id="echoid-head115" xml:space="preserve">Omnes ſtellæ 12. Tertiæ magnit. 2. Quartæ 6. Quintæ 4.</head> <pb o="175" file="211" n="212" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve">Canis @@-<lb/>ior.</note> <note position="right" xml:space="preserve"> <lb/>## FORMÆ STELLARVM ## Longit. ### Latit. ### Mani- \\ tudo <lb/># # # G. # M. # G. # M. <lb/>######## CANIS MAIOR. Conſtellatio XXXVIII. <lb/> 1 # In ore ſplẽdidiſſima vocata Canis, Cãdens # 71 # 0 # # 39 # 10 # 1 2 # In auribus # 73 # 0 # # 35 # 0 # # 4 3 # In capite # 74 # 40 # 36 # 30 # 5 4 # In collo duarum Borea # 76 # 40 # 37 # 45 # 4 5 # Auſtralis # 78 # 40 # 40 # 0 # # 4 6 # In pectore # 73 # 50 # 42 # 30 # 5 7 # In genu dextro duarum Borea # 69 # 30 # 41 # 15 # 5 8 # Auſtralis # 69 # 20 # 42 # 30 # 5 9 # In extremo prioris pedis # 64 # 20 # 41 # 20 # 3 10 # In genu ſiniſtro duarum præcedens # 68 # 0 # # 46 # 30 # 5 11 # Sequens # 69 # 30 # 45 # 50 # 5 12 # In humero ſiniſtro duarum ſequens # 78 # 0 # # 46 # 0 # # 4 13 # Quæ præit # 75 # 0 # # 47 # 0 # # 5 14 # In eductione femoris ſiniſtri # 80 # 0 # # 48 # 45 # 3 15 # Sub aluo inter femora # 77 # 0 # # 51 # 20 # 3 # * 16 # In poplite cruris dextri # 76 # 20 # 55 # 10 # 4 # * 17 # In extremo ipſius pedis # 63 # 0 # # 53 # 45 # 3 18 # In extrema cauda # 85 # 30 # 50 # 30 # 3 ######## Omnes ſtellæ 18. Primæ magnit. 1. Tertiæ 5. Quartæ 5. Quintæ 7. ######## INFORMES CIRCACANEM. 1 # A Septentrione ad verticem canis # 72 # 50 # 25 # 15 # 4 # * 2 # Sub poſteriorib. pedibus ad rectam lineam # 63 # 20 # 61 # 30 # 4 3 # Quæ in magis Boream (Auſtralis # 64 # 40 # 58 # 45 # 4 4 # Quæ etiam hac ſeptentrionalior # 66 # 20 # 57 # 0 # # 4 5 # Reſidua ipſarum quatuor maxime Borea # 67 # 30 # 56 # 0 # # 4 6 # Ad occaſum quaſi ad rectam lineam trium # 50 # 20 # 55 # 30 # 4 7 # Media (pręcedens # 53 # 40 # 57 # 40 # 4 8 # Sequens trium # 55 # 40 # 59 # 30 # 4 9 # Sub his duarum lucidarum ſequens # 52 # 20 # 59 # 40 # 2 10 # Antecedens # 49 # 20 # 57 # 40 # 2 11 # Reliqua Auſtralior ſupra dictis # 45 # 30 # 59 # 30 # 4 ####### Omnes ſtellæ 11. Secundæ magnit. 2. Quartæ 9.</note> <note position="right" xml:space="preserve">Canis @@-<lb/>nor.</note> <note position="right" xml:space="preserve">####### PROCYON, SIVE CANIS MINOR, QVIET ####### Antecanis. Conſtellatio XXXIX. 1 # In ceruice # 78 # 20 # 14 # 0 # # 4 2 # In femore fulgens Procyon, ſeu canis # 82 # 30 # 16 # 10 # 1 ####### Omnes ſtellæ 2. Primæ magnit. 1. Quartæ 1.</note> <note position="right" xml:space="preserve">Nauis.</note> <note position="right" xml:space="preserve"> ####### ARGVS, SIVE NAVIS. Conſtellatio XL. 1 # In extrema naue duarum præcedens # 93 # 40 # 42 # 40 # 5 2 # Sequens # 97 # 40 # 43 # 20 # 3 </note> <pb o="176" file="212" n="213" rhead="Comment. in I. Cap. Sphæræ"/> <note position="right" xml:space="preserve"> <lb/># ## FORMÆ STELLARVM ### Longit. ### Latit. ## Magni- \\ tudo. <lb/># # # G. # M. # # G. # M. <lb/># 3 # In puppi duarum, quæ Borea # 92 # 10 # 45 # 0 # # 4 <lb/># 4 # Quæ magis in Auſtrum # 92 # 10 # 46 # 0 # # 4 <lb/># 5 # Pręcedens duas # 88 # 40 # 45 # 30 # 4 <lb/># 6 # In medio ſcuto fulgens # 89 # 40 # 47 # 15 # 4 <lb/># 7 # Sub ſcuto præcedentis trium # 88 # 50 # 49 # 45 # 4 <lb/># 8 # Sequens # 92 # 40 # 49 # 50 # 4 <lb/># 9 # Media trium # 91 # 40 # 49 # 15 # 4 <lb/># 10 # In extremo gubernaculo # 97 # 20 # 49 # 50 # 4 <lb/># 11 # In carina puppis duarum Borea # 87 # 20 # 53 # 0 # # 4 <lb/>* # 12 # Auſtralis # 97 # 20 # 58 # 40 # 3 <lb/># 13 # In ſolio puppis Borea # 93 # 30 # 55 # 30 # 5 <lb/># 14 # In eodem ſolio trium præcedens # 95 # 30 # 58 # 30 # 5 <lb/># 15 # Media # 96 # 40 # 57 # 15 # 4 <lb/># 16 # Sequens # 99 # 50 # 57 # 45 # 4 <lb/># 17 # Lucida ſequens in tranſtro # 104 # 30 # 58 # 20 # 2 <lb/># 18 # Sub hac duarum obſcurarum præcedens # 101 # 30 # 60 # 0 # # 5 <lb/>* # 19 # Sequens # 104 # 20 # 59 # 20 # 5 <lb/>* # 20 # Supra dictam fulgentem duarum præcedẽs # 106 # 30 # 56 # 40 # 5 <lb/># 21 # Sequens # 107 # 40 # 57 # 0 # # 5 <lb/># 22 # In ſcutulis, & ſtatione mali Borea trium # 119 # 0 # # 51 # 30 # 4 <lb/>* # 23 # Media # 119 # 30 # 55 # 40 # 4 <lb/># 24 # Auſtralis trium # 117 # 20 # 57 # 10 # 4 <lb/># 25 # Sub his duarum coniunctarum Borea # 122 # 30 # 60 # 0 # # 4 <lb/># 26 # Auſtralior # 122 # 20 # 61 # 15 # 4 <lb/># 27 # In medio mali duarum Auſtralis # 113 # 30 # 51 # 30 # 4 <lb/># 28 # Borea # 112 # 40 # 49 # 0 # # 4 <lb/># 29 # In ſummo veli duarum antecedens # 111 # 20 # 43 # 20 # 4 <lb/># 30 # Sequens # 112 # 20 # 43 # 30 # 4 <lb/># 31 # Sub tertia, quæ ſequitur ſcutum # 98 # 30 # 54 # 30 # 2 <lb/># 32 # In ſectione inſtrati # 100 # 50 # 51 # 15 # 2 <lb/># 33 # Inter remos in carina # 95 # 0 # # 63 # 0 # # 4 <lb/># 34 # Quæ ſequitur hanc obſcura # 102 # 20 # 64 # 30 # 6 <lb/># 35 # Lucida, quæ ſequitur hanc in ſtratio ne # 113 # 20 # 63 # 50 # 2 <lb/># 36 # Ae Auſtrum magis intra carinam fulgens # 121 # 50 # 69 # 40 # 2 <lb/># 37 # Sequentium hanc trium antecedens # 128 # 30 # 65 # 40 # 3 <lb/># 38 # Media # 134 # 40 # 65 # 50 # 3 <lb/># 39 # Sequens # 139 # 20 # 65 # 50 # 2 <lb/># 40 # Sequentium duarum ad ſectionẽ præcedẽs # 144 # 20 # 62 # 50 # 3 <lb/># 41 # Sequens # 151 # 20 # 62 # 15 # 3 <lb/># 42 # In temone Boreo, & antecedente, q̃ præit # 57 # 20 # 65 # 50 # 4 <lb/># 43 # Quę ſequitur # 73 # 30 # 65 # 40 # 3 <lb/># 44 # Quę in temone reliquo præcedit. Canopus # 70 # 30 # 75 # 0 # # 1 <lb/># 45 # Reliqua ſequens hanc # 82 # 20 # 71 # 50 # 3 <lb/></note> <pb o="177" file="213" n="214" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve"> <lb/>## FORMÆ STELLARVM ### Longit. ### Latit. ## Magni- \\ tudo. <lb/># # # G. # M. # G. # M. <lb/>######## Omnes ſtellæ 45. Primæ magnit. 1. Secundæ 6. Tertiæ 8. <lb/>######## Quartę 22. Quintæ 7. Sextę 1. <lb/>######## HYDRA. Conſtellatio XLI. <lb/>1 # In capite quinq; p̃cedẽtiũ duarũ in narib<emph style="sub">9</emph><unsure/> # 97 # 20 # 15 # 0 # # 4 <lb/>2 # Borea duarum, & in oculo (Auſtralis # 98 # 40 # 13 # 40 # 4 <lb/>3 # Sequentium duarum Borea, & in occpite # 99 # 0 # # 11 # 30 # 4 <lb/>4 # Auſtralis earum, & in hiatu # 98 # 50 # 14 # 45 # 4 <lb/>5 # Quæ ſequitur has omnes in gena # 100 # 50 # 12 # 15 # 4 <lb/>6 # In productione ceruicis duarum præcedẽs # 103 # 40 # 11 # 50 # 5 # * <lb/>7 # Quæ ſequitur # 106 # 40 # 13 # 40 # 4 <lb/>8 # In flexu colli trium media # 111 # 40 # 15 # 20 # 4 <lb/>9 # Sequens hanc # 114 # 0 # # 14 # 50 # 4 # * <lb/>10 # Quæ maxime auſtralis # 111 # 40 # 17 # 10 # 4 <lb/>11 # Ab Auſtro duarũ cõtiguaruũ obſcura, & Bo # 112 # 30 # 19 # 45 # 6 <lb/>12 # Lucida earum ſequens (rea # 113 # 20 # 20 # 30 # 2 <lb/>13 # Poſt flexum colli trium a@tecedens # 119 # 20 # 26 # 30 # 4 <lb/>14 # Sequens # 124 # 30 # 23 # 15 # 4 <lb/>15 # Media earum # 122 # 0 # # 26 # 0 # # 4 <lb/>16 # Quæ in rectam lineam trium præcedit # 131 # 20 # 24 # 30 # 3 <lb/>17 # Media # 133 # 20 # 23 # 0 # # 4 <lb/>18 # Sequens # 136 # 20 # 22 # 10 # 3 <lb/>19 # Sub baſe crateris duarum Borea # 144 # 50 # 25 # 45 # 4 <lb/>20 # Auſtralis # 145 # 40 # 50 # 10 # 4 <lb/>21 # Poſt has in triquetro præcedens # 155 # 30 # 31 # 20 # 4 <lb/>22 # Earum Auſtralis # 157 # 50 # 34 # 10 # 4 <lb/>23 # Sequens earundem trium # 159 # 30 # 31 # 40 # 3 <lb/>24 # Poſt coruum proxima caudæ # 173 # 20 # 13 # 40 # 4 # * <lb/>25 # In extrema cauda # 186 # 50 # 17 # 40 # 4 # * <lb/>######## Omnes ſtellæ 25. Secundę magnit. 1. Tertiæ 3. Quartę 19. <lb/>######## Quintę 1. Sextæ 1. <lb/>######## INFORMES CIRCA HYDRAM. <lb/>1 # A capite ad Auſtrum # 95 # 13 # 13 # 0 # # 3 # * <lb/>2 # Sequens eas, quæ ſunt in collo # 124 # 20 # 16 # 0 # # 3 # * <lb/>######## CRATER SIVE PATERA, VEL VRNA. <lb/>######## Conſtellatio XLII. <lb/>1 # In baſi crateris, quę & Hydrę communis # 139 # 40 # 23 # 0 # # 4 <lb/>2 # In medio cratere Auſtralis duarum # 146 # 0 # # 19 # 30 # 4 <lb/>3 # Borea ipſarum # 143 # 30 # 18 # 0 # # 4 <lb/>4 # In Auſtralij circunſerentia orificij # 150 # 20 # 18 # 30 # 4 <lb/>5 # In Boreo ambitu # 142 # 40 # 13 # 40 # 4 <lb/>6 # In Auſtrali anſa # 152 # 30 # 16 # 30 # 4 <lb/>7 # In anſa Borea # 145 # 0 # # 11 # 50 # 4 <lb/></note> <pb o="178" file="214" n="215" rhead="Comment. in I. Cap. Sphæræ"/> <note position="right" xml:space="preserve"> <lb/># ## FORMÆ STELLARVM ## Longit. ### Latit. ### Magni- \\ tudo. <lb/># # # # G. # M. # G. # M. <lb/>######## Omnes ſtellæ 7. Quartæ magnitudinis. <lb/>######## CORVVS. Conſtellatio XLIII. <lb/># 1 # In roſtro, & Hydrę communis # 158 # 40 # 21 # 30 # 3 <lb/>* # 2 # In ceruice # 157 # 40 # 19 # 40 # 3 <lb/>* # 3 # In pectore # 160 # 0 # # 18 # 10 # 5 <lb/># 4 # In ala dextra, & præcedente # 160 # 50 # 14 # 50 # 3 <lb/># 5 # In ala ſequente duarum antecedens # 160 # 0 # # 12 # 30 # 3 <lb/># 6 # Sequens # 161 # 20 # 11 # 45 # 4 <lb/># 7 # In extremo pede communis Hydræ # 163 # 50 # 19 # 10 # 3 <lb/>######## Omnes ſtellę 7. Tertiæ magnit. 5. Quartæ 1. Quintæ 1. <lb/>######## CENTAVRVS. Conſtellatio XLIIII. <lb/>* # 1 # In capite quatuor maximæ Auſtralis # 183 # 50 # 21 # 40 # 5 <lb/>* # 2 # Quæ magis in Boream # 183 # 20 # 18 # 50 # 5 <lb/># 3 # Mediantium duarum præcedens # 182 # 30 # 20 # 30 # 4 <lb/># 4 # Sequens, & reliqua ex quatuor # 183 # 20 # 20 # 0 # # 5 <lb/>* # 5 # In humero ſiniſtro, & pręcedente # 179 # 30 # 25 # 40 # 3 <lb/># 6 # In humero dextro # 189 # 0 # # 22 # 30 # 3 <lb/>* # 7 # In armo ſiniſtro # 182 # 30 # 27 # 30 # 4 <lb/>* # 8 # In ſcuto quatuor p̃cedẽtium duarũ Borea # 191 # 30 # 22 # 20 # 4 <lb/># 9 # Auſtralis # 192 # 30 # 23 # 45 # 4 <lb/># 10 # Reliquarũ duarum, quæ in ſummitate ſcuti # 195 # 20 # 18 # 15 # 4 <lb/>* # 11 # Quæ magis in Auſtrum # 196 # 50 # 20 # 50 # 4 <lb/># 12 # In latere dextro trium præcedens # 186 # 40 # 28 # 20 # 4 <lb/># 13 # Media # 187 # 20 # 29 # 20 # 4 <lb/># 14 # Sequens # 188 # 30 # 28 # 0 # # 4 <lb/># 15 # In brachio dextro # 189 # 40 # 26 # 30 # 4 <lb/># 16 # In dextro cubito # 196 # 10 # 25 # 15 # 3 <lb/># 17 # In extrema manu dextra # 200 # 50 # 24 # 0 # # 4 <lb/># 18 # In eductione corporis humani lucens # 191 # 20 # 33 # 30 # 3 <lb/># 19 # Duarum obſcurarum ſequens # 191 # 0 # # 31 # 0 # # 5 <lb/># 20 # Præcedens # 189 # 50 # 30 # 20 # 5 <lb/># 21 # In ductu dorſi # 185 # 30 # 33 # 50 # 5 <lb/># 22 # Antecedens hanc in dorſo equi # 182 # 20 # 37 # 30 # 5 <lb/># 23 # In lumbis trium ſequens # 179 # 10 # 40 # 0 # # 3 <lb/># 24 # Media # 178 # 20 # 40 # 20 # 4 <lb/>* # 25 # Antecedens trium # 176 # 0 # # 41 # 0 # # 5 <lb/>* # 26 # In dextra coxa duarũ cõtiguarũ pręcedẽtis # 176 # 0 # # 46 # 10 # 3 <lb/># 27 # Sequens # 176 # 40 # 46 # 45 # 4 <lb/># 28 # In pectore ſub ala equi # 191 # 40 # 40 # 45 # 4 <lb/>* # 29 # Sub aluo duarum pręcedens # 189 # 40 # 43 # 0 # # 2 <lb/>* # 30 # Sequens # 191 # 0 # # 43 # 45 # 3 <lb/># 31 # In cauo pedis dextri # 183 # 20 # 51 # 10 # 2 <lb/></note> <pb o="179" file="215" n="216" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve"> <lb/>## FORMÆ STELLARVM ### Longit. ### Latit. ## Magni- \\ tudo. <lb/># # # G. # M. # G. # M. <lb/>32 # In ſura eiuſdem # 188 # 40 # 51 # 40 # 2 <lb/>33 # In cauo pedis ſiniſtri # 179 # 40 # 55 # 10 # 4 # * <lb/>34 # Sub muſculo eiuſdem # 184 # 30 # 55 # 40 # 2 # * <lb/>35 # In ſummo pede dextro priore # 211 # 40 # 41 # 10 # 1 # * <lb/>36 # In genu ſiniſtro # 179 # 30 # 45 # 20 # 2 <lb/>37 # Deforis ſub femore dextro # 188 # 0 # # 49 # 10 # 4 # * <lb/>######## Omnes ſtellæ 37. Primæ magnit. 1. Secundæ 5. Tertiæ 7. <lb/>######## Quartæ 16. Quintæ 8. <lb/>######## BESTIA CENTAVRI, SIVE LVPVS. <lb/>######## Conſtellatio XLV. <lb/>1 # In ε<unsure/>ũmo pede poſteriorè<unsure/> ad manũ Centauri # 201 # 20 # 24 # 50 # 3 <lb/>2 # In cauo eiuſdem pedis # 299 # 10 # 29 # 10 # 3 <lb/>3 # In armo duarum pręcedens # 204 # 20 # 21 # 15 # 4 # * <lb/>4 # Sequens # 207 # 30 # 21 # 0 # # 4 <lb/>5 # In medio corpore # 206 # 20 # 25 # 10 # 4 <lb/>6 # In aluo # 203 # 30 # 27 # 0 # # 5 <lb/>7 # In coxa # 204 # 10 # 29 # 0 # # 5 <lb/>8 # In ductu coxæ duarum Borea # 208 # 0 # # 28 # 30 # 5 <lb/>9 # Auſtralis # 207 # 0 # # 30 # 0 # # 5 <lb/>10 # In ſummo lumbo # 208 # 40 # 33 # 10 # 5 <lb/>11 # In extrema cauda trium Auſtralis # 195 # 20 # 31 # 20 # 5 <lb/>12 # Media # 165 # 10 # 30 # 0 # # 4 <lb/>13 # Septentrionalis trium # 196 # 20 # 29 # 20 # 4 <lb/>14 # In ceruice duarum Auſtralis # 212 # 10 # 17 # 0 # # 4 # * <lb/>15 # Borea # 212 # 40 # 15 # 20 # 4 <lb/>16 # In rictu duarum pręcedens # 209 # 0 # # 13 # 30 # 4 <lb/>17 # Sequens # 210 # 0 # # 12 # 50 # 4 <lb/>18 # In priore pede duarum Auſtralior # 230 # 40 # 11 # 30 # 4 # * <lb/>19 # Quæ magis in Boream # 229 # 50 # 10 # 0 # # 4 # * <lb/>######## Omnes ſtellæ 19. Tertiæ magnit. 2. Quartæ 11. Quintæ 6. <lb/>######## LAR, SIVE THVRIBVLVM, SEV ARA. <lb/>######## Conſtellatio XLVI. <lb/>1 # In baſi duarum Borea # 231 # 0 # # 22 # 40 # 5 <lb/>2 # Auſtralis # 233 # 40 # 25 # 45 # 4 <lb/>3 # In media arula # 229 # 30 # 26 # 30 # 4 <lb/>4 # In foculo trium Borea # 224 # 0 # # 30 # 20 # 5 <lb/>5 # Reliquarum duarum contiguarũ Auſtralis # 228 # 30 # 34 # 10 # 4 <lb/>6 # Borea # 228 # 20 # 33 # 20 # 4 <lb/>7 # In media flamma # 224 # 20 # 34 # 10 # 4 <lb/></note> <pb o="180" file="216" n="217" rhead="Comment. in I. Cap. Sphæræ"/> <note position="right" xml:space="preserve"> <lb/># ## FORMÆ STELLARVM ### Longit. ### Latit. ## Magni- \\ tudo. <lb/># # # G. # M. # G. # M. <lb/>########### Omnes ſtellæ 7. Quartæ magnit. 5. Quintæ 2. <lb/>########### CORONA AVSTRINA, QVÆ ET ROTA \\ Ixionis. Conſtellatio XLVII. <lb/># 1 # Quæ ad ambitum Auſtralem foris præcedit # 242 # 30 # 21 # 30 # 4 <lb/># 2 # Quæ hanc ſequitur in corona # 245 # 0 # 21 # 0 # 5 <lb/># 3 # Sequens hanc, # 246 # 30 # 20 # 20 # 5 <lb/># 4 # Quæ etiam hanc ſequitur # 248 # 10 # 20 # 0 # 4 <lb/># 5 # Poſt hanc ante genu Sagittarij # 249 # 30 # 18 # 30 # 5 <lb/># 6 # Borea in genu lucens # 250 # 40 # 17 # 10 # 4 <lb/># 7 # Magis Borea # 250 # 10 # 16 # 0 # 4 <lb/># 8 # Adhuc magis in Boream # 249 # 50 # 15 # 20 # 4 <lb/># 9 # In ambitu Boreo duarum ſequens # 248 # 30 # 15 # 50 # 6 <lb/># 10 # Præcedens # 248 # 0 # 14 # 50 # 6 <lb/># 11 # Ex interuallo præcedens has # 245 # 10 # 14 # 40 # 5 <lb/># 12 # Quæ etiam hanc antecedit # 243 # 0 # 15 # 50 # 5 <lb/># 13 # Reliquæ magis in Auſtrum # 242 # 30 # 18 # 30 # 5 <lb/>########### Omnesſtellæ 13. Quartæ magnit. 5. Quintæ 6. Sextæ 2. <lb/>########### PISC IS AVSTRINVS, SIVE NOTIVS, \\ Conſtellatio XLVIII. <lb/># 1 # In ore, atq; eadem, quę in extrema aqua # 300 # 20 # 23 # 0 # 1 <lb/># 2 # In capite trium præcedens # 294 # 0 # 21 # 20 # 4 <lb/>* # 3 # Media # 297 # 30 # 22 # 15 # 4 <lb/># 4 # Sequens # 299 # 0 # 22 # 30 # 4 <lb/># 5 # Quæ ad branchiam # 297 # 40 # 16 # 15 # 4 <lb/># 6 # In ſpina Auſtrali, at que dorſo # 289 # 30 # 19 # 30 # 5 <lb/># 7 # In aluo duarum ſequens # 294 # 30 # 15 # 10 # 5 <lb/># 8 # Antecedens # 292 # 10 # 14 # 30 # 4 <lb/># 9 # In Spina Septentrionali ſequens trium # 288 # 30 # 15 # 15 # 4 <lb/># 10 # Media # 285 # 10 # 30 # 30 # 4 <lb/># 11 # Præcedens trium # 284 # 20 # 18 # 10 # 4 <lb/>* # 12 # In extrema cauda # 284 # 20 # 15 # 15 # 4 <lb/>########### Omnes ſtellæ præter primam 11. Quartæ magnit. 9. Quintæ 2. <lb/>########### INFORMES CIRCA PISCEM NOTIVM. <lb/># 1 # Præcedentium piſcem lucidarũ, quę anteit # 271 # 20 # 22 # 20 # 3 <lb/># 2 # Media # 274 # 30 # 22 # 10 # 3 <lb/># 3 # Sequens trium # 277 # 20 # 21 # 0 # 3 <lb/># 4 # Quæ hanc pręcedit obſcura # 175 # 20 # 20 # 50 # 5 <lb/># 5 # Cæterarum ad ſeptentrionem Auſtralior # 277 # 10 # 16 # 0 # 4 <lb/># 6 # Quæ magis in Boream # 277 # 10 # 14 # 50 # 4 <lb/>########### Omnes ſtellæ 6. Tertiæ magnit. 3. Quartæ 2. \\ Quintæ 1. <lb/></note> <pb o="181" file="217" n="218" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div354" type="section" level="1" n="112"> <head xml:id="echoid-head116" xml:space="preserve">IN PLAGA ERGO AVSTRALI STELLÆ <lb/>omnes 316. Primæ magnitud. 7. Secundæ 18. Tertiæ 60. Quar-<lb/>tæ 168. Quintæ 53. Sextæ 9. Neb. 1.</head> <head xml:id="echoid-head117" xml:space="preserve">IN TOTO AVTEM FIRMAMENTO STELLÆ <lb/>omnes, præter tres in cincinno. 1022. vt ſupra dictum eſt.</head> <p> <s xml:id="echoid-s7118" xml:space="preserve">Ex his omnibus liquido conſtat, prope polum antarcticum nullas ſtellas <lb/> <anchor type="note" xlink:label="note-217-01a" xlink:href="note-217-01"/> contineri, cum omnium propinquiſſima illi polo ſit ſtella 34. </s> <s xml:id="echoid-s7119" xml:space="preserve">ſub muſculo ſi-<lb/>niſtri pedis Cẽtauri, quippe quæ gradibus 28. </s> <s xml:id="echoid-s7120" xml:space="preserve">min. </s> <s xml:id="echoid-s7121" xml:space="preserve">39. </s> <s xml:id="echoid-s7122" xml:space="preserve">à polo antarctico diſtat; <lb/></s> <s xml:id="echoid-s7123" xml:space="preserve">propterea ꝙ eius declinatio, ut paulo poſt docebimus, comprehendit grad. </s> <s xml:id="echoid-s7124" xml:space="preserve">61. </s> <s xml:id="echoid-s7125" xml:space="preserve"><lb/>min. </s> <s xml:id="echoid-s7126" xml:space="preserve">21. </s> <s xml:id="echoid-s7127" xml:space="preserve">Si enim uera referũt, qui ex Luſitania, & </s> <s xml:id="echoid-s7128" xml:space="preserve">ex alijs ptouincijs Hiſpaniæ <lb/>in Indias nauigarunt, ſtella, quæ uiciniſſima polo eſt, & </s> <s xml:id="echoid-s7129" xml:space="preserve">ad quã aſpicientes na-<lb/>uis curſum in Oceano dirigunt, 30. </s> <s xml:id="echoid-s7130" xml:space="preserve">ferme grad. </s> <s xml:id="echoid-s7131" xml:space="preserve">ut inſtrumẽtis ipſi obſeruarũt, <lb/>à polo autarctico abeſt. </s> <s xml:id="echoid-s7132" xml:space="preserve">Vnde fabuloſum erit, quod uulgo dici ſolet, iuxta po-<lb/>lum antarcticum eſſe ſtellas lucidiſſimas formam crucis referentes; </s> <s xml:id="echoid-s7133" xml:space="preserve">niſi intel-<lb/>ligamus ſtellas in Centauro, quarum 29. </s> <s xml:id="echoid-s7134" xml:space="preserve">31. </s> <s xml:id="echoid-s7135" xml:space="preserve">32. </s> <s xml:id="echoid-s7136" xml:space="preserve">& </s> <s xml:id="echoid-s7137" xml:space="preserve">34. </s> <s xml:id="echoid-s7138" xml:space="preserve">figurã inſtar crucis con-<lb/>ſtituunt, ſuntq́ue omnes ſecundæ magnitudinis.</s> <s xml:id="echoid-s7139" xml:space="preserve"/> </p> <div xml:id="echoid-div354" type="float" level="2" n="1"> <note position="right" xlink:label="note-217-01" xlink:href="note-217-01a" xml:space="preserve">Iuxta polũ <lb/>antaict@cũ <lb/>nullas eſſe <lb/>ſtellas.</note> </div> </div> <div xml:id="echoid-div356" type="section" level="1" n="113"> <head xml:id="echoid-head118" xml:space="preserve">VSVS PRÆCEDENTIS TABVLAE.</head> <p> <s xml:id="echoid-s7140" xml:space="preserve">EX <emph style="sc">PRAEMISSA</emph> tabula tria circa ſtellas ſingulas cognoſcun-<lb/> <anchor type="note" xlink:label="note-217-02a" xlink:href="note-217-02"/> tur, Longitudo, Latitudo, & </s> <s xml:id="echoid-s7141" xml:space="preserve">Magnitudo. </s> <s xml:id="echoid-s7142" xml:space="preserve">Si enim quamlibet ſtel-<lb/>lam in propria conſtellatione accipias, habebis mox in eadem li-<lb/>nea, primum quidem gradus, ac minuta longitudinis eius; </s> <s xml:id="echoid-s7143" xml:space="preserve">De-<lb/>inde gradus & </s> <s xml:id="echoid-s7144" xml:space="preserve">minuta latitudinis; </s> <s xml:id="echoid-s7145" xml:space="preserve">poſtremo magnitudinem. <lb/></s> <s xml:id="echoid-s7146" xml:space="preserve"><emph style="sc">Exempl vm</emph>. </s> <s xml:id="echoid-s7147" xml:space="preserve">In 26. </s> <s xml:id="echoid-s7148" xml:space="preserve">conſtellatione, nempe Leonis, accipio 27. </s> <s xml:id="echoid-s7149" xml:space="preserve">ſtellam, <lb/>quæ eſt in extremo caudæ: </s> <s xml:id="echoid-s7150" xml:space="preserve">In eadem igitur linea reperio longitudinem huius <lb/>ſtellæ continere grad. </s> <s xml:id="echoid-s7151" xml:space="preserve">137. </s> <s xml:id="echoid-s7152" xml:space="preserve">min. </s> <s xml:id="echoid-s7153" xml:space="preserve">50. </s> <s xml:id="echoid-s7154" xml:space="preserve">Latitudinem uero grad. </s> <s xml:id="echoid-s7155" xml:space="preserve">11. </s> <s xml:id="echoid-s7156" xml:space="preserve">min. </s> <s xml:id="echoid-s7157" xml:space="preserve">50. </s> <s xml:id="echoid-s7158" xml:space="preserve">Ipſam <lb/>denique ſtellam eſſe magnitudinis primæ: </s> <s xml:id="echoid-s7159" xml:space="preserve">atque ita de cęteris. </s> <s xml:id="echoid-s7160" xml:space="preserve">Intelligenda eſt <lb/>autem hæc longitudo (ſicut & </s> <s xml:id="echoid-s7161" xml:space="preserve">reliquæ omnes in tabula ſuperiori contentæ) <lb/> <anchor type="note" xlink:label="note-217-03a" xlink:href="note-217-03"/> nõ à principio ♈, primi mobilis, ſed à prima ſtella aſteriſmi ♈, quæ nimirũ in <lb/>cornu dextro exiſtit, ita ut reſpectu illius omnes aliæ ſint orientaliores. </s> <s xml:id="echoid-s7162" xml:space="preserve">Nico-<lb/>laus enim Copernicus loca omnium ſtellarum non computauit ad princ@p@ũ <lb/>♈, primi mobilis, quemadmodum Ptolemæus, & </s> <s xml:id="echoid-s7163" xml:space="preserve">omnesalij Aſtronomi cõſue <lb/>uerunt ſtellarum loca numerare, ſed ad primam ſtellã Arietis. </s> <s xml:id="echoid-s7164" xml:space="preserve">Quoniam enim <lb/>ſtellæ fixę ſemper eandem longitudinem habent à prima ſtella Arietis, nõ aũt <lb/>à principio ♈, primi mobilis, nempe ab illa communi ſectione Zodiaci cum <lb/>Aequatore, quæ principium ♈, dici ſolet, cum ab hoc puncto pedetentim ſem <lb/>per ad ſigna orientalia tendant, ueluti ſupra oſtendimus; </s> <s xml:id="echoid-s7165" xml:space="preserve">Placuit Copernico <lb/>ſtellarum longitudines<unsure/> potius ad primam ſtellam Arietis referre, quàm ad ini <lb/>tium ♈, primi mobilis, ut ſicuti latitudines earum ſemper eædem permanẽt, <lb/> <anchor type="note" xlink:label="note-217-04a" xlink:href="note-217-04"/> ita quoque longitudines earundem nullam ſuſciperent uariationem.</s> <s xml:id="echoid-s7166" xml:space="preserve"/> </p> <div xml:id="echoid-div356" type="float" level="2" n="1"> <note position="right" xlink:label="note-217-02" xlink:href="note-217-02a" xml:space="preserve">Vſus præce-<lb/>dentis tabu <lb/>læ ſtellarũ.</note> <note position="right" xlink:label="note-217-03" xlink:href="note-217-03a" xml:space="preserve">Longitudi-<lb/>nes ſtellarũ <lb/>in præcedẽ-<lb/>ti tabula in <lb/>cipiũt a pri<unsure/> <lb/>ma ſte<unsure/>lla <lb/>Arie<unsure/>us.</note> <note position="right" xlink:label="note-217-04" xlink:href="note-217-04a" xml:space="preserve">Veræ longi-<lb/>tudines ſtel <lb/>la@ũ quid, <lb/>& quomo<unsure/>-<lb/>do inueſti-<lb/>gentur.</note> </div> <p> <s xml:id="echoid-s7167" xml:space="preserve"><emph style="sc">Qvod</emph> ſi quis ſingularum ſtellarum diſtantias ab æquinoctio uerno, hoc <lb/>eſt, à principio ♈, primi mobilis, (quæ quidem diſtantiæ dicuntur ueræ long <lb/>tudines ſtellarum) more Ptolemæi, cęterorumq́ue Aſtronomorum noſſe <lb/>deſideret, haud magno labore ad optatum finem perueniet hac ratione.</s> <s xml:id="echoid-s7168" xml:space="preserve"> <pb o="182" file="218" n="219" rhead="Comment. in I. Cap. Sphæræ"/> Addiſcaturprimum uerus locus primæ ſtellæ Arietis, ſiue (quod idem eſt) di-<lb/>ctæ ſtellæ u<unsure/>era longitudo; </s> <s xml:id="echoid-s7169" xml:space="preserve">Deinde cuiuſlibet ſtellæ ex tabula ſuperiori lõgitu <lb/>do excerpatur, cui primæ ſtellæ Arietis uera longitudo adijciatur. </s> <s xml:id="echoid-s7170" xml:space="preserve">Nam excre <lb/>ſcẽs ſumma, ſi minor fuerit, quàm gr. </s> <s xml:id="echoid-s7171" xml:space="preserve">360. </s> <s xml:id="echoid-s7172" xml:space="preserve">mox indicabit diſtantiã ſtellæ propo-<lb/>ſitæ ab initio ♈, primi mobilis, ſi uero exceſſerit gr. </s> <s xml:id="echoid-s7173" xml:space="preserve">360. </s> <s xml:id="echoid-s7174" xml:space="preserve">num<unsure/>erus, qui relin-<lb/>quitur, abiectis grad. </s> <s xml:id="echoid-s7175" xml:space="preserve">360. </s> <s xml:id="echoid-s7176" xml:space="preserve">dictam offeret diſtantiam. </s> <s xml:id="echoid-s7177" xml:space="preserve"># <emph style="sc">Exemplvm</emph>. <lb/></s> <s xml:id="echoid-s7178" xml:space="preserve">Iuxta obſeruationes Petri Appiani, qui uera ſtellarum fixarum loca examina-<lb/>uit anno M. </s> <s xml:id="echoid-s7179" xml:space="preserve">D. </s> <s xml:id="echoid-s7180" xml:space="preserve">XXXII. </s> <s xml:id="echoid-s7181" xml:space="preserve">prima ſtella Arietis receſſit à principio ♈, primi mo-<lb/>bilis orientem uerſus gr. </s> <s xml:id="echoid-s7182" xml:space="preserve">26. </s> <s xml:id="echoid-s7183" xml:space="preserve">min. </s> <s xml:id="echoid-s7184" xml:space="preserve">38. </s> <s xml:id="echoid-s7185" xml:space="preserve">Si igitur ſcire cupiam, quantum ab eodem <lb/>principio amota ſit ſpica ♍, accipio ex tabula ſuperiori in conſtellatione ♍, <lb/>quæ eſt 27. </s> <s xml:id="echoid-s7186" xml:space="preserve">Conſtellatio, diſtantiam dictæ ſtellæ à prima ſtella ♈, nempe grad. </s> <s xml:id="echoid-s7187" xml:space="preserve"><lb/>170. </s> <s xml:id="echoid-s7188" xml:space="preserve">min. </s> <s xml:id="echoid-s7189" xml:space="preserve">0. </s> <s xml:id="echoid-s7190" xml:space="preserve">cui addo 26. </s> <s xml:id="echoid-s7191" xml:space="preserve">gr. </s> <s xml:id="echoid-s7192" xml:space="preserve">min. </s> <s xml:id="echoid-s7193" xml:space="preserve">38. </s> <s xml:id="echoid-s7194" xml:space="preserve">quibus prima ſtella ♈, ab æquinoctio verno <lb/>receſſit, efficiunturq́; </s> <s xml:id="echoid-s7195" xml:space="preserve">grad. </s> <s xml:id="echoid-s7196" xml:space="preserve">196. </s> <s xml:id="echoid-s7197" xml:space="preserve">min. </s> <s xml:id="echoid-s7198" xml:space="preserve">38. </s> <s xml:id="echoid-s7199" xml:space="preserve">Atque tanta eſt uera longitudo illius <lb/>ſtellæ, quàm ſpicam ♍, dicunt. </s> <s xml:id="echoid-s7200" xml:space="preserve">Item ſi inquirere lubeat quãtum diſtet à verno <lb/>ęquinoctio ſtella illa, quę in umbilico Pegaſi, & </s> <s xml:id="echoid-s7201" xml:space="preserve">in capite Andromedę exiſtit, <lb/>ſumo ex 19. </s> <s xml:id="echoid-s7202" xml:space="preserve">conſtellatione, quę eſt Pegaſi, uel ex 20. </s> <s xml:id="echoid-s7203" xml:space="preserve">quę eſt Andromedę, dictę <lb/>ſtellę diſtantiam à prima ſtella ♈, nempe gr. </s> <s xml:id="echoid-s7204" xml:space="preserve">341. </s> <s xml:id="echoid-s7205" xml:space="preserve">min. </s> <s xml:id="echoid-s7206" xml:space="preserve">10. </s> <s xml:id="echoid-s7207" xml:space="preserve">cui addo gr. </s> <s xml:id="echoid-s7208" xml:space="preserve">26. </s> <s xml:id="echoid-s7209" xml:space="preserve">min. </s> <s xml:id="echoid-s7210" xml:space="preserve"><lb/>38. </s> <s xml:id="echoid-s7211" xml:space="preserve">efficiunturq́ue grad. </s> <s xml:id="echoid-s7212" xml:space="preserve">367. </s> <s xml:id="echoid-s7213" xml:space="preserve">min. </s> <s xml:id="echoid-s7214" xml:space="preserve">48. </s> <s xml:id="echoid-s7215" xml:space="preserve">a quibus ſi reijciantur grad. </s> <s xml:id="echoid-s7216" xml:space="preserve">360. </s> <s xml:id="echoid-s7217" xml:space="preserve">ſupere-<lb/>runt grad. </s> <s xml:id="echoid-s7218" xml:space="preserve">7. </s> <s xml:id="echoid-s7219" xml:space="preserve">min. </s> <s xml:id="echoid-s7220" xml:space="preserve">48. </s> <s xml:id="echoid-s7221" xml:space="preserve">Tanta igitur eſt longitudo uera ſtellæ propoſitæ. </s> <s xml:id="echoid-s7222" xml:space="preserve">Atque <lb/>ita de cęteris.</s> <s xml:id="echoid-s7223" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7224" xml:space="preserve"><emph style="sc">Praet erevndvm</emph> tamen non eſt, Nicolaum Copernicum accu-<lb/>ratum ſtellarum obſeruatorem anno M D XXV. </s> <s xml:id="echoid-s7225" xml:space="preserve">reperiſſe ſtellam primam <lb/>♈, nonſolum receſſiſſe ab ęquinoctio uerno gr. </s> <s xml:id="echoid-s7226" xml:space="preserve">26. </s> <s xml:id="echoid-s7227" xml:space="preserve">min. </s> <s xml:id="echoid-s7228" xml:space="preserve">38. </s> <s xml:id="echoid-s7229" xml:space="preserve">ut uult Appianus, <lb/>ſed grad. </s> <s xml:id="echoid-s7230" xml:space="preserve">27. </s> <s xml:id="echoid-s7231" xml:space="preserve">min. </s> <s xml:id="echoid-s7232" xml:space="preserve">21. </s> <s xml:id="echoid-s7233" xml:space="preserve">Quare ſi illius obſeruationibus potius uelis fidem habe-<lb/>re, quam Appiani, reperies iuxta documentum pręcedens longitudinem ſpi-<lb/>cę ♍, hoc eſt, diſtantiam eius ab initio ♈, primi mobilis eſſe grad. </s> <s xml:id="echoid-s7234" xml:space="preserve">197. </s> <s xml:id="echoid-s7235" xml:space="preserve">min. </s> <s xml:id="echoid-s7236" xml:space="preserve">21. <lb/></s> <s xml:id="echoid-s7237" xml:space="preserve">Longitudinem uero capitis Andromedę complecti grad. </s> <s xml:id="echoid-s7238" xml:space="preserve">8. </s> <s xml:id="echoid-s7239" xml:space="preserve">min. </s> <s xml:id="echoid-s7240" xml:space="preserve">31. </s> <s xml:id="echoid-s7241" xml:space="preserve">Sed quoniã <lb/>ſtellę paulatim ab occaſu in ortum progrediuntur, addenda erunt hoc tem-<lb/>pore plura Minuta. </s> <s xml:id="echoid-s7242" xml:space="preserve">Nam ab anno M D XXV. </s> <s xml:id="echoid-s7243" xml:space="preserve">uſque ad annum Iubilęi <lb/>M D LXXV. </s> <s xml:id="echoid-s7244" xml:space="preserve">quo Romę ſecundum hanc tabulam globum Aſtronomicum <lb/>quàm correctiſſimè conſtruximus, ſtellę fixę ferè progreſſę ſunt min 26. </s> <s xml:id="echoid-s7245" xml:space="preserve">Qua-<lb/>re longitudinibus in pręcedenti tabula repertis addendi erunt grad. </s> <s xml:id="echoid-s7246" xml:space="preserve">27. </s> <s xml:id="echoid-s7247" xml:space="preserve">min. </s> <s xml:id="echoid-s7248" xml:space="preserve"><lb/>47. </s> <s xml:id="echoid-s7249" xml:space="preserve">ut uerę longitudines inueniãtur. </s> <s xml:id="echoid-s7250" xml:space="preserve">Id quod nos in eo globo pręſtitimus. </s> <s xml:id="echoid-s7251" xml:space="preserve">Hac <lb/>ratione ſpica ♍, diſtabit a principio ♈, grad. </s> <s xml:id="echoid-s7252" xml:space="preserve">197. </s> <s xml:id="echoid-s7253" xml:space="preserve">min. </s> <s xml:id="echoid-s7254" xml:space="preserve">47. </s> <s xml:id="echoid-s7255" xml:space="preserve">Caput uero Andro<unsure/>-<lb/>medę ab eodem aberit grad. </s> <s xml:id="echoid-s7256" xml:space="preserve">8. </s> <s xml:id="echoid-s7257" xml:space="preserve">min. </s> <s xml:id="echoid-s7258" xml:space="preserve">57.</s> <s xml:id="echoid-s7259" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">In quo ſi-<lb/>gno, & gra-<lb/>du Ecclipti-<lb/>cæ quæuis <lb/>ft<unsure/>ella repe-<lb/>@iatur.</note> <p> <s xml:id="echoid-s7260" xml:space="preserve"><emph style="sc">Hinc</emph> etiã facili negotio elicies, in quonã ſigno Zodiaci, & </s> <s xml:id="echoid-s7261" xml:space="preserve">gradu quęli-<lb/>bet ſtella reperiatur. </s> <s xml:id="echoid-s7262" xml:space="preserve">Si enim gradus uerę longitudinis inuentæ diuidantur per <lb/>30. </s> <s xml:id="echoid-s7263" xml:space="preserve">illico in numero Quotiẽte habebuntur integra ſigna, quibus ſtella ab ęqui <lb/>noctio uerno amouetur; </s> <s xml:id="echoid-s7264" xml:space="preserve">reliquus autem numerus graduum, ac minutorum, ſe <lb/>quenti ſigno dandus erit. </s> <s xml:id="echoid-s7265" xml:space="preserve"><emph style="sc">Exemplvm</emph>. </s> <s xml:id="echoid-s7266" xml:space="preserve">Longitudo ſpicę ♍, inuenta fuit <lb/>gr. </s> <s xml:id="echoid-s7267" xml:space="preserve">197. </s> <s xml:id="echoid-s7268" xml:space="preserve">min. </s> <s xml:id="echoid-s7269" xml:space="preserve">47. </s> <s xml:id="echoid-s7270" xml:space="preserve">(Nunc enim ſequimur Copernici obſeruationem, tanquam ue <lb/>niorẽ, additis tamen adhuc min. </s> <s xml:id="echoid-s7271" xml:space="preserve">26. </s> <s xml:id="echoid-s7272" xml:space="preserve">ut diximus.) </s> <s xml:id="echoid-s7273" xml:space="preserve">Diuido 197. </s> <s xml:id="echoid-s7274" xml:space="preserve">per 30. </s> <s xml:id="echoid-s7275" xml:space="preserve">eritq́ue nu <lb/>merus Quotiẽs 6. </s> <s xml:id="echoid-s7276" xml:space="preserve">reliqui autẽ gr. </s> <s xml:id="echoid-s7277" xml:space="preserve">17. </s> <s xml:id="echoid-s7278" xml:space="preserve">min. </s> <s xml:id="echoid-s7279" xml:space="preserve">47. </s> <s xml:id="echoid-s7280" xml:space="preserve">Quamobrẽ ſpica ♍, receſſit ab ini <lb/>tio ♈, primi mobilis ſex ſignis integris, eſtq́; </s> <s xml:id="echoid-s7281" xml:space="preserve">in gr. </s> <s xml:id="echoid-s7282" xml:space="preserve">17. </s> <s xml:id="echoid-s7283" xml:space="preserve">min. </s> <s xml:id="echoid-s7284" xml:space="preserve">47. </s> <s xml:id="echoid-s7285" xml:space="preserve">ſeptimi ſigni, nẽ-<lb/>pe ♎. </s> <s xml:id="echoid-s7286" xml:space="preserve">Pronuncio ergo, hoc tꝑe uerum locum ſpicę ♍, eſſe in gr. </s> <s xml:id="echoid-s7287" xml:space="preserve">17. </s> <s xml:id="echoid-s7288" xml:space="preserve">min. </s> <s xml:id="echoid-s7289" xml:space="preserve">47. <lb/></s> <s xml:id="echoid-s7290" xml:space="preserve">♎. </s> <s xml:id="echoid-s7291" xml:space="preserve">Eadem ratione inuenietur locus uerus capitis Andromedę in gr. </s> <s xml:id="echoid-s7292" xml:space="preserve">8. </s> <s xml:id="echoid-s7293" xml:space="preserve">min. </s> <s xml:id="echoid-s7294" xml:space="preserve">57. </s> <s xml:id="echoid-s7295" xml:space="preserve"><lb/>Eodemq́; </s> <s xml:id="echoid-s7296" xml:space="preserve">modo loca omnium ſtellarum fix arum inquires ſiue iuxta obſerua-<lb/>tiones Appiani, ſiue Nicolai Copernici, ſiue alterius cuiuſpiam, &</s> <s xml:id="echoid-s7297" xml:space="preserve">c.</s> <s xml:id="echoid-s7298" xml:space="preserve"/> </p> <pb o="183" file="219" n="220" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div358" type="section" level="1" n="114"> <head xml:id="echoid-head119" xml:space="preserve">DE STELLARVM DECLINATIONIBVS <lb/>inueſtigandis.</head> <p> <s xml:id="echoid-s7299" xml:space="preserve"><emph style="sc">Qvoniam</emph> ſtellæ ſixæ propter motum illum tradiſſimum ab occaſu in <lb/>ortum continuè mutant declinationes ab Aequatore, operæpretium me facta <lb/>rum exiſtimo, ſi breuiter hoc loco doceam, qua ratione ex ſinubus ſtellarum <lb/>declinationes, quarum longitudines, latitudineſque notę ſint, inquirantur. </s> <s xml:id="echoid-s7300" xml:space="preserve">In-<lb/>credibilem enim vſum apud Aſtronomos hæc res habet, pręſertim in inſtrumẽ <lb/>torum conſtructionibus. </s> <s xml:id="echoid-s7301" xml:space="preserve">Quamuis autem multis modis id, quod proponitur, <lb/>exequi poſſimus, ut alibi oſtendimus: </s> <s xml:id="echoid-s7302" xml:space="preserve">placuit tamen hoc loco eam tantummo-<lb/>do uiam explicare, quàm Petrus Nonius in libello de crepuſpulis demonſtra-<lb/> <anchor type="note" xlink:label="note-219-01a" xlink:href="note-219-01"/> uit, & </s> <s xml:id="echoid-s7303" xml:space="preserve">quàm nos clarius in ijs, quæ ad primũ Mobile ſpectant, demonſtrabimus. <lb/></s> <s xml:id="echoid-s7304" xml:space="preserve">Via autẽ eſt eiuſmodi. </s> <s xml:id="echoid-s7305" xml:space="preserve">Fiat, ut quadratũ ſinus totius ad rcctangulum contentũ <lb/>ſub ſinu maximæ declinationis Eclipticæ, & </s> <s xml:id="echoid-s7306" xml:space="preserve">ſinu complementi latitudinis ſtel-<lb/>læ propoſitæ, ita ſinus uerſus longitudinis ſtellæ ab initio ♋, computatæ, ſi la-<lb/>titudo ſtellæ fuerit borealis, vel à principio ♑, ſi ſtellæ latitudo auſtralis fue-<lb/>rit, (Hæc autem longitudo à ♋, numeranda eſt ſecundum ſucceſſionẽ ſigno-<lb/>rum, ſi ſtella extiterit in ſemicirculo Eclipticæ deſcendente, hoc eſt, ſi eius ve <lb/>ra longitudo à principio ♈, maior fuerit, quàm gr. </s> <s xml:id="echoid-s7307" xml:space="preserve">90. </s> <s xml:id="echoid-s7308" xml:space="preserve">minor autẽ quàm grad. </s> <s xml:id="echoid-s7309" xml:space="preserve"><lb/>270. </s> <s xml:id="echoid-s7310" xml:space="preserve">Contra uero ſignorum ſucceſſionem, ſi ſtella in aſcẽdente Eclipticę ſemi-<lb/>circulo extiterit, hoc eſt, ſi eius longitudo uera à principio ♈, minor fuerit, <lb/>quàm gr. </s> <s xml:id="echoid-s7311" xml:space="preserve">90. </s> <s xml:id="echoid-s7312" xml:space="preserve">uel maior, quàm gr. </s> <s xml:id="echoid-s7313" xml:space="preserve">270. </s> <s xml:id="echoid-s7314" xml:space="preserve">Hac enim ratione lõgitudo ſtellę à prin-<lb/>cipio ♋, computata minor ſemper erit ſemicirculo. </s> <s xml:id="echoid-s7315" xml:space="preserve">Contrario modo numerã <lb/>da erit longitudo à principio ♑. </s> <s xml:id="echoid-s7316" xml:space="preserve">Nã ſi ſtella extiterit in ſemicirculo Eclipticæ <lb/>deſcendẽte, ſupputanda erit longitudo contra ſucceſſionẽ ſignorum, ſi uero in <lb/>ſemicirculo Eclipticæ aſcendente, ſecundũ ſignorũ ſucceſſionẽ. </s> <s xml:id="echoid-s7317" xml:space="preserve">I<unsure/>ta enim rur-<lb/>ſus longitudo ſtellæ à principio ♑, ſupputata minor ſemper ſemicirculo eua-<lb/>det) ad aliud. </s> <s xml:id="echoid-s7318" xml:space="preserve">Inuenietur enim numerus, ex quo hac arte declinationem ſtellę <lb/>deprehendemus. </s> <s xml:id="echoid-s7319" xml:space="preserve">Conferatur cũ ſinu complementi differentiæ inter maximã <lb/>declinatione Eclipticæ, & </s> <s xml:id="echoid-s7320" xml:space="preserve">complementũ latitudinis ſtellæ, numerus inuentus. </s> <s xml:id="echoid-s7321" xml:space="preserve"><lb/>Nam ſi numerus inuentus æqualis fuerit illi ſinui complementi, ſtella nullam <lb/>habebit declinationẽ, ſed in Aequatore exiſtet: </s> <s xml:id="echoid-s7322" xml:space="preserve">Si aũt minor fuerit, detracto <lb/>hoc ex illo, relinquetur ſinus declinationis ſtellæ, eiuſdem denominationis cũ <lb/>latitudine, hoc eſt, borealis, ſi ſtellæ latitudo borealis ſuerit, auſtralis vero, ſi <lb/>auſtralis: </s> <s xml:id="echoid-s7323" xml:space="preserve">Si denique numerus inuentus fuerit maior ſinu illius complementi, <lb/>detracto hoc ex illo, reliquus erit ſinus declinationis ſtellæ, contrariæ deno-<lb/>minationis cum latitudine, hoc eſt, borealis, ſi ſtella latitudinem habuerit au-<lb/>ſtralem, auſtralis vero. </s> <s xml:id="echoid-s7324" xml:space="preserve">ſi borealem. </s> <s xml:id="echoid-s7325" xml:space="preserve">Exemplis quibuſda<unsure/>m res planior fiet.</s> <s xml:id="echoid-s7326" xml:space="preserve"/> </p> <div xml:id="echoid-div358" type="float" level="2" n="1"> <note position="right" xlink:label="note-219-01" xlink:href="note-219-01a" xml:space="preserve">Declinatio <lb/>nes ſteilarũ <lb/>quo pacto <lb/>inueſtigen-<lb/>tur.</note> </div> <p> <s xml:id="echoid-s7327" xml:space="preserve"><emph style="sc">Invenienda</emph> ſit declinatio Arcturi, quæ ſtella eſt informis in Boo-<lb/> <anchor type="note" xlink:label="note-219-02a" xlink:href="note-219-02"/> te, ſeu cõſtellatione 5. </s> <s xml:id="echoid-s7328" xml:space="preserve">Quoniã ſtella hæc in tabula longitudinẽ habet gr. </s> <s xml:id="echoid-s7329" xml:space="preserve">170. <lb/></s> <s xml:id="echoid-s7330" xml:space="preserve">min. </s> <s xml:id="echoid-s7331" xml:space="preserve">20. </s> <s xml:id="echoid-s7332" xml:space="preserve">adijciemus gr. </s> <s xml:id="echoid-s7333" xml:space="preserve">27. </s> <s xml:id="echoid-s7334" xml:space="preserve">min. </s> <s xml:id="echoid-s7335" xml:space="preserve">47. </s> <s xml:id="echoid-s7336" xml:space="preserve">ut fiat longitudo uera à principio ♈. </s> <s xml:id="echoid-s7337" xml:space="preserve">grad. </s> <s xml:id="echoid-s7338" xml:space="preserve"><lb/>198. </s> <s xml:id="echoid-s7339" xml:space="preserve">min. </s> <s xml:id="echoid-s7340" xml:space="preserve">7. </s> <s xml:id="echoid-s7341" xml:space="preserve">quæ quoniam maior eſt, quàm gr. </s> <s xml:id="echoid-s7342" xml:space="preserve">90. </s> <s xml:id="echoid-s7343" xml:space="preserve">minor autẽ quàm gr. </s> <s xml:id="echoid-s7344" xml:space="preserve">270. </s> <s xml:id="echoid-s7345" xml:space="preserve">exi-<lb/>ſtet dicta ſtella in ſemicirculo Eclipticę deſcendente, numerandaq́; </s> <s xml:id="echoid-s7346" xml:space="preserve">c<unsure/>rit eius <lb/>longitudo à principio ♋, (quoniã latitudiuẽ habet borealẽ) ſecundũ ſucceſ-<lb/>fionem ſignorum, quæ longitudo, ſi gr. </s> <s xml:id="echoid-s7347" xml:space="preserve">90. </s> <s xml:id="echoid-s7348" xml:space="preserve">detrahantur ex eius longitudine ve <lb/>ra, reperietur continere gr. </s> <s xml:id="echoid-s7349" xml:space="preserve">108. </s> <s xml:id="echoid-s7350" xml:space="preserve">min. </s> <s xml:id="echoid-s7351" xml:space="preserve">7. </s> <s xml:id="echoid-s7352" xml:space="preserve">cuius ſinus uerſus erit 131095. </s> <s xml:id="echoid-s7353" xml:space="preserve">poſito <lb/>ſinu toto 100000. </s> <s xml:id="echoid-s7354" xml:space="preserve">Latitudo autem eiuſdem ſtellę borealis eſt grad. </s> <s xml:id="echoid-s7355" xml:space="preserve">31. </s> <s xml:id="echoid-s7356" xml:space="preserve">min. </s> <s xml:id="echoid-s7357" xml:space="preserve">30. </s> <s xml:id="echoid-s7358" xml:space="preserve"><lb/>eiusq́; </s> <s xml:id="echoid-s7359" xml:space="preserve">complementum grad. </s> <s xml:id="echoid-s7360" xml:space="preserve">58. </s> <s xml:id="echoid-s7361" xml:space="preserve">min. </s> <s xml:id="echoid-s7362" xml:space="preserve">30. </s> <s xml:id="echoid-s7363" xml:space="preserve">Differentia quoque inter maximã de- <pb o="184" file="220" n="221" rhead="Comment. in I. Cap. Sphæræ"/> clinationem Eclipti@æ, hoc eſt, inter grad. </s> <s xml:id="echoid-s7364" xml:space="preserve">23. </s> <s xml:id="echoid-s7365" xml:space="preserve">min. </s> <s xml:id="echoid-s7366" xml:space="preserve">30. </s> <s xml:id="echoid-s7367" xml:space="preserve">& </s> <s xml:id="echoid-s7368" xml:space="preserve">complementum lati-<lb/>tudinis ſtellæ, hoc eſt, grad. </s> <s xml:id="echoid-s7369" xml:space="preserve">58. </s> <s xml:id="echoid-s7370" xml:space="preserve">min. </s> <s xml:id="echoid-s7371" xml:space="preserve">30. </s> <s xml:id="echoid-s7372" xml:space="preserve">continet gr. </s> <s xml:id="echoid-s7373" xml:space="preserve">35. </s> <s xml:id="echoid-s7374" xml:space="preserve">min. </s> <s xml:id="echoid-s7375" xml:space="preserve">0. </s> <s xml:id="echoid-s7376" xml:space="preserve">& </s> <s xml:id="echoid-s7377" xml:space="preserve">ſinus comple-<lb/>menti huius differentiæ eſt 81915. </s> <s xml:id="echoid-s7378" xml:space="preserve">Itaq; </s> <s xml:id="echoid-s7379" xml:space="preserve">ſi fiat, vt 10000000000. </s> <s xml:id="echoid-s7380" xml:space="preserve">quadratum ſi-<lb/>nus totius ad 3399816736. </s> <s xml:id="echoid-s7381" xml:space="preserve">rectangulum contentum ſub 39874. </s> <s xml:id="echoid-s7382" xml:space="preserve">ſinu recto ma-<lb/>ximę declinationis Eclipticę, & </s> <s xml:id="echoid-s7383" xml:space="preserve">85264. </s> <s xml:id="echoid-s7384" xml:space="preserve">ſinu complementi latitudinis ſtellæ ꝓ-<lb/>poſitæ, ita 131095. </s> <s xml:id="echoid-s7385" xml:space="preserve">ſinus verſus longitudinis ſtellæ a ♋, ſecundum ſucceſſionẽ <lb/>ſignorum ad aliud, (hoc eſt, ſi iuxta regulam proportionum, quam Trium vo-<lb/>cant, rectangulum dictum, quod habetur ex multiplicatione ſinus maximę de-<lb/>clinationis Eclipticæ per ſi num complemẽti latitudinis ſtellæ, multiplicemus <lb/>per ſinum uerſum longitudinis ſtellæ, nempe ſecundum numerum regulæ <lb/>Trium duca mus in tertium, productumq; </s> <s xml:id="echoid-s7386" xml:space="preserve">diuidamus per quadratum ſinus to-<lb/>tius, nimirum per primum numerum regulæ Trium, quod facillime ſiet, ſi ex <lb/>producto abijciantur decem priores figurę ad manum dextram) inuenietur <lb/>hic numerus 44569. </s> <s xml:id="echoid-s7387" xml:space="preserve">quem, quia minor eſt, quàm 81915. </s> <s xml:id="echoid-s7388" xml:space="preserve">ſinus complementi <lb/>differentiæ inter maximam declinationem Eclipticæ, & </s> <s xml:id="echoid-s7389" xml:space="preserve">complementum lati-<lb/>tudinis ſtellæ, auferemus ex 81915. </s> <s xml:id="echoid-s7390" xml:space="preserve">ſinu complementi dictæ differentiæ, relin-<lb/>queturq́ue ſinus declinationis borealis Arctcri 37346. </s> <s xml:id="echoid-s7391" xml:space="preserve">cui in tabula ſinuum <lb/>reſpondet arcus grad. </s> <s xml:id="echoid-s7392" xml:space="preserve">21. </s> <s xml:id="echoid-s7393" xml:space="preserve">min. </s> <s xml:id="echoid-s7394" xml:space="preserve">56. </s> <s xml:id="echoid-s7395" xml:space="preserve">Tanta ergo cſt declinatio Arcturi ab Aequa-<lb/>tore in boream.</s> <s xml:id="echoid-s7396" xml:space="preserve"/> </p> <div xml:id="echoid-div359" type="float" level="2" n="2"> <note position="right" xlink:label="note-219-02" xlink:href="note-219-02a" xml:space="preserve">Declinatio <lb/>Arcturi.</note> </div> <p> <s xml:id="echoid-s7397" xml:space="preserve"><emph style="sc">Sit</emph> rurſus inquirenda declinatio, quam habet Hircus ſtella lucidiſſima <lb/> <anchor type="note" xlink:label="note-220-01a" xlink:href="note-220-01"/> in ſiniſtro humero Aurigæ, & </s> <s xml:id="echoid-s7398" xml:space="preserve">eſt tertia in conſtellatione 12. </s> <s xml:id="echoid-s7399" xml:space="preserve">Longitudo huius <lb/>ſtellæ in tabula habet grad. </s> <s xml:id="echoid-s7400" xml:space="preserve">48. </s> <s xml:id="echoid-s7401" xml:space="preserve">min. </s> <s xml:id="echoid-s7402" xml:space="preserve">20. </s> <s xml:id="echoid-s7403" xml:space="preserve">cui ſi addantur grad. </s> <s xml:id="echoid-s7404" xml:space="preserve">27. </s> <s xml:id="echoid-s7405" xml:space="preserve">min. </s> <s xml:id="echoid-s7406" xml:space="preserve">47. </s> <s xml:id="echoid-s7407" xml:space="preserve">confla-<lb/>bitur uera eius longitudo à principio ♈, grad. </s> <s xml:id="echoid-s7408" xml:space="preserve">76. </s> <s xml:id="echoid-s7409" xml:space="preserve">min. </s> <s xml:id="echoid-s7410" xml:space="preserve">20. </s> <s xml:id="echoid-s7411" xml:space="preserve">quæ quoniam mi-<lb/>nor eſt, quàm grad. </s> <s xml:id="echoid-s7412" xml:space="preserve">90. </s> <s xml:id="echoid-s7413" xml:space="preserve">exiſtet data ſtella in ſemicirculo Eclipticæ aſcendente, <lb/>numerandaque erit eius longitudo à ♋, (quoniam eius latitudo borealis eſt) <lb/>contra ſignorum ſucceſſionem; </s> <s xml:id="echoid-s7414" xml:space="preserve">quæ longitudo, ſi eius longitudo vera detra-<lb/>hatur ex grad. </s> <s xml:id="echoid-s7415" xml:space="preserve">90. </s> <s xml:id="echoid-s7416" xml:space="preserve">comprehendet gra. </s> <s xml:id="echoid-s7417" xml:space="preserve">13. </s> <s xml:id="echoid-s7418" xml:space="preserve">min. </s> <s xml:id="echoid-s7419" xml:space="preserve">40. </s> <s xml:id="echoid-s7420" xml:space="preserve">cuius ſinus verſus erit 2832. <lb/></s> <s xml:id="echoid-s7421" xml:space="preserve">Latitudo autem eiuſdem ſtellę borealis eſt grad. </s> <s xml:id="echoid-s7422" xml:space="preserve">22. </s> <s xml:id="echoid-s7423" xml:space="preserve">min. </s> <s xml:id="echoid-s7424" xml:space="preserve">30. </s> <s xml:id="echoid-s7425" xml:space="preserve">eiuſque comple-<lb/>mentum grad. </s> <s xml:id="echoid-s7426" xml:space="preserve">67. </s> <s xml:id="echoid-s7427" xml:space="preserve">min. </s> <s xml:id="echoid-s7428" xml:space="preserve">30. </s> <s xml:id="echoid-s7429" xml:space="preserve">Differentia quoque inter grad. </s> <s xml:id="echoid-s7430" xml:space="preserve">23. </s> <s xml:id="echoid-s7431" xml:space="preserve">min. </s> <s xml:id="echoid-s7432" xml:space="preserve">30. </s> <s xml:id="echoid-s7433" xml:space="preserve">maximæ <lb/>declinationis Eclipticæ, & </s> <s xml:id="echoid-s7434" xml:space="preserve">grad. </s> <s xml:id="echoid-s7435" xml:space="preserve">67. </s> <s xml:id="echoid-s7436" xml:space="preserve">minut. </s> <s xml:id="echoid-s7437" xml:space="preserve">30. </s> <s xml:id="echoid-s7438" xml:space="preserve">complementi latitudinis ſtellæ, <lb/>complectitur grad. </s> <s xml:id="echoid-s7439" xml:space="preserve">44. </s> <s xml:id="echoid-s7440" xml:space="preserve">min. </s> <s xml:id="echoid-s7441" xml:space="preserve">0. </s> <s xml:id="echoid-s7442" xml:space="preserve">Sinus uero complementi huius differentiæ eſt <lb/>71923. </s> <s xml:id="echoid-s7443" xml:space="preserve">Itaque ſi fiat, vt 10000000000. </s> <s xml:id="echoid-s7444" xml:space="preserve">quadratũ ſinus totius ad 3683839238. </s> <s xml:id="echoid-s7445" xml:space="preserve"><lb/>rectangulum comprehẽſum ſub 29874. </s> <s xml:id="echoid-s7446" xml:space="preserve">ſinu recto maximæ declinationis Ecli <lb/>pticæ, & </s> <s xml:id="echoid-s7447" xml:space="preserve">92387. </s> <s xml:id="echoid-s7448" xml:space="preserve">ſinu complemẽti latitudinis ſtellæ datæ, ita 2832. </s> <s xml:id="echoid-s7449" xml:space="preserve">ſinus uerſus <lb/>longitudinis ſtellæ à ♋, contra ſucceſſionem ſignorũ ad aliud, inuenietur hic <lb/>numerus 1043. </s> <s xml:id="echoid-s7450" xml:space="preserve">quem, quia minor eſt, quám 71933. </s> <s xml:id="echoid-s7451" xml:space="preserve">ſinus complementidifferen <lb/>tiæ inter maximam Eclipticæ declinationem, & </s> <s xml:id="echoid-s7452" xml:space="preserve">complementum latitudinis <lb/>ſtellæ, auferemus ex 71933. </s> <s xml:id="echoid-s7453" xml:space="preserve">ſinu complementi dictæ differentiæ, re<unsure/>manebitq; </s> <s xml:id="echoid-s7454" xml:space="preserve"><lb/>70896. </s> <s xml:id="echoid-s7455" xml:space="preserve">ſinus declinationis borealis Hirci, cui in tabula ſinuum reſpondent gr. </s> <s xml:id="echoid-s7456" xml:space="preserve"><lb/>45. </s> <s xml:id="echoid-s7457" xml:space="preserve">min. </s> <s xml:id="echoid-s7458" xml:space="preserve">9. </s> <s xml:id="echoid-s7459" xml:space="preserve">pro declinatione Hirci ab Aequatore in boream.</s> <s xml:id="echoid-s7460" xml:space="preserve"/> </p> <div xml:id="echoid-div360" type="float" level="2" n="3"> <note position="left" xlink:label="note-220-01" xlink:href="note-220-01a" xml:space="preserve">Declinatio <lb/>Hirci.</note> </div> <p> <s xml:id="echoid-s7461" xml:space="preserve"><emph style="sc">Rvrsvs</emph> exploranda ſit declinatio illius ſtellæ, quæ in humero dextro <lb/> <anchor type="note" xlink:label="note-220-02a" xlink:href="note-220-02"/> ♒, collocatur, eſtq; </s> <s xml:id="echoid-s7462" xml:space="preserve">ſecunda in conſte<unsure/>llatione ♒, & </s> <s xml:id="echoid-s7463" xml:space="preserve">magnitudinis 3. </s> <s xml:id="echoid-s7464" xml:space="preserve">Longi-<lb/>tudo huius ſtellæ in tabula habet grad. </s> <s xml:id="echoid-s7465" xml:space="preserve">299. </s> <s xml:id="echoid-s7466" xml:space="preserve">min. </s> <s xml:id="echoid-s7467" xml:space="preserve">40. </s> <s xml:id="echoid-s7468" xml:space="preserve">cui ſi addantur grad. </s> <s xml:id="echoid-s7469" xml:space="preserve">27. <lb/></s> <s xml:id="echoid-s7470" xml:space="preserve">minu. </s> <s xml:id="echoid-s7471" xml:space="preserve">47. </s> <s xml:id="echoid-s7472" xml:space="preserve">conficietur vera eius longitudo à principio ♈, grad. </s> <s xml:id="echoid-s7473" xml:space="preserve">327. </s> <s xml:id="echoid-s7474" xml:space="preserve">minu. </s> <s xml:id="echoid-s7475" xml:space="preserve">27. </s> <s xml:id="echoid-s7476" xml:space="preserve"><lb/>quæ quoniam maior eſt, quàm grad. </s> <s xml:id="echoid-s7477" xml:space="preserve">270. </s> <s xml:id="echoid-s7478" xml:space="preserve">exiſtet dicta ſtella in Eclipticæ ſemi-<lb/>circulo aſcendente, numerandaque erit eius longitudo à ♋, (quoniam latitu-<lb/>dinem habet borealem) contra ſucceſſionem ſignorum: </s> <s xml:id="echoid-s7479" xml:space="preserve">quæ longitudo, ſi <lb/>eius longitudo uera ſubtrahatur ex grad. </s> <s xml:id="echoid-s7480" xml:space="preserve">360. </s> <s xml:id="echoid-s7481" xml:space="preserve">& </s> <s xml:id="echoid-s7482" xml:space="preserve">reliquo numero addantur <pb o="185" file="221" n="222" rhead="Ioan. de Sacro Boſco."/> grad. </s> <s xml:id="echoid-s7483" xml:space="preserve">90. </s> <s xml:id="echoid-s7484" xml:space="preserve">complectetur grad. </s> <s xml:id="echoid-s7485" xml:space="preserve">122. </s> <s xml:id="echoid-s7486" xml:space="preserve">min. </s> <s xml:id="echoid-s7487" xml:space="preserve">33. </s> <s xml:id="echoid-s7488" xml:space="preserve">cuius ſinus uerſus erit 153803. </s> <s xml:id="echoid-s7489" xml:space="preserve">La-<lb/>titudo autem eiuſdem ſtellæ borealis eſt grad. </s> <s xml:id="echoid-s7490" xml:space="preserve">11. </s> <s xml:id="echoid-s7491" xml:space="preserve">min. </s> <s xml:id="echoid-s7492" xml:space="preserve">0. </s> <s xml:id="echoid-s7493" xml:space="preserve">eiuſq́; </s> <s xml:id="echoid-s7494" xml:space="preserve">complemen-<lb/>tum grad. </s> <s xml:id="echoid-s7495" xml:space="preserve">79. </s> <s xml:id="echoid-s7496" xml:space="preserve">min. </s> <s xml:id="echoid-s7497" xml:space="preserve">0. </s> <s xml:id="echoid-s7498" xml:space="preserve">Differentia quoque inter grad. </s> <s xml:id="echoid-s7499" xml:space="preserve">23. </s> <s xml:id="echoid-s7500" xml:space="preserve">min. </s> <s xml:id="echoid-s7501" xml:space="preserve">30. </s> <s xml:id="echoid-s7502" xml:space="preserve">maximæ decli <lb/>nationis Eclipticæ, & </s> <s xml:id="echoid-s7503" xml:space="preserve">grad. </s> <s xml:id="echoid-s7504" xml:space="preserve">79. </s> <s xml:id="echoid-s7505" xml:space="preserve">min. </s> <s xml:id="echoid-s7506" xml:space="preserve">0. </s> <s xml:id="echoid-s7507" xml:space="preserve">complementi latitudinis ſtellæ, com-<lb/>prehendit gr. </s> <s xml:id="echoid-s7508" xml:space="preserve">55. </s> <s xml:id="echoid-s7509" xml:space="preserve">min. </s> <s xml:id="echoid-s7510" xml:space="preserve">30. </s> <s xml:id="echoid-s7511" xml:space="preserve">ſinus uero complementi huius differentiæ eſt 56640.</s> <s xml:id="echoid-s7512" xml:space="preserve"/> </p> <div xml:id="echoid-div361" type="float" level="2" n="4"> <note position="left" xlink:label="note-220-02" xlink:href="note-220-02a" xml:space="preserve">Declinatio <lb/>a. ſtellæ A <lb/>quarij, quæ <lb/>in dextro <lb/>humero col <lb/>locatur, eſt <lb/>que magni-<lb/>t<unsure/>udinis 3.</note> </div> <p> <s xml:id="echoid-s7513" xml:space="preserve">It aque ſi fiat, ut 10000000000. </s> <s xml:id="echoid-s7514" xml:space="preserve">quadratum ſinustotius ad 3914111588. </s> <s xml:id="echoid-s7515" xml:space="preserve">re-<lb/>ctangulum comprehenſum ſub 39874. </s> <s xml:id="echoid-s7516" xml:space="preserve">ſinu recto maximæ declinationis Ecli-<lb/>pticæ, & </s> <s xml:id="echoid-s7517" xml:space="preserve">98162. </s> <s xml:id="echoid-s7518" xml:space="preserve">ſinu complementi latitudinis ſtellæ, ita 153803. </s> <s xml:id="echoid-s7519" xml:space="preserve">ſinus uerſus <lb/>longitudinis ſtellæ à ♋, contra ſucceſsionem ſignorum ad aliud, inuenietur <lb/>hic numerus 60200. </s> <s xml:id="echoid-s7520" xml:space="preserve">à quo, quoniam maior eſt, quàm 56640. </s> <s xml:id="echoid-s7521" xml:space="preserve">ſinus complemen <lb/>ti di<unsure/>fferentiæ inter maximam Eclipticæ declinationem, & </s> <s xml:id="echoid-s7522" xml:space="preserve">complementum Ia-<lb/>titudinis ſtellæ, auferemus 56640. </s> <s xml:id="echoid-s7523" xml:space="preserve">ſinum complementi dictę differentię, re-<lb/>manebitq́ue 3560. </s> <s xml:id="echoid-s7524" xml:space="preserve">ſinus declinationis auſtralis dictæ ſtellæ, cui in tabula ſi-<lb/>nuum reſpondent grad. </s> <s xml:id="echoid-s7525" xml:space="preserve">2. </s> <s xml:id="echoid-s7526" xml:space="preserve">min. </s> <s xml:id="echoid-s7527" xml:space="preserve">2. </s> <s xml:id="echoid-s7528" xml:space="preserve">pro declinatione datæ ſtellæ ab Aequatore <lb/>in auſtrum.</s> <s xml:id="echoid-s7529" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7530" xml:space="preserve"><emph style="sc">Postremo</emph> inueſtigandum ſit, quantam declinationem habeat 34. <lb/></s> <s xml:id="echoid-s7531" xml:space="preserve"> <anchor type="note" xlink:label="note-221-01a" xlink:href="note-221-01"/> ſtella in Centauro, quæ maxime auſtralis eſt, exiſtitq́; </s> <s xml:id="echoid-s7532" xml:space="preserve">ſub muſculo pedis ſini-<lb/>ſtri, & </s> <s xml:id="echoid-s7533" xml:space="preserve">eſt magnitudinis 2. </s> <s xml:id="echoid-s7534" xml:space="preserve">Longitudo huius ftellæ in tabula habet gr. </s> <s xml:id="echoid-s7535" xml:space="preserve">184. </s> <s xml:id="echoid-s7536" xml:space="preserve">min. <lb/></s> <s xml:id="echoid-s7537" xml:space="preserve">30. </s> <s xml:id="echoid-s7538" xml:space="preserve">cui ſi addantur grad. </s> <s xml:id="echoid-s7539" xml:space="preserve">27. </s> <s xml:id="echoid-s7540" xml:space="preserve">min. </s> <s xml:id="echoid-s7541" xml:space="preserve">47. </s> <s xml:id="echoid-s7542" xml:space="preserve">componetur uera eius longitudo à princi-<lb/>pio ♈, grad. </s> <s xml:id="echoid-s7543" xml:space="preserve">212. </s> <s xml:id="echoid-s7544" xml:space="preserve">min. </s> <s xml:id="echoid-s7545" xml:space="preserve">17. </s> <s xml:id="echoid-s7546" xml:space="preserve">quæ quoniam maior eſt, quàm grad. </s> <s xml:id="echoid-s7547" xml:space="preserve">90. </s> <s xml:id="echoid-s7548" xml:space="preserve">minor autem <lb/>quà<unsure/>m grad. </s> <s xml:id="echoid-s7549" xml:space="preserve">270. </s> <s xml:id="echoid-s7550" xml:space="preserve">exiſtet dicta ſtella in ſemicirculo deſcendente Eclypticæ, nu <lb/>merandaq́; </s> <s xml:id="echoid-s7551" xml:space="preserve">erit eius longitudo à<unsure/> ♑, (quia latitudinem habet auſtralem) cõtra <lb/>ſucceſsionem ſignorum: </s> <s xml:id="echoid-s7552" xml:space="preserve">quæ longitudo, ſi eius longitudo uera ex gra. </s> <s xml:id="echoid-s7553" xml:space="preserve">270. </s> <s xml:id="echoid-s7554" xml:space="preserve">de-<lb/>matur, continebit gr. </s> <s xml:id="echoid-s7555" xml:space="preserve">57. </s> <s xml:id="echoid-s7556" xml:space="preserve">min. </s> <s xml:id="echoid-s7557" xml:space="preserve">43. </s> <s xml:id="echoid-s7558" xml:space="preserve">cuius ſinus uerſus erit 46590. </s> <s xml:id="echoid-s7559" xml:space="preserve">Lati<unsure/>tudo por-<lb/>ro eiuſdem ſtellæ auſtralis eſt gra. </s> <s xml:id="echoid-s7560" xml:space="preserve">55. </s> <s xml:id="echoid-s7561" xml:space="preserve">min. </s> <s xml:id="echoid-s7562" xml:space="preserve">40. </s> <s xml:id="echoid-s7563" xml:space="preserve">eiuſq́; </s> <s xml:id="echoid-s7564" xml:space="preserve">complementum grad. </s> <s xml:id="echoid-s7565" xml:space="preserve">34. </s> <s xml:id="echoid-s7566" xml:space="preserve"><lb/>minu. </s> <s xml:id="echoid-s7567" xml:space="preserve">20. </s> <s xml:id="echoid-s7568" xml:space="preserve">Ac proinde differentia inter grad. </s> <s xml:id="echoid-s7569" xml:space="preserve">23. </s> <s xml:id="echoid-s7570" xml:space="preserve">min. </s> <s xml:id="echoid-s7571" xml:space="preserve">30. </s> <s xml:id="echoid-s7572" xml:space="preserve">maximæ declinationis <lb/>Eclipticæ, & </s> <s xml:id="echoid-s7573" xml:space="preserve">grad 34. </s> <s xml:id="echoid-s7574" xml:space="preserve">min. </s> <s xml:id="echoid-s7575" xml:space="preserve">20. </s> <s xml:id="echoid-s7576" xml:space="preserve">complementi latitudinis ſtellæ, comprehendet <lb/>grad. </s> <s xml:id="echoid-s7577" xml:space="preserve">10. </s> <s xml:id="echoid-s7578" xml:space="preserve">min. </s> <s xml:id="echoid-s7579" xml:space="preserve">50. </s> <s xml:id="echoid-s7580" xml:space="preserve">ſinus uero complementi huius differentię erit 98219. </s> <s xml:id="echoid-s7581" xml:space="preserve">Itaque <lb/>ſi fiat, ut 10000000000. </s> <s xml:id="echoid-s7582" xml:space="preserve">quadratum ſinus totius ad 2248893600. </s> <s xml:id="echoid-s7583" xml:space="preserve">rectangulum <lb/>contentum ſub 39874. </s> <s xml:id="echoid-s7584" xml:space="preserve">ſinu recto maximæ declinationis Eclipticæ, & </s> <s xml:id="echoid-s7585" xml:space="preserve">56400. </s> <s xml:id="echoid-s7586" xml:space="preserve"><lb/>ſinu complementi latitudinis ſtellę, ita 46590. </s> <s xml:id="echoid-s7587" xml:space="preserve">ſinus uerſus longitudinis ſtel-<lb/>læ à ♑, contra ſucceſſionem ſignorũ ad aliud, reperietur hic numerus 10459. </s> <s xml:id="echoid-s7588" xml:space="preserve"><lb/>quem quia, minor eſt, quàm 98217. </s> <s xml:id="echoid-s7589" xml:space="preserve">ſinus complementi differentię inter maxi-<lb/>mam Eclipticæ declinationem, & </s> <s xml:id="echoid-s7590" xml:space="preserve">complementum latitudinis ſtellę, detrahe-<lb/>mus ex 98217. </s> <s xml:id="echoid-s7591" xml:space="preserve">ſinu complementi dictę differentię relinqueturq; </s> <s xml:id="echoid-s7592" xml:space="preserve">87758. </s> <s xml:id="echoid-s7593" xml:space="preserve">ſinus <lb/>declinationis auſtralis propoſitę ſt<unsure/>ellę, cui in tabula ſinum reſpondent gra. </s> <s xml:id="echoid-s7594" xml:space="preserve"><lb/>61. </s> <s xml:id="echoid-s7595" xml:space="preserve">min. </s> <s xml:id="echoid-s7596" xml:space="preserve">21. </s> <s xml:id="echoid-s7597" xml:space="preserve">pro declinatione dictę ſtellę ab Aequatore in auſtrum. </s> <s xml:id="echoid-s7598" xml:space="preserve">Ex his exem <lb/>plis ſatis arbitror præceptum à nobis traditum percipi, quo ſtellarum declina <lb/>tiones in ueſtigentur. </s> <s xml:id="echoid-s7599" xml:space="preserve">Alia pręcepta ad eaſdem declinationes perquirenda de-<lb/>monſtrau imus in ijs, quæ ad doctrinam primi mobilis pertinent.</s> <s xml:id="echoid-s7600" xml:space="preserve"/> </p> <div xml:id="echoid-div362" type="float" level="2" n="5"> <note position="right" xlink:label="note-221-01" xlink:href="note-221-01a" xml:space="preserve">Declinatio<unsure/> <lb/>34. ſtellę Cẽ <lb/>tauri, quæ <lb/>ſub muſcu-<lb/>lo ẽ ſiniſtrĩ<unsure/> <lb/>pedis, eſtq. <lb/>magnitudi <lb/>nis 2.</note> </div> </div> <div xml:id="echoid-div364" type="section" level="1" n="115"> <head xml:id="echoid-head120" xml:space="preserve">DE QVANTITATE STELLARVM.</head> <p> <s xml:id="echoid-s7601" xml:space="preserve"><emph style="sc">Constitvto</emph> numero ſtellarum, quę in ſex differentias magnitudi-<lb/>num di@@ribuuntur, explicataq. </s> <s xml:id="echoid-s7602" xml:space="preserve">ratione, qua carum declinationes inueſtigen-<lb/>tur, proponenda iam eſt quantitas earundem ſtellarum in quacun que differen <lb/>tia magnitudinum. </s> <s xml:id="echoid-s7603" xml:space="preserve">Hoc autem commodi<unsure/>ſſime efficiemus, ſi tabulas quaſdam <lb/>ſnbijciamus hoc loco, in quibus & </s> <s xml:id="echoid-s7604" xml:space="preserve">proportiones diametiorum ſtellarum tam <pb o="186" file="222" n="223" rhead="Comment. in. I. Cap. Sphæræ"/> f<unsure/>ixarum, quam errantium, ad diametrum terræ, & </s> <s xml:id="echoid-s7605" xml:space="preserve">proportiones magnitudinũ <lb/>ſtellarum earundem ad terræ magnitudinem, contineantur: </s> <s xml:id="echoid-s7606" xml:space="preserve">Quibus in tabulis <lb/>ſecuti ſumus Franciſcum Maurolycum Abbatem in Appendice Dialogorum <lb/>de Coſmographia.</s> <s xml:id="echoid-s7607" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div365" type="section" level="1" n="116"> <head xml:id="echoid-head121" xml:space="preserve">Proportiones diametrorum ſtellarum omnium ad <lb/>di<unsure/>ametrum terræ.</head> <note position="left" xml:space="preserve">Proportio. <lb/>n<unsure/>es diame-<lb/>tro@ũ<unsure/> ſtella <lb/>rũ ad terræ <lb/>diametrũ.</note> <note position="right" xml:space="preserve"> <lb/>Diameter cuiuſlibet ſtellę magnitudinis primæ ad \\ diametrum terræ proportionem habet, quam # 19 # ad # 4 <lb/>Diameter cuiuſli<unsure/>bet ſtellæ magnitudinis ſecundæ ad \\ diametrum terrę proportionem habet, quam # 269 # ad # 60. <lb/>Diameter cuiuslibet ſtellæ magnitudinis tertiæ ad \\ diametrum terrę proportionem habet, quam # 25 # ad # 6. <lb/>Diameter cuiuslibet ſtellæ magnitudinis quartę ad \\ diametrum terrę proportionem habet, quam # 19 # ad # 5. <lb/>Diameter cuiuslibet ſtellæ magnitudinis quintæ ad \\ diametrum terrę proportionem habet, quam # 119 # ad # 36. <lb/>Diameter cuiuslibet ſtellæ magnitudinis ſextæ ad \\ Diametrum terrę proportionem habet, quam # 21 # ad # 8. <lb/>Diameter variant ad diametrum terræ proportio- \\ nem, habet quam # 9 # ad # 2. <lb/>Diameter ♃ ad di<unsure/>ametrum terræ proporrio- \\ nem habet, quam # 32 # ad # 7. <lb/>Diameter ☌ ad diametrum terræ proportio- \\ nem habet, quam # 7 # ad # 6. <lb/>Diameter *** ad diametrum terræ proportio- \\ nem habet, quam # 11 # ad # 2. <lb/>Diameter ♀ ad diametrum terrę proportio- \\ nem habet, quam # 3 # ad # 10. <lb/>Diameter ☿ ad diametrum terrę proportio- \\ nem habet, quam # 1 # ad # 28. <lb/>Diameter ☽ ad diametrum terræ proportio- \\ nem habet, quam # 5 # ad # 17. <lb/>Diameter *** ad diametrum ☽ proportio- \\ nem habet, quam # 187 # ad # 10. <lb/></note> <p> <s xml:id="echoid-s7608" xml:space="preserve"><emph style="sc">Itaqve</emph> ſi diuidantur ſinguli termini antecedentes harum proportio-<lb/>num per ſingulos terminos conſequentes, eluceſcet, quoties diameter cuiuſ-<lb/>uis ſtellæ contineat diametrum terrę, quando nimirum diameter ſtellę diame <lb/>trum terrę exced@t, cuiuſmodi ſunt diametri omniũ aſtrorum, exceptis diame-<lb/>tr<unsure/>is Veneris, Mercurij, & </s> <s xml:id="echoid-s7609" xml:space="preserve">Lunę; </s> <s xml:id="echoid-s7610" xml:space="preserve">uel certe, quoties diameter terrę diametrum <lb/>ſtellę co<unsure/>ntineat, quãdo uidelicet diameter ſtellę a terrę diametro ſuperatur, <pb o="187" file="223" n="224" rhead="Ioan. de Sacro Boſco."/> quales ſunt diametri inferiorum trium planetarum. </s> <s xml:id="echoid-s7611" xml:space="preserve">Hic enim dinidendi erũt <lb/>termini conſequentes per antecedentes. </s> <s xml:id="echoid-s7612" xml:space="preserve">Verum hæc omnia in ſubie cta tabula <lb/>inſpicere licebit.</s> <s xml:id="echoid-s7613" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div366" type="section" level="1" n="117"> <head xml:id="echoid-head122" style="it" xml:space="preserve">Quoties diameter cuiuſuis ſtellæ diametrum terræ, uel diameter <lb/>terræ diametrum ſtellæ in ſe contineat.</head> <note position="right" xml:space="preserve">Quoties dia <lb/>mei<unsure/>er cu-<lb/>iuſuis ſtellę <lb/>diametrum <lb/>terr<unsure/>æ conti-<lb/>neat, aut cõ <lb/>tra.</note> <note position="right" xml:space="preserve"> <lb/>Diameter cuiuslibet ſtellę magnitudinis primę \\ continet diametros terræ # 4 {3/4} <lb/> Diameter cuiuslibet ſteliæ magnitudinis ſecundæ \\ continet diametros terræ # 4 {29/60} Diameter cuiuslibet ſtellæ magnitudinis tertię \\ continet diametros terrę # 4 {1/6} Diameter cuiuslibet ſtellæ magnitudinis quartæ \\ continet diametros terrę # 3 {4/5} Diameter cuiuslibet ſtellæ magnitudinis quintæ \\ continet diametros terrę # 33 {11/38} Diameter cuiuslibet ſtellæ magnitudinis ſextæ \\ continet diametros terrę # 2 {5/8} Diameter variant continet diametros terrę # 4 {2/1} Diameter ♃ continet diametros terrę # 4 {4/7} Diameter ☌ continet diametros terrę # 1 {1/6} Diameter *** continet diametros terrę # 5 {1/2} Diameter terrę continet diametros ♀ # 3 {1/@} Diameter terrę continet diametros ☿ # 28 Diameter terræ continet diametros ☽ # 3 {2/5} Diameter *** continet diametros ☽ # 18 {7/10<unsure/>} </note> <p> <s xml:id="echoid-s7614" xml:space="preserve"><emph style="sc">Cvm</emph> autem ſphęræ inter ſe proportionem habeant diametrorum tripli-<lb/> <anchor type="note" xlink:label="note-223-03a" xlink:href="note-223-03"/> catam, non difficile erit uel mediocriter in Arithmeticis verſato colligere ex <lb/>priori tabula omnes proportiones, quas ſtellarum magnitudines habeant ad <lb/>terrę magnitudinem, ueluti apparet in ſubſequenti tabula, in qua dictæ pro-<lb/>portiones in numeris integris, & </s> <s xml:id="echoid-s7615" xml:space="preserve">minimis continentur.</s> <s xml:id="echoid-s7616" xml:space="preserve"/> </p> <div xml:id="echoid-div366" type="float" level="2" n="1"> <note position="right" xlink:label="note-223-03" xlink:href="note-223-03a" xml:space="preserve">18. duod.</note> </div> </div> <div xml:id="echoid-div368" type="section" level="1" n="118"> <head xml:id="echoid-head123" style="it" xml:space="preserve">Proportiones magnitudinum ftellarum omnium <lb/>ad magnitudinem terrę.</head> <note position="right" xml:space="preserve">Proportio-<lb/>nes magni-<lb/>tudinũ ſtel-<lb/>larũ ad ter <lb/>ræ magnitu <lb/>dinem.</note> <note position="right" xml:space="preserve"> <lb/>Stella quæuis primæ magnitudinis ad \\ terram proportionem haber, quam # 6859 # ad # 64 <lb/>Stella quęuis ſecundæ magnitudinis ad \\ terram proportionem habet, quam # 19465109 # ad # 216000 <lb/> Stella quæuis tertię magnitudinis ad \\ terram proportionem habet, quam # 15625 # ad # 216 </note> <pb o="188" file="224" n="225" rhead="Comment. in I. Cap. Sphæræ"/> <note position="right" xml:space="preserve"> <lb/>Stella quæuis quartæ magnitudinis ad \\ terram proportionem habet, quam # 6859 # ad # 12@ <lb/>Stella quæuis quintæ magnitudinis ad \\ terram propor<unsure/>tionem habet, quam # 1685159 # ad # 46656 <lb/>Stella quæuis ſextæ magnitudinis ad \\ terram proportionem habet, quam # 9261 # ad # 512 <lb/>Saturnus ſe habet ad terram, vt # 729 # ad # 8 <lb/>Iuppiter ſ<unsure/>e habet ad terram, vt # 32768 # ad # 543 <lb/>Mars ſe habet ad terram, vt # 343 # ad # 216 <lb/>Sol ſe habet ad terram, vt # 1331 # ad # 8 <lb/>Venus ſe habet ad terram, vt # 127 # ad # 1000 <lb/>Mercurius ſe habet ad terram, vt # 1 # ad # 21952 <lb/>Luna ſe habet ad terram, vt # 125 # ad # 4913 <lb/>Solſe habet ad Lunam, vt # 6539203 # ad # 1000 <lb/></note> <p> <s xml:id="echoid-s7617" xml:space="preserve"><emph style="sc">Qvod</emph> ſi diuidantur omnium harum proportionum termini anteceden-<lb/>tes per terminos conſequentes, manifeſtum erit, quoties magnitudo cuiuſuis <lb/>aſtri magnitudinem terræ in ſe cõtineat, exceptis tribus planetis inferioribus. <lb/></s> <s xml:id="echoid-s7618" xml:space="preserve">In his enim diuidendi erunt termini conſequentes per antecedentes, ut co-<lb/>gn<unsure/>oſcatur, quoties magnitudo terræ magnitudinem cuiuſt<unsure/>ibet illorum com-<lb/>prehendat, ueluti in ſequenti tabula perſpicuum eſt.</s> <s xml:id="echoid-s7619" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div369" type="section" level="1" n="119"> <head xml:id="echoid-head124" style="it" xml:space="preserve">Quoties magnitudo cuiuſuis ſtellæ magnitudinem terræ, uel magnitu-<lb/>do terrę magnitudinem ſtellæ in ſe contineat.</head> <note position="left" xml:space="preserve">Quotiesma <lb/>gnitudo cu <lb/>iuſuis ſtel <lb/>læ magnitu <lb/>dinem ter-<lb/>ræ comple-<lb/>ctatur, aut <lb/>contra.</note> <note position="right" xml:space="preserve"> <lb/>Quæuis ſtella primæ magnitudinis in ſe \\ cont<unsure/>inet terræ magnitudinem # 107 {11/64} # vel # 107 {1/6} <lb/> Quæuis ſtella ſecundæ magnitudinis in ſe \\ continet terræ magnitudinem # 90 {25109/216000} # vel # 90 {1/8} Quæuis ſtella tertiæ magnitudinis in ſe \\ continet terrę magnitudinem # 72 {73/216} # vel # 72 {1/3} Quæuis ſtella quartæ magnitudinis in ſe \\ continet terræ magnitudinem # 54 {109/125} # vel # 54 {11/12} Quæuis ſtella quintæ magnitudinis in ſe \\ continet terræ magnitudinem # 36 {5543/466@6} # vel # 36 {1<unsure/>/8} Quæuis ſtella ſextæ magnitudinis in ſe \\ continet terræ magni<unsure/>tudinem # 18 {45/5<unsure/>12} # vel # 18 {1/10} Saturnus in ſe continet terræ magnitudinem # 91 {1/8} Iuppiter in ſe continet terræ magnitudinem # 95 {183/345} # vel # 95 {1/2} Mars in ſe continet terræ magnitudinem # 1 {127/216} # vel # 1 {1/2} Sol in ſe continet terræ magnitudinem # 166 {3/8} </note> <pb o="189" file="225" n="226" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve"> <lb/>Terra in ſe continet Veneris magnitud@nem # 37 {1/2@} <lb/>Terra in ſe @ontinet Mercurij magnitudinem # 21952 <lb/>Terra in ſe continet Lunę magnitudinem # 39 {38/125} # vel # 39 {1/3} <lb/>Sol in ſe continet Lunæ magni<unsure/>tudinem # 6539 {203/1000} # vel # 6539 {7/@} <lb/></note> <p> <s xml:id="echoid-s7620" xml:space="preserve"><emph style="sc">Priores</emph> numeri huius tabulæ reſpondent numeris ſuperiorum tabula-<unsure/> <lb/>rum pręciſ<unsure/>e, poſteriores autem non, ſed aliquantulum deficiunt à veritate, po <lb/>ſiti tamen ſunt, quòd minores ſint, ac facilius percipiantur.</s> <s xml:id="echoid-s7621" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">Sol inter a-<lb/>ſtra maxi-<lb/>mus eft, & <lb/>Mercurius <lb/>minimus.</note> <p> <s xml:id="echoid-s7622" xml:space="preserve"><emph style="sc">Ex his</emph> igitur omnibus tabulis ſatis perſpicue liquet, Solem inter omnia <lb/>aſtra mundi eſſe maximum; </s> <s xml:id="echoid-s7623" xml:space="preserve">Mercurium uero minimum. </s> <s xml:id="echoid-s7624" xml:space="preserve">Item omnes ſtellas tã <lb/>f<unsure/>ixas, quàn<unsure/> errantes, maiores eſſe ipſa terra, tribus duntaxat Planetis exceptis <lb/>Venere, Mercurio, ac Luna. </s> <s xml:id="echoid-s7625" xml:space="preserve">Hi etenim minores ſunt, quàm terra.</s> <s xml:id="echoid-s7626" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7627" xml:space="preserve"><emph style="sc">Qvod</emph> ſi curioſus quiſpiam ſcire deſideret, quotnam ſlellæ requirantur <lb/> <anchor type="note" xlink:label="note-225-03a" xlink:href="note-225-03"/> in quacunque differentia magnitudinum, vt totam ſu perficiem concauam Fir-<lb/>mamenti explere poſſint, ita ut ſeſe mutuo cõtingant, id facile aſſe quetur par <lb/>tim ex his, quæ hoc loco de proportionib. </s> <s xml:id="echoid-s7628" xml:space="preserve">diametrorum ſtellarum, & </s> <s xml:id="echoid-s7629" xml:space="preserve">terrę di-<lb/>ximus, partim vero ex ijs, quæ ad finem huius cap. </s> <s xml:id="echoid-s7630" xml:space="preserve">ſcribemus. </s> <s xml:id="echoid-s7631" xml:space="preserve">Cum enim dia-<lb/>meter concaui firmamenti contineat 22612 {1/2}. </s> <s xml:id="echoid-s7632" xml:space="preserve">diametr<unsure/>os terræ, diameter autẽ <lb/>cuiuſuis ſtellæ magni<unsure/>tudinis primæ contineat 4 {3/4}. </s> <s xml:id="echoid-s7633" xml:space="preserve">diametros terræ; </s> <s xml:id="echoid-s7634" xml:space="preserve">Si f<unsure/>iat <lb/>vt 4 {3/4}. </s> <s xml:id="echoid-s7635" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s7636" xml:space="preserve">ita 22612 {1/2}. </s> <s xml:id="echoid-s7637" xml:space="preserve">ad aliud, inuenientur in diametro concaui Firmamẽ <lb/>ti diametri unius ſtellæ magnitudinis primę 4760. </s> <s xml:id="echoid-s7638" xml:space="preserve">& </s> <s xml:id="echoid-s7639" xml:space="preserve">paulo amplius. </s> <s xml:id="echoid-s7640" xml:space="preserve">Et ſi hanc <lb/>diametrum multiplicemus per 3 {1/7}. </s> <s xml:id="echoid-s7641" xml:space="preserve">continebit circumferentia circuli maximi <lb/>in concauo Firmamenti 15960. </s> <s xml:id="echoid-s7642" xml:space="preserve">diametros vnius ſtellæ magnitudinis primæ, & </s> <s xml:id="echoid-s7643" xml:space="preserve"><lb/>paulo amplius. </s> <s xml:id="echoid-s7644" xml:space="preserve">Quam circumferentiam ſi multiplicemus per diametrum, nẽpe <lb/>per 4760. </s> <s xml:id="echoid-s7645" xml:space="preserve">reperiemus ſuperficiem concauã Firmamenii continere 71209600. <lb/></s> <s xml:id="echoid-s7646" xml:space="preserve">diametros quadratas unius ſtellæ magnitudinis primæ. </s> <s xml:id="echoid-s7647" xml:space="preserve">In quibus totidem ſtel <lb/>læ magnitudinis primæ ſe mutuo tangentes deſcribi poſſunt. </s> <s xml:id="echoid-s7648" xml:space="preserve">Ex quo etiam <lb/>apparet, illos decipi, qui putant, plures ſtellas eſſe re ipſa in Firmamẽto, quàm <lb/>filios Ifrael, pro pter @erba ſcripturæ ſupra allata. </s> <s xml:id="echoid-s7649" xml:space="preserve">Cum enim in egreſſu ex Ae-<lb/>gypto numerata fint 603550. </s> <s xml:id="echoid-s7650" xml:space="preserve">filiorum cſrael ſupra 21. </s> <s xml:id="echoid-s7651" xml:space="preserve">annos, qui nimirum ad <lb/>bolla procedebant, ut cap. </s> <s xml:id="echoid-s7652" xml:space="preserve">1. </s> <s xml:id="echoid-s7653" xml:space="preserve">Numer. </s> <s xml:id="echoid-s7654" xml:space="preserve">recte colligunt nonnulli Doctores, ſi nu-<lb/>merentur ẽt pueri, & </s> <s xml:id="echoid-s7655" xml:space="preserve">mulieres, numerum eorum maiorem fuiſſe, ꝗ̃ 2000000. </s> <s xml:id="echoid-s7656" xml:space="preserve"><lb/>Quis igitur dubitat, in totſeculis annorum multo plures fuiſſe, ꝗ̃ 71209600? </s> <s xml:id="echoid-s7657" xml:space="preserve"><lb/>Quocirca, cum reipſa multo pauciores ſint ſtellæ, quod inter quaslibet duas <lb/>magnum ſpatium interiectum fit, ſintque uaſta ſpatia non pauca in cælo, in <lb/>quibus nulla ſtella appareat, ita ut nullo modo ſe mutuo tangant, perſpicuum <lb/>eſt, multo pauciores eſſe ſtellas in Firmamento filijs Iſrael. </s> <s xml:id="echoid-s7658" xml:space="preserve">Eadem ratione <lb/>reperietur numerus ſtellarum cuiuſcunque magnitudinis, quæ totum Firma-<lb/>mentum replere poſſint.</s> <s xml:id="echoid-s7659" xml:space="preserve"/> </p> <div xml:id="echoid-div369" type="float" level="2" n="1"> <note position="right" xlink:label="note-225-03" xlink:href="note-225-03a" xml:space="preserve">Quot ſtellæ <lb/>magnitudi-<lb/>nis requirã<unsure/> <lb/>tur ut re-<lb/>pleant totũ <lb/>Firmamen@ <lb/>tum.</note> </div> <p> <s xml:id="echoid-s7660" xml:space="preserve"><emph style="sc">Alphraganvs</emph> igitur in ratione, quam auctor noſter attulit in con-<lb/> <anchor type="note" xlink:label="note-225-04a" xlink:href="note-225-04"/> f<unsure/>irmationem ſecundæ partis quartæ concluſionis, quod nimirum terra inſtar <lb/>puncti ſeſe habeat collata cum Firmamento, intelligit minimas ſtellas uiſu <lb/>perceptibiles, ea, nimirum, quas nos cum Aſtronomis alijs ſextæ magnitudi-<lb/>nis appellauimus, quarum quælibet maior eſt, quàm terra octodecies, & </s> <s xml:id="echoid-s7661" xml:space="preserve">am-<lb/>plius. </s> <s xml:id="echoid-s7662" xml:space="preserve">Quo circaiure optimo concludi poteſt, terram eſſe ueluti punctum re-<lb/>ſpectu cæli, quandoquidem ſtella tanto maior exiſtens, quàm terra, tanquam <lb/>punctum, comparata cum cælo exiſtimatur.</s> <s xml:id="echoid-s7663" xml:space="preserve"/> </p> <div xml:id="echoid-div370" type="float" level="2" n="2"> <note position="right" xlink:label="note-225-04" xlink:href="note-225-04a" xml:space="preserve">Alphraga-<lb/>nus de qui <lb/>bus ſtellis <lb/>loquatur.</note> </div> <pb o="190" file="226" n="227" rhead="Comment. in I. Cap. Sphæræ"/> <p> <s xml:id="echoid-s7664" xml:space="preserve"><emph style="sc">Non</emph> autem abs re fuerit, hocloco breuiter etiam declarare, quonam pa-<lb/> <anchor type="note" xlink:label="note-226-01a" xlink:href="note-226-01"/> cto terra ſeſe habeat cum ſingulis orbib. </s> <s xml:id="echoid-s7665" xml:space="preserve">cęleſtibus collata. </s> <s xml:id="echoid-s7666" xml:space="preserve">Non.</s> <s xml:id="echoid-s7667" xml:space="preserve">n.</s> <s xml:id="echoid-s7668" xml:space="preserve">reſpectu cu-<lb/>iuſq; </s> <s xml:id="echoid-s7669" xml:space="preserve">cæli exiſtimari debet inſenſibilis magnitudinis. </s> <s xml:id="echoid-s7670" xml:space="preserve">Quamobrem certiſſime <lb/>tenendum eſt, terram inſenſibilis eſſe magnitudinis, ſi cum cælo Iouis, Satur-<lb/>ni, Firmamenti, & </s> <s xml:id="echoid-s7671" xml:space="preserve">alijs ſuperioribus cęlis comparetur, ut omnes rationes addu <lb/>ctæ manifeſte confirmant: </s> <s xml:id="echoid-s7672" xml:space="preserve">At uero reſpectu cæli Martis, atque Solis, eſſe quidẽ <lb/>alicuius quantitatis, ſed non tantę, quę ſit alicuius momenti, ut luce clarius cõ <lb/>ſtat ex illis rationibus, quas ex umbris, & </s> <s xml:id="echoid-s7673" xml:space="preserve">inſtrumentis Mathematicorum de-<lb/>promptas propoſuimus; </s> <s xml:id="echoid-s7674" xml:space="preserve">Sunt enim illę experientię in Sole pręcipue obſerua-<lb/>tę Si denique conferatur cum cœlo Veneris, Mercurij, ac Lunę, eam omnino <lb/>iam cenſendam eſſe notabilis magnitudinis, maxime reſpectu orbis Lunaris. <lb/></s> <s xml:id="echoid-s7675" xml:space="preserve">Cum enim corpus Lunare reſpectu orbis, in quo exiſtit, ſenſibilem prę ſe ferat <lb/>quantitatem, ac molem; </s> <s xml:id="echoid-s7676" xml:space="preserve">ut ſenſibus eſt manifeſtum; </s> <s xml:id="echoid-s7677" xml:space="preserve">quo modo Terra, quę mul-<lb/>to maior eſt corpore Lunari, dici poterit non habere molem, ac quantitatem <lb/>notabilem reſpectu cęli Lunæ? </s> <s xml:id="echoid-s7678" xml:space="preserve">Hęc omnia magis peſpicua erunt ex communi <lb/>hac ſententia Aſtronomorum, qui aſſerunt, Si quis in orbe lunari conſtitutus <lb/>terram intueretur, appareret ei ter maior, & </s> <s xml:id="echoid-s7679" xml:space="preserve">paulo amplius, quàm Luna hinc <lb/>è terris conſpicitur: </s> <s xml:id="echoid-s7680" xml:space="preserve">Ex orbe uero Solis bis maior iudicaretur terra conſpecta, <lb/>quàm hinc è terra Venus nobis apparet: </s> <s xml:id="echoid-s7681" xml:space="preserve">Ex cęlo deinde Martis terra, ſi luceret, <lb/>ęſtimaretur ęqualis uni ſtellę minimę, quales ſunt in ſexta magnitudine cõ-<lb/>prehenſę: </s> <s xml:id="echoid-s7682" xml:space="preserve">Ex ſuperioribus denique cęlis, maxime ex Fitmamento, nullo pacto <lb/>cerneretur, ſed omnino inſtar puncti exiſteret inſenſibilis.</s> <s xml:id="echoid-s7683" xml:space="preserve"/> </p> <div xml:id="echoid-div371" type="float" level="2" n="3"> <note position="left" xlink:label="note-226-01" xlink:href="note-226-01a" xml:space="preserve">Quomodo <lb/>terra ſe ha-<lb/>beat cũ ſin <lb/>gulis cœlis <lb/>collata.</note> </div> <note position="left" xml:space="preserve">Terram So-<lb/>le eſſe mi-<lb/>norem, Lu-<lb/>na uero ma <lb/>iorem.</note> <p> <s xml:id="echoid-s7684" xml:space="preserve"><emph style="sc">Vervm</emph> quia mira fortaſſe alicui uidebuntur ea, quę de quantitate aſtro-<lb/>rum reſpectu magnitudinis terrę affirmauimus, breuiter nunc oſtendemus, ter <lb/>ram, quãuis ingenti mole nobis prędita eſſe uideatur, multo minorẽ eſſe cor-<lb/>pore Solari, Lunam uero contra, quamuis eius magnitudinem eandẽ eſſe, quã <lb/>Solis, ſenſus iudicet, longe minorem eſſe ipſa terra. </s> <s xml:id="echoid-s7685" xml:space="preserve">Rationes autem ſubtiliſſi-<lb/>mas, quibus peritiſſimi Aſtronomi hęc omnia Geometrice concludunt, quo-<lb/>niam altioris ſunt conſiderationis, quàm ut hoc loco explicari poſſint, ſpe-<lb/>ctantq́; </s> <s xml:id="echoid-s7686" xml:space="preserve">ad Theoricas planetarum, omnino prętermittemus, ſi quis autem earũ <lb/>deſiderio tenetur, petendę erunt ex Ptolemęo ſummo harum rerũ artifice, & </s> <s xml:id="echoid-s7687" xml:space="preserve"><lb/>alijs Aſtronomis. </s> <s xml:id="echoid-s7688" xml:space="preserve">Quod igitur Sol ſit longe maior, quàm terra, ex rationibus <lb/>Perſpectiuorum manifeſtum eſſe poteſt. </s> <s xml:id="echoid-s7689" xml:space="preserve">Si enim Sol eſſet terræ ęqualis, proij-<lb/>ceretur umbra terrę ęquabiliter in modum cylindri in infinitum; </s> <s xml:id="echoid-s7690" xml:space="preserve">Si vero mi-<lb/>nor exiſteret Sol, quàm terra, augeretur ſemper vmbra terrę proiecta in infini <lb/>tum: </s> <s xml:id="echoid-s7691" xml:space="preserve">Quorum illud à Vitellione lib. </s> <s xml:id="echoid-s7692" xml:space="preserve">2. </s> <s xml:id="echoid-s7693" xml:space="preserve">Perſpectiuę propoſ. </s> <s xml:id="echoid-s7694" xml:space="preserve">26. </s> <s xml:id="echoid-s7695" xml:space="preserve">Hoc uero pro-<lb/>poſ. </s> <s xml:id="echoid-s7696" xml:space="preserve">28. </s> <s xml:id="echoid-s7697" xml:space="preserve">clariſſime demonſtratur. </s> <s xml:id="echoid-s7698" xml:space="preserve">Quocirca nocte ſerena occultarentur ſemper <lb/>aliquę ſtellę fixę, quę nimirum in umbra terrę exiſterent, uel certe non tan-<lb/>tum haberent ſplendorem, quantum alię ſtellę, quę tunc à Sole illuſtrantur: <lb/></s> <s xml:id="echoid-s7699" xml:space="preserve">Eademq́; </s> <s xml:id="echoid-s7700" xml:space="preserve">ratione, quando Mars, Iuppiter, & </s> <s xml:id="echoid-s7701" xml:space="preserve">Saturnus Soli per diametrũ obij-<lb/>citur, paterentur eclipſim, quod nunquam viſum fuit. </s> <s xml:id="echoid-s7702" xml:space="preserve">Quare Sol multo maior <lb/>exiſtet, quàm terra: </s> <s xml:id="echoid-s7703" xml:space="preserve">Ita enim fiet, ut umbra terrę proijciatur in formam pyra-<lb/>midis, ſeu potius coni, deſinatq́ue in punctum indiuiſibile, adeo ut ad ſtellas <lb/>fixas, & </s> <s xml:id="echoid-s7704" xml:space="preserve">dictos planetas minime pertingat, ut ab eodem Vitellione demonſtra <lb/>tur propoſ. </s> <s xml:id="echoid-s7705" xml:space="preserve">27. </s> <s xml:id="echoid-s7706" xml:space="preserve">eiuſdem lib. </s> <s xml:id="echoid-s7707" xml:space="preserve">Vnde mirum non eſt, quod neque vllę ſtellę fixę, <lb/>neque ſuperiores illi Planetę defectum luminis patiantur, quamuis è diame-<lb/>tro Solem aſpiciant. </s> <s xml:id="echoid-s7708" xml:space="preserve">Quod autem Luna multo minor exiſtat, quàm terra, de-<lb/>monſtratiue ex dictis ita deduci poteſt. </s> <s xml:id="echoid-s7709" xml:space="preserve">Quoniam enim oſtenſum eſt, terrę vm- <pb o="191" file="227" n="228" rhead="Ioan. de Sacro Boſco."/> bram eſſe conicam, ita ut ſemper anguſtior efficiatur, tandemq́ue in punctum <lb/>deſinat, neceſſe eſt, umbræ denſitatem habere minorem diametrum, quàm ſit <lb/>terrę diameter. </s> <s xml:id="echoid-s7710" xml:space="preserve">Quare cum tota Luna intra dictam umbram aliquando abſcõ-<lb/>datur, longo etiam temporis interuallo, ut in eius eclipſibus apparet, quis nõ <lb/>uidet, eius diametrum minorem eſſe diametro umbræ, & </s> <s xml:id="echoid-s7711" xml:space="preserve">ex conſequenti lon-<lb/>ge adhuc minorem terræ diametro? </s> <s xml:id="echoid-s7712" xml:space="preserve">Quoniam igitur Luna multo minor, quã <lb/>terra, exiſtit, & </s> <s xml:id="echoid-s7713" xml:space="preserve">nihilominus tanta nobis apparet, perſpicuũ eſt, eam nobis ad-<lb/>modum eſſe uicinam, ut iam ſenſibilis ſit omnino, ac perceptibilis diſtantia à <lb/>ſuperficie terrę ad eius centrum, ſi cum diſtantia à ſuperficie terrę ad cęlũ Lu-<lb/>næ conferatur. </s> <s xml:id="echoid-s7714" xml:space="preserve">Quare recte Ptolemæus, ac Ioannes de Regiomonte Dict. </s> <s xml:id="echoid-s7715" xml:space="preserve">4. </s> <s xml:id="echoid-s7716" xml:space="preserve">Al <lb/>mag. </s> <s xml:id="echoid-s7717" xml:space="preserve">c. </s> <s xml:id="echoid-s7718" xml:space="preserve">1. </s> <s xml:id="echoid-s7719" xml:space="preserve">præcipiunt, uerũ locũ ☽, per eclipſes Lunares inueftigãdũ eſſe, nõ au-<lb/>tem per inſtrumenta. </s> <s xml:id="echoid-s7720" xml:space="preserve">Nobis enim, aiunt, in ſuperficie terræ exiſtentibus maxi-<lb/>mus, & </s> <s xml:id="echoid-s7721" xml:space="preserve">ſenſibilis error continget, ſi per inſtrumenta locum uerum ☽, uenari <lb/>uelimus, & </s> <s xml:id="echoid-s7722" xml:space="preserve">propter nimiam eius uicinitatem; </s> <s xml:id="echoid-s7723" xml:space="preserve">quod minime contingeret, ſi in <lb/>centro terrę collocati eſſemus.</s> <s xml:id="echoid-s7724" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7725" xml:space="preserve"><emph style="sc">Locvs</emph> hic me admonet, ut, quoniam de omnib@s ſtellis, quæ uiſu com-<lb/> <anchor type="note" xlink:label="note-227-01a" xlink:href="note-227-01"/> mode percipiuntur, uerba fecimus, aliquid etiam dicam (multi enim uiri gra-<lb/>ues, atque eruditi meam hac de re ſententiam flagitarunt) de ſtella illa noua, <lb/>quę anno 1572. </s> <s xml:id="echoid-s7726" xml:space="preserve">in conſtellatione Caſſiopeiæ apparuit, & </s> <s xml:id="echoid-s7727" xml:space="preserve">anno 1573. </s> <s xml:id="echoid-s7728" xml:space="preserve">euanuit. <lb/></s> <s xml:id="echoid-s7729" xml:space="preserve">Apparuit quidem ſtella illa tantæ magnitudinis, ac ſplendoris in principio, <lb/>ut Veneris ſtellam uinceret: </s> <s xml:id="echoid-s7730" xml:space="preserve">ſed poſt aliquot menſes ita diminuta ſuit, ut æ <lb/>qualis iudicaretur ſtellę polari, uel cuiuis alij ſtellę magnitudinis tertię, atq; </s> <s xml:id="echoid-s7731" xml:space="preserve"><lb/>in hac quantitate ad finem uſque ſemper uiſa fuit. </s> <s xml:id="echoid-s7732" xml:space="preserve">Res ſane admiranda, & </s> <s xml:id="echoid-s7733" xml:space="preserve">pro-<lb/>digio perſimilis, & </s> <s xml:id="echoid-s7734" xml:space="preserve">quæ multorum ingenia exercuerit. </s> <s xml:id="echoid-s7735" xml:space="preserve">Nonnulli enim, licet <lb/> <anchor type="note" xlink:label="note-227-02a" xlink:href="note-227-02"/> pauci, putarunt, eam ſtellam nouam non fuiſſe, ſed unam ex antiquis illis tre <lb/>decim, quæ ſemper in Caſſiopeia ab Aſtr onomis ſunt obſeruatæ: </s> <s xml:id="echoid-s7736" xml:space="preserve">uiſam autem <lb/>tunc eſſe maiorem ſolito, propter exhalationem in ſuprema aeris regione in-<lb/>ter ipſam, & </s> <s xml:id="echoid-s7737" xml:space="preserve">noſtrum aſpectum interiectam; </s> <s xml:id="echoid-s7738" xml:space="preserve">indeq́; </s> <s xml:id="echoid-s7739" xml:space="preserve">factum eſſe, ut plerique il-<lb/>lam fuiſſe nouam crediderint. </s> <s xml:id="echoid-s7740" xml:space="preserve">Alijuero exiſtimatunt, ſtellam illam fuiſſe mi-<lb/> <anchor type="note" xlink:label="note-227-03a" xlink:href="note-227-03"/> nimam aliquam in Firmamento ex earum numero, quæ extra ſex magnitudi-<lb/>nes ſunt, & </s> <s xml:id="echoid-s7741" xml:space="preserve">plerunque propter exiguitatem deliteſcunt, ita ut non appareant, <lb/>ideoq́ue, ut ſupra diximus, ab Aſtronomis non ſunt in numerum ſtellarum re-<lb/>latæ: </s> <s xml:id="echoid-s7742" xml:space="preserve">propter exhalationem autem inter poſitam uiſam eam tunc fuiſſe tanta <lb/>magnitudine, ut ab omnibus fere noua exiſtimaretur. </s> <s xml:id="echoid-s7743" xml:space="preserve">Alj denique, ſtellam illã <lb/> <anchor type="note" xlink:label="note-227-04a" xlink:href="note-227-04"/> ſuiſſe cometam in ſuptema aeris regione, arbitrati ſunt.</s> <s xml:id="echoid-s7744" xml:space="preserve"/> </p> <div xml:id="echoid-div372" type="float" level="2" n="4"> <note position="right" xlink:label="note-227-01" xlink:href="note-227-01a" xml:space="preserve">Digreſſio <lb/>de ſtella il-<lb/>la noua, q̃ <lb/>an. 1572. ap <lb/>paruit, & <lb/>anno 1574. <lb/>euanuit.</note> <note position="right" xlink:label="note-227-02" xlink:href="note-227-02a" xml:space="preserve">Prima ſen-<lb/>tẽtia de no <lb/>ua ſtella.</note> <note position="right" xlink:label="note-227-03" xlink:href="note-227-03a" xml:space="preserve">Secũda ſen <lb/>tẽtia de no <lb/>ua ſtella.</note> <note position="right" xlink:label="note-227-04" xlink:href="note-227-04a" xml:space="preserve">Tertia ſen-<lb/>tẽtia de no <lb/>ſta ſtella. <lb/>Con futatio <lb/>primæ ſen-<lb/>tentię.</note> </div> <p> <s xml:id="echoid-s7745" xml:space="preserve"><emph style="sc">Vervm</emph> nulla harum opinionum mihi uera eſſe uidetur. </s> <s xml:id="echoid-s7746" xml:space="preserve">Quod enim <lb/>ftella illa non fuerit una ex tredecim illis in Caſſiopeia notatis, certo certius <lb/>eſſe puto. </s> <s xml:id="echoid-s7747" xml:space="preserve">Nam Franciſcus Maurolycus abbat Meſſanenſis in contemplatione <lb/>ſiderum exercitatiſſimus, (quippe qui ſexaginta ipſos annos in eo ſtudio po-<lb/>ſuerit) in Sicilia, alijq́; </s> <s xml:id="echoid-s7748" xml:space="preserve">Aſtronomi permulti tum in utraque Germania, tum <lb/>in Hiſpania, & </s> <s xml:id="echoid-s7749" xml:space="preserve">Gallia qui non ſemel illas tredecim ſtellas Caſſiopeiæ numera <lb/>runt, eodem illo tempore, quo noua hęc apparuit, pręter tredecim illas, no-<lb/>uam hanc, de qua loquimur, in Caſſiopeia animaduerterunt, utiam non tre-<lb/>decim, ut olim, ſed quatuordecim ſtellas in Caſſiopeia eſſe intelligerent. </s> <s xml:id="echoid-s7750" xml:space="preserve">Cu-<lb/>ius rei etiam teſtis ſum ego ipſe, qui Romę<unsure/> anno 1573. </s> <s xml:id="echoid-s7751" xml:space="preserve">menſe Decembri, prę-<lb/>ter nouum illud aſtrum, (diminutum tamen, ita ut ſtellis tertię magnitudinis <lb/>par uideretur) in Caſſiopeia alia tredecim cõſpexi: </s> <s xml:id="echoid-s7752" xml:space="preserve">nec uero ego unus Romæ, <lb/>ſed complures alij mecum, quibus nuper ortum ſidus monſtrabam, ſępius ob- <pb o="192" file="228" n="229" rhead="Comment. in I. Cap. Sphæræ"/> ſ<unsure/>eruarunt. </s> <s xml:id="echoid-s7753" xml:space="preserve">Mirum autem eſt, auctores huiuſce ſententiæ ſolos inter omnes @ <lb/>Aſtronomos uidiſſe, illam ueterem eſſe ſtellam, ipſam autem ſtellam non uidiſ <lb/>ſe; </s> <s xml:id="echoid-s7754" xml:space="preserve">ut facile quis ſuſpicari poſſit, eos non admodum diligentes fuiſſe in huius <lb/>ſtellæ obſeruatione, & </s> <s xml:id="echoid-s7755" xml:space="preserve">uet erum auctoritate potius, quàm noua obſeruatione <lb/>nixos aſſeu eraſſe, aſtrum illud ab alijs nõ differre, ne uidelicet nouum quid in <lb/>alijs ſtellis Caſſiopeiæ, quæ ſunt tertiæ magnitudinis,) ſecundam dico, quæ in <lb/>cęlo concederent: </s> <s xml:id="echoid-s7756" xml:space="preserve">Id quod uel ex eo apparet, quod ſtella illa noua cum tribus <lb/> <anchor type="note" xlink:label="note-228-01a" xlink:href="note-228-01"/> eius pectore cer nitur, quartam, quæ eſt ſuper cathedram ad coxas; </s> <s xml:id="echoid-s7757" xml:space="preserve">& </s> <s xml:id="echoid-s7758" xml:space="preserve">duodeci-<lb/>mam, quæ in aſcenſu medio cathedræ ſita eſt, efficiebat figuram eam, quam <lb/>Geom etrę Rhombum uocant; </s> <s xml:id="echoid-s7759" xml:space="preserve">ſtella autem undecima Caſſiopeię, quę eſt quar <lb/>tæ magnitudinis, quamque huius ſententiæ auctores, quod maior propter <lb/>uapores interpoſitos (ut putant) uideretur, nouam uiſam eſſe exiſtimant, effi <lb/>cit perpe@uo eam figuram, quæà Geometris Trapexium appellatur, ita ut mi-<lb/>nus diſtet ipſa à quarta ſtella, quàm duodeci-<lb/>ma à ſecunda, cum tamen noua illa omnium <lb/>conſenſum, qui eam obſeruarunt, æque diſta-<lb/> <anchor type="figure" xlink:label="fig-228-01a" xlink:href="fig-228-01"/> ret à quarta, atque duodecima aſecunda, ut <lb/>ex appoſita figura perſpicuum eſt. </s> <s xml:id="echoid-s7760" xml:space="preserve">Itaque ſatis <lb/>conſtat, niſi fallor, auctores hos nulla ratio-<lb/>ne ductos affirmare, quod aſtrum omnes no-<lb/>uum uocant, id uetus fuiſſe, & </s> <s xml:id="echoid-s7761" xml:space="preserve">ſtellam unde-<lb/>cimam Caſſiopeiæ tum maiorem eſſe uiſam, <lb/>pręſertim cum eam ipſam omnes Aſtronomi <lb/>prope nouam ſtellam conſpexerint, inter nouã <lb/>& </s> <s xml:id="echoid-s7762" xml:space="preserve">quartam ſtellam Caſſiopeiæ collocatam, <lb/>ut in figura deſcripſimus: </s> <s xml:id="echoid-s7763" xml:space="preserve">quod quidem ego <lb/>cum multis alijs Romæ ſæ pius obſeruaui: </s> <s xml:id="echoid-s7764" xml:space="preserve">Deinde ſi exhalatio illa interpoſita <lb/>tanta fuit, ut eius interpoſitu in utraque Germania, Hiſpania, Gallia, Italia, <lb/>Sicilia, & </s> <s xml:id="echoid-s7765" xml:space="preserve">alijs fortaſſe regionibus, aſtrum illud undecimum Caſſiopeiæ ma-<lb/>ius apparuerit, quàm re ipſa eſt, qui fieri poteſt, ut eandem ob cauſam, & </s> <s xml:id="echoid-s7766" xml:space="preserve">reli-<lb/>qua aſtra uicina non apparuerint maiora, ſed eiuſdem omnino magnitudinis. <lb/></s> <s xml:id="echoid-s7767" xml:space="preserve">qua ſemper uiſa ſunt, atque hodie uidentur? </s> <s xml:id="echoid-s7768" xml:space="preserve">Dicet fortaſſe quiſpiam, exhala-<lb/>tionem illam tantam ſcilicet fuiſſe, ut inter aſpectum & </s> <s xml:id="echoid-s7769" xml:space="preserve">illã tantummodo ſtel <lb/>lam, non autem inter alias interijceret ur; </s> <s xml:id="echoid-s7770" xml:space="preserve">uerum ut id contingere in una regio <lb/>ne potuerit, in pluribus certè, tanto præſertim interuallo diſiunctis, haudqua-<lb/>quam potuit, ut perſpicuũ eſt ex aſpe ctus diuerſitate. </s> <s xml:id="echoid-s7771" xml:space="preserve">Liquetigitur, mihi certè <lb/>exploratum eſt, ſtellam illã, de qua agimus, nõ potuiſſe eſſe unam exillis tre-<lb/>decim, quæ quotidie in Caſſiopeia cernuntur. </s> <s xml:id="echoid-s7772" xml:space="preserve">Ac poſterior hæc ratio a me al-<lb/>lata refellit etiam ſecundam ſententiam. </s> <s xml:id="echoid-s7773" xml:space="preserve">Si enim propter exhalationem (ut <lb/> <anchor type="note" xlink:label="note-228-02a" xlink:href="note-228-02"/> arbitrantur) ſtellula illa, quæ alias cerni non poteſt, tanta magnitudine ſe <lb/>conſpiciendam præbuit, profecto eadem de cauſa ſtella undecima Caſſiope-<lb/>iæ (ut alias ſilentio præteream) prope quam obſeruata eſt illa noua, ſe oſten-<lb/>diſſet multo maiorem, cum tamen eo cempore eiuſdem magnitudinis, hoc eſt <lb/>quartæ, ſit omnibus uiſa, cuius nimirum & </s> <s xml:id="echoid-s7774" xml:space="preserve">antea, & </s> <s xml:id="echoid-s7775" xml:space="preserve">poſtea uiſa eſt, atque etiã <lb/>nunc uidetur.</s> <s xml:id="echoid-s7776" xml:space="preserve"/> </p> <div xml:id="echoid-div373" type="float" level="2" n="5"> <note position="left" xlink:label="note-228-01" xlink:href="note-228-01a" xml:space="preserve">Quam figu <lb/>ratu ſtella <lb/>noua cum <lb/>ſtellis Caſ. <lb/>ſiopeiæ effi <lb/>ciebat.</note> <figure xlink:label="fig-228-01" xlink:href="fig-228-01a"> <image file="228-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/228-01"/> </figure> <note position="left" xlink:label="note-228-02" xlink:href="note-228-02a" xml:space="preserve">Conſutatio <lb/>ſecundæ sẽ <lb/>tentiæ.</note> </div> <p> <s xml:id="echoid-s7777" xml:space="preserve"><emph style="sc">Qvod</emph> etiam ſtella illa noua non fuerit Cometa in ſuprema aer<unsure/>is regio-<lb/> <anchor type="note" xlink:label="note-228-03a" xlink:href="note-228-03"/> ne, ita perſpicuũ faciemus. </s> <s xml:id="echoid-s7778" xml:space="preserve">Periti Aſtrono mi ubique locorum notauerunt, il-<lb/>lam ſtellam eũdem ſitum habere inter ſtellas fixas, eum nimirum, quem ſupe- <pb o="193" file="229" n="230" rhead="Ioan. de Sacro Boſco."/> rior figura demo ſtrat: </s> <s xml:id="echoid-s7779" xml:space="preserve">ita ut omnes eam prope id punctum collocarint, ubi <lb/>colurus æquinoctiorum circulũ arcticum interſecat, & </s> <s xml:id="echoid-s7780" xml:space="preserve">quod à polo arctico gra <lb/>dibus prope 23 {1/2}. </s> <s xml:id="echoid-s7781" xml:space="preserve">ab Aequatore autẽ fere 66 {1/2} diſtare perhibuerint; </s> <s xml:id="echoid-s7782" xml:space="preserve">adeo <lb/>ut nullam pene aſpectus uarietatẽ in ea tam uarijs locis deprehẽderint. </s> <s xml:id="echoid-s7783" xml:space="preserve">Quod <lb/>cũ ita ſit, quis dubitare poterit, illam non in ſuprema regione aeris, ubi cęteri <lb/>Cometæ generantur, ſed ſupra Lunam locum eſſe ſortitam? </s> <s xml:id="echoid-s7784" xml:space="preserve">Nunquam enim <lb/>unus & </s> <s xml:id="echoid-s7785" xml:space="preserve">idem Cometa è diuerſis regionibus in eodem prorſus cernitur loco, <lb/>ſi cum ſideribus conferatur: </s> <s xml:id="echoid-s7786" xml:space="preserve">ſiquidem ob uicinitatem (ut conſtat inter Aſtrono-<lb/>mos) non paruam ſubit uarietatem aſpectus: </s> <s xml:id="echoid-s7787" xml:space="preserve">immo & </s> <s xml:id="echoid-s7788" xml:space="preserve">Luna ipſa, ſecundum om <lb/>nes Aſtronomos, quòd terræ ualde propinqua ſit, non caret aſpectus diuerſita-<lb/>te. </s> <s xml:id="echoid-s7789" xml:space="preserve">Cum ergo noua illa ſtella nullam omnino uiſa ſit habere diuerſitatem aſpe <lb/>ctus in tam uarijs regionibus obſeruata, argumento ſane eſt, illam altiorem <lb/>Luna extitiſſe; </s> <s xml:id="echoid-s7790" xml:space="preserve">atque adeo Cometam nullo modo fuiſſe, niſi & </s> <s xml:id="echoid-s7791" xml:space="preserve">Cometas in <lb/>ætherea regione gigni dicamus.</s> <s xml:id="echoid-s7792" xml:space="preserve"/> </p> <div xml:id="echoid-div374" type="float" level="2" n="6"> <note position="left" xlink:label="note-228-03" xlink:href="note-228-03a" xml:space="preserve">Conſutatio <lb/>tertię ſentẽ <lb/>tiæ.</note> </div> <note position="right" xml:space="preserve">Sententia <lb/>commenta-<lb/>toris de no <lb/>ua ſtella.</note> <p> <s xml:id="echoid-s7793" xml:space="preserve"><emph style="sc">Itaqve</emph> ut breuiter, quod ſentio, dicam, cenſeo ſtellam illam, quęcun-<lb/>que illa fuerit, in Firmamento, ubi ſtellæ fixæ ſunt, extitiſſe. </s> <s xml:id="echoid-s7794" xml:space="preserve">Nam eam in re-<lb/>gione ætherea, & </s> <s xml:id="echoid-s7795" xml:space="preserve">non in elementari apparuiſſe, conſtat ex ijs, quæ paulo ante <lb/>in confutatione tertiæ ſententię, eorum nimirum, qui eam Cometam facie-<lb/>bant in ſuprema aeris regione exiſtentem, adduximus: </s> <s xml:id="echoid-s7796" xml:space="preserve">propterea uidelicet, <lb/>quòd in ea non ſit deprehenſa aſpectus diuerſitas. </s> <s xml:id="echoid-s7797" xml:space="preserve">Eodem enim argumento <lb/>philoſophi, & </s> <s xml:id="echoid-s7798" xml:space="preserve">Aſtronomi confutant Ariſtotelis ſententiam de uia lactea, quam <lb/>ipſe in ſuprema regione aeris dicebat ex uaporibus, & </s> <s xml:id="echoid-s7799" xml:space="preserve">exhalationibus ui ſtel-<lb/>larum, quæ in circulo lacteo conſpiciuntur, ad eam regionem excitatis & </s> <s xml:id="echoid-s7800" xml:space="preserve">at-<lb/>tractis continenter generari. </s> <s xml:id="echoid-s7801" xml:space="preserve">Cum enim ubique terrarum per eadem ſidera <lb/>Firmainenti, Caſſiopeiam, Cygnum, Aquilam, Sagittarium, Geminos, & </s> <s xml:id="echoid-s7802" xml:space="preserve">alia, la <lb/>ctea uia ducta uideatur, ut copio ſius in ſecundo cap. </s> <s xml:id="echoid-s7803" xml:space="preserve">explicabimus, dubium eſ-<lb/>ſe non poteſt, quin multo altior ſit, quàm ſuprema aeris regio, atque in ipſo <lb/>Firmamento ſita, propterea quòd nullam habet diuerſitatem aſpectus: </s> <s xml:id="echoid-s7804" xml:space="preserve">quam <lb/>utique haberet, ſi in aere, ut uolebat Ariſtoteles, collocaretur. </s> <s xml:id="echoid-s7805" xml:space="preserve">Iam uero, ut <lb/> <anchor type="note" xlink:label="note-229-02a" xlink:href="note-229-02"/> credam ſtellam illam nouam in Firmamento, non in alio quouis orbe cæleſti, <lb/>extitiſſe, hoc maxime adducor argumento, quòd neque ego, neque ullus om-<lb/>nino Aſtromomus, quod quidem ſciam, alium motum in ea animaduerterit, <lb/>præter eum, quem in fixis ſideribus obſeruamus. </s> <s xml:id="echoid-s7806" xml:space="preserve">Nam conſtantem ſemper mo-<lb/>tum, eundemque plane ſitum inter alias ſtellas fixas totum biennium (tam-<lb/>diu enim ferme durauit) retinuit. </s> <s xml:id="echoid-s7807" xml:space="preserve">Quòd ſi in orbe alicuius planetæ fuiſſet, <lb/>cum orbis ille ſane alienum à ſtellis fixis motum habeat, proculdubio & </s> <s xml:id="echoid-s7808" xml:space="preserve">ſtel-<lb/>la ipſa eundem motum, curſumque habuiſſet; </s> <s xml:id="echoid-s7809" xml:space="preserve">ſecus autem rem habuiſſe, Aſtro <lb/>nomi deprehenderunt. </s> <s xml:id="echoid-s7810" xml:space="preserve">Atque hoc idem argumentum euidenter concludit, <lb/>multo minus ſtellam illam in elementari regione extitiſſe: </s> <s xml:id="echoid-s7811" xml:space="preserve">quòd ibi nulla ra-<lb/>tione eundemſemper ſitum, ac diſtantiam cum ſtellis fixis potuiſſet retinere. <lb/></s> <s xml:id="echoid-s7812" xml:space="preserve">Quæ cum ita ſint, ita mihi perſuadeo, ſtellam illam uel tunc à Deo Opt. </s> <s xml:id="echoid-s7813" xml:space="preserve">Max. </s> <s xml:id="echoid-s7814" xml:space="preserve"><lb/>procreatam eſſe in cęlo octauo, ut magnum aliquid portẽderet, (quod cuiuſ-<lb/>modi ſit, adhuc ignoratur) uel certe in ipſo cœlo gigni poſſe Cometas, ſicut in <lb/>aere, licet rarius id contingat: </s> <s xml:id="echoid-s7815" xml:space="preserve">quod quidem aperte ſatentur non pauci ex an-<lb/>tiquis philoſophis, multique ex recentioribus complures auctoritates, & </s> <s xml:id="echoid-s7816" xml:space="preserve"><lb/>hiſtorias adducunt, quibus perſuadeant, ſæpius ſtellas eiuſmodi longis <lb/>temporum interuallis, alias ad aliud ſignificandum, in cœlo exortas eſſe. </s> <s xml:id="echoid-s7817" xml:space="preserve"><lb/>Hoc ſi uerum eſt, uideant Peripatetici, quomodo Ariſtotelis opinionem de <pb o="194" file="230" n="231" rhead="Comment. in I. Cap. Sphæræ"/> materia cæli defendere poſſint. </s> <s xml:id="echoid-s7818" xml:space="preserve">Dicendum enim fortaſſe erit, cœlum non eſ-<lb/>ſe Quintam quandam eſſentiam, ſed mutabile corpus, licet minus corruptibi-<lb/>le ſit, quàm corpora hæc inferiora: </s> <s xml:id="echoid-s7819" xml:space="preserve">quod ſane ante Ariſtotelem Plato cum <lb/>multis alijs philoſophis ſenſit, & </s> <s xml:id="echoid-s7820" xml:space="preserve">poſt Chriſtum non pauci, inter quos D. </s> <s xml:id="echoid-s7821" xml:space="preserve">Am-<lb/>broſius, Baſilius, Gregorius Niſenus, & </s> <s xml:id="echoid-s7822" xml:space="preserve">cætera ſere Eccleſiæ lumina, non ob-<lb/>ſcure docuerunt. </s> <s xml:id="echoid-s7823" xml:space="preserve">Quicquid tandem ſit, (meam enim ſniam in tanta re non in-<lb/>terpono) mihi in præſentia ſatis eſt, paucis demonſtraſſe, aſtrũ illud, de quo lo-<lb/>quimur, in Firmamento ſedem habuiſſe: </s> <s xml:id="echoid-s7824" xml:space="preserve">quo pacto illic, aut unde tam repente <lb/>extiterit, quid portenderit, cur poſt biennium euanuerit, præter Deum ſcire <lb/>adhuc arbitror neminem. </s> <s xml:id="echoid-s7825" xml:space="preserve">Illud omnibus exploratum eſſe debet, Deũ non ade-<lb/>miſſe ſibi ſtellas eſficiendi poteſtatem: </s> <s xml:id="echoid-s7826" xml:space="preserve">quare & </s> <s xml:id="echoid-s7827" xml:space="preserve">illam tum potuiſſe, & </s> <s xml:id="echoid-s7828" xml:space="preserve">nunc poſ <lb/>ſe, ſi uelit, uel innumerabiles procreate. </s> <s xml:id="echoid-s7829" xml:space="preserve">Quare autem tum potiſſimum pro-<lb/>creata ſit, oculto Dei iudicio, qui nihil fruſtra ſacit, ſed omnia ſumma proui-<lb/>dentia ad ſuos fines dirigit, quoad mortalibus patefaciat, permittendum eſt. <lb/></s> <s xml:id="echoid-s7830" xml:space="preserve">Subijciam hic ſententiam cuiuſdam Paulini Pridiani Medici, & </s> <s xml:id="echoid-s7831" xml:space="preserve">Aſtronomi, <lb/>qui Antuerpiæ idem ſidus nouum contemplatus eſt. </s> <s xml:id="echoid-s7832" xml:space="preserve">Deinde aſferam quoque <lb/>nonnulla ex Franciſci Maurolyci Abbatis diſputatione, quæ mihi è Sicilia ſu-<lb/>perioribus annis miſſa eſt, totidem uerbis excerpta: </s> <s xml:id="echoid-s7833" xml:space="preserve">ut omnibus manifeſtum <lb/>fiat, Aſtronomos in regionibus longo etiam interuallo diſſitis eundem ſitum <lb/>in noua noſtra ſtella obſeruaſſe. </s> <s xml:id="echoid-s7834" xml:space="preserve">Ita igitur Paulinus Pridianus anno 1572. </s> <s xml:id="echoid-s7835" xml:space="preserve"><lb/>inter cętera ſcripſit: </s> <s xml:id="echoid-s7836" xml:space="preserve">[Iam admirabili, & </s> <s xml:id="echoid-s7837" xml:space="preserve">vere tremendo Deo iudicio, conſpicuuni <lb/> <anchor type="note" xlink:label="note-230-01a" xlink:href="note-230-01"/> eſt aſtrum clarum, & </s> <s xml:id="echoid-s7838" xml:space="preserve">lucidum, quod antehac non apparuit, neque uiſum eſt: </s> <s xml:id="echoid-s7839" xml:space="preserve">formæ <lb/>quidem à reliquis ſte llis haud differens, ſed luce, ſplendore, & </s> <s xml:id="echoid-s7840" xml:space="preserve">mole quoque maius <lb/>apparens, & </s> <s xml:id="echoid-s7841" xml:space="preserve">quod non modo primæ magnitudinis ſtellis, ſed & </s> <s xml:id="echoid-s7842" xml:space="preserve">ipſis Planetis clarius <lb/>ac fulgentius conſpicitur: </s> <s xml:id="echoid-s7843" xml:space="preserve">lucidiſſimo, ac clariſſimo Veneris aſtro haud quaquam ce-<lb/>dens. </s> <s xml:id="echoid-s7844" xml:space="preserve">Quod præter hæc & </s> <s xml:id="echoid-s7845" xml:space="preserve">ſtare etiam ſuo loco videtur, nec alio, quàm diurno mo-<lb/>tu progredi, ac unà cum Firmamento reuolui: </s> <s xml:id="echoid-s7846" xml:space="preserve">contra plane aliorum cæleſtium <lb/>ignium, ac ignitorum Meteoron naturam, quæ motu aliquo proprio ciuntur. </s> <s xml:id="echoid-s7847" xml:space="preserve">Iuxta <lb/>Caſſiopeiam autem Septentrionem verſus, noua hęc ſtella conſpicitur: </s> <s xml:id="echoid-s7848" xml:space="preserve">cum ea, quæ in pe-<lb/>ctore eſt Caſſiopeiæ, & </s> <s xml:id="echoid-s7849" xml:space="preserve">altera, quæ ſupra ſedem prope crura; </s> <s xml:id="echoid-s7850" xml:space="preserve">& </s> <s xml:id="echoid-s7851" xml:space="preserve">tertia in medio ca-<lb/>thedræ, ita conſtituta atque locata, ut Rhombi figuram ac formam exprimat: </s> <s xml:id="echoid-s7852" xml:space="preserve">Cuius <lb/>ſuperiorem, & </s> <s xml:id="echoid-s7853" xml:space="preserve">ad mundi polum uergentem angulum ipſa noua efformat ſtella, &</s> <s xml:id="echoid-s7854" xml:space="preserve">c.</s> <s xml:id="echoid-s7855" xml:space="preserve">] <lb/>Maurolycus autem de eadem ſtella ita ſcripſit eodem anno 1572.</s> <s xml:id="echoid-s7856" xml:space="preserve">] Hoc anno <lb/> <anchor type="note" xlink:label="note-230-02a" xlink:href="note-230-02"/> ſignum inſolitum, & </s> <s xml:id="echoid-s7857" xml:space="preserve">mirabilius Cometis apparuit, ſtella ſcilicet inſignis, & </s> <s xml:id="echoid-s7858" xml:space="preserve">eximij <lb/>ſplendoris, in loco, vbi nulla ſtella notabatur. </s> <s xml:id="echoid-s7859" xml:space="preserve">Nec mihi Cometa ex ijs, qui in aere ge-<lb/>nerantur, eſſe uidetur: </s> <s xml:id="echoid-s7860" xml:space="preserve">altior enim apparet, & </s> <s xml:id="echoid-s7861" xml:space="preserve">de numero inerrantium. </s> <s xml:id="echoid-s7862" xml:space="preserve">Fortaſſe ſicut <lb/>fulgere incepit, ita deſinet; </s> <s xml:id="echoid-s7863" xml:space="preserve">præſertim cum quidam Philoſophi, quibus Cardanus aſſen-<lb/>titur, opinentur Cometas, ac nou{as} ſtellas etiam in cælo, ex aggregatione ſplendoris æ <lb/>planetis, aſtrisque reliquis fieri poſſe. </s> <s xml:id="echoid-s7864" xml:space="preserve">Vtcunque ſit, nequeo ſatis admirari huius ſtel-<lb/>læ nouam noſtri temporis fulſionem. </s> <s xml:id="echoid-s7865" xml:space="preserve">Certum enim eſt, non eße aliquam de numero <lb/>ſtellarum primæ magnitudinis, quæ in Ptolemaicis, & </s> <s xml:id="echoid-s7866" xml:space="preserve">Alphonſinis numeris notatæ <lb/>ſunt, & </s> <s xml:id="echoid-s7867" xml:space="preserve">quæ ab orbe condito lucent, & </s> <s xml:id="echoid-s7868" xml:space="preserve">quindecim ſunt; </s> <s xml:id="echoid-s7869" xml:space="preserve">quas hæc ſiella noua ita <lb/>ſplendore ſuperat, ut deinceps ſecundæ magnitudinis appellandæ ſint, modo hæc per-<lb/>duret. </s> <s xml:id="echoid-s7870" xml:space="preserve">Hanc ego ſtellam in hoc Meſſanæ Horizonte obſeruans in Meridiano extan-<lb/>tem; </s> <s xml:id="echoid-s7871" xml:space="preserve">circa tertiam noctis horam, reperi altitudinem eius eſſe graduum 62: </s> <s xml:id="echoid-s7872" xml:space="preserve">Vnde con-<lb/>iecturam feci, eum locari quaſi in ſummitate circuli arctici: </s> <s xml:id="echoid-s7873" xml:space="preserve">ut diſtet hic à meo uer-<lb/>tice per gradus 28. </s> <s xml:id="echoid-s7874" xml:space="preserve">& </s> <s xml:id="echoid-s7875" xml:space="preserve">proinde ab Aequatore per gradus 66 {1/2}. </s> <s xml:id="echoid-s7876" xml:space="preserve">fere: </s> <s xml:id="echoid-s7877" xml:space="preserve">quoniam Meſ-<lb/>ſanę latitudo habet gradus 38 {1/2}. </s> <s xml:id="echoid-s7878" xml:space="preserve">& </s> <s xml:id="echoid-s7879" xml:space="preserve">eam ſitam in eo puncto, in quo Colurus æquino- <pb o="195" file="231" n="232" rhead="Ioan. de Sacro Boſco."/> @iorum ſecat arcticum circulum, aut ipſi puncto uiciniſſimam, &</s> <s xml:id="echoid-s7880" xml:space="preserve">c.</s> <s xml:id="echoid-s7881" xml:space="preserve">] Hactenus de <lb/>quarta concluſione noſtri auctoris dictum ſit.</s> <s xml:id="echoid-s7882" xml:space="preserve"/> </p> <div xml:id="echoid-div375" type="float" level="2" n="7"> <note position="right" xlink:label="note-229-02" xlink:href="note-229-02a" xml:space="preserve">Stellam no <lb/>uam fuiſſe <lb/>in Firma-<lb/>mento.</note> <note position="left" xlink:label="note-230-01" xlink:href="note-230-01a" xml:space="preserve">Quid Pau-<lb/>linus Pridia <lb/>nus de no-<lb/>ua ſtella <lb/>ſeribat.</note> <note position="left" xlink:label="note-230-02" xlink:href="note-230-02a" xml:space="preserve">Quid Mau <lb/>rolycus de <lb/>eadem ſtel. <lb/>la noua di <lb/>xerit.</note> </div> </div> <div xml:id="echoid-div377" type="section" level="1" n="120"> <head xml:id="echoid-head125" xml:space="preserve">TERRAM ESSE IMMOBILEM.</head> <p style="it"> <s xml:id="echoid-s7883" xml:space="preserve"><emph style="sc">Qvod</emph> autem terra in medio omnium teneatur immobiliter, cum <lb/> <anchor type="note" xlink:label="note-231-01a" xlink:href="note-231-01"/> ſit ſumme grauis, ſic perſuadere uidetur eius grauitas. </s> <s xml:id="echoid-s7884" xml:space="preserve">Omne gra-<lb/>ue naturaliter tendit ad centrum; </s> <s xml:id="echoid-s7885" xml:space="preserve">Centrum quidem punctus in medio Fir-<lb/>mamenti: </s> <s xml:id="echoid-s7886" xml:space="preserve">Terra igitur, cum ſit ſumme grauis, ad punctum illum naturali-<lb/>ter tendit.</s> <s xml:id="echoid-s7887" xml:space="preserve"/> </p> <div xml:id="echoid-div377" type="float" level="2" n="1"> <note position="right" xlink:label="note-231-01" xlink:href="note-231-01a" xml:space="preserve">Terram nõ <lb/>moueri mo <lb/>tu recto.</note> </div> </div> <div xml:id="echoid-div379" type="section" level="1" n="121"> <head xml:id="echoid-head126" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s7888" xml:space="preserve"><emph style="sc">Ostendit</emph> hactenus auctor terram in medio omnium cælorum, ele-<lb/>mentorumque exiſtere, tanquam centrum totius Vniuerſi; </s> <s xml:id="echoid-s7889" xml:space="preserve">Nũc in quinta hac <lb/>concluſione conatur probare, eam ita in medio mundi eſſe ſitam, ut omnis mo <lb/>tus localis ſit expers. </s> <s xml:id="echoid-s7890" xml:space="preserve">Id autem duabus rationibus exequitur, quarum prima ſu-<lb/>mitur à terræ grauitate. </s> <s xml:id="echoid-s7891" xml:space="preserve">Cum enim terra omnium corporum ſit grauiſſima, <lb/>feretur ſuapte natura, cum nullibi impediatur, ad infimum locum, nempe ad <lb/>centrum mundi, ibique quieſcet.</s> <s xml:id="echoid-s7892" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s7893" xml:space="preserve">ITEM, quicquid à medio mouetur, uerſus circumferentiam cæli <lb/>aſcendit: </s> <s xml:id="echoid-s7894" xml:space="preserve">Terra à medio mouetur. </s> <s xml:id="echoid-s7895" xml:space="preserve">Igitur aſcendit, quod pro impoſsibili <lb/>relinquitur.</s> <s xml:id="echoid-s7896" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div380" type="section" level="1" n="122"> <head xml:id="echoid-head127" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s7897" xml:space="preserve"><emph style="sc">Probat</emph> idem ab incommodo. </s> <s xml:id="echoid-s7898" xml:space="preserve">Quoniam enim in præcedenti concluſio-<lb/>ne plurimis phænomenis confirmatum eſt, terram in medio mundi exiſtere: </s> <s xml:id="echoid-s7899" xml:space="preserve">ſi <lb/>motu locali a medio amoueretur, aſcenderet utique uerſus circunferentiam <lb/>cæli, quod pugnat cum phęnomenis, eſtque contra naturam grauitatis terræ.</s> <s xml:id="echoid-s7900" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7901" xml:space="preserve"><emph style="sc">Sed</emph> quoniam auctor excluſit à terra motum localem duntaxat rectum, non <lb/> <anchor type="note" xlink:label="note-231-02a" xlink:href="note-231-02"/> autem circularem, idcirco opus erit confirmare in vniuerſum, terram eſſe im-<lb/>mobilem ex Ptolemæo, Ariſtotele, cæterisq́; </s> <s xml:id="echoid-s7902" xml:space="preserve">Aſtronomis, & </s> <s xml:id="echoid-s7903" xml:space="preserve">Philoſophis, hoc <lb/>modo. </s> <s xml:id="echoid-s7904" xml:space="preserve">Si terra nõ perſiſteret immobilis, moueretur aut motu recto, aut motu <lb/>circulari. </s> <s xml:id="echoid-s7905" xml:space="preserve">Recto motu cieri nequit, quia cum ſupra demonſtratum ſit, eam exi-<lb/>ſtere in mundi centro, ſi motu recto ferretur, recederet à centro, atq@ adeo in <lb/>eadem prorſus incideremus abſurda, quæ conſequi diximus, ſi terra non eſſet <lb/>in medio mundi conſtituta. </s> <s xml:id="echoid-s7906" xml:space="preserve">Præterea ſi motu recto incederet, moueretur uel <lb/>naturaliter, uel uiolenter. </s> <s xml:id="echoid-s7907" xml:space="preserve">At natural@cer non ita mouebitur, cum|ſuapte na-<lb/>tura ad locum infimũ, qui eſt in centro Vniuerſi, tendat: </s> <s xml:id="echoid-s7908" xml:space="preserve">Certũ autem eſt eam <lb/>aſcendere, in quamcunque partem motu recto impellatur. </s> <s xml:id="echoid-s7909" xml:space="preserve">Violenter quo<unsure/>que <lb/>motu recto moueri non poteſt, quoniam nullum cor<unsure/>pus ipſa grauius reperi-<lb/>tur, quod ſuo pondere eam à centro mundipropelleret. </s> <s xml:id="echoid-s7910" xml:space="preserve">Rurſus ſi terra motu <lb/>recto ferretur, ſumma uelocitate eam moueri neceſſe eſſet, cum ſit ſumme gra <lb/>uis: </s> <s xml:id="echoid-s7911" xml:space="preserve">Quo conceſſo, quis non uidet, minus grauia, cuiuſmodi ſunt arborum fo-<lb/>lia, paleæ, & </s> <s xml:id="echoid-s7912" xml:space="preserve">reliqua omnia corpora, poſt ipſam in aere debere relinqui, cum <lb/>eius motum celerrimum conſequi nequeant, quippe cum tanta grauitate non <lb/>ſit prædita? </s> <s xml:id="echoid-s7913" xml:space="preserve">At hæc omnia communi experientiæ repugnant. </s> <s xml:id="echoid-s7914" xml:space="preserve">Videmus enim <pb o="196" file="232" n="233" rhead="Comment. in I. Cap. Sphæræ"/> huiuſmodicorpora, ni uento aliquo, aut impetu auellantur, immota terræ ſu-<lb/>perficiei adhærere. </s> <s xml:id="echoid-s7915" xml:space="preserve">Nonigitur motu recto terra fertur.</s> <s xml:id="echoid-s7916" xml:space="preserve"/> </p> <div xml:id="echoid-div380" type="float" level="2" n="1"> <note position="right" xlink:label="note-231-02" xlink:href="note-231-02a" xml:space="preserve">Terrã om-<lb/>nino immo <lb/>bilem eſſe.</note> </div> <p> <s xml:id="echoid-s7917" xml:space="preserve"><emph style="sc">Qvod</emph> autem nec motu circulari agitetur, ut multi opinati ſunt, ita con-<lb/>@i<unsure/>rmari poterit. </s> <s xml:id="echoid-s7918" xml:space="preserve">Si terra circulariter mouetur, mouebitur aut ſuper axẽ mundi <lb/>ab oriente in occidentem, uel ab occidente in oriẽtem; </s> <s xml:id="echoid-s7919" xml:space="preserve">aut ſuper alium axem. <lb/></s> <s xml:id="echoid-s7920" xml:space="preserve">Si ſuper axem mundi moueri dicatur, efficitur, ut nubes, aues, & </s> <s xml:id="echoid-s7921" xml:space="preserve">omnia, quę in <lb/>aere exiſtunt, in contrariam partem cernantur moueri, nimirum in occidẽtẽ, <lb/>ſi terra ad orientem uoluitur, uel in orientem, ſi terra in occidentem labitur: </s> <s xml:id="echoid-s7922" xml:space="preserve"><lb/>quoniam uidelicet conſequi non poſſent motum terræ rapidiſſimum, ut pote <lb/>qui in ſpatio 24. </s> <s xml:id="echoid-s7923" xml:space="preserve">horarum abſoluitur. </s> <s xml:id="echoid-s7924" xml:space="preserve">Neq; </s> <s xml:id="echoid-s7925" xml:space="preserve">uero dici poteſt, aerem eadem cele <lb/>ritate cum terra circumduci, quo niam conſtat, ipſum modo huc, modo illuc <lb/>fluctuare, prout nimirum in hanc, uel illam partem à uarijs uentis agitatur, ut <lb/>quotidiana experientia nos docet. </s> <s xml:id="echoid-s7926" xml:space="preserve">Præterea, ſi terra tanta celeritate circa axẽ <lb/>mundi volueretur, ut uidelicet circuitum expleret ſpacio 24. </s> <s xml:id="echoid-s7927" xml:space="preserve">horarum, ſicut <lb/>quidam fabulantur, omnia ædificia corruerent, & </s> <s xml:id="echoid-s7928" xml:space="preserve">nulla ratione diu conſiſtere <lb/>poſſent: </s> <s xml:id="echoid-s7929" xml:space="preserve">quod omnino falſum eſſe, nemo eſt, qui non uideat. </s> <s xml:id="echoid-s7930" xml:space="preserve">Neque enim va-<lb/>let reſponſio quorundam, qui dicunt ædificia non corruere, propter nimiam <lb/>celeritatem motus, quemadmodum neque aqua in uaſe aliquo cõtenta, effluit <lb/>ſi uas uelociſſime circumducatur: </s> <s xml:id="echoid-s7931" xml:space="preserve">Non ualet inquam, hæc reſponſio, quia to-<lb/>tus impetus aquæ imprimitur uerſus partes inferiores uaſis, non autem uerſus <lb/>orificium eius: </s> <s xml:id="echoid-s7932" xml:space="preserve">At uero impetus imprimitur ædificijs uerſus partes extimas <lb/>terræ: </s> <s xml:id="echoid-s7933" xml:space="preserve">vnde conſiſtere minime poſſent, quemadmodum neque aqua in uaſe po <lb/>ſita, quod circumuoluatur quàntumuis uelociter, ſi orificium eius ad partes <lb/>exteriores uergat. </s> <s xml:id="echoid-s7934" xml:space="preserve">Pari ratione effi ceretur, lapidem, ſeu ſagittam aliquam ma-<lb/>gna ui ſurſum directe proiectam, non in eundem locum recidere, ueluti in na-<lb/>ui aliqua celerrime mota accidere conſpicimus. </s> <s xml:id="echoid-s7935" xml:space="preserve">Quæ omnia abſurda ſunt. </s> <s xml:id="echoid-s7936" xml:space="preserve">Rur <lb/>ſus, fi terra motu circulari cieretur, eſſet talis motus uel terræ naturalis, uel <lb/>præter naturam: </s> <s xml:id="echoid-s7937" xml:space="preserve">Naturalis eſſe non poteſt. </s> <s xml:id="echoid-s7938" xml:space="preserve">Cum enim unicorpori ſimplici <lb/>vnus tantum motus naturaliter conueniat; </s> <s xml:id="echoid-s7939" xml:space="preserve">Terra autem ſuapte natura motu <lb/>recto ad mundi centrum, ſi extra ipſum reperitur, pergat; </s> <s xml:id="echoid-s7940" xml:space="preserve">non poterit ſecũdum <lb/>propriam naturam moueri circulariter. </s> <s xml:id="echoid-s7941" xml:space="preserve">Neque etiam circumuertetur circu-<lb/>lariter præter naturam, nempe ad motum cæli; </s> <s xml:id="echoid-s7942" xml:space="preserve">quoniam hac ratione ſemper <lb/>eadem cæli pars ucrtici noſtro immineret; </s> <s xml:id="echoid-s7943" xml:space="preserve">Vnde neque aſtra orirentur, neque <lb/>occiderent: </s> <s xml:id="echoid-s7944" xml:space="preserve">quod abſurdum eſt.</s> <s xml:id="echoid-s7945" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7946" xml:space="preserve"><emph style="sc">Sivero</emph> dicatur terra moueri ſuper alium axem, qui nimirum oblique <lb/>ſecat axem mundi, præterquam quòd in eadem fere incommoda relaberemur, <lb/>ſequitur quotidie in una, eademq́ue ciuitate altitudinem poli uariam exiſtere, <lb/>quia uidelicet illa urbs ad motum terræ non deſcriberet circulum parallelum <lb/>circa polum; </s> <s xml:id="echoid-s7947" xml:space="preserve">Vnde nunc propius ad illum accederet, nunc longius ab eodem <lb/>amoueretur, ac proinde poli altitudinem uariaret; </s> <s xml:id="echoid-s7948" xml:space="preserve">quod falſum eſt. </s> <s xml:id="echoid-s7949" xml:space="preserve">Videmus <lb/>enim Romæ v.</s> <s xml:id="echoid-s7950" xml:space="preserve">g. </s> <s xml:id="echoid-s7951" xml:space="preserve">polum arcticum perpetuo eãdem habere exaltationem ſupra <lb/>Horizontem. </s> <s xml:id="echoid-s7952" xml:space="preserve">Concludamus igitur cum communi Aſtronomorum, atque Phi <lb/>loſophorum ſententia, terram eſſe omnis motus localis tam recti, quàm cir-<lb/>cularis, expertem; </s> <s xml:id="echoid-s7953" xml:space="preserve">cælos autem ipſos continue circa ipſam circumagi, præſer-<lb/>tim quia hoc conceſſo, multo facilius omnia phænomena defenduntur, nul-<lb/>lumq́ue inconueniens inde conſequitur.</s> <s xml:id="echoid-s7954" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7955" xml:space="preserve"><emph style="sc">Favent</emph> huic quoque ſententiæ ſacræ literæ, quæ plurimis in locis ter-<lb/>ram eſſe immobilem affirmant, Solemq. </s> <s xml:id="echoid-s7956" xml:space="preserve">ac cætera aſtra moueri teſtantur: </s> <s xml:id="echoid-s7957" xml:space="preserve">Le- <pb o="197" file="233" n="234" rhead="Ioan. de Sacro Boſco."/> gimus enim in pſalmo 103. </s> <s xml:id="echoid-s7958" xml:space="preserve">[Qui fundaſti terram ſuper ſtabilitatem ſuam, non in-<lb/>@linabitur in ſeculum ſeculi.</s> <s xml:id="echoid-s7959" xml:space="preserve">] Item in Eccleſiaſte cap. </s> <s xml:id="echoid-s7960" xml:space="preserve">1. </s> <s xml:id="echoid-s7961" xml:space="preserve">[Terra in æternum ſtat, <lb/>@ritur Sol, & </s> <s xml:id="echoid-s7962" xml:space="preserve">occidit, & </s> <s xml:id="echoid-s7963" xml:space="preserve">ad locum ſuum reuertitur, ibiq́ue renaſcens gyrat per me-<lb/>ridiem, & </s> <s xml:id="echoid-s7964" xml:space="preserve">flectitur ad aquilonem.</s> <s xml:id="echoid-s7965" xml:space="preserve">] Quid clarius dici poterat? </s> <s xml:id="echoid-s7966" xml:space="preserve">Clariſſimum quo-<lb/>que teſtimonium, quod Sol moueatur, perhibet nobis pſalmus 18. </s> <s xml:id="echoid-s7967" xml:space="preserve">in quo ita <lb/>legitur. </s> <s xml:id="echoid-s7968" xml:space="preserve">[In sole poſuit tabernaculum ſuum, & </s> <s xml:id="echoid-s7969" xml:space="preserve">ipſe tanquam ſponſus procedens de <lb/>thalamo ſuo, exultauit ut Gigas ad currendam uiam, à ſummo cœlo egreſſio eius: </s> <s xml:id="echoid-s7970" xml:space="preserve">Et <lb/>occurſus eius uſque ad ſummum eius, nec eſt qui ſe abſcondat à calore eius.</s> <s xml:id="echoid-s7971" xml:space="preserve">] Rur-<lb/>ſus inter miracula refertur, quod Deus aliquando Solem aut retroduxit, aut <lb/>prorſus, ut confiſteret, effecit.</s> <s xml:id="echoid-s7972" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7973" xml:space="preserve"><emph style="sc">Hvivs</emph> autem immobilitatis terræ in medio mundo diuerſi diuerſas aſſi <lb/> <anchor type="note" xlink:label="note-233-01a" xlink:href="note-233-01"/> gnarunt cauſas. </s> <s xml:id="echoid-s7974" xml:space="preserve">Quidam enim (inter quos eſt, teſte Ariſtotelein 2. </s> <s xml:id="echoid-s7975" xml:space="preserve">lib. </s> <s xml:id="echoid-s7976" xml:space="preserve">de cæ-<lb/>lo, Xenophon Colophonius) dixerunt, terrã ex altera parte eſſe infinite pro-<lb/>fundam, atque ob id eam non cadere deorſum. </s> <s xml:id="echoid-s7977" xml:space="preserve">Sed hæc opinio falſaeſt. </s> <s xml:id="echoid-s7978" xml:space="preserve">Pri-<lb/>mum, quia hoc modo terra non eſſet rotunda, ac ſphærica, cuius contrarium <lb/>ſupra demonſtrauimus. </s> <s xml:id="echoid-s7979" xml:space="preserve">Deinde, quoniam ſecundum Ariſtotelẽ in 3. </s> <s xml:id="echoid-s7980" xml:space="preserve">li. </s> <s xml:id="echoid-s7981" xml:space="preserve">Phyſi. <lb/></s> <s xml:id="echoid-s7982" xml:space="preserve">& </s> <s xml:id="echoid-s7983" xml:space="preserve">1. </s> <s xml:id="echoid-s7984" xml:space="preserve">de cœlo, & </s> <s xml:id="echoid-s7985" xml:space="preserve">alios philoſophos, nullum datur actu infinitum. </s> <s xml:id="echoid-s7986" xml:space="preserve">Tertio, quòd <lb/>hac ratione cælum nullo modo circũuolui poſſet: </s> <s xml:id="echoid-s7987" xml:space="preserve">impediretur enim ab infini <lb/>ta illa profunditate terræ: </s> <s xml:id="echoid-s7988" xml:space="preserve">Neque enim cęlum infinito interuallo à nobis di-<lb/>ſtat, quod abſurdum eſt.</s> <s xml:id="echoid-s7989" xml:space="preserve"/> </p> <div xml:id="echoid-div381" type="float" level="2" n="2"> <note position="right" xlink:label="note-233-01" xlink:href="note-233-01a" xml:space="preserve">Varlæ ſem-<lb/>tentiæ, cur <lb/>terra fit im <lb/>mobilia, & <lb/>carum con-<lb/>futatio.</note> </div> <p> <s xml:id="echoid-s7990" xml:space="preserve"><emph style="sc">Alii</emph> putarunt, ut Thales Mileſius, terram aquis ſupernatare, atque ab <lb/>illis ſuſtentari, ne decidat. </s> <s xml:id="echoid-s7991" xml:space="preserve">Verum hoc ridiculum eſt. </s> <s xml:id="echoid-s7992" xml:space="preserve">Nam cum aqua le@ior <lb/>ſit multo, quàm terra, qui fieri poteſt, ut grauius corpus ſuſtineat, præſertim <lb/>cum ubique uideamus partes terræ ſub aquam deſcendere? </s> <s xml:id="echoid-s7993" xml:space="preserve">Præterea in@erro <lb/>gandi ſunt huiuſmodi philoſophi, cui innitatur aqua, ne ſimul cum terra deci <lb/>dat. </s> <s xml:id="echoid-s7994" xml:space="preserve">Aqua etenim, cum ſit fluxibilis, conſiſtere nequit, ni ſolido alicui corpo-<lb/>ri ſit innixa.</s> <s xml:id="echoid-s7995" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7996" xml:space="preserve"><emph style="sc">Qvidam</emph> affirmarunt, ut Anaxagoras, & </s> <s xml:id="echoid-s7997" xml:space="preserve">Democritus, terram prædi-<lb/>tam eſſe figura admodum ampla, atq; </s> <s xml:id="echoid-s7998" xml:space="preserve">lata, atque idcirco eam comprimere ae-<lb/>rem, ab eoq́ue ſuſtineri, ne decidat. </s> <s xml:id="echoid-s7999" xml:space="preserve">Cęterum, & </s> <s xml:id="echoid-s8000" xml:space="preserve">hoc fictum eſt, ac fabulæ ani-<lb/>li perſimile. </s> <s xml:id="echoid-s8001" xml:space="preserve">Terra enim figuram ſphæricam obtinet, & </s> <s xml:id="echoid-s8002" xml:space="preserve">non planam, uti ſupra <lb/>demonſtrauimus. </s> <s xml:id="echoid-s8003" xml:space="preserve">Immo etiam ſi haberet talem formam, tamen contra expe-<lb/>rientiam eſt, corpora lata ita in aere ſuſtentari, ut tandem non decidant. </s> <s xml:id="echoid-s8004" xml:space="preserve">Quã-<lb/>uis enim difficile huiuſmodi corpora propter latitudinem deſcendant, <lb/>quia nimirum uix aerem ſecare poſſunt, paulatim tamen deorſum tendere <lb/>cernuntur.</s> <s xml:id="echoid-s8005" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8006" xml:space="preserve"><emph style="sc">Nonnvlli</emph> denique, ut Anaximander Mileſius, propius ad uerita-<lb/>tem accedentes, ideo rerram in medio quieſcere teſtatiſunt, quia eſt in medio <lb/>mundi poſita. </s> <s xml:id="echoid-s8007" xml:space="preserve">Hinc enim fit, aiunt, ut terra, uel inclinetur ad motum uerſus <lb/>omnem partem cœli, cum non ſit maior ratio, cur magis ad hanc, quàm ad il-<lb/>lam partem moueri debeat, uel certe attrahatur æqualiter ab omnibus par-<lb/>tibus cęli. </s> <s xml:id="echoid-s8008" xml:space="preserve">Quocirca, quoniam non poteſt eodẽ temporis momento ad omnes <lb/>partes ferri, quieſcit in medio, ſeu centro mundi. </s> <s xml:id="echoid-s8009" xml:space="preserve">Sed & </s> <s xml:id="echoid-s8010" xml:space="preserve">hæc opinio erronea <lb/>eſt. </s> <s xml:id="echoid-s8011" xml:space="preserve">Primum, quia ſi propter hanc cauſam terra non moueretur, detineretur <lb/>violenter in medio Vniuerſi, & </s> <s xml:id="echoid-s8012" xml:space="preserve">non naturaliter. </s> <s xml:id="echoid-s8013" xml:space="preserve">Deinde, quoniam falſum eſt, <lb/>terram inclinariad motũ uerſus partes cęli, cũ hac ratione ſurſum tenderet, <lb/>quod illius naturæ repugnat. </s> <s xml:id="echoid-s8014" xml:space="preserve">Videmus enim partes terræ naturaliter deſcende <lb/>re maximo impetu, niſi impediantur, & </s> <s xml:id="echoid-s8015" xml:space="preserve">ſemper à cęlo uerſus centrum, quoad <pb o="198" file="234" n="235" rhead="Comment. in I. Cap. Sphæræ"/> eius fieri poteſt, recedere. </s> <s xml:id="echoid-s8016" xml:space="preserve">Pari ratione falſum eſt, terram attrahi à cœlo, cu@ <lb/>potius terram uideamus à cœlo remoueri ſuapte natura. </s> <s xml:id="echoid-s8017" xml:space="preserve">Tertio, quia ſi pro-<lb/>pter hanc eauſam terra in centro quieſceret immobilis, eadem ratione confi@ <lb/>maretur, ignem uel aerem in centro mundi poſitum debere quieſcere. </s> <s xml:id="echoid-s8018" xml:space="preserve">Non <lb/>enim maior eſſet ratio, cur in hanc, uel illam partem moueretur, cum ęqua-<lb/>lem habeat inclinationem ad omnes cęli partes: </s> <s xml:id="echoid-s8019" xml:space="preserve">quod tamen nemo philoſo-<lb/>phorum conceſſit.</s> <s xml:id="echoid-s8020" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8021" xml:space="preserve"><emph style="sc">Dicendvm</emph> eſtigitur, nullam aliam eſſe cauſam, propter quam terra <lb/> <anchor type="note" xlink:label="note-234-01a" xlink:href="note-234-01"/> in medio mundi quieſcat, quàm ipſius grauitatem. </s> <s xml:id="echoid-s8022" xml:space="preserve">Hinc enim fit, ut ſemper <lb/>quęrat eſſe in infimo loco, qui eſt remotiſſimus à cęlo, centrum uidelicet to-<lb/>tius Vniuerſi, quod cum ſemel poſſederit, naturaliter abeo diuelli nõ poteſt, <lb/>quia contra ſuam naturam, ac inclinationem aſcenderet. </s> <s xml:id="echoid-s8023" xml:space="preserve">Eandem ob cauſam <lb/>omnia grauia naturaliter ad mundi cẽ<unsure/>trum maximo impetu, niſi quid obſtet, <lb/>deferuntur: </s> <s xml:id="echoid-s8024" xml:space="preserve">Ita ut ſi eſſet tota terra ab una parte ad alteram perforata, & </s> <s xml:id="echoid-s8025" xml:space="preserve">gra-<lb/>ue aliquod incideret in ſoramen illud, perueniret ſolum maximo impetu ad <lb/>centrum, non autem ad alteram partem, quia tunc aſcenderet, licet in princi-<lb/>pio, ob motus impetum, huc, illucq́ue fluctuaret aliquantiſper, donec, paula-<lb/>tim remiſſo motus impetu, in medio quieſceret. </s> <s xml:id="echoid-s8026" xml:space="preserve">De hac quoque terrę immo-<lb/>bilitate eleganter ſic ſcribit Manilius.</s> <s xml:id="echoid-s8027" xml:space="preserve"/> </p> <div xml:id="echoid-div382" type="float" level="2" n="3"> <note position="left" xlink:label="note-234-01" xlink:href="note-234-01a" xml:space="preserve">Cur terra <lb/>in medio <lb/>quieſcat@</note> </div> <p style="it"> <s xml:id="echoid-s8028" xml:space="preserve">Nec uero tibi Natura admiranda uideri <lb/>Pendentis terræ debet@ cum pendeatipſe<unsure/> <lb/>Mundus, & </s> <s xml:id="echoid-s8029" xml:space="preserve">in nullo ponat ueſtigia fundo. <lb/></s> <s xml:id="echoid-s8030" xml:space="preserve">Quod patet ex ipſo motu, curſuq́ue uolantis, <lb/>Cum ſuſpenſus eat Phœ<unsure/>bus, curſumq́; </s> <s xml:id="echoid-s8031" xml:space="preserve">reflectat <lb/>Huc illue, agiles & </s> <s xml:id="echoid-s8032" xml:space="preserve">ſeruet in æthere metas. </s> <s xml:id="echoid-s8033" xml:space="preserve"><lb/>Cum Luna, & </s> <s xml:id="echoid-s8034" xml:space="preserve">Stellæ uolitent per inania mundi. </s> <s xml:id="echoid-s8035" xml:space="preserve"><lb/>Terra quoque aerias leges imitata pependit. </s> <s xml:id="echoid-s8036" xml:space="preserve"><lb/>Eſt igitur tellus mediam ſortita cauernam <lb/>Aeris, & </s> <s xml:id="echoid-s8037" xml:space="preserve">toto pariter ſublata profundo. </s> <s xml:id="echoid-s8038" xml:space="preserve"><lb/>Nec patulas diſtenta plagas, ſed condita in orbem <lb/>Vndique ſurgentem pariter, pariterq́ue cadentem. </s> <s xml:id="echoid-s8039" xml:space="preserve"><lb/>Hæc eſt Naturæ facies. </s> <s xml:id="echoid-s8040" xml:space="preserve">. </s> <s xml:id="echoid-s8041" xml:space="preserve">. </s> <s xml:id="echoid-s8042" xml:space="preserve">. </s> <s xml:id="echoid-s8043" xml:space="preserve">. </s> <s xml:id="echoid-s8044" xml:space="preserve">. </s> <s xml:id="echoid-s8045" xml:space="preserve">.</s> <s xml:id="echoid-s8046" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8047" xml:space="preserve"><emph style="sc">Ex his</emph>, quę diximus, facile ſolui poteſt ratio illa communis Lactantij <lb/> <anchor type="note" xlink:label="note-234-02a" xlink:href="note-234-02"/> Firmiani, & </s> <s xml:id="echoid-s8048" xml:space="preserve">uulgi, contra antipodas: </s> <s xml:id="echoid-s8049" xml:space="preserve">Aiunt enim, ſi eſſent antipodes, ſeu ho-<lb/>mines nobis contrapoſiti, nõ poſſent cõſiſtere, ſed deciderent. </s> <s xml:id="echoid-s8050" xml:space="preserve">Solui, inquam, <lb/>poteſt, quia antipodes ſua grauitate ſemper ad centrum mundi uergunt, fi-<lb/>cut & </s> <s xml:id="echoid-s8051" xml:space="preserve">nos; </s> <s xml:id="echoid-s8052" xml:space="preserve">Quinimo, ſi conſiſtere non poſſent, caderent in cœlum, ideſt, in <lb/>locum ſuperiorem, quod eſt contra grauium naturam, & </s> <s xml:id="echoid-s8053" xml:space="preserve">inclinationem. </s> <s xml:id="echoid-s8054" xml:space="preserve">Non <lb/>eſt ergo mirum, illos non cadere, ſed po@ius ualde mirabile eſſet, ſi in cœ<unsure/>lum <lb/>deciderent.</s> <s xml:id="echoid-s8055" xml:space="preserve"/> </p> <div xml:id="echoid-div383" type="float" level="2" n="4"> <note position="left" xlink:label="note-234-02" xlink:href="note-234-02a" xml:space="preserve">Cur Antipo <lb/>des non ca <lb/>dant.</note> </div> </div> <div xml:id="echoid-div385" type="section" level="1" n="123"> <head xml:id="echoid-head128" style="it" xml:space="preserve">DE AMBITV TERRAE.</head> <p style="it"> <s xml:id="echoid-s8056" xml:space="preserve"><emph style="sc">TOtivs</emph> autem orbis terræ ambitus, auctoritate Ambrosij <lb/> <anchor type="note" xlink:label="note-234-03a" xlink:href="note-234-03"/> Theodosij, Macrobij, & </s> <s xml:id="echoid-s8057" xml:space="preserve">Eratoſthenis philoſophorũ 252000. <lb/></s> <s xml:id="echoid-s8058" xml:space="preserve">ſtadia continere definitur, unicuique quidem 360. </s> <s xml:id="echoid-s8059" xml:space="preserve">partium Zo-<lb/>diaci 700. </s> <s xml:id="echoid-s8060" xml:space="preserve">ſtadia deputando.</s> <s xml:id="echoid-s8061" xml:space="preserve"/> </p> <div xml:id="echoid-div385" type="float" level="2" n="1"> <note position="left" xlink:label="note-234-03" xlink:href="note-234-03a" xml:space="preserve">Tetræ ambi <lb/>tus ſecun-<lb/>dum Ma-<lb/>crobium, & <lb/>Eratoſthe-<lb/>nem.</note> </div> </div> <div xml:id="echoid-div387" type="section" level="1" n="124"> <head xml:id="echoid-head129" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s8062" xml:space="preserve"><emph style="sc">Haec</emph> eſt ſexta, atque ultima concluſio, Terram uidelicet ambitu ſuo ha <pb o="199" file="235" n="236" rhead="Ioan. de Sacro Boſco."/> bere certam, ac determinatam quantitatem, non antem eſſe infinitæ profundi-<lb/>@atis, ut quidam falſo opinabantur. </s> <s xml:id="echoid-s8063" xml:space="preserve">Quam quidem hunc in modum confirmat. <lb/></s> <s xml:id="echoid-s8064" xml:space="preserve">Ex ſententia Ambroſij Theodoſij Macrobij (non enim tria hæc nomina tres <lb/>auctores, ut nonnulli uolunt, ſed unum ſignificant duntaxat) in commentarijs, <lb/>quos in ſomnium Scipionis edidit, lib. </s> <s xml:id="echoid-s8065" xml:space="preserve">1. </s> <s xml:id="echoid-s8066" xml:space="preserve">& </s> <s xml:id="echoid-s8067" xml:space="preserve">Eratoſthenis, totus ambitus terræ <lb/>continet ſtadia 252000. </s> <s xml:id="echoid-s8068" xml:space="preserve">propterea quòd uni gradui terræ ex 360. </s> <s xml:id="echoid-s8069" xml:space="preserve">congruunt ſta <lb/>dia 700. </s> <s xml:id="echoid-s8070" xml:space="preserve">Nota igitur, & </s> <s xml:id="echoid-s8071" xml:space="preserve">determiuata eſſe quantitas terræ.</s> <s xml:id="echoid-s8072" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">Ambit@ t@@ <lb/>ræ ſume@-<lb/>dus eſt pe-<lb/>nes circul@ <lb/>maximum.</note> <p> <s xml:id="echoid-s8073" xml:space="preserve"><emph style="sc">Svmendvs</emph> autem eſt hic ambitus orbis terreni non penes quemuis cir-<lb/>culum in terra deſcriptum, ſed ſecundum circulum terræ maximum, qui uide <lb/>licet idem cum terra centrum poſſidet, qualis eſt Meridianus circulus. </s> <s xml:id="echoid-s8074" xml:space="preserve">Aequi <lb/>noctialis, Horizon, uel quiuis alius maximus in terræ ſuperſicie deſcriptus: <lb/></s> <s xml:id="echoid-s8075" xml:space="preserve">Quemadmodum etiam ſpiſſitudo, ſeu profunditas terræ, uel cuiuſuis corporis <lb/> <anchor type="note" xlink:label="note-235-02a" xlink:href="note-235-02"/> ſphærici, penes eius diametrum, quę eſt maxima linea in circulo ſeu ſphæra, <lb/>cum per eius centrum tranſeat, determinari debet, non autem per alias lineas, <lb/>quæ ſexcentis modis uariari poſſunt:</s> <s xml:id="echoid-s8076" xml:space="preserve"/> </p> <div xml:id="echoid-div387" type="float" level="2" n="1"> <note position="right" xlink:label="note-235-02" xlink:href="note-235-02a" xml:space="preserve">15. tertij.</note> </div> <p style="it"> <s xml:id="echoid-s8077" xml:space="preserve">SVMPTO enim Aſtrolabio, uel Quadrante, in ſtellatæ noctis cla-<lb/> <anchor type="note" xlink:label="note-235-03a" xlink:href="note-235-03"/> ritate, per utrumque mediclinij for amen polo perſpecto, notetur graduum <lb/>multitudo, in quaſteterit mediclinium. </s> <s xml:id="echoid-s8078" xml:space="preserve">Deinde procedat Coſmimetra dire-<lb/>cte uerſus Septentrionem à Meridie, donec in alteri{us} noctis claritate, uiſo <lb/>ut prius, polo, ſteterit altius uno gradu mediclinium. </s> <s xml:id="echoid-s8079" xml:space="preserve">Poſt hoc menſuretur <lb/>huius itineris ſpatium, & </s> <s xml:id="echoid-s8080" xml:space="preserve">inuenientur 700. </s> <s xml:id="echoid-s8081" xml:space="preserve">ſtadia Deinde datis unicuique <lb/>360. </s> <s xml:id="echoid-s8082" xml:space="preserve">graduum tot ſtadijs, terreni orbis ambitus inuentus erit.</s> <s xml:id="echoid-s8083" xml:space="preserve"/> </p> <div xml:id="echoid-div388" type="float" level="2" n="2"> <note position="right" xlink:label="note-235-03" xlink:href="note-235-03a" xml:space="preserve">Quomod@ <lb/>terræ ambi <lb/>tus inueſti. <lb/>gandus ſit.</note> </div> </div> <div xml:id="echoid-div390" type="section" level="1" n="125"> <head xml:id="echoid-head130" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s8084" xml:space="preserve"><emph style="sc">Qvoniam</emph> auctor aſſumpſerat, tanquam ratum & </s> <s xml:id="echoid-s8085" xml:space="preserve">certum, uni gradu@ <lb/>orbis terreni reſpondere 700. </s> <s xml:id="echoid-s8086" xml:space="preserve">ſtadia, atque adeo omnes 360. </s> <s xml:id="echoid-s8087" xml:space="preserve">gradus, hoc eſt, to <lb/>tum ambitum terræ, comprehendere ſtadia 252000 quod aliquis negare poſ <lb/>ſet, immo ulgus, & </s> <s xml:id="echoid-s8088" xml:space="preserve">multi etiam, qui docti uideri uolunt, arbitrantur, impoſſi-<lb/>bile eſſe, ut terræ ambitus menſuretur, propterea quòd ob multa impedimen-<lb/>ta rupiũ inacceſſibilium, ualliũ, fluminum, lacuum, Oceani, maris mediterra-<lb/> <anchor type="note" xlink:label="note-235-04a" xlink:href="note-235-04"/> nei, &</s> <s xml:id="echoid-s8089" xml:space="preserve">c. </s> <s xml:id="echoid-s8090" xml:space="preserve">circumiri tota nequeat. </s> <s xml:id="echoid-s8091" xml:space="preserve">Idcirco pręſcribit uiam, qua uſi ſunt Aſtrono-<lb/>mi, & </s> <s xml:id="echoid-s8092" xml:space="preserve">qua quilibet, ſi placet, uti poterit in metiendo terrę ambitu. </s> <s xml:id="echoid-s8093" xml:space="preserve">Satis enim <lb/>erit, ſi accurate, ac diligenter metiatur quis ſpatium itineris, quod uni gradui <lb/>terręcongruit, & </s> <s xml:id="echoid-s8094" xml:space="preserve">nõ totum circuitum. </s> <s xml:id="echoid-s8095" xml:space="preserve">Nam cum terra ſit ſphęrica, ut demon-<lb/>ſtratum eſt, ex cognita quauis parte ambitus,, quæ ad totum ambitum propor-<lb/>tionem habeat notam, ueniemus facile per regulam proportionum in cogni-<lb/>tionem totius ambitus terræ. </s> <s xml:id="echoid-s8096" xml:space="preserve">Via autem, quam tradit, perſpicua eſt in litera, <lb/>& </s> <s xml:id="echoid-s8097" xml:space="preserve">admodũ facilis ijs, qui uel mediocriter in inſtrumentis Mathematicis, maxi-<lb/>me in Aſtrolabio, & </s> <s xml:id="echoid-s8098" xml:space="preserve">Quadrante uerſati fuerint. </s> <s xml:id="echoid-s8099" xml:space="preserve">Id ſolummodo circa eam intel <lb/>ligendum eſt, nulla ratione per Aſtrolabium, quadrantemve polum poſſe con <lb/>ſpici: </s> <s xml:id="echoid-s8100" xml:space="preserve">ſtella enim polaris, quam prope polum intuemur, uerus polus nõ eſt, ſed <lb/>circa uerum polum circulum deſcribit diſtantem à polo grad. </s> <s xml:id="echoid-s8101" xml:space="preserve">fere 3.</s> <s xml:id="echoid-s8102" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s8103" xml:space="preserve">Vnde <lb/>ueram altitudinem oſtendere nequit. </s> <s xml:id="echoid-s8104" xml:space="preserve">Quare alia ratione inquirenda erit alti-<lb/>tudo poli@ Quod quonam pacto fieri debeat, non eſt huius loci, ſed ſpectat ad <pb o="200" file="236" n="237" rhead="Comment. in I. Cap. Sphæræ"/> tractationem uſus Aſtrolabij, uel Quadrantis; </s> <s xml:id="echoid-s8105" xml:space="preserve">de quo tamen re nonnihil etiã <lb/>dicemus, cum de Meridiano circulo diſpu@abimus.</s> <s xml:id="echoid-s8106" xml:space="preserve"/> </p> <div xml:id="echoid-div390" type="float" level="2" n="1"> <note position="right" xlink:label="note-235-04" xlink:href="note-235-04a" xml:space="preserve">Satis eſt, @ <lb/>@ueſtigetur <lb/>interuallũ <lb/>vnius gra-<lb/>dus in ter-<lb/>ra, ut totus <lb/>ambitus h@ <lb/>beatur.</note> </div> <p> <s xml:id="echoid-s8107" xml:space="preserve"><emph style="sc">Neqve</emph> uero neceſſe eſt, integrum gradum perambulare, ſeu dimetiri, <lb/> <anchor type="note" xlink:label="note-236-01a" xlink:href="note-236-01"/> ut habeamus totum terræ ambitum, ſed ſatis @rit mẽſurare ſpatium dimidiati <lb/>gradus, uel tertiæ partis unius gradus, uel deniq́; </s> <s xml:id="echoid-s8108" xml:space="preserve">quamcunque particulã, cu-<lb/>@us proportio ad totum terrę circulum cognita ſit. </s> <s xml:id="echoid-s8109" xml:space="preserve">Ex hac etenim particula <lb/>cog@ita, beneficio regulæ proportionum, totum ambitum facile eliciemus. </s> <s xml:id="echoid-s8110" xml:space="preserve">Vt <lb/>quoniam uerbi gratia quartæ parti unius grad. </s> <s xml:id="echoid-s8111" xml:space="preserve">reſpondere inueniuntur ſtadia <lb/>175. </s> <s xml:id="echoid-s8112" xml:space="preserve">continebunt huiuſmodi partes quartæ 1440. </s> <s xml:id="echoid-s8113" xml:space="preserve">nempe totus terræ ambitus, <lb/>ſtadia 252000. </s> <s xml:id="echoid-s8114" xml:space="preserve">uti prius. </s> <s xml:id="echoid-s8115" xml:space="preserve">Pari ratione, ſi dimidiato gradui reſpondent ſtadia <lb/>350. </s> <s xml:id="echoid-s8116" xml:space="preserve">reſpondebunt toti ambitui, qui conſtat ex dimidiatis partibus 720. </s> <s xml:id="echoid-s8117" xml:space="preserve">iterum <lb/>ſtadia 252000. </s> <s xml:id="echoid-s8118" xml:space="preserve">& </s> <s xml:id="echoid-s8119" xml:space="preserve">ſic de cęteris.</s> <s xml:id="echoid-s8120" xml:space="preserve"/> </p> <div xml:id="echoid-div391" type="float" level="2" n="2"> <note position="left" xlink:label="note-236-01" xlink:href="note-236-01a" xml:space="preserve">Satis eſt, ſi <lb/>ſpatium di <lb/>midiati gra <lb/>dus in ter-<lb/>ra, vel ter-<lb/>@@æ partis <lb/>@nius gra-<lb/>dus menſu <lb/>retur, ut to-<lb/>tus mbi@ <lb/>cognoſca-<lb/>t<unsure/>ur.</note> </div> </div> <div xml:id="echoid-div393" type="section" level="1" n="126"> <head xml:id="echoid-head131" xml:space="preserve">VIÆ AD INVESTIGANDVM AMBITVM TERRÆ <lb/>commodiores, quàm ea, quæ ab auctore tradita eſt.</head> <p> <s xml:id="echoid-s8121" xml:space="preserve"><emph style="sc">Vervm</emph> quia laborioſum opus eſt, ac difficile, ita directe ſub Meridiano <lb/> <anchor type="note" xlink:label="note-236-02a" xlink:href="note-236-02"/> circulo in Septentrionẽ, uel Auſtrum incedere, donec reperiatur altitudo po-<lb/>li maioruno gradu; </s> <s xml:id="echoid-s8122" xml:space="preserve">ideo commodius fortaſſe eadem menſura ambitus terreni <lb/>obtinebitur hac ratione. </s> <s xml:id="echoid-s8123" xml:space="preserve">Notentur duę ciuitates ſub eodem Meridiano poſi-<lb/>tæ, quarum eleuationibus poli diligẽter percognitis, detrahatur minor eleua-<lb/>tio, quã ſcilicet ciuitas magis Auſtralis obtinet, ex maiori, quam habet ciuitas <lb/>Borealior: </s> <s xml:id="echoid-s8124" xml:space="preserve">Id enim quod ſupererit, oſtendet ſpatium inter utramq; </s> <s xml:id="echoid-s8125" xml:space="preserve">ciuitatem <lb/>interiectum quo ad gradus: </s> <s xml:id="echoid-s8126" xml:space="preserve">Quo menſurato per ſtadia, uel aliam menſuram, fa <lb/>cile per proportionum regulam in cognitionem ambitus terreſtris deduceris.</s> <s xml:id="echoid-s8127" xml:space="preserve"/> </p> <div xml:id="echoid-div393" type="float" level="2" n="1"> <note position="left" xlink:label="note-236-02" xlink:href="note-236-02a" xml:space="preserve">Var@æ viæ, <lb/>quibus ter-<lb/>ræ ambitus <lb/>@xplor@tur.</note> </div> <p> <s xml:id="echoid-s8128" xml:space="preserve"><emph style="sc">Exemplvm</emph>. </s> <s xml:id="echoid-s8129" xml:space="preserve">Notentur ſub uno eodemque Meridiano duæ ciuitates, qua-<lb/>rum ea, quæ Auſtralior eſt, habeat v.</s> <s xml:id="echoid-s8130" xml:space="preserve">g. </s> <s xml:id="echoid-s8131" xml:space="preserve">altitudinem poli gr. </s> <s xml:id="echoid-s8132" xml:space="preserve">10. </s> <s xml:id="echoid-s8133" xml:space="preserve">Illius uero, quæ <lb/>eſt Septentrionalior, eiuſdem poli altitudo ſit gr. </s> <s xml:id="echoid-s8134" xml:space="preserve">12. </s> <s xml:id="echoid-s8135" xml:space="preserve">min. </s> <s xml:id="echoid-s8136" xml:space="preserve">30. </s> <s xml:id="echoid-s8137" xml:space="preserve">Si igitur minor <lb/>altitudo à maiori ſubtrahatur, erit ſpatiũ inter duas ciuitates poſitũ gr. </s> <s xml:id="echoid-s8138" xml:space="preserve">2. </s> <s xml:id="echoid-s8139" xml:space="preserve">min. <lb/></s> <s xml:id="echoid-s8140" xml:space="preserve">30. </s> <s xml:id="echoid-s8141" xml:space="preserve">Quod ſpatium ex auctoris ſententia, ſi Eratoſthenes, & </s> <s xml:id="echoid-s8142" xml:space="preserve">Macrobius emenſi <lb/>fuiſſent, contineret ſtadia 1750. </s> <s xml:id="echoid-s8143" xml:space="preserve">Quare grad. </s> <s xml:id="echoid-s8144" xml:space="preserve">360. </s> <s xml:id="echoid-s8145" xml:space="preserve">totius ambitus complectẽtur <lb/>ſtadia 252000. </s> <s xml:id="echoid-s8146" xml:space="preserve">Pariratione, ſi ſpatium itineris inter duas quaſcunq: </s> <s xml:id="echoid-s8147" xml:space="preserve">ciuitates, <lb/>etiamſi non iaceant ſub eodem Meridiano, cognitum fuerit; </s> <s xml:id="echoid-s8148" xml:space="preserve">cognoſci poterit <lb/>per doctrinam ſphæricorũ triangulornm totius ambitus terreſtris magnitudo, <lb/>dummodo utriuſque ciuitatis altitudo poli, & </s> <s xml:id="echoid-s8149" xml:space="preserve">longitudo, quę ab occidente <lb/>ſumitur, perſpecta fuerit. </s> <s xml:id="echoid-s8150" xml:space="preserve">Ex altitudine enim poli, & </s> <s xml:id="echoid-s8151" xml:space="preserve">longitudine utriſq; </s> <s xml:id="echoid-s8152" xml:space="preserve">loci <lb/>cognoſcentur gradus circuli maximi ſpatium itinerariũ metientis. </s> <s xml:id="echoid-s8153" xml:space="preserve">Igitur quot <lb/>ſtadia, aut milliaria uni gradui tribuenda ſint, ignotũ non erit. </s> <s xml:id="echoid-s8154" xml:space="preserve">Ex quo totus <lb/>ambitus explorabitur. </s> <s xml:id="echoid-s8155" xml:space="preserve">Sed quia hęc ratio dimetiendi ambitũ terrę obſcurior <lb/>eſt, & </s> <s xml:id="echoid-s8156" xml:space="preserve">ad Coſmographiam pertinet, conſulto à<unsure/> nobis prætermittitur.</s> <s xml:id="echoid-s8157" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8158" xml:space="preserve"><emph style="sc">Qvod</emph> ſi quis cupiat, explorare, quantus ſit ambitus terrę ab ortu in oc-<lb/>caſum, uel contra; </s> <s xml:id="echoid-s8159" xml:space="preserve">Auctor enim ſolum id docuit obſeruare ab uno polo ad al-<lb/>terum polum, nempe à Septentrione in Auſtrum, uel contra; </s> <s xml:id="echoid-s8160" xml:space="preserve">quamuis hinc <lb/>qu<unsure/>oque cõſtet ambitus terrę ab ortu, uel occaſu, cum ſit, ob rotunditatem ter-<lb/>rę, omnino æqualis ambitui terræ à polo ad polum: </s> <s xml:id="echoid-s8161" xml:space="preserve">id hac arte conſequipote <lb/>rit. </s> <s xml:id="echoid-s8162" xml:space="preserve">Notentur duæ ciuitates ſub Æquinoctiali circulo poſitæ, obſeruet<unsure/>urq́ue <lb/>diligenter in utraque ciuitate hora, qua eclipſis aliqua Lunæ initium habuit. <lb/></s> <s xml:id="echoid-s8163" xml:space="preserve">Cognito enim, quot horis prius eclipſis Lunæ in una ciuitate initiũ habuit, <lb/>quam in alte@a, cognoſcẽtur & </s> <s xml:id="echoid-s8164" xml:space="preserve">gradus Aequatoris inter utramque interiecti:</s> <s xml:id="echoid-s8165" xml:space="preserve"> <pb o="201" file="237" n="238" rhead="Ioan. de Sacro Boſco."/> Singulis enim horis correſpondent 15. </s> <s xml:id="echoid-s8166" xml:space="preserve">grad. </s> <s xml:id="echoid-s8167" xml:space="preserve">Aequinoctialis circuli, vt alibi di-<lb/>ctum eſt. </s> <s xml:id="echoid-s8168" xml:space="preserve">Emenſo igitur ſpatio illorum graduum, facile in notitiam totius am-<lb/>bitus per proportionum regulam veniemus. </s> <s xml:id="echoid-s8169" xml:space="preserve">EXEMPLVM. </s> <s xml:id="echoid-s8170" xml:space="preserve">Sit initium <lb/>vnius eiuſdemq́ue eclipſis Lunaris factum in ciuitate orientaliori, decima <lb/>hora cum tertia parte poſt meridiem; </s> <s xml:id="echoid-s8171" xml:space="preserve">In ciuitate vero magis occidentali, <lb/>nona hora poſt meridiem. </s> <s xml:id="echoid-s8172" xml:space="preserve">Igitur una hora integra, & </s> <s xml:id="echoid-s8173" xml:space="preserve">tertia horæ parte citius <lb/>habuit meridiem ciuitas orientalior, quàm magis occidentalis. </s> <s xml:id="echoid-s8174" xml:space="preserve">Quare ſpatiũ <lb/>interiectum inter vtramque continet grad. </s> <s xml:id="echoid-s8175" xml:space="preserve">20. </s> <s xml:id="echoid-s8176" xml:space="preserve">Quod ſi quis metiretur, depre-<lb/>henderet ſecundum præfatos auctores continere ſtadia 14000. </s> <s xml:id="echoid-s8177" xml:space="preserve">atque adeo in <lb/>toto ambitu terræ contineri diceret ſtadia 252000.</s> <s xml:id="echoid-s8178" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8179" xml:space="preserve"><emph style="sc">Possvmvs</emph> quoque facillime ambitum terræ inueſtigare ex aliqua ſtella <lb/> <anchor type="note" xlink:label="note-237-01a" xlink:href="note-237-01"/> fixa, ut ex ſpica ♍, vel quauis alia. </s> <s xml:id="echoid-s8180" xml:space="preserve">Si enim in terra ſumantur ſub eodem Meri-<lb/>diano duo loca, quorum interuallum itinerarium exploratum habeatur, & </s> <s xml:id="echoid-s8181" xml:space="preserve">in <lb/>vtroque loco altitudo meridiana ſtellæ propoſitæ, & </s> <s xml:id="echoid-s8182" xml:space="preserve">cognitæ obſeruetur, erit <lb/>differentia altitudinum, numerus graduum Meridiani inter duo loca interie-<lb/>ctorum. </s> <s xml:id="echoid-s8183" xml:space="preserve">Quare cum notum ſit, quotnam ſtadia dictis gradibus conueniant, <lb/>ignorari nequaquam poterunt ſtadia, quæ toti ambitui terrenis orbis deben-<lb/>tur. </s> <s xml:id="echoid-s8184" xml:space="preserve">Atque hęc ratio inueſtigandi ambitus terreni mihi magis probatur; </s> <s xml:id="echoid-s8185" xml:space="preserve">quo-<lb/>niam non requirit in ullo loco cognitionem altitudinis poli, ſiue longitudi-<lb/>nis, quæ haberi non poteſt, niſi diuturna obſeruatione: </s> <s xml:id="echoid-s8186" xml:space="preserve">neque uero hac in re <lb/>nimium fidendum eſt tabulis, quę ciuitatum latitudines, longitudineſque cõ-<lb/>tinen@. </s> <s xml:id="echoid-s8187" xml:space="preserve">Qua quidem ratione menſurandi terram uſum fuiſſe Poſſidonium re-<lb/>fert Franciſcus Maurolycus in ſuis Dialogis coſmographicis, ex quibus etiam <lb/>ſubſequentes duos modos accepimus, quorum primus fuit Eratoſtheni fami-<lb/>liaris; </s> <s xml:id="echoid-s8188" xml:space="preserve">Alter vero ab ipſo Maurolyco excogitatus.</s> <s xml:id="echoid-s8189" xml:space="preserve"/> </p> <div xml:id="echoid-div394" type="float" level="2" n="2"> <note position="right" xlink:label="note-237-01" xlink:href="note-237-01a" xml:space="preserve">Ratio Poſſi-<lb/>donij facilli <lb/>ma, qua am <lb/>bitus terræ <lb/>inueſtige-<lb/>tur.</note> </div> <p> <s xml:id="echoid-s8190" xml:space="preserve"><emph style="sc">Erathostenes</emph> hanc ferme inibat rationem in indagando terræ ambi-<lb/> <anchor type="note" xlink:label="note-237-02a" xlink:href="note-237-02"/> tu. </s> <s xml:id="echoid-s8191" xml:space="preserve">Erexit Alexandriæ gnomonem in Horizonte ad angulos rectos; </s> <s xml:id="echoid-s8192" xml:space="preserve">Dein-<lb/>de a Sole, dum in principio ♋, exiſtebat, intellexit duos radios tempore me-<lb/>ridiei proijci, vnum per ciuitatem Syenen, (quæ Auſtralior eſt, quàm Alexan-<lb/>dria, in eodemq́ue fere Meridiano, in quo Alexandria) qui recte tendebatin <lb/>centrum mundi, cum Syene ſub ip-<lb/> <anchor type="figure" xlink:label="fig-237-01a" xlink:href="fig-237-01"/> ſo tropico ♋, ſita ſit: </s> <s xml:id="echoid-s8193" xml:space="preserve">alterum per <lb/>gnomonis dicti uerticem, atque ita <lb/>ex proportione gnomonis ad ſuam <lb/>vmbram uia Geometrica ſpatiũ in-<lb/>ter Alexãdriam, ac Syenen inuenit. <lb/></s> <s xml:id="echoid-s8194" xml:space="preserve">Quod ut planius fiat, Sit circulus <lb/>in terra deſcriptus per Alexãdriam <lb/>ac Syenen, in quo A, ſit locus Ale-<lb/>xandrię; </s> <s xml:id="echoid-s8195" xml:space="preserve">B, locus Syenes; </s> <s xml:id="echoid-s8196" xml:space="preserve">Stylus Ale <lb/>xandriæ erectus A D; </s> <s xml:id="echoid-s8197" xml:space="preserve">Radius Solis <lb/>per Syenen ad centrum mundi ten <lb/>dens FBC; </s> <s xml:id="echoid-s8198" xml:space="preserve">Radius per uerticem <lb/>gnomonis incedens E D G, pro-<lb/>ijciensq́ue vmbram A G, ſepten-<lb/>trionem uerſus; </s> <s xml:id="echoid-s8199" xml:space="preserve">Intelligaturq́ue <lb/>gnomon A D, pro duci uſque ad cẽ-<lb/>tr@m C. </s> <s xml:id="echoid-s8200" xml:space="preserve">Quoniam igitur in trian- <pb o="202" file="238" n="239" rhead="Comment. in I. Cap. Sphæræ"/> gulo A D G, arcus A G, circa errorem pro recta linea accipi poteſt, cum ſit in-<lb/> <anchor type="figure" xlink:label="fig-238-01a" xlink:href="fig-238-01"/> ſenſibilis magnitudinis, ſi cum toto <lb/>ambitu conferatur, eſtq́. </s> <s xml:id="echoid-s8201" xml:space="preserve">angulus A, <lb/>rectus, & </s> <s xml:id="echoid-s8202" xml:space="preserve">duo latera A D, A G, co-<lb/>gnita; </s> <s xml:id="echoid-s8203" xml:space="preserve">A D, quidem per hypothe-<lb/>ſin, cum ſit gnomon ad libitum aſ-<lb/>ſumptus; </s> <s xml:id="echoid-s8204" xml:space="preserve">A G, uero per aliquam <lb/>menſuram; </s> <s xml:id="echoid-s8205" xml:space="preserve">uel certe ex ijs, quæ à <lb/>nobis demonſtrata ſunt lib. </s> <s xml:id="echoid-s8206" xml:space="preserve">5. </s> <s xml:id="echoid-s8207" xml:space="preserve">no-<lb/>ſtrę Gnomonices propos. </s> <s xml:id="echoid-s8208" xml:space="preserve">1. </s> <s xml:id="echoid-s8209" xml:space="preserve">ubi oſtẽ <lb/>dimus, quanam ratione proportio <lb/>ſtyli ad ſuam vmbram rectã cogno-<lb/>ſcatur ex altitudine Solis cognita: <lb/></s> <s xml:id="echoid-s8210" xml:space="preserve">Cognoſcetur quoque per doctrinã <lb/>triangulorum, (vt in noſtri@ trian-<lb/> <anchor type="note" xlink:label="note-238-01a" xlink:href="note-238-01"/> gulis demonſtrauimus) angulus <lb/>ADG. </s> <s xml:id="echoid-s8211" xml:space="preserve">Quoniam enim latera A D, <lb/>AG, nota ſunt erunt quoque eorũ <lb/>quad rata nota; </s> <s xml:id="echoid-s8212" xml:space="preserve">quæ cum æqualia ſint quadrato ex D G, notum quoque erit <lb/>quadratum rectæ D G, atque adeo & </s> <s xml:id="echoid-s8213" xml:space="preserve">recta D G, cognita erit. </s> <s xml:id="echoid-s8214" xml:space="preserve">Quia uero ſi <lb/>D G, ſtatuatur ſinus totus, recta A G, ſinus eſt anguli A D G, ut in tractatio-<lb/>ne ſinuum demonſtrauimus; </s> <s xml:id="echoid-s8215" xml:space="preserve">ſi fiat, ut D G, quatenus cognita hactenus eſt, ad <lb/>ſinum totum, ita A G, quatenus nota eſt in partibus vmbræ, ad aliud cognita <lb/>fiet A G, quatenus ſinus eſt anguli A D G; </s> <s xml:id="echoid-s8216" xml:space="preserve">ideoque ex tabula ſinuum angu-<lb/>lus A D G, notus erit; </s> <s xml:id="echoid-s8217" xml:space="preserve">ac proinde & </s> <s xml:id="echoid-s8218" xml:space="preserve">angulus alternus A C B, qui illi æqualis <lb/>eſt? </s> <s xml:id="echoid-s8219" xml:space="preserve">propterea quòd radii EBC, EDC, pene paralleli ſint, ob nimiam paruita-<lb/> <anchor type="note" xlink:label="note-238-02a" xlink:href="note-238-02"/> tem diſtantiæ Syenes ab Alexandria, ſi cum Sole comparetur: </s> <s xml:id="echoid-s8220" xml:space="preserve">Quare & </s> <s xml:id="echoid-s8221" xml:space="preserve">arcus <lb/>A B, angulo C, ſubtenſus notus erit, nempe ſpatium interceptum inter Alexã <lb/>driam, & </s> <s xml:id="echoid-s8222" xml:space="preserve">Syenen. </s> <s xml:id="echoid-s8223" xml:space="preserve">Hæc autem ratio Eratoſthenis paulo aliter à Cleomede re-<lb/>fertur, quàm à Maurolyco. </s> <s xml:id="echoid-s8224" xml:space="preserve">Hac ratione deprehendit Eratoſthenes, (ſi uera <lb/>retulit auctor de ambitu terræ ex ſententia Eratoſthenis) arcum AB, eſſe grad. <lb/></s> <s xml:id="echoid-s8225" xml:space="preserve">8 {5/6}. </s> <s xml:id="echoid-s8226" xml:space="preserve">ſpatiumque itineris comprehendere ſtadia 6183 {1/3}. </s> <s xml:id="echoid-s8227" xml:space="preserve">Quare per regulam <lb/>proportionum collegit, gradibus 360. </s> <s xml:id="echoid-s8228" xml:space="preserve">nimirum toti ambitui<unsure/> terræ, deberi ſta-<lb/>dia 252000.</s> <s xml:id="echoid-s8229" xml:space="preserve"/> </p> <div xml:id="echoid-div395" type="float" level="2" n="3"> <note position="right" xlink:label="note-237-02" xlink:href="note-237-02a" xml:space="preserve">Ratio E@a-<lb/>thoſtenis in <lb/>ambitu ter <lb/>rę inquiren <lb/>do.</note> <figure xlink:label="fig-237-01" xlink:href="fig-237-01a"> <image file="237-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/237-01"/> </figure> <figure xlink:label="fig-238-01" xlink:href="fig-238-01a"> <image file="238-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/238-01"/> </figure> <note position="left" xlink:label="note-238-01" xlink:href="note-238-01a" xml:space="preserve">47. primi.</note> <note position="left" xlink:label="note-238-02" xlink:href="note-238-02a" xml:space="preserve">29. primi.</note> </div> <p> <s xml:id="echoid-s8230" xml:space="preserve"><emph style="sc">Franciscvs</emph> Maurolycus Abbas hanc rationem indagandi ambitus <lb/>terreni excogitauit. </s> <s xml:id="echoid-s8231" xml:space="preserve">Sit terræ circuitus B C D, in quo eligatur editiſſimus <lb/>aliquis mons, (ipſe in Sicilia montem Aetnam ad hoc negotium eligendum <lb/>cenſuit) cuius altitudo AB, per præcepta menſurandarum altitudinũ nota red <lb/>datur. </s> <s xml:id="echoid-s8232" xml:space="preserve">Deinde ex A, uertice montis per pręcepta metiendarum longitudinum <lb/>menſurandũ erit totũ illud ſpatiũ pelagi, ſeu terrę, (ubi tamen mõtes nõ ſint) <lb/>quod inde conſpicitur, ita ut radius uiſualis AC, terrę ſuperficiem contingat <lb/>in puncto C. </s> <s xml:id="echoid-s8233" xml:space="preserve">Sitigitur ſpatiũ uiſum BC, quod etiãſi curuũ ſit, nõ autẽ planũ, <lb/>a plano tamen ſenſibili differentia non diſcrepat, propterea, quòd arcus BC, <lb/>admodum exiguus eſt, ſi cum toto ambitu terrę comparetur. </s> <s xml:id="echoid-s8234" xml:space="preserve">Quibus rite pera-<lb/>ctis, ita Geometricã inſtituemus ratiocinationem. </s> <s xml:id="echoid-s8235" xml:space="preserve">Intelligo quatuor recta<unsure/>s li-<lb/>neas, quarum prima eſt AB, ipſa montis aſſumpti celſitudo; </s> <s xml:id="echoid-s8236" xml:space="preserve">Secunda radius vi-<lb/>ſualis AC; </s> <s xml:id="echoid-s8237" xml:space="preserve">Tertia AD, quę conſtat ex celſitudi<unsure/>ne montis, terręque diametro; <lb/></s> <s xml:id="echoid-s8238" xml:space="preserve">Quarta deniq; </s> <s xml:id="echoid-s8239" xml:space="preserve">BC, interuallũ conſpectũ, poterit enim citra errorem pro recta <pb o="203" file="239" n="240" rhead="Ioan. de Sacro Boſco."/> accipi, ut dictũ eſt. </s> <s xml:id="echoid-s8240" xml:space="preserve">Qm̃ igitur rectæ AB, BC, notæ ſunt, @runt quoq; </s> <s xml:id="echoid-s8241" xml:space="preserve">ipſarũ qu@ <lb/>drata cognita, q̃ cum æq ualia ſint <lb/> <anchor type="figure" xlink:label="fig-239-01a" xlink:href="fig-239-01"/> <anchor type="note" xlink:label="note-239-01a" xlink:href="note-239-01"/> <anchor type="note" xlink:label="note-239-02a" xlink:href="note-239-02"/> quadrato A C, erit, & </s> <s xml:id="echoid-s8242" xml:space="preserve">quadratũ re-<lb/>ctæ A C, notũ: </s> <s xml:id="echoid-s8243" xml:space="preserve">At quadratum rectæ <lb/>A C, (cũ recta A C, circulũ contin-<lb/>gat) æquale eſt rectãgulo contento <lb/>ſub D A, A B, Igitur rectangulum <lb/>ſub D A, A B, cognitũ erit: </s> <s xml:id="echoid-s8244" xml:space="preserve">Eſt autẽ <lb/>A B, altitudo mõtis nota. </s> <s xml:id="echoid-s8245" xml:space="preserve">Quare & </s> <s xml:id="echoid-s8246" xml:space="preserve"><lb/>recta A D, nota erit; </s> <s xml:id="echoid-s8247" xml:space="preserve">fi nimirum re-<lb/>ctangulũ notũ, quo ſub AB, AD, cõ-<lb/>tinetur, ꝑ rectã AB, diuidatur. </s> <s xml:id="echoid-s8248" xml:space="preserve">Quo <lb/>tiens. </s> <s xml:id="echoid-s8249" xml:space="preserve">n. </s> <s xml:id="echoid-s8250" xml:space="preserve">numerus dabit rectã AD: </s> <s xml:id="echoid-s8251" xml:space="preserve">ex <lb/>qua ſi dematur AB, altitudo mõtis, <lb/>nota relinquet̃ terræ diameter BD. <lb/></s> <s xml:id="echoid-s8252" xml:space="preserve">Quaꝑꝑ ex diametro BD, iuxta ea, q̃ <lb/>ab Archimede in libello de circuli <lb/>dimenſione demonſtrata ſunt, ut <lb/>mox dicemus, tota circunferentia <lb/>terræ cognoſcetur, quod eſt propoſitum.</s> <s xml:id="echoid-s8253" xml:space="preserve"/> </p> <div xml:id="echoid-div396" type="float" level="2" n="4"> <figure xlink:label="fig-239-01" xlink:href="fig-239-01a"> <image file="239-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/239-01"/> </figure> <note position="right" xlink:label="note-239-01" xlink:href="note-239-01a" xml:space="preserve">47. primi.</note> <note position="right" xlink:label="note-239-02" xlink:href="note-239-02a" xml:space="preserve">37. tertij.</note> </div> <p> <s xml:id="echoid-s8254" xml:space="preserve"><emph style="sc">Omnes</emph> autem prædictæ @iæ inueſtigandi circuitus terreni, præter ulti-<lb/>mam, quam proxime ex Maurolyco demonſtrauimus, innituntur huic conclu <lb/>ſioni Geometricę.</s> <s xml:id="echoid-s8255" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s8256" xml:space="preserve">SI fuerint duo, uel plures circuli circaidem centrum deſcripti, & </s> <s xml:id="echoid-s8257" xml:space="preserve">à <lb/> <anchor type="note" xlink:label="note-239-03a" xlink:href="note-239-03"/> centro ad circunferentiam uſque maximi circuli educantur duæ rectæ li-<lb/>neæ, erunt arcus omnium circulorum inter dictas lineas rectas comprehen-<lb/>ſi ſimiles inter ſeſe.</s> <s xml:id="echoid-s8258" xml:space="preserve"/> </p> <div xml:id="echoid-div397" type="float" level="2" n="5"> <note position="right" xlink:label="note-239-03" xlink:href="note-239-03a" xml:space="preserve">Lineærect@ <lb/>ab uno pun <lb/>cto egrediẽ <lb/>tes ſecan@ <lb/>omnes cir-<lb/>culos ex e@ <lb/>puncto, ut <lb/>centro, de-<lb/>ſcriptos in <lb/>arcus ſimi-<lb/>les.</note> </div> <p> <s xml:id="echoid-s8259" xml:space="preserve"><emph style="sc">Qvam</emph> quidem conclufionem, qm̃ plurimum Aſtronomis conducit, & </s> <s xml:id="echoid-s8260" xml:space="preserve"><lb/>Geometris, conabimur hocloco breuiter demonſtrare. </s> <s xml:id="echoid-s8261" xml:space="preserve">Sint circa centrũ E, <lb/>circuli deſcripti ACBD, FHGI, <lb/>KMLN, & </s> <s xml:id="echoid-s8262" xml:space="preserve">ex centro E, educãtur <lb/>rectæ EC, ED, quę ſi efficiant u-<lb/> <anchor type="figure" xlink:label="fig-239-02a" xlink:href="fig-239-02"/> nam lineam rectam, certum erit, <lb/>omnes circulos in arcus ſimiles <lb/>ab ipſis ſecari, nempe in ſemicir-<lb/>culos. </s> <s xml:id="echoid-s8263" xml:space="preserve">Ducantur rurſus ex eodẽ <lb/>centro E, duę rectę EA, ED, effi <lb/>cientes angulum A E D, rectum: <lb/></s> <s xml:id="echoid-s8264" xml:space="preserve">Perſpicuum igitur eſt, arcus AD, <lb/>FI, KN, eſſe ſimiles, cum ſint cir-<lb/>culorum quadrantes. </s> <s xml:id="echoid-s8265" xml:space="preserve">Productis <lb/> <anchor type="note" xlink:label="note-239-04a" xlink:href="note-239-04"/> enim rectis A E, D E, vſque ad <lb/>B, C, erunt quatuor anguli ad <lb/>E, recti. </s> <s xml:id="echoid-s8266" xml:space="preserve">Igitur arcus AD, DB, <lb/>BC, CA, ęquales erunt; </s> <s xml:id="echoid-s8267" xml:space="preserve">Eodẽ pa <lb/>cto arc<emph style="sub">9</emph> FI, IC, GH, HF, ęquales <lb/>@ru nt: </s> <s xml:id="echoid-s8268" xml:space="preserve">Item arcus KN, NL, LM, <pb o="204" file="240" n="241" rhead="Comment. in I. Cap. Sphæræ"/> M K. </s> <s xml:id="echoid-s8269" xml:space="preserve">Qu are quilibet illorum ſui circuli quadrans erit. </s> <s xml:id="echoid-s8270" xml:space="preserve">Ducantur denique re-<lb/>ctæ E D, E O, efficientes angulum D E O, non rectum. </s> <s xml:id="echoid-s8271" xml:space="preserve">Dico adhuc arcus <lb/> <anchor type="figure" xlink:label="fig-240-01a" xlink:href="fig-240-01"/> D O, I P, N Q, eſſe ſimiles, hoc <lb/>eſt, talem partem eſſe D O, qua-<lb/>drantis D A, qualis pars eſt arcus <lb/>I P, quadrãtis I F, & </s> <s xml:id="echoid-s8272" xml:space="preserve">arcus N Q, <lb/>quadrantis N <emph style="sc">K</emph>. </s> <s xml:id="echoid-s8273" xml:space="preserve">Quoniam. </s> <s xml:id="echoid-s8274" xml:space="preserve">n. </s> <s xml:id="echoid-s8275" xml:space="preserve">eſt, <lb/>ut angulus D E O, ad angulum <lb/>D E A, ita arcus D O, ad arcum <lb/> <anchor type="note" xlink:label="note-240-01a" xlink:href="note-240-01"/> D A, & </s> <s xml:id="echoid-s8276" xml:space="preserve">arcus I P, ad arcum I F, & </s> <s xml:id="echoid-s8277" xml:space="preserve"><lb/>arcus N K, manifeſtũ eſt, ſupradi-<lb/>ctos arcus inter ſe eſſe ſimiles, cũ <lb/>ad quadrãtes ſuorũ circulorũ ean <lb/>dem habeant proportionẽ. </s> <s xml:id="echoid-s8278" xml:space="preserve">Quod <lb/>ẽt hac ratione colligi põt. </s> <s xml:id="echoid-s8279" xml:space="preserve">Vt an-<lb/>gulus D E O, ad quatuor rectos, <lb/>quibus totæ circũferentiæ ſubtẽ <lb/>duntur, ita (per 2. </s> <s xml:id="echoid-s8280" xml:space="preserve">coroll. </s> <s xml:id="echoid-s8281" xml:space="preserve">vltimæ <lb/> <anchor type="note" xlink:label="note-240-02a" xlink:href="note-240-02"/> propoſ. </s> <s xml:id="echoid-s8282" xml:space="preserve">li. </s> <s xml:id="echoid-s8283" xml:space="preserve">6. </s> <s xml:id="echoid-s8284" xml:space="preserve">à nobis demõſtratũ) <lb/>arcus D O, ad totam circunferen <lb/>tiam D A C B, & </s> <s xml:id="echoid-s8285" xml:space="preserve">arcus I P, ad circunferentiam totam I F H G, & </s> <s xml:id="echoid-s8286" xml:space="preserve">arcus N Q, <lb/>ad totã circunferentiã N K M L. </s> <s xml:id="echoid-s8287" xml:space="preserve">Igitur arcus D O, I P, N Q, ſimiles ſunt, <lb/>cum ad circunferentias, quarum ſunt arcus, eandem habeant proportionem.</s> <s xml:id="echoid-s8288" xml:space="preserve"/> </p> <div xml:id="echoid-div398" type="float" level="2" n="6"> <figure xlink:label="fig-239-02" xlink:href="fig-239-02a"> <image file="239-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/239-02"/> </figure> <note position="right" xlink:label="note-239-04" xlink:href="note-239-04a" xml:space="preserve">26. tertij.</note> <figure xlink:label="fig-240-01" xlink:href="fig-240-01a"> <image file="240-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/240-01"/> </figure> <note position="left" xlink:label="note-240-01" xlink:href="note-240-01a" xml:space="preserve">33. ſexti.</note> <note position="left" xlink:label="note-240-02" xlink:href="note-240-02a" xml:space="preserve">Al@a demõ<unsure/> <lb/>@tratio.</note> </div> <p> <s xml:id="echoid-s8289" xml:space="preserve"><emph style="sc">Aliter</emph> idem theorema hoc modo demonſtrari poteſt, ſine proportio-<lb/> <anchor type="note" xlink:label="note-240-03a" xlink:href="note-240-03"/> nibus. </s> <s xml:id="echoid-s8290" xml:space="preserve">Ex centro E, circulorum A B C D, F G H I, ducantur duæ rectæ E A, <lb/> <anchor type="figure" xlink:label="fig-240-02a" xlink:href="fig-240-02"/> E B. </s> <s xml:id="echoid-s8291" xml:space="preserve">Dico arcus A B, F G, <lb/>inter ſe ſimiles eſſe. </s> <s xml:id="echoid-s8292" xml:space="preserve">Nã pro <lb/>ductis rectis A E, B E, vſque <lb/>ad C, D, ducãtur rectæ B C, <lb/>G H: </s> <s xml:id="echoid-s8293" xml:space="preserve">Sumantur quoque in <lb/>arcubus A B, F G, puncta, <lb/>K, L, vtcunque, ad q̃ ducant̃ <lb/>rectę A K, B K, F L, G L. </s> <s xml:id="echoid-s8294" xml:space="preserve">Qm̃ <lb/>igitur anguli E, G, H, trian <lb/>guli E G H, ęquales ſunt an <lb/>gulis E, B, C, triãguli EBC, <lb/> <anchor type="note" xlink:label="note-240-04a" xlink:href="note-240-04"/> ꝙ tã illi, ꝗ̃ hi duobus ſint re <lb/>ctis æquales: </s> <s xml:id="echoid-s8295" xml:space="preserve">ſi dematur an-<lb/>gulus cõis E, erunt duo an-<lb/>gulis B, C, æquales: </s> <s xml:id="echoid-s8296" xml:space="preserve">Sed tam <lb/>hi duo, ꝗ̃ illi duo, inter ſe ę-<lb/> <anchor type="note" xlink:label="note-240-05a" xlink:href="note-240-05"/> quales ſunt, quod tam rectæ <lb/>E G, E H, inter ſe, quàm rectæ E B, E C, inter ſe æquales ſint, ex defin. </s> <s xml:id="echoid-s8297" xml:space="preserve">circuli. <lb/></s> <s xml:id="echoid-s8298" xml:space="preserve">Igitur angulus EHG, angulo ECB, æqualis erit. </s> <s xml:id="echoid-s8299" xml:space="preserve">Rurſus, quia in quadrilatero <lb/> <anchor type="note" xlink:label="note-240-06a" xlink:href="note-240-06"/> FLGH, duo anguli oppoſiti FHG, GLF, æquales ſunt duobus rectis: </s> <s xml:id="echoid-s8300" xml:space="preserve">Item duo <lb/>anguli oppoſiti ACB, A K B C, in quadrilatero A K B C, demptis æqualibus <lb/>FHG, ACB, erunt reliqui anguli BKA, GLF, æquales: </s> <s xml:id="echoid-s8301" xml:space="preserve">& </s> <s xml:id="echoid-s8302" xml:space="preserve">idcirco, per definitio-<lb/>nem, arcus AB, FG, ſimiles inter ſe erunt: </s> <s xml:id="echoid-s8303" xml:space="preserve">quod erat oſtendendum.</s> <s xml:id="echoid-s8304" xml:space="preserve"/> </p> <div xml:id="echoid-div399" type="float" level="2" n="7"> <note position="left" xlink:label="note-240-03" xlink:href="note-240-03a" xml:space="preserve">Alia demõ-<lb/>ftratio ſine <lb/>prop@rtioni <lb/>bus.</note> <figure xlink:label="fig-240-02" xlink:href="fig-240-02a"> <image file="240-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/240-02"/> </figure> <note position="left" xlink:label="note-240-04" xlink:href="note-240-04a" xml:space="preserve">32. primi.</note> <note position="left" xlink:label="note-240-05" xlink:href="note-240-05a" xml:space="preserve">5. primi.</note> <note position="left" xlink:label="note-240-06" xlink:href="note-240-06a" xml:space="preserve">22. tertij.</note> </div> <pb o="205" file="241" n="242" rhead="Ioan. de Sacro Boſco."/> <p> <s xml:id="echoid-s8305" xml:space="preserve">Hoc Theoremate demonſtrato, omnes prædictæ uiæ locum habent. </s> <s xml:id="echoid-s8306" xml:space="preserve">Ita <lb/>enim fiet, ut quando in cęlo fa-<lb/>cta eſt uarietas unius gradus, in <lb/>terra quoque unius gradus ua-<lb/>rietas acciderit. </s> <s xml:id="echoid-s8307" xml:space="preserve">Nam ſi ab extre <lb/> <anchor type="figure" xlink:label="fig-241-01a" xlink:href="fig-241-01"/> mitatibus illius gradus cœleſtis <lb/>duæ rectæ lineæ concipiantur <lb/>educi ad centrum mundi, inter <lb/>cipient eæ neceſſario unũ quo-<lb/>que gradum in ſuperficie terrę, <lb/>per ea, quæ proxime demonſtra <lb/>ta ſunt, ut perſpicuũ eſt in hac <lb/>figura adiecta. </s> <s xml:id="echoid-s8308" xml:space="preserve">Eademq́ eſt ratio <lb/>de ſpatio quocunq; </s> <s xml:id="echoid-s8309" xml:space="preserve">cęleſti: </s> <s xml:id="echoid-s8310" xml:space="preserve">Sem <lb/>per. </s> <s xml:id="echoid-s8311" xml:space="preserve">n. </s> <s xml:id="echoid-s8312" xml:space="preserve">dictæ lineę in terra ſpatiũ <lb/>ſimile comprehendent. </s> <s xml:id="echoid-s8313" xml:space="preserve">Qđ qui <lb/>dem in omnibus uijs prædictis, <lb/>ut certiſſimum, aſſumebatur: <lb/></s> <s xml:id="echoid-s8314" xml:space="preserve">Aliàs nihil omnino per eas con <lb/>cludi potuiſſet, ut patet.</s> <s xml:id="echoid-s8315" xml:space="preserve"/> </p> <div xml:id="echoid-div400" type="float" level="2" n="8"> <figure xlink:label="fig-241-01" xlink:href="fig-241-01a"> <image file="241-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/241-01"/> </figure> </div> <p style="it"> <s xml:id="echoid-s8316" xml:space="preserve">Ex his autem, iuxta circuli, & </s> <s xml:id="echoid-s8317" xml:space="preserve">diametri regulam, diameter terræ ſic in-<lb/> <anchor type="note" xlink:label="note-241-01a" xlink:href="note-241-01"/> ueniri poterit. </s> <s xml:id="echoid-s8318" xml:space="preserve">Aufer uigeſimam ſecundam partem de circuitu terræ, & </s> <s xml:id="echoid-s8319" xml:space="preserve"><lb/>remanentis tertia pars, hoc eſt, 80181. </s> <s xml:id="echoid-s8320" xml:space="preserve">ſtadia, & </s> <s xml:id="echoid-s8321" xml:space="preserve">ſemis, & </s> <s xml:id="echoid-s8322" xml:space="preserve">tertia pars <lb/>ſtadij, erit terreni orbis diameter, ſiue ſpiſſitudo.</s> <s xml:id="echoid-s8323" xml:space="preserve"/> </p> <div xml:id="echoid-div401" type="float" level="2" n="9"> <note position="right" xlink:label="note-241-01" xlink:href="note-241-01a" xml:space="preserve">Diameter <lb/>terræ qu@ <lb/>pacto ex <lb/>ambitu co-<lb/>gnito @ru@@</note> </div> </div> <div xml:id="echoid-div403" type="section" level="1" n="127"> <head xml:id="echoid-head132" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s8324" xml:space="preserve"><emph style="sc">Postqvam</emph> auctor expoſuit, quantus ſit orbis terreſtris ambitus, & </s> <s xml:id="echoid-s8325" xml:space="preserve"><lb/>quanam is ratione indagari debeat; </s> <s xml:id="echoid-s8326" xml:space="preserve">docet nunc, quanam arte ex cognito terræ <lb/>ambitu profunditas, ſiue diameter eiuſdem terræ cognoſci poſſit. </s> <s xml:id="echoid-s8327" xml:space="preserve">Dicit enim, <lb/>ſi à toto ambitu terreno auferatur pars uigeſima ſecunda (quæ quidem habe-<lb/>bitur in numero Quotiente, ſi ambitus per 22. </s> <s xml:id="echoid-s8328" xml:space="preserve">diuidatur) nempe ſi ex 252000. <lb/></s> <s xml:id="echoid-s8329" xml:space="preserve">ſtadijs detrahantur ſtadia 11454 {6/11}. </s> <s xml:id="echoid-s8330" xml:space="preserve">erit remanentis numeri, ſtadiorum ui <lb/>delicet 240545 {5/11}. </s> <s xml:id="echoid-s8331" xml:space="preserve">tertia pars, (quam ſimiliter offeret numerus Quotiens, ſi <lb/>dictus numerus remanens per 3. </s> <s xml:id="echoid-s8332" xml:space="preserve">diuidatur) hoc eſt, ſtadia 80181 {9/11}. </s> <s xml:id="echoid-s8333" xml:space="preserve">ſiue ut <lb/>ipſe ait, 80181. </s> <s xml:id="echoid-s8334" xml:space="preserve">& </s> <s xml:id="echoid-s8335" xml:space="preserve">ſemis, & </s> <s xml:id="echoid-s8336" xml:space="preserve">tetia fere pars, tota profunditas, ſeu diameter globi <lb/>terreni, i<unsure/>uxta circuli, & </s> <s xml:id="echoid-s8337" xml:space="preserve">diametri regulam.</s> <s xml:id="echoid-s8338" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8339" xml:space="preserve"><emph style="sc">Desvmitvr</emph> autem hæc regula ex libello Archimedis de dimenſio-<lb/> <anchor type="note" xlink:label="note-241-02a" xlink:href="note-241-02"/> ne circuli, in quo Archimedes demonſtrauit, proportionem circumferentiæ cu <lb/>iuſque circuli ad eius diametrum eſſe fere triplam ſeſquiſeptimam, qualis eſt <lb/>22. </s> <s xml:id="echoid-s8340" xml:space="preserve">ad 7. </s> <s xml:id="echoid-s8341" xml:space="preserve">ita ut ſi circũferentia alicuius circuli ſecta ſit in partes 22. </s> <s xml:id="echoid-s8342" xml:space="preserve">æquales, dia <lb/>meter eius contineat huiuſmodi partes fere 7. </s> <s xml:id="echoid-s8343" xml:space="preserve">Et contra, ſi diameter alicuius <lb/>circuli diuiſa ſuerit in ſeptem partes æquales, circunferentia eius comple-<lb/>ctatur huiuſmodi partes 22. </s> <s xml:id="echoid-s8344" xml:space="preserve">Vnde ſi diameter alicuius circuli ſumatur ter, <lb/>addaturq́ue ſe ptima pars diametri, efficietur linea recta circunferentiæ cir-<lb/>culi fere æqualis. </s> <s xml:id="echoid-s8345" xml:space="preserve">Quæ omnia in hac propoſita figura conſpiciuntur. </s> <s xml:id="echoid-s8346" xml:space="preserve">Quæ <lb/>cum ita ſint, perſpicuum eſt, ſi ex ambitu circuli, nempe ex 22. </s> <s xml:id="echoid-s8347" xml:space="preserve">auferatur <lb/>pars uigeſima ſecunda, utpote unitas, remanentis numeri, hoc eſt, 21. </s> <s xml:id="echoid-s8348" xml:space="preserve">tertiam <lb/>partem, videli cet 7. </s> <s xml:id="echoid-s8349" xml:space="preserve">eſſe diametrũ circuli. </s> <s xml:id="echoid-s8350" xml:space="preserve">Ex quibus manifeſta eſt auctoris re- <pb o="206" file="242" n="243" rhead="Comment. in I. Cap. Sphæræ"/> <anchor type="figure" xlink:label="fig-242-01a" xlink:href="fig-242-01"/> gula, qua præcipit ex ambitu terreno diametrum, ſiue profunditatem terræ <lb/>explorare.</s> <s xml:id="echoid-s8351" xml:space="preserve"/> </p> <div xml:id="echoid-div403" type="float" level="2" n="1"> <note position="right" xlink:label="note-241-02" xlink:href="note-241-02a" xml:space="preserve">Proporti@ <lb/>cuiuſuis cit <lb/>culi ad e-<lb/>ius diame-<lb/>trum quæ.</note> <figure xlink:label="fig-242-01" xlink:href="fig-242-01a"> <image file="242-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/242-01"/> </figure> </div> </div> <div xml:id="echoid-div405" type="section" level="1" n="128"> <head xml:id="echoid-head133" style="it" xml:space="preserve">REGVLA, QVA DI AMETER EX CIRCVNFE-<lb/>rentia, & circumferentia ex diametro inueniatur.</head> <p> <s xml:id="echoid-s8352" xml:space="preserve">Ex eadem hac proportione circũferentiæ circuli ad eius diametrum, quam <lb/>nimirum habent 22. </s> <s xml:id="echoid-s8353" xml:space="preserve">ad 7. </s> <s xml:id="echoid-s8354" xml:space="preserve">alij ſcriptores hanc eliciunt regulam, & </s> <s xml:id="echoid-s8355" xml:space="preserve">multo com <lb/>modiorem regula noſtri auctoris, ad inquirendam diametrum ex circunferen <lb/>tia cognita, uel contra, ad inueniendam circunferentiam ex nota diametro. <lb/></s> <s xml:id="echoid-s8356" xml:space="preserve">Prima pars regulæ, qua ex circunferentia cognita diameter eruitur, hæc eſt.</s> <s xml:id="echoid-s8357" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8358" xml:space="preserve"><emph style="sc">Dividatvr</emph> circunferentia per 3 {7/1}. </s> <s xml:id="echoid-s8359" xml:space="preserve">nimirum per denominatorem <lb/> <anchor type="note" xlink:label="note-242-01a" xlink:href="note-242-01"/> proportionis triplæ ſeſquiſeptimæ, quam habere diximus, ſecundum Ar<unsure/>chime <lb/>dem, circunferentiam ad diamet@ũ. </s> <s xml:id="echoid-s8360" xml:space="preserve">Numerus enim in tali diuiſione exiens erit <lb/>diameter circuli. </s> <s xml:id="echoid-s8361" xml:space="preserve">Vt ſi circũferentia alicuius circuli cõtinens. </s> <s xml:id="echoid-s8362" xml:space="preserve">palmos 1540. </s> <s xml:id="echoid-s8363" xml:space="preserve">di-<lb/>uidatur per 3 {1/7}. </s> <s xml:id="echoid-s8364" xml:space="preserve">prodibunt palmi 490 pro magnitudine diametri. </s> <s xml:id="echoid-s8365" xml:space="preserve">Quæ regula <lb/>ita quoque proponi poteſt. </s> <s xml:id="echoid-s8366" xml:space="preserve">Multipliciter circũferentia per 7. </s> <s xml:id="echoid-s8367" xml:space="preserve">productusq́. </s> <s xml:id="echoid-s8368" xml:space="preserve">nu-<lb/>merus diuidatur per 22. </s> <s xml:id="echoid-s8369" xml:space="preserve">inuenieturq́ue diameter. </s> <s xml:id="echoid-s8370" xml:space="preserve">Quoniam enim, quæ propor <lb/>tio eſt 22. </s> <s xml:id="echoid-s8371" xml:space="preserve">ad 7. </s> <s xml:id="echoid-s8372" xml:space="preserve">ea eſt circunferentiæ cuiuſl bet circuli ad diametrum, ut Archi <lb/>medes demonſtrauit: </s> <s xml:id="echoid-s8373" xml:space="preserve">fit, ut ſi circunferentia, hoceſt, tertius numerus regulæ <lb/>proportionum, multiplicetur per 7. </s> <s xml:id="echoid-s8374" xml:space="preserve">nempe per ſecundum numerum eiuſdẽ re <lb/>gulæ, productusq́ numerus per primum numerum, ideſt, per 22. </s> <s xml:id="echoid-s8375" xml:space="preserve">diuidatur, pro <lb/>quarto numero regulæ proportionũ reperiatur diameter. </s> <s xml:id="echoid-s8376" xml:space="preserve">Vt in proximo exem <lb/>plo, ſi circunferentia 1540. </s> <s xml:id="echoid-s8377" xml:space="preserve">multiplicetur per 7. </s> <s xml:id="echoid-s8378" xml:space="preserve">productusq́ numerus per 22. <lb/></s> <s xml:id="echoid-s8379" xml:space="preserve">diuidatur, reperietur diameter 490. </s> <s xml:id="echoid-s8380" xml:space="preserve">ut prius. </s> <s xml:id="echoid-s8381" xml:space="preserve">Hac ratione, ſi ambitum terræ ſe-<lb/>cundum Eratoſthenem, nempe ſtadia 252000. </s> <s xml:id="echoid-s8382" xml:space="preserve">multiplicemus per 7 producen <lb/>tur 1764000. </s> <s xml:id="echoid-s8383" xml:space="preserve">quibus d@uiſis per 22. </s> <s xml:id="echoid-s8384" xml:space="preserve">prodibunt 80181. </s> <s xml:id="echoid-s8385" xml:space="preserve">& </s> <s xml:id="echoid-s8386" xml:space="preserve">{18/22}. </s> <s xml:id="echoid-s8387" xml:space="preserve">hoc eſt {9/11}. </s> <s xml:id="echoid-s8388" xml:space="preserve">pro <lb/>diametro terræ, ſicuti prius iuxta auctoris regulam. </s> <s xml:id="echoid-s8389" xml:space="preserve">Poſterior autem regulæ <lb/>pars, qua ex diametro nota viciſſim circunferentia elicitur, ita ſe habet.</s> <s xml:id="echoid-s8390" xml:space="preserve"/> </p> <div xml:id="echoid-div405" type="float" level="2" n="1"> <note position="left" xlink:label="note-242-01" xlink:href="note-242-01a" xml:space="preserve">Diameter <lb/>circuli quo <lb/>pacto ex cir <lb/>cunferentia <lb/>nota elicia-<lb/>@ut.</note> </div> <p> <s xml:id="echoid-s8391" xml:space="preserve"><emph style="sc">Mvltiplicetvr</emph> diameter per 3 {1/7}. </s> <s xml:id="echoid-s8392" xml:space="preserve">nempe per denominatorem <lb/> <anchor type="note" xlink:label="note-242-02a" xlink:href="note-242-02"/> proportionis triplæ ſeſquiſeptimæ, quàm ſecundum Archimedem, circũferen-<lb/>tia habet ad diametrum. </s> <s xml:id="echoid-s8393" xml:space="preserve">Productus namque numerus indicabit illico circunfe <lb/>rentiam. </s> <s xml:id="echoid-s8394" xml:space="preserve">Vt ſi diameter alicuius circuli habens palmos 490. </s> <s xml:id="echoid-s8395" xml:space="preserve">multiplicetur per <lb/>3 {1/7}. </s> <s xml:id="echoid-s8396" xml:space="preserve">inuenietur circunferentia palmorum 1540. </s> <s xml:id="echoid-s8397" xml:space="preserve">Quæ etiam regula hoc modo <lb/>proponi poteſt. </s> <s xml:id="echoid-s8398" xml:space="preserve">Multiplicetur diameter per 22. </s> <s xml:id="echoid-s8399" xml:space="preserve">productusq́ue numerus per 7. <lb/></s> <s xml:id="echoid-s8400" xml:space="preserve">diuidatur, prouenietq́. </s> <s xml:id="echoid-s8401" xml:space="preserve">quantitas circunferentiæ. </s> <s xml:id="echoid-s8402" xml:space="preserve">Quoniam enim, ut ab Archi <lb/>mede demonſtratũ eſt, quæ proportio eſt 22. </s> <s xml:id="echoid-s8403" xml:space="preserve">ad 7. </s> <s xml:id="echoid-s8404" xml:space="preserve">ea eſt circunferentiæ cuiuſli <pb o="207" file="243" n="244" rhead="Ioan. de Sacro Boſco."/> bet circuli ad diametrum; </s> <s xml:id="echoid-s8405" xml:space="preserve">erit conuertendo, eadẽ proportio 7. </s> <s xml:id="echoid-s8406" xml:space="preserve">ad 22. </s> <s xml:id="echoid-s8407" xml:space="preserve">quæ dia-<lb/>metri ad circun ferentiam. </s> <s xml:id="echoid-s8408" xml:space="preserve">Quare ſi diameter, ideſt, tertius numerus regulæ <lb/>proportionum, multiplicetur per 2. </s> <s xml:id="echoid-s8409" xml:space="preserve">nimirum per ſecundum numerum eiuſdẽ <lb/>regulæ, productusque numerus per primum numerũ, hoc eſt, per 7. </s> <s xml:id="echoid-s8410" xml:space="preserve">diuidatur, <lb/>reperiretur quartus eiuſdem regulæ numerus, ideſt, circunferentia circuli. </s> <s xml:id="echoid-s8411" xml:space="preserve">Vt <lb/>in proximo exemplo, ſi diameter 490. </s> <s xml:id="echoid-s8412" xml:space="preserve">mnltiplicetur per 22. </s> <s xml:id="echoid-s8413" xml:space="preserve">numerusque pro-<lb/>ductus per 7. </s> <s xml:id="echoid-s8414" xml:space="preserve">diuidatur, reperietur circunferentia 1540. </s> <s xml:id="echoid-s8415" xml:space="preserve">ut prius. </s> <s xml:id="echoid-s8416" xml:space="preserve">Duplex au-<lb/>tem hoc præceptum continetur his carminibus.</s> <s xml:id="echoid-s8417" xml:space="preserve"/> </p> <div xml:id="echoid-div406" type="float" level="2" n="2"> <note position="left" xlink:label="note-242-02" xlink:href="note-242-02a" xml:space="preserve">Circunferẽ-<lb/>tia circuli <lb/>quo pacto <lb/>ex diame-<lb/>tro nota in-<lb/>ueniatur.</note> </div> <p style="it"> <s xml:id="echoid-s8418" xml:space="preserve">Circuitus circi per ſeptem multiplicetur, <lb/>Per duo uiginti productum deinde ſecato: <lb/></s> <s xml:id="echoid-s8419" xml:space="preserve">Hinc numerus, Quotiens qui dicitur, eſt diametrus.</s> <s xml:id="echoid-s8420" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s8421" xml:space="preserve">Per duo uiginti ſi multiplices diametrum, <lb/>Per ſeptemq́ ſeces numerum, quiprodijt inde: <lb/></s> <s xml:id="echoid-s8422" xml:space="preserve">Circuitum circi Quotiens numerus tibi reddet.</s> <s xml:id="echoid-s8423" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8424" xml:space="preserve"><emph style="sc">Hinc</emph> facile intelligitur modus, quo uſus eſt Franciſcus Maurolycus in <lb/>inueſtigando terreni orbis ambitu. </s> <s xml:id="echoid-s8425" xml:space="preserve">Prius enim uia Geometrica didicit quãti <lb/>tatem diametri terræ, ex qua poſtea iuxta hanc proportionem diametri ad cir-<lb/>cunferentiam demonſtratam ab Archimede, venatus eſt circunferentiam maxi <lb/>mi circuli per terrę centrum deſcripti.</s> <s xml:id="echoid-s8426" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8427" xml:space="preserve"><emph style="sc">Caetervm</emph> circunferentia circuli cuiuslibet ad eius diametrum non <lb/>habet præciſe eam proportionem, quam 22. </s> <s xml:id="echoid-s8428" xml:space="preserve">ad 7. </s> <s xml:id="echoid-s8429" xml:space="preserve">ſed paulo minorem. </s> <s xml:id="echoid-s8430" xml:space="preserve">Vt enim <lb/>Archimedes in libello de Dimenſione acutiſſime demõſtrauit. </s> <s xml:id="echoid-s8431" xml:space="preserve">Cuiuslibet cir-<lb/>culi circunferentia ad ſuam diametrum proportionẽ minorem quidem habe<unsure/>t <lb/>tripla ſeſquiſeptima, ſeu (quod idem eſt) tripl@@ſuperdecupartiente ſeptuageſi-<lb/>mas: </s> <s xml:id="echoid-s8432" xml:space="preserve">maiorem uero tripla ſuperdecupartiente ſeptuageſimas primas. </s> <s xml:id="echoid-s8433" xml:space="preserve">Itaque ſi <lb/>ſumatur diameter ter cum ſeptima parte, hoc eſt, cum {10/70}. </s> <s xml:id="echoid-s8434" xml:space="preserve">efficietur linea <lb/>paulo maior, quàm circunferentia: </s> <s xml:id="echoid-s8435" xml:space="preserve">At uero ſi ſumatur diameter cum {10/70}. <lb/></s> <s xml:id="echoid-s8436" xml:space="preserve">cõficietur linea paulò minor, quàm circũſerentia. </s> <s xml:id="echoid-s8437" xml:space="preserve">Adeo ut uera proportio cir-<lb/>cunferentiæ ad diametrum conſiſtat) licet occulta ſit) inter duas, quarũ deno-<lb/>minatores ſun 3 {10/70}. </s> <s xml:id="echoid-s8438" xml:space="preserve">3 {10/71}. </s> <s xml:id="echoid-s8439" xml:space="preserve">Communis tamen uſus artificum obtinuit, ut <lb/> <anchor type="note" xlink:label="note-243-01a" xlink:href="note-243-01"/> prior proportio, nempe tripla ſeſquiſeptima, potius uſurpetur tanquam uera, <lb/>quàm illa, cuius denominator eſt {10/71}. </s> <s xml:id="echoid-s8440" xml:space="preserve">Sumunt enim diametrũ ter cum ſepti-<lb/>ma eius parte, ut circunferentię lineam rectam æqualem exhibeant; </s> <s xml:id="echoid-s8441" xml:space="preserve">quoniam <lb/>uidelicet parũ à uero deficit, & </s> <s xml:id="echoid-s8442" xml:space="preserve">facilior fit operatio per 3 {1/7}. </s> <s xml:id="echoid-s8443" xml:space="preserve">quam per 3 {10/71}. <lb/></s> <s xml:id="echoid-s8444" xml:space="preserve">proptereaq́ nobis eadẽ proportione uti quoq; </s> <s xml:id="echoid-s8445" xml:space="preserve">licebit, dummodo memores ſi <lb/>mus, per documẽta ſuperiora ex diametro nota inueniri circunferentiã paulo <lb/>maiorem, diametrum uero ex nota circunferentia paulo minorem, quàm uere <lb/>ſit. </s> <s xml:id="echoid-s8446" xml:space="preserve">Nam cum ſecundum Archimedem minor ſit proportio circunferentiæ ad <lb/>diametrũ, quàm tripla ſeſquiſeptima, hoc eſt, quàm 22. </s> <s xml:id="echoid-s8447" xml:space="preserve">ad 7. </s> <s xml:id="echoid-s8448" xml:space="preserve">fit, ſi diameter fue <lb/>rit 7. </s> <s xml:id="echoid-s8449" xml:space="preserve">circunferentiam eſſe paulo minorem quàm 22. </s> <s xml:id="echoid-s8450" xml:space="preserve">Numerus enim minor, <lb/>quàm 22. </s> <s xml:id="echoid-s8451" xml:space="preserve">minorem proportionem habet ad 7. </s> <s xml:id="echoid-s8452" xml:space="preserve">quàm 22. </s> <s xml:id="echoid-s8453" xml:space="preserve">ad 7. </s> <s xml:id="echoid-s8454" xml:space="preserve">Vnde cum ſecun-<lb/>dum regulam ſuperiorem, ſi diameter fuerit 7. </s> <s xml:id="echoid-s8455" xml:space="preserve">circunferentia reperiatur 22. </s> <s xml:id="echoid-s8456" xml:space="preserve">li <lb/>quido conſtat, maiorem inuenir<unsure/>i circunferentiam ex diametro nota, quàm re <lb/>ipſa ſit. </s> <s xml:id="echoid-s8457" xml:space="preserve">Rurſus efficiatur, ſi circunferentia fuerit 22. </s> <s xml:id="echoid-s8458" xml:space="preserve">diametrum eſſe paulo mi-<lb/>norem, quàm 7. </s> <s xml:id="echoid-s8459" xml:space="preserve">Numerus enaim 22. </s> <s xml:id="echoid-s8460" xml:space="preserve">d numer um maiorem, quàm 7. </s> <s xml:id="echoid-s8461" xml:space="preserve">minor<unsure/>em <lb/>habet proportionem, quam ad 7. </s> <s xml:id="echoid-s8462" xml:space="preserve">Quare cum iuxta ſuperiorem regulam, ſi cir-<lb/>cunferentia fuerit 22. </s> <s xml:id="echoid-s8463" xml:space="preserve">diameter reperiatur 7. </s> <s xml:id="echoid-s8464" xml:space="preserve">perſpicuum eſt, minorem reperi-<lb/>ri diametrum ex nota circunfereutia, quàm re ipſa ſit.</s> <s xml:id="echoid-s8465" xml:space="preserve"/> </p> <div xml:id="echoid-div407" type="float" level="2" n="3"> <note position="right" xlink:label="note-243-01" xlink:href="note-243-01a" xml:space="preserve">Ex regulis <lb/>ſuperiori-<lb/>bus reperi-<lb/>tur circũfe-<lb/>rẽtia maior <lb/>exdiame@@o <lb/>nota diame <lb/>ter uero mi <lb/>nor ex nota <lb/>circunferen <lb/>tia, quàmr<unsure/>e <lb/>ipſa ſit.</note> </div> <pb o="208" file="244" n="245" rhead="Comment. in I. Cap. Sphæræ"/> </div> <div xml:id="echoid-div409" type="section" level="1" n="129"> <head xml:id="echoid-head134" style="it" xml:space="preserve">REGVLAE, QVIBVSET SVPERFICIES MA-<lb/>ximi circuli in orbe terreno, uel etiam in quacunque ſphæra, <lb/>& ſuperficies conuexa eiuſdem orbis terreni, uel <lb/>etiam cuiuſque ſpære, immo, & tota <lb/>ſoliditas inueniatur.</head> <p> <s xml:id="echoid-s8466" xml:space="preserve"><emph style="sc">Hactenvs</emph> ex probatis auctoribus uarios modos recenſuimus, quibus <lb/>terræ ambitus inueſtigetur, præceptaq́ue propoſuimus, quibus ex circumferen-<lb/>tia nota diameter, & </s> <s xml:id="echoid-s8467" xml:space="preserve">contra ex nota diametro circumferentia inueniatur: </s> <s xml:id="echoid-s8468" xml:space="preserve">Nũc <lb/>uero tradam alia præcepta, quibus ex diametro, & </s> <s xml:id="echoid-s8469" xml:space="preserve">circumferentia terrę, uel cu <lb/>iuſuis alterius ſphæræ, ſuperficies maximi circuli in terra, uel alia ſphæra, inue <lb/>ſtiganda ſit; </s> <s xml:id="echoid-s8470" xml:space="preserve">& </s> <s xml:id="echoid-s8471" xml:space="preserve">ex hac ſuperficie ſuperficies conuexa eiuſdem terræ, uel ſphęrę, <lb/>& </s> <s xml:id="echoid-s8472" xml:space="preserve">denique ex hac conuexa ſuperficie ſoliditas tota terræ, uel alterius ſphæræ. <lb/></s> <s xml:id="echoid-s8473" xml:space="preserve">Ita enim fiet, ut terr@ magnitudo omni ex parte cognita reddatur, non autem <lb/>tantum quo ad ambitum, quod auctor noſter pręſtitit hoc loco.</s> <s xml:id="echoid-s8474" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">Quarte re-<lb/>periatur a-<lb/>rea cuiuſuis <lb/>circuli.</note> <p> <s xml:id="echoid-s8475" xml:space="preserve"><emph style="sc">Qvod</emph> igitur ad primum attinet, ſi multiplicetur ſemidiameter cuiuſuis <lb/>circuli in dimidiatam partem circumferentiæ, ſeu ambirus circuli, producetur <lb/>area, ſeu ſuperficies circuli intra circumferentiam contenta. </s> <s xml:id="echoid-s8476" xml:space="preserve">Vt ſi circumferen-<lb/>tia alicuius circuli fuerit 132. </s> <s xml:id="echoid-s8477" xml:space="preserve">Diameter uero. </s> <s xml:id="echoid-s8478" xml:space="preserve">42. </s> <s xml:id="echoid-s8479" xml:space="preserve">Si 21. </s> <s xml:id="echoid-s8480" xml:space="preserve">diametri dimidiũ, mul-<lb/>tiplicemus per 66. </s> <s xml:id="echoid-s8481" xml:space="preserve">circunferentiæ dimidiatam partem, producetur hic nume-<lb/>rus 1386. </s> <s xml:id="echoid-s8482" xml:space="preserve">pro area circuli. </s> <s xml:id="echoid-s8483" xml:space="preserve">Quod quidem ſupra à nobis demonſtratum eſt in tra <lb/>ctatione de figuris Iſoperimetris, propoſ. </s> <s xml:id="echoid-s8484" xml:space="preserve">4. </s> <s xml:id="echoid-s8485" xml:space="preserve">in qua habetur, rectangulum com-<lb/>prehẽſum ſub ſemidiametro cuiuſuis circuli, & </s> <s xml:id="echoid-s8486" xml:space="preserve">dimidiata parte circũferentiæ <lb/>eiuſdem, æquale eſſe circulo. </s> <s xml:id="echoid-s8487" xml:space="preserve">Itaque ſi multiplicetur ſemidiameter terræ, nem <lb/>pe ſtadia 40090 {10/11} ſecundum Era toſthenem per dimidiatam partem ambi-<lb/>tus, hoc eſt, ſecundum Eratoſthenem, per ſtadia 126000. </s> <s xml:id="echoid-s8488" xml:space="preserve">producetur area maxi <lb/>mi circuli in terra, ſtadiorum 5052454545 {5/11}. </s> <s xml:id="echoid-s8489" xml:space="preserve">hoc eſt, ſuperficies plana ma-<lb/>ximi circuli in terra comprehendet tot quadrata, quorum quodlibet in ſingu-<lb/>lis lateribus unum ſtadium complectatur, quot unitates ſunt in dicto numero. <lb/></s> <s xml:id="echoid-s8490" xml:space="preserve">Areæ enim figurarum planarum menſurantur per quadrata earum linearum, <lb/>per quas latera, ſeu ambitus earundem figurarum menſurari ſolent.</s> <s xml:id="echoid-s8491" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8492" xml:space="preserve"><emph style="sc">Qvod</emph> vero attinet ad ſecundum, ſi area circuli maximi in ſphæra per 4. <lb/></s> <s xml:id="echoid-s8493" xml:space="preserve"> <anchor type="note" xlink:label="note-244-02a" xlink:href="note-244-02"/> multiplicetur, procreabitur ſuperficies tota conuexa ſphæræ. </s> <s xml:id="echoid-s8494" xml:space="preserve">Vt ſi fuerit ſphę-<lb/>ra, cuius maximi circuli ambitus ſit 132. </s> <s xml:id="echoid-s8495" xml:space="preserve">Diameter uero 42. </s> <s xml:id="echoid-s8496" xml:space="preserve">erit ex prima regu-<lb/>la area circuli maximi 1386. </s> <s xml:id="echoid-s8497" xml:space="preserve">ut dictum eſt, quæ ſi mnltiplicetur per 4. </s> <s xml:id="echoid-s8498" xml:space="preserve">exurget <lb/>mox ſuperficies conuexa dictæ ſphęrę 5544. </s> <s xml:id="echoid-s8499" xml:space="preserve">Hoc autem clariſl<unsure/>ime ab Archime <lb/>de eſt demonſtratum lib. </s> <s xml:id="echoid-s8500" xml:space="preserve">1. </s> <s xml:id="echoid-s8501" xml:space="preserve">de ſphæra & </s> <s xml:id="echoid-s8502" xml:space="preserve">cylindro, propoſ. </s> <s xml:id="echoid-s8503" xml:space="preserve">31. </s> <s xml:id="echoid-s8504" xml:space="preserve">in qua concludi-<lb/>tur, Supei<unsure/>ficiem conuexam cuiuslibet ſphęrę eſſe quadruplam maximi circuli <lb/>in ſphæra. </s> <s xml:id="echoid-s8505" xml:space="preserve">Itaque ſi area maximi circuli in terra, qui continet, ut diximus, ſta-<lb/>dia quadrata 5051454545 {5/11}. </s> <s xml:id="echoid-s8506" xml:space="preserve">multiplicetur per 4. </s> <s xml:id="echoid-s8507" xml:space="preserve">inuenietur ambitus orbis <lb/>terreni, ſecundum totam conuexam ſuperſiciem, ſtadior@m quadratorum <lb/>20205818181 {9/11}. </s> <s xml:id="echoid-s8508" xml:space="preserve">Poteſt tamen eadem ſuperficies conuexaiuueniri facilius, <lb/>etiamſi aream maximi circuli non habeamus, hac ratione.</s> <s xml:id="echoid-s8509" xml:space="preserve"/> </p> <div xml:id="echoid-div409" type="float" level="2" n="1"> <note position="left" xlink:label="note-244-02" xlink:href="note-244-02a" xml:space="preserve">Qua via ſu <lb/>perficies cõ <lb/>uexa cuiuſ-<lb/>libet ſphæ-<lb/>ræ inuenia-<lb/>tur.</note> </div> <p> <s xml:id="echoid-s8510" xml:space="preserve"><emph style="sc">Mvltiplicetvr</emph> tota diameter in totam circunferentiam maxi-<lb/>mi circuli. </s> <s xml:id="echoid-s8511" xml:space="preserve">Productus enim numerus dabit ſuperficiem conuexam ſphærę. </s> <s xml:id="echoid-s8512" xml:space="preserve">Vt <lb/>ſi multiplicetur diameter terræ continens ſtadia 80181 {9/11}. </s> <s xml:id="echoid-s8513" xml:space="preserve">per totũ ambitũ. <lb/></s> <s xml:id="echoid-s8514" xml:space="preserve">uidelicet per ſtadia 252000. </s> <s xml:id="echoid-s8515" xml:space="preserve">producetur conuexa ſuperficies terræ ſtadiorum <pb o="209" file="245" n="246" rhead="Ioan. de Sacro Boſco."/> quadratorũ 20205818181 {9/11}. </s> <s xml:id="echoid-s8516" xml:space="preserve">ut prius. </s> <s xml:id="echoid-s8517" xml:space="preserve">Quod ita demonſtrabim us. </s> <s xml:id="echoid-s8518" xml:space="preserve">Quoniã <lb/>rectangulum contentum ſub diametro ſphærę, & </s> <s xml:id="echoid-s8519" xml:space="preserve">circunferentia maximi cir-<lb/>culi ſimile eſt rectangulo contento ſub ſemidiametro ſphæræ, & </s> <s xml:id="echoid-s8520" xml:space="preserve">ſemicircunfe <lb/>rentia maximi circuli, quòd latera illius ad latera huius duplam habeant pro-<lb/>portionẽ, atq; </s> <s xml:id="echoid-s8521" xml:space="preserve">adeo permutando latera illius eandem proportionem habeant <lb/>inter ſe, quam latera huius, habebit illud ad hoc duplicatam proportionẽ la-<lb/> <anchor type="note" xlink:label="note-245-01a" xlink:href="note-245-01"/> terum homologorum. </s> <s xml:id="echoid-s8522" xml:space="preserve">Cum ergo latera homologa duplam proportionem ha <lb/>beant, habebit illud rectangnlnm ad hoc proportionem quadruplam, quæ du <lb/>plæ proportionis eſt duplicata, ut in his numeris apparet, 1. </s> <s xml:id="echoid-s8523" xml:space="preserve">2. </s> <s xml:id="echoid-s8524" xml:space="preserve">4. </s> <s xml:id="echoid-s8525" xml:space="preserve">Sed rectangu-<lb/>lum hoc contentum ſub ſemidiametro, & </s> <s xml:id="echoid-s8526" xml:space="preserve">ſemicircunfere@tia miximi circuli <lb/>æquale eſt areæ maximi circuli in ſphæra, ut ſupra demonſtrauimus propoſ. </s> <s xml:id="echoid-s8527" xml:space="preserve">4. <lb/></s> <s xml:id="echoid-s8528" xml:space="preserve">in tractatione figurarum Iſoperimetrarum. </s> <s xml:id="echoid-s8529" xml:space="preserve">Igitur rect@ngulum illud ſub tota <lb/>diametro, & </s> <s xml:id="echoid-s8530" xml:space="preserve">tota circunferentia contentum quadruplum eſt maximi circuli <lb/>in ſphæra; </s> <s xml:id="echoid-s8531" xml:space="preserve">ac proinde æquale ſuper@iciei conuexę ſphęrę; </s> <s xml:id="echoid-s8532" xml:space="preserve">quandoquidẽ & </s> <s xml:id="echoid-s8533" xml:space="preserve">hæc <lb/>eiuſdem circuli maximi quadrupla eſt, ut Archimedes demonſtrauit lib. </s> <s xml:id="echoid-s8534" xml:space="preserve">1. </s> <s xml:id="echoid-s8535" xml:space="preserve">de <lb/>ſphæra, & </s> <s xml:id="echoid-s8536" xml:space="preserve">cylindro propoſ. </s> <s xml:id="echoid-s8537" xml:space="preserve">31.</s> <s xml:id="echoid-s8538" xml:space="preserve"/> </p> <div xml:id="echoid-div410" type="float" level="2" n="2"> <note position="right" xlink:label="note-245-01" xlink:href="note-245-01a" xml:space="preserve">20. ſexiij.</note> </div> <p> <s xml:id="echoid-s8539" xml:space="preserve"><emph style="sc">Iam</emph> uero, ut ad tertium ueniamus, tota ſoliditas ſphæræ producetur. </s> <s xml:id="echoid-s8540" xml:space="preserve">ſi <lb/> <anchor type="note" xlink:label="note-245-02a" xlink:href="note-245-02"/> ſemidiameter ſphęrę multiplicetur in tertiam partẽ ambitus ſphęrę, ſeu ſuper <lb/>ficiei conuexę ſphæræ: </s> <s xml:id="echoid-s8541" xml:space="preserve">Rectangulum enim ſolidũ comprehenſum ſub ſemidia <lb/>metro ſphærę, & </s> <s xml:id="echoid-s8542" xml:space="preserve">tertia parte ambitus ſphæræ æquale eſt ipſi ſphæræ, ut ſupra <lb/>in tractatione figurarũ Iſoperimetrarũ propoſ. </s> <s xml:id="echoid-s8543" xml:space="preserve">16. </s> <s xml:id="echoid-s8544" xml:space="preserve">demonſtrauimus. </s> <s xml:id="echoid-s8545" xml:space="preserve">Hac ratio-<lb/>ne, ſi ſemidiameter terrę ſtadiorum 40090.</s> <s xml:id="echoid-s8546" xml:space="preserve">{10/11}. </s> <s xml:id="echoid-s8547" xml:space="preserve">multiplicetur per tertiã par-<lb/>tem ſuperficiei conuexæ, nempe per ſtadia 6735272727 {3/11}. </s> <s xml:id="echoid-s8548" xml:space="preserve">producetur ſoli <lb/>ditas terræ ſtadiorum cubicorum 270023206611570.</s> <s xml:id="echoid-s8549" xml:space="preserve">{30/121}. </s> <s xml:id="echoid-s8550" xml:space="preserve">hoc eſt, ſoliditas <lb/>terræ tot cubos comprehendet, quorum quilibet in ſingulis lateribus unum <lb/>ſtadium complectitur, quot ſunt unitates in dicto numero. </s> <s xml:id="echoid-s8551" xml:space="preserve">Areæ enim ſolida-<lb/>rum figurarum menſurãtur per cubos earum linearum, per quarum quadrata <lb/>ambitus, ſeu ſuperficies conuexæ earundem figurarum ſolent menſurari.</s> <s xml:id="echoid-s8552" xml:space="preserve"/> </p> <div xml:id="echoid-div411" type="float" level="2" n="3"> <note position="right" xlink:label="note-245-02" xlink:href="note-245-02a" xml:space="preserve">Qua ratio-<lb/>ne ſoliditas <lb/>ſphæ@æ re-<lb/>periatur.</note> </div> </div> <div xml:id="echoid-div413" type="section" level="1" n="130"> <head xml:id="echoid-head135" xml:space="preserve">DE VARIIS MENSVRIS <lb/>Mathematicorum.</head> <p> <s xml:id="echoid-s8553" xml:space="preserve"><emph style="sc">Vt</emph> autem ambitus terræ habeatur non ſolum in ſtadijs, uerum etiam in <lb/> <anchor type="note" xlink:label="note-245-03a" xlink:href="note-245-03"/> paſſibus, milliarijs, leucis, & </s> <s xml:id="echoid-s8554" xml:space="preserve">alijs menſuris, enumerandę erunt menſurę, qui-<lb/>bus Mathematici, maxime Geometrę, utuntur. </s> <s xml:id="echoid-s8555" xml:space="preserve">Mathematici enim, ne confu-<lb/>ſio oriretur ob diuerſitatem menſurarum in uarijs regionibus (quęlibet nam-<lb/>que regio proprias habet propemodum menſuras,) utiliter excogitarunt quaſ-<lb/>dam menſuras, quę certę, ac ratę apud omnes nationes haberentur. </s> <s xml:id="echoid-s8556" xml:space="preserve">Pręcipuæ <lb/>autem menſurę continentur in ſubiecta ſormula.</s> <s xml:id="echoid-s8557" xml:space="preserve"/> </p> <div xml:id="echoid-div413" type="float" level="2" n="1"> <note position="right" xlink:label="note-245-03" xlink:href="note-245-03a" xml:space="preserve">Variæ me@ <lb/>ſurę ap@@ <lb/>Geometr@ <lb/>vſitatæ.</note> </div> <note position="right" xml:space="preserve"> <lb/>#### Granum hordei, menſurarum omnium minima, atque principium <lb/>Digitus grana habet ſecundum latitudinem diſpoſita # 4 <lb/>Palmus digitos continet # 4 # vel Grana # 16 <lb/>Pes continet palmos # 4 # vel Digitos # 16 <lb/>Cubitus paruus, iuxta Vitruuium, continet pedes # ## {1/2}.uel Palmos # 6 <lb/>Cubitus communis pedes complectitur # 4 # uel Palmos # 16 <lb/></note> <pb o="210" file="246" n="247" rhead="Comment. in I. Cap. Sphæræ"/> <note position="right" xml:space="preserve"> <lb/>Cubitus magnus conſtat pedibus # 9 # vel Palmis # 36 <lb/>Paſſus ſimplex primæ differentiæ pedes habet # 2 # vel Palmos # 8 <lb/>Paſſus duplex primę @differentię habet pedes # 4 # vel Palmos # 16 <lb/>Paſſus ſimplex ſecundę differentię continet pedes # 2 {1/2} # vel Palmos # 10 <lb/>Paſſus duplex ſecundę differ. dictus Geometricus, \\ habet pedes # 5 # vel Palmos # 10 <lb/>Paſſus ſimplex tertiæ differentię pedes obtinet # 3 # vel Palmos # 12 <lb/>Paſſus duplex tertię differentiæ conſtat pedibus # 6 # vel Palmis # 24 <lb/>Vlna communis complectitur pedes # 4 # vel Palmos # 16 <lb/>Vlna agreſtis conſtat pedibus # 6 # vel Palmis # 24 <lb/>Pertica comprehendit pedes # 10 # vel Palmos # 40 <lb/>Stadium habet pafſus Geometricos # 125 # vel pedes # 625 <lb/>Miliarium continet ſtadia # 8 # vel Paſſ. Geo. 1000 <lb/>Leuca Gallica, ſiue Hiſpania continet milliaria # 1 {1/2} uel Paſſ. Geo. 1500 <lb/>Leuca Germanica communis milliaria habet # 4 # vel Paſſ. Geo. 4000 <lb/>Leuca Sueuica omnium maxima habet miliaria # 5 # vel Paſſ. Geo. 5000 <lb/></note> <p> <s xml:id="echoid-s8558" xml:space="preserve"><emph style="sc">Caetervm</emph> harum menſurarum ualor intelligendus eſt tantummo-<lb/> <anchor type="note" xlink:label="note-246-02a" xlink:href="note-246-02"/> do ſecundum longitudinem, ita ut v. </s> <s xml:id="echoid-s8559" xml:space="preserve">g. </s> <s xml:id="echoid-s8560" xml:space="preserve">ſtadia octo in longitudine conficiant <lb/>unum milliarium in longitudine, & </s> <s xml:id="echoid-s8561" xml:space="preserve">quatuor digiti in longitudine conſtituãt <lb/>unum palmum in longitudine, &</s> <s xml:id="echoid-s8562" xml:space="preserve">c. </s> <s xml:id="echoid-s8563" xml:space="preserve">Non autem ſecundum latitudinem. </s> <s xml:id="echoid-s8564" xml:space="preserve">Non. </s> <s xml:id="echoid-s8565" xml:space="preserve">n. <lb/></s> <s xml:id="echoid-s8566" xml:space="preserve">octo ſtadia quadrata æquiualent uni milliario quadrato, cum quadratũ unius <lb/>milliarij comprehendat ſtadia quadrata 64. </s> <s xml:id="echoid-s8567" xml:space="preserve">quia nimirum numerus quadra-<lb/>tus octonarij (qui numerus ſtadiorum complectitur unum milliarium) eſt 64. </s> <s xml:id="echoid-s8568" xml:space="preserve"><lb/>Ita quoque unus palmus quadratus continebit 16, digitos quadratos, propte-<lb/>rea quod numerus quadratus quaternarij (quatuor enim digiti palmum con-<lb/>ſtituunt) ſit 16. </s> <s xml:id="echoid-s8569" xml:space="preserve">&</s> <s xml:id="echoid-s8570" xml:space="preserve">c. </s> <s xml:id="echoid-s8571" xml:space="preserve">Hoc ideo dixerim, ne mireris, ſtadia, quæ in tota conuexa <lb/>ſuperficie terræ compreh enduntur, non poſſe reduci ad milliaria, diuiſione fa-<lb/>cta per 8. </s> <s xml:id="echoid-s8572" xml:space="preserve">ſed per 64.</s> <s xml:id="echoid-s8573" xml:space="preserve"/> </p> <div xml:id="echoid-div414" type="float" level="2" n="2"> <note position="left" xlink:label="note-246-02" xlink:href="note-246-02a" xml:space="preserve">Quomodo <lb/>menſurę ſu <lb/>pradictæ in <lb/>telligendæ <lb/>ſint.</note> </div> <p> <s xml:id="echoid-s8574" xml:space="preserve">Ex his autem facile cuilibet erit, ſi omnino præceptis Arithmeticis non <lb/> <anchor type="note" xlink:label="note-246-03a" xlink:href="note-246-03"/> fuerit deſtitutus, menſuram quamcunque in aliam transformare. </s> <s xml:id="echoid-s8575" xml:space="preserve">Si enim men <lb/>ſura minor in maiorem cõmutanda eſt, diuidendus eſt numerus minoris men <lb/>ſuræ per numerum, ſecundum quem minor in maiore continetur. </s> <s xml:id="echoid-s8576" xml:space="preserve">Vt ſi pafſus <lb/>46000. </s> <s xml:id="echoid-s8577" xml:space="preserve">redigendi ſint ad milliaria, diuidendi erunt per 1000. </s> <s xml:id="echoid-s8578" xml:space="preserve">quoniam paſſus <lb/>1000. </s> <s xml:id="echoid-s8579" xml:space="preserve">conficiunt unum milliarium, efficienturq́ue milliaria 46. </s> <s xml:id="echoid-s8580" xml:space="preserve">Ita quoq; </s> <s xml:id="echoid-s8581" xml:space="preserve">quo <lb/>niam 8. </s> <s xml:id="echoid-s8582" xml:space="preserve">ſtadia conficiunt milliarium, ex 252000. </s> <s xml:id="echoid-s8583" xml:space="preserve">ſtadiis efficiuntur milliaria <lb/>31500. </s> <s xml:id="echoid-s8584" xml:space="preserve">Pari ratione cum 20000. </s> <s xml:id="echoid-s8585" xml:space="preserve">palmi efficiant milliarium, continebuntur in <lb/>palmis 560000. </s> <s xml:id="echoid-s8586" xml:space="preserve">milliaria 28. </s> <s xml:id="echoid-s8587" xml:space="preserve">&</s> <s xml:id="echoid-s8588" xml:space="preserve">c. </s> <s xml:id="echoid-s8589" xml:space="preserve">Si uero maior aliqua menſura in minorem cõ <lb/>uertenda ſit, multiplicandus erit uumerus maioris menſuræ per numerum, ſe <lb/>cundum quem minor in maiore continetur, Vt ſi uelim ſcire, quot paſſus effi-<lb/>ciantur ex 46. </s> <s xml:id="echoid-s8590" xml:space="preserve">milliarijs. </s> <s xml:id="echoid-s8591" xml:space="preserve">Multiplico 46. </s> <s xml:id="echoid-s8592" xml:space="preserve">per 1000. </s> <s xml:id="echoid-s8593" xml:space="preserve">(totiens enim paſſus in mil-<lb/>liario continetur,) efficioq́ue paſſus 46000. </s> <s xml:id="echoid-s8594" xml:space="preserve">atque ita de cæteris.</s> <s xml:id="echoid-s8595" xml:space="preserve"/> </p> <div xml:id="echoid-div415" type="float" level="2" n="3"> <note position="left" xlink:label="note-246-03" xlink:href="note-246-03a" xml:space="preserve">Qua ratio-<lb/>ne una mẽ <lb/>ſura in aliã <lb/>tranſmute-<lb/>@ur.</note> </div> <pb o="211" file="247" n="248" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div417" type="section" level="1" n="131"> <head xml:id="echoid-head136" xml:space="preserve">VARIÆ SENTENTIÆ AVCTORVM <lb/>in ambitu terræ præfiniendo.</head> <p> <s xml:id="echoid-s8596" xml:space="preserve"><emph style="sc">Tametsi</emph> omnes rationos ſuperius adductę, quibus ambitus orbis ter-<lb/> <anchor type="note" xlink:label="note-247-01a" xlink:href="note-247-01"/> reni inueſtigatur, Geometricis demonſtrationibus innituntur, tamen quia ſpa <lb/>tium terreſtre ſimili interuallo cœleſti reſpondens non ad amuſſim menſurari <lb/>poteſt, propter impedimenta uel montium, nel uallium &</s> <s xml:id="echoid-s8597" xml:space="preserve">c. </s> <s xml:id="echoid-s8598" xml:space="preserve">uel etiam, quia ra-<lb/>ro recto itinere ab uno loco ad alterum acceditur, quin immo ſemper ſunt iti <lb/>nera inflexa: </s> <s xml:id="echoid-s8599" xml:space="preserve">Quòd ſi in demonſtratione Maurolyci non requiratur, ut ſpaciũ <lb/>ullum perambulemus, eſt tamẽ admodum difficile, radio uiſuali exacte, & </s> <s xml:id="echoid-s8600" xml:space="preserve">prę-<lb/>cisè punctum illud contactus in terræ ſuperficie diſcernere; </s> <s xml:id="echoid-s8601" xml:space="preserve">Inde effectum eſt, <lb/>ut diuerſi artifices ambitum globi ex terra, & </s> <s xml:id="echoid-s8602" xml:space="preserve">aqua confecti emenſi, eum non <lb/>eiuſdem magnitudinis inuenerint, ſed ualde inter ſeſe diſcrepent in terminan <lb/>da quantitate dicti ambitus. </s> <s xml:id="echoid-s8603" xml:space="preserve">Quorum ſententias uiſum eſt hoc loco recenſe-<lb/>re, ut ex illis eam, quę magis ad ueritatem accedit, eligamus.</s> <s xml:id="echoid-s8604" xml:space="preserve"/> </p> <div xml:id="echoid-div417" type="float" level="2" n="1"> <note position="right" xlink:label="note-247-01" xlink:href="note-247-01a" xml:space="preserve">Cur uarij <lb/>auctores va <lb/>rium inue-<lb/>nerint rer-<lb/>t<unsure/>æ ambitu.</note> </div> <note position="right" xml:space="preserve">Terræ ambi<unsure/> <lb/>tus ſecundũ <lb/>Atiſtotelẽ.</note> <p> <s xml:id="echoid-s8605" xml:space="preserve"><emph style="sc">Aristoteles</emph> igitur ad finem lib. </s> <s xml:id="echoid-s8606" xml:space="preserve">2. </s> <s xml:id="echoid-s8607" xml:space="preserve">de cœlo refert ſententiam quorun-<lb/>dam antiqu orum, qui aſſerebant ambitum terræ continere ſtadia 400000. </s> <s xml:id="echoid-s8608" xml:space="preserve">qui <lb/>efficiunt milliaria 50000. </s> <s xml:id="echoid-s8609" xml:space="preserve">Itaq; </s> <s xml:id="echoid-s8610" xml:space="preserve">ſecundum hanc opinionẽ conueniunt uni gra <lb/>dui terreſtri ſtadia 1111 {1/9}. </s> <s xml:id="echoid-s8611" xml:space="preserve">milliaria vero 138 {8/9}. </s> <s xml:id="echoid-s8612" xml:space="preserve">Diameter autẽ continebit ſta <lb/>dia 127262 {8/11}. </s> <s xml:id="echoid-s8613" xml:space="preserve">At milliaria 15909 {1/11}. </s> <s xml:id="echoid-s8614" xml:space="preserve">Semidiameter ſtadia 636364 {4/17}. <lb/></s> <s xml:id="echoid-s8615" xml:space="preserve">Milliaria 7954 {6/15}. </s> <s xml:id="echoid-s8616" xml:space="preserve">Verum quia hęc ſententia plus æquo tribuit magnitudini <lb/>terræ, pugnatq́; </s> <s xml:id="echoid-s8617" xml:space="preserve">nimis cũ recentiorum obſeruationibus, ab omnibus reijcitur.</s> <s xml:id="echoid-s8618" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8619" xml:space="preserve"><emph style="sc">Hipparchvs</emph>, teſte Plinio, tribuebat circunferentiæ terræ ſtadia <lb/> <anchor type="note" xlink:label="note-247-03a" xlink:href="note-247-03"/> 277000. </s> <s xml:id="echoid-s8620" xml:space="preserve">id eſt, milliaria 34625. </s> <s xml:id="echoid-s8621" xml:space="preserve">ita ut ſpatium unius gradus comprehendat ſta-<lb/>dia 769 {9/71}. </s> <s xml:id="echoid-s8622" xml:space="preserve">milliaria 96 {13/72}. </s> <s xml:id="echoid-s8623" xml:space="preserve">Itaque Hipparco erit diameter terræ ſtadio-<lb/>rum 88136 {4/11}. </s> <s xml:id="echoid-s8624" xml:space="preserve">milliariorum 11017 {1/22}. </s> <s xml:id="echoid-s8625" xml:space="preserve">Semidiameter vero continebit ſta <lb/>dia 44068 {2/11}. </s> <s xml:id="echoid-s8626" xml:space="preserve">milliaria 5508 {23/44}. </s> <s xml:id="echoid-s8627" xml:space="preserve">Sed eadem de cauſa hæc ſententia, qua <lb/>prior exploditur ab Aſtronomis.</s> <s xml:id="echoid-s8628" xml:space="preserve"/> </p> <div xml:id="echoid-div418" type="float" level="2" n="2"> <note position="right" xlink:label="note-247-03" xlink:href="note-247-03a" xml:space="preserve">Terrę ambi<unsure/> <lb/>tus ſecun-<lb/>dũ Hippar-<lb/>chum.</note> </div> <note position="right" xml:space="preserve">Terræ am-<lb/>bitus ſecu@ <lb/>dum Erato <lb/>ſthenem.</note> <p> <s xml:id="echoid-s8629" xml:space="preserve"><emph style="sc">Eratosthenes</emph>, ut habetur apud Macrobium lib. </s> <s xml:id="echoid-s8630" xml:space="preserve">1. </s> <s xml:id="echoid-s8631" xml:space="preserve">in Somnium <lb/>Scipionis, aſſignabat ambitui terræ ſtadia 252000. </s> <s xml:id="echoid-s8632" xml:space="preserve">q̃efficiunt milliaria 31500. <lb/></s> <s xml:id="echoid-s8633" xml:space="preserve">Deprehenderat enim in uno gradu terræ contineri ſtadia 700. </s> <s xml:id="echoid-s8634" xml:space="preserve">id eſt, milliaria <lb/>87 {1/2}. </s> <s xml:id="echoid-s8635" xml:space="preserve">Vnde diameter terræ habebit ſtadia 80181 {9/11}. </s> <s xml:id="echoid-s8636" xml:space="preserve">milliaria 10022 {8/11}. </s> <s xml:id="echoid-s8637" xml:space="preserve"><lb/>In ſemidiametro erunt ſtadia 40090 {10/11}. </s> <s xml:id="echoid-s8638" xml:space="preserve">milliaria 5011 {4/11}. </s> <s xml:id="echoid-s8639" xml:space="preserve">Si tamen Cleo <lb/>medi credimus, Eratoſthenes in toto terræ ambitu contineri dicebat ſtadia tã-<lb/>tummodo 250000. </s> <s xml:id="echoid-s8640" xml:space="preserve">Verum neque hanc ſententiam amplectuntur Aſtronomi <lb/>noſtri temporis, quòd minorem reperiant ambitum terrę, quàm Eratoſthenes.</s> <s xml:id="echoid-s8641" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8642" xml:space="preserve"><emph style="sc">Ptolemaevs</emph> totum terreni orbis ambitum affirmat continere ſtadia <lb/>180000. </s> <s xml:id="echoid-s8643" xml:space="preserve">hoc eſt. </s> <s xml:id="echoid-s8644" xml:space="preserve">milliaria 22500. </s> <s xml:id="echoid-s8645" xml:space="preserve">Ita ut uni gradui in terra reſpondeant ſtadia <lb/> <anchor type="note" xlink:label="note-247-05a" xlink:href="note-247-05"/> 500. </s> <s xml:id="echoid-s8646" xml:space="preserve">ſiue milliaria 62 {1/2}. </s> <s xml:id="echoid-s8647" xml:space="preserve">Hac ratione Diametri terræ lõgitudo cõplectetur ſta <lb/>dia 57272 {84/11}. </s> <s xml:id="echoid-s8648" xml:space="preserve">milliaria 7159 {1/11}. </s> <s xml:id="echoid-s8649" xml:space="preserve">Semidiameter habebit ſtadia 28636 {4/11}. <lb/></s> <s xml:id="echoid-s8650" xml:space="preserve">milliaria 3579 {6/11}. </s> <s xml:id="echoid-s8651" xml:space="preserve">Tota autem ſuperficies conuexa terræ comprehendet ſta <lb/>dia 10309090909 {1/11}. </s> <s xml:id="echoid-s8652" xml:space="preserve">milliaria 161079545 {5/11}.</s> <s xml:id="echoid-s8653" xml:space="preserve"/> </p> <div xml:id="echoid-div419" type="float" level="2" n="3"> <note position="right" xlink:label="note-247-05" xlink:href="note-247-05a" xml:space="preserve">Terræ am-<lb/>bitus ſecum <lb/>dum Ptole-<lb/>męum.</note> </div> <p> <s xml:id="echoid-s8654" xml:space="preserve"><emph style="sc">Alphraganvs</emph>, Almæon, Thebitius, & </s> <s xml:id="echoid-s8655" xml:space="preserve">auctore Alphragano, plu <lb/> <anchor type="note" xlink:label="note-247-06a" xlink:href="note-247-06"/> rimi ſapientes, adſcribunt terrę circumferentiæ 163200. </s> <s xml:id="echoid-s8656" xml:space="preserve">ſtadia, ſiue milliaria <lb/>20400. </s> <s xml:id="echoid-s8657" xml:space="preserve">Tribuunt enim ſingulis gradibus ſtadia duntaxat 453 {1/3}′. </s> <s xml:id="echoid-s8658" xml:space="preserve">hoc eſt, mil-<lb/>liaria 56 {2/3}. </s> <s xml:id="echoid-s8659" xml:space="preserve">Quocirca iuxta hos auctores Diameter terreſtris continebit ſta-<lb/>dia 51927 {3/11}. </s> <s xml:id="echoid-s8660" xml:space="preserve">milliaria uero 6490 {10/11}. </s> <s xml:id="echoid-s8661" xml:space="preserve">Semidiameter conſtabit ſtadijs <lb/>25963 {7/11}. </s> <s xml:id="echoid-s8662" xml:space="preserve">milliarijs autem 3245 {5/11}. </s> <s xml:id="echoid-s8663" xml:space="preserve">Superficies conuexa erit ſtadiorum <lb/>8474530909 {1/11}. </s> <s xml:id="echoid-s8664" xml:space="preserve">milliariorum uero 132414545 {5/11}.</s> <s xml:id="echoid-s8665" xml:space="preserve"/> </p> <div xml:id="echoid-div420" type="float" level="2" n="4"> <note position="right" xlink:label="note-247-06" xlink:href="note-247-06a" xml:space="preserve">Terrę ambi <lb/>tus ſecun dũ <lb/>Alphagra-<lb/>num, Al-<lb/>męonem, et <lb/>Thebith.</note> </div> <pb o="212" file="248" n="249" rhead="Comment. in I. Cap. Sphæræ"/> <p> <s xml:id="echoid-s8666" xml:space="preserve"><emph style="sc">Pernellvs</emph> Ambianas iu ſua Coſmotheoria vult, ambitum terrę cõ-<lb/> <anchor type="note" xlink:label="note-248-01a" xlink:href="note-248-01"/> plecti ſtadia 166114 {8/2@}. </s> <s xml:id="echoid-s8667" xml:space="preserve">Milliaria vero 24514 {20<unsure/>/100}. </s> <s xml:id="echoid-s8668" xml:space="preserve">Ait enim, ſe cõperiſſe <lb/>vni gradui in terra reſpõdere ſtadia 544 {381/500}. </s> <s xml:id="echoid-s8669" xml:space="preserve">milliaria vero 68 {381/4000}. <lb/></s> <s xml:id="echoid-s8670" xml:space="preserve">Quare ex hac ſententia habebit diameter terrę ftadia 62400 {3/271} milliaria <lb/>autem 7800 {3/2200}. </s> <s xml:id="echoid-s8671" xml:space="preserve">Semidiameter complectetur ſtadia 31200 {3/500} mil-<lb/>l@aria vero 3900 {3/4400}. </s> <s xml:id="echoid-s8672" xml:space="preserve">Cõuexa autẽ ſuperficies terrę cotinebit hac rõne <lb/>ſtiadia 12237535707 {5893/13750}. </s> <s xml:id="echoid-s8673" xml:space="preserve">millisria uero 191211495 {717143/880900}.</s> <s xml:id="echoid-s8674" xml:space="preserve"/> </p> <div xml:id="echoid-div421" type="float" level="2" n="5"> <note position="left" xlink:label="note-248-01" xlink:href="note-248-01a" xml:space="preserve">Terræ am-<lb/>bitus ſecun <lb/>dum Ferne <lb/>lium Am-<lb/>b<unsure/>ianatem.</note> </div> <p> <s xml:id="echoid-s8675" xml:space="preserve"><emph style="sc">Recentiores</emph> tandem rerum Aſtronomicarum periti, qui non ſe-<lb/> <anchor type="note" xlink:label="note-248-02a" xlink:href="note-248-02"/> mel totum Oceanum nauigijs traiecerunt, teſtantur totum ambitum terræ <lb/>complecti ſtadia 152640. </s> <s xml:id="echoid-s8676" xml:space="preserve">milliaria vero 19080. </s> <s xml:id="echoid-s8677" xml:space="preserve">Vni enim gradui in mari dicũt <lb/>correſpondere ſtadia tantummodo 424. </s> <s xml:id="echoid-s8678" xml:space="preserve">milliaria autem 53. </s> <s xml:id="echoid-s8679" xml:space="preserve">Itaque ſi hoc ue-<lb/>rum eſt, habebit diametri terrenæ lon@itudo ſtadia 48567 {3/11}. </s> <s xml:id="echoid-s8680" xml:space="preserve">At milliaria <lb/>6070 {10/11}. </s> <s xml:id="echoid-s8681" xml:space="preserve">Semidiameter uero ſtadia 24283 {7/11}. </s> <s xml:id="echoid-s8682" xml:space="preserve">milliaria autem 3035 {5/11}. <lb/></s> <s xml:id="echoid-s8683" xml:space="preserve">Superficies denique conuexa terrę complectetur ſtadia 7413318509 {1/11}. </s> <s xml:id="echoid-s8684" xml:space="preserve">mil <lb/>liaria uero 115832945 {5/17}.</s> <s xml:id="echoid-s8685" xml:space="preserve"/> </p> <div xml:id="echoid-div422" type="float" level="2" n="6"> <note position="left" xlink:label="note-248-02" xlink:href="note-248-02a" xml:space="preserve">Terræ am-<lb/>bitus ſecun <lb/>dum recen-<lb/>t@ores.</note> </div> <p> <s xml:id="echoid-s8686" xml:space="preserve">HÆ igitur ſunt ſeptem opiniones, quæ alicuius momenti ſunt circa quan-<lb/>titatem ambitus terreni, quarum priores tres omnino tanquam falſæ ab om-<lb/>nibus reijciuntur: </s> <s xml:id="echoid-s8687" xml:space="preserve">Poſteriores autem quatuor probabiles ſunt, habentq́; </s> <s xml:id="echoid-s8688" xml:space="preserve">ſin-<lb/>gulæ ſuos defenſores. </s> <s xml:id="echoid-s8689" xml:space="preserve">Communis namq́ue ſchola fere Aſtronomorum ample-<lb/>ctitur ſententiam Ptolemęi, tanquam veriorem, quam & </s> <s xml:id="echoid-s8690" xml:space="preserve">nos in ſequentibus <lb/> <anchor type="note" xlink:label="note-248-03a" xlink:href="note-248-03"/> ſequemur, ne a communi via recedere uideamur. </s> <s xml:id="echoid-s8691" xml:space="preserve">Alij potius Alphragani opi <lb/>nioni adhærent; </s> <s xml:id="echoid-s8692" xml:space="preserve">propterea quod poſt Ptolemæum multi ſapientes, ut auctor <lb/>eſt Alphraganus, eam comprobarunt. </s> <s xml:id="echoid-s8693" xml:space="preserve">Vnde fortaſſis rece ntiorum opinio, quæ <lb/>parum ab Alphragano recedit, verior erit. </s> <s xml:id="echoid-s8694" xml:space="preserve">Pauci denique in ſententiam Fer-<lb/>nelij Ambianatis ire uidentur.</s> <s xml:id="echoid-s8695" xml:space="preserve"/> </p> <div xml:id="echoid-div423" type="float" level="2" n="7"> <note position="left" xlink:label="note-248-03" xlink:href="note-248-03a" xml:space="preserve">Ptolemæi <lb/>ſentẽtia de <lb/>ambitu ter <lb/>ræ commu-<lb/>nis eſt.</note> </div> <p> <s xml:id="echoid-s8696" xml:space="preserve"><emph style="sc">Svnt</emph> etiam nonnulli, qui conantur omnes dictas opiniones ad concor-<lb/>diam reducere. </s> <s xml:id="echoid-s8697" xml:space="preserve">Dicunt enim, præfatos auctores non uſos fuiſſe eadem mẽſura, <lb/>ſed eos, qui maiorem ponebãt terræ ambitum, aſſumpſiſſe paſſus minores; </s> <s xml:id="echoid-s8698" xml:space="preserve">Eos <lb/>uero. </s> <s xml:id="echoid-s8699" xml:space="preserve">qui minorem eſſe dicebant, maioribus paſſibus eſſe vſos. </s> <s xml:id="echoid-s8700" xml:space="preserve">Vnde non tanta <lb/>crit diſcrepantia inter dictos Aſtronomos, quanta eſſe uidetur. </s> <s xml:id="echoid-s8701" xml:space="preserve">Sed qui rem ac-<lb/>curatius conſiderabit, ſacile perſpiciet, nullam poſſe concordiam inter omnes <lb/>opiniones reperiri, quamuis inter duas, uel tres aliquo modo repe-<lb/>riatur. </s> <s xml:id="echoid-s8702" xml:space="preserve">Vt au tem omnes opiniones prædictas ob oculos poſitas <lb/>habeas, appoſui ſequentes tabellas, iu quibus ſecundum <lb/>omnes ſententias continetur ambitus terræ, quan-<lb/>titas vnius gradus terreſtris, Diameter terræ, <lb/>& </s> <s xml:id="echoid-s8703" xml:space="preserve">ſemidiameter iuxta poſteriores quoque <lb/>quatuor opiniones, ſuperficies con-<lb/>uexa terræ; </s> <s xml:id="echoid-s8704" xml:space="preserve">& </s> <s xml:id="echoid-s8705" xml:space="preserve">hæc omnia <lb/>tam in ſtadijs, quam <lb/>in milliarijs.</s> <s xml:id="echoid-s8706" xml:space="preserve"/> </p> <pb o="213" file="249" n="250" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve"> <lb/>### Ambitus terræ continet, vult <lb/>Ariſtoteles # Stadia # 400000 <lb/># Milliaria # 50000 <lb/>Hipparchus # Stadia # 277000 <lb/># Milliaria # 34625 <lb/>Eratoſthenes # Stadia # 252000 <lb/># Milliaria # 31500 <lb/>Ptolemęus # Stadia # 180000 <lb/># Milliaria # 22500 <lb/>Alphraganus # Stadia # 163200 <lb/># Milliaria # 20400 <lb/>Fernelius # Stadia # 196114 {8/25} <lb/># Milliaria # 24514 {29/100} <lb/>Recentiores # Stadia # 152640 <lb/># Milliaria # 19080 <lb/>### Vnus gradus in terra continet, ut vult <lb/>Ariſtoteles # Stadia # 1111 {1/9} <lb/># Milliaria # 138 {8/9} <lb/>Hipparchus # Stadia # 769 {4/9} <lb/># Milliaria # 96 {13/72} <lb/>Eratoſthenes # Stadia # 700 <lb/># Milliaria # 87 {1/2} <lb/>Ptolemęus # Stadia # 500 <lb/># Milliaria # 62 {1/2} <lb/>Alphraganus # Stadia # 453 {5/3} <lb/># Milliaria # 56 {2/3} <lb/>Fernelius # Stadia # 544 {381/500} <lb/># Milliaria # 98 {381/4000} <lb/>Recentiores # Stadia # 424 <lb/># Milliaria # 53 <lb/>### Diameter terræ continet, ut vult <lb/>Ariſtoteles # Stadia # 127272 {8/15} <lb/># Milliaria # 15909 {1/11} <lb/>Hipparchus # Stadia # 88136 {4/11} <lb/># Milliaria # 11017 {1/11} <lb/>Eratoſthenes # Stadia # 80181 {9/11} <lb/># Milliaria # 10822 {8/11} <lb/>Ptolemęus # Stadia # 57272 {8/11} <lb/># Milliaria # 7159 {1/11} <lb/>Alphraganus # Stadia # 51927 {3/11} <lb/># Milliaria # 6490 {10/11} <lb/></note> <pb o="214" file="250" n="251" rhead="Comment. in I. Cap. Sphæræ"/> <note position="right" xml:space="preserve"> <lb/>Fernelius # Stadia # 62400 {3/275} <lb/># Milliaria # 7800 {3/2200} <lb/>Recentiores # Stadia # 48567 {3/11} <lb/># Milliaria # 6070 {10/11} <lb/>### Semidiameter terræ habet, vt vult. <lb/>Ariſtoteles # Stadia # 63636 {4/11} <lb/># Milliaria # 79548 {6/11} <lb/>Hipparchus # Stadia # 44069 {2/11} <lb/># Milliaria # 5508 {23/44} <lb/>Eratoſthenes # Stadia # 40090 {10/11} <lb/># Milliaria # 5011 {4/21} <lb/>Ptolemęus # Stadia # 28636 {4/11} <lb/># Milliaria # 3579 {6/11} <lb/>Alphraganus # Stadia # 25963 {7/11} <lb/># Milliaria # 3245 {5/11} <lb/>Fernelius # Stadia # 31200 {3/150} <lb/># Milliaria # 3900 {3/4400} <lb/>Recentiores # Stadia # 24283<unsure/> {7/11} <lb/># Milliaria # 3035 {@/11} <lb/>### Superficies conuexa terræ continet, vt vult. <lb/>Ptolemęus # Stadia # 10309090909 {1/11} <lb/># Milliaria # 161079545 {5/11} <lb/>Alphraganus # Stadia # 8474530909 {1/11} <lb/># Milliaria # 132414545 {5/15<unsure/>} <lb/>Fernelius # Stadia # 12237535707 {5893/13750} <lb/># Milliaria # 191211495 {377143/880000} <lb/>Recentiores # Stadia # 7413308509 {1/11} <lb/># Milliaria # 115832945 {5/11} <lb/></note> </div> <div xml:id="echoid-div425" type="section" level="1" n="132"> <head xml:id="echoid-head137" xml:space="preserve">DISTANTIÆ COELORVM A TERRA, <lb/>craſſitudinesq́ue, & Ambitus eorundem.</head> <p> <s xml:id="echoid-s8707" xml:space="preserve"><emph style="sc">Qvoniam</emph> vero verba fecimus de quantitate terræ tum ſecundum am-<lb/>bitum maximi airculi in ea deſcripti. </s> <s xml:id="echoid-s8708" xml:space="preserve">tum ſecundum diametrũ, ſemidiametrum <lb/>ſuperficiemq; </s> <s xml:id="echoid-s8709" xml:space="preserve">conuexam eius, non abs re fuerit, paucis quoque iudicare hoc <lb/>loco ſemidiametr@s, id eſt, diſtantias à centro mundi, omniũ cælorũ, craſſitudi-<lb/>nesq́;</s> <s xml:id="echoid-s8710" xml:space="preserve">, & </s> <s xml:id="echoid-s8711" xml:space="preserve">ambitus, ſiue circũferentias eorundẽ. </s> <s xml:id="echoid-s8712" xml:space="preserve">Id autem tribus tabulis exeque-<lb/>mur, quarũ prima continet omniũ cælorũ ſemidiametros: </s> <s xml:id="echoid-s8713" xml:space="preserve">Secunda uero eorũ <lb/>craſſitudines: </s> <s xml:id="echoid-s8714" xml:space="preserve">Tertia deniq́; </s> <s xml:id="echoid-s8715" xml:space="preserve">eorundẽ ambitus in circulis maximis, tã ſecundum <lb/>concauũ, quã ſecundũ conuexũ eorum. </s> <s xml:id="echoid-s8716" xml:space="preserve">Ex præceptis autem ſuperioribus facile <lb/>quiuis explorare poterit, ſi id deſideret, ſuperficies tã concauas, quã conuexas, <lb/>immo & </s> <s xml:id="echoid-s8717" xml:space="preserve">ſoliditates eorundem cælorum. </s> <s xml:id="echoid-s8718" xml:space="preserve">Secuti uero ſumus in his tabulis ferè <lb/>ſemper Franciſcum Maurolycum in appendice Dialogorũ de Coſmographia.</s> <s xml:id="echoid-s8719" xml:space="preserve"/> </p> <pb o="215" file="251" n="252" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve"> <lb/>### Semidiametri cęlorum tam ſecundum concauum, \\ quam ſecundum conuexum. <lb/>Semidiameter conuaui ☽, continet ſe \\ midiametro terrę 33 {7/10} # vel mil- \\ liaria # 120630 {15/22} <lb/>Semidiameter conuexi ☽, & concaui \\ ☿, continet ſemidiametros terrę 64 {1/6} # vel mil- \\ liaria # 229687 {1/2} <lb/>Semidiameter conuexi ☿, & comcaui \\ ♀, continet ſemidiametros terræ 167 {2/3} # vel mil- \\ liaria # 600167 {14/33} <lb/>Semidiameter conuexi ♀, uel concaui \\ ***, cõtinet ſemidiametros terrę 1121 {7/20} # vel mil- \\ liaria # 4013923 {7/22} <lb/>Semidiameter conuexi ***, vel concaui \\ ***, continet ſemidiametros terrę 1216 {1/12} # vel mil- \\ liaria # 4353025 {25/44} <lb/>Semidiameter conuexi ***, uel concaui \\ ♃, continet ſemidiametros terrę 8853 {3/4} # vel mil- \\ liaria # 31692400 {25/44} <lb/>Semidiameter conuexi ♃, uel concaui \\ variant, continet ſemidiametros terrę 14378 {1/3} # vel mil- \\ liaria # 51467897 {8/11} <lb/>Semidiameter conuexi variant, uel concaui \\ Fi<unsure/>rmamenti cõtinet ſemidiametros \\ terræ ſecundum Alphragnum 22612 {1/2} # vel mil- \\ liaria # 80942471 {13/22} <lb/>Semidiameter conuexi Firmamenti ſe- \\ cundum Alphragnum continet ſe- \\ mi<unsure/>diametros terræ 45225 # vel mil- \\ liaria # 161884941 {2/11<unsure/>} <lb/>### Craſſitudines cœlorum, quæ quidem habentur, ſi ſemidiametri vſque ad \\ concaua ſingulorum cęlorum extenſæ ex ſemidiametris vſ- \\ que ad eorundem conuexa porrectis ſubtrahantur. <lb/>Craſſitudo cœli ☽, continet \\ ſemidiametros terræ 31 {9/15} # vel mil- \\ liaria # 109056 {9/11} <lb/>Craſſitudo cęli ☿, continet \\ ſemidiametro terræ 103 {1/2} # vel mil- \\ liaria # 370579 {61/69} <lb/>Craſſitudo cęli ♀, continet \\ ſemidiametros terrę 933 {41/60} # vel mil \\ liaria # 34137755 {59/66} <lb/>Craſſitudo cœli ***, continet \\ ſemidiametros terrę 94 {11/15} # vel mil- \\ liaria # 339102 {1/4} <lb/>Craſſitudo cœli ***, continet \\ ſemidiametros terræ 7637 {2/3} # vel mil- \\ liaria # 27339375 <lb/>Craſſitudo cœli ♃, continet \\ ſemidiametros terrę 5524 {7/12} # vel mil- \\ liaria # 19775497 {7/44} <lb/>Craſſitudo cœli variant, continet \\ ſemidiametros terræ 8234 {1/6} # vel mil- \\ liaria # 29474573 {19/22} <lb/>Craſſitudo Firmamenti, continet, ex \\ Alphragano, ſemidiametros terræ 22612 {1/2} # vel mil \\ liaria # 80942571 {13/22} <lb/></note> <pb o="216" file="252" n="253" rhead="Comment. in II. Cap. Sphæræ"/> <note position="left" xml:space="preserve">Quot mil-<lb/>lial<unsure/>ia in 1. <lb/>hora pun-<lb/>ctum quod <lb/>uis Aequa-<lb/>toris con ſi-<lb/>ciat in Fir-<lb/>mamento.</note> <note position="right" xml:space="preserve"> <lb/>## Ambitus eęlorum tam ſecundum concauum, quàm \\ ſecundum conuexum ad milliaria reducti. <lb/>Ambitus concaui ☽, continet milliaria # 758250 <lb/>Ambitus conuexi ☽, uel concaui ☿, uel continet milliaria # 1443750 <lb/>Ambitus conuexi ☿, uel concaui ♀, continet milliaria. # 3772500 <lb/>Ambitus conuexi ♀, uel concaui ☽, continet milliaria # 25230375 <lb/>Ambitus conuexi ☽, uel concaui ***, continet milliaria. # 27361875 <lb/>Ambitus conuexi ***, uel concaui ♃, continet milliaria. # 199209375 <lb/>Ambitus conuexi ♃, uel concaui variant, continet milliaria. # 323512500 <lb/>Ambitus cõuexi variant, uel cõcaui Firmamẽti continet milliaria # 508781250 <lb/>Ambitus conuexi Firmamenti continet milliaria # 1017562500 <lb/> </note> <p> <s xml:id="echoid-s8720" xml:space="preserve">Ex his conſtat, punctum quodlibet Firmamenti in Aequatore poſitũ con-<lb/>ſicere ſingulis horis milliaria 42398437 {1/2}. </s> <s xml:id="echoid-s8721" xml:space="preserve">quoniam uidelicet in 24. </s> <s xml:id="echoid-s8722" xml:space="preserve">horis ab-<lb/>ſoluit milliaria 1017562500. </s> <s xml:id="echoid-s8723" xml:space="preserve">Ex quo fit, co gitatione uix apptehendi poſſe ce-<lb/>leritatem motus Firmamẽti, quod antiquitas primum mobile putauit eſſe. </s> <s xml:id="echoid-s8724" xml:space="preserve">Id <lb/>quod & </s> <s xml:id="echoid-s8725" xml:space="preserve">Ariſtoteles aſſirmauit. </s> <s xml:id="echoid-s8726" xml:space="preserve">Eſt enim tantum illud ſpatium, quod in 1. </s> <s xml:id="echoid-s8727" xml:space="preserve">ho-<lb/>ra punctum Æquatoris quoduis in Firmamenti conuexo conficit, quantum <lb/>uix in annis 2904. </s> <s xml:id="echoid-s8728" xml:space="preserve">peragraret quis, etiam ſi quotidie ſine ulla intermiſſione <lb/>40. </s> <s xml:id="echoid-s8729" xml:space="preserve">milliaria cõficeret, quod incredibile uidetur. </s> <s xml:id="echoid-s8730" xml:space="preserve">Nam uelocior eſt motus illius <lb/> <anchor type="note" xlink:label="note-252-03a" xlink:href="note-252-03"/> puncti, quam motus ſagittæ alicuius, aut uis, quæ in eo temporis ſpatio, quo <lb/>ſemel ſalutatio angelica recitatur, cõficeret milliaria 176660 hoc eſt, circum <lb/>iret totam terram ab ortu in occaſum ſub Æquatore ſæpius, quàm ſepties; <lb/></s> <s xml:id="echoid-s8731" xml:space="preserve">cum ambitus terrę milliariorum 22500. </s> <s xml:id="echoid-s8732" xml:space="preserve">in hoc numero 176660. </s> <s xml:id="echoid-s8733" xml:space="preserve">contineatur <lb/>ſæpius; </s> <s xml:id="echoid-s8734" xml:space="preserve">quàm ſepties, quæ uelocitas captum ingenij humani excedit. </s> <s xml:id="echoid-s8735" xml:space="preserve">Hoc au-<lb/>tem ita eſſe, fac le ſibi quiuis perſuadebit, ſi attente conſideret, in quadrante <lb/>unius horæ u<unsure/>ix dici poſſe 60. </s> <s xml:id="echoid-s8736" xml:space="preserve">ſalutationes angelicas, atq; </s> <s xml:id="echoid-s8737" xml:space="preserve">adeo 240. </s> <s xml:id="echoid-s8738" xml:space="preserve">in 1. </s> <s xml:id="echoid-s8739" xml:space="preserve">hora. </s> <s xml:id="echoid-s8740" xml:space="preserve"><lb/>Hinc. </s> <s xml:id="echoid-s8741" xml:space="preserve">n. </s> <s xml:id="echoid-s8742" xml:space="preserve">efficitur, tempus, quo angelica ſalutatio ſemel recitatur, eſſe {1/240}. </s> <s xml:id="echoid-s8743" xml:space="preserve"><lb/>unius horę: </s> <s xml:id="echoid-s8744" xml:space="preserve">conſtat autem punctum Aequatoris in Firmamenti conuexo cõfi-<lb/>cere milliaria 176660. </s> <s xml:id="echoid-s8745" xml:space="preserve">in {1/240}. </s> <s xml:id="echoid-s8746" xml:space="preserve">vnius horę, cũ in 1. </s> <s xml:id="echoid-s8747" xml:space="preserve">hora milliaria 42398437 <lb/>{1/2}. </s> <s xml:id="echoid-s8748" xml:space="preserve">abſoluat, ut diximus. </s> <s xml:id="echoid-s8749" xml:space="preserve">Quare neceſſe eſt, ut ſagitta, aut auis conficiat quoq; </s> <s xml:id="echoid-s8750" xml:space="preserve"><lb/>milliaria 176660. </s> <s xml:id="echoid-s8751" xml:space="preserve">hoc eſt, circumeat terram ſępius, quàm ſepties, in ſpatio tem <lb/>poris unius ſalutationis angelicæ, ſi motum Firmamenti conſequi uelit. </s> <s xml:id="echoid-s8752" xml:space="preserve">Vel <lb/>(ſi maius) tanta eſt uelocitas motus illius puncti Firmamenti in 1. </s> <s xml:id="echoid-s8753" xml:space="preserve">hora, quan-<lb/>ta eſſet alicuius ſagittæ, aut auis, quæ totam terram ab ortu in occaſum ſub <lb/>Æquatore in 1. </s> <s xml:id="echoid-s8754" xml:space="preserve">hora circnmiret millies, octingẽties, octogies, & </s> <s xml:id="echoid-s8755" xml:space="preserve">quater; </s> <s xml:id="echoid-s8756" xml:space="preserve">quod <lb/>terrę ambitus milliaria complectens 22500. </s> <s xml:id="echoid-s8757" xml:space="preserve">contineatur in miliarijs <lb/> <anchor type="note" xlink:label="note-252-04a" xlink:href="note-252-04"/> 42398437 {1/2}. </s> <s xml:id="echoid-s8758" xml:space="preserve">(quæ in 1. </s> <s xml:id="echoid-s8759" xml:space="preserve">hora ab illo puncto Aequatoris conficiuntur,) toties, <lb/>quot unitates ſunt in hoc numero 1885. </s> <s xml:id="echoid-s8760" xml:space="preserve">& </s> <s xml:id="echoid-s8761" xml:space="preserve">amplius, quæ celeritas ęgre conci-<lb/>pi poteſt.</s> <s xml:id="echoid-s8762" xml:space="preserve"/> </p> <div xml:id="echoid-div425" type="float" level="2" n="1"> <note position="left" xlink:label="note-252-03" xlink:href="note-252-03a" xml:space="preserve">Mirab@lis <lb/>velocitas <lb/>Firmamen <lb/>@i<unsure/>.</note> <note position="left" xlink:label="note-252-04" xlink:href="note-252-04a" xml:space="preserve">Circulum à <lb/>ſtella pola-<lb/>ri deſcriptũ <lb/>tantę eſſe <lb/>magnitudi-<lb/>@is, ut in <lb/>tra illũ to-<lb/>ta ſphera So <lb/>lis colloca-<lb/>ta eum non <lb/>tangat.</note> </div> <p> <s xml:id="echoid-s8763" xml:space="preserve"><emph style="sc">Rvrsvs</emph> ex his, quæ diximus, colligere licebit, ſtellam polarem, quæ no <lb/>ſtro tempore à polo ar<unsure/>ctico abeſt ferme grad. </s> <s xml:id="echoid-s8764" xml:space="preserve">3 {1/2}. </s> <s xml:id="echoid-s8765" xml:space="preserve">deſcribere circulum, culus <lb/>diameter multo maior eſt, quàm diameter totius cęli Solis: </s> <s xml:id="echoid-s8766" xml:space="preserve">adeo ut tota ſphæ-<lb/>ra Solis intra illum circulum collocata eum non tangeret, quod prorſus uide <lb/>tur incr<unsure/>edibile, cum ſiella pola@is uix locum murare uideatur. </s> <s xml:id="echoid-s8767" xml:space="preserve">Hoc autem ita <pb o="217" file="253" n="254" rhead="Ioan. de Sacro Boſco."/> colligetur. </s> <s xml:id="echoid-s8768" xml:space="preserve">Quoniam ſemidiameter conuexi Firmamenti continet ſemidia-<lb/>metros terræ 45225. </s> <s xml:id="echoid-s8769" xml:space="preserve">ſi fiat, ut ſinus totus 100000. </s> <s xml:id="echoid-s8770" xml:space="preserve">ad 45225. </s> <s xml:id="echoid-s8771" xml:space="preserve">ſemidiametrum <lb/>Firmamenti, ita 12208. </s> <s xml:id="echoid-s8772" xml:space="preserve">chorda graduum 7. </s> <s xml:id="echoid-s8773" xml:space="preserve">quibus diameter dicti circuli ſtellę <lb/>polaris ſubtenditur; </s> <s xml:id="echoid-s8774" xml:space="preserve">inuenietur dicta chorda, ſiue diameter illius circuli conti <lb/>nere 5521. </s> <s xml:id="echoid-s8775" xml:space="preserve">ſemidiametros terræ. </s> <s xml:id="echoid-s8776" xml:space="preserve">Cum ergo diameter conuexi ſphæræ Solaris <lb/>cõplectatur ſemidiametros terræ duntaxat 2432. </s> <s xml:id="echoid-s8777" xml:space="preserve">& </s> <s xml:id="echoid-s8778" xml:space="preserve">paulo amplius, perſpicuum <lb/>eſt, diametrum ſphæræ Solis non efficere dimidium diametri prædicti circuli. <lb/></s> <s xml:id="echoid-s8779" xml:space="preserve">Quare cum circuli habeant proportionem diametrorum duplicatam, nempe <lb/>eam, quam diametrorum quadrata habent; </s> <s xml:id="echoid-s8780" xml:space="preserve">erit circulus maximus in ſphęra So <lb/> <anchor type="note" xlink:label="note-253-01a" xlink:href="note-253-01"/> lis minor quàm {1/4}. </s> <s xml:id="echoid-s8781" xml:space="preserve">dicti circuli. </s> <s xml:id="echoid-s8782" xml:space="preserve">Ex quo ſequitur, ſphæram Solis intra illum <lb/>circulum poſitum dictum circulum nequaquam tangere poſſe.</s> <s xml:id="echoid-s8783" xml:space="preserve"/> </p> <div xml:id="echoid-div426" type="float" level="2" n="2"> <note position="right" xlink:label="note-253-01" xlink:href="note-253-01a" xml:space="preserve">2. duod.</note> </div> </div> <div xml:id="echoid-div428" type="section" level="1" n="133"> <head xml:id="echoid-head138" xml:space="preserve">DIGRESSIO DE ARENAE NVMERO.</head> <p> <s xml:id="echoid-s8784" xml:space="preserve">ARCHIMEDIS tempore (vt ipſemet in lib. </s> <s xml:id="echoid-s8785" xml:space="preserve">de arenæ numero refert) <lb/> <anchor type="note" xlink:label="note-253-02a" xlink:href="note-253-02"/> arbitrabantur nonnulli, numerum arenæ, non quidem ſolum eius, quæ circa <lb/>Syracuſas, & </s> <s xml:id="echoid-s8786" xml:space="preserve">reliquam Siciliam, ſed & </s> <s xml:id="echoid-s8787" xml:space="preserve">illius, quæ in omni regione habitabili, <lb/>pariter atque in habitabili continetur, infinitum eſſe. </s> <s xml:id="echoid-s8788" xml:space="preserve">Alij uero, non quidẽ eſſe <lb/>inſinitum dicebant eum arenæ numerum, propterea quòd infinitum dari non <lb/>poſſit, ſed nullum dari poſſe determinatũ numerum credebant, qui illius mul-<lb/>titudinem exuperaret, aut ei par eſſet; </s> <s xml:id="echoid-s8789" xml:space="preserve">immo uero potius è contrario, nume-<lb/>rum quemcunque propoſitum, & </s> <s xml:id="echoid-s8790" xml:space="preserve">determinatum, à numero illo arenæ ſupera-<lb/>tum it<unsure/>i. </s> <s xml:id="echoid-s8791" xml:space="preserve">Ex quo infert Archimedes, eos, qui ita opinantur, ſi eiuſmodi aerenæ <lb/>aceruum animo comprehenderent, cuiuſmodi eſſet, ſi uniuerſæ terra, reple-<lb/>to in ea mari, & </s> <s xml:id="echoid-s8792" xml:space="preserve">cauitatibus omnibus, altiſſimorum montium uertices exæ-<lb/>quaret, atque huius ipſius rurſus alterum multiplicem excogitarent, ſine ul-<lb/>lo dubio exiſtimaturos, illius multitudinem numeros omnes longe, multũq́; <lb/></s> <s xml:id="echoid-s8793" xml:space="preserve">ſuperare. </s> <s xml:id="echoid-s8794" xml:space="preserve">Horum omnium errorem Archimedes in eo lib. </s> <s xml:id="echoid-s8795" xml:space="preserve">quem de Arenæ nu <lb/>mero inſcripſit, Geometrice, & </s> <s xml:id="echoid-s8796" xml:space="preserve">quidem acutiſſime reſellit, inueſtigãs numerũ, <lb/>qui non ſolum arenæ multitudinem ſuperet, quæ terræ undique repletæ, ut di <lb/>ximus, æqualis eſſet, ſed etiam quæ ipſi mundo (poſito etiam mundo multo <lb/>maiore, quàm re ipſa eſt) parem haberet magnitudinem. </s> <s xml:id="echoid-s8797" xml:space="preserve">Atque hoc eſt Archi-<lb/> <anchor type="note" xlink:label="note-253-03a" xlink:href="note-253-03"/> medi propoſitum in lib. </s> <s xml:id="echoid-s8798" xml:space="preserve">de arenæ numero, ubi prius ſubtili quadam ratione de <lb/>monſtrat, quanam uia diſtantia Solis à terra ſit inueſtiganda, inuento prius an <lb/>gulo, qui minor ſit angulo, quem duæ lineæ rectę à centro uiſus egredientes, <lb/>Solemq́ue tangentes comprehendunt, qua de re conſule eius ſcripta, & </s> <s xml:id="echoid-s8799" xml:space="preserve">com-<lb/>mentarios Federici Commandini.</s> <s xml:id="echoid-s8800" xml:space="preserve"/> </p> <div xml:id="echoid-div428" type="float" level="2" n="1"> <note position="right" xlink:label="note-253-02" xlink:href="note-253-02a" xml:space="preserve">Arenæ nu-<lb/>merum ſe-<lb/>cũdũ quoſ <lb/>dam eſſe in<unsure/> <lb/>finitum, ſe-<lb/>cũ dũ quoſ-<lb/>dã uero fi-<lb/>nitũ quidẽ, <lb/>ſed ab om-<lb/>ni dato nu-<lb/>mero ſupe-<lb/>rari.</note> <note position="right" xlink:label="note-253-03" xlink:href="note-253-03a" xml:space="preserve">Archime-<lb/>dis propoſi <lb/>tum in lib. <lb/>de arenæ <lb/>numero.</note> </div> <p> <s xml:id="echoid-s8801" xml:space="preserve">Nos igitur ueſtigiis Archimedis inh ærentes, numerum quoque inquire-<lb/>mus, qui longe maior ſit numero arenæ, etiam minutiſſimæ, quæ totum mun-<lb/>dum uſque ad Firmamentum repleret. </s> <s xml:id="echoid-s8802" xml:space="preserve">Multi enim à me contenderunt, ut hoc <lb/>loco rem hanc explicarem. </s> <s xml:id="echoid-s8803" xml:space="preserve">Quod quidem eo libentius feci, quod ſciam, id mul <lb/>tis fore iucundiſſimum; </s> <s xml:id="echoid-s8804" xml:space="preserve">præſertim uero quòd negotium hoc non ſit prorſus à <lb/>noſtro inſtituto alienum: </s> <s xml:id="echoid-s8805" xml:space="preserve">quando quidem multa hoc loco adduximus de diftã <lb/>tiis, ac magnitudinibus cœlorum, ex quibus facili negotio id, quod propoſui-<lb/>mus, colligere poſſumus. </s> <s xml:id="echoid-s8806" xml:space="preserve">Vt autem illuſtrior, atque admirabilior diſputatio <lb/>noſtra euadat, ponamus totum mundum ad Firmamentum uſque longe maio <lb/>rem eſſe, quàm ab Aſtronomis deprehenſus eſt; </s> <s xml:id="echoid-s8807" xml:space="preserve">Item arenulas mundum uniuer <lb/>ſum replentes multò eſſe maiores, quàm vſpiam reperiuntur. </s> <s xml:id="echoid-s8808" xml:space="preserve">Nam ſi demon- <pb o="218" file="254" n="255" rhead="Comment. in I. cap. Sphæræ"/> ſtratum à nobis fuerit, numerum à nobis inuentum maiorem eſſe numerum <lb/>arenularum minorum, quàm vſpiam ſint, & </s> <s xml:id="echoid-s8809" xml:space="preserve">maiorem mundum replentium, <lb/>quàm noſter hic mundus ſit: </s> <s xml:id="echoid-s8810" xml:space="preserve">perſpicuum erit, eundem numerum multo maio-<lb/>rem eſſe numero arenularum etiam minutiſſimarum in rerum natura exiſten-<lb/>tium, quæ totum mundum ad Firmamentum uſque, quantus ab Aſtronomis <lb/>deprehenſus eſt, replerent. </s> <s xml:id="echoid-s8811" xml:space="preserve">Hæc ergo ordine à nobis ponantur.</s> <s xml:id="echoid-s8812" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8813" xml:space="preserve">I. </s> <s xml:id="echoid-s8814" xml:space="preserve"><emph style="sc">Terr ae</emph> diametrum multo minorem eſſe, quàm milliariorũ 10000. <lb/></s> <s xml:id="echoid-s8815" xml:space="preserve">quod quidem licet ueriſſimum ſit, cum ſecundum Ptolemæum, & </s> <s xml:id="echoid-s8816" xml:space="preserve">communio-<lb/>rem Aſtronomorum ſententiam, diameter terrę contineat ſolum milliaria <lb/>7159 {1/11}. </s> <s xml:id="echoid-s8817" xml:space="preserve">vt ſupra diximus, tamẽ ut & </s> <s xml:id="echoid-s8818" xml:space="preserve">facilior reddatur ſupputatio, & </s> <s xml:id="echoid-s8819" xml:space="preserve">maio-<lb/>rem mundum efficiamus, quàm re ipſa eſt, eam ſtatuamus milliariorũ 10000.</s> <s xml:id="echoid-s8820" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8821" xml:space="preserve">II. </s> <s xml:id="echoid-s8822" xml:space="preserve"><emph style="sc">Diametrvm</emph> concaui Firmamenti longe minorem eſſe, quàm <lb/>100000. </s> <s xml:id="echoid-s8823" xml:space="preserve">diametrorum terræ; </s> <s xml:id="echoid-s8824" xml:space="preserve">quod licet uerum ſit, cum ſecundum Alphraga-<lb/>num diameter illa comprehendat diametros terræ duntaxat 45225. </s> <s xml:id="echoid-s8825" xml:space="preserve">eam ta-<lb/>men accipiamus continere 100000. </s> <s xml:id="echoid-s8826" xml:space="preserve">diametros terrę, propter cauſam ante ad-<lb/>ductam. </s> <s xml:id="echoid-s8827" xml:space="preserve">Et quoniã terrę diametrum aſſumpſimus complecti milliaria 10000. <lb/></s> <s xml:id="echoid-s8828" xml:space="preserve">(cum tamen multo minor ſit) continebit diameter concaui Firmamenti pau-<lb/>ciora milliaria, quàm 1000000000. </s> <s xml:id="echoid-s8829" xml:space="preserve">Sed ob rationem dictam ponamus illam <lb/>comprehendere milliaria 1000000000.</s> <s xml:id="echoid-s8830" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8831" xml:space="preserve">III. </s> <s xml:id="echoid-s8832" xml:space="preserve"><emph style="sc">Sphaervlam</emph>, quę ęqualis ſit uni grano papaueris, maiorẽ non <lb/>eſſe arenulis 10000. </s> <s xml:id="echoid-s8833" xml:space="preserve">quantumuis minimis. </s> <s xml:id="echoid-s8834" xml:space="preserve">Id quod facile quiuis concedet, cum <lb/>vix intellectus capere poſſit, unum granum papaueris diuidi poſſet in 10000. <lb/></s> <s xml:id="echoid-s8835" xml:space="preserve">particulas ęquales: </s> <s xml:id="echoid-s8836" xml:space="preserve">@eque enim tam exiguę arenulę alicubi uiſę ſunt. </s> <s xml:id="echoid-s8837" xml:space="preserve">Verum <lb/>ut & </s> <s xml:id="echoid-s8838" xml:space="preserve">admirabilior fiat demonſtratio, & </s> <s xml:id="echoid-s8839" xml:space="preserve">plures arenulę in mundo continean-<lb/>tur, ſtatuamus illam ſphęrulam comprehendere 10000. </s> <s xml:id="echoid-s8840" xml:space="preserve">arenulas.</s> <s xml:id="echoid-s8841" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8842" xml:space="preserve">IIII. </s> <s xml:id="echoid-s8843" xml:space="preserve"><emph style="sc">Diametrvm</emph> grani papaueris minorem non eſſe parte qua-<lb/>drageſima unius digiti Geometrici. </s> <s xml:id="echoid-s8844" xml:space="preserve">Hoc ita eſſe, expertus eſt Archimedes, <lb/>qui dicit, ſe inueniſſe, grana papaueris 35. </s> <s xml:id="echoid-s8845" xml:space="preserve">in una linea recta poſita, & </s> <s xml:id="echoid-s8846" xml:space="preserve">ſe inui-<lb/>cem tangentia, longitudinem digiti Geometrici ſuperare: </s> <s xml:id="echoid-s8847" xml:space="preserve">adeo ut unum gra-<lb/>num papaueris maius ſit, quàm {1/35}. </s> <s xml:id="echoid-s8848" xml:space="preserve">digiti. </s> <s xml:id="echoid-s8849" xml:space="preserve">Ex quo fit, unum granum papa-<lb/>ueris multo maius eſſe quàm {1/40}. </s> <s xml:id="echoid-s8850" xml:space="preserve">digiti, nõ autem minus. </s> <s xml:id="echoid-s8851" xml:space="preserve">Nos autem ſtatua <lb/>mus, illud eſſe {1/40}. </s> <s xml:id="echoid-s8852" xml:space="preserve">digiti, ut euidentior fiat demonſtratio, quamuis tam mi-<lb/>nuta grana papaueris non reperiantur.</s> <s xml:id="echoid-s8853" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8854" xml:space="preserve">V. </s> <s xml:id="echoid-s8855" xml:space="preserve"><emph style="sc">Milliarivm</emph> eſſe longe minus, quàm 100000. </s> <s xml:id="echoid-s8856" xml:space="preserve">digitorum. </s> <s xml:id="echoid-s8857" xml:space="preserve">Nam <lb/>cum quatuor digiti conſtituant palmum, & </s> <s xml:id="echoid-s8858" xml:space="preserve">quatuor pal mi pedem, & </s> <s xml:id="echoid-s8859" xml:space="preserve">quinque <lb/>pedes paſſum Geometricum, & </s> <s xml:id="echoid-s8860" xml:space="preserve">mille paſſus Geometrici milliare; </s> <s xml:id="echoid-s8861" xml:space="preserve">effi citur, <lb/> <anchor type="note" xlink:label="note-254-01a" xlink:href="note-254-01"/> 80000. </s> <s xml:id="echoid-s8862" xml:space="preserve">digitos componere unum milliare. </s> <s xml:id="echoid-s8863" xml:space="preserve">Quare multo minus eſt milliare, <lb/>quàm 100000. </s> <s xml:id="echoid-s8864" xml:space="preserve">digitorum. </s> <s xml:id="echoid-s8865" xml:space="preserve">Ponamus tamen, ut facilior demonſtratio fiat, digi-<lb/>tos 100000. </s> <s xml:id="echoid-s8866" xml:space="preserve">conficere unum milliare.</s> <s xml:id="echoid-s8867" xml:space="preserve"/> </p> <div xml:id="echoid-div429" type="float" level="2" n="2"> <note position="left" xlink:label="note-254-01" xlink:href="note-254-01a" xml:space="preserve">Qua ratio-<lb/>ne numer@ <lb/>a@enularũ <lb/>totum mũ-<lb/>dum uſque <lb/>ad cõcauũ <lb/>Firmamen <lb/>ti replentiũ <lb/>inueſt@ge-<lb/>tur.</note> </div> <p> <s xml:id="echoid-s8868" xml:space="preserve"><emph style="sc">Ita qve</emph> quoniam poſitum eſt, diametrum grani papaueris {1/40}. </s> <s xml:id="echoid-s8869" xml:space="preserve">digi-<lb/>ti, (licet multo minus ſit) ita ut 40. </s> <s xml:id="echoid-s8870" xml:space="preserve">grana papaueris digitum conſtituant: </s> <s xml:id="echoid-s8871" xml:space="preserve">ha-<lb/>bebit ſphęra, cuius diameter digito ſit ęqualis, ad granum papaueris propor-<lb/>tionem, quam 64000. </s> <s xml:id="echoid-s8872" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s8873" xml:space="preserve">quandoquidem ſphærę habent propor-<lb/> <anchor type="note" xlink:label="note-254-02a" xlink:href="note-254-02"/> <anchor type="note" xlink:label="note-254-03a" xlink:href="note-254-03"/> tionem diametrorum triplicatam: </s> <s xml:id="echoid-s8874" xml:space="preserve">Vt in appoſitis his quatuor nu-<lb/>meris continuè proportionalibus in proportione 40 diametrorum <lb/>grani papaueris, hoc eſt in proportione digiti, ad 1. </s> <s xml:id="echoid-s8875" xml:space="preserve">apparet; </s> <s xml:id="echoid-s8876" xml:space="preserve">ita ut <lb/>ſphęra diametrum habens digito æqualem contineat grana papaue <lb/>ris 64000. </s> <s xml:id="echoid-s8877" xml:space="preserve">Quare cum ſtatuerimus, unum granum papaueris cõtine <pb o="219" file="255" n="256" rhead="Ioan. de Sacro Boſco."/> re arenulas 10000. </s> <s xml:id="echoid-s8878" xml:space="preserve">cõplectetur eadẽ ſdhæra diametrum habens digito æqualẽ <lb/>arenulas 640000000. </s> <s xml:id="echoid-s8879" xml:space="preserve">immo multo maior erit hic numer<emph style="sub">9</emph> numero arenularũ, <lb/>quæ in ſphæra diametiũ digito ęqualem habente includitur: </s> <s xml:id="echoid-s8880" xml:space="preserve">propterea quòd <lb/>& </s> <s xml:id="echoid-s8881" xml:space="preserve">pauciora grana papaueris, quàm 40. </s> <s xml:id="echoid-s8882" xml:space="preserve">digitũ conſtituunt, & </s> <s xml:id="echoid-s8883" xml:space="preserve">arenulæ maiores <lb/>ſunt, quàm ut 10000. </s> <s xml:id="echoid-s8884" xml:space="preserve">unum granum papaueris efficere poſſint. </s> <s xml:id="echoid-s8885" xml:space="preserve">Nos tamen, <lb/>ut ſupputatio ſit expeditior, ponamus ſphæram, cuius diameter ſit digito <lb/>æqualis, compre hendere arenulas non ſolum 640000000. </s> <s xml:id="echoid-s8886" xml:space="preserve">ſed 1000000000.</s> <s xml:id="echoid-s8887" xml:space="preserve"/> </p> <div xml:id="echoid-div430" type="float" level="2" n="3"> <note position="left" xlink:label="note-254-02" xlink:href="note-254-02a" xml:space="preserve">18. duod.</note> <note position="right" xlink:label="note-254-03" xlink:href="note-254-03a" xml:space="preserve"> <lb/>1 <lb/>40 <lb/>1600 <lb/>64000 <lb/>. . <lb/></note> </div> <p> <s xml:id="echoid-s8888" xml:space="preserve"><emph style="sc">Deinde</emph> quia accepimus, digitos 100000. </s> <s xml:id="echoid-s8889" xml:space="preserve">conſtituere unum milliare, <lb/>licet milliare multo minus ſit; </s> <s xml:id="echoid-s8890" xml:space="preserve">habebit ſphæra diametrum habens milliari æ-<lb/>qualem ad ſphæram, quæ diametrum digito æqualem habeat, proportionem, <lb/>quam 1000000000000000. </s> <s xml:id="echoid-s8891" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s8892" xml:space="preserve">propterea quod ſphærę habent triplicatam <lb/>proportionem diametrorum: </s> <s xml:id="echoid-s8893" xml:space="preserve">ut in quatuor his nu-<lb/> <anchor type="note" xlink:label="note-255-01a" xlink:href="note-255-01"/> <anchor type="note" xlink:label="note-255-02a" xlink:href="note-255-02"/> meris appatet, qui continue proportionales ſunt <lb/>in proportione 100000. </s> <s xml:id="echoid-s8894" xml:space="preserve">digitorum, hoc eſt, in pro-<lb/>portione unius milliarij, ad 1. </s> <s xml:id="echoid-s8895" xml:space="preserve">Cum ergo ſphęra dia <lb/>metrum habens digito ęqualem poſita ſit cõtinere <lb/>arenulas 1000000000. </s> <s xml:id="echoid-s8896" xml:space="preserve">quamuis lõge pauciores cõ-<lb/>tineat, ut oſtenſum eſt: </s> <s xml:id="echoid-s8897" xml:space="preserve">continebit ſphæra, cuius diameter milliario ſit æqua-<lb/>lis, has omnes arenulas 1000000000000000000000000. </s> <s xml:id="echoid-s8898" xml:space="preserve">immo hic numerus <lb/>multo maior erit numero arenularum, quæ in ſphæra diametrum milliario <lb/>æqualem habente continetur; </s> <s xml:id="echoid-s8899" xml:space="preserve">propterea quòd & </s> <s xml:id="echoid-s8900" xml:space="preserve">pauciores arenulæ, quàm <lb/>1000000000. </s> <s xml:id="echoid-s8901" xml:space="preserve">ſphæram replent, cuius diameter digito ſit æqualis, & </s> <s xml:id="echoid-s8902" xml:space="preserve">pauciores <lb/>digiti, quàm 100000. </s> <s xml:id="echoid-s8903" xml:space="preserve">milliarium efficiunt. </s> <s xml:id="echoid-s8904" xml:space="preserve">Nos tamen, ob cauſam paulo ante <lb/>dictam, recipiamus arenulas 1000000000000000000000000. </s> <s xml:id="echoid-s8905" xml:space="preserve">replere ſphęrã, <lb/>cuius diameter milliario ſit ęqualis.</s> <s xml:id="echoid-s8906" xml:space="preserve"/> </p> <div xml:id="echoid-div431" type="float" level="2" n="4"> <note position="right" xlink:label="note-255-01" xlink:href="note-255-01a" xml:space="preserve">18. duod.</note> <note position="right" xlink:label="note-255-02" xlink:href="note-255-02a" xml:space="preserve"> <lb/>1 <lb/>100000 <lb/>10000000000 <lb/>1000000000000000 <lb/></note> </div> <p> <s xml:id="echoid-s8907" xml:space="preserve"><emph style="sc">Postremo</emph> cum poſitũ à nobis ſit, diametrũ cõcaui Firmamẽti cõplecti <lb/>milliaria 1000000000. </s> <s xml:id="echoid-s8908" xml:space="preserve">quãuis re ipſa multo minor ſit: </s> <s xml:id="echoid-s8909" xml:space="preserve">habebit ſphęra, cuius <lb/>diameter ęqualis ſit diametro cõcaui Firmamẽti, ad ſpherã, quę diametrũ mil <lb/>liario ęqualẽ habeat proportionem, ꝗ̃ 1000000000000000000000000000. <lb/></s> <s xml:id="echoid-s8910" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s8911" xml:space="preserve">propterea quod ſphęrę proportionem habent triplicatam diametrorum. </s> <s xml:id="echoid-s8912" xml:space="preserve"><lb/>ut patet in his quatuor numeris, qui <lb/> <anchor type="note" xlink:label="note-255-03a" xlink:href="note-255-03"/> continuam proportionem habent in <lb/> <anchor type="note" xlink:label="note-255-04a" xlink:href="note-255-04"/> proportione 1000000000. </s> <s xml:id="echoid-s8913" xml:space="preserve">milliario <lb/>rum, ideſt, in proportione diametri <lb/>concaui Firmamenti, ad 1. </s> <s xml:id="echoid-s8914" xml:space="preserve">Quare eũ <lb/>ſphęra diametrum habens milliario <lb/>ęqualem poſita ſit continere arenulas 1000000000000000000000000. </s> <s xml:id="echoid-s8915" xml:space="preserve">li-<lb/>cet multo pauciores re ipſa includat, ut demonſtrauimus: </s> <s xml:id="echoid-s8916" xml:space="preserve">continebit ſphæra <lb/> <anchor type="note" xlink:label="note-255-05a" xlink:href="note-255-05"/> initra concauum Firmamenti tõprehenſa, ipſumq; </s> <s xml:id="echoid-s8917" xml:space="preserve">prorſus att ngens, arenulas <lb/>000000000000000000000000000000000000000000000000000 <lb/>. </s> <s xml:id="echoid-s8918" xml:space="preserve">. </s> <s xml:id="echoid-s8919" xml:space="preserve">. </s> <s xml:id="echoid-s8920" xml:space="preserve">. </s> <s xml:id="echoid-s8921" xml:space="preserve">. </s> <s xml:id="echoid-s8922" xml:space="preserve">. </s> <s xml:id="echoid-s8923" xml:space="preserve">. </s> <s xml:id="echoid-s8924" xml:space="preserve">. </s> <s xml:id="echoid-s8925" xml:space="preserve">. <lb/></s> <s xml:id="echoid-s8926" xml:space="preserve">immo numerus hic longe maior erit numero arenularum, quę in toto mun-<lb/>do uſque ad concauum Firmamenti continentur: </s> <s xml:id="echoid-s8927" xml:space="preserve">propterea quòd & </s> <s xml:id="echoid-s8928" xml:space="preserve">paucio-<lb/>res arenulæ, quàm 1000000000000000000000000. </s> <s xml:id="echoid-s8929" xml:space="preserve">ſphęram replent haben-<lb/>tem diametrũ mill iario ęqualem, & </s> <s xml:id="echoid-s8930" xml:space="preserve">pauciora milliaria, quàm 1000000000. </s> <s xml:id="echoid-s8931" xml:space="preserve"><lb/>in diametro concaui Firmamenti continentur. </s> <s xml:id="echoid-s8932" xml:space="preserve">Numerus ergo ultimo loco in <lb/>uentus, qui nimirum poſt figuram 1. </s> <s xml:id="echoid-s8933" xml:space="preserve">habet 51. </s> <s xml:id="echoid-s8934" xml:space="preserve">cifras, longe maior eſt numero <lb/>arenularum totum mundum uſque ad concauum Firmamenti replentium, <pb o="220" file="256" n="257" rhead="Comment. in I. Cap. Sphæræ"/> etiamſi arenulæ tam exiguæ eſſent, vt 10000. </s> <s xml:id="echoid-s8935" xml:space="preserve">efficerent ſphærulam grano, pa <lb/>paueris ęqualem.</s> <s xml:id="echoid-s8936" xml:space="preserve"/> </p> <div xml:id="echoid-div432" type="float" level="2" n="5"> <note position="right" xlink:label="note-255-03" xlink:href="note-255-03a" xml:space="preserve">18. duod.</note> <note position="right" xlink:label="note-255-04" xlink:href="note-255-04a" xml:space="preserve"> <lb/>1000000000 <lb/>1000000000000000000 <lb/>1000000000000000000000000000 <lb/></note> <note position="right" xlink:label="note-255-05" xlink:href="note-255-05a" xml:space="preserve">Qui nume <lb/>rus maior <lb/>ſit numero <lb/>arenularũ, <lb/>q̃@ũ 10000. <lb/>grano papa <lb/>ueris æqua <lb/>les ſint re-<lb/>plentiũ to-<lb/>tuni mũ dũ <lb/>uſque ad <lb/>concauum <lb/>Firmamẽt@</note> </div> <p> <s xml:id="echoid-s8937" xml:space="preserve"><emph style="sc">Liqvido</emph> ergo ex dictis conſtat, nos certò deprehendere poſſe, quot <lb/>arenulæ totum mundum replere poſſent, ſi nobis eſſet exploratum, quot are-<lb/>nulæ grano papaueris fint æquales, & </s> <s xml:id="echoid-s8938" xml:space="preserve">quot grana papaueris digitum conſti-<lb/>tuant, ac denique quot milliaria, quorum ſingula 80000. </s> <s xml:id="echoid-s8939" xml:space="preserve">digitos continent, in <lb/>diametro concaui Firmamenti comprehendatur. </s> <s xml:id="echoid-s8940" xml:space="preserve">Sed quoniam hæc adhuc <lb/>ignota ſunt, atque incerta, aſſumpſimus (Archimedẽ in hoc ſecuti) diametrum <lb/>mundi multo maiorem, quàm re ipſa ſit ſecundum peritos Aſtronomos; <lb/></s> <s xml:id="echoid-s8941" xml:space="preserve">Item poſuimus plures arenulas æquales eſſe grano papaueris, quàm <lb/>re ipſa ſint; </s> <s xml:id="echoid-s8942" xml:space="preserve">& </s> <s xml:id="echoid-s8943" xml:space="preserve">plura grana papaueris digitũ conſtituere, quàm <lb/>vere conſtituant: </s> <s xml:id="echoid-s8944" xml:space="preserve">ut nimirum hac ratione maior numerus <lb/>arenularum conſurgeret: </s> <s xml:id="echoid-s8945" xml:space="preserve">qui utique longe maior <lb/>erit, ut diximus, numero arenæ, quæ uere in-<lb/>tra concauum Firmamenti poteſt com-<lb/>prehendi. </s> <s xml:id="echoid-s8946" xml:space="preserve">Quod quidem <lb/>multis incredibi-<lb/>le videtur.</s> <s xml:id="echoid-s8947" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div434" type="section" level="1" n="134"> <head xml:id="echoid-head139" xml:space="preserve">PRIMI CAPITIS FINIS.</head> <pb o="221" file="257" n="258"/> </div> <div xml:id="echoid-div435" type="section" level="1" n="135"> <head xml:id="echoid-head140" xml:space="preserve">CAPVT SECVNDVM <lb/>DE CIRCVLIS, EX QVIBVS SPHAERA <lb/>materialis componitur, & illa ſupercæleſtis, quæ <lb/>per iſtam repræſentatur, componi <lb/>intelligitur.</head> <p style="it"> <s xml:id="echoid-s8948" xml:space="preserve"><emph style="sc">HOrvm</emph> autem circulornm quidam ſunt maiores, qui-<lb/> <anchor type="note" xlink:label="note-257-01a" xlink:href="note-257-01"/> dam minores, ut ſenſui patet. </s> <s xml:id="echoid-s8949" xml:space="preserve">Maior autem circulus in <lb/>ſphæra dicitur, qui deſcriptus in ſuperficie ſphæræ ſuper <lb/>eius centrum diuidit ſphæram in duo æqualia. </s> <s xml:id="echoid-s8950" xml:space="preserve">Minor ue-<lb/>rò, qui deſcriptus in ſuperficie ſphęræ eam non diuidit in <lb/>duo æqualia, ſed in portiones inæquales. </s> <s xml:id="echoid-s8951" xml:space="preserve">Inter circulos <lb/>uero maiores, primo dicendum eſt de Aequinoctiali.</s> <s xml:id="echoid-s8952" xml:space="preserve"/> </p> <div xml:id="echoid-div435" type="float" level="2" n="1"> <note position="right" xlink:label="note-257-01" xlink:href="note-257-01a" xml:space="preserve">Maior cir-<lb/>culus, & mi <lb/>nor in ſphæ <lb/>ra quid.</note> </div> </div> <div xml:id="echoid-div437" type="section" level="1" n="136"> <head xml:id="echoid-head141" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s8953" xml:space="preserve">PROPOSVIT auctor in primo cap. </s> <s xml:id="echoid-s8954" xml:space="preserve">principia, ac ſundamenta <lb/> <anchor type="note" xlink:label="note-257-02a" xlink:href="note-257-02"/> totius Aſtronomiæ; </s> <s xml:id="echoid-s8955" xml:space="preserve">Nunc uero in hoc ſecundo cap. </s> <s xml:id="echoid-s8956" xml:space="preserve">explicat decem <lb/>illos circulos primarios, ex quibus ſphæra materialis componitur, <lb/>& </s> <s xml:id="echoid-s8957" xml:space="preserve">cœleſtis ſphæra, cuius gratia hæc inſtituitur, componi intelligi-<lb/>tur; </s> <s xml:id="echoid-s8958" xml:space="preserve">quoniam uidelicet ſine his nullo modo cauſæ reddi poſſunt apparentia-<lb/>rum cœleſtium, cuiuſmodi ſunt aſcenſiones, & </s> <s xml:id="echoid-s8959" xml:space="preserve">deſcenſiones ſignorum, ortus, <lb/>& </s> <s xml:id="echoid-s8960" xml:space="preserve">occaſus ſiderum, diuerſitas dierum, ac noctium in diuerſis regionibus &</s> <s xml:id="echoid-s8961" xml:space="preserve">c. <lb/></s> <s xml:id="echoid-s8962" xml:space="preserve">Poteſt autem non incongrue hoc caput in tres particulas diuidi. </s> <s xml:id="echoid-s8963" xml:space="preserve">In prima <lb/>enim tractat auctor circulos ſphęræ in genere: </s> <s xml:id="echoid-s8964" xml:space="preserve">In ſecunda de eiſdem circulis <lb/>in particulari diſſerit, explicans ſingulorum nomina, officia, atque utilitates: </s> <s xml:id="echoid-s8965" xml:space="preserve"><lb/>In tertia deniq; </s> <s xml:id="echoid-s8966" xml:space="preserve">ſubiungit, in mundo quinque Zonas ex hiſce circulis cõſtitui.</s> <s xml:id="echoid-s8967" xml:space="preserve"/> </p> <div xml:id="echoid-div437" type="float" level="2" n="1"> <note position="right" xlink:label="note-257-02" xlink:href="note-257-02a" xml:space="preserve">Argumen-<lb/>tũ ſecundi <lb/>cap. eiuſdẽ-<lb/>q́ue diuiſio</note> </div> <p> <s xml:id="echoid-s8968" xml:space="preserve"><emph style="sc">Dividit</emph> itaque in prima parte circulos omnes ſphæræ in maiores, & </s> <s xml:id="echoid-s8969" xml:space="preserve"><lb/>minores, qui ab alijs dicuntur maximi, & </s> <s xml:id="echoid-s8970" xml:space="preserve">nõ maximi: </s> <s xml:id="echoid-s8971" xml:space="preserve">quorũ definitiones per-<lb/>ſpicuæ ſunt in litera Ex maioribus circulis, ſiue maximis auctor noſter in ſe-<lb/>cundo hoc capite explicat tantummodo ſex, nempe Aequinoctialem circulũ, <lb/> <anchor type="note" xlink:label="note-257-03a" xlink:href="note-257-03"/> Zodiacum, Colurum Solſtitiorum, Colurum æquinoctiorum, Meridianum, <lb/>atque Horizontem: </s> <s xml:id="echoid-s8972" xml:space="preserve">ex minoribus uero, ſiue non maximis, ſolum qua@uor de-<lb/>clarat, nimirum Tropicum ♋, Tropicum ♑, circulum Arcticum, & </s> <s xml:id="echoid-s8973" xml:space="preserve">circulum <lb/>Antarcticum. </s> <s xml:id="echoid-s8974" xml:space="preserve">Atque hos decem circulos ſphæræ breuiter quidem in 1. </s> <s xml:id="echoid-s8975" xml:space="preserve">cap. </s> <s xml:id="echoid-s8976" xml:space="preserve">ex <lb/>poſuimus: </s> <s xml:id="echoid-s8977" xml:space="preserve">nunc uero cum auctore plura de eiſdem dicenda erunt.</s> <s xml:id="echoid-s8978" xml:space="preserve"/> </p> <div xml:id="echoid-div438" type="float" level="2" n="2"> <note position="right" xlink:label="note-257-03" xlink:href="note-257-03a" xml:space="preserve">Auctor 10. <lb/>tantum cir-<lb/>culos ſphæ-<lb/>ræ conſide-<lb/>rat.</note> </div> <p> <s xml:id="echoid-s8979" xml:space="preserve"><emph style="sc">Astronomi</emph> autem, ut perfectam cognitionem motuum cęleſtium <lb/>adipiſcerentur, præter decem illos circulos primarios, plures alios excogita-<lb/>runt, tum maximos, tum non maximos. </s> <s xml:id="echoid-s8980" xml:space="preserve">Inter maximos potiſſimum locum <lb/>obtinent hi, qui nunc ſequuntur. </s> <s xml:id="echoid-s8981" xml:space="preserve"><emph style="sc">Verticales</emph>, qui per uerticem cu-<lb/> <anchor type="note" xlink:label="note-257-04a" xlink:href="note-257-04"/> iuſlibet loci ad ſingula Horizontis puncta deducuntur. </s> <s xml:id="echoid-s8982" xml:space="preserve"><emph style="sc">Horarii</emph>, qui totum <lb/>cęlum in 24. </s> <s xml:id="echoid-s8983" xml:space="preserve">horas ſecant, atque hi ſunt in triplici differentia. </s> <s xml:id="echoid-s8984" xml:space="preserve">Aut enim diſtri <lb/>buunt cęlum in 24. </s> <s xml:id="echoid-s8985" xml:space="preserve">horas æquales, initio facto à meridie, quo pacto incedunt <lb/>per polos mundi: </s> <s xml:id="echoid-s8986" xml:space="preserve">Aut in 24. </s> <s xml:id="echoid-s8987" xml:space="preserve">horas æquales, incipiendo ab ortu, uel occaſu So-<lb/>lis, qua ratione contingunt duos circulos parallelos, quorũ unus eſt maximus <pb o="222" file="258" n="259" rhead="Comment. in I. Cap. Sphæræ"/> ſemper apparentium, alter uero maximus ſemper occultorum; </s> <s xml:id="echoid-s8988" xml:space="preserve">Aut deniq; </s> <s xml:id="echoid-s8989" xml:space="preserve">in <lb/>24. </s> <s xml:id="echoid-s8990" xml:space="preserve">horas inæquales, quando nimirum neque per mundi polos incedũt, neque <lb/>dictos parallelos contingunt, ſed diuidunt omnia ſegmenta parallelorum ſu-<lb/>pra Horizontem, itemq́; </s> <s xml:id="echoid-s8991" xml:space="preserve">infra Horizontem exiſtentia, in 12. </s> <s xml:id="echoid-s8992" xml:space="preserve">partes æquales: <lb/></s> <s xml:id="echoid-s8993" xml:space="preserve">ſed de hac uarietate horarum plura dicemus in 3. </s> <s xml:id="echoid-s8994" xml:space="preserve">cap. </s> <s xml:id="echoid-s8995" xml:space="preserve"><emph style="sc">Circvli</emph> domo-<lb/> <anchor type="note" xlink:label="note-258-01a" xlink:href="note-258-01"/> rum cęleſtium, qui totum cęlum in 12. </s> <s xml:id="echoid-s8996" xml:space="preserve">partes ſecant, quæ domus cęleſtes di-<lb/>cuntur. </s> <s xml:id="echoid-s8997" xml:space="preserve"><emph style="sc">Circvli</emph> poſitionnm, qui per communes ſectiones Horizon-<lb/>tis, & </s> <s xml:id="echoid-s8998" xml:space="preserve">Meridiani, necnon per centrum cuiuſque ſtellæ tranſire definiuntur. <lb/></s> <s xml:id="echoid-s8999" xml:space="preserve"><emph style="sc">Circvli</emph> declinationum, qui per polos mundi, & </s> <s xml:id="echoid-s9000" xml:space="preserve">ſingula Æquatoris <lb/> <anchor type="note" xlink:label="note-258-02a" xlink:href="note-258-02"/> puncta educuntur. </s> <s xml:id="echoid-s9001" xml:space="preserve"><emph style="sc">Circvli</emph> latitudinum, qui per polos Zodiaci, & </s> <s xml:id="echoid-s9002" xml:space="preserve">ſin-<lb/>gula Eclipticæ puncta deſcribuntur. </s> <s xml:id="echoid-s9003" xml:space="preserve">Denique quamplurimi alij circuli repe-<lb/>riuntur apud Aſtronomos. </s> <s xml:id="echoid-s9004" xml:space="preserve">Vt enim maximos omittamus, conſiderantur pro-<lb/>pemodum infiniti circuli non maximi. </s> <s xml:id="echoid-s9005" xml:space="preserve">Nam quilibet maximus habet ſuos pa-<lb/>rallelos: </s> <s xml:id="echoid-s9006" xml:space="preserve">Vt Horizon habet circulos parallelos circa verticem capitis deſcri-<lb/>ptos, qui dici ſolent circuli altitudinum. </s> <s xml:id="echoid-s9007" xml:space="preserve">Aequator habet parallelos circulos <lb/>circa polos mũdi deſcriptos, cuiuſmodi ſunt illi circuli, quos ſingulæ ſtellæ, & </s> <s xml:id="echoid-s9008" xml:space="preserve"><lb/>planetæ, ſiue puncta cęli quælibet, ad motum diurnum deſeribunt quotidie. <lb/></s> <s xml:id="echoid-s9009" xml:space="preserve">Zodiacus habet quoq; </s> <s xml:id="echoid-s9010" xml:space="preserve">ſuos parallelos circa polos Zodiaci deſcriptos, quales <lb/>ſunt ij, quos fingulæ ftellæ & </s> <s xml:id="echoid-s9011" xml:space="preserve">planetæ, ſeu quælibet puncta cęli, ad motum pro <lb/>prium nonæ Sphæræ ab occidente in orientem conficiunt. </s> <s xml:id="echoid-s9012" xml:space="preserve">Idemq́ue dicẽdum <lb/>eſt de alijs circulis maximis. </s> <s xml:id="echoid-s9013" xml:space="preserve">Verum de his circulis omnibus agendum eſt alio <lb/>in loco; </s> <s xml:id="echoid-s9014" xml:space="preserve">Satis enim nunc nobis erit, decem illos priores, qui primarij dicũtur, <lb/>in hoc 2. </s> <s xml:id="echoid-s9015" xml:space="preserve">cap. </s> <s xml:id="echoid-s9016" xml:space="preserve">exponere: </s> <s xml:id="echoid-s9017" xml:space="preserve">quoniam hi proprie ad ſphæram ſpectant.</s> <s xml:id="echoid-s9018" xml:space="preserve"/> </p> <div xml:id="echoid-div439" type="float" level="2" n="3"> <note position="right" xlink:label="note-257-04" xlink:href="note-257-04a" xml:space="preserve">Verticales <lb/>circuli. <lb/>Horarij cir-<lb/>@uli.</note> <note position="left" xlink:label="note-258-01" xlink:href="note-258-01a" xml:space="preserve">Citculi do-<lb/>morum cœ <lb/>leftium, & <lb/>poſitionũ.</note> <note position="left" xlink:label="note-258-02" xlink:href="note-258-02a" xml:space="preserve">Circuli de <lb/>clinationũ, <lb/>& latitudi-<lb/>num.</note> </div> <p> <s xml:id="echoid-s9019" xml:space="preserve"><emph style="sc">Dicvntvr</emph> in ſphæra illi circuli, qui idem cum ſphæra centrum poſ-<lb/>ſident, maximi, ſiue maiores, quia, ut demonſtrat Theodoſius lib. </s> <s xml:id="echoid-s9020" xml:space="preserve">1. </s> <s xml:id="echoid-s9021" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s9022" xml:space="preserve">6. <lb/></s> <s xml:id="echoid-s9023" xml:space="preserve"> <anchor type="note" xlink:label="note-258-03a" xlink:href="note-258-03"/> circuli, qui per ſphæræ centrum dncuntur, ſunt omnium maximi, ita ut maior <lb/>illis dari non poſſit: </s> <s xml:id="echoid-s9024" xml:space="preserve">quemadmodum etiam linea, quæ in circulo aliquo per cẽ <lb/>trum ducitur, nempe diameter, eſt omnium maxima. </s> <s xml:id="echoid-s9025" xml:space="preserve">Illi autem circuli, quo-<lb/>rum centrum diuerſum eſt à centro ſphæræ, appellantur non maximi, ſiue mi <lb/>nores, quoniam, ut Theodoſius demonſtrat loco citato, circuli, qui non per <lb/>centrum ſphæræ ducuntur, minores exiſtunt ijs, qui per centrum ſphæræ tran <lb/>ſeunt, & </s> <s xml:id="echoid-s9026" xml:space="preserve">quo remotiores à centro ſphæræ fuerint, eo etiã minores efficiuntur.</s> <s xml:id="echoid-s9027" xml:space="preserve"/> </p> <div xml:id="echoid-div440" type="float" level="2" n="4"> <note position="left" xlink:label="note-258-03" xlink:href="note-258-03a" xml:space="preserve">Maximi cir <lb/>culi, & non <lb/>maximi in <lb/>ſphæra cur <lb/>ſic dicti.</note> </div> <p> <s xml:id="echoid-s9028" xml:space="preserve"><emph style="sc">Vt</emph> autem ea, quæ de circulis cęleſtibus dicenda erunt, perfectius intelli-<lb/>gantur, adducam in medium aliquot proprietates circulorum ſphæræ tam ma <lb/>iorum, quàm minorum, demonſtratas à Theodoſio in ſphæricis elementis. </s> <s xml:id="echoid-s9029" xml:space="preserve">Ex <lb/>quibus quidem multa in ſequentibus ſunt demonſtranda.</s> <s xml:id="echoid-s9030" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div442" type="section" level="1" n="137"> <head xml:id="echoid-head142" xml:space="preserve">I.</head> <p> <s xml:id="echoid-s9031" xml:space="preserve"><emph style="sc">Omnes</emph> circuli ſphæræ maximi ſecant feſe mutuo bifariam, & </s> <s xml:id="echoid-s9032" xml:space="preserve">contra, cir <lb/> <anchor type="note" xlink:label="note-258-04a" xlink:href="note-258-04"/> culi in ſphæra ſeſe mutuo bifariam ſecantes, ſunt maximi. </s> <s xml:id="echoid-s9033" xml:space="preserve">Primum demõſtrat <lb/>Theod. </s> <s xml:id="echoid-s9034" xml:space="preserve">lib. </s> <s xml:id="echoid-s9035" xml:space="preserve">1. </s> <s xml:id="echoid-s9036" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s9037" xml:space="preserve">11. </s> <s xml:id="echoid-s9038" xml:space="preserve">Secundum uero propoſ. </s> <s xml:id="echoid-s9039" xml:space="preserve">12. </s> <s xml:id="echoid-s9040" xml:space="preserve">eiuſdem libri.</s> <s xml:id="echoid-s9041" xml:space="preserve"/> </p> <div xml:id="echoid-div442" type="float" level="2" n="1"> <note position="left" xlink:label="note-258-04" xlink:href="note-258-04a" xml:space="preserve">@@oprieta-<lb/>tes nonnul-<lb/>la circulo-<lb/>@ũ in ſphæ-<lb/>ra.</note> </div> </div> <div xml:id="echoid-div444" type="section" level="1" n="138"> <head xml:id="echoid-head143" xml:space="preserve">II.</head> <p> <s xml:id="echoid-s9042" xml:space="preserve"><emph style="sc">Omnes</emph> circuli ſphæræ maximi ſunt inter ſe æquales. </s> <s xml:id="echoid-s9043" xml:space="preserve">Quod quidem fa-<lb/>cile conſtat ex æqualitate diametrorum. </s> <s xml:id="echoid-s9044" xml:space="preserve">Eſt enim cuiuſlibet circuli maximi <lb/>diameter eadem, quæ diameter ſphæræ. </s> <s xml:id="echoid-s9045" xml:space="preserve">Imo<unsure/> ſi alter altero eſſet maior, non <lb/>eſſet uterque inaximus. </s> <s xml:id="echoid-s9046" xml:space="preserve">Minor enim illorum maximus non eſſet, cum alter eo <lb/>maior detur.</s> <s xml:id="echoid-s9047" xml:space="preserve"/> </p> <pb o="223" file="259" n="260" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div445" type="section" level="1" n="139"> <head xml:id="echoid-head144" xml:space="preserve">III.</head> <p> <s xml:id="echoid-s9048" xml:space="preserve"><emph style="sc">Circvli</emph> in ſphęra non maximi ſe inuicem ſecantes, ſe mutuo biſariam <lb/>non ſecant. </s> <s xml:id="echoid-s9049" xml:space="preserve">Nam ſi mutuo ſe bifariam ſecarent, eſſent ipſi per propoſ. </s> <s xml:id="echoid-s9050" xml:space="preserve">17. </s> <s xml:id="echoid-s9051" xml:space="preserve">lib. </s> <s xml:id="echoid-s9052" xml:space="preserve">1. <lb/></s> <s xml:id="echoid-s9053" xml:space="preserve">Theodoſij, circuli maximi, quod eſt contra hypotheſim. </s> <s xml:id="echoid-s9054" xml:space="preserve">Poteſt tamen unus eo <lb/>rum diuidi aliquando bifariam, ſed cum hoc accidit, alter tunc nequaquam bi <lb/>fariam ſecabitur, niſi ambo circuli ſint maximi.</s> <s xml:id="echoid-s9055" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div446" type="section" level="1" n="140"> <head xml:id="echoid-head145" xml:space="preserve">IIII.</head> <p> <s xml:id="echoid-s9056" xml:space="preserve"><emph style="sc">Inter</emph> cir culos ſphęræ non maximos ſolum ij ſunt æquales inter ſe, qui <lb/>æqualiter a centro ſphærę remouentur. </s> <s xml:id="echoid-s9057" xml:space="preserve">Et contra circuli non maximi inter ſe <lb/>ęquales ęqualiter recedunt à centro ſphęræ. </s> <s xml:id="echoid-s9058" xml:space="preserve">Vtrumque demonſtratur à Theo <lb/>doſio lib. </s> <s xml:id="echoid-s9059" xml:space="preserve">1. </s> <s xml:id="echoid-s9060" xml:space="preserve">prepoſ. </s> <s xml:id="echoid-s9061" xml:space="preserve">6.</s> <s xml:id="echoid-s9062" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div447" type="section" level="1" n="141"> <head xml:id="echoid-head146" xml:space="preserve">V.</head> <p> <s xml:id="echoid-s9063" xml:space="preserve"><emph style="sc">Omnis</emph> circulus maximus in ſphęra tranſiens per polos alterius circuli <lb/>ſiue maximi, ſiue non maximi, diuidit eum bifariam, & </s> <s xml:id="echoid-s9064" xml:space="preserve">ad angulos rectos. </s> <s xml:id="echoid-s9065" xml:space="preserve">Et <lb/>contra circulus in ſp hæra diuidens alium circulum bifariam, & </s> <s xml:id="echoid-s9066" xml:space="preserve">ad angulos re-<lb/>ctos eſt, circulus maximus, inceditq́; </s> <s xml:id="echoid-s9067" xml:space="preserve">per polos illius. </s> <s xml:id="echoid-s9068" xml:space="preserve">Illud demonſtrat Theo. <lb/></s> <s xml:id="echoid-s9069" xml:space="preserve">lib. </s> <s xml:id="echoid-s9070" xml:space="preserve">1. </s> <s xml:id="echoid-s9071" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s9072" xml:space="preserve">15. </s> <s xml:id="echoid-s9073" xml:space="preserve">Hoc uero in ſcholio eiuſdem propos. </s> <s xml:id="echoid-s9074" xml:space="preserve">theoremate 3. </s> <s xml:id="echoid-s9075" xml:space="preserve">a nobis. </s> <s xml:id="echoid-s9076" xml:space="preserve"><lb/>eſt demonſtratum.</s> <s xml:id="echoid-s9077" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div448" type="section" level="1" n="142"> <head xml:id="echoid-head147" xml:space="preserve">VI.</head> <p> <s xml:id="echoid-s9078" xml:space="preserve"><emph style="sc">Omnis</emph> circulus maximus in ſphęra, per cuius polos tranſit alius circulus <lb/>in ſphęra maximus, tranſit uiciſſi@@ per polos illius. </s> <s xml:id="echoid-s9079" xml:space="preserve">Hoc eſt demonſtratum à <lb/>nobis theoremate 1. </s> <s xml:id="echoid-s9080" xml:space="preserve">ſcholijs propoſ. </s> <s xml:id="echoid-s9081" xml:space="preserve">15. </s> <s xml:id="echoid-s9082" xml:space="preserve">lib. </s> <s xml:id="echoid-s9083" xml:space="preserve">1. </s> <s xml:id="echoid-s9084" xml:space="preserve">Theodoſij.</s> <s xml:id="echoid-s9085" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div449" type="section" level="1" n="143"> <head xml:id="echoid-head148" xml:space="preserve">VII.</head> <p> <s xml:id="echoid-s9086" xml:space="preserve"><emph style="sc">Circvlvs</emph> in ſphęra maximus, qui aliquem circulum non maximum <lb/>tangit, tanget quoque alium non maximum illi ęqualem, & </s> <s xml:id="echoid-s9087" xml:space="preserve">parallelũ. </s> <s xml:id="echoid-s9088" xml:space="preserve">Quod <lb/>quidem oſtendit Theodoſius lib. </s> <s xml:id="echoid-s9089" xml:space="preserve">2. </s> <s xml:id="echoid-s9090" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s9091" xml:space="preserve">6.</s> <s xml:id="echoid-s9092" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div450" type="section" level="1" n="144"> <head xml:id="echoid-head149" xml:space="preserve">VIII.</head> <p> <s xml:id="echoid-s9093" xml:space="preserve"><emph style="sc">Circvlvs</emph> in ſphęra maximus ſecãs circulos non maximos non per po <lb/>los eorum, hoc eſt, oblique, ſecat illos in partes inæquales, ita tamen, ut ęqua-<lb/>lium, ac parallelorum circulorum ſegmenta alterna inter ſe ſint ęqualia. </s> <s xml:id="echoid-s9094" xml:space="preserve">Hoc <lb/>perſpicuum eſt ex 19. </s> <s xml:id="echoid-s9095" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s9096" xml:space="preserve">lib. </s> <s xml:id="echoid-s9097" xml:space="preserve">2. </s> <s xml:id="echoid-s9098" xml:space="preserve">Theodoſij.</s> <s xml:id="echoid-s9099" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div451" type="section" level="1" n="145"> <head xml:id="echoid-head150" xml:space="preserve">IX.</head> <p> <s xml:id="echoid-s9100" xml:space="preserve"><emph style="sc">Qvando</emph> tres circuli in ſphęra maximi ſe mutuo ſecant ad angulos <lb/>rectos, erunt duo poli cuiuslibet illorum præciſe in communibus ſectionibus <lb/>circunfer entiarum aliorum duorum. </s> <s xml:id="echoid-s9101" xml:space="preserve">Et contra, quando ſunt circuli maximi <lb/>in ſphæra, ita ut duo poli cuiuſuis illorum reperiantur in communibus ſectio-<lb/>nibus aliorum duorum, ſecabunt ſe mutuo ad angulos rectos. </s> <s xml:id="echoid-s9102" xml:space="preserve">Quorum utrun <lb/>que facile deduci poteſt ex Theodoſio, ſeu proprietatibus adductis, uidelicet <lb/>ex 5. </s> <s xml:id="echoid-s9103" xml:space="preserve">& </s> <s xml:id="echoid-s9104" xml:space="preserve">6.</s> <s xml:id="echoid-s9105" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9106" xml:space="preserve"><emph style="sc">Exemplvm</emph> quoque utriuſque habes in ſphæra materiali. </s> <s xml:id="echoid-s9107" xml:space="preserve">Si enim <lb/>Æquatuor, Meridianus, & </s> <s xml:id="echoid-s9108" xml:space="preserve">Horizon, ita adaptẽtur, ut ſe mutuo ad angulos re <lb/>ctos ſecent, quod tum demum fiet, cum uterque mundi polus præciſe in Ho-<lb/>rizonte iacebit, ficut accidit in ſphęra recta) uidebis polos Æquatoris eſſe in <lb/>communibus ſectiouibus Meridiani, atque Horizontis; </s> <s xml:id="echoid-s9109" xml:space="preserve">polos Meridiani in <lb/>communibus ſectionibus Aequatoris Horizontisq́ue; </s> <s xml:id="echoid-s9110" xml:space="preserve">polos denique Horizon <lb/>tis in communibus ſectionibus Aequatoris, ac Meridiani, &</s> <s xml:id="echoid-s9111" xml:space="preserve">c. </s> <s xml:id="echoid-s9112" xml:space="preserve">Citauimus au- <pb o="224" file="260" n="261" rhead="Comment. in II. Cap. Sphæræ"/> tem propoſitiones Theodoſij in his proprietatibus ſecundum exemplar Græ-<lb/>cum, iuxta quod nunc Theodoſium unà cum triangulis, & </s> <s xml:id="echoid-s9113" xml:space="preserve">tractatione ſinuum <lb/>in lucem edimus, ubi propoſitiones, illas, quas Arabes addiderunt, in ſcholia <lb/>reijcim us.</s> <s xml:id="echoid-s9114" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">Procl’ quo <lb/>pacto circu <lb/>los ſphæræ <lb/>diuidat.</note> <p> <s xml:id="echoid-s9115" xml:space="preserve"><emph style="sc">Proclvs</emph> in ſphæra, quam conſcripſit, aliam diuiſionem circulorum <lb/>ſphęræ inſtituit. </s> <s xml:id="echoid-s9116" xml:space="preserve">Non enim decẽ illos circulos primarios diuidit in maximos, <lb/>& </s> <s xml:id="echoid-s9117" xml:space="preserve">nõ maximos, ſed in circulos ęquidiſtãtes, parallelosve, in obliquos, & </s> <s xml:id="echoid-s9118" xml:space="preserve">in eos, <lb/>qui per polos mundi ſunt ducti. </s> <s xml:id="echoid-s9119" xml:space="preserve">Æquidiſtantes circulos appellat eos, quorum <lb/>poli ijdem ſunt, qui poli mundi; </s> <s xml:id="echoid-s9120" xml:space="preserve">cuiuſmodi ſunt quinque circuli in ſphæra, ni-<lb/>mirũ Æequator, tropicus ♋, tropicus ♑, circulus arcticus, & </s> <s xml:id="echoid-s9121" xml:space="preserve">circulus antarcti <lb/>cus: </s> <s xml:id="echoid-s9122" xml:space="preserve">Hi enim circuli æquidiſtantes ſunt inter ſe, ut conſtat ex propoſ. </s> <s xml:id="echoid-s9123" xml:space="preserve">a. </s> <s xml:id="echoid-s9124" xml:space="preserve">lib. </s> <s xml:id="echoid-s9125" xml:space="preserve">2. <lb/></s> <s xml:id="echoid-s9126" xml:space="preserve">Theodoſij. </s> <s xml:id="echoid-s9127" xml:space="preserve">Obliquos cireulos uocat eos, qui circulos parallelos, quos ſecãt, <lb/> <anchor type="figure" xlink:label="fig-260-01a" xlink:href="fig-260-01"/> <pb o="225" file="261" n="262" rhead="Ioan. de Sacro Boſco."/> ad angulos inæquales, & </s> <s xml:id="echoid-s9128" xml:space="preserve">obliquos ſecant: </s> <s xml:id="echoid-s9129" xml:space="preserve">quales ſunt apud ipſum Zodiacus, <lb/>& </s> <s xml:id="echoid-s9130" xml:space="preserve">circulus lacteus, quibus adiungendus eſt Horizon quicunque obliquus. </s> <s xml:id="echoid-s9131" xml:space="preserve">Il-<lb/>los denique per polos mundi duci ait, qui parallelos circulos, ſeu ęquidiſtan-<lb/>tes ad angulos rectos, ac bifariam diuidunt; </s> <s xml:id="echoid-s9132" xml:space="preserve">qui numero ſunt cres, Colurus ſol <lb/>ſtitiorum, Colurus æquinoctiorum, & </s> <s xml:id="echoid-s9133" xml:space="preserve">Meridianus, quibus adiungi poteſt Ho-<lb/>rizon rectus.</s> <s xml:id="echoid-s9134" xml:space="preserve"/> </p> <div xml:id="echoid-div451" type="float" level="2" n="1"> <figure xlink:label="fig-260-01" xlink:href="fig-260-01a"> <image file="260-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/260-01"/> </figure> </div> <p> <s xml:id="echoid-s9135" xml:space="preserve"><emph style="sc">Nonnvlli</emph> alij circulos cœleſtes alia ratione diuidunt. </s> <s xml:id="echoid-s9136" xml:space="preserve">Dicunt enim, <lb/> <anchor type="note" xlink:label="note-261-01a" xlink:href="note-261-01"/> alios circulos eſſe intrinſecos, alios uero extrinſecos Intrinſeci ſunt, qui in cę-<lb/>lo f<unsure/>ixi omnino concipiuntur, ita ut uná cum eo circumducantur. </s> <s xml:id="echoid-s9137" xml:space="preserve">Inde a qui-<lb/>buſdam mobiles nominantur, quales ſunt omnes circuli primarij ſphæræ, ex-<lb/>cepto Meridiano, & </s> <s xml:id="echoid-s9138" xml:space="preserve">Horizonte. </s> <s xml:id="echoid-s9139" xml:space="preserve">Hi enim duo extrinſeci dicuntur, quia ita in <lb/>cœlo concipiendi ſunt, ut ſemper firmum ſitum obtineant, & </s> <s xml:id="echoid-s9140" xml:space="preserve">nulla ratione ad <lb/>motum cœli circumuoluantur, ſed ſemper in eodem loco permaneant. </s> <s xml:id="echoid-s9141" xml:space="preserve">Qua <lb/>de cauſa à pleriſque immobiles dicti fuere.</s> <s xml:id="echoid-s9142" xml:space="preserve"/> </p> <div xml:id="echoid-div452" type="float" level="2" n="2"> <note position="right" xlink:label="note-261-01" xlink:href="note-261-01a" xml:space="preserve">Alia diui-<lb/>ſio circulo <lb/>rũ ſphęræ.</note> </div> <p> <s xml:id="echoid-s9143" xml:space="preserve"><emph style="sc">Exemplvm</emph> decem circulorum ſphærę, qui primarij dicuntur, habes in <lb/>propoſita figura, quæ ſphæram materialem repræſentat.</s> <s xml:id="echoid-s9144" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div454" type="section" level="1" n="146"> <head xml:id="echoid-head151" style="it" xml:space="preserve">DE AEQVINOCTI ALI CIRCVLO.</head> <p style="it"> <s xml:id="echoid-s9145" xml:space="preserve">EST igitur Aequinoctialis circulus quidam diuidens ſphæram, <lb/>in duo æqualia ſecundum quamlibet ſui partem æque diſtans <lb/>ab utroque polo.</s> <s xml:id="echoid-s9146" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div455" type="section" level="1" n="147"> <head xml:id="echoid-head152" xml:space="preserve">COMMENTARIS.</head> <p> <s xml:id="echoid-s9147" xml:space="preserve"><emph style="sc">ABsolvta</emph> prima parte huius capitis, aggreditur iam ſecun-<lb/> <anchor type="note" xlink:label="note-261-02a" xlink:href="note-261-02"/> dam partem, in qua ſigillatim de omnibus circulis diſſeritur. </s> <s xml:id="echoid-s9148" xml:space="preserve">Agit <lb/>autem prius de circulis maximis, deinde de non maximis: </s> <s xml:id="echoid-s9149" xml:space="preserve">Et in-<lb/>ter maximos primo loco explicat Æquinoctialem circulum, quo-<lb/>niam cognitio eius facilior eſt, & </s> <s xml:id="echoid-s9150" xml:space="preserve">reliqui fere omnes per ipſum <lb/>explicari ſolent. </s> <s xml:id="echoid-s9151" xml:space="preserve">Eſt quoque circulus Aequinoctialis omnium nobiliſſimus, <lb/>cum ſit menſura, ut mox dicetur, motus nobiliſſimi, nem pe primi mobilis; <lb/></s> <s xml:id="echoid-s9152" xml:space="preserve">Mouetur enim motu maxime æquabili: </s> <s xml:id="echoid-s9153" xml:space="preserve">Vnde ita ſeſe habet hic circulus cum <lb/>alijs circulis cœleſtibus comparatus, quemadmodum primum mobile colla-<lb/>tum cum alijs orbibus cœleſtibus. </s> <s xml:id="echoid-s9154" xml:space="preserve">Quamobrem Philoſophi primum motorẽ, <lb/>ideſt, Deum Opt. </s> <s xml:id="echoid-s9155" xml:space="preserve">Max. </s> <s xml:id="echoid-s9156" xml:space="preserve">in circulo Aequinoctiali, tamquam in ſede propria <lb/>collocabant.</s> <s xml:id="echoid-s9157" xml:space="preserve"/> </p> <div xml:id="echoid-div455" type="float" level="2" n="1"> <note position="right" xlink:label="note-261-02" xlink:href="note-261-02a" xml:space="preserve">Aequino-<lb/>ctialis circu <lb/>lus quid.</note> </div> <p> <s xml:id="echoid-s9158" xml:space="preserve"><emph style="sc">Definit</emph> igitur circulum Ae quinoctinoctialem dicens, eũ circulũ in ſphæ <lb/>ra materiali appellari Aequinoctialem, qui ſphæram in duas partes æquales <lb/>diuidit, æqualiterq́ue ab utroque polo ſecundum omnem ſui partem diſtat. <lb/></s> <s xml:id="echoid-s9159" xml:space="preserve">Atque hic eadem ratione in cœlo erit concipiendus collocari in medio inter <lb/>duos mundi polos.</s> <s xml:id="echoid-s9160" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">Qũo Aequi <lb/>noctialis. <lb/>circulus in <lb/>cęlo deſcri-<lb/>bi concipia <lb/>tur.</note> <p> <s xml:id="echoid-s9161" xml:space="preserve"><emph style="sc">Qvem</emph> quidem nonnulli ita concipiunt deſcribi. </s> <s xml:id="echoid-s9162" xml:space="preserve">A centro mundi per <lb/>centrum Solis, dum eſt in principio ♈@uel ♎. </s> <s xml:id="echoid-s9163" xml:space="preserve">imaginantur duci lineam rectã, <lb/>quæ ſpatio 24. </s> <s xml:id="echoid-s9164" xml:space="preserve">horarum deſcribat circulum Aequinoctialem. </s> <s xml:id="echoid-s9165" xml:space="preserve">Sed quoniam <lb/>Sol nunquam perficit integrum circulum, cum non ad idẽ punctum reuerta- <pb o="226" file="262" n="263" rhead="Comment. in II. Cap. Sphæræ"/> tur propter motum proprium, quem habet ab occaſu in ortum, melius fortaf <lb/>ſe dicetur Æequator deſcribi a linea recta, quæ à<unsure/> centro mundi ad initium ♈, <lb/>uel ♎, primi mobilis extenditur. </s> <s xml:id="echoid-s9166" xml:space="preserve">Ex circũductione enim huius lineę deſcribe-<lb/>tur in die naturali circulus maximus, & </s> <s xml:id="echoid-s9167" xml:space="preserve">perfectus, ſemper rectus ad axem mun-<lb/>di, ęqualiterq́; </s> <s xml:id="echoid-s9168" xml:space="preserve">diſtans omni ex parte à mundi polis: </s> <s xml:id="echoid-s9169" xml:space="preserve">quæ omnia requiruntur ad <lb/>ęquinoctialem circulum.</s> <s xml:id="echoid-s9170" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9171" xml:space="preserve"><emph style="sc">Svnt</emph> autem omnes circuli cœleſtes, atque adeo & </s> <s xml:id="echoid-s9172" xml:space="preserve">ęquinoctialis, conci-<lb/> <anchor type="note" xlink:label="note-262-01a" xlink:href="note-262-01"/> piendi in primo mobili, quod quidem nobis potiſſimum refert ſphæra mate-<lb/>rialis. </s> <s xml:id="echoid-s9173" xml:space="preserve">Neque multum intereſt, ſiue eos in concauo, ſiue in conuexo primi mo-<lb/>bilis intelligamus: </s> <s xml:id="echoid-s9174" xml:space="preserve">Tamen quia nos intra cœlum incluſi, in eiuſq́. </s> <s xml:id="echoid-s9175" xml:space="preserve">centro exi-<lb/>ſtentes, concauam cœli ſuperficiẽ intuemur, compellimur quodammodo cir-<lb/>culos cœleſtes in eadem ſuperficie concaua primi mo bilis conſiderare, ſicut <lb/>etiam, quia ſumus extra ſphæram materialem poſiti, cogimur eoſdem quodam <lb/>modo circulos in extima, ſeu conuexa eius ſuperficie defignare. </s> <s xml:id="echoid-s9176" xml:space="preserve">Quod etiam <lb/>fit in globo Coſmographico, & </s> <s xml:id="echoid-s9177" xml:space="preserve">Aſtronomico. </s> <s xml:id="echoid-s9178" xml:space="preserve">Quoniam uero ex decem ſphæ-<lb/>ræ circulis primarijs Meridianus, atque Horizon ſunt prorſus immobiles in <lb/>quacunque regione ita ut, etiamſi cœlum primum perpetuo, ac indeſinenter <lb/>circumferatur, prędicti duo circuli nihilominus immoti omnino concipiãtur, <lb/>& </s> <s xml:id="echoid-s9179" xml:space="preserve">firmi; </s> <s xml:id="echoid-s9180" xml:space="preserve">Alij uero octo mobiles exiſtunt, quippe cum continuè circumuolua-<lb/>tur cum primo mobili; </s> <s xml:id="echoid-s9181" xml:space="preserve">non erit inconueniens, ſi octo hoſce circulos mobiles <lb/>in conuexa ſuperficie primi mobilis, duos autem illos in concaua ſuperficie <lb/>cœli Empyrei immobilis, ſub quo collocatur primũ mobile, & </s> <s xml:id="echoid-s9182" xml:space="preserve">totus mundus, <lb/>conſideremus. </s> <s xml:id="echoid-s9183" xml:space="preserve">Ita enim fiet, ut alij circuli mobiles intra hos immobiles perpe <lb/>tuo circumducantur: </s> <s xml:id="echoid-s9184" xml:space="preserve">quemadmodum etiam in ſphæra materiali cernimus, Me <lb/>rid<unsure/>ianum, & </s> <s xml:id="echoid-s9185" xml:space="preserve">Horizõtem alijs circulis ſupereminere, ut his ſine ceſſatione mo <lb/>tis, illi duo immoti prorſus permaneant.</s> <s xml:id="echoid-s9186" xml:space="preserve"/> </p> <div xml:id="echoid-div456" type="float" level="2" n="2"> <note position="left" xlink:label="note-262-01" xlink:href="note-262-01a" xml:space="preserve">Vbi pof<unsure/>iſſi <lb/>mũ ſphęræ <lb/>circuli in <lb/>cęlo ſint cõ <lb/>cipiendi.</note> </div> <note position="left" xml:space="preserve">Ae@noctia <lb/>lis circulus <lb/>cur ſic di-<lb/>ctus. Idẽ cur <lb/>Aequato@, <lb/>& cingulus <lb/>primi mo-<lb/>bilis dica-<lb/>@ur.</note> <p style="it"> <s xml:id="echoid-s9187" xml:space="preserve">ET dicitur Aequinoctialis, quoniam quando Sol tranſit per illum, <lb/>(quod fit in bis in anno, in principio Arietis ſcilicet, & </s> <s xml:id="echoid-s9188" xml:space="preserve">in principio Li-<lb/>bræ) eſt æquinoctium in uniuerſa terra. </s> <s xml:id="echoid-s9189" xml:space="preserve">Vnde etiam appellatur Aequator <lb/>diei, & </s> <s xml:id="echoid-s9190" xml:space="preserve">noctis, quia adæquat diem artificialem nocti. </s> <s xml:id="echoid-s9191" xml:space="preserve">Et dicitur cingulus pri <lb/>mi motus. </s> <s xml:id="echoid-s9192" xml:space="preserve">Vnde ſciendum, quod primus motus, di citur motus primi <lb/>mobilis, hoc eſt, nonę ſphæræ, ſiue cœli ultimi, qui eſt ab oriente per occi-<lb/>dentem, rediens iterum in orientem: </s> <s xml:id="echoid-s9193" xml:space="preserve">qui ctiam dicitur motus rationalis, ad <lb/>ſimilitudinem motus rationis, qui eſt in microcoſmo, id eſt, in homine, ſcili-<lb/>cet quando fit conſider atio à creatore per creatur as in creator em, ibi ſiſten-<lb/>do. </s> <s xml:id="echoid-s9194" xml:space="preserve">Secundus motus eſt firmamenti, & </s> <s xml:id="echoid-s9195" xml:space="preserve">planetarum, contrarius huic, ab <lb/>occidente per orientem iterum rediens in occidentem: </s> <s xml:id="echoid-s9196" xml:space="preserve">qui motus dicitur ir-<lb/>rationalis, ſiue ſenſualis, ad ſimilitudinem mo<unsure/>tus microcoſmi, qui eſt à cor-<lb/>ruptibilibus ad creatorem, iterum rediens ad corruptibilia. </s> <s xml:id="echoid-s9197" xml:space="preserve">Dicitur ergo <lb/>cingulus primi motus, quia cingit, ſiue diuidit primum mobile, ſcilicet ſphæ-<lb/>ram nonam, in duo æqualia, æquidiſtans a polis mundi.</s> <s xml:id="echoid-s9198" xml:space="preserve"/> </p> <pb o="227" file="263" n="264" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div458" type="section" level="1" n="148"> <head xml:id="echoid-head153" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s9199" xml:space="preserve"><emph style="sc">Explicat</emph> hoc loco nomina, & </s> <s xml:id="echoid-s9200" xml:space="preserve">oſſicia circuli Aequinoctialis, docens, tum <lb/>vocari Aequinoctialem, quia per illum tranſiens Sol, in principio videlicet <lb/>♈, & </s> <s xml:id="echoid-s9201" xml:space="preserve">♎, efficit æquinoctium in uniuerſa terra, hoc eſt, diem artificialem ęqua <lb/>lem nocti artificiali conſtituit.</s> <s xml:id="echoid-s9202" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9203" xml:space="preserve"><emph style="sc">Eandem</emph> ob cauſam ait, ipſum appellari Aequatorem diei, ac noctis. </s> <s xml:id="echoid-s9204" xml:space="preserve">Item <lb/>nominari cingulum primi motus, quod nimirum primum motum diuidat in <lb/>duo æqualia. </s> <s xml:id="echoid-s9205" xml:space="preserve">Cum enim motus diuidatur ad diuiſionem mobilis, ut uolunt <lb/>philoſophi, diuidet utique Aequator motum primi mobilis bifariam, quan-<lb/>doquidem & </s> <s xml:id="echoid-s9206" xml:space="preserve">primum mobile in duas medietates diuidit. </s> <s xml:id="echoid-s9207" xml:space="preserve">In gratiam huius <lb/>repetit duplicem illum motum cælorum, ab ortu videlicet in occaſum, & </s> <s xml:id="echoid-s9208" xml:space="preserve">ab <lb/>occaſu in ortum, vt perſpicuum eſt in litera.</s> <s xml:id="echoid-s9209" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">Varia nomi <lb/>na circuli ę-<lb/>quinoctia-<lb/>liss.</note> <p> <s xml:id="echoid-s9210" xml:space="preserve"><emph style="sc">Graeci</emph> appellant hunc circulum ἰσημέρινον, id eſt, Aequidialem, quia <lb/>nimirum. </s> <s xml:id="echoid-s9211" xml:space="preserve">Sole in eo decurrente, fit dies æqualis nocti. </s> <s xml:id="echoid-s9212" xml:space="preserve">Vnde quemadmodum <lb/>Latini eum denominant à nocte, ita Græcis placuit ei nomen imponere a die. <lb/></s> <s xml:id="echoid-s9213" xml:space="preserve">A Ptolemæo dicitur Linea, Circulus, feu orbis æquationis diei. </s> <s xml:id="echoid-s9214" xml:space="preserve">Ab Alphraga-<lb/>no Circulus Aequinoctij. </s> <s xml:id="echoid-s9215" xml:space="preserve">Volunt etiam plerique, eum hiſce nominib. </s> <s xml:id="echoid-s9216" xml:space="preserve">appella-<lb/>ri, non quòd Sol in eo exiſtens æquinoctium efficiat ubique; </s> <s xml:id="echoid-s9217" xml:space="preserve">ſed quod in ſphę <lb/>ra recta, quæ illi ſubiacet, noctes dierum artificialium magnitudinem nunquã <lb/>excedant, ſed perpetuo dies noctibus ſint æquales, ubicunque Sol exiſtat, ut in <lb/>3. </s> <s xml:id="echoid-s9218" xml:space="preserve">cap. </s> <s xml:id="echoid-s9219" xml:space="preserve">ex ponemus. </s> <s xml:id="echoid-s9220" xml:space="preserve">Solet etiam nonnunquam circulus Aequinoctialis dici ab <lb/>Aſtronomis Maximus parallelorum. </s> <s xml:id="echoid-s9221" xml:space="preserve">Appellant enim circulos parallelos eos, <lb/>quos ſtellæ, & </s> <s xml:id="echoid-s9222" xml:space="preserve">ſingula cæli puncta ad motum diurnum deſcribũt, quorum om-<lb/>nium maximus eſt, ut conſtat, Aequator.</s> <s xml:id="echoid-s9223" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9224" xml:space="preserve"><emph style="sc">Qvod</emph> autem communiter dici ſolet; </s> <s xml:id="echoid-s9225" xml:space="preserve">In uniuerſa terra æquinoctium fieri <lb/> <anchor type="note" xlink:label="note-263-02a" xlink:href="note-263-02"/> bis in anno, Sole nimirum exiſtente in principio ♈, & </s> <s xml:id="echoid-s9226" xml:space="preserve">♎, intelligendum eſt, <lb/>vbi contingit uiciſſitudo diei, & </s> <s xml:id="echoid-s9227" xml:space="preserve">noctis ſpacio 24. </s> <s xml:id="echoid-s9228" xml:space="preserve">horarum, hoc eſt, ubi Aequi <lb/>noctialis circulus interſecat Horizontem, & </s> <s xml:id="echoid-s9229" xml:space="preserve">ab eodẽ interſecatur. </s> <s xml:id="echoid-s9230" xml:space="preserve">Quod ideo <lb/>dixerim, ut excludamus ab hac propoſitione uniuerſali regiones illas; </s> <s xml:id="echoid-s9231" xml:space="preserve">quæ di-<lb/>recte polis mundi ſubiacent. </s> <s xml:id="echoid-s9232" xml:space="preserve">In illis etenim regionibus dies, quæ unica tantũ <lb/>eſt in anno continet ſex menſes, & </s> <s xml:id="echoid-s9233" xml:space="preserve">nox totidem, ut prope finem 3. </s> <s xml:id="echoid-s9234" xml:space="preserve">cap. </s> <s xml:id="echoid-s9235" xml:space="preserve">conſta-<lb/>bit: </s> <s xml:id="echoid-s9236" xml:space="preserve">uel certe propoſitio illa communis intelligenda eſt negatiue, quaſi dicatur <lb/>diem non eſſe inæqualem nocti, quod quidem uerum eſt, etiam ſub polis, Sole <lb/>in Aequinoctiali circulo exiſtente: </s> <s xml:id="echoid-s9237" xml:space="preserve">quia tunc dies non eſt nocti inæqualis.</s> <s xml:id="echoid-s9238" xml:space="preserve"/> </p> <div xml:id="echoid-div458" type="float" level="2" n="1"> <note position="right" xlink:label="note-263-02" xlink:href="note-263-02a" xml:space="preserve">Qũo intelli <lb/>gatur, bis in <lb/>anno fieri <lb/>æquinoctiũ <lb/>in uniuerſ@ <lb/>terra.</note> </div> <p> <s xml:id="echoid-s9239" xml:space="preserve"><emph style="sc">In</emph> omnibus uero regionibus, in quibus Aequator, & </s> <s xml:id="echoid-s9240" xml:space="preserve">Horizon ſeſe mutuo <lb/> <anchor type="note" xlink:label="note-263-03a" xlink:href="note-263-03"/> interſecant, fieri æquinoctiũ, dum Sol in Aequatore moratur, facile hac ratio-<lb/>ne poterit demonſtrari. </s> <s xml:id="echoid-s9241" xml:space="preserve">Quoniam uterq; </s> <s xml:id="echoid-s9242" xml:space="preserve">circulus, Aequator, ſ. </s> <s xml:id="echoid-s9243" xml:space="preserve">atq; </s> <s xml:id="echoid-s9244" xml:space="preserve">Horizon, <lb/>eſt maximus, diuidet alter alterum bifariam per propoſ. </s> <s xml:id="echoid-s9245" xml:space="preserve">11. </s> <s xml:id="echoid-s9246" xml:space="preserve">lib. </s> <s xml:id="echoid-s9247" xml:space="preserve">1. </s> <s xml:id="echoid-s9248" xml:space="preserve">Theodoſij, ut <lb/>ſupra dictum eſt, & </s> <s xml:id="echoid-s9249" xml:space="preserve">propterea in quacun que regione, ubi hi duo circuli ſe mu <lb/>tuo ſecant, exiſtet una medietas Aequatoris ſupra Horizontem, altera uero in <lb/>fra. </s> <s xml:id="echoid-s9250" xml:space="preserve">Cum igitur Sol ab ortu in occaſum æquabiliter feratur, efficitur, vt tantũ <lb/>temporis conſumat ſupra hemiſphærium, quæ quidem mora diem efficit ar-<lb/>tificialem, quantum ſub hemiſphęrio, quę mora noctem artificialem cõſtituit.</s> <s xml:id="echoid-s9251" xml:space="preserve"/> </p> <div xml:id="echoid-div459" type="float" level="2" n="2"> <note position="right" xlink:label="note-263-03" xlink:href="note-263-03a" xml:space="preserve">Cur Sole <lb/>exiſtente in <lb/>Aequatore, <lb/>fiat æquin@ <lb/>ctium.</note> </div> <p style="it"> <s xml:id="echoid-s9252" xml:space="preserve">VNDE notandum, quòd polus mundi, qui nobis ſemper apparet, <lb/>dicitur polus ſeptentrionalis, arcticus, uel borealis. </s> <s xml:id="echoid-s9253" xml:space="preserve">Septentrionalis dici-<lb/>tur à ſeptentrione, hoc eſt, à minori urſa, quæ dicitur à ſeptem, & </s> <s xml:id="echoid-s9254" xml:space="preserve">trion, <pb o="228" file="264" n="265" rhead="Comment. in II. Cap. Sphæræ"/> quod eſt bos; </s> <s xml:id="echoid-s9255" xml:space="preserve">quia ſeptem ſtellæ, quæ ſunt in vrſa, tarde mouentur ad mo-<lb/> <anchor type="note" xlink:label="note-264-01a" xlink:href="note-264-01"/> dum bouis, cum ſint propinquę polo. </s> <s xml:id="echoid-s9256" xml:space="preserve">Vel dicuntur illæ ſeptem ſtellæ ſe-<lb/>ptentriones, quaſi ſeptem teriones, eo quod terunt partes circa polum. <lb/></s> <s xml:id="echoid-s9257" xml:space="preserve">Arcticus quidem dicitur ab ἄρκτος, quod eſt urſa. </s> <s xml:id="echoid-s9258" xml:space="preserve">Eſt enim iuxta maiorem <lb/>urſam. </s> <s xml:id="echoid-s9259" xml:space="preserve">Borealis uero dicitur, quia eſt in illa parte, à qua uenit Boreas. </s> <s xml:id="echoid-s9260" xml:space="preserve">Po-<lb/>lus uero oppoſitus dicitur Antarcticus, quaſi contra Arcticum poſitus. </s> <s xml:id="echoid-s9261" xml:space="preserve"><lb/>Dicitur & </s> <s xml:id="echoid-s9262" xml:space="preserve">meridionalis, quia ex parte meridiei eſt. </s> <s xml:id="echoid-s9263" xml:space="preserve">Dicitur etiam au-<lb/>ſtralis, quia eſt in illa parte, à qua uenit auſter. </s> <s xml:id="echoid-s9264" xml:space="preserve">Iſta duo puncta in Firma-<lb/>mento ſtabilia, dicuntur poli mundi; </s> <s xml:id="echoid-s9265" xml:space="preserve">quia ſphæræ axem terminant, & </s> <s xml:id="echoid-s9266" xml:space="preserve">ad il-<lb/>los uoluitur mundus, quorum unus ſemper nobis apparet, reliquus uero ſem <lb/>per occultatur. </s> <s xml:id="echoid-s9267" xml:space="preserve">Vnde Virg. </s> <s xml:id="echoid-s9268" xml:space="preserve">1. </s> <s xml:id="echoid-s9269" xml:space="preserve">Georg.</s> <s xml:id="echoid-s9270" xml:space="preserve"/> </p> <div xml:id="echoid-div460" type="float" level="2" n="3"> <note position="left" xlink:label="note-264-01" xlink:href="note-264-01a" xml:space="preserve">Peius nobis <lb/>ſem ꝑ appa-<lb/>rens cur di <lb/>catur Septẽ <lb/>trionalis, ar <lb/>cticus, & bo <lb/>realis. Oppo <lb/>ſitus uero, <lb/>antarcticus <lb/>meridiona-<lb/>lis, & auſtra <lb/>lis.</note> </div> <p> <s xml:id="echoid-s9271" xml:space="preserve">Hic vertex nobis ſemper ſublimis, at illum <lb/>Sub pedibus ſtyx atrauidet, manesq́; </s> <s xml:id="echoid-s9272" xml:space="preserve">profundi.</s> <s xml:id="echoid-s9273" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div462" type="section" level="1" n="149"> <head xml:id="echoid-head154" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s9274" xml:space="preserve"><emph style="sc">Declarat</emph> hoc loco polos circuli Aequinoctialis, à quibus ipſum Aequi-<lb/>noctialem circulum æqualiter diſtare dixerat. </s> <s xml:id="echoid-s9275" xml:space="preserve">Verum hæc omnia clara ſunt <lb/>in littera. </s> <s xml:id="echoid-s9276" xml:space="preserve">Supereſt, vt uſum multiplicem, officia, at que utilitates, propter <lb/>quas Aſtronomi circulum Aequinoctialem in cœlo excogitarunt, explicem.</s> <s xml:id="echoid-s9277" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div463" type="section" level="1" n="150"> <head xml:id="echoid-head155" xml:space="preserve">OFFICIA ÆQVINOCTIALIS CIRCVLI.</head> <head xml:id="echoid-head156" xml:space="preserve">I.</head> <p> <s xml:id="echoid-s9278" xml:space="preserve"><emph style="sc">Est</emph> menſura, & </s> <s xml:id="echoid-s9279" xml:space="preserve">regula primi motus. </s> <s xml:id="echoid-s9280" xml:space="preserve">Oſtendit enim, primum mobile cir-<lb/> <anchor type="note" xlink:label="note-264-02a" xlink:href="note-264-02"/> cumuolui ſpacio 24. </s> <s xml:id="echoid-s9281" xml:space="preserve">horarum, quippe cum ſingulis horis 15. </s> <s xml:id="echoid-s9282" xml:space="preserve">gradus Aequino-<lb/>ctialis circuli in primo mobili deſcripti eleuentur uniformiter ſupra Horizon <lb/>tem, ut obſeruationes Aſtronomorum docent.</s> <s xml:id="echoid-s9283" xml:space="preserve"/> </p> <div xml:id="echoid-div463" type="float" level="2" n="1"> <note position="left" xlink:label="note-264-02" xlink:href="note-264-02a" xml:space="preserve">Aequator <lb/>mẽſura eſt, <lb/>& regula <lb/>primi mo-<lb/>tus.</note> </div> </div> <div xml:id="echoid-div465" type="section" level="1" n="151"> <head xml:id="echoid-head157" xml:space="preserve">II.</head> <p> <s xml:id="echoid-s9284" xml:space="preserve"><emph style="sc">Mensvrat</emph> tempus. </s> <s xml:id="echoid-s9285" xml:space="preserve">Ex una namque reuolutione Aequinoctialis circu-<lb/> <anchor type="note" xlink:label="note-264-03a" xlink:href="note-264-03"/> li, addita particula correſpondente illi parti Zodiaci, quàm interim Sol motu <lb/>proprio orientem uerſus conficit, dies naturalis conſtituitur, ut in cap. </s> <s xml:id="echoid-s9286" xml:space="preserve">dice-<lb/>tur. </s> <s xml:id="echoid-s9287" xml:space="preserve">Ex eleuatione uero 15. </s> <s xml:id="echoid-s9288" xml:space="preserve">graduum illius cognoſcimus, horam inte gram <lb/>eſſe tranſactam. </s> <s xml:id="echoid-s9289" xml:space="preserve">Ex unius denique gradus aſcenſione, 4. </s> <s xml:id="echoid-s9290" xml:space="preserve">minuta horæ eſſe ela-<lb/>pſa, deprehendimus.</s> <s xml:id="echoid-s9291" xml:space="preserve"/> </p> <div xml:id="echoid-div465" type="float" level="2" n="1"> <note position="left" xlink:label="note-264-03" xlink:href="note-264-03a" xml:space="preserve">Aequator <lb/>menſurat <lb/>tempus.</note> </div> <note position="left" xml:space="preserve">Aequator <lb/>irregularita <lb/>tem motus <lb/>Zodiaci ab <lb/>ortu in oc-<lb/>caſum ad <lb/>regularitatẽ <lb/>reducit.</note> </div> <div xml:id="echoid-div467" type="section" level="1" n="152"> <head xml:id="echoid-head158" xml:space="preserve">III.</head> <p> <s xml:id="echoid-s9292" xml:space="preserve"><emph style="sc">Irregvlaritatem</emph> motus Zodiaci ab ortu in occaſum, quàm habet pro-<lb/>pter obliquum eius ſitum, ueluti regula, ac canon certiſſimus dirigit. </s> <s xml:id="echoid-s9293" xml:space="preserve">Nam ut <lb/>ex 3. </s> <s xml:id="echoid-s9294" xml:space="preserve">cap. </s> <s xml:id="echoid-s9295" xml:space="preserve">conſtabit, Zodiaci partes æquales inæqualiter aſcendunt ſupra Hori-<lb/>zontem quemcunque ſiue rectum, ſiue obliquum. </s> <s xml:id="echoid-s9296" xml:space="preserve">Vnde tota hæc inęqualitas <lb/>miro artificio reducitur ab Aſtronomis ad æqualitatem per motum uniſormẽ <lb/>Aequinoctialis circuli, ita ut ex confinibus Aequinoctialis circuli arcubus co <lb/>gnoſcamus tempora ortus, & </s> <s xml:id="echoid-s9297" xml:space="preserve">occaſus omnium arcuum Zodiaci.</s> <s xml:id="echoid-s9298" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">Aequator <lb/>eſſi cit æqui <lb/>@octia.</note> </div> <div xml:id="echoid-div468" type="section" level="1" n="153"> <head xml:id="echoid-head159" xml:space="preserve">IIII.</head> <p> <s xml:id="echoid-s9299" xml:space="preserve"><emph style="sc">Distingvit</emph> æquinoctia. </s> <s xml:id="echoid-s9300" xml:space="preserve">Diuidit enim Zodiacum circulum obli- <pb o="229" file="265" n="266" rhead="Ioan. de Sacro Boſco."/> que in duobus punctis, nempe in principio ♈, & </s> <s xml:id="echoid-s9301" xml:space="preserve">♎, ad quæ cum proprio mo-<lb/>tu Sol peruenit, æqualia diei, noctisq́ue ſpacia efficit: </s> <s xml:id="echoid-s9302" xml:space="preserve">Vnde & </s> <s xml:id="echoid-s9303" xml:space="preserve">dicta puncta æ-<lb/>quinoctialia dicuntur ab Aſtronomis. </s> <s xml:id="echoid-s9304" xml:space="preserve">Quæ eleganter deſcribit Manilius poe <lb/>ta dicens.</s> <s xml:id="echoid-s9305" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div469" type="section" level="1" n="154"> <head xml:id="echoid-head160" style="it" xml:space="preserve">Libra, Ariesq́ue parem reddunt noctemq́ue, diemq́ue.</head> <p> <s xml:id="echoid-s9306" xml:space="preserve">Quibus antem diebus anni olim duo æquinoctia contigerint, & </s> <s xml:id="echoid-s9307" xml:space="preserve">quibus hoc <lb/>tempore contingant, aperiemus, quando de Coluris agemus.</s> <s xml:id="echoid-s9308" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div470" type="section" level="1" n="155"> <head xml:id="echoid-head161" xml:space="preserve">V.</head> <note position="right" xml:space="preserve">Aequator <lb/>terminus <lb/>eſt a quo <lb/>declinatio <lb/>nes nume <lb/>rantur.</note> <p> <s xml:id="echoid-s9309" xml:space="preserve"><emph style="sc">Est</emph> terminus, à quo initium ſumunt declinationes omnium punctorum <lb/>Eclipticæ, ſtellarumq́ue. </s> <s xml:id="echoid-s9310" xml:space="preserve">Eſt enim declinatio diſtantia ſtellæ, punctiue Eclipti-<lb/>cæ ab Aequatore uerſus alterutrum polorum mundi. </s> <s xml:id="echoid-s9311" xml:space="preserve">Penes quid uero capien-<lb/>da ſit, & </s> <s xml:id="echoid-s9312" xml:space="preserve">menſuranda hæc diſtantia, ſiue declinatio, dicemus, cum de Eclipti-<lb/>ca egerimus.</s> <s xml:id="echoid-s9313" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">Declinatio <lb/>quid.</note> </div> <div xml:id="echoid-div471" type="section" level="1" n="156"> <head xml:id="echoid-head162" xml:space="preserve">VI.</head> <p> <s xml:id="echoid-s9314" xml:space="preserve"><emph style="sc">Indicat</emph>, quæ pars cœli dicatur Septentrionalis, Borealisve, & </s> <s xml:id="echoid-s9315" xml:space="preserve">quæ <lb/> <anchor type="note" xlink:label="note-265-03a" xlink:href="note-265-03"/> Auſtralis, ſeu Meridionalis. </s> <s xml:id="echoid-s9316" xml:space="preserve">Quæ enim interijcitur inter polum ſeptentriona-<lb/>lem, ſiue Arcticum, & </s> <s xml:id="echoid-s9317" xml:space="preserve">Aequinoctialem circulum, Septentrionalis nuncupatur: <lb/></s> <s xml:id="echoid-s9318" xml:space="preserve">Reliqua uero, quæ ponitur inter eundem Aequinoctialem circulum, & </s> <s xml:id="echoid-s9319" xml:space="preserve">polum <lb/> <anchor type="note" xlink:label="note-265-04a" xlink:href="note-265-04"/> Auſtralem, ſiue Antarcticum. </s> <s xml:id="echoid-s9320" xml:space="preserve">Meridionalis appellatur. </s> <s xml:id="echoid-s9321" xml:space="preserve">Ex quo facile percipi <lb/>poteſt, quænam ſidera, quæve conſtellationes, uel ſ<unsure/>igna Septentrionalia, uel <lb/>Auſtralia appellentur. </s> <s xml:id="echoid-s9322" xml:space="preserve">Itẽ quando planetæ dicantur Septentrionales, & </s> <s xml:id="echoid-s9323" xml:space="preserve">quan-<lb/> <anchor type="note" xlink:label="note-265-05a" xlink:href="note-265-05"/> do Auſtrales. </s> <s xml:id="echoid-s9324" xml:space="preserve">Quandocunque enim fuerint in ea parte cęli, quam Septentrio-<lb/>nalem diximus uocari, ſeptentrionales dicuntur: </s> <s xml:id="echoid-s9325" xml:space="preserve">quãdo uero in ea extiterint, <lb/>quam nominauimus Auſtralem, Auſtrales uocantur. </s> <s xml:id="echoid-s9326" xml:space="preserve">Vnde dum Sol mouetur <lb/>ab initio ♈, uſque ad principium ♎, Septentrionalis appellatur; </s> <s xml:id="echoid-s9327" xml:space="preserve">Dum uero à <lb/>principio ♎, ad principium ♈, tendit, Meridionalis, ſiue Auſtralis dici conſue <lb/> <anchor type="note" xlink:label="note-265-06a" xlink:href="note-265-06"/> uit. </s> <s xml:id="echoid-s9328" xml:space="preserve">Sumitur quidem, & </s> <s xml:id="echoid-s9329" xml:space="preserve">aliter pars ſeptentrionalis, Auſtralisq́; </s> <s xml:id="echoid-s9330" xml:space="preserve">apud Aſtrono-<lb/>mos, ut docebimus, quando de Eclipticæ utilitatibus uerba faciemus. </s> <s xml:id="echoid-s9331" xml:space="preserve">Sed hæc <lb/>eſt potiſſima acceptio partis ſeptentrionalis, & </s> <s xml:id="echoid-s9332" xml:space="preserve">Auſtralis apud auctores. </s> <s xml:id="echoid-s9333" xml:space="preserve">Im-<lb/>mo & </s> <s xml:id="echoid-s9334" xml:space="preserve">apud Coſmographos Aequator, in terra deſcriptus diſtribuit totam ter-<lb/>ram in partem Borealem, & </s> <s xml:id="echoid-s9335" xml:space="preserve">Auſtralem.</s> <s xml:id="echoid-s9336" xml:space="preserve"/> </p> <div xml:id="echoid-div471" type="float" level="2" n="1"> <note position="right" xlink:label="note-265-03" xlink:href="note-265-03a" xml:space="preserve">Aequator <lb/>dirimit par <lb/>tem cęli b@ <lb/>realem ab <lb/>auſtrali.</note> <note position="right" xlink:label="note-265-04" xlink:href="note-265-04a" xml:space="preserve">Borealis <lb/>pars cęli, & <lb/>auſtralis q̃.</note> <note position="right" xlink:label="note-265-05" xlink:href="note-265-05a" xml:space="preserve">Septentrio-<lb/>nalia, au-<lb/>ftraliave <lb/>aſtra, uel ſi <lb/>gna, quæ.</note> <note position="right" xlink:label="note-265-06" xlink:href="note-265-06a" xml:space="preserve">Aequator <lb/>in terra par <lb/>titur terrã <lb/>totam in <lb/>partem bo-<lb/>realẽ, & au <lb/>ſtralem.</note> </div> </div> <div xml:id="echoid-div473" type="section" level="1" n="157"> <head xml:id="echoid-head163" xml:space="preserve">VII.</head> <p> <s xml:id="echoid-s9337" xml:space="preserve"><emph style="sc">Praefinit</emph> nobis longitudinem, ſeu quantitatem diei artificialis, no <lb/> <anchor type="note" xlink:label="note-265-07a" xlink:href="note-265-07"/> ctisq́ue in quacunque orbis terreni habitatione. </s> <s xml:id="echoid-s9338" xml:space="preserve">Eſt enim in quauis regione, A <lb/>quolibet anni tempore, dies artificialis tanta, quantus eſt arcus Aequinoctia-<lb/>lis circuli, qui ſupra hemiſphærium aſcendit, dũ ſupra idem hemiſphæriũ Sol <lb/>commoratur. </s> <s xml:id="echoid-s9339" xml:space="preserve">Hic aũt arcus Aequatoris hac ratione deprehendetur ex ſphæ. <lb/></s> <s xml:id="echoid-s9340" xml:space="preserve">ra materiali rite, & </s> <s xml:id="echoid-s9341" xml:space="preserve">accurate fabricata. </s> <s xml:id="echoid-s9342" xml:space="preserve">Statuatur ſphæra materialis in propria <lb/> <anchor type="note" xlink:label="note-265-08a" xlink:href="note-265-08"/> poſitione, ideſt, in debita eleuatione poli, gradusq́; </s> <s xml:id="echoid-s9343" xml:space="preserve">ille Eclipticæ, in quo Sol <lb/>die propoſito exiſtit, in Horizonte ex parte orientis collocetur, diligenterq́; <lb/></s> <s xml:id="echoid-s9344" xml:space="preserve">notetur punctum illud Aequatoris, quod tunc in Horizonte ex eadem parte <lb/>exiſtit: </s> <s xml:id="echoid-s9345" xml:space="preserve">Deinde circumuoluatur ſphæra, donec idem gradus Eclipticæ, addito <lb/>inſuper dimidiato fere gradu, in Horizonte reperiatur ex parte occidentis, ite <lb/>rumq́; </s> <s xml:id="echoid-s9346" xml:space="preserve">punctum illud Aequatoris ſignetur, quod tunc Horizontem ex parte <lb/>orientis præciſe, ac ad amuſſim contingere conſpicitur. </s> <s xml:id="echoid-s9347" xml:space="preserve">Quibus peractis, nu-<lb/>merentur gradus Aequinoctialis circuli inter duo illa puncta interiecti, initio <lb/>facto à primo puncto, & </s> <s xml:id="echoid-s9348" xml:space="preserve">uerſus partes orientales procedendo. </s> <s xml:id="echoid-s9349" xml:space="preserve">Nam dicti gra-<lb/>dus Aequatoris deproment arcum diurnum propoſitum, hoc eſt, qui ſimul cũ <pb o="230" file="266" n="267" rhead="Comment. in II. Cap. Sphæræ"/> Sole, dum in hemiſphærio ſupero moratur, ſupra Horizontem emergit, Qua-<lb/>re ſi arcus præfatus per 15. </s> <s xml:id="echoid-s9350" xml:space="preserve">diuidatur, prodibunt mox horæ in illo die conten-<lb/>tæ, dummodo memor ſis, ſingulos gradus, qui fortaſſis ex diuiſione relinquun <lb/>tur, quaterna minuta horæ complecti. </s> <s xml:id="echoid-s9351" xml:space="preserve"><emph style="sc">Ex e m p l v m</emph>. </s> <s xml:id="echoid-s9352" xml:space="preserve">Sole exiſtente in <lb/>principio ♋, ſi ſphæra materialis ita ſtatuatur, ut inter polum Arcticũ, & </s> <s xml:id="echoid-s9353" xml:space="preserve">Ho-<lb/>rizoncem intercipiantur 42. </s> <s xml:id="echoid-s9354" xml:space="preserve">grad. </s> <s xml:id="echoid-s9355" xml:space="preserve">Meridiani, (quot nimirum gradibus Romæ <lb/> <anchor type="note" xlink:label="note-266-01a" xlink:href="note-266-01"/> polus arcticus ſopra Horizontem extollitur) & </s> <s xml:id="echoid-s9356" xml:space="preserve">primus gradus ♋, in Hori-<lb/>zonte tum ex parte orientis, tum ex parte occidentis, ponatur, notenturq́ue <lb/>duo puncta in Aequatore, deprehendetur arcus diurnus comptehendere grad. <lb/></s> <s xml:id="echoid-s9357" xml:space="preserve">226. </s> <s xml:id="echoid-s9358" xml:space="preserve">min. </s> <s xml:id="echoid-s9359" xml:space="preserve">6. </s> <s xml:id="echoid-s9360" xml:space="preserve">fere, qui ad horas reductus, diuiſione facta per 15. </s> <s xml:id="echoid-s9361" xml:space="preserve">monſtrabit diẽ <lb/>artificialem Romæ die 22. </s> <s xml:id="echoid-s9362" xml:space="preserve">Iunij, quando uidelicet Sol in principio ♋, exiſtit, <lb/>conſtare horis 15. </s> <s xml:id="echoid-s9363" xml:space="preserve">& </s> <s xml:id="echoid-s9364" xml:space="preserve">min. </s> <s xml:id="echoid-s9365" xml:space="preserve">fere 4. </s> <s xml:id="echoid-s9366" xml:space="preserve">Ex cognita autem magnitudine diei artificia-<lb/>lis facile cognoſcetur quantitas noctis artificialis. </s> <s xml:id="echoid-s9367" xml:space="preserve">Si enim diem artificialem <lb/>ex 24. </s> <s xml:id="echoid-s9368" xml:space="preserve">horis, nempe ex tota die naturali abſtuleris, remanebit nox artificialis. </s> <s xml:id="echoid-s9369" xml:space="preserve"><lb/>Hac ratione, ſi 15. </s> <s xml:id="echoid-s9370" xml:space="preserve">hor. </s> <s xml:id="echoid-s9371" xml:space="preserve">& </s> <s xml:id="echoid-s9372" xml:space="preserve">4. </s> <s xml:id="echoid-s9373" xml:space="preserve">min. </s> <s xml:id="echoid-s9374" xml:space="preserve">auferantur ex 24. </s> <s xml:id="echoid-s9375" xml:space="preserve">hor. </s> <s xml:id="echoid-s9376" xml:space="preserve">comprehendet Romæ <lb/>nox die 12. </s> <s xml:id="echoid-s9377" xml:space="preserve">Iunij horas 8. </s> <s xml:id="echoid-s9378" xml:space="preserve">& </s> <s xml:id="echoid-s9379" xml:space="preserve">min. </s> <s xml:id="echoid-s9380" xml:space="preserve">56. </s> <s xml:id="echoid-s9381" xml:space="preserve">Poterit tamen quiuis, fi uu<unsure/>lt, eodem arti-<lb/>ficio quantitatem noctis elicere, quo diei magnitudinem inueſtigari diximus.</s> <s xml:id="echoid-s9382" xml:space="preserve"/> </p> <div xml:id="echoid-div473" type="float" level="2" n="1"> <note position="right" xlink:label="note-265-07" xlink:href="note-265-07a" xml:space="preserve">Aequator <lb/>indicat lon <lb/>gitudinem <lb/>diei, & no-<lb/>ctis arti fi-<lb/>cialis.</note> <note position="right" xlink:label="note-265-08" xlink:href="note-265-08a" xml:space="preserve">Quanta ſit <lb/>dies arti fi-<lb/>cialis, & <lb/>qũo exſphę <lb/>ta materia <lb/>li deprehẽ <lb/>datur.</note> <note position="left" xlink:label="note-266-01" xlink:href="note-266-01a" xml:space="preserve">Altitudo <lb/>poli Romæ <lb/>quanta ſit.</note> </div> </div> <div xml:id="echoid-div475" type="section" level="1" n="158"> <head xml:id="echoid-head164" xml:space="preserve">VIII.</head> <p> <s xml:id="echoid-s9383" xml:space="preserve"><emph style="sc">Mirvm</emph> in modum deſeruit Coſmographis, & </s> <s xml:id="echoid-s9384" xml:space="preserve">Geographis. </s> <s xml:id="echoid-s9385" xml:space="preserve">Nam ſine cir <lb/> <anchor type="note" xlink:label="note-266-02a" xlink:href="note-266-02"/> culo Aequinoctiali nulla terræ deſcriptio abſoluta eſſe poteſt, nullaq́; </s> <s xml:id="echoid-s9386" xml:space="preserve">ciuitas <lb/>in globo terreſtri, aut in mappa mũdi proprio in loco reponetur. </s> <s xml:id="echoid-s9387" xml:space="preserve">Penes enim <lb/>Aequinoctialem circulum & </s> <s xml:id="echoid-s9388" xml:space="preserve">longitudo ciuitatum, & </s> <s xml:id="echoid-s9389" xml:space="preserve">latitudo deſumitur, ut <lb/>apertius do<unsure/>cebimus, cum de circulo Meridiano, qui ad id quoque negotium <lb/>requiritur, egerimus.</s> <s xml:id="echoid-s9390" xml:space="preserve"/> </p> <div xml:id="echoid-div475" type="float" level="2" n="1"> <note position="left" xlink:label="note-266-02" xlink:href="note-266-02a" xml:space="preserve">Aequator <lb/>ntilis eſt <lb/>coſmogra-<lb/>@his.</note> </div> <p> <s xml:id="echoid-s9391" xml:space="preserve"><emph style="sc">Habet</emph> quidem Aequinoctialis circulus præter ea, quæ dicta ſunt, plu-<lb/>rima alia officia, utilitatesq́ue apud Aſtronomos, quibus breuitatis memor ſu-<lb/>perſedendum nunc eſſe cenſeo. </s> <s xml:id="echoid-s9392" xml:space="preserve">Proprijs enim in locis, quando res exiget, <lb/>multo commodius explicari poterunt. </s> <s xml:id="echoid-s9393" xml:space="preserve">Satis nunc fit, potiſſima officia ipſius <lb/>demonſtraſſe-</s> </p> <p> <s xml:id="echoid-s9394" xml:space="preserve"><emph style="sc">Qvoniam</emph> vero in ſeptimo officio Aequatoris neceſſe fuit reducere <lb/>gradus, & </s> <s xml:id="echoid-s9395" xml:space="preserve">minuta Aequinoctialis circuli ad horas, ac minuta horarum, utile <lb/>eſſe iudicaui hoc loco proponere duas tabellas, per quarum priorem fa-<lb/>cillimo negocio reducuntur gradus, Minuta, Secunda, & </s> <s xml:id="echoid-s9396" xml:space="preserve">Tertia, <lb/>Aequinoctialis circuli ad horas, minuta, ſecunda, & </s> <s xml:id="echoid-s9397" xml:space="preserve">ad tertia <lb/>horarum: </s> <s xml:id="echoid-s9398" xml:space="preserve">per poſteriorem uero uiciſſim eadem facilitate <lb/>tranſmutantur horæ, minuta, ſecunda, ac tertia ho-<lb/>rarum in gradus, minuta, ſecunda, ac tertia <lb/>Aequinoctialis circuli. </s> <s xml:id="echoid-s9399" xml:space="preserve">Quamuis enim <lb/>vtrumque per diuifionem effici poſ-<lb/>ſit, tamen multo expeditius <lb/>idem dictæ tabellæ <lb/>conficiunt.</s> <s xml:id="echoid-s9400" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div477" type="section" level="1" n="159"> <head xml:id="echoid-head165" style="it" xml:space="preserve">DVPLEX TABVLA, QVA PARTES AEQVA-<lb/>toris in tempus: & contra tempus in partes Aequa-<lb/>toris conuertuntur.</head> <pb o="231" file="267" n="268" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div478" type="section" level="1" n="160"> <head xml:id="echoid-head166" xml:space="preserve">CONVERSIO \\ gradum, minutorum, & \\ ſecundorum Aequatoris \\ in horas, minuta, ſecun- \\ da, & tertia. CONVERSIO \\ horarum, minutorum, \\ ſecundorum, & tertio- \\ rum in gradus, minuta, \\ & ſecunda Aequatoris.</head> <note position="right" xml:space="preserve"> <lb/> G. # H. # M. # G. # H. # M. # G. # H. # M. # H. # G. # M. # G. # M. # M. # G. # M. 1 # 0 # 4 # 31 # 2 # 4 # 70 # 4 # 40 # 1 # 15 # 1 # 0 # 15 # 31 # 7 # 45 2 # 0 # 8 # 32 # 2 # 8 # 80 # 5 # 20 # 2 # 30 # 2 # 0 # 30 # 32 # 8 # 0 3 # 0 # 12 # 33 # 2 # 12 # 90 # 6 # 0 # 3 # 45 # 3 # 0 # 45 # 33 # 8 # 15 4 # 0 # 16 # 34 # 2 # 16 # 100 # 6 # 40 # 4 # 60 # 4 # 0 # 0 # 34 # 8 # 30 5 # 0 # 20 # 35 # 2 # 20 # 110 # 7 # 20 # 5 # 75 # 5 # 1 # 15 # 35 # 8 # 45 6 # 0 # 24 # 36 # 2 # 24 # 120 # 8 # 0 # 6 # 90 # 6 # 1 # 30 # 36 # 9 # 0 7 # 0 # 28 # 38 # 2 # 28 # 130 # 8 # 40 # 7 # 105 # 7 # 1 # 45 # 37 # 9 # 15 8 # 0 # 32 # 38 # 2 # 32 # 140 # 9 # 20 # 8 # 120 # 8 # 2 # 0 # 38 # 9 # 30 9 # 0 # 36 # 29 # 2 # 36 # 150 # 10 # 0 # 9 # 135 # 9 # 2 # 15 # 39 # 9 # 45 10 # 0 # 40 # 40 # 2 # 40 # 160 # 10 # 40 # 10 # 150 # 10 # 2 # 30 # 40 # 10 # 0 11 # 0 # 44 # 41 # 2 # 44 # 170 # 11 # 20 # 11 # 165 # 11 # 2 # 45 # 41 # 10 # 15 12 # 0 # 48 # 42 # 2 # 48 # 180 # 12 # 0 # 12 # 180 # 12 # 3 # 0 # 42 # 10 # 30 13 # 0 # 52 # 43 # 2 # 52 # 190 # 12 # 40 # 13 # 195 # 13 # 3 # 15 # 43 # 10 # 45 14 # 0 # 56 # 44 # 2 # 56 # 200 # 13 # 20 # 14 # 210 # 14 # 3 # 30 # 44 # 11 # 0 15 # 1 # 0 # 45 # 3 # 0 # 210 # 14 # 0 # 15 # 225 # 15 # 3 # 45 # 45 # 11 # 15 16 # 1 # 4 # 46 # 3 # 4 # 220 # 14 # 40 # 16 # 140 # 16 # 4 # 0 # 46 # 11 # 30 17 # 1 # 8 # 47 # 3 # 8 # 230 # 15 # 20 # 17 # 255 # 17 # 4 # 15 # 47 # 11 # 45 18 # 1 # 12 # 48 # 3 # 12 # 240 # 16 # 0 # 18 # 270 # 18 # 4 # 30 # 48 # 12 # 0 19 # 1 # 16 # 49 # 3 # 16 # 250 # 16 # 40 # 19 # 285 # 19 # 4 # 45 # 49 # 12 # 15 20 # 1 # 20 # 50 # 3 # 20 # 260 # 17 # 20 # 20 # 300 # 20 # 5 # 0 # 50 # 12 # 30 21 # 1 # 24 # 51 # 3 # 24 # 270 # 18 # 0 # 21 # 215 # 21 # 5 # 15 # 51 # 12 # 45 22 # 1 # 28 # 52 # 3 # 28 # 280 # 18 # 40 # 22 # 330 # 22 # 5 # 30 # 52 # 13 # 0 23 # 1 # 32 # 53 # 3 # 32 # 290 # 19 # 20 # 23 # 345 # 23 # 5 # 45 # 53 # 13 # 15 24 # 1 # 36 # 54 # 3 # 36 # 300 # 2<unsure/>0 # 0 # 24 # 460 # 24 # 6 # 0 # 54 # 13 # 30 25 # 1 # 40 # 55 # 3 # 40 # 310 # 20 # 40 # # # 25 # 6 # 15 # 55 # 13 # 45 26 # 1 # 44 # 56 # 3 # 44 # 320 # 21 # 20 # # # 26 # 6 # 30 # 56 # 14 # 0 27 # 1 # 58 # 57 # 3 # 48 # 330 # 22 # 0 # # # 27 # 6 # 45 # 57 # 14 # 15 28 # 1 # 52 # 58 # 3 # 52 # 340 # 22 # 40 # # # 28 # 7 # 0 # 58 # 14 # 30 29 # 1 # 56 # 59 # 3 # 56 # 350 # 23 # 20 # # # 29 # 7 # 15 # 59 # 14 # 45 30 # 2 # 0 # 60 # 4 # 0 # 360 # 24 # 0 # # # 30 # 7 # 30 # 60 # 15 # 0 M. # M. # S. # M. # M. # S. # # # # # S. # M. # S. # S. # M. # S. S. # S. # T. # S. # S. # T. # # # # # T. # S. # T. # T. # S. # T. </note> <pb o="232" file="268" n="269" rhead="Comment. in II. Cap. Sphæræ"/> </div> <div xml:id="echoid-div479" type="section" level="1" n="161"> <head xml:id="echoid-head167" xml:space="preserve">VSVS TABVLARVM PRÆCEDENTIVM.</head> <p> <s xml:id="echoid-s9401" xml:space="preserve"><emph style="sc">Si</emph> gradus in horas ſunt commutandi, accipiendi erunt gradus in priori ta-<lb/> <anchor type="note" xlink:label="note-268-01a" xlink:href="note-268-01"/> bella ſub titulo G. </s> <s xml:id="echoid-s9402" xml:space="preserve">& </s> <s xml:id="echoid-s9403" xml:space="preserve">mox duæ ſubſequentes columnę iudicabunt horas, minu <lb/>taq́; </s> <s xml:id="echoid-s9404" xml:space="preserve">horarum, quæ gradibus acceptis debentur. </s> <s xml:id="echoid-s9405" xml:space="preserve">Sic uides gradibus 4. </s> <s xml:id="echoid-s9406" xml:space="preserve">reſponde <lb/>re min. </s> <s xml:id="echoid-s9407" xml:space="preserve">16. </s> <s xml:id="echoid-s9408" xml:space="preserve">horæ. </s> <s xml:id="echoid-s9409" xml:space="preserve">Item gradib. </s> <s xml:id="echoid-s9410" xml:space="preserve">27. </s> <s xml:id="echoid-s9411" xml:space="preserve">horam 1. </s> <s xml:id="echoid-s9412" xml:space="preserve">min. </s> <s xml:id="echoid-s9413" xml:space="preserve">48. </s> <s xml:id="echoid-s9414" xml:space="preserve">Item gradibus 45. </s> <s xml:id="echoid-s9415" xml:space="preserve">horas 3. <lb/></s> <s xml:id="echoid-s9416" xml:space="preserve">min. </s> <s xml:id="echoid-s9417" xml:space="preserve">0. </s> <s xml:id="echoid-s9418" xml:space="preserve">Item gradibus 250. </s> <s xml:id="echoid-s9419" xml:space="preserve">horas 86. </s> <s xml:id="echoid-s9420" xml:space="preserve">min. </s> <s xml:id="echoid-s9421" xml:space="preserve">40. </s> <s xml:id="echoid-s9422" xml:space="preserve">&</s> <s xml:id="echoid-s9423" xml:space="preserve">c. </s> <s xml:id="echoid-s9424" xml:space="preserve">Quod ſi numerus graduum <lb/>præciſe in prædicta tabella non reperiatur, accipiendus erit numerus proxi-<lb/>me minor, cum horis, ac minutis reſpondentibus: </s> <s xml:id="echoid-s9425" xml:space="preserve">Deinde reliqui gradus ite-<lb/>rum ſumendi cum horis & </s> <s xml:id="echoid-s9426" xml:space="preserve">minutis correſpondentibus: </s> <s xml:id="echoid-s9427" xml:space="preserve">Atque tandem poſte-<lb/>riores horæ, ac minuta cum prioribus coniungenda. </s> <s xml:id="echoid-s9428" xml:space="preserve">Vt ſi ſcire lubeat, quot<unsure/> <lb/>horæ reſpondeant gradibus 215. </s> <s xml:id="echoid-s9429" xml:space="preserve">Accipiendæ erunt hocæ 14. </s> <s xml:id="echoid-s9430" xml:space="preserve">reſpondentes gra <lb/>dibus 210. </s> <s xml:id="echoid-s9431" xml:space="preserve">Deinde ſumenda min. </s> <s xml:id="echoid-s9432" xml:space="preserve">20. </s> <s xml:id="echoid-s9433" xml:space="preserve">reſpondentia reliquis gradibus 5. </s> <s xml:id="echoid-s9434" xml:space="preserve">Atque <lb/>ita gradibus 215. </s> <s xml:id="echoid-s9435" xml:space="preserve">debentur horæ 14. </s> <s xml:id="echoid-s9436" xml:space="preserve">min. </s> <s xml:id="echoid-s9437" xml:space="preserve">20. </s> <s xml:id="echoid-s9438" xml:space="preserve">& </s> <s xml:id="echoid-s9439" xml:space="preserve">ſic de cæteris.</s> <s xml:id="echoid-s9440" xml:space="preserve"/> </p> <div xml:id="echoid-div479" type="float" level="2" n="1"> <note position="left" xlink:label="note-268-01" xlink:href="note-268-01a" xml:space="preserve">Qua ratio-<lb/>ne ex præce <lb/>dentibus ta <lb/>bulis redu-<lb/>cantur gra <lb/>dus acminu <lb/>ta ad hora, <lb/>& co<unsure/>tra.</note> </div> <p> <s xml:id="echoid-s9441" xml:space="preserve"><emph style="sc">Si</emph> vero minuta, uel ſecunda graduum in horas ſunt conuertenda, accipien <lb/>da erunt minuta, uel ſecunda graduum, ſupra titulos M, vel S, & </s> <s xml:id="echoid-s9442" xml:space="preserve">illico ſequen <lb/>tes duæ c<unsure/>olumnæ oſtendent minuta, ſecunda, uel tertia horarum, vt literæ, <lb/>quæ ad pedem tabellæ ſunt poſitæ, indicant. </s> <s xml:id="echoid-s9443" xml:space="preserve">Hac ratione cernis, minutis 56. <lb/></s> <s xml:id="echoid-s9444" xml:space="preserve">vnius gradus reſpondere min. </s> <s xml:id="echoid-s9445" xml:space="preserve">3. </s> <s xml:id="echoid-s9446" xml:space="preserve">ſec. </s> <s xml:id="echoid-s9447" xml:space="preserve">44. </s> <s xml:id="echoid-s9448" xml:space="preserve">unius horæ. </s> <s xml:id="echoid-s9449" xml:space="preserve">Item ſecundis 25. </s> <s xml:id="echoid-s9450" xml:space="preserve">unius <lb/>gradus deberi ſec. </s> <s xml:id="echoid-s9451" xml:space="preserve">1. </s> <s xml:id="echoid-s9452" xml:space="preserve">ter. </s> <s xml:id="echoid-s9453" xml:space="preserve">40. </s> <s xml:id="echoid-s9454" xml:space="preserve">unius horæ.</s> <s xml:id="echoid-s9455" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9456" xml:space="preserve"><emph style="sc">Havd</emph> aliter ex poſſeriori tabella reducentur horæ, minuta, ſecunda, ac <lb/>terria horatum ad gradus, minuta ſecunda, & </s> <s xml:id="echoid-s9457" xml:space="preserve">tertia, &</s> <s xml:id="echoid-s9458" xml:space="preserve">c.</s> <s xml:id="echoid-s9459" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9460" xml:space="preserve"><emph style="sc">Qvod</emph> ſi huiuſcemodi@ tabellis u ti quis noluerit, reducentur gradus, mi-<lb/> <anchor type="note" xlink:label="note-268-02a" xlink:href="note-268-02"/> nuta, &</s> <s xml:id="echoid-s9461" xml:space="preserve">c. </s> <s xml:id="echoid-s9462" xml:space="preserve">hoc modo. </s> <s xml:id="echoid-s9463" xml:space="preserve">Multiplicentur gradus, minuta, ſecunda, &</s> <s xml:id="echoid-s9464" xml:space="preserve">c. </s> <s xml:id="echoid-s9465" xml:space="preserve">per 4. </s> <s xml:id="echoid-s9466" xml:space="preserve">Nam <lb/>producti numeri dabunt partes temporis proxime minores. </s> <s xml:id="echoid-s9467" xml:space="preserve">Vt productus nu-<lb/>merus ex gradibus dabit minuta hora@um, productus uero numerus ex minu-<lb/>tis graduum dabit ſecunda horarum, &</s> <s xml:id="echoid-s9468" xml:space="preserve">c. </s> <s xml:id="echoid-s9469" xml:space="preserve">E X E M P L V M. </s> <s xml:id="echoid-s9470" xml:space="preserve">Si grad. </s> <s xml:id="echoid-s9471" xml:space="preserve">9. </s> <s xml:id="echoid-s9472" xml:space="preserve">min. </s> <s xml:id="echoid-s9473" xml:space="preserve">40. <lb/></s> <s xml:id="echoid-s9474" xml:space="preserve">ſec. </s> <s xml:id="echoid-s9475" xml:space="preserve">20. </s> <s xml:id="echoid-s9476" xml:space="preserve">multiplicentur per 4. </s> <s xml:id="echoid-s9477" xml:space="preserve">producentur hor. </s> <s xml:id="echoid-s9478" xml:space="preserve">o minut. </s> <s xml:id="echoid-s9479" xml:space="preserve">36. </s> <s xml:id="echoid-s9480" xml:space="preserve">ſec. </s> <s xml:id="echoid-s9481" xml:space="preserve">160. </s> <s xml:id="echoid-s9482" xml:space="preserve">ter. </s> <s xml:id="echoid-s9483" xml:space="preserve">80. </s> <s xml:id="echoid-s9484" xml:space="preserve">hoc <lb/>eſt, hor. </s> <s xml:id="echoid-s9485" xml:space="preserve">0. </s> <s xml:id="echoid-s9486" xml:space="preserve">min. </s> <s xml:id="echoid-s9487" xml:space="preserve">38. </s> <s xml:id="echoid-s9488" xml:space="preserve">ſec. </s> <s xml:id="echoid-s9489" xml:space="preserve">41. </s> <s xml:id="echoid-s9490" xml:space="preserve">ter. </s> <s xml:id="echoid-s9491" xml:space="preserve">20. </s> <s xml:id="echoid-s9492" xml:space="preserve">Rurſus ſi grad. </s> <s xml:id="echoid-s9493" xml:space="preserve">20. </s> <s xml:id="echoid-s9494" xml:space="preserve">min. </s> <s xml:id="echoid-s9495" xml:space="preserve">40. </s> <s xml:id="echoid-s9496" xml:space="preserve">multiplicen-<lb/>tur per 4. </s> <s xml:id="echoid-s9497" xml:space="preserve">gig@entur hor. </s> <s xml:id="echoid-s9498" xml:space="preserve">0. </s> <s xml:id="echoid-s9499" xml:space="preserve">min. </s> <s xml:id="echoid-s9500" xml:space="preserve">80. </s> <s xml:id="echoid-s9501" xml:space="preserve">ſec. </s> <s xml:id="echoid-s9502" xml:space="preserve">160. </s> <s xml:id="echoid-s9503" xml:space="preserve">hoc eſt, hor. </s> <s xml:id="echoid-s9504" xml:space="preserve">1. </s> <s xml:id="echoid-s9505" xml:space="preserve">min. </s> <s xml:id="echoid-s9506" xml:space="preserve">22. </s> <s xml:id="echoid-s9507" xml:space="preserve">ſec. </s> <s xml:id="echoid-s9508" xml:space="preserve">40. </s> <s xml:id="echoid-s9509" xml:space="preserve">atque <lb/>ita de cæteris.</s> <s xml:id="echoid-s9510" xml:space="preserve"/> </p> <div xml:id="echoid-div480" type="float" level="2" n="2"> <note position="left" xlink:label="note-268-02" xlink:href="note-268-02a" xml:space="preserve">Quo pacto <lb/>ex grad & <lb/>min. fiant <lb/>horæ, & <lb/>min. & con <lb/>tra, qũo ex <lb/>hor. & min. <lb/>fiant grad. <lb/>& minu@a.</note> </div> <p> <s xml:id="echoid-s9511" xml:space="preserve"><emph style="sc">Iam</emph> uero, ſi horæ, minuta, &</s> <s xml:id="echoid-s9512" xml:space="preserve">c. </s> <s xml:id="echoid-s9513" xml:space="preserve">diuidantur per 4. </s> <s xml:id="echoid-s9514" xml:space="preserve">producentur partes Ae-<lb/>quatoris proxime maior@@. </s> <s xml:id="echoid-s9515" xml:space="preserve">Vt ex tertijs horarum producentur ſecunda gra-<lb/>duum; </s> <s xml:id="echoid-s9516" xml:space="preserve">ex ſecundis horarum producentur minuta graduum; </s> <s xml:id="echoid-s9517" xml:space="preserve">ex minutis hora-<lb/>rum producentur gradus; </s> <s xml:id="echoid-s9518" xml:space="preserve">& </s> <s xml:id="echoid-s9519" xml:space="preserve">ex horis deniq; </s> <s xml:id="echoid-s9520" xml:space="preserve">producentur partes unius partis <lb/>Aequatoris, quæ comprehendat grad. </s> <s xml:id="echoid-s9521" xml:space="preserve">60. </s> <s xml:id="echoid-s9522" xml:space="preserve">quemadmodum, & </s> <s xml:id="echoid-s9523" xml:space="preserve">unus gradus com <lb/>plectitur min. </s> <s xml:id="echoid-s9524" xml:space="preserve">60. </s> <s xml:id="echoid-s9525" xml:space="preserve">E X E M P L V M. </s> <s xml:id="echoid-s9526" xml:space="preserve">Si hor. </s> <s xml:id="echoid-s9527" xml:space="preserve">0. </s> <s xml:id="echoid-s9528" xml:space="preserve">minu. </s> <s xml:id="echoid-s9529" xml:space="preserve">38. </s> <s xml:id="echoid-s9530" xml:space="preserve">ſec. </s> <s xml:id="echoid-s9531" xml:space="preserve">41. </s> <s xml:id="echoid-s9532" xml:space="preserve">ter. </s> <s xml:id="echoid-s9533" xml:space="preserve">20. </s> <s xml:id="echoid-s9534" xml:space="preserve">diui-<lb/>dantur per 4. </s> <s xml:id="echoid-s9535" xml:space="preserve">producentur partes 0. </s> <s xml:id="echoid-s9536" xml:space="preserve">( quatum quælibet complectatur grad. <lb/></s> <s xml:id="echoid-s9537" xml:space="preserve">60.) </s> <s xml:id="echoid-s9538" xml:space="preserve">g@ad. </s> <s xml:id="echoid-s9539" xml:space="preserve">9 {1/2}. </s> <s xml:id="echoid-s9540" xml:space="preserve">min. </s> <s xml:id="echoid-s9541" xml:space="preserve">10 {1/4}. </s> <s xml:id="echoid-s9542" xml:space="preserve">ſec. </s> <s xml:id="echoid-s9543" xml:space="preserve">5. </s> <s xml:id="echoid-s9544" xml:space="preserve">hoc eſt, part. </s> <s xml:id="echoid-s9545" xml:space="preserve">0. </s> <s xml:id="echoid-s9546" xml:space="preserve">grad. </s> <s xml:id="echoid-s9547" xml:space="preserve">9. </s> <s xml:id="echoid-s9548" xml:space="preserve">minu. </s> <s xml:id="echoid-s9549" xml:space="preserve">40. </s> <s xml:id="echoid-s9550" xml:space="preserve">ſec. </s> <s xml:id="echoid-s9551" xml:space="preserve">20. </s> <s xml:id="echoid-s9552" xml:space="preserve">Nam <lb/>grad. </s> <s xml:id="echoid-s9553" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s9554" xml:space="preserve">facit min. </s> <s xml:id="echoid-s9555" xml:space="preserve">30. </s> <s xml:id="echoid-s9556" xml:space="preserve">quæ cum min. </s> <s xml:id="echoid-s9557" xml:space="preserve">10. </s> <s xml:id="echoid-s9558" xml:space="preserve">faciunt min. </s> <s xml:id="echoid-s9559" xml:space="preserve">40. </s> <s xml:id="echoid-s9560" xml:space="preserve">Item min. </s> <s xml:id="echoid-s9561" xml:space="preserve">{1/4}. </s> <s xml:id="echoid-s9562" xml:space="preserve">facit ſec. </s> <s xml:id="echoid-s9563" xml:space="preserve"><lb/>15. </s> <s xml:id="echoid-s9564" xml:space="preserve">quæ cum ſec. </s> <s xml:id="echoid-s9565" xml:space="preserve">5. </s> <s xml:id="echoid-s9566" xml:space="preserve">faciunt ſec. </s> <s xml:id="echoid-s9567" xml:space="preserve">20. </s> <s xml:id="echoid-s9568" xml:space="preserve">Rurſus ſi hor. </s> <s xml:id="echoid-s9569" xml:space="preserve">1. </s> <s xml:id="echoid-s9570" xml:space="preserve">minu. </s> <s xml:id="echoid-s9571" xml:space="preserve">22. </s> <s xml:id="echoid-s9572" xml:space="preserve">ſec. </s> <s xml:id="echoid-s9573" xml:space="preserve">40. </s> <s xml:id="echoid-s9574" xml:space="preserve">diuidantur <lb/>per 4. </s> <s xml:id="echoid-s9575" xml:space="preserve">prouenient par. </s> <s xml:id="echoid-s9576" xml:space="preserve">{1/4}. </s> <s xml:id="echoid-s9577" xml:space="preserve">(ex illis, quarum quælibet complectitur grad. </s> <s xml:id="echoid-s9578" xml:space="preserve">60.) </s> <s xml:id="echoid-s9579" xml:space="preserve"><lb/>grad. </s> <s xml:id="echoid-s9580" xml:space="preserve">5 {1/2}. </s> <s xml:id="echoid-s9581" xml:space="preserve">min. </s> <s xml:id="echoid-s9582" xml:space="preserve">10. </s> <s xml:id="echoid-s9583" xml:space="preserve">hoc eſt, grad. </s> <s xml:id="echoid-s9584" xml:space="preserve">20. </s> <s xml:id="echoid-s9585" xml:space="preserve">minu. </s> <s xml:id="echoid-s9586" xml:space="preserve">40. </s> <s xml:id="echoid-s9587" xml:space="preserve">propterea quòd part. </s> <s xml:id="echoid-s9588" xml:space="preserve">{1/4}. </s> <s xml:id="echoid-s9589" xml:space="preserve">(ex illis, <lb/>quarum quælibet grad. </s> <s xml:id="echoid-s9590" xml:space="preserve">60. </s> <s xml:id="echoid-s9591" xml:space="preserve">continer) facir grad. </s> <s xml:id="echoid-s9592" xml:space="preserve">15. </s> <s xml:id="echoid-s9593" xml:space="preserve">quæ cum grad. </s> <s xml:id="echoid-s9594" xml:space="preserve">5. </s> <s xml:id="echoid-s9595" xml:space="preserve">faciunt gr. </s> <s xml:id="echoid-s9596" xml:space="preserve"><lb/>20. </s> <s xml:id="echoid-s9597" xml:space="preserve">Item grad. </s> <s xml:id="echoid-s9598" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s9599" xml:space="preserve">facit mi@u. </s> <s xml:id="echoid-s9600" xml:space="preserve">30. </s> <s xml:id="echoid-s9601" xml:space="preserve">quæ cum min. </s> <s xml:id="echoid-s9602" xml:space="preserve">10. </s> <s xml:id="echoid-s9603" xml:space="preserve">faciunt min. </s> <s xml:id="echoid-s9604" xml:space="preserve">40. </s> <s xml:id="echoid-s9605" xml:space="preserve">atque ita <lb/>de cæteris.</s> <s xml:id="echoid-s9606" xml:space="preserve"/> </p> <pb o="233" file="269" n="270" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div482" type="section" level="1" n="162"> <head xml:id="echoid-head168" style="it" xml:space="preserve">DE ZODIACO CIRCVLO.</head> <note position="right" xml:space="preserve">Zodiacus <lb/>quid.</note> <p style="it"> <s xml:id="echoid-s9607" xml:space="preserve"><emph style="sc">Est</emph> alius circulus in ſphæra, qui interſecat Aequinoctialem, <lb/>& </s> <s xml:id="echoid-s9608" xml:space="preserve">interſecatur ab eodem in duas partes æquales, & </s> <s xml:id="echoid-s9609" xml:space="preserve">una <lb/>eius medietas declinat uerſus Septentrionem, alia uerſus <lb/>Auſtrum.</s> <s xml:id="echoid-s9610" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div483" type="section" level="1" n="163"> <head xml:id="echoid-head169" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s9611" xml:space="preserve">P<unsure/><emph style="sc">Ost</emph> tractationem de Aequatore agit ſecundo loco auctor de <lb/>Zodiaco, eo quòd reliquorum circulorum cognitio ex huius no-<lb/>titia dependeat<unsure/>. </s> <s xml:id="echoid-s9612" xml:space="preserve">Deſcribens igitur circulum Zodiacum ait, eum <lb/>eſſe circulum in ſphæra, intellige maximum, qui inter ſecat Ac-<lb/>quinoctialem circulum, & </s> <s xml:id="echoid-s9613" xml:space="preserve">ab eodem interſecatur in duas par@@s <lb/>æquales, quarum una in ſeptentrionem, altera in Auſtrum uergit. </s> <s xml:id="echoid-s9614" xml:space="preserve">Huius cir-<lb/> <anchor type="note" xlink:label="note-269-02a" xlink:href="note-269-02"/> culi polos diximus in 1. </s> <s xml:id="echoid-s9615" xml:space="preserve">cap. </s> <s xml:id="echoid-s9616" xml:space="preserve">cum de circulis ſphærę generatim ageremus, re-<lb/>moueri à polis mundi quarta parte, & </s> <s xml:id="echoid-s9617" xml:space="preserve">inſuper nonageſima unius qnadrantis, <lb/>hoc eſt, gradibus 23 {1/2}. </s> <s xml:id="echoid-s9618" xml:space="preserve">Ex quo fit, ut medium punctum utriuſque medietatis <lb/>ipſius eandem diſtantiam habeat prorſus ab Aequatore, unum quidem in Bo-<lb/>ream, alterum uero in Auſtrum vergens.</s> <s xml:id="echoid-s9619" xml:space="preserve"/> </p> <div xml:id="echoid-div483" type="float" level="2" n="1"> <note position="right" xlink:label="note-269-02" xlink:href="note-269-02a" xml:space="preserve">Diſtãtia po<unsure/> <lb/>lorũ Zodia <lb/>ci à polis <lb/>mundi.</note> </div> <p> <s xml:id="echoid-s9620" xml:space="preserve"><emph style="sc">Hvnc</emph> autem circulum Aſtronomi in cæleſtibus orbibus ex@@gitarunt <lb/> <anchor type="note" xlink:label="note-269-03a" xlink:href="note-269-03"/> præcipue ob motum Planetar um. </s> <s xml:id="echoid-s9621" xml:space="preserve">Oòſeruarunt etenim diuturna experientia, <lb/>Solem, Lunam, ac reliquos Planetas proprijs ſuis motib. </s> <s xml:id="echoid-s9622" xml:space="preserve">ab occidente in ori@n <lb/>tem deflectere ab Aequinoctiali circulo, modo ad ſeptentrionem, modo ad <lb/>meridionalem plagam, & </s> <s xml:id="echoid-s9623" xml:space="preserve">hoc certa quadam, ac determinata diſtant a, elonga-<lb/>tio neque, quæ nimirum comprehendit gr. </s> <s xml:id="echoid-s9624" xml:space="preserve">23. </s> <s xml:id="echoid-s9625" xml:space="preserve">min. </s> <s xml:id="echoid-s9626" xml:space="preserve">30. </s> <s xml:id="echoid-s9627" xml:space="preserve">maxime ſi de Sole ſer-<lb/>mo habeat@r: </s> <s xml:id="echoid-s9628" xml:space="preserve">(Alij namque planetæ nonnihil variant hanc diſtantiam) Dein <lb/>de eoſdem redire; </s> <s xml:id="echoid-s9629" xml:space="preserve">& </s> <s xml:id="echoid-s9630" xml:space="preserve">acced@re ad Aequinoctialem circulum, ſemperq́, eandem <lb/>illos uiam tea<unsure/>ere, ut 1. </s> <s xml:id="echoid-s9631" xml:space="preserve">cap. </s> <s xml:id="echoid-s9632" xml:space="preserve">pluribus experimentis comprobauimus, cum de cę <lb/>lorum motibus diſputaremus. </s> <s xml:id="echoid-s9633" xml:space="preserve">Rurſus manifeſtiſſimis indicijs deprehenderunt, <lb/>ut ibidem oſtendimus, Firmamentum cum omnibus ſtellis fixis ab occaſu in <lb/>ortum ſuper polos diſtantes à polis mundi grad. </s> <s xml:id="echoid-s9634" xml:space="preserve">23 {1/2}. </s> <s xml:id="echoid-s9635" xml:space="preserve">moueri. </s> <s xml:id="echoid-s9636" xml:space="preserve">Vnde notarunt <lb/>in cœlo circulum maximum, quem Zodiacum appellarunt, ut eſſer uia omniũ <lb/>planetarum, & </s> <s xml:id="echoid-s9637" xml:space="preserve">cingulus ſecundi motus, etiam ſtellarum fixarum, quemadmo <lb/> <anchor type="note" xlink:label="note-269-04a" xlink:href="note-269-04"/> dum Aequator cingulus exiſtit primi motus. </s> <s xml:id="echoid-s9638" xml:space="preserve">Primum autem inuentorem Zo-<lb/>diaci refert Plinius ſu<gap/>e Anaximandrum Milleſium.</s> <s xml:id="echoid-s9639" xml:space="preserve"/> </p> <div xml:id="echoid-div484" type="float" level="2" n="2"> <note position="right" xlink:label="note-269-03" xlink:href="note-269-03a" xml:space="preserve">Zodiacus <lb/>cur ab Aſtro <lb/>nomis exco <lb/>gitatus ſit.</note> <note position="right" xlink:label="note-269-04" xlink:href="note-269-04a" xml:space="preserve">Anaximan <lb/>der primus <lb/>Zodiaci in-<lb/>uentor.</note> </div> <p> <s xml:id="echoid-s9640" xml:space="preserve"><emph style="sc">Qvamvis</emph> autem Zodiacus cœlo inh<unsure/>æreat, & </s> <s xml:id="echoid-s9641" xml:space="preserve">ubique idem ſit, tamen <lb/> <anchor type="note" xlink:label="note-269-05a" xlink:href="note-269-05"/> nec in Horizonte recto, nec in obliquo e@ſdem ſemper a ngulos efficit, ſed eos <lb/>continue mutat, & </s> <s xml:id="echoid-s9642" xml:space="preserve">uari<unsure/>at. </s> <s xml:id="echoid-s9643" xml:space="preserve">Nunc enim rectiores angulos, nunc obliquiores ef <lb/>fingit, atque conformat cum quocunque Horizonte propter diuetſam eius ad <lb/>Horizontem quemcunque inclinationem. </s> <s xml:id="echoid-s9644" xml:space="preserve">Vnde oritur tota difformitas, ſiue <lb/>irregularitas ortus, & </s> <s xml:id="echoid-s9645" xml:space="preserve">occaſus ſignorum, ut in 3. </s> <s xml:id="echoid-s9646" xml:space="preserve">cap. </s> <s xml:id="echoid-s9647" xml:space="preserve">explicabimus.</s> <s xml:id="echoid-s9648" xml:space="preserve"/> </p> <div xml:id="echoid-div485" type="float" level="2" n="3"> <note position="right" xlink:label="note-269-05" xlink:href="note-269-05a" xml:space="preserve">Zodiacum <lb/>uarios an-<lb/>gulos cum <lb/>Horizonte <lb/>quouis eſſi-<lb/>cere.</note> </div> <p style="it"> <s xml:id="echoid-s9649" xml:space="preserve">ET DICITVR iſte circulus Zodiacus à Ζωη`;</s> <s xml:id="echoid-s9650" xml:space="preserve">, quod eſt uita, quia <lb/> <anchor type="note" xlink:label="note-269-06a" xlink:href="note-269-06"/> ſecundum motum Planetarum ſub illo eſt omnis uita in rebus inferiori-<lb/>bus. </s> <s xml:id="echoid-s9651" xml:space="preserve">Vel dicitur à Ζωδιον, quod eſt animal, quia cum diuidatur in 12. </s> <s xml:id="echoid-s9652" xml:space="preserve">par <lb/>tes ęquales, quęlibet pars app@llatur ſignum, & </s> <s xml:id="echoid-s9653" xml:space="preserve">nomen habet ſpeciale à <pb o="234" file="270" n="271" rhead="Comment. in II. Cap. Sphæræ"/> nomine alicuius animalis, propter proprietatem aliquam conuenientem <lb/>tam ipſi, quàm animali. </s> <s xml:id="echoid-s9654" xml:space="preserve">Vel propter d ſpoſitionem ſtellarum fixarum in <lb/>illis partibus ad modum huiuſmodi animalium.</s> <s xml:id="echoid-s9655" xml:space="preserve"/> </p> <div xml:id="echoid-div486" type="float" level="2" n="4"> <note position="right" xlink:label="note-269-06" xlink:href="note-269-06a" xml:space="preserve">Zodiacus <lb/>unde ſic di-<lb/>ctus ſit.</note> </div> </div> <div xml:id="echoid-div488" type="section" level="1" n="164"> <head xml:id="echoid-head170" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s9656" xml:space="preserve"><emph style="sc">Dvplicem</emph> rationem affert, cur hic circulus dicatur Zodiacus; </s> <s xml:id="echoid-s9657" xml:space="preserve">uel ni-<lb/>mirum à Ζωὴ, id eſt, vita, propterea quod propter continuum motum Plane <lb/>tarum ſub hoc circulo omnia hæc inferiora uitam habent, ut paſſim Ariſtote-<lb/>les in ſuis operibus refert: </s> <s xml:id="echoid-s9658" xml:space="preserve">uel à Ζώδιον, quod eſt animal, quia iſte circulus <lb/>diſtribuitur ab Aſtrologis in 12. </s> <s xml:id="echoid-s9659" xml:space="preserve">partes æquales, quarum quęlibet, una dem-<lb/>pta, nomen ſortitur alicuius animalis: </s> <s xml:id="echoid-s9660" xml:space="preserve">Atque hę 12. </s> <s xml:id="echoid-s9661" xml:space="preserve">partes ſigna dicuntur, de <lb/>quibus ſtatim dicetur.</s> <s xml:id="echoid-s9662" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9663" xml:space="preserve"><emph style="sc">Cvr</emph> autem hęc ſigna denominentur à peculiaribus animalibus, duplicem <lb/> <anchor type="note" xlink:label="note-270-01a" xlink:href="note-270-01"/> quoque cauſam aſſignat. </s> <s xml:id="echoid-s9664" xml:space="preserve">Prima eſt, quoniam (ut iudicarij uolunt) conſtella-<lb/>tiones illę habent uirtutes, proprietatesve communes illis animalibus, à qui-<lb/>bus denominationem ſuſcipiunt, hoc eſt, quia in his inferioribus producunt <lb/>effectus conſormes huiuſmodi animalibus. </s> <s xml:id="echoid-s9665" xml:space="preserve">Verbi gratia, Primum ſignum di-<lb/>citur Aries, quia quemadmodum Aries eſt animal calidum, ſic ẽt Sol in ea par <lb/>te cœli exiſtens, quę Aries dicitur, incipit calorem ſuum depromere, atque hęc <lb/>inferiora calefacere. </s> <s xml:id="echoid-s9666" xml:space="preserve">Secundum ſignum dictum eſt Taurus, quoniã ſicut Tau-<lb/>rus fortior eſt Ariete, ſic etiam Sol in ſigno Tauri conſtitutus maiores uires <lb/>exercet, quàm in Ariete: </s> <s xml:id="echoid-s9667" xml:space="preserve">Vel etiam, quia, Sole exiſtente in Tauro, incipiunt <lb/>apparere labores boum, ſeu taurorum, nimirum ſegetes. </s> <s xml:id="echoid-s9668" xml:space="preserve">Tertium ſignum no-<lb/>men ſumpſit à Geminis, quoniam, Sole in eo decurrente, geminatur quodam-<lb/>modo calor in his inferioribus. </s> <s xml:id="echoid-s9669" xml:space="preserve">Quartum cancer appellatur, quia, cum Sol ad <lb/>Cancrum peruenit, incipit retrogredi more Cancri, & </s> <s xml:id="echoid-s9670" xml:space="preserve">à nobis diſcedere. </s> <s xml:id="echoid-s9671" xml:space="preserve">Quin <lb/>tum dicitur Leo, nam ſicut Leo eſt animalium fortiſſimus, ita quoque Sol in <lb/>Leone exiſtens maximam inducit ſiccitatem, & </s> <s xml:id="echoid-s9672" xml:space="preserve">calorem. </s> <s xml:id="echoid-s9673" xml:space="preserve">Sextum ſignum vo-<lb/>catur Virgo, quia in eo exiſtens Sol ſterilis eſt quodammodo, nihilq; </s> <s xml:id="echoid-s9674" xml:space="preserve">de nouo <lb/>producit, ſed producta ſolum ad maturitatẽ perducit. </s> <s xml:id="echoid-s9675" xml:space="preserve">Septimum denominatur <lb/>Libra, eo quod, Sole in eo exiſtente, dies & </s> <s xml:id="echoid-s9676" xml:space="preserve">noctes tanquam in Libra, ſeu ſtate-<lb/>ra aliqua librentur, adæquentur que. </s> <s xml:id="echoid-s9677" xml:space="preserve">Octauum Scorpius nominatur:</s> <s xml:id="echoid-s9678" xml:space="preserve">nam que-<lb/>admodum Scorpius ſua cauda pungit, & </s> <s xml:id="echoid-s9679" xml:space="preserve">lędit, ita etiam, dum in hoc ſigno <lb/>Sol moratur, frigora in cautos lędere, ac pungere ſolent. </s> <s xml:id="echoid-s9680" xml:space="preserve">Nonum dictum eſt <lb/>Sagittarius, quoniam, Sole in eo exiſtente, mittuntur ad nos grandines, atq; <lb/></s> <s xml:id="echoid-s9681" xml:space="preserve">imbres, ueluti ſagittę. </s> <s xml:id="echoid-s9682" xml:space="preserve">Decimum uocatur Capricornus, quia ſicut caper ſem-<lb/>per ſeſe ad arbores, & </s> <s xml:id="echoid-s9683" xml:space="preserve">frondes erigit, ita etiam Sol, quando ad ſignum hoc <lb/>peruenit, ad nos iterum incipit aſcendere. </s> <s xml:id="echoid-s9684" xml:space="preserve">Vndecimum appellatur Aquarius, <lb/>propterea quod, exiſtente Sole in eo ſigno, aquę pluuiarum abundare ſoleant. </s> <s xml:id="echoid-s9685" xml:space="preserve"><lb/>Duodecimum denique à piſcibus nomen habet, quoniam, Sole in piſcibus mo <lb/>rante, ita frequentes exiſtunt pluuię, ut omnia, ueluti piſces, natare uidean-<lb/>tur. </s> <s xml:id="echoid-s9686" xml:space="preserve">Hęc uero omnia intelligenda ſunt in habitatione, quęab Aequatore in <lb/>Septentrionem uergit. </s> <s xml:id="echoid-s9687" xml:space="preserve">Nam ij, qui in parte Meridionali degunt, omnino con <lb/>traria his experiuntur.</s> <s xml:id="echoid-s9688" xml:space="preserve"/> </p> <div xml:id="echoid-div488" type="float" level="2" n="1"> <note position="left" xlink:label="note-270-01" xlink:href="note-270-01a" xml:space="preserve">Signa Zo-<lb/>diaci cur <lb/>ab animali <lb/>bus deno-<lb/>minentur.</note> </div> <p> <s xml:id="echoid-s9689" xml:space="preserve"><emph style="sc">Secvnda</emph> cauſa eſt, quia ſtellę exiſtentes in ea parte Zodiaci, quę v.</s> <s xml:id="echoid-s9690" xml:space="preserve">g. <lb/></s> <s xml:id="echoid-s9691" xml:space="preserve">Scorpius dicitur, referunt imaginem, ſeu figuram Scorpij. </s> <s xml:id="echoid-s9692" xml:space="preserve">Item ſtellę in ea <pb o="235" file="271" n="272" rhead="Ioan. de Sacro Boſco."/> parte, quę à Sagittario denominatur, collocatæ exprimunt quodam modo ho <lb/>minem, qui ex arcu tenſo ſagittam iaculatur, & </s> <s xml:id="echoid-s9693" xml:space="preserve">ſic de cęteris.</s> <s xml:id="echoid-s9694" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9695" xml:space="preserve"><emph style="sc">Qvod</emph> ſi neutra harum cauſarum placet, poterimus dicere ideo 12. </s> <s xml:id="echoid-s9696" xml:space="preserve">has <lb/>partes obtinuiſſe prædicta nomina animalium; </s> <s xml:id="echoid-s9697" xml:space="preserve">quoniam cũ in toto Firmamen <lb/>to reperiantur 48. </s> <s xml:id="echoid-s9698" xml:space="preserve">conſtellationes, ſeu imagines, de quibus, in 1. </s> <s xml:id="echoid-s9699" xml:space="preserve">cap. </s> <s xml:id="echoid-s9700" xml:space="preserve">dictũ eſt, <lb/>ubi & </s> <s xml:id="echoid-s9701" xml:space="preserve">nomina, & </s> <s xml:id="echoid-s9702" xml:space="preserve">ſtellas earum ſigillatim recenſuimus, duodecim intra Zodia-<lb/>cum continentur, nempe Aries, Taurus, Gemini, &</s> <s xml:id="echoid-s9703" xml:space="preserve">c. </s> <s xml:id="echoid-s9704" xml:space="preserve">Vnde & </s> <s xml:id="echoid-s9705" xml:space="preserve">12. </s> <s xml:id="echoid-s9706" xml:space="preserve">partibus, in <lb/>quas Zodiacus diuiditur, eadem nomina Aſtronomi dedere. </s> <s xml:id="echoid-s9707" xml:space="preserve">Sed quia eadem <lb/> <anchor type="note" xlink:label="note-271-01a" xlink:href="note-271-01"/> videtur difficultas remanere, cur uidelicet 48. </s> <s xml:id="echoid-s9708" xml:space="preserve">illę imagines cęleſtes talibus <lb/>ſint nominibus pręditę, dicendũ eſt, ueteres huiuſmodi nomina conſtellationi <lb/>bus impoſuiſſe, (quid quid dicant Aſtrologi iudicarij, ob memoriam quorun-<lb/>dam uirorum illuſtrium, uel etiam alicuius fabulę, uel hiſtoriæ. </s> <s xml:id="echoid-s9709" xml:space="preserve">Sic enim quæ <lb/>dam conſtellatio dicitur Hercules, ob memoriam Herculis: </s> <s xml:id="echoid-s9710" xml:space="preserve">@quædam Argona-<lb/>uis, propter primam nauem, qua homines ſeſe fluctibus Oceani crediderunt, <lb/>&</s> <s xml:id="echoid-s9711" xml:space="preserve">c. </s> <s xml:id="echoid-s9712" xml:space="preserve">Veruntamen negandum non eſt, impoſitores horum nominũ habuiſſe ma-<lb/>gnam rationem figurarum, quas ſtellæ efficiunt. </s> <s xml:id="echoid-s9713" xml:space="preserve">Nam in memoriam coronæ <lb/>Ariadnes eã conſtellationem coronã dixerunt, quæ ſimilitudinem cuiuſdam <lb/>coronę præſefert, atque ita de reliquis dicendum eſt.</s> <s xml:id="echoid-s9714" xml:space="preserve"/> </p> <div xml:id="echoid-div489" type="float" level="2" n="2"> <note position="right" xlink:label="note-271-01" xlink:href="note-271-01a" xml:space="preserve">Cur anti@ <lb/>cõſtellatio-<lb/>nibusnomi <lb/>na illa, de <lb/>ꝗ bus ſupra <lb/>indideri n@.</note> </div> <p> <s xml:id="echoid-s9715" xml:space="preserve"><emph style="sc">Hinc</emph> perſpicuum eſt, ſi rationem habeamus 12. </s> <s xml:id="echoid-s9716" xml:space="preserve">ſignorum, ſeu conſtella-<lb/> <anchor type="note" xlink:label="note-271-02a" xlink:href="note-271-02"/> tionum, quæ in Zodiaco comprehenduntur, hoc nomen proprie cõuenire Zo <lb/>diaco fitmamenti, in quo huiuſmodi conſtellationes exiſtunt, non autem Zo-<lb/>diaco primi mobilis, cum ibi nullum extet veſtigium talium imaginum: </s> <s xml:id="echoid-s9717" xml:space="preserve">Si ue-<lb/>ro quis mauult dici Zodiacum à Ζωὴ, ideſt, uita, quàm à Ζώδιον, quod eſt ani-<lb/>mal; </s> <s xml:id="echoid-s9718" xml:space="preserve">recte dicere poterit, hoc nomen primum eſſe impoſitum Zodiaco primi <lb/>mobilis: </s> <s xml:id="echoid-s9719" xml:space="preserve">Nam propter motum planetarum ſub Zopiaco primi mobilis omnia <lb/>hæc inferiora uitam habent, ut philoſophi aſſerunt.</s> <s xml:id="echoid-s9720" xml:space="preserve"/> </p> <div xml:id="echoid-div490" type="float" level="2" n="3"> <note position="right" xlink:label="note-271-02" xlink:href="note-271-02a" xml:space="preserve">Cui Zodia-<lb/>co hoc no-<lb/>men magis <lb/>conueniat.</note> </div> <p style="it"> <s xml:id="echoid-s9721" xml:space="preserve">ISTE uero circulus Latine dicitur Signifer, quiafert ſigna, uel quia <lb/>diuiditur in ea. </s> <s xml:id="echoid-s9722" xml:space="preserve"><emph style="sc">A</emph>b <emph style="sc">A</emph>riſtotele uero in lib. </s> <s xml:id="echoid-s9723" xml:space="preserve">2. </s> <s xml:id="echoid-s9724" xml:space="preserve">de generatione, & </s> <s xml:id="echoid-s9725" xml:space="preserve">corruptio-<lb/>ne dicitur circulus obliquus, ubi dicit, quod ſecundum acceſſum, & </s> <s xml:id="echoid-s9726" xml:space="preserve">receſ-<lb/>ſum Solis in circulo obliquo fiunt generationes, & </s> <s xml:id="echoid-s9727" xml:space="preserve">corruptiones in rebus <lb/>inferioribus.</s> <s xml:id="echoid-s9728" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div492" type="section" level="1" n="165"> <head xml:id="echoid-head171" xml:space="preserve">COMMENTARIVS.</head> <note position="right" xml:space="preserve">Alia noml@ <lb/>na Zodia@</note> <p> <s xml:id="echoid-s9729" xml:space="preserve"><emph style="sc">Addvcit</emph> duo alia nomina, quibus circulus Zodiacus ab Aſtronomis ſo-<lb/>let appellari, dicens cum a Latinis dici ſigniferum, uel quia defert 12. </s> <s xml:id="echoid-s9730" xml:space="preserve">ſigna <lb/>prędicta, uel certe, quia in ea diuiditur; </s> <s xml:id="echoid-s9731" xml:space="preserve">quæ appellatio ualde familiaris eſt poe <lb/>tis. </s> <s xml:id="echoid-s9732" xml:space="preserve">Ita enim cum uocat Claudianus in eo Epigrammate, quod de Archime-<lb/>dis ſphæra conſcripſit, ubi ſic ait.</s> <s xml:id="echoid-s9733" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s9734" xml:space="preserve">Percurrit proprium mentitus ſignifer annum, <lb/>Et ſimulata nouo Cynthia menſe redit.</s> <s xml:id="echoid-s9735" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9736" xml:space="preserve">Ita quoque Lucanus eum nominat lib. </s> <s xml:id="echoid-s9737" xml:space="preserve">3. </s> <s xml:id="echoid-s9738" xml:space="preserve">ſic ſcribens.</s> <s xml:id="echoid-s9739" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s9740" xml:space="preserve">Aethiopumq́; </s> <s xml:id="echoid-s9741" xml:space="preserve">ſolum, quod non premeretur ab ulla <lb/>Signiferi regione poli ni poplite lapſo <lb/>Vltima curuati procederet vngula Tauri.</s> <s xml:id="echoid-s9742" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9743" xml:space="preserve"><emph style="sc">Deinde</emph> ait, Zodiacum ab Ariſtotele lib. </s> <s xml:id="echoid-s9744" xml:space="preserve">2. </s> <s xml:id="echoid-s9745" xml:space="preserve">de Oener. </s> <s xml:id="echoid-s9746" xml:space="preserve">& </s> <s xml:id="echoid-s9747" xml:space="preserve">corrupt. </s> <s xml:id="echoid-s9748" xml:space="preserve">appel- <pb o="236" file="272" n="273" rhead="Comment. in II. Cap. Sphæræ"/> lari circulum obliquum. </s> <s xml:id="echoid-s9749" xml:space="preserve">Quo etiam nomine multi eum Aſtronomi uocare cõ <lb/>ſueuerunt. </s> <s xml:id="echoid-s9750" xml:space="preserve">Dicitur autem hic circulus odliquus, tũ quia ſecat ad obliquos an-<lb/>gulos & </s> <s xml:id="echoid-s9751" xml:space="preserve">Aequatorem, & </s> <s xml:id="echoid-s9752" xml:space="preserve">Colurnm æquinoctiorum, tum quia, ſi conferatur cũ <lb/>circulis parallelis, obliquum ſitum obtinet in ſphæra, cũ non æqualiter à po-<lb/>lis mundi ſecundum omnes ſui partes remoueatur, ſed una eius medietas in <lb/>Auſtrum, altera uero in Boream uergat. </s> <s xml:id="echoid-s9753" xml:space="preserve">Vnde fit, ut Sol, & </s> <s xml:id="echoid-s9754" xml:space="preserve">cęteri planetæ, qui <lb/>ſub Zodiaco perpetuo mouentur, interdum ad nos propius accedant, quando <lb/>uidelicet exiſtunt in medietate uerſus ſeptentrionem, interdum longius à no <lb/>bis recedant, quando nimirum reliquam medietatem, quæ in Auſtrum decli-<lb/>nat, percurrunt.</s> <s xml:id="echoid-s9755" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9756" xml:space="preserve"><emph style="sc">Qvod</emph> fi quis cauſam requirat, cur Natura tribuerit hanc obliquitatem <lb/> <anchor type="note" xlink:label="note-272-01a" xlink:href="note-272-01"/> uiæ Solis, teliquorumq́; </s> <s xml:id="echoid-s9757" xml:space="preserve">planetarum, reſpondendum eſt cum Philoſophis, id <lb/>factum eſſe, duas potiſfimum ob cauſas. </s> <s xml:id="echoid-s9758" xml:space="preserve">Prima eſt uiciſſitudo temporum: </s> <s xml:id="echoid-s9759" xml:space="preserve">Nam <lb/>propter motũ Solis ſub hoc circulo obliquo eſficitur Vet, deinde Æſtas, poſtea <lb/>Autumnus, ac ultimo Hyems, ut mox dicemus. </s> <s xml:id="echoid-s9760" xml:space="preserve">Similiter in ſphæra obliqua, <lb/>ob eundem motum Solis ſub Zodiaco, efficiũtur interdum dies artificiales no <lb/>ctibus æquales, interdum dies artificiales excedunt noctes, interdum denique <lb/>dies artificiales à noctibus ſuperantur, ut luce clarius conſtabit ex 3. </s> <s xml:id="echoid-s9761" xml:space="preserve">cap. </s> <s xml:id="echoid-s9762" xml:space="preserve">Quod <lb/>ſi Zodiacus, quem Sol proprio motu perambulat, non eſſet obliquus, nunquã <lb/>temporum uarietas exiſteret in quacunq; </s> <s xml:id="echoid-s9763" xml:space="preserve">regione, eo quòd Sol ſemper eandẽ <lb/>haberet diſtantiam à uertice capitis. </s> <s xml:id="echoid-s9764" xml:space="preserve">Secunda cauſa eſt diuerſitas, ac uarietas <lb/>effectuum: </s> <s xml:id="echoid-s9765" xml:space="preserve">Nam propter obliquitatem Zodiaci Sol, & </s> <s xml:id="echoid-s9766" xml:space="preserve">alij planetæ, ut dictum <lb/>eſt, nunc propius ad nos accedunt, nunc longius diſtant à nobis: </s> <s xml:id="echoid-s9767" xml:space="preserve">Ex qua viciſſi-<lb/>tudine oritur rota diuerſitas in effectibus. </s> <s xml:id="echoid-s9768" xml:space="preserve">Nã ſi Zodiacus non eſſet obliquus, <lb/>ſemper ijdem producerentur effectus, cum planetæ perpetuo eandem propin-<lb/>quitatem, remotionemve haberent.</s> <s xml:id="echoid-s9769" xml:space="preserve"/> </p> <div xml:id="echoid-div492" type="float" level="2" n="1"> <note position="left" xlink:label="note-272-01" xlink:href="note-272-01a" xml:space="preserve">Zodiacus <lb/>curobliquũ <lb/>ſitum hẽat <lb/>in ſphæra.</note> </div> <note position="left" xml:space="preserve">Nomina <lb/>12. ſignorũ <lb/>Zodiaci, & <lb/>ordo.</note> <p style="it"> <s xml:id="echoid-s9770" xml:space="preserve">NOMINA autem ſignorum, ordinatio, & </s> <s xml:id="echoid-s9771" xml:space="preserve">numerus in his patent <lb/>uerſibus.</s> <s xml:id="echoid-s9772" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9773" xml:space="preserve">Sunt Aries, Taurus, Gemini, Cancer, Leo, Virgo, <lb/>Libraq́ue, Scorpius, Arcitenens, Caper, Amphora, Piſces.</s> <s xml:id="echoid-s9774" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div494" type="section" level="1" n="166"> <head xml:id="echoid-head172" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s9775" xml:space="preserve"><emph style="sc">Qvoniam</emph> dixerat auctor, Zodiacum diuidi ab Aſtronomis in 12. </s> <s xml:id="echoid-s9776" xml:space="preserve">par-<lb/>tes æquales, quæ ſigna nũcupantur, explicat iam duobus carminibus, quomo-<lb/>do appellentur huiuſmodi ſigna duodecim, & </s> <s xml:id="echoid-s9777" xml:space="preserve">quonam ordine ſeſe habeãt in <lb/>Zodiaco. </s> <s xml:id="echoid-s9778" xml:space="preserve">Quod & </s> <s xml:id="echoid-s9779" xml:space="preserve">nos iamdudum in 1. </s> <s xml:id="echoid-s9780" xml:space="preserve">cap. </s> <s xml:id="echoid-s9781" xml:space="preserve">præſtitimus, cum de motibus cœlo <lb/>rum ageremus, ubi etiam characteres, quibus ab Aſtronomis deſignari ſolẽt, ap <lb/>poſuimus, atque eoſdem nunc hoc loco in gratiam ſtudioſorũ repetemus, ut <lb/>firmius memoriæ hęreãt. </s> <s xml:id="echoid-s9782" xml:space="preserve">Sunt igitur 12. </s> <s xml:id="echoid-s9783" xml:space="preserve">ſigna cęleſtia hiſce nominibus prædi <lb/>ta, habentq́; </s> <s xml:id="echoid-s9784" xml:space="preserve">hunc ordinem inter ſeſe, & </s> <s xml:id="echoid-s9785" xml:space="preserve">talibus characteribus exprimi ſolent. <lb/></s> <s xml:id="echoid-s9786" xml:space="preserve"> <anchor type="note" xlink:label="note-272-03a" xlink:href="note-272-03"/> <pb o="237" file="273" n="274" rhead="Ioan. de Sacro Boſco."/> Eſt autem quodlibet ſignum ſuperius ſibi reſpondenti inferiori per diame-<lb/>trum oppoſitum in Zodiaco, ut Aries Libræ, Taurus Scorpio, Gemini Sagit-<lb/>tario, &</s> <s xml:id="echoid-s9787" xml:space="preserve">c.</s> <s xml:id="echoid-s9788" xml:space="preserve"/> </p> <div xml:id="echoid-div494" type="float" level="2" n="1"> <note position="right" xlink:label="note-272-03" xlink:href="note-272-03a" xml:space="preserve"> <lb/>♈ # ♉ # ♊ # ♋ # ♌ # ♍ <lb/>Aries # Taurus # Gemini # Cancer # Leo # Virgo <lb/>♎ # ♏ # ♐ # ♑ # ♒ # ♓ <lb/>Libra # Scorpius # Sagittarius. # Capricornus # Aquarius # Piſces <lb/></note> </div> <p> <s xml:id="echoid-s9789" xml:space="preserve"><emph style="sc">Caetervm</emph> apud Aſtronomos duobus modis accipi ſolet ſignum. <lb/></s> <s xml:id="echoid-s9790" xml:space="preserve"> <anchor type="note" xlink:label="note-273-01a" xlink:href="note-273-01"/> Vno modo pro ſexta parte totius Zodiaci, quo pacto dicitur ſignum Phyſicum, <lb/>ſiue naturale, propterea quòd naturaliter quodãmodo ſine ullo adhibito ar-<lb/> <anchor type="note" xlink:label="note-273-02a" xlink:href="note-273-02"/> tificio circulus quiuis in 6. </s> <s xml:id="echoid-s9791" xml:space="preserve">partes æquales diuiditur, eadem nimirum crurium <lb/>circini diſtenſione, qua circulus eſt deſcriptus, ut conſtat ex corollario pro-<lb/>poſ. </s> <s xml:id="echoid-s9792" xml:space="preserve">15. </s> <s xml:id="echoid-s9793" xml:space="preserve">lib. </s> <s xml:id="echoid-s9794" xml:space="preserve">4. </s> <s xml:id="echoid-s9795" xml:space="preserve">Euclidis. </s> <s xml:id="echoid-s9796" xml:space="preserve">Talibus autem fignis uti ſobent Aſtronomi in compo-<lb/>nendis tabulis motuum, ut uidere eſt apud Alphonſum regẽ Hiſpaniæ, & </s> <s xml:id="echoid-s9797" xml:space="preserve">alios, <lb/>qui tabulas compoſuerunt. </s> <s xml:id="echoid-s9798" xml:space="preserve">Alio modo accipitur ſignum pro duodecima par-<lb/> <anchor type="note" xlink:label="note-273-03a" xlink:href="note-273-03"/> te Zodiaci, ſeu (quod idẽ eſt) pro dimidiata parte ſigni phyſici, naturalisve, di-<lb/>citurq́ue ſignum commune, eo quod communiter Aſtronomi eo uti ſoleant, <lb/>in qua ſignificatione hoc loco auctor noſter ſignum quoque accepit. </s> <s xml:id="echoid-s9799" xml:space="preserve">Dicun-<lb/>tur autem ſortaſſis huiuſmodi partes Zodiaci ſigna, propterea quòd per illa <lb/>deſignantur motus omnium aſtrorum, uel etiam, quod deſignent uaria anni <lb/>tempora, ut mox dicemus.</s> <s xml:id="echoid-s9800" xml:space="preserve"/> </p> <div xml:id="echoid-div495" type="float" level="2" n="2"> <note position="right" xlink:label="note-273-01" xlink:href="note-273-01a" xml:space="preserve">Duplex ac-<lb/>ceptio ſi-<lb/>gni.</note> <note position="right" xlink:label="note-273-02" xlink:href="note-273-02a" xml:space="preserve">Signũ phy-<lb/>ſicũ quod.</note> <note position="right" xlink:label="note-273-03" xlink:href="note-273-03a" xml:space="preserve">Signũ co@ <lb/>mune qđ.</note> </div> <p> <s xml:id="echoid-s9801" xml:space="preserve"><emph style="sc">Eadem</emph> hæc duodecim ſigna cęleſtia elegantiſſime deſcribit Manlius <lb/>duodecim carminibus, in quibus etiam exprimit ordinem, & </s> <s xml:id="echoid-s9802" xml:space="preserve">nomina, & </s> <s xml:id="echoid-s9803" xml:space="preserve">quonã <lb/>pacto ab Aſtronomis ſolent depingi in globo cęleſti; </s> <s xml:id="echoid-s9804" xml:space="preserve">Sunt autem carmina hęc.</s> <s xml:id="echoid-s9805" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s9806" xml:space="preserve">Aurato princeps ARIES in vellere fulgens <lb/>Reſpicit admirans aduerſum ſurgere TAVRVM <lb/>Summiſſo uultu GEMINOS, & </s> <s xml:id="echoid-s9807" xml:space="preserve">fronte uocantem: <lb/></s> <s xml:id="echoid-s9808" xml:space="preserve">Quos ſequitur CANCER: </s> <s xml:id="echoid-s9809" xml:space="preserve">Cancrum LEO: </s> <s xml:id="echoid-s9810" xml:space="preserve">VIRGO Leonem; </s> <s xml:id="echoid-s9811" xml:space="preserve"><lb/>Aequato tum LIBRA die cum temporenoctis <lb/>Attrahit ardenti fulgentem SCORPION aſtro, <lb/>In cuius caudam contentum dirigit arcum <lb/>MIXTVSEQVO, uolucrem miſſurus iamq́ue ſagittam. </s> <s xml:id="echoid-s9812" xml:space="preserve"><lb/>Tum uenit anguſto CAPRICORNVS ſidere flexus. </s> <s xml:id="echoid-s9813" xml:space="preserve"><lb/>Poſt hunc inflexam diffundit AQV ARIVS vrnam, <lb/>PISCIBVS aſſuetas auide ſubeuntibus undas <lb/>Quos Aries tangit claudentes ultima ſigna.</s> <s xml:id="echoid-s9814" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9815" xml:space="preserve"><emph style="sc">Qvae</emph> quidem carmina perpulchre explicant figuras duodecim ſignorum <lb/>Zodiaci, quæ in globo cęleſti ſolent depingi.</s> <s xml:id="echoid-s9816" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9817" xml:space="preserve"><emph style="sc">De nominibvs</emph> iſtorum duodecim ſignorum ſupra uerba fecimus, <lb/>cur nimirum hęc nomina illis attribuita ſint ab Aſtronomis; </s> <s xml:id="echoid-s9818" xml:space="preserve">Dicendum iam eſt <lb/>de numero, & </s> <s xml:id="echoid-s9819" xml:space="preserve">ordine eorundem, nempe cur 12. </s> <s xml:id="echoid-s9820" xml:space="preserve">tantum ſigna in Zodiaco <lb/>Aſtronomi conſtituerint, non plura pauciorave: </s> <s xml:id="echoid-s9821" xml:space="preserve">Et cur ab Ariete initium uo-<lb/>Iuerint ſumere potius, quàm ab alio figno, cum in circulo non ſit proprie prin-<lb/>cipium, ſed à quolibet puncto initium capere liceat ſine ullo diſcrimine. </s> <s xml:id="echoid-s9822" xml:space="preserve">Quã-<lb/>uis enim omnia hæc à uoluntate, arbitrioq́ue Aſtronomorum pendeant, ta-<lb/>men non temere ea ab ipſis eſſe inſtituta credendum eſt. </s> <s xml:id="echoid-s9823" xml:space="preserve">Quod igitur ad nu-<lb/>merum ſignorum attinet, afferuntur ab Aſtronomis nonnullæ rationes, quæ <lb/>oſtendunt, conuenienter admodum Zodiacum in 12. </s> <s xml:id="echoid-s9824" xml:space="preserve">ſigna diuiſum fuiſſe. </s> <s xml:id="echoid-s9825" xml:space="preserve">Pri-<lb/> <anchor type="note" xlink:label="note-273-04a" xlink:href="note-273-04"/> ma eſt hæc. </s> <s xml:id="echoid-s9826" xml:space="preserve">Cum ſint quatuor elementa, ex quibus omnia generantur, Ignis <lb/>videlicet, Aer, Aqua, & </s> <s xml:id="echoid-s9827" xml:space="preserve">Terra; </s> <s xml:id="echoid-s9828" xml:space="preserve">Vnumquodque autem tres potiſſimum ter-<lb/>minos poſſideat, nempe principium, medium, ac finem; </s> <s xml:id="echoid-s9829" xml:space="preserve">Res item generabiles ge <pb o="238" file="274" n="275" rhead="Comment. in I. cap. Sphæræ"/> nerentur primum, deinde conſeruentur, tertio denique corrumpantur: </s> <s xml:id="echoid-s9830" xml:space="preserve">Si ter-<lb/>narium horum terminorum numerum multiplicemus cum quaternario ele-<lb/>mentorum numero, duodenarium efficiemus. </s> <s xml:id="echoid-s9831" xml:space="preserve">Tantus igitur non immerito de-<lb/>buit eſſe ſignorum numerus in Zod@aco, ut ſingula elementa iuxta triplicem <lb/>prædictum terminum terna ſigna obtinerent. </s> <s xml:id="echoid-s9832" xml:space="preserve">Atque ita attribuerunt Aſtrono-<lb/>mi Igni Arietem, Leonem, & </s> <s xml:id="echoid-s9833" xml:space="preserve">Sagittarium, quoniam hæc tria ſigna ſunt calida <lb/> <anchor type="note" xlink:label="note-274-01a" xlink:href="note-274-01"/> & </s> <s xml:id="echoid-s9834" xml:space="preserve">ſicca, (vt Iudiciarij aſſerunt,) que madmodũ Ignis. </s> <s xml:id="echoid-s9835" xml:space="preserve">Aeri aſſignarunt Geminos <lb/>Libram, & </s> <s xml:id="echoid-s9836" xml:space="preserve">Aquarium. </s> <s xml:id="echoid-s9837" xml:space="preserve">Nã hæc tria ſigna calida & </s> <s xml:id="echoid-s9838" xml:space="preserve">humida exiſtunt, ſicut Aer. <lb/></s> <s xml:id="echoid-s9839" xml:space="preserve">Aquæ aſcripſerunt Cancrum, Scorpium, ac P@ſces, quod hæc tria ſigna ſint <lb/>frigida, & </s> <s xml:id="echoid-s9840" xml:space="preserve">humida, ueluti Aqua. </s> <s xml:id="echoid-s9841" xml:space="preserve">Terræ denique conceſſerunt Taurum, Virgi-<lb/>nem, & </s> <s xml:id="echoid-s9842" xml:space="preserve">Capricornum; </s> <s xml:id="echoid-s9843" xml:space="preserve">propterea quòd tria hæc ſigna frigida ſunt, & </s> <s xml:id="echoid-s9844" xml:space="preserve">ſicca, ut <lb/>Terra. </s> <s xml:id="echoid-s9845" xml:space="preserve">Vt autem facile memoria teneatur, quænam ſigna ad quodlibet elemen <lb/>tum pertineant, accipiendi ſunt quatuor digiti in manu, quorum primus refe-<lb/>rat Ignem, ſecundus Terram, tertius Aerem, quartus Aquam: </s> <s xml:id="echoid-s9846" xml:space="preserve">Deinde eo ordi-<lb/>ne omnia ſigna in illis computanda, quo ea ſupra recenſuimus. </s> <s xml:id="echoid-s9847" xml:space="preserve">Ita enim fiet, <lb/>ut tria ſigna cadentia ſupra primum digitum tribuãtur Igni, dicanturq́; </s> <s xml:id="echoid-s9848" xml:space="preserve">Ignea, <lb/>propter caliditatem, & </s> <s xml:id="echoid-s9849" xml:space="preserve">ſiccitatem: </s> <s xml:id="echoid-s9850" xml:space="preserve">Vnde & </s> <s xml:id="echoid-s9851" xml:space="preserve">cholerica appellantur. </s> <s xml:id="echoid-s9852" xml:space="preserve">Q@æ uero ſu <lb/>pra ſecundum digitum ceciderint, pertineant ad terram, dicanturq́ue Terrea, <lb/>propter frigiditatem, & </s> <s xml:id="echoid-s9853" xml:space="preserve">ſiccitatem: </s> <s xml:id="echoid-s9854" xml:space="preserve">Vnde etiam Melancholica uocantur. </s> <s xml:id="echoid-s9855" xml:space="preserve">Dein-<lb/>de quæ ceciderint ſupra tertium digitum, adſcribantur Aeri, cum ſint calida, <lb/>atque humida, dicanturq́ue Aerea, & </s> <s xml:id="echoid-s9856" xml:space="preserve">Sanguinea. </s> <s xml:id="echoid-s9857" xml:space="preserve">Quæ denique in quarto digi-<lb/>to collocata fuerint, Aquæ dentur, ob frigiditatem, & </s> <s xml:id="echoid-s9858" xml:space="preserve">humiditatem, dicantur-<lb/>q́ue Aquea, & </s> <s xml:id="echoid-s9859" xml:space="preserve">Phlegmatica. </s> <s xml:id="echoid-s9860" xml:space="preserve">Quæ omnia in hac formula licet intueri.</s> <s xml:id="echoid-s9861" xml:space="preserve"/> </p> <div xml:id="echoid-div496" type="float" level="2" n="3"> <note position="right" xlink:label="note-273-04" xlink:href="note-273-04a" xml:space="preserve">Zodiacus <lb/>cur in 12. <lb/>ſigna diui-<lb/>datur.</note> <note position="left" xlink:label="note-274-01" xlink:href="note-274-01a" xml:space="preserve">Quæ ſigna <lb/>dicantur <lb/>ignea, & <lb/>cholerica: <lb/>& quæ ter <lb/>tea, & melã <lb/>cholica: & <lb/>quæ aerea, <lb/>& ſangui-<lb/>nea, & quæ <lb/>aquea, & <lb/>phlegmati <lb/>ca.</note> </div> <note position="right" xml:space="preserve"> <lb/>IGNIS # TERRA # AER # AQVA <lb/>♈ # ♉ # ♊ # ♋ <lb/>♌ # ♍ # ♎ # ♏ <lb/>♐ # ♑ # ♒ # ♓ <lb/>IGNEA. # TERRA. # AEREA. # AQVEA. <lb/>CHOLERI \\ CA # MELANCHO- \\ LICA # SANGVI- \\ NEA # PHLEG- \\ MATICA <lb/></note> <p> <s xml:id="echoid-s9862" xml:space="preserve"><emph style="sc">Secvnda</emph> ratio talis eſt. </s> <s xml:id="echoid-s9863" xml:space="preserve">Cum Sol ſpatio totius anni totum Zodia-<lb/>cum percurrat, temporumq́ue interualla, & </s> <s xml:id="echoid-s9864" xml:space="preserve">diſcrimina diſtinguat, uiſum eſt <lb/>Aſtronomis, rationi eſſe ualde conſentaneum, ſi in tot partes æquales Zodiacũ <lb/>partirentur, quot temporum uarietates notabiles ex Solis motu in Zodiaco <lb/>efficiuntur: </s> <s xml:id="echoid-s9865" xml:space="preserve">Sunt autem ſenſibiles temporum diuerſitates duodecim. </s> <s xml:id="echoid-s9866" xml:space="preserve">Tot igi-<lb/>tur ſigna recte in Zodiaco conſtituta fuere. </s> <s xml:id="echoid-s9867" xml:space="preserve">Sunt enim in anno quatuor vulga <lb/>tæ ſatis, & </s> <s xml:id="echoid-s9868" xml:space="preserve">præcipuæ partes, Ver ſcilicet, Aeſtas, Autumnus, & </s> <s xml:id="echoid-s9869" xml:space="preserve">Hyems, quæ in <lb/>ſuis complexionibus, qualitatibusq́ue non eodem modo ſe habent. </s> <s xml:id="echoid-s9870" xml:space="preserve">Nam Ver <lb/>humidum eſt, & </s> <s xml:id="echoid-s9871" xml:space="preserve">calidum: </s> <s xml:id="echoid-s9872" xml:space="preserve">Aeſtas calida, & </s> <s xml:id="echoid-s9873" xml:space="preserve">ſicca, Autumnus ſiccus, & </s> <s xml:id="echoid-s9874" xml:space="preserve">frigidus <lb/>Hyems denique frigida, & </s> <s xml:id="echoid-s9875" xml:space="preserve">humida, ut non ſolum philoſophi, uerumetiam <lb/> <anchor type="note" xlink:label="note-274-03a" xlink:href="note-274-03"/> Medici aſſerunt. </s> <s xml:id="echoid-s9876" xml:space="preserve">Quoniam igitur quatuor hæc tempora ex motu obliquo So-<lb/>lis ſub Zodiaco, propter quem nunc maxime ad nos accedit, nunc longiſſime <lb/>à nobis abeſt, nunc medio modo ſe habet, efficiuntur, diuiſus eſt ab Aſtrono- <pb o="239" file="275" n="276" rhead="Ioan. de Sacro Boſco."/> mis totus Zodiacus in 4. </s> <s xml:id="echoid-s9877" xml:space="preserve">partes, ſiue quadrantes correſpondentes prædictis qua <lb/>tuor anni temporibus. </s> <s xml:id="echoid-s9878" xml:space="preserve">Primus Quadrans reſpondens tempori Verno initium <lb/> <anchor type="note" xlink:label="note-275-01a" xlink:href="note-275-01"/> ſumit à primo gradu ♈, finem uero habet in extremitate ♊, uel primo gra-<lb/>du ♋. </s> <s xml:id="echoid-s9879" xml:space="preserve">Secundus quadrans, in quo Sol exiſtens Aeſtatẽ efficit, à primo gradu <lb/>♋, incipit, deſinitq́ue in fine ♍, ſeu primo gradu ♎. </s> <s xml:id="echoid-s9880" xml:space="preserve">Tertio quadrantis prin <lb/>cipium ſtatuitur in 1. </s> <s xml:id="echoid-s9881" xml:space="preserve">gradu ♎, terminus autem eiuſdem in fine ♐, uel primo <lb/>gradu ♑. </s> <s xml:id="echoid-s9882" xml:space="preserve">Atque hic quadrans reſpondet Autumno. </s> <s xml:id="echoid-s9883" xml:space="preserve">Quartus denique qua-<lb/>drans, in quo dum Sol commoratur, Hyems efficitur, initium ſumit à primo <lb/>gradu ♑, finemq́ue habet in ultimo gradu ♓. </s> <s xml:id="echoid-s9884" xml:space="preserve">Sed quia in quolibet horũ tem <lb/>porum tres adhuc manifeſtæ diuerſitates cernuntur. </s> <s xml:id="echoid-s9885" xml:space="preserve">Principiũ enim, Medium, <lb/>ac Finis cuiuſuis illorum non ſunt eiuſdem prorſus complexionis, extrema ſi <lb/>quidem uniuſcuiuſque commune quid habent cum complexionibus tempo-<lb/>rum uicinorum. </s> <s xml:id="echoid-s9886" xml:space="preserve">Vnde licet Ver ſit calidum atque humidum, non tamen quæ-<lb/>uis eius pars æqualiter eſt calida, & </s> <s xml:id="echoid-s9887" xml:space="preserve">humida. </s> <s xml:id="echoid-s9888" xml:space="preserve">Principium enim eius propter <lb/>propinquitatem hyemis præteritæ, quæ humida etiam eſt, & </s> <s xml:id="echoid-s9889" xml:space="preserve">non calida, ma-<lb/>gis humidum eſt, quàm calidum: </s> <s xml:id="echoid-s9890" xml:space="preserve">Medium uero temperate humidum eſt, & </s> <s xml:id="echoid-s9891" xml:space="preserve">ca <lb/>lidum: </s> <s xml:id="echoid-s9892" xml:space="preserve">Finis denique ob uicinitatem æſtatis futuræ, quæ calida quoque eſt, <lb/>non autem humida, magis calidus exiſtit, quàm humidus: </s> <s xml:id="echoid-s9893" xml:space="preserve">Eademq́ue eſt ratio <lb/>habenda de reliquis tribus anni temporibus. </s> <s xml:id="echoid-s9894" xml:space="preserve">Quocirca optimo conſilio Aſtro <lb/>nomi quemlibet Zodiaci quadrãtem in tres alias partes æquales diſtribuerũt, <lb/>quæ eſſent tres manſiones Solis in tribus partibus cuiuſlibet horum quatuor <lb/>temporũ. </s> <s xml:id="echoid-s9895" xml:space="preserve">Ex quo efficitur, duodecim eſſe ſigna Zodiaci. </s> <s xml:id="echoid-s9896" xml:space="preserve">Cæterum, ut in prom-<lb/>ptu habeantur omnia ſigna, quæ principio, medio, atque extremo cuiuſque <lb/>quatuor temporum anni prædictorum reſpondent, numeranda erunt omnia ſi-<lb/>gna in tribus digitis, initio facto ab ♈, ita ut ſupra quemlibet digitum qua-<lb/>tuor ſigna cadant. </s> <s xml:id="echoid-s9897" xml:space="preserve">Ita enim fiet ut 4. </s> <s xml:id="echoid-s9898" xml:space="preserve">ſigna prima digiti reſpondeant quatuor <lb/>temporum initijs, primum quidem initio Veris, ſecundum initio Aeftatis, ter-<lb/> <anchor type="note" xlink:label="note-275-02a" xlink:href="note-275-02"/> tium initio Autumni, quartum denique initio Hyemis: </s> <s xml:id="echoid-s9899" xml:space="preserve">quæ ſigna dici ſolent <lb/>Mobilia: </s> <s xml:id="echoid-s9900" xml:space="preserve">Nam in ipſis fit mutatio unius tẽporis in aliud. </s> <s xml:id="echoid-s9901" xml:space="preserve">Ita quoq; </s> <s xml:id="echoid-s9902" xml:space="preserve">eodem or-<lb/>dine reſpondebunt quatuor ſigna ſecundi digiti medijs eorundem partibus: <lb/></s> <s xml:id="echoid-s9903" xml:space="preserve">Vnde & </s> <s xml:id="echoid-s9904" xml:space="preserve">Fixa uocantur, quòd in illis complexio cuiuſlibet temporis firma <lb/>eſt, & </s> <s xml:id="echoid-s9905" xml:space="preserve">fixa. </s> <s xml:id="echoid-s9906" xml:space="preserve">Denique eadem ratione quatuor ſigna in poſtremo digito indica-<lb/>bunt extremas eorundem temporum partes: </s> <s xml:id="echoid-s9907" xml:space="preserve">quæ quidem Communia appel-<lb/>lantur, quia cum ſint extrema illorum temporum, commune quid habet quod <lb/>libet tempus cum qualitatibus temporum ſubſequentiũ. </s> <s xml:id="echoid-s9908" xml:space="preserve">Hæc omnia ob ocu-<lb/>los ſunt poſita in ſequenti formula.</s> <s xml:id="echoid-s9909" xml:space="preserve"/> </p> <div xml:id="echoid-div497" type="float" level="2" n="4"> <note position="left" xlink:label="note-274-03" xlink:href="note-274-03a" xml:space="preserve">Qualitates <lb/>quatuor tẽ <lb/>porũ anni.</note> <note position="right" xlink:label="note-275-01" xlink:href="note-275-01a" xml:space="preserve">Quadrãtes <lb/>Zodiaci qui <lb/>bus tempo-<lb/>ribus anni <lb/>reſpondeãt</note> <note position="right" xlink:label="note-275-02" xlink:href="note-275-02a" xml:space="preserve">Signa Mo-<lb/>bilia, Fixa, <lb/>& Commu-<lb/>nia quæ.</note> </div> <note position="right" xml:space="preserve"> <lb/># INITIVM # MEDIVM # FINIS <lb/>VERIS # ♈ # ♉ # ♊ <lb/>AESTATIS # ♋ # ♌ # ♍ <lb/>AVTVMNI # ♎ # ♏ # ♐ <lb/>HYEMIS # ♑ # ♒ # ♊ <lb/># MOBILIA # FIXA # COMMVNIA <lb/></note> <p> <s xml:id="echoid-s9910" xml:space="preserve"><emph style="sc">Tertia</emph> ratio eſt. </s> <s xml:id="echoid-s9911" xml:space="preserve">Ex 48. </s> <s xml:id="echoid-s9912" xml:space="preserve">imaginibus cœli, conſtellationibusve, quas <pb o="240" file="276" n="277" rhead="Comment. in II. Cap. Sphæræ"/> Aſtrologiex 1022. </s> <s xml:id="echoid-s9913" xml:space="preserve">ſtellis fixis Firmamenti confecerunt, de quibus quidem ver <lb/>ba fecimus in 1. </s> <s xml:id="echoid-s9914" xml:space="preserve">cap. </s> <s xml:id="echoid-s9915" xml:space="preserve">(quarum hiſtorias, ſeu fabulas ſi plenus cognoſcere de ſide <lb/>ras, conſulendus erit Hyginius, uel Ioannes Steflerinus in ſphæram Procli, vel <lb/>etiam Alexander Piccolomineus in opoſculo de ſtellis fixis) includuntur in <lb/>Zodiaco 12. </s> <s xml:id="echoid-s9916" xml:space="preserve">dũtaxat, uempe Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, <lb/>Scorpius Sagittarius, Capricornus, Aquarius, & </s> <s xml:id="echoid-s9917" xml:space="preserve">Piſces, ut in 1. </s> <s xml:id="echoid-s9918" xml:space="preserve">cap. </s> <s xml:id="echoid-s9919" xml:space="preserve">dictum eſt. <lb/></s> <s xml:id="echoid-s9920" xml:space="preserve">Quamobrem uoluerunt Aſtronomi Zodiacum in totidem partes æquales di-<lb/>ſtribuere, ut ijſdem nominibus appellari poſſent.</s> <s xml:id="echoid-s9921" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9922" xml:space="preserve"><emph style="sc">Qvarta</emph> ratio huiuſmodi eſſe poteſt. </s> <s xml:id="echoid-s9923" xml:space="preserve">Obſeruatum fuit, ſpatio unius <lb/>anni Lunam communiter cõiungi cum Sole ſub Zodiaco duodecies, totiesq. <lb/></s> <s xml:id="echoid-s9924" xml:space="preserve">illi opponi, hoc eſt, duodecim in annuo ſpatio contingere Nouilunia, toti-<lb/>demq́ue plenilunia, quamuis tredecies Luna totum Zodiacum percurrat ſpa-<lb/>tio unius anni. </s> <s xml:id="echoid-s9925" xml:space="preserve">Quare placuit tot etiã in partes Zodiacũ ſecare, & </s> <s xml:id="echoid-s9926" xml:space="preserve">non in plu-<lb/>res, paucioresve; </s> <s xml:id="echoid-s9927" xml:space="preserve">quoniam uidelicet ex vario iſto aſpectu Lunæ ad Solem tem <lb/>porum interualla diſcernuntur. </s> <s xml:id="echoid-s9928" xml:space="preserve">Vt tempus, quod intercedit ab una coniun-<lb/>ctione ad alteram, dicitur Menſis: </s> <s xml:id="echoid-s9929" xml:space="preserve">quod uero a coniunctione ad oppoſitionem, <lb/>& </s> <s xml:id="echoid-s9930" xml:space="preserve">ab oppoſitione ad coniunctionem interponitur, dimidium menſem conſti-<lb/>tuit: </s> <s xml:id="echoid-s9931" xml:space="preserve">Quod denique mediat inter coniunctionem, oppoſitionemve, & </s> <s xml:id="echoid-s9932" xml:space="preserve">quadra-<lb/>turam, quando nimirum ſemiplena apparet Luna, hebdomadam efficit, ſiue <lb/>ſeptimanam.</s> <s xml:id="echoid-s9933" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9934" xml:space="preserve"><emph style="sc">Qvinta</emph> & </s> <s xml:id="echoid-s9935" xml:space="preserve">ultima ratio deſumitur à dignitate numeri duodenarij. </s> <s xml:id="echoid-s9936" xml:space="preserve">Eſt <lb/>etenim numerus duodenarius inter omnes primus, qui habeat dimidiatã par-<lb/>tem, tertiam, quartam, ſextam, ac duodecimam. </s> <s xml:id="echoid-s9937" xml:space="preserve">Quæ omnes neceſſariæ ſunt in <lb/>Zodiaco, tum ut commode in 12. </s> <s xml:id="echoid-s9938" xml:space="preserve">partes diſtribueretur reſpondentes 12. </s> <s xml:id="echoid-s9939" xml:space="preserve">uarie-<lb/>tatibus temporum, & </s> <s xml:id="echoid-s9940" xml:space="preserve">in 4. </s> <s xml:id="echoid-s9941" xml:space="preserve">quadrantes, qui Ver, Aeſtatem, Autumnum, & </s> <s xml:id="echoid-s9942" xml:space="preserve">Hye <lb/>mem efficiunt; </s> <s xml:id="echoid-s9943" xml:space="preserve">tum maxime, ut facile omnes aſpectus ſiderum, de quibus in <lb/>in theoricis Planetarum agitur, exhiberi poſsint. </s> <s xml:id="echoid-s9944" xml:space="preserve">Per dimidiatam enim partẽ <lb/> <anchor type="note" xlink:label="note-276-01a" xlink:href="note-276-01"/> Zodiaci deſignatur aſpectus diametralis, ſeu oppoſitio aſtrorum: </s> <s xml:id="echoid-s9945" xml:space="preserve">per tertiam <lb/>partem aſpectus triangularis: </s> <s xml:id="echoid-s9946" xml:space="preserve">per quartam quadratus: </s> <s xml:id="echoid-s9947" xml:space="preserve">per ſextã denique aſpe-<lb/>ctus hexagonus denotatur. </s> <s xml:id="echoid-s9948" xml:space="preserve">Conſtat igitur Aſtronomos non ſine ratione Zo-<lb/>diacum diuiſiſſe in 12. </s> <s xml:id="echoid-s9949" xml:space="preserve">prædicta ſigna cœleſtia.</s> <s xml:id="echoid-s9950" xml:space="preserve"/> </p> <div xml:id="echoid-div498" type="float" level="2" n="5"> <note position="left" xlink:label="note-276-01" xlink:href="note-276-01a" xml:space="preserve">Aſpectus ſi <lb/>derum qui <lb/>ſint.</note> </div> <note position="left" xml:space="preserve">Aſtronomi <lb/>cur princi-<lb/>pium Zo-<lb/>diaci ſtatue <lb/>rint in prin <lb/>cipio Arie-<lb/>tis.</note> <p> <s xml:id="echoid-s9951" xml:space="preserve"><emph style="sc">Rationes</emph> uero, quæ Aſtronomos mouerunt, ut à principio ♈, po-<lb/>tius, quàm ab alio quouis puncto Zodiaci, initium ſumerent, ſunt tres potiſſi-<lb/>mum. </s> <s xml:id="echoid-s9952" xml:space="preserve">Prima eſt Prolemæi: </s> <s xml:id="echoid-s9953" xml:space="preserve">quoniam uidelicet, Sole exiſtente in principio ♈, <lb/>hoc eſt, quando f@t ęquinoctium Vernum, incipit tempus accommodatiſſi mũ <lb/>generationibus rerum; </s> <s xml:id="echoid-s9954" xml:space="preserve">tunc enim omnia uireſcunt, atque florent: </s> <s xml:id="echoid-s9955" xml:space="preserve">Sole uero <lb/>ingrediente primum gradũ ♎, ideſt, quando contingit ęquinoctium Autum-<lb/>nale, incipit tempus priori omnino contrarium, quod nimirum magis eſt ac-<lb/>commodatum rerum corruptionibus; </s> <s xml:id="echoid-s9956" xml:space="preserve">tunc enim incipiunt decidere folia ex <lb/>arboribus, omniaq́ue quodammodo frigeſcere; </s> <s xml:id="echoid-s9957" xml:space="preserve">ut experientia conſtat: </s> <s xml:id="echoid-s9958" xml:space="preserve">Non <lb/>igitur ſine ratione inter omnia puncta Zodiaci elegerunt Aſtronomi primum <lb/>punctum ♈, ut eſſet initium totius Zodiaci. </s> <s xml:id="echoid-s9959" xml:space="preserve">Accedit etiam, quod Sole ingre-<lb/>diente ſignum ♈, incipit Ver, ſeu tempus humidum, primæ animaliũ ætati ma <lb/>xime conforme: </s> <s xml:id="echoid-s9960" xml:space="preserve">Deinde ſubeunte Sole ſignum ♋, incidit Æſtas, ſiue tempus, <lb/>calidum, ſecundę animalium ætati conueniens: </s> <s xml:id="echoid-s9961" xml:space="preserve">Perueniente poſtea Sole ad ſi <lb/>gnum ♎, Autumnus incipit, ſeu tempus ſiccum, quod tertiæ ætati animalium <lb/>congruit: </s> <s xml:id="echoid-s9962" xml:space="preserve">Exiſtente denique Sole in ſigno ♑, incipit Hyems, hoc eſt tempus <lb/>frigidum, quod quartæ, ac ultimæ ætati animalium conuenit, atq; </s> <s xml:id="echoid-s9963" xml:space="preserve">reſpondet.</s> <s xml:id="echoid-s9964" xml:space="preserve"> <pb o="241" file="277" n="278" rhead="Ioan. de Sacro Boſco."/> Solent etenim auctores vitam animãtium in quatuor præcipuas ætates diſtri <lb/> <anchor type="note" xlink:label="note-277-01a" xlink:href="note-277-01"/> buere: </s> <s xml:id="echoid-s9965" xml:space="preserve">In prima aiunt dominari humiditatem, ut uidem us in pueris: </s> <s xml:id="echoid-s9966" xml:space="preserve">In ſecun <lb/>da caliditatem, ut conſtat experientia in iuuenibus & </s> <s xml:id="echoid-s9967" xml:space="preserve">adoleſcentibus: </s> <s xml:id="echoid-s9968" xml:space="preserve">In ter-<lb/>tia ſiccitatem, ut cernimus in uiris iam perfecta ætate conſtituris: </s> <s xml:id="echoid-s9969" xml:space="preserve">In quarta <lb/>deniq; </s> <s xml:id="echoid-s9970" xml:space="preserve">frigiditatem, ut conſpicuum eſt in ſenibus. </s> <s xml:id="echoid-s9971" xml:space="preserve">Verum hæc Ptolemæi ratio <lb/>locum ſolummodo habet, & </s> <s xml:id="echoid-s9972" xml:space="preserve">vim in regionibus, quæ recedunt ab Aequatore <lb/>verſus ſeptẽtrionem. </s> <s xml:id="echoid-s9973" xml:space="preserve">Si enim proponeretur illis, qui habitant ultra Aequino <lb/>ctialem circulum uerſus Auſtrũ, nullius eſſet momenti. </s> <s xml:id="echoid-s9974" xml:space="preserve">Probaret enim in Zo-<lb/>diaco initium debere ſumi a principio ♎. </s> <s xml:id="echoid-s9975" xml:space="preserve">Vt enim nobis, Sole exiſtente in ♈ <lb/>eſt Ver, ita illis, Sole exiſtẽte in ♎. </s> <s xml:id="echoid-s9976" xml:space="preserve">Et ſicut nobis incipit Aeſtas, Sole exiſtẽte <lb/>in ♋, ita illis fit Aeſtas, Sole ingrediente ſignũ ♑. </s> <s xml:id="echoid-s9977" xml:space="preserve">Et denique omnia, quę no <lb/>bis accidunt in quibuſuis ſignis, eadem illis contingant in ſignis oppoſitis ne <lb/>ceſſe eſt, ut facile uideri poteſt in ſphæra materiali. </s> <s xml:id="echoid-s9978" xml:space="preserve">Nõ eſt tamen idcirco par <lb/>uipendenda hæc ratio, tum quia Ptolemæus, & </s> <s xml:id="echoid-s9979" xml:space="preserve">alij Aſtronomi, qui hiſce ſi-<lb/>gnis nomina impoſuerunt, & </s> <s xml:id="echoid-s9980" xml:space="preserve">ordinem inter ea ſtatuerunt, in regionibus, quę <lb/>ab Aequatore in ſeptentrionem deflectunt, habitarunt, ut mirum non ſit, eos <lb/>rationem habuiſſe huius partis ſphæræ Septentrionalis, in qua nimirum cur-<lb/>ſus ſiderum obſeruarunt; </s> <s xml:id="echoid-s9981" xml:space="preserve">tum etiam, quia pars hæc Septentrionalis dignior <lb/>eſt, ac nobilior parte Auſtrali, quod ſatis indicat ſtructura, ac diſpoſitio Vni-<lb/>uerſi. </s> <s xml:id="echoid-s9982" xml:space="preserve">Eſt enim pars Septentrionalis dextra, quoniam eſt ſemper Soli exorien-<lb/> <anchor type="note" xlink:label="note-277-02a" xlink:href="note-277-02"/> ti ſupra Horizontem quemcunque ad dextram; </s> <s xml:id="echoid-s9983" xml:space="preserve">Auſtralis uero eidem ad ſini-<lb/>c<unsure/>tram. </s> <s xml:id="echoid-s9984" xml:space="preserve">Quod etiam ex eo conſtare poteſt, quod pars cęli Septẽtrionalis mul-<lb/>to pluribus ſtellis prope polum arcticum eſt exornata, quam Auſtralis, cum <lb/>prope polum antarcticum nullæ ſtellæ exiſtant, ut ſupra dictum eſt.</s> <s xml:id="echoid-s9985" xml:space="preserve"/> </p> <div xml:id="echoid-div499" type="float" level="2" n="6"> <note position="right" xlink:label="note-277-01" xlink:href="note-277-01a" xml:space="preserve">Qua tuot<unsure/> <lb/>præcipuæ <lb/>æta@es ani-<lb/>mantium.</note> <note position="right" xlink:label="note-277-02" xlink:href="note-277-02a" xml:space="preserve">Pars Vni-<lb/>uerſi borea-<lb/>lis ex dex-<lb/>tra.</note> </div> <p> <s xml:id="echoid-s9986" xml:space="preserve"><emph style="sc">Alia</emph> ratio eſt. </s> <s xml:id="echoid-s9987" xml:space="preserve">Cum in Zodiaco quatuor ſint puncta principalia, quæ Car <lb/> <anchor type="note" xlink:label="note-277-03a" xlink:href="note-277-03"/> dinalia dicuntur, quibus totus Zodiacus in quatuor quadrantes diſtribuit@r, <lb/>quorum ſinguli ſingulis quatuor anni partibus, Veri ſcilic<unsure/>et, Aeſtati, Autum-<lb/>no, atque Hyemi, correſpondent, ut dictum eſt; </s> <s xml:id="echoid-s9988" xml:space="preserve">nempe principium ♈, princi <lb/>pium ♋, principium ♎, & </s> <s xml:id="echoid-s9989" xml:space="preserve">principium ♑:</s> <s xml:id="echoid-s9990" xml:space="preserve"><unsure/> quorũ quidem duo, videlicet prio-<lb/>cipium ♈, & </s> <s xml:id="echoid-s9991" xml:space="preserve">♎, dicuntur æquinoctialia, duo vero, nimirum principium ♋, & </s> <s xml:id="echoid-s9992" xml:space="preserve"><lb/>♑, Solſtitialia: </s> <s xml:id="echoid-s9993" xml:space="preserve">Non iniuria, aut temere ab aliquo horum exordiendum eſſe, <lb/> <anchor type="note" xlink:label="note-277-04a" xlink:href="note-277-04"/> Aſtronomi ſtatuerunt. </s> <s xml:id="echoid-s9994" xml:space="preserve">Quare ex illis omnium nobiliſſimum deligendum <lb/>fuit, nempe principium ♈. </s> <s xml:id="echoid-s9995" xml:space="preserve">Hoc enim nobilius eſt duobus punctis ſolſtitiali-<lb/>bus: </s> <s xml:id="echoid-s9996" xml:space="preserve">Nam Sol exiſtens in quolibet punctorum ſolſtitialium breuiſſimos pa-<lb/>rallelos deſcribit, & </s> <s xml:id="echoid-s9997" xml:space="preserve">maximam facit dierum, noctiumq́. </s> <s xml:id="echoid-s9998" xml:space="preserve">artificialium inæqua-<lb/>litatem: </s> <s xml:id="echoid-s9999" xml:space="preserve">Vnde minus præſtantia ſunt puncta ſolſtitialia punctis æquinoctia-<lb/>libus. </s> <s xml:id="echoid-s10000" xml:space="preserve">In his etenim Sol dec urrens æqualiter diſtat ab utroq; </s> <s xml:id="echoid-s10001" xml:space="preserve">mundi polo pa-<lb/>rallelum deſcribit maximum, dies adæquat noctibus, producit maximã tem-<lb/>periem, atque (quod diligenter animaduertendum eſt) in omnibus mundi par <lb/>tibus conſpicitur in ſpacio 24. </s> <s xml:id="echoid-s10002" xml:space="preserve">horarum, etiam ſub polis mundi, quod in nul-<lb/>lo alio puncto Zodiaci fieri poteſt. </s> <s xml:id="echoid-s10003" xml:space="preserve">Idem quoque principium ♈, nobilius eſſe <lb/>principio ♎, ex eo conſtare poteſt, quod Sol in eo exiſtens producat Ver in <lb/>parte Septentrionali, ingred. </s> <s xml:id="echoid-s10004" xml:space="preserve">aturq́ue ſigna, quæ ab Aequatore verſus Septen <lb/>trionem declinant, ſeu partem cæli Septentrionalem, quæ nobilior eſt parte <lb/>Auſtrali, ut diximus.</s> <s xml:id="echoid-s10005" xml:space="preserve"/> </p> <div xml:id="echoid-div500" type="float" level="2" n="7"> <note position="right" xlink:label="note-277-03" xlink:href="note-277-03a" xml:space="preserve">Quatuor <lb/>puncta Gar <lb/>din alia in <lb/>Zodiaco <lb/>quæ.</note> <note position="right" xlink:label="note-277-04" xlink:href="note-277-04a" xml:space="preserve">Principium <lb/>Arietis no-<lb/>bilius eſt re <lb/>liqu@s trib@ <lb/>punctis Cat <lb/>dinalibus.</note> </div> <p> <s xml:id="echoid-s10006" xml:space="preserve"><emph style="sc">Vltima</emph> ratio propria eſt quorundam Aſtronomorum, qui dicunt ratio-<lb/>ni maxime conuenire, ut inde initium capiatur in Zodiaco, ubi Sol in princi-<lb/>pio mundi, quando creatus eſt, extitit: </s> <s xml:id="echoid-s10007" xml:space="preserve">Atqui ueriſimile eſt, aiunt, mundum <pb o="242" file="278" n="279" rhead="Comment. in 2. Cap. Sphæræ."/> eſſe fabricatum, Sole tenente primũ punctum ♈; </s> <s xml:id="echoid-s10008" xml:space="preserve">propterea quod in lege Moy <lb/> <anchor type="note" xlink:label="note-278-01a" xlink:href="note-278-01"/> ſis Deus præcepit, vt eo tempore quo Sol ingreditur ſignum ♈, anni initium <lb/>ſumerent Iudæi, Paſchæq́; </s> <s xml:id="echoid-s10009" xml:space="preserve">celebritatem peragerent, cum prius cum Aegyptijs <lb/>annum ab Autumno inchoaſſent. </s> <s xml:id="echoid-s10010" xml:space="preserve">In hac ſententia ſunt multi Doctores ſacri, <lb/>vt Euſebius in Chronico: </s> <s xml:id="echoid-s10011" xml:space="preserve">Cyrillus in catecheſi 14. </s> <s xml:id="echoid-s10012" xml:space="preserve">S. </s> <s xml:id="echoid-s10013" xml:space="preserve">Leo ſerm. </s> <s xml:id="echoid-s10014" xml:space="preserve">9. </s> <s xml:id="echoid-s10015" xml:space="preserve">de paſſione. <lb/></s> <s xml:id="echoid-s10016" xml:space="preserve">Ambr. </s> <s xml:id="echoid-s10017" xml:space="preserve">lib. </s> <s xml:id="echoid-s10018" xml:space="preserve">1. </s> <s xml:id="echoid-s10019" xml:space="preserve">Hexam. </s> <s xml:id="echoid-s10020" xml:space="preserve">c. </s> <s xml:id="echoid-s10021" xml:space="preserve">4. </s> <s xml:id="echoid-s10022" xml:space="preserve">Theodoretus q. </s> <s xml:id="echoid-s10023" xml:space="preserve">72. </s> <s xml:id="echoid-s10024" xml:space="preserve">in Exodum: </s> <s xml:id="echoid-s10025" xml:space="preserve">S. </s> <s xml:id="echoid-s10026" xml:space="preserve">Damaſcenus lib. </s> <s xml:id="echoid-s10027" xml:space="preserve">2. </s> <s xml:id="echoid-s10028" xml:space="preserve"><lb/>c. </s> <s xml:id="echoid-s10029" xml:space="preserve">7. </s> <s xml:id="echoid-s10030" xml:space="preserve">Iſidorus lib. </s> <s xml:id="echoid-s10031" xml:space="preserve">5. </s> <s xml:id="echoid-s10032" xml:space="preserve">Etymolog. </s> <s xml:id="echoid-s10033" xml:space="preserve">c. </s> <s xml:id="echoid-s10034" xml:space="preserve">de temporibus: </s> <s xml:id="echoid-s10035" xml:space="preserve">Venerabilis Beda in lib. </s> <s xml:id="echoid-s10036" xml:space="preserve">de ra-<lb/>tione temporum: </s> <s xml:id="echoid-s10037" xml:space="preserve">Strabus in 12. </s> <s xml:id="echoid-s10038" xml:space="preserve">Exo. </s> <s xml:id="echoid-s10039" xml:space="preserve">Rabanus ibid. </s> <s xml:id="echoid-s10040" xml:space="preserve">Hiſtoria ſcholaſtica c. </s> <s xml:id="echoid-s10041" xml:space="preserve">25. </s> <s xml:id="echoid-s10042" xml:space="preserve">de <lb/>Exodi hiſtoria: </s> <s xml:id="echoid-s10043" xml:space="preserve">Gloſſa interlinearis in cap. </s> <s xml:id="echoid-s10044" xml:space="preserve">35. </s> <s xml:id="echoid-s10045" xml:space="preserve">Gen. </s> <s xml:id="echoid-s10046" xml:space="preserve">in illud [Verno.</s> <s xml:id="echoid-s10047" xml:space="preserve">] & </s> <s xml:id="echoid-s10048" xml:space="preserve">pleriq; </s> <s xml:id="echoid-s10049" xml:space="preserve"><lb/>alij: </s> <s xml:id="echoid-s10050" xml:space="preserve">quibus fere communis nũc ſchola Theologornm aſtipulatur, propterea <lb/>quod eo anni tempore, quo Sol ſignum ♈, ſubit, Chriſtus æterni Dei filius <lb/>carnem humanam aſſumpſit, & </s> <s xml:id="echoid-s10051" xml:space="preserve">ſanctiſſima ſua paſſione mundum redemit. </s> <s xml:id="echoid-s10052" xml:space="preserve"><lb/>Probabile igitur, inquiunt, eſſe videtur, eodem tempore conditum fuiſſe mun <lb/>dum, quo & </s> <s xml:id="echoid-s10053" xml:space="preserve">redẽptus eſt. </s> <s xml:id="echoid-s10054" xml:space="preserve">Scio omnes pene Hebræos, Aegyptios, & </s> <s xml:id="echoid-s10055" xml:space="preserve">nonnullos <lb/>etiam Doctores eccleſiaſticos putare, mun dum factum fuiſſe circa Autumni <lb/>tempus, propterea quòd plantæ, ac arbores cum maturis iam fructibus fuerũt <lb/>productæ, vt conſtat ex pomo vetito noſtris primis parentibus, quod ſolũ con <lb/>tingit circa Autumnũ. </s> <s xml:id="echoid-s10056" xml:space="preserve">Quod etiã inde colligi poteſt, quòd Deus præceperit, <lb/>ob memoriam illius beneficii, quo Hebręos à ſeruitute Aegypti liberauerat, <lb/>annum deinceps ab eo tempore, nempe à Verno, quo in eos tantum beneſi-<lb/>cium contulerat, inchoandum eſſe, non autem amplius ab Autumno, quo ut <lb/>ipſi interpretantur.) </s> <s xml:id="echoid-s10057" xml:space="preserve">mundus eſt creatus. </s> <s xml:id="echoid-s10058" xml:space="preserve">Verum hæ rationes non admodum <lb/>firmæ ſunt. </s> <s xml:id="echoid-s10059" xml:space="preserve">Ad primam enim dici poteſt, Deum creaſse Paradiſum terreſtrem, <lb/>in quo poſiti fuere primi parentes, unà cum omnibus fructibus, etiamſi tunc <lb/>fuerit tempus Vernum. </s> <s xml:id="echoid-s10060" xml:space="preserve">Neque uero ualet id, quod aliqui dicunt, tunc creatos <lb/>fuiſse fructus, cum arbores eos naturaliter deinceps eſsent producturæ: </s> <s xml:id="echoid-s10061" xml:space="preserve">quia <lb/>hac ratione deberent omnes fructus eodem tempore eſse maturi, nẽpe in Au-<lb/>tumno, ut ipſi uolunt, quod tamen fieri ncn uidemus. </s> <s xml:id="echoid-s10062" xml:space="preserve">Itaque licet creati fue-<lb/>rint omnes tempore Verno, arboribus tamen inditæ ſuerunt à Deo tales natu <lb/>ræ, ut poſtea ſingulæ propriis temporibus fructus producerent. </s> <s xml:id="echoid-s10063" xml:space="preserve">Dici etiam <lb/>poſset, fructus tunc ſolum in Paradiſo fuiſse maturos, qui qualitatibus tempo <lb/>rum, atque uarietatibus non erat obnoxius, atque ſubiectus; </s> <s xml:id="echoid-s10064" xml:space="preserve">extra uero Para-<lb/>diſum nequaquam. </s> <s xml:id="echoid-s10065" xml:space="preserve">Ad ſecũdam rationem reſponderi poteſt, Deum uoluiſse, <lb/>ut Hebręi, relicto errore Aegyptiorum, annum inchoarent rurſum à Verno <lb/>tempore, quo mundus fuerat conditus, & </s> <s xml:id="echoid-s10066" xml:space="preserve">quo ei placuit eos a tam dura ſerui-<lb/>tute liberare. </s> <s xml:id="echoid-s10067" xml:space="preserve">Quicquid deniq; </s> <s xml:id="echoid-s10068" xml:space="preserve">ſit de tempore, quo mũdus fuerit creatus, cui <lb/>libet per me licet, ut teneat, quod vult: </s> <s xml:id="echoid-s10069" xml:space="preserve">mihicerte probabilius uidetur, eum <lb/>incepiſse rempore Verno, quando nimirum Sol in principio ♈, exiſtit.</s> <s xml:id="echoid-s10070" xml:space="preserve"/> </p> <div xml:id="echoid-div501" type="float" level="2" n="8"> <note position="left" xlink:label="note-278-01" xlink:href="note-278-01a" xml:space="preserve">Mundum <lb/>creatũ fuiſ-<lb/>ſe Verno, <lb/>tempore.</note> </div> <p> <s xml:id="echoid-s10071" xml:space="preserve">Hoc idem ſentire uidetur Virgilius lib. </s> <s xml:id="echoid-s10072" xml:space="preserve">2. </s> <s xml:id="echoid-s10073" xml:space="preserve">Georg. </s> <s xml:id="echoid-s10074" xml:space="preserve">ubi ita canit.</s> <s xml:id="echoid-s10075" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s10076" xml:space="preserve">Non alios prima creſcentis origine mundi.</s> <s xml:id="echoid-s10077" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s10078" xml:space="preserve">Illuxiſſe dies, aliumve habuiſſe tenorem.</s> <s xml:id="echoid-s10079" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s10080" xml:space="preserve">Crediderim. </s> <s xml:id="echoid-s10081" xml:space="preserve">Ver illud erat, Ver magnus agebat</s> </p> <p style="it"> <s xml:id="echoid-s10082" xml:space="preserve">Orbis, & </s> <s xml:id="echoid-s10083" xml:space="preserve">hybernis parcebant flatibus Euri,</s> </p> <p style="it"> <s xml:id="echoid-s10084" xml:space="preserve">Cum primum lucem pecudes hauſere, uirumque</s> </p> <p style="it"> <s xml:id="echoid-s10085" xml:space="preserve">Ferrea progenies duris caput extulit armis,</s> </p> <p style="it"> <s xml:id="echoid-s10086" xml:space="preserve">Immiſſæque, ſeræ ſyluis, & </s> <s xml:id="echoid-s10087" xml:space="preserve">ſidera cęlo.</s> <s xml:id="echoid-s10088" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10089" xml:space="preserve">Conſtat igitur, nullum punctum Zodiaci aptius potuiſse dare principium Zo <lb/>diaco, quàm primum punctum Arietis.</s> <s xml:id="echoid-s10090" xml:space="preserve"/> </p> <pb o="243" file="279" n="280" rhead="Ioan. de Sacro Boſco."/> <p> <s xml:id="echoid-s10091" xml:space="preserve"><emph style="sc">Dvbitabit</emph> fortaſſe aliquis, cum Aſtronomi omnes annum incipiant <lb/> <anchor type="note" xlink:label="note-279-01a" xlink:href="note-279-01"/> ab æquinoctio verno, quod fit, Sole ingrediente principium ♈, ob rationes <lb/>enarratas, cur antiqui omnes, & </s> <s xml:id="echoid-s10092" xml:space="preserve">nos cum eccleſia Romana in noſtris Calen-<lb/>darijs, non ab eodem loco, ſed potius à ſolſtitio brumali, quod olim circa ini-<lb/>tium Ianuarij contingebat, Sole videlicet intrante primum gradum ♑, anni <lb/>initium ſumamus. </s> <s xml:id="echoid-s10093" xml:space="preserve">Cui breuiter reſponderi poteſt, viſum eſſe commodius an <lb/>tiquis in ſolſtitio hyemali anni principium ſtatuere, quàm in æquinoctio ver <lb/>no, quia punctum illud ſolſtitij, quod eſt initium ♑, eſt finis deſcendentis, & </s> <s xml:id="echoid-s10094" xml:space="preserve"><lb/>principium aſcendentis ſemicirculi: </s> <s xml:id="echoid-s10095" xml:space="preserve">(Vocatur ſemicirculus deſcẽdens, medie-<lb/> <anchor type="note" xlink:label="note-279-02a" xlink:href="note-279-02"/> tas Zodiaci à principio ♋, per ♎, vſque ad princiꝑium ♑, quia in eo ſemper <lb/>Sol a vertice noſtri capitis deſcendit: </s> <s xml:id="echoid-s10096" xml:space="preserve">Semicirculus autem aſcendens appella <lb/>tur altera Zodiaci medietas ab initio ♑, per ♈, ad initium ♋, quia in eo Sol <lb/>rurſus ad noſtri capitis verticem aſcendit. </s> <s xml:id="echoid-s10097" xml:space="preserve">Quod quidem intelligẽdum eſt in <lb/>habitatione Septentrionali. </s> <s xml:id="echoid-s10098" xml:space="preserve">Nam contrarium prorſus dicendum eſſet in habi <lb/>tatione Mer<unsure/>idionali:) </s> <s xml:id="echoid-s10099" xml:space="preserve">Eſt finis receſſus Solis, ac principium acceſſus eiuſdem <lb/>ad nos: </s> <s xml:id="echoid-s10100" xml:space="preserve">Eſt finis decrementi dierum, & </s> <s xml:id="echoid-s10101" xml:space="preserve">principium incrementi eorundem; <lb/></s> <s xml:id="echoid-s10102" xml:space="preserve">Eſt finis incrementi noctium, & </s> <s xml:id="echoid-s10103" xml:space="preserve">initium decrementi earundem, reſpectu <lb/>partis Septentrionalis, quæ dignior eſt Auſtrali, & </s> <s xml:id="echoid-s10104" xml:space="preserve">quam inſtitutores anni in-<lb/>coluerunt. </s> <s xml:id="echoid-s10105" xml:space="preserve">Hæc autem omnia manifeſta erunt in 3. </s> <s xml:id="echoid-s10106" xml:space="preserve">cap. </s> <s xml:id="echoid-s10107" xml:space="preserve">Hoc idem dubiũ, cur <lb/>videlicet antiqui potius a ſolſtitio brumali annum voluerint inchoare, quam <lb/>ab æquinoctio verno, ſoluit Ianus apud Ouid. </s> <s xml:id="echoid-s10108" xml:space="preserve">lib. </s> <s xml:id="echoid-s10109" xml:space="preserve">1. </s> <s xml:id="echoid-s10110" xml:space="preserve">Faſt. </s> <s xml:id="echoid-s10111" xml:space="preserve">vb Ouidius Ianum <lb/>interrogat, quare principium anni non conſtituatur in æquinoctio uerno@ <lb/>quando videlicet omnia florent, atque vireſcunt, his carminibus.</s> <s xml:id="echoid-s10112" xml:space="preserve"/> </p> <div xml:id="echoid-div502" type="float" level="2" n="9"> <note position="right" xlink:label="note-279-01" xlink:href="note-279-01a" xml:space="preserve">Cur in Ca-<lb/>lẽdario Ro-<lb/>mano an-<lb/>nus incipiat <lb/>à ſolſtitio <lb/>brumali, nõ <lb/>autem ab <lb/>æquinoctio <lb/>verno.</note> <note position="right" xlink:label="note-279-02" xlink:href="note-279-02a" xml:space="preserve">Semicircu-<lb/>lus Zodiaci <lb/>deſcendens, <lb/>& aſcendẽ@ <lb/>qui.</note> </div> <p style="it"> <s xml:id="echoid-s10113" xml:space="preserve">Die age, frigoribus quare nouns incipit annus,</s> </p> <p style="it"> <s xml:id="echoid-s10114" xml:space="preserve">Qui melius per Ver incipiendus erat?</s> <s xml:id="echoid-s10115" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s10116" xml:space="preserve">Omnia tunc florent; </s> <s xml:id="echoid-s10117" xml:space="preserve">tunc eſt noua temporis ætas:</s> <s xml:id="echoid-s10118" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s10119" xml:space="preserve">Et noua de græuido palmite gemma tumet.</s> <s xml:id="echoid-s10120" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s10121" xml:space="preserve">Et modo formatis operitur frondibus arbor:</s> <s xml:id="echoid-s10122" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s10123" xml:space="preserve">Prodit & </s> <s xml:id="echoid-s10124" xml:space="preserve">in ſummum ſeminis herba ſolum.</s> <s xml:id="echoid-s10125" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s10126" xml:space="preserve">Et tepidum volucres c<unsure/>oncemtibus aera mulcent:</s> <s xml:id="echoid-s10127" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s10128" xml:space="preserve">Ludit & </s> <s xml:id="echoid-s10129" xml:space="preserve">in pratis, luxuriatq́; </s> <s xml:id="echoid-s10130" xml:space="preserve">pecus.</s> <s xml:id="echoid-s10131" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s10132" xml:space="preserve">Tunc blandi Soles, ignotaq́; </s> <s xml:id="echoid-s10133" xml:space="preserve">venit hirundo,</s> </p> <p style="it"> <s xml:id="echoid-s10134" xml:space="preserve">Et luteum celſa ſub trabe fingit opus.</s> <s xml:id="echoid-s10135" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s10136" xml:space="preserve">Tunc patitur cultus ager, & </s> <s xml:id="echoid-s10137" xml:space="preserve">renouatur aratro.</s> <s xml:id="echoid-s10138" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s10139" xml:space="preserve">Hæc nouitas anni iure vocanda fuit.</s> <s xml:id="echoid-s10140" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s10141" xml:space="preserve">Quæſieram multis: </s> <s xml:id="echoid-s10142" xml:space="preserve">non multis ille moratus</s> </p> <p style="it"> <s xml:id="echoid-s10143" xml:space="preserve">Contulit in verſus ſic ſua verba duos.</s> <s xml:id="echoid-s10144" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s10145" xml:space="preserve">BRVMA noui prima eſt, veterisq́; </s> <s xml:id="echoid-s10146" xml:space="preserve">nouiſſima Solis:</s> <s xml:id="echoid-s10147" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s10148" xml:space="preserve">Principium capiunt Phœbus, & </s> <s xml:id="echoid-s10149" xml:space="preserve">annus idem.</s> <s xml:id="echoid-s10150" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10151" xml:space="preserve"><emph style="sc">Nos</emph> quoque Chriſtiani aliam poſſumus addere cauſam, cur Eccleſia an-<lb/>num in ciprat à Solſtitio Brumali, quia videlicet illo tempore natus eſt Sal-<lb/>uator mundi ad illuminandas hominum tenebras. </s> <s xml:id="echoid-s10152" xml:space="preserve">Quamuis autem Solſti-<lb/>tium Brumale non fiat iuxta principium Ianuarij, ſed 22. </s> <s xml:id="echoid-s10153" xml:space="preserve">die Decembris, ẽt <lb/>poſt Calendarij correctionem, retinuit tamen Eccleſia adhuc vſum antiquo-<lb/>rum, vt anni principiũ cum Iulio Cæſare in prima die Ianuarij conſtituar. </s> <s xml:id="echoid-s10154" xml:space="preserve">Hęc <lb/>igitur cauſa eſt, cur in Calendariis Romanis annus incipiat a Calendis Ianua-<lb/>ru: </s> <s xml:id="echoid-s10155" xml:space="preserve">Quamuis Aſtronomi cõſiderantes alias rationes iam dictas, inchoent com <lb/>putationes annorum ab ęquinoctio Verno, ibidemque eaſdem finiant.</s> <s xml:id="echoid-s10156" xml:space="preserve"/> </p> <pb o="244" file="280" n="281" rhead="Comment. in II. Cap. Sphæræ."/> <p> <s xml:id="echoid-s10157" xml:space="preserve"><emph style="sc">Mvlta</emph> eſſent hoc loco dicẽda de varijs proprietatibus, appellationibuſ-<lb/>q́ue ſignorum, quæ quoniam ſpectant magis ad Aſtrologos iudiciarios, omit-<lb/>tenda nunc ſunt: </s> <s xml:id="echoid-s10158" xml:space="preserve">Solu m declarandum erit, quęnam ſigna dicantur domus, & </s> <s xml:id="echoid-s10159" xml:space="preserve"><lb/>exaltationes huius, aut illius Planetæ. </s> <s xml:id="echoid-s10160" xml:space="preserve">Signa igitur 12. </s> <s xml:id="echoid-s10161" xml:space="preserve">Zodiaci dicũtur domus <lb/>Planetarum, eo quod quilibet Planeta in propria domo exiſtẽs maxime uirtu <lb/>tem ſu am exercet & </s> <s xml:id="echoid-s10162" xml:space="preserve">oſtendit in his inferioribus; </s> <s xml:id="echoid-s10163" xml:space="preserve">Habet autẽ quilibet Plane-<lb/>ta duo ſigna pro duplici domo, Sole ac Luna exceptis, quibus ſingulis ſingula <lb/> <anchor type="note" xlink:label="note-280-01a" xlink:href="note-280-01"/> ſigna pro domibus tribuuntur. </s> <s xml:id="echoid-s10164" xml:space="preserve">Itaq; </s> <s xml:id="echoid-s10165" xml:space="preserve">ſignum ♌, dicitur domus ***. </s> <s xml:id="echoid-s10166" xml:space="preserve">quia cum <lb/>♌, ſit ſignum igneum, incidatq́; </s> <s xml:id="echoid-s10167" xml:space="preserve">in Æſtatem, Sol in eo decurrens maximum <lb/>æ@tum producit in terris. </s> <s xml:id="echoid-s10168" xml:space="preserve">Signum uero ♋, dicitur domus ☽. </s> <s xml:id="echoid-s10169" xml:space="preserve">quia cum ♋, ſit <lb/>ſignum aqueũ, maxime humectat Luna hæc inferiora in ♋, exiſtens. </s> <s xml:id="echoid-s10170" xml:space="preserve">Duo de-<lb/>inde ſigna circunſtantia, nẽpe ♍, & </s> <s xml:id="echoid-s10171" xml:space="preserve">♊, uocantur donus ☿. </s> <s xml:id="echoid-s10172" xml:space="preserve">Duo uero alia ad-<lb/>huc circunſtantia, ut ♎, & </s> <s xml:id="echoid-s10173" xml:space="preserve">♉, domus ♀. </s> <s xml:id="echoid-s10174" xml:space="preserve">Duo poſtea adhuc circumſtantia, ui-<lb/>delicet, ♏, & </s> <s xml:id="echoid-s10175" xml:space="preserve">♈, domus ***. </s> <s xml:id="echoid-s10176" xml:space="preserve">At duo adhuc circuſtantia, ſcilicet ♐, & </s> <s xml:id="echoid-s10177" xml:space="preserve">♓, domus <lb/>♃. </s> <s xml:id="echoid-s10178" xml:space="preserve">Duo deniq; </s> <s xml:id="echoid-s10179" xml:space="preserve">reliqua, quæ omnia hæc complectuntur, nimirum ♑, & </s> <s xml:id="echoid-s10180" xml:space="preserve">♒, <lb/>dicuntur domus variant. </s> <s xml:id="echoid-s10181" xml:space="preserve">Quamuis uero ſinguli horum quinq; </s> <s xml:id="echoid-s10182" xml:space="preserve">Planetarú binas poſ <lb/>ſideant domos, tamen ex his duabus ſemper altera eſt magis principalis, & </s> <s xml:id="echoid-s10183" xml:space="preserve">al <lb/>tera minus, ita ut Planeta non habeat eaſdem uires in vtraque domo. </s> <s xml:id="echoid-s10184" xml:space="preserve">Mer-<lb/> <anchor type="note" xlink:label="note-280-02a" xlink:href="note-280-02"/> curius etenim maiorem habet vim, & </s> <s xml:id="echoid-s10185" xml:space="preserve">uirtutem in ♍, exiſtens, quàm in ♊. </s> <s xml:id="echoid-s10186" xml:space="preserve">Ve <lb/>nus maiorem in ♉, quam in ♎. </s> <s xml:id="echoid-s10187" xml:space="preserve">Mars maio rem in ♏, quam in ♈. </s> <s xml:id="echoid-s10188" xml:space="preserve">Iuppiter <lb/>maiorem in ♐, quam in ♓. </s> <s xml:id="echoid-s10189" xml:space="preserve">Saturnus denique maiorem uim exercet in ♒, <lb/>quam in ♑. </s> <s xml:id="echoid-s10190" xml:space="preserve">Rurſus ſignum illud, quod per diametrum opponitur domui ali <lb/>cuius Planetæ, dicitur detrimentũ illius Planetæ. </s> <s xml:id="echoid-s10191" xml:space="preserve">Vt quia ſigno ♌, quod eſt <lb/>domus ***, opponitur ſignũ ♒. </s> <s xml:id="echoid-s10192" xml:space="preserve">per diametrum, dicetur ſignum ♒, detrimen <lb/> <anchor type="note" xlink:label="note-280-03a" xlink:href="note-280-03"/> tum ***. </s> <s xml:id="echoid-s10193" xml:space="preserve">Sic quoque quodlibet horum ſignorum ♉, & </s> <s xml:id="echoid-s10194" xml:space="preserve">♎. </s> <s xml:id="echoid-s10195" xml:space="preserve">dicetur detrimen-<lb/>tum ***, ſed maius detrimentum erit ſignũ ♉, quia opponitur ſigno ♏, quod <lb/>eſt præcipuum domicilium ***, & </s> <s xml:id="echoid-s10196" xml:space="preserve">ita de reliquis. </s> <s xml:id="echoid-s10197" xml:space="preserve">Has porro domos ſequens <lb/>tabella tibi proponet ob oculos.</s> <s xml:id="echoid-s10198" xml:space="preserve"/> </p> <div xml:id="echoid-div503" type="float" level="2" n="10"> <note position="left" xlink:label="note-280-01" xlink:href="note-280-01a" xml:space="preserve">Quæ ſigna <lb/>Zodiaci <lb/>quorũ pla-<lb/>netarũ do-<lb/>mus ſint.</note> <note position="left" xlink:label="note-280-02" xlink:href="note-280-02a" xml:space="preserve">Quæ do-<lb/>m<unsure/>us ſint <lb/>principia-<lb/>liores.</note> <note position="left" xlink:label="note-280-03" xlink:href="note-280-03a" xml:space="preserve">Detrimen-<lb/>tum plane-<lb/>tæ cuiuſuis <lb/>quod ſignũ <lb/>ſit.</note> </div> <note position="right" xml:space="preserve"> <lb/>Planetarum # Domus <lb/>*** # ♌ <lb/>☽ # ♋ <lb/>☿ # ♍ Principalis <lb/># ♊ minus princip. <lb/>♀ # ♉ Principalis <lb/># ♎ Minus princip. <lb/></note> <note position="right" xml:space="preserve"> <lb/>Planetarum # Domus <lb/>*** # ♏ Priu cipalis <lb/># ♈ Minus princip. <lb/>♃ # ♐ Principalis <lb/># ♓ Minus princip. <lb/>variant # ♑ Minus princip. <lb/># ♒ Principalis <lb/></note> <p> <s xml:id="echoid-s10199" xml:space="preserve"><emph style="sc">Qvaedam</emph> ex 12. </s> <s xml:id="echoid-s10200" xml:space="preserve">ſignis dicuntur exaltationes Planetarum, ut ſignum <lb/> <anchor type="note" xlink:label="note-280-06a" xlink:href="note-280-06"/> ♈, dicitur exaltatio ***, quia Sole ingrediente ſignum ♈, incipiũt augeri dies <lb/>ſupra noctes, & </s> <s xml:id="echoid-s10201" xml:space="preserve">cal or Solis in his inferioribus incrementum ſuſcipere. </s> <s xml:id="echoid-s10202" xml:space="preserve">At cũ <lb/>inrgeditur ſignum ♎, incipiunt noctes excedere quantitatem dierũ, & </s> <s xml:id="echoid-s10203" xml:space="preserve">calor <lb/>Solis paulatim debilitari. </s> <s xml:id="echoid-s10204" xml:space="preserve">Vnde ſignũ ♎, dicitut caſus ***. </s> <s xml:id="echoid-s10205" xml:space="preserve">Semper enim ſignũ <lb/> <anchor type="note" xlink:label="note-280-07a" xlink:href="note-280-07"/> per diametrum illi ſigno, quod eſt exaltatio alicuius Planetæ, oppoſitũ, uoca-<lb/>tur caſus eiuſdem Planetæ. </s> <s xml:id="echoid-s10206" xml:space="preserve">Signum itaque ♉, eſt exaltatio ☽: </s> <s xml:id="echoid-s10207" xml:space="preserve">at ſignum ♏, <lb/>caſus ☽. </s> <s xml:id="echoid-s10208" xml:space="preserve">Signum ♋, eſt exaltatio ♃, & </s> <s xml:id="echoid-s10209" xml:space="preserve">ſignum ♑: </s> <s xml:id="echoid-s10210" xml:space="preserve">caſus ♃: </s> <s xml:id="echoid-s10211" xml:space="preserve">Signũ ♍, eſt exal-<lb/>tatio ☿, at uero ſignum ♓, caſus ☿. </s> <s xml:id="echoid-s10212" xml:space="preserve">Signum ♎, eſt exaltatio variant, & </s> <s xml:id="echoid-s10213" xml:space="preserve">ſignum ♈.</s> <s xml:id="echoid-s10214" xml:space="preserve"> <pb o="245" file="281" n="282" rhead="Ioan. de Sacro Boſco."/> caſus variant. </s> <s xml:id="echoid-s10215" xml:space="preserve">Signum ♑, eſt exaltatio ***, & </s> <s xml:id="echoid-s10216" xml:space="preserve">ſignum ♋, caſus ***. </s> <s xml:id="echoid-s10217" xml:space="preserve">Signum denique <lb/>♓, eſt exaltatio ♀, & </s> <s xml:id="echoid-s10218" xml:space="preserve">ſignum ♍, caſus ♀. </s> <s xml:id="echoid-s10219" xml:space="preserve">Quæ omnia in ſequenti formula expli <lb/>cantur.</s> <s xml:id="echoid-s10220" xml:space="preserve"/> </p> <div xml:id="echoid-div504" type="float" level="2" n="11"> <note position="left" xlink:label="note-280-06" xlink:href="note-280-06a" xml:space="preserve">Exaltatio <lb/>cuiuſuis pla <lb/>netæ quod <lb/>fignum di-<lb/>catur.</note> <note position="left" xlink:label="note-280-07" xlink:href="note-280-07a" xml:space="preserve">Caſus pla-<lb/>netæ cuiuſ-<lb/>uis quod ſi-<lb/>gnum dica-<lb/>tur.</note> </div> <note position="right" xml:space="preserve"> <lb/>Planetarum # Exaltationes # Caſus <lb/>☽ # ♉ # ♏ <lb/>☿ # ♍ # ♓ <lb/>♀ # ♓ # ♍ <lb/>*** # ♈ # ♎ <lb/>*** # ♑ # ♋ <lb/>♃ # ♋ # ♑ <lb/>variant # ♎ # ♈ <lb/></note> <note position="right" xml:space="preserve">Diuiſio Zo <lb/>dia ci in gra <lb/>dus, minu-<lb/>ta, &c.</note> <p style="it"> <s xml:id="echoid-s10221" xml:space="preserve">QVODLIBET autem ſignum diuiditur in 30. </s> <s xml:id="echoid-s10222" xml:space="preserve">gradus: </s> <s xml:id="echoid-s10223" xml:space="preserve">Vnde patet, <lb/>quod in toto Zodiaco ſunt 360. </s> <s xml:id="echoid-s10224" xml:space="preserve">gradus. </s> <s xml:id="echoid-s10225" xml:space="preserve">Secundum autem Aſtronomos ite-<lb/>rum quilibet gradus diuiditur in 60. </s> <s xml:id="echoid-s10226" xml:space="preserve">Minuta: </s> <s xml:id="echoid-s10227" xml:space="preserve">quodlibet Minutum in 60. </s> <s xml:id="echoid-s10228" xml:space="preserve">Se <lb/>cunda: </s> <s xml:id="echoid-s10229" xml:space="preserve">quodlibet ſecundum in 60. </s> <s xml:id="echoid-s10230" xml:space="preserve">Tertia, & </s> <s xml:id="echoid-s10231" xml:space="preserve">ſic deinceps uſque ad decem. </s> <s xml:id="echoid-s10232" xml:space="preserve">Et <lb/>ſicut diuiditur Zodiacus ab Aſtronomis, ita quilibet circulus in ſphæra ſiue <lb/>maior, ſiue minor, in partes conſimiles diſtribuitur.</s> <s xml:id="echoid-s10233" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div506" type="section" level="1" n="167"> <head xml:id="echoid-head173" xml:space="preserve">COMMENTARIVS.</head> <note position="right" xml:space="preserve">Gradus ꝗd, <lb/>& quot ſin@ <lb/>in toto Zo-<lb/>diaco ſecũ-<lb/>dum longi <lb/>tudinem.</note> <p> <s xml:id="echoid-s10234" xml:space="preserve">DIVISO Zodiaco in 12. </s> <s xml:id="echoid-s10235" xml:space="preserve">ſigna communia, diuidit nunc ſigna in alias par <lb/>tes, docens, quoduis ſignum ab Aſtronomis diſtribui in 30. </s> <s xml:id="echoid-s10236" xml:space="preserve">partes æquales, quæ <lb/>Gradus uocantur. </s> <s xml:id="echoid-s10237" xml:space="preserve">Vnde quoniam 12. </s> <s xml:id="echoid-s10238" xml:space="preserve">ſigna in toto Zodiaco comprehendun-<lb/>tur, ſi 12. </s> <s xml:id="echoid-s10239" xml:space="preserve">per 30. </s> <s xml:id="echoid-s10240" xml:space="preserve">multiplicentur, efficientur 360. </s> <s xml:id="echoid-s10241" xml:space="preserve">quot nimirum gradus in toto <lb/>Zodiaco continentur. </s> <s xml:id="echoid-s10242" xml:space="preserve">Deinde ait, quẽuis gradum ſubdiuidi in 60. </s> <s xml:id="echoid-s10243" xml:space="preserve">partes æqua-<lb/>les, quæ minuta dicuntur: </s> <s xml:id="echoid-s10244" xml:space="preserve">Quodlibet Minutum in 60. </s> <s xml:id="echoid-s10245" xml:space="preserve">ſecunda: </s> <s xml:id="echoid-s10246" xml:space="preserve">Quoduis ſecun <lb/>dum in 60. </s> <s xml:id="echoid-s10247" xml:space="preserve">Tertia, & </s> <s xml:id="echoid-s10248" xml:space="preserve">ſic ſemper procedendo diuiſione hac ſexagenaria, donec <lb/>ad Decima perueniatur. </s> <s xml:id="echoid-s10249" xml:space="preserve">Nam raro Aſtronomi ultra Decima progrediuntur. </s> <s xml:id="echoid-s10250" xml:space="preserve">Si-<lb/>cut autem Zodiacus in 360. </s> <s xml:id="echoid-s10251" xml:space="preserve">gradus diuiditur, ita quoque quicunque alius cir-<lb/>culus in cœlo ſiue maximus, ſiue non maximus, in totidem gradus ſolet diſtri-<lb/>bui, eodemq́; </s> <s xml:id="echoid-s10252" xml:space="preserve">pacto quilibet gradus in 60 Minuta: </s> <s xml:id="echoid-s10253" xml:space="preserve">Minutũ in 60. </s> <s xml:id="echoid-s10254" xml:space="preserve">Secunda, &</s> <s xml:id="echoid-s10255" xml:space="preserve">c. <lb/></s> <s xml:id="echoid-s10256" xml:space="preserve">Verũ hocloco paulo copioſius explicanda uidetur hæc diuiſio Zodiaci in 360. </s> <s xml:id="echoid-s10257" xml:space="preserve"><lb/>gradus, & </s> <s xml:id="echoid-s10258" xml:space="preserve">cuiuslibet gradus in 60. </s> <s xml:id="echoid-s10259" xml:space="preserve">Minuta, & </s> <s xml:id="echoid-s10260" xml:space="preserve">Minuti in 60. </s> <s xml:id="echoid-s10261" xml:space="preserve">Secunda, &</s> <s xml:id="echoid-s10262" xml:space="preserve">c. </s> <s xml:id="echoid-s10263" xml:space="preserve">Quæ <lb/>quidem diuiſio Zodiaci appellari ſolet diuiſio ſecundum longitudinem.</s> <s xml:id="echoid-s10264" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10265" xml:space="preserve">ASTRONOMI igitur animaduertentes, circulum quemuis primaria <lb/>ac naturali quodammodo diuiſione ſecari in 6. </s> <s xml:id="echoid-s10266" xml:space="preserve">partes æquales, eadem nimirum <lb/>crurium circini extenſione, qua circulus deſcribitur, eo quod ſemidiameter cu-<lb/> <anchor type="note" xlink:label="note-281-04a" xlink:href="note-281-04"/> iuſque circuli ſit latus Hexagoni ęquialteri in eo deſcripti, diuiſerunt totum <lb/>Zodiacum in 6. </s> <s xml:id="echoid-s10267" xml:space="preserve">partes æquales, quæ conſtituunt ſex ſigna phyſica, ſeu natura <lb/>lia, ut ſupra diximus. </s> <s xml:id="echoid-s10268" xml:space="preserve">Deinde quod@ibet ſignum phyſicum, hoc eſt, ſextam to-<lb/>tius Zodiaci partem, partiti ſunt in 60. </s> <s xml:id="echoid-s10269" xml:space="preserve">partes æquales, quas Gradus appella-<lb/>runt, à quotidiano fortaſſe Solis, aliorumque Planetarum per has partes <lb/>progreſſu. </s> <s xml:id="echoid-s10270" xml:space="preserve">Gradatim enim Planetæ quaſi gradiendo per dictas partes Zodia-<lb/>cum perambulant. </s> <s xml:id="echoid-s10271" xml:space="preserve">Vnde factũ eſt, ut in toto Zodiaco contineantur gradus 360.</s> <s xml:id="echoid-s10272" xml:space="preserve"> <pb o="246" file="282" n="283" rhead="Comment. in 2. Cap. Sphæræ"/> Poſt hæc Gradũ quemuis iterum in 60. </s> <s xml:id="echoid-s10273" xml:space="preserve">particulas æquales diſtribuerũt, quas <lb/>Minuta dixerunt, & </s> <s xml:id="echoid-s10274" xml:space="preserve">Minutum in 60. </s> <s xml:id="echoid-s10275" xml:space="preserve">Secunda. </s> <s xml:id="echoid-s10276" xml:space="preserve">Secundũ in 60. </s> <s xml:id="echoid-s10277" xml:space="preserve">Tertia, & </s> <s xml:id="echoid-s10278" xml:space="preserve">ſic de-<lb/>inceps in infinitum progrediendo, quãuis raro admodum ad Decima Aſtrono <lb/>mi perueniant, & </s> <s xml:id="echoid-s10279" xml:space="preserve">multo rarius ea trãſcendant: </s> <s xml:id="echoid-s10280" xml:space="preserve">Atq; </s> <s xml:id="echoid-s10281" xml:space="preserve">in has minutiſſimas par-<lb/>ticulas Zodiacum diuiſerunt, ut ſummam præciſionem in loco, & </s> <s xml:id="echoid-s10282" xml:space="preserve">motu Solis, <lb/> <anchor type="note" xlink:label="note-282-01a" xlink:href="note-282-01"/> aliorumq́; </s> <s xml:id="echoid-s10283" xml:space="preserve">Planetarum conſequerentur. </s> <s xml:id="echoid-s10284" xml:space="preserve">Maluerunt autem hoc peragere ſe-<lb/>xagenaria diuiſione, quàm alia, quòd tamen illis licuiſſet; </s> <s xml:id="echoid-s10285" xml:space="preserve">tum quia numerus <lb/>ſenarius inter omnes numeros perfectos, qui nimirum conſtituuntur ex om-<lb/>nibus ſuis partibus aliquotis, eſt primus, habetq́; </s> <s xml:id="echoid-s10286" xml:space="preserve">quandam cum ſexagenario <lb/>numero affinitatem, cum ipſum decies metiatur; </s> <s xml:id="echoid-s10287" xml:space="preserve">tum quia ſexagenarius nume <lb/>rus ad hanc ſectionem commodior uiſus eſt, & </s> <s xml:id="echoid-s10288" xml:space="preserve">aptior. </s> <s xml:id="echoid-s10289" xml:space="preserve">Habet enim partem di-<lb/>midiatam, tertiam, quartam, quintã, ac ſextam, quibus partibus antiquicon-<lb/>tenti erant, vt uitarent moleſtiam, & </s> <s xml:id="echoid-s10290" xml:space="preserve">faſtidium in min oribus partibus. </s> <s xml:id="echoid-s10291" xml:space="preserve">Conti-<lb/>net quidem idem numerus alias etiam partes, nempe decimam, duodecimam, <lb/>decimamquintam, uigeſimam, & </s> <s xml:id="echoid-s10292" xml:space="preserve">denique trigeſimam, ſed harum rationem <lb/>non habebant antiqui Mathematici.</s> <s xml:id="echoid-s10293" xml:space="preserve"/> </p> <div xml:id="echoid-div506" type="float" level="2" n="1"> <note position="right" xlink:label="note-281-04" xlink:href="note-281-04a" xml:space="preserve">15. quarti.</note> <note position="left" xlink:label="note-282-01" xlink:href="note-282-01a" xml:space="preserve">Aſtronomi <lb/>cur diuiſio-<lb/>ne ſexage-<lb/>naria utan-<lb/>tur.</note> </div> <p> <s xml:id="echoid-s10294" xml:space="preserve"><emph style="sc">Potest</emph> & </s> <s xml:id="echoid-s10295" xml:space="preserve">alia ratio afferri, cur totus Zodiacus in 360. </s> <s xml:id="echoid-s10296" xml:space="preserve">grad. </s> <s xml:id="echoid-s10297" xml:space="preserve">ſectus ſit. <lb/></s> <s xml:id="echoid-s10298" xml:space="preserve">Quoniam enim ab una coniunctione Lunæ cum Sole ad aliam, hoc eſt, ab <lb/>vno Nouilunio ad aliud, intercedunt dies ferme 30. </s> <s xml:id="echoid-s10299" xml:space="preserve">nempe ſpacium unius <lb/>menſis, placuit Aſtronomis quodlibet ſignum commune in 30. </s> <s xml:id="echoid-s10300" xml:space="preserve">partes diſtri-<lb/>buere, quæ gradus dicuntur à greſſu luminarium: </s> <s xml:id="echoid-s10301" xml:space="preserve">Vel etiam quia Sol 30. </s> <s xml:id="echoid-s10302" xml:space="preserve">fe-<lb/>re dies conſumit, ut integrum ſignum commune percurrat, ſingulis nimirum <lb/>diebus ſingulos gradus propemodum conficiendo: </s> <s xml:id="echoid-s10303" xml:space="preserve">Vnde merito tantum ſpa-<lb/>cium uni gradui conceſſum fuit, quantum Sol mundi lampas fulgentiſſima <lb/>in die naturaliter fere progreditur. </s> <s xml:id="echoid-s10304" xml:space="preserve">Hac enim ratione, ſicut integro anno to-<lb/>tus Zodiacus, & </s> <s xml:id="echoid-s10305" xml:space="preserve">ſingulis menſibus ſigna ſingula, ita quoque ſingulis diebus <lb/>quaſi ſinguli gradus in Zodiaco reſpondebunt. </s> <s xml:id="echoid-s10306" xml:space="preserve">Qua ex re factum eſt, ut to-<lb/>tus Zodiacus complectatur gradus. </s> <s xml:id="echoid-s10307" xml:space="preserve">360. </s> <s xml:id="echoid-s10308" xml:space="preserve">ſignum autem phyſicum gradus 60. </s> <s xml:id="echoid-s10309" xml:space="preserve"><lb/>Ne igitur diuiſionis variatio confuſionem gigneret, diuiſus eſt rurfus gradus <lb/>in 60. </s> <s xml:id="echoid-s10310" xml:space="preserve">Minuta, Minutum in 60. </s> <s xml:id="echoid-s10311" xml:space="preserve">Secunda, &</s> <s xml:id="echoid-s10312" xml:space="preserve">c. </s> <s xml:id="echoid-s10313" xml:space="preserve">Hæ igitur ſunt potiſſimum ratio-<lb/>nes, quæ impulerunt Aſtronomos, ut hac diuiſione ſexagenaria vterentur in <lb/>diuiſione Zodiaci.</s> <s xml:id="echoid-s10314" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10315" xml:space="preserve"><emph style="sc">Ptolemae vs</emph> videtur primus <lb/> <anchor type="note" xlink:label="note-282-02a" xlink:href="note-282-02"/> <anchor type="note" xlink:label="note-282-03a" xlink:href="note-282-03"/> fuiſſe, qui circulum in 360. </s> <s xml:id="echoid-s10316" xml:space="preserve">gradus <lb/>partitus ſit. </s> <s xml:id="echoid-s10317" xml:space="preserve">Nam ante illum Erato-<lb/>ſthenes, & </s> <s xml:id="echoid-s10318" xml:space="preserve">Hipparchus videntur eun-<lb/>dem diuiſiſſe in partes 83. </s> <s xml:id="echoid-s10319" xml:space="preserve">De qua re <lb/>lege cap. </s> <s xml:id="echoid-s10320" xml:space="preserve">10. </s> <s xml:id="echoid-s10321" xml:space="preserve">& </s> <s xml:id="echoid-s10322" xml:space="preserve">11. </s> <s xml:id="echoid-s10323" xml:space="preserve">li. </s> <s xml:id="echoid-s10324" xml:space="preserve">1. </s> <s xml:id="echoid-s10325" xml:space="preserve">Almageſti Pto <lb/>lemęi. </s> <s xml:id="echoid-s10326" xml:space="preserve">Potiſſima tamen ratio huiuſce <lb/>diuiſionis uidetur eſſe, quòd uterque <lb/>numerus 360. </s> <s xml:id="echoid-s10327" xml:space="preserve">& </s> <s xml:id="echoid-s10328" xml:space="preserve">60. </s> <s xml:id="echoid-s10329" xml:space="preserve">habeat plurimas <lb/>partes aliquotas. </s> <s xml:id="echoid-s10330" xml:space="preserve">Prior enim habet <lb/>omnes has. </s> <s xml:id="echoid-s10331" xml:space="preserve">1. </s> <s xml:id="echoid-s10332" xml:space="preserve">2. </s> <s xml:id="echoid-s10333" xml:space="preserve">3. </s> <s xml:id="echoid-s10334" xml:space="preserve">4. </s> <s xml:id="echoid-s10335" xml:space="preserve">5. </s> <s xml:id="echoid-s10336" xml:space="preserve">6. </s> <s xml:id="echoid-s10337" xml:space="preserve">7. </s> <s xml:id="echoid-s10338" xml:space="preserve">8. </s> <s xml:id="echoid-s10339" xml:space="preserve">9. </s> <s xml:id="echoid-s10340" xml:space="preserve">10. </s> <s xml:id="echoid-s10341" xml:space="preserve">12. <lb/></s> <s xml:id="echoid-s10342" xml:space="preserve">15. </s> <s xml:id="echoid-s10343" xml:space="preserve">18. </s> <s xml:id="echoid-s10344" xml:space="preserve">20. </s> <s xml:id="echoid-s10345" xml:space="preserve">24. </s> <s xml:id="echoid-s10346" xml:space="preserve">30. </s> <s xml:id="echoid-s10347" xml:space="preserve">36. </s> <s xml:id="echoid-s10348" xml:space="preserve">40. </s> <s xml:id="echoid-s10349" xml:space="preserve">45. </s> <s xml:id="echoid-s10350" xml:space="preserve">60. </s> <s xml:id="echoid-s10351" xml:space="preserve">72. </s> <s xml:id="echoid-s10352" xml:space="preserve"><lb/>90. </s> <s xml:id="echoid-s10353" xml:space="preserve">120. </s> <s xml:id="echoid-s10354" xml:space="preserve">180. </s> <s xml:id="echoid-s10355" xml:space="preserve">Poſterior autem om-<lb/>nes has 1. </s> <s xml:id="echoid-s10356" xml:space="preserve">2. </s> <s xml:id="echoid-s10357" xml:space="preserve">3. </s> <s xml:id="echoid-s10358" xml:space="preserve">4. </s> <s xml:id="echoid-s10359" xml:space="preserve">5. </s> <s xml:id="echoid-s10360" xml:space="preserve">6. </s> <s xml:id="echoid-s10361" xml:space="preserve">10. </s> <s xml:id="echoid-s10362" xml:space="preserve">12. </s> <s xml:id="echoid-s10363" xml:space="preserve">15. </s> <s xml:id="echoid-s10364" xml:space="preserve">20. </s> <s xml:id="echoid-s10365" xml:space="preserve">30. </s> <s xml:id="echoid-s10366" xml:space="preserve"><lb/>Quibus ſi adiungantur ipſi numeri <lb/>360. </s> <s xml:id="echoid-s10367" xml:space="preserve">& </s> <s xml:id="echoid-s10368" xml:space="preserve">60. </s> <s xml:id="echoid-s10369" xml:space="preserve">diſponanturque ita, ut di- <pb o="247" file="283" n="284" rhead="Ioan. de Sacro Boſco."/> midiata earum pars, in qua partes minores continentur, ſtatuatur ad ſiniſtram, <lb/>reliqua vero pars dimidiata continens maiores partes, ad dexteram, ueluti hic <lb/>factum eſſe uides, denominabunt ſe binæ mutuo. </s> <s xml:id="echoid-s10370" xml:space="preserve">Nam 1. </s> <s xml:id="echoid-s10371" xml:space="preserve">eſt {1/360}. </s> <s xml:id="echoid-s10372" xml:space="preserve">numeri <lb/>360. </s> <s xml:id="echoid-s10373" xml:space="preserve">At 360. </s> <s xml:id="echoid-s10374" xml:space="preserve">faciunt {1/1}. </s> <s xml:id="echoid-s10375" xml:space="preserve">numeri eiuſdem 360. </s> <s xml:id="echoid-s10376" xml:space="preserve">Item 5. </s> <s xml:id="echoid-s10377" xml:space="preserve">conſtituunt {1/72}. </s> <s xml:id="echoid-s10378" xml:space="preserve">eiuſ-<lb/>dem, at 72. </s> <s xml:id="echoid-s10379" xml:space="preserve">efficiunt {1/1}. </s> <s xml:id="echoid-s10380" xml:space="preserve">&</s> <s xml:id="echoid-s10381" xml:space="preserve">c. </s> <s xml:id="echoid-s10382" xml:space="preserve">Sic quoque 3. </s> <s xml:id="echoid-s10383" xml:space="preserve">faciunt {1/20}. </s> <s xml:id="echoid-s10384" xml:space="preserve">numeri 60. </s> <s xml:id="echoid-s10385" xml:space="preserve">at 20. </s> <s xml:id="echoid-s10386" xml:space="preserve">con-<lb/>ſtituunt {1/3}. </s> <s xml:id="echoid-s10387" xml:space="preserve">eiuſdem numeri 60. </s> <s xml:id="echoid-s10388" xml:space="preserve">&</s> <s xml:id="echoid-s10389" xml:space="preserve">c.</s> <s xml:id="echoid-s10390" xml:space="preserve"/> </p> <div xml:id="echoid-div507" type="float" level="2" n="2"> <note position="left" xlink:label="note-282-02" xlink:href="note-282-02a" xml:space="preserve">Ptolemæus <lb/>primus di-<lb/>uiſit circu-<lb/>lũ in 360. <lb/>partes.</note> <note position="right" xlink:label="note-282-03" xlink:href="note-282-03a" xml:space="preserve"> <lb/>## Partes aliquotæ \\ numeri 360 # ## Partes aliquotæ \\ numeri 60 <lb/>1 # 360 # 1 # 60 <lb/>2 # 180 # 2 # 30 <lb/>3 # 120 # 3 # 20 <lb/>4 # 90 # 4 # 15 <lb/>5 # 72 # 5 # 12 <lb/>6 # 60 # 6 # 20 <lb/>8 # 45 <lb/>9 # 40 <lb/>10 # 36 <lb/>12 # 30 <lb/>15 # 24 <lb/>18 # 20 <lb/></note> </div> <p> <s xml:id="echoid-s10391" xml:space="preserve">VT autem cognoſcatur, quot particulæ cuiuſque diuiſionis unum gradum <lb/>conſtituant, uel etiam totum Zodiacum, libuit hic ſubnectere duas tabellas, in <lb/>quarum priori gradus integer in Minuta, Secunda, Tertia, Quatta, Quinta, Sex <lb/> <anchor type="note" xlink:label="note-283-01a" xlink:href="note-283-01"/> ta, Septima, Octaua, Nona, ac Decima: </s> <s xml:id="echoid-s10392" xml:space="preserve">In poſteriori uero totus Zodiacus ſecun <lb/>dum longitudinem in Gradus, Minuta, Secunda, &</s> <s xml:id="echoid-s10393" xml:space="preserve">c. </s> <s xml:id="echoid-s10394" xml:space="preserve">diſtribuitur.</s> <s xml:id="echoid-s10395" xml:space="preserve"/> </p> <div xml:id="echoid-div508" type="float" level="2" n="3"> <note position="right" xlink:label="note-283-01" xlink:href="note-283-01a" xml:space="preserve">Quot Mi-<lb/>nuta, Secun <lb/>da, Tertia <lb/>&c. unus <lb/>Gradus con <lb/>tineat.</note> </div> <note position="right" xml:space="preserve">Quot Gra-<lb/>dus, Minu-<lb/>ta, Secũda, <lb/>& Tertia, <lb/>&c. in toto <lb/>Zodiaco cõ <lb/>tineantur.</note> <note position="right" xml:space="preserve"> <lb/>## GRADVS VNVS CONTINET <lb/>Minuta # 60 <lb/>Secunda # 3600 <lb/>Tertia # 216000 <lb/>Quarta # 12960000 <lb/>Quinta # 777600000 <lb/>Sexta # 46656000000 <lb/>Septima # 2799360000000 <lb/>Octaua # 167961600000000 <lb/>Nona # 10077696000000000 <lb/>Decima # 604661760000000000 <lb/>## ZODIACVS CONTINET <lb/> Gradus # 360 Minuta # 21600 Secunda # 1296000 Tertia # 77760000 Quarta # 4665600000 Quinta # 279936000000 Sexta # 16796160000000 Septima # 1007769600000000 Octaua # 60466176000000000 Nona # 3627970560000000000 Decima # 21767823600000000000 </note> <p> <s xml:id="echoid-s10396" xml:space="preserve">Vtramque hanc tabellam quiuis extendere poterit proprio marte in infini-<lb/>tum. </s> <s xml:id="echoid-s10397" xml:space="preserve">Si enim Decima multiplicentur per 60. </s> <s xml:id="echoid-s10398" xml:space="preserve">habebuntur Vndecima, & </s> <s xml:id="echoid-s10399" xml:space="preserve">ſi hæc <pb o="248" file="284" n="285" rhead="Comment. in II. Cap. Sphæræ"/> rurſus pro 60. </s> <s xml:id="echoid-s10400" xml:space="preserve">multiplicentur, proueni ent Duodecima, &</s> <s xml:id="echoid-s10401" xml:space="preserve">c.</s> <s xml:id="echoid-s10402" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10403" xml:space="preserve">LATINI quoque integrũ, ſeu Totum quodcunque, atque adeo Gradũ, <lb/> <anchor type="note" xlink:label="note-284-01a" xlink:href="note-284-01"/> Aſſem appellant, ipſumq́; </s> <s xml:id="echoid-s10404" xml:space="preserve">in duodecim æquales pattes diuidunt, quarum unde <lb/>eim dicunt, Deuncem: </s> <s xml:id="echoid-s10405" xml:space="preserve">decem, Dextantem: </s> <s xml:id="echoid-s10406" xml:space="preserve">nouem, Dodrantem: </s> <s xml:id="echoid-s10407" xml:space="preserve">octo, Beſſem: <lb/></s> <s xml:id="echoid-s10408" xml:space="preserve">ſeptem, Septuncem: </s> <s xml:id="echoid-s10409" xml:space="preserve">ſex, hoc eſt, dimidiatam partem, Semiſſem: </s> <s xml:id="echoid-s10410" xml:space="preserve">quinque, Quin-<lb/>cuncem: </s> <s xml:id="echoid-s10411" xml:space="preserve">quatuor, T@ientem: </s> <s xml:id="echoid-s10412" xml:space="preserve">tres, Quadrantem: </s> <s xml:id="echoid-s10413" xml:space="preserve">duas, Sextantem: </s> <s xml:id="echoid-s10414" xml:space="preserve">unam deni-<lb/>que, Vnciam. </s> <s xml:id="echoid-s10415" xml:space="preserve">Quoniam uero frequens eſt: </s> <s xml:id="echoid-s10416" xml:space="preserve">uſus horum uocabulorum apud an-<lb/>tiquos, præſertim apud Plinium, Vitruuium, Columellam, & </s> <s xml:id="echoid-s10417" xml:space="preserve">alios ſcriptores tã <lb/>ueteres, quàm recentiores, non abs re me fa cturum arbitror, ſi tabellam appo-<lb/>nam, in qua primo loco contineantur nomina 12. </s> <s xml:id="echoid-s10418" xml:space="preserve">partium Aſſis, ſeu integri <lb/>gradus: </s> <s xml:id="echoid-s10419" xml:space="preserve">ſecundo loco Minuta, quæ ſingu lis 12. </s> <s xml:id="echoid-s10420" xml:space="preserve">partibus reſpondeat. </s> <s xml:id="echoid-s10421" xml:space="preserve">Tertio loco, <lb/>fractiones uulgares, quę ualorem earundem partium exprimant.</s> <s xml:id="echoid-s10422" xml:space="preserve"/> </p> <div xml:id="echoid-div509" type="float" level="2" n="4"> <note position="left" xlink:label="note-284-01" xlink:href="note-284-01a" xml:space="preserve">Aſſis, eiuſ-<lb/>q́ue partes.</note> </div> </div> <div xml:id="echoid-div511" type="section" level="1" n="168"> <head xml:id="echoid-head174" xml:space="preserve">TABELLA CONTINENS NOMINA DVODECIM</head> <head xml:id="echoid-head175" xml:space="preserve">partium Aſſis, earumque ualorem.</head> <note position="left" xml:space="preserve">Vt Zodia-<lb/>cus, ita qui <lb/>libet crrcu-<lb/>lus diuidi-<lb/>tur.</note> <note position="right" xml:space="preserve"> <lb/>As, uel Aſſis # minuta # 60 # #### Gradusinteger <lb/>Deunx # minuta # 55 # Partes # {55/60} # vel # {11/12} <lb/>Dextans # minuta # 50 # Partes # {50/60} # vel # {10/12} # vel # {5/6} <lb/>Dodrans # minuta # 45 # Partes # {45/60} # vel # {6/12} # vel # {3/4} <lb/>Bes, uel Beſſis, # minuta # 40 # Partes # {40/60} # vel # {8/12} # vel # {2/3} <lb/>Septunx # minuta # 35 # Partes # {35/60} # vel # {7/12} <lb/>Semis, uel Semiſſis # minuta # 30 # Partes # {30/60} # vel # {6/12} # vel # {1/2} <lb/>Quincunx # minuta # 25 # Partes # {25/60} # vel # {5/12} <lb/>Triens # minuta # 20 # Partes # {20/60} # vel # {4/12} # vel # {1/3} <lb/> Quadrans # minuta # 15 # Partes # {15/60} # vel # {3/12} # vel # {1/4} Sextans # minuta # 10 # Partes # {10/60} # vel # {2/12} # vel # {1/6} Vncia # minuta # 5 # Partes # {5/60} # vel # {1/12} </note> <note position="left" xml:space="preserve">Gradus Ae-<lb/>quatoris cur <lb/>dicantur Tẽ <lb/>pora.</note> <p> <s xml:id="echoid-s10423" xml:space="preserve">QVEMADMODVM autẽ Zodiacus diuiditur, ita prorſus & </s> <s xml:id="echoid-s10424" xml:space="preserve">Aequino <lb/>ctialis circulus, & </s> <s xml:id="echoid-s10425" xml:space="preserve">Meridianus, & </s> <s xml:id="echoid-s10426" xml:space="preserve">denique quilibet alius circulus ſphæræ ſiue <lb/>maximus, ſiue non, ab Aſtronomis diuidi ſolet; </s> <s xml:id="echoid-s10427" xml:space="preserve">quamuis gradus Aequinoctialis <lb/>circuli, quod conſtanti, ac perpetua lege tempora diurna, nocturnaque deſi-<lb/> <anchor type="note" xlink:label="note-284-05a" xlink:href="note-284-05"/> gnent, eademque in horas æquales diſtribuant: </s> <s xml:id="echoid-s10428" xml:space="preserve">Græci χρόν{ου}ς Latini vero Tem <lb/>pora denominarunt, ut vt à Zodiaci gradibus diſtinguerentur.</s> <s xml:id="echoid-s10429" xml:space="preserve"/> </p> <div xml:id="echoid-div511" type="float" level="2" n="1"> <note position="left" xlink:label="note-284-05" xlink:href="note-284-05a" xml:space="preserve">Vt gradus, <lb/>ita quoque <lb/>Hora@, & <lb/>quodcunq;@ <lb/>Integrũ di-<lb/>niditur in <lb/>Minuta, Se <lb/>cunda, &c.</note> </div> <p> <s xml:id="echoid-s10430" xml:space="preserve">EODEM etiam modo, quo diuiſus eſt gradus, diſtribui ſolet & </s> <s xml:id="echoid-s10431" xml:space="preserve">hora, & </s> <s xml:id="echoid-s10432" xml:space="preserve"><lb/>quoduis integrum, nempein 60. </s> <s xml:id="echoid-s10433" xml:space="preserve">minuta: </s> <s xml:id="echoid-s10434" xml:space="preserve">minutũ in 60. </s> <s xml:id="echoid-s10435" xml:space="preserve">ſecunda, & </s> <s xml:id="echoid-s10436" xml:space="preserve">c. </s> <s xml:id="echoid-s10437" xml:space="preserve">Itẽ in Deun <lb/>cem, Dextantem, Dodrantem, &</s> <s xml:id="echoid-s10438" xml:space="preserve">c. </s> <s xml:id="echoid-s10439" xml:space="preserve">Subdiuidunt quoq. </s> <s xml:id="echoid-s10440" xml:space="preserve">veteres Vnciam in alias <lb/>particulas, quas breuitati ſtudẽs hic omitto, poterit autem quiuis perfectius <lb/>hæc omnia percipere ex libro Budæi, quẽ de Aſſe, eiuſq. </s> <s xml:id="echoid-s10441" xml:space="preserve">partibus inſcripſit.</s> <s xml:id="echoid-s10442" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">Zodiacus in <lb/>ter oẽs cir-<lb/>culos ſphæ-<lb/>ræ ſolus la-<lb/>titudinem <lb/>habet 12. <lb/>graduum.</note> <p style="it"> <s xml:id="echoid-s10443" xml:space="preserve">CVM omnis etiam circulus in ſphęra præter Zodiacum intelliga-<lb/>tur, ſicut linea, uel circunferentia, ſolus Zodiacus intelligitur, ut ſuper-<lb/>ficies. </s> <s xml:id="echoid-s10444" xml:space="preserve">habens in latitudine ſua duodecim gradus, de cuiuſmodi gradibus <pb o="249" file="285" n="286" rhead="Ioan. de Sacro Boſco."/> iam locuti ſumus. </s> <s xml:id="echoid-s10445" xml:space="preserve">Vnde patet, quòd quidam mentiuntur in Aſtrologia <lb/>dicentes, ſigna eſſe quadrata, niſiabutentes nomine, idem appellent qua-<lb/>dratum & </s> <s xml:id="echoid-s10446" xml:space="preserve">quadrangulum. </s> <s xml:id="echoid-s10447" xml:space="preserve">Signum enim habet gradus 30. </s> <s xml:id="echoid-s10448" xml:space="preserve">in longitudi-<lb/>ne, 12. </s> <s xml:id="echoid-s10449" xml:space="preserve">uero in latitudine.</s> <s xml:id="echoid-s10450" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div513" type="section" level="1" n="169"> <head xml:id="echoid-head176" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s10451" xml:space="preserve">HACTENVS egit auctor de diuiſione Zodiaci ſecundũ longitudinem <lb/>Hic iam eiuſdẽ quantitatem, ſeu diuiſionẽ ſecundum latitudinẽ explicat. </s> <s xml:id="echoid-s10452" xml:space="preserve">Habet <lb/>enim, ait, Zodiacus inter reliquos ſphęræ circulos hoc propriũ, & </s> <s xml:id="echoid-s10453" xml:space="preserve">peculiare, ꝙ <lb/>cum omnes alij in ſuperficie cœli concipiantur, ueluti lineę, ſeu circũferentiæ <lb/>indiuiſibiles ſecundũ latitudinem, ſolus Zodiacus intelligatur, ut ſuperficies <lb/>quædam habens in latitudine ſua gradus 12. </s> <s xml:id="echoid-s10454" xml:space="preserve">ſecundum totum circuitum. </s> <s xml:id="echoid-s10455" xml:space="preserve">Et <lb/>quoniam quodlibet ſignum diximus habere in longitudine gradus 30. </s> <s xml:id="echoid-s10456" xml:space="preserve">infert, <lb/>quoſdam decipi in Aſtrologia dicentes, ſigna Zodiaci eſſe quadrata, niſi nomi-<lb/>ne quadrati velint intelligere quadrangulum, quod commune eſt ad quadra-<lb/>tum, & </s> <s xml:id="echoid-s10457" xml:space="preserve">altera parte longius. </s> <s xml:id="echoid-s10458" xml:space="preserve">Erit enim quoduis ſignum hac ratione altera parte <lb/>lougius habens in quolibet latere longiori 30. </s> <s xml:id="echoid-s10459" xml:space="preserve">gradus, in breuiori autem 12.</s> <s xml:id="echoid-s10460" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">Zodiacus: <lb/>car latus po <lb/>natur ab A <lb/>ſtronomis.</note> <p> <s xml:id="echoid-s10461" xml:space="preserve">TRIBVERVNT ſoli Zodiaco inter omnes alios circulos hanc latitu-<lb/>dinem Aſtronomi duas ob cauſas. </s> <s xml:id="echoid-s10462" xml:space="preserve">Primum, ut intra ſe continere poſſet figuras, <lb/>atque nomina ſignorum. </s> <s xml:id="echoid-s10463" xml:space="preserve">Deinde propter irregularem Planetarum motum ſub <lb/>ipſo. </s> <s xml:id="echoid-s10464" xml:space="preserve">Quamuis enim planetæ omnes ſub Zodiaco perpetuo ferantur, non ta-<lb/>men omnes eodem modo mouentur. </s> <s xml:id="echoid-s10465" xml:space="preserve">Sol enim in medio ipſius diſcurrens ne-<lb/>que ad dextram, neque ad ſiniſtram declinat vnquam: </s> <s xml:id="echoid-s10466" xml:space="preserve">At reliqui Planetæ om-<lb/>nes nunc à medio Zodiaco dèuiant in Septentrionem, nunc in Auſtrum, ita vt <lb/>hæc deuiatio in vtramuis partem à medio Zodiaco complectatur fere grad. </s> <s xml:id="echoid-s10467" xml:space="preserve">6. <lb/></s> <s xml:id="echoid-s10468" xml:space="preserve"> <anchor type="note" xlink:label="note-285-02a" xlink:href="note-285-02"/> Vnde facta<unsure/>m eſt, ut totus Zodiacus in latitudine obtineat grad. </s> <s xml:id="echoid-s10469" xml:space="preserve">12.</s> <s xml:id="echoid-s10470" xml:space="preserve"/> </p> <div xml:id="echoid-div513" type="float" level="2" n="1"> <note position="right" xlink:label="note-285-02" xlink:href="note-285-02a" xml:space="preserve">Latitudo <lb/>Zodiaci ſi-<lb/>cut potius <lb/>12. gra. quã <lb/>16. comple-<lb/>ctatur.</note> </div> <p> <s xml:id="echoid-s10471" xml:space="preserve">VERVM obijciet aliquis, Martem, & </s> <s xml:id="echoid-s10472" xml:space="preserve">Venerem, non ſolum 6. </s> <s xml:id="echoid-s10473" xml:space="preserve">grad. </s> <s xml:id="echoid-s10474" xml:space="preserve">à me-<lb/>dio Zodiaco ſiue in Septentrionem, ſiue in Auſtrum recedere, ſed interdum fe-<lb/>re 8. </s> <s xml:id="echoid-s10475" xml:space="preserve">grad. </s> <s xml:id="echoid-s10476" xml:space="preserve">Quare rectius Zodiaci latitudinem eſſe debere 16. </s> <s xml:id="echoid-s10477" xml:space="preserve">grad. </s> <s xml:id="echoid-s10478" xml:space="preserve">ut nũquam <lb/>planetę extra Zodiacum reperiantur oberrare. </s> <s xml:id="echoid-s10479" xml:space="preserve">Ad hanc nihilominus obiectio-<lb/>nem reſpondendum eſt, hanc ob cauſam nonnullos Ioan. </s> <s xml:id="echoid-s10480" xml:space="preserve">Regiom. </s> <s xml:id="echoid-s10481" xml:space="preserve">ſecutos tri-<lb/>buere Zodiaco grad. </s> <s xml:id="echoid-s10482" xml:space="preserve">16. </s> <s xml:id="echoid-s10483" xml:space="preserve">in latitudine: </s> <s xml:id="echoid-s10484" xml:space="preserve">quod tamen neceſſarium eſſe omnes alij <lb/>Aſtronomi negant. </s> <s xml:id="echoid-s10485" xml:space="preserve">Dicunt enim, magis eſſe rationi conſentaneũ, ut Zodiacus <lb/>ſecundũ latitudinẽ in 12. </s> <s xml:id="echoid-s10486" xml:space="preserve">grad. </s> <s xml:id="echoid-s10487" xml:space="preserve">ſecetur, propterea ꝙ hanc latitudinem nunquã <lb/>alij planetæ excedunt; </s> <s xml:id="echoid-s10488" xml:space="preserve">Quòd aũt aliquando Mars, & </s> <s xml:id="echoid-s10489" xml:space="preserve">Venus pluribus gradibus <lb/>quàm 6. </s> <s xml:id="echoid-s10490" xml:space="preserve">a medio Zodiaco deuient, id raro admodũ contingit, & </s> <s xml:id="echoid-s10491" xml:space="preserve">ſolum ratione <lb/>magnitudinis epicyclorum, quos habent; </s> <s xml:id="echoid-s10492" xml:space="preserve">ut hæc deuiatio ſufficiens cauſa eſſe <lb/>nequeat, cur Zodiaco tribuantur grad’ 16. </s> <s xml:id="echoid-s10493" xml:space="preserve">in latitudine. </s> <s xml:id="echoid-s10494" xml:space="preserve">Accedit etiam, ꝙ con-<lb/>ueniens eſſe videtur, ut ſicuttotus Zodiacus in longitudine continet 12. </s> <s xml:id="echoid-s10495" xml:space="preserve">ſigna, <lb/>ita etiam in latitudine totidem partes comprehenderet, nimirum 12. </s> <s xml:id="echoid-s10496" xml:space="preserve">gradus. <lb/></s> <s xml:id="echoid-s10497" xml:space="preserve">Pari ratione quemadmodũ unus gradus eſt pars trigeſima unius ſigni, ita quo-<lb/>que tota làtitudo Zodiaci eſſet trigeſima pars totius ambitus, ſeu circuitus eiuſ <lb/>dem Zodiaci, cuiuſmodi ſunt 12. </s> <s xml:id="echoid-s10498" xml:space="preserve">grad. </s> <s xml:id="echoid-s10499" xml:space="preserve">latitudinis, reſpectu 360. </s> <s xml:id="echoid-s10500" xml:space="preserve">gr. </s> <s xml:id="echoid-s10501" xml:space="preserve">longitudi-<lb/>nis. </s> <s xml:id="echoid-s10502" xml:space="preserve">Denique ſicut ambitus totius Zodiaci in longitudine comprehendit 360. </s> <s xml:id="echoid-s10503" xml:space="preserve"><lb/>grad. </s> <s xml:id="echoid-s10504" xml:space="preserve">ſic etiã totidem gradus contineret unũ ſignũ in tota area, uel ſuperficie. </s> <s xml:id="echoid-s10505" xml:space="preserve"><lb/>Nam 12. </s> <s xml:id="echoid-s10506" xml:space="preserve">multiplicata per 30. </s> <s xml:id="echoid-s10507" xml:space="preserve">efficiunt 360. </s> <s xml:id="echoid-s10508" xml:space="preserve">grad. </s> <s xml:id="echoid-s10509" xml:space="preserve">aream uidelicet unius ſigni.</s> <s xml:id="echoid-s10510" xml:space="preserve"/> </p> <pb o="250" file="286" n="287" rhead="Comment. in 2. Cap. Sphæræ."/> <p style="it"> <s xml:id="echoid-s10511" xml:space="preserve">LINEA autem diuidens Zodiacum in circuitu, ita quòd ex una par <lb/> <anchor type="note" xlink:label="note-286-01a" xlink:href="note-286-01"/> te ſui relinquat ſex gradus, & </s> <s xml:id="echoid-s10512" xml:space="preserve">ex alia parte alios ſex, dicitur linea eclip-<lb/>tica; </s> <s xml:id="echoid-s10513" xml:space="preserve">quoniam quando Sol, & </s> <s xml:id="echoid-s10514" xml:space="preserve">Luna ſunt linealiter ſub illa, contingit eclip-<lb/>ſis Solis, aut Lunæ: </s> <s xml:id="echoid-s10515" xml:space="preserve">Solis, ut ſi fiat uouilunium, & </s> <s xml:id="echoid-s10516" xml:space="preserve">Luna interponatur recte <lb/>inter aſpectum noſtrum, & </s> <s xml:id="echoid-s10517" xml:space="preserve">corpus Solare: </s> <s xml:id="echoid-s10518" xml:space="preserve">Lunæ, ut in plenilunio, quando <lb/> <anchor type="note" xlink:label="note-286-02a" xlink:href="note-286-02"/> Sol Lunæ opponitur diametraliter. </s> <s xml:id="echoid-s10519" xml:space="preserve">Vnde eclipſis Lunæ nihil aliud eſt, <lb/>quam interpoſitio terrę inter corpus Solis, & </s> <s xml:id="echoid-s10520" xml:space="preserve">Lunæ.</s> <s xml:id="echoid-s10521" xml:space="preserve"/> </p> <div xml:id="echoid-div514" type="float" level="2" n="2"> <note position="left" xlink:label="note-286-01" xlink:href="note-286-01a" xml:space="preserve">Ecliptica li <lb/>nea quid, & <lb/>cur ſic dica <lb/>tur.</note> <note position="left" xlink:label="note-286-02" xlink:href="note-286-02a" xml:space="preserve">Eclipſis lu-<lb/>@æ quid.</note> </div> </div> <div xml:id="echoid-div516" type="section" level="1" n="170"> <head xml:id="echoid-head177" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s10522" xml:space="preserve">EXPLICAT hoc loco, quid ſit linea ecliptica, dicens, cum Zodiacus in <lb/>latitudine habeat 12. </s> <s xml:id="echoid-s10523" xml:space="preserve">grad. </s> <s xml:id="echoid-s10524" xml:space="preserve">ſi intelligatur linea per medium horum 12. </s> <s xml:id="echoid-s10525" xml:space="preserve">gr. </s> <s xml:id="echoid-s10526" xml:space="preserve">diſcin <lb/>dere totum circuitum Zodiaci, ita ut ex una parte relinquantur ſex grad. </s> <s xml:id="echoid-s10527" xml:space="preserve">toti-<lb/>demq́. </s> <s xml:id="echoid-s10528" xml:space="preserve">ex altera, dicetur linea illa, ecliptica, eo, ꝙ, quando Luna Soli coniungi-<lb/>tur exiſtens ſub hac linea præciſe, contingat eclipſis Solis: </s> <s xml:id="echoid-s10529" xml:space="preserve">quando uero eidem <lb/>opponitur per diametrum in eadem exiſtens linea, eclipſis Lunæ accidat. </s> <s xml:id="echoid-s10530" xml:space="preserve">Vbi <lb/>etiã obiter declarat, quid ſit eclipſis Lunæ. </s> <s xml:id="echoid-s10531" xml:space="preserve">Quæ omnia perſpicua ſunt in lite-<lb/>ra. </s> <s xml:id="echoid-s10532" xml:space="preserve">Verum de Eclipſi tam Solis, quàm Lunæ plura dicemus cap. </s> <s xml:id="echoid-s10533" xml:space="preserve">4.</s> <s xml:id="echoid-s10534" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10535" xml:space="preserve">VOCATVR hæc linea Ecliptica, quæ a probatis auctoribus pro Zodia-<lb/> <anchor type="note" xlink:label="note-286-03a" xlink:href="note-286-03"/> co abſolute uſurpatur, nulla habita ratione latitudinis Zodiaci: </s> <s xml:id="echoid-s10536" xml:space="preserve">Via Solis, eo <lb/>quòd ſemper ſub illa Sol propria motu incedat. </s> <s xml:id="echoid-s10537" xml:space="preserve">Eadem de cauſa dicitur orbita <lb/>Solis, Iter Solare, Locus Solis, Planum Solis, Circulus Solis, locus eclipticus, <lb/>& </s> <s xml:id="echoid-s10538" xml:space="preserve">apud Ptolemæum circulus per medium animalium, circulus ſignorum, & </s> <s xml:id="echoid-s10539" xml:space="preserve">a-<lb/>lijs huiuſmodi nominib us appellari ſolet a uarijs ſcriptoribus.</s> <s xml:id="echoid-s10540" xml:space="preserve"/> </p> <div xml:id="echoid-div516" type="float" level="2" n="1"> <note position="left" xlink:label="note-286-03" xlink:href="note-286-03a" xml:space="preserve">Varia noia <lb/>Eclipticæ.</note> </div> <p> <s xml:id="echoid-s10541" xml:space="preserve">DESCRIBITVR linea ecliptica hac ratione in cœlo. </s> <s xml:id="echoid-s10542" xml:space="preserve">Concipiatur li-<lb/> <anchor type="note" xlink:label="note-286-04a" xlink:href="note-286-04"/> nea recta a centro terræ, ſeu mundi totius egrediens tranſire per centrum cor-<lb/>poris ſolaris uſque ad primum mobile. </s> <s xml:id="echoid-s10543" xml:space="preserve">Nam ex motu annuo Solis ab occaſu in <lb/>ortum deſcribetur circulus, cuius circumferentia in primo mobili exiſtens ap-<lb/>pellatur linea eclipta. </s> <s xml:id="echoid-s10544" xml:space="preserve">Sol enim proprio motu ſemper eodem pacto, eiſdemq́. <lb/></s> <s xml:id="echoid-s10545" xml:space="preserve">terminis ab Aequatore recedit, ut mox aperiemus. </s> <s xml:id="echoid-s10546" xml:space="preserve">Quod ſi per totum Zodiaci <lb/>ambitum ex utraque parte huic lineæ adijciantur grad. </s> <s xml:id="echoid-s10547" xml:space="preserve">6. </s> <s xml:id="echoid-s10548" xml:space="preserve">uel ſecundum ali-<lb/>quos grad. </s> <s xml:id="echoid-s10549" xml:space="preserve">8. </s> <s xml:id="echoid-s10550" xml:space="preserve">conſtituetur totus circulus Zodiacus.</s> <s xml:id="echoid-s10551" xml:space="preserve"/> </p> <div xml:id="echoid-div517" type="float" level="2" n="2"> <note position="left" xlink:label="note-286-04" xlink:href="note-286-04a" xml:space="preserve">Ecliptica <lb/>qũo conci-<lb/>piatur de-<lb/>ſcribi in cę-<lb/>lo.</note> </div> <p style="it"> <s xml:id="echoid-s10552" xml:space="preserve">SOL quidem ſemper decurrit ſub Ecliptica, omnes uero alij Planetæ <lb/> <anchor type="note" xlink:label="note-286-05a" xlink:href="note-286-05"/> declinant uel uerſus Septentrionem, uel uerſus Auſtrum: </s> <s xml:id="echoid-s10553" xml:space="preserve">Quandoquidem <lb/>autem ſunt ſub Ecliptica.</s> <s xml:id="echoid-s10554" xml:space="preserve"/> </p> <div xml:id="echoid-div518" type="float" level="2" n="3"> <note position="left" xlink:label="note-286-05" xlink:href="note-286-05a" xml:space="preserve">Sol ſempet <lb/>mouetur <lb/>ſub eclipti-<lb/>ca, alij uero <lb/>planetæ nõ.</note> </div> </div> <div xml:id="echoid-div520" type="section" level="1" n="171"> <head xml:id="echoid-head178" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s10555" xml:space="preserve">HIC docet, quonam pacto ſeſe habeat Sol, & </s> <s xml:id="echoid-s10556" xml:space="preserve">alij Planetæ reſpectu cõme-<lb/>moratæ lineæ Eclipticæ, aſſerens, Solem perpetuo ſub Ecliptica decurrere, nõ <lb/>declinando ad ullam partem, alios uero Planetas omnes ab eadem deuiare mo <lb/>do uerſus ſeptentrionem, modo uerſus Auſtrum, modo uero (quando uideli-<lb/>cet a Septentrione in Auſtrum, uel ex Auſtro in Septentrionem tendunt) ſub <lb/>Ecliptica conſiſtere.</s> <s xml:id="echoid-s10557" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10558" xml:space="preserve">OBSERVATVM enim, & </s> <s xml:id="echoid-s10559" xml:space="preserve">notatum eſt ab Aſtronomis, Solem ineodem <lb/>climate ſingulis annis iuxta idem Horizontis punctum oriri, & </s> <s xml:id="echoid-s10560" xml:space="preserve">occidere, quan- <pb o="251" file="287" n="288" rhead="Ioan. de Sacro Boſco."/> do in eodem ſigno, & </s> <s xml:id="echoid-s10561" xml:space="preserve">gradu Zodiaci exiſtit, ut in primo gradu ♋. </s> <s xml:id="echoid-s10562" xml:space="preserve">Id quod fa-<lb/> <anchor type="note" xlink:label="note-287-01a" xlink:href="note-287-01"/> cile obſeruari poteſt ex umbra alicuius ſtyli in muro infixi, qui orientem, oc-<lb/>cidentemve Solem reſpicit. </s> <s xml:id="echoid-s10563" xml:space="preserve">Similiter in meridiẽ umbram eiuſdem meridianã <lb/>ſtatis anni temporibus perpetuo eſſe eandem, nempe eam in Solſtitio æſtiuo <lb/>habere ſingulis annis eandẽ longitudinẽ, ſimiliter in æquinoctio vtroq;</s> <s xml:id="echoid-s10564" xml:space="preserve">, nec-<lb/>non in Solſtitio brumali; </s> <s xml:id="echoid-s10565" xml:space="preserve">ita ut in uno Solſtitio æſtiuo longior umbra meri-<lb/>diana nunquã uiſa fuerit, quàm in alio Solſtitio æſtiuo, neq; </s> <s xml:id="echoid-s10566" xml:space="preserve">in vino æquino-<lb/>ctio longiot, quàm in alio, neque in uno Solſtitio brumali, quàm in alio; </s> <s xml:id="echoid-s10567" xml:space="preserve">idẽ-<lb/>que dicẽdum eſt de omnibus alijs temporibus anni, ſeu punctis Zodiaci. </s> <s xml:id="echoid-s10568" xml:space="preserve">Pari <lb/>ratione compertum habent Aſtronomi, Solem, dum maxime ab Aequatore <lb/>declinat, quando uidelicet exiſtit in principio ♋, uel ♑, cõſtanter ſingulis an <lb/>nis eodem ſpatio ab eo dimoueri, atque idem obſeruarunt, dum eſt in quouis <lb/>alio puncto Zodiaci. </s> <s xml:id="echoid-s10569" xml:space="preserve">Quamobrem neceſſario concluſerunt, Solem eandẽ per-<lb/>petuo ſemitam, ſeu iter tenere, quo ab occaſu in ortum proprio motu deue-<lb/>hatur, quod quidem iter lineam eclipticam dixerunt, ſeu iter ſolare, vt dictũ <lb/>eſt. </s> <s xml:id="echoid-s10570" xml:space="preserve">Hinc factum eſt, ut omnes uno ore fateantur, Solem ſemper in ecliptica li <lb/>nea moueri, ita ut eius centrũ nunquam ab ea deuiet uel ad ſiniſtram uel ad <lb/>dextram; </s> <s xml:id="echoid-s10571" xml:space="preserve">quoniã nimirũ eius iter conſtans eſt, & </s> <s xml:id="echoid-s10572" xml:space="preserve">ſemper eodem ſe habẽs mo-<lb/>do, quod quidem eclipticã lineam nuncuparunt, propter eclipſes, quæ ſub ip-<lb/>ſa fiunt. </s> <s xml:id="echoid-s10573" xml:space="preserve">Contraria his omnibus in alijs planetis deprehenderunt. </s> <s xml:id="echoid-s10574" xml:space="preserve">Luna enim <lb/>v.</s> <s xml:id="echoid-s10575" xml:space="preserve">g. </s> <s xml:id="echoid-s10576" xml:space="preserve">diuerſis temporibus in eodem Zodiaci gradu exiſtẽs non ſemper in eodẽ <lb/>puncto Horizontis oriri, & </s> <s xml:id="echoid-s10577" xml:space="preserve">occidere conſpicitur, neque umbram meridianã <lb/>eadem longitudine proijcere, neque æqualiter ab Aequatore remoueri, ſed <lb/>nunc magis, ab eo diſtare. </s> <s xml:id="echoid-s10578" xml:space="preserve">Quod idẽ obſeruarũt in reliquis quin-<lb/>que Planetis. </s> <s xml:id="echoid-s10579" xml:space="preserve">Quocirca recte collegerũt, omnes Planetas, uno Sole excepto, <lb/>euagari huc, illucq́, ab ecliptica, & </s> <s xml:id="echoid-s10580" xml:space="preserve">non ſemper eadẽ via eos incedere ab occi-<lb/>dente in orientẽ. </s> <s xml:id="echoid-s10581" xml:space="preserve">Ita enim uidemus Lunam aliquando in principio ♋, exiſtẽ <lb/>tem recedere ab Aequatore grad. </s> <s xml:id="echoid-s10582" xml:space="preserve">fere 28. </s> <s xml:id="echoid-s10583" xml:space="preserve">aliquãdo vero grad. </s> <s xml:id="echoid-s10584" xml:space="preserve">ferme 18. </s> <s xml:id="echoid-s10585" xml:space="preserve">Vnde <lb/>mirum in modum umbram eius meridianam uariari neceſſe eſt. </s> <s xml:id="echoid-s10586" xml:space="preserve">Idemq́; </s> <s xml:id="echoid-s10587" xml:space="preserve">obſer <lb/>uatum eſt in omnibus alijs punctis Zodiaci, non ſolum in Luna, uerum etiam <lb/>in alijs Planetis. </s> <s xml:id="echoid-s10588" xml:space="preserve">Omnes enim ab occaſu in ortum tendunt, non per eclipticã <lb/>ſemper, ſed euagantur nunc in Septentrionem, nunc in Auſtrum, ſeu Meri-<lb/>diem, uarietate mira, conſtanti tamen, & </s> <s xml:id="echoid-s10589" xml:space="preserve">ſingulis peculiari, ac propria. <lb/></s> <s xml:id="echoid-s10590" xml:space="preserve"> <anchor type="note" xlink:label="note-287-02a" xlink:href="note-287-02"/> </s> </p> <div xml:id="echoid-div520" type="float" level="2" n="1"> <note position="right" xlink:label="note-287-01" xlink:href="note-287-01a" xml:space="preserve">Qũo depre <lb/>henſum ſit, <lb/>Solẽ ſemp<unsure/> <lb/>ſub eclip@i-<lb/>ca moueri, <lb/>alios uero <lb/>planetasnõ</note> <note position="right" xlink:label="note-287-02" xlink:href="note-287-02a" xml:space="preserve">Pars Zodia-<lb/>ci borealis, <lb/>& auſtralis <lb/>quæ. Itẽ q̃ <lb/>ſint ſigna <lb/>Borealia, <lb/>uel auſtra-<lb/>lia.</note> </div> <p style="it"> <s xml:id="echoid-s10591" xml:space="preserve">PARS uero Zodiaci, quæ declinat ab Aequinoctiali uerſus Septen-<lb/>trionem, dicitur Septentrionalis, uel Borealis, uel Arctica. </s> <s xml:id="echoid-s10592" xml:space="preserve">Etilla ſex ſi-<lb/>gna, quæ ſunt à principio Arietis uſque ad finem Virginis, dicuntur ſigna <lb/>Septentrionalia, uel Borealia. </s> <s xml:id="echoid-s10593" xml:space="preserve">Alia uero pars Zodiaci, quæ declinat ab <lb/>Aequinoctiali uerſus Meridiem, dicitur Meridionalis, uel Auſtralis, uel <lb/>Antarctica. </s> <s xml:id="echoid-s10594" xml:space="preserve">Et ſex ſigna, quæ ſunt à principio Libræ, uſque in finem Pi-<lb/>ſcium, dicuntur Meridionalia, uel Auſtralia.</s> <s xml:id="echoid-s10595" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div522" type="section" level="1" n="172"> <head xml:id="echoid-head179" xml:space="preserve">COMMENTARIS.</head> <p> <s xml:id="echoid-s10596" xml:space="preserve"><emph style="sc">Qvoniam</emph> in ſexto officio Aequatoris diximus, totũ cœlum ab Aequa ro-<lb/>re dirimi in duo hemiſphæria, quorũ illud, quod ad polũ Arcticũ uergit, Se-<lb/>ptentrionale, Boreale, ſeu Arcticũ dicitur, reliquũ uero ad alterum polũ ſpe- <pb o="252" file="288" n="289" rhead="Comment. in II. Cap Sphæræ"/> ctans, Meridionale, Auſtraleve vocatur: </s> <s xml:id="echoid-s10597" xml:space="preserve">Rurſus vna medietas Zodiaci ab Aequa <lb/>tore in Septentrionale hemiſphærium declinat, altera uero in Meridionale effi <lb/>citur, ut illa medietas dicatur quoque Septentrionalis, hæc vero Meridionalis, <lb/>ſignaq́; </s> <s xml:id="echoid-s10598" xml:space="preserve">in utra que medietate comprehenſa ſortiantur eadem nomina, ut per-<lb/> <anchor type="note" xlink:label="note-288-01a" xlink:href="note-288-01"/> ſpicue hoc loco auctor explicat. </s> <s xml:id="echoid-s10599" xml:space="preserve">Quare cum priora ſex ſigna, nempe Aries, Tau <lb/>rus, Gemini, Cancer; </s> <s xml:id="echoid-s10600" xml:space="preserve">Leo, & </s> <s xml:id="echoid-s10601" xml:space="preserve">Virgo ſint Septentrionalia; </s> <s xml:id="echoid-s10602" xml:space="preserve">Poſteriora autem ſex, <lb/>uidelicet Libra, Sco@pius, Sagittarius, Capricornus, Aquarius, & </s> <s xml:id="echoid-s10603" xml:space="preserve">Piſces, Meri-<lb/>dionalia, fit, ut Planetæ in prioribus ſex decurrentes dicantur Septentriona-<lb/>les; </s> <s xml:id="echoid-s10604" xml:space="preserve">In poſterioribus vero ſex commorantes, Meridionales vocentur.</s> <s xml:id="echoid-s10605" xml:space="preserve"/> </p> <div xml:id="echoid-div522" type="float" level="2" n="1"> <note position="left" xlink:label="note-288-01" xlink:href="note-288-01a" xml:space="preserve">Planetæ qñ <lb/>boreales, & <lb/>quando au <lb/>ſtrales.</note> </div> <note position="left" xml:space="preserve">Prima acce <lb/>ptio ſigni.</note> <p style="it"> <s xml:id="echoid-s10606" xml:space="preserve">CVM autem dicitur, quod in Ariete eſt Sol, uel in alio ſigno, ſcien-<lb/>dum, quòd hæc præpoſitio (in) ſumitur pro (ſub) ſecundum quod nunc ac-<lb/>cipimus ſignum.</s> <s xml:id="echoid-s10607" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div524" type="section" level="1" n="173"> <head xml:id="echoid-head180" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s10608" xml:space="preserve">EXPLICATVRVS, quonam modo Sol, & </s> <s xml:id="echoid-s10609" xml:space="preserve">reliqui Planetæ, immo & </s> <s xml:id="echoid-s10610" xml:space="preserve"><lb/>ſtellæ fixæ, in ſigno aliquo dicãtur eſſe, adducit quatuor acceptiones ſigni, quę <lb/>vſitatæ ſunt apud Aſtronomos. </s> <s xml:id="echoid-s10611" xml:space="preserve">Primo modo dicitur ſignũ duodecima pars ſu-<lb/>perficiei Zodiaci, nẽpe quadrilaterũ habens in <lb/> <anchor type="figure" xlink:label="fig-288-01a" xlink:href="fig-288-01"/> longitudine 30. </s> <s xml:id="echoid-s10612" xml:space="preserve">grad. </s> <s xml:id="echoid-s10613" xml:space="preserve">in latitudine uero 12. </s> <s xml:id="echoid-s10614" xml:space="preserve">gra. <lb/></s> <s xml:id="echoid-s10615" xml:space="preserve">& </s> <s xml:id="echoid-s10616" xml:space="preserve">in hac acceptione locuti hactenus ſumus de <lb/>ſigno. </s> <s xml:id="echoid-s10617" xml:space="preserve">Habet aũt hæc prima acceptio ſigni origi <lb/> <anchor type="note" xlink:label="note-288-03a" xlink:href="note-288-03"/> nem a prima acceptione Zodiaci, in qua ſumi-<lb/>tur Zodiacus pro faſcia illa, ſeu Zona in primo <lb/>mobili continens ſecundum totum ambitum <lb/>grad. </s> <s xml:id="echoid-s10618" xml:space="preserve">360. </s> <s xml:id="echoid-s10619" xml:space="preserve">In latitudine uero 12. </s> <s xml:id="echoid-s10620" xml:space="preserve">grad. </s> <s xml:id="echoid-s10621" xml:space="preserve">Nam ſi zo <lb/>diacus in hac acceptione in 12. </s> <s xml:id="echoid-s10622" xml:space="preserve">partes ſecetur, habebuntur 12. </s> <s xml:id="echoid-s10623" xml:space="preserve">ſigna in prima <lb/> <anchor type="note" xlink:label="note-288-04a" xlink:href="note-288-04"/> acceptione. </s> <s xml:id="echoid-s10624" xml:space="preserve">Et quia hac ratione ſignũ non eſt in orbibus Planetarũ, immo nec <lb/>in ſphæra ſtellarũ fixarũ, ſed in primo duntaxat mobili, docet auctor, cum Aſtro <lb/>nomi dicunt, Solẽ, uél quemuis alium planetã eſſe in tali ſigno, v. </s> <s xml:id="echoid-s10625" xml:space="preserve">g. </s> <s xml:id="echoid-s10626" xml:space="preserve">in Ariete, <lb/>præpo ſitionem [in] ſumi pro [ſub] ut ſit ſenſus, Sol, uel alius Planeta quiuis <lb/>eſt ſub ſigno ♈, ita ut linea recta à centro mundi per centrum Solis, uel alte-<lb/>rius Planetæ eductai eo ſigno, in quo Sol, uel Planeta dicitur eſſe, terminetur.</s> <s xml:id="echoid-s10627" xml:space="preserve"/> </p> <div xml:id="echoid-div524" type="float" level="2" n="1"> <figure xlink:label="fig-288-01" xlink:href="fig-288-01a"> <image file="288-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/288-01"/> </figure> <note position="left" xlink:label="note-288-03" xlink:href="note-288-03a" xml:space="preserve">Prima acce <lb/>ptio Zodia-<lb/>ci.</note> <note position="left" xlink:label="note-288-04" xlink:href="note-288-04a" xml:space="preserve">Qũo intel-<lb/>ligendũ ſit <lb/>Solẽ eſſe in <lb/>quouis ſi-<lb/>gno in pri-<lb/>ma accep. <lb/>tione.</note> </div> <p style="it"> <s xml:id="echoid-s10628" xml:space="preserve">IN alia autem ſignificatione dicitur ſignũ pyramis quadrilatera, cu-<lb/> <anchor type="note" xlink:label="note-288-05a" xlink:href="note-288-05"/> ius baſis illa ſuperficies, quam appellauimus ſi-<lb/> <anchor type="figure" xlink:label="fig-288-02a" xlink:href="fig-288-02"/> gnum, uertex uero eius eſt in centro terræ. </s> <s xml:id="echoid-s10629" xml:space="preserve">Et ſe-<lb/>cundum hoc proprie loquendo poſſumus dicere <lb/>planetas eße in ſignis.</s> <s xml:id="echoid-s10630" xml:space="preserve"/> </p> <div xml:id="echoid-div525" type="float" level="2" n="2"> <note position="left" xlink:label="note-288-05" xlink:href="note-288-05a" xml:space="preserve">Scđa accep <lb/>tio ſigni.</note> <figure xlink:label="fig-288-02" xlink:href="fig-288-02a"> <image file="288-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/288-02"/> </figure> </div> </div> <div xml:id="echoid-div527" type="section" level="1" n="174"> <head xml:id="echoid-head181" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s10631" xml:space="preserve">SECVNDO modo capitur ſignũ pro pyramide <lb/>quadrilatera, cuius baſis eſt ſignũ in prima acceptio <lb/> <anchor type="note" xlink:label="note-288-06a" xlink:href="note-288-06"/> ne, uertex aũt cẽtrũ totius uniuerſi. </s> <s xml:id="echoid-s10632" xml:space="preserve">Ortũ aũt quoq; <lb/></s> <s xml:id="echoid-s10633" xml:space="preserve">habuit hoc ſignum in ſecunda acceptione a ſecunda <lb/>accept one Zodiaci, qñ nimirũ Zodiacus ſumitur a-<lb/>pud Aſtronomos nõ pro illa faſcia, ſuperficieve, ſed <lb/>pro corpore, ſeu ſolido, quod cõtinetur Zodiaco in <lb/>prima acceptione, & </s> <s xml:id="echoid-s10634" xml:space="preserve">duabus ſuperficiebus conicis cõ <pb o="253" file="289" n="290" rhead="Ioan. de Sacro Boſco."/> cauis, qua, um utraq; </s> <s xml:id="echoid-s10635" xml:space="preserve">uerticem habet in mundi centro, baſes autem earundem <lb/>ſunt duo circuli minores æquidiſtantes lineæ elipticæ, recedentesq́; </s> <s xml:id="echoid-s10636" xml:space="preserve">ab eadẽ <lb/>grad. </s> <s xml:id="echoid-s10637" xml:space="preserve">6. </s> <s xml:id="echoid-s10638" xml:space="preserve">Ita enim diuidetur Zodiacus in 12. </s> <s xml:id="echoid-s10639" xml:space="preserve">pyramides quadrilateras, quæ con <lb/> <anchor type="note" xlink:label="note-289-01a" xlink:href="note-289-01"/> ſtituunt 12. </s> <s xml:id="echoid-s10640" xml:space="preserve">ſigna in ſecunda acceptione. </s> <s xml:id="echoid-s10641" xml:space="preserve">Iuxta hanc ſigni acceptionem ait au-<lb/>ctor<unsure/>, proprie dici poſſe, Planetas eſſe in ſignis. </s> <s xml:id="echoid-s10642" xml:space="preserve">Semper enim continebuntur in <lb/>aliqua dictarum 12. </s> <s xml:id="echoid-s10643" xml:space="preserve">pyramidum.</s> <s xml:id="echoid-s10644" xml:space="preserve"/> </p> <div xml:id="echoid-div527" type="float" level="2" n="1"> <note position="left" xlink:label="note-288-06" xlink:href="note-288-06a" xml:space="preserve">Secunda ac <lb/>ceptio Z@. <lb/>dia@.</note> <note position="right" xlink:label="note-289-01" xlink:href="note-289-01a" xml:space="preserve">Sed proprie <lb/>eſt in ſigenis <lb/>in ſecunda <lb/>acceptione.</note> </div> <p style="it"> <s xml:id="echoid-s10645" xml:space="preserve">TERTIO modo dicitur ſignum, vt intelligantur ſex circuli tran-<lb/> <anchor type="note" xlink:label="note-289-02a" xlink:href="note-289-02"/> ſeuntes per polos Zodiaci, & </s> <s xml:id="echoid-s10646" xml:space="preserve">per principia 12. </s> <s xml:id="echoid-s10647" xml:space="preserve">ſignorum. </s> <s xml:id="echoid-s10648" xml:space="preserve">Illi ſex circuli <lb/>diuidunt totam ſuperficiem ſphæræ in 12. </s> <s xml:id="echoid-s10649" xml:space="preserve">partes, latas in medio, arctiores <lb/>vero iuxta polos Zodiaci: </s> <s xml:id="echoid-s10650" xml:space="preserve">& </s> <s xml:id="echoid-s10651" xml:space="preserve">quælibet pars talis dicitur ſignum, & </s> <s xml:id="echoid-s10652" xml:space="preserve">no-<lb/>men habet ſpeciale à nomine illius ſigni, quod intercipitur inter ſuas duas <lb/>lineas. </s> <s xml:id="echoid-s10653" xml:space="preserve">Et ſecundum hanc acceptionem, ſtellæ, quæ ſunt iuxta polos extra <lb/>Zodiacum, dicuntur eſſe in ſignis.</s> <s xml:id="echoid-s10654" xml:space="preserve"/> </p> <div xml:id="echoid-div528" type="float" level="2" n="2"> <note position="right" xlink:label="note-289-02" xlink:href="note-289-02a" xml:space="preserve">Tertia acce <lb/>ptio figni.</note> </div> </div> <div xml:id="echoid-div530" type="section" level="1" n="175"> <head xml:id="echoid-head182" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s10655" xml:space="preserve"><emph style="sc">In tertia</emph> acceptione eſt ſignum quoque ſuperficies quædam, ſicut in <lb/>prima. </s> <s xml:id="echoid-s10656" xml:space="preserve">Si enim deſcribantur ſex circuli maximi in ſphæra per utrumque po-<lb/>lum Zodiaci, & </s> <s xml:id="echoid-s10657" xml:space="preserve">per initia 12. </s> <s xml:id="echoid-s10658" xml:space="preserve">ſignorum in prima acceptione incedentes, ita ut <lb/>primus tranſeat per principum <lb/> <anchor type="figure" xlink:label="fig-289-01a" xlink:href="fig-289-01"/> ♈, & </s> <s xml:id="echoid-s10659" xml:space="preserve">♎: </s> <s xml:id="echoid-s10660" xml:space="preserve">Secundus per initium <lb/>♉, & </s> <s xml:id="echoid-s10661" xml:space="preserve">♏; </s> <s xml:id="echoid-s10662" xml:space="preserve">Tertius per initium <lb/>♊, & </s> <s xml:id="echoid-s10663" xml:space="preserve">♐; </s> <s xml:id="echoid-s10664" xml:space="preserve">Quartus per initium <lb/>♋, & </s> <s xml:id="echoid-s10665" xml:space="preserve">♑: </s> <s xml:id="echoid-s10666" xml:space="preserve">Quintus per princi-<lb/>pium ♌, & </s> <s xml:id="echoid-s10667" xml:space="preserve">♒; </s> <s xml:id="echoid-s10668" xml:space="preserve">Sextus tandem <lb/>per principium, ♍, & </s> <s xml:id="echoid-s10669" xml:space="preserve">♓; </s> <s xml:id="echoid-s10670" xml:space="preserve">di-<lb/>uiditur tota ſuperficies cæli in <lb/>12. </s> <s xml:id="echoid-s10671" xml:space="preserve">partes æquales ab uno po-<lb/>lo Zodiaci, ad alterum, amplio-<lb/>res quidem in medio, ubi eſt Zo <lb/>diacus, anguſtiores uero in fi-<lb/>ne, nempe iuxta polos Zodiaci, <lb/>vbi uidelicet omnes circuli ſex <lb/>prædicti ſe mutuo interſecant. <lb/></s> <s xml:id="echoid-s10672" xml:space="preserve">Quæ quidem partes appellantur <lb/>ſigna intertia acceptione, deno-<lb/>minanturq́. </s> <s xml:id="echoid-s10673" xml:space="preserve">ab illis ſignis primæ <lb/>acceptionis, quæ circulis dictis includuntur, uel quæ in ſignis tertiæ acceptio-<lb/>nis, quæ circulis dictis includuntur, uel quæ in ſignis tertiæ acceptionis repe <lb/>riuntur; </s> <s xml:id="echoid-s10674" xml:space="preserve">ut illa pars, in qua exiſtit ſignum ♈, in prima acceptione, uocatur <lb/> <anchor type="note" xlink:label="note-289-03a" xlink:href="note-289-03"/> ſignum ♈, & </s> <s xml:id="echoid-s10675" xml:space="preserve">ſic de reliquis. </s> <s xml:id="echoid-s10676" xml:space="preserve">Proueniunt etiam hæc ſigna in tertia acceptio-<lb/>ne ex diuiſione Zodiaci in tertia acceptione, quando uidelicet accipitur pro <lb/> <anchor type="note" xlink:label="note-289-04a" xlink:href="note-289-04"/> tota cæli ſuperficie, ſiue conuexa, ſiue concaua. </s> <s xml:id="echoid-s10677" xml:space="preserve">Hoc tertio modo omnes ſtel <lb/>læ, & </s> <s xml:id="echoid-s10678" xml:space="preserve">omnia cœli puncti, etiam iuxta polos Zodiaci, ipſis duntaxat polis Zo-<lb/>diaci exceptis, qui ad omnia ſigna æque bene poſſunt referri, dicnntur eſſe in <lb/>aliquo ſigno, id eſt, ſub aliquo ſigno, ſi punctum cæli nõ eſt in primo mobili.</s> <s xml:id="echoid-s10679" xml:space="preserve"/> </p> <div xml:id="echoid-div530" type="float" level="2" n="1"> <figure xlink:label="fig-289-01" xlink:href="fig-289-01a"> <image file="289-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/289-01"/> </figure> <note position="right" xlink:label="note-289-03" xlink:href="note-289-03a" xml:space="preserve">Tertia acce <lb/>ptio Zodia-<lb/>ci.</note> <note position="right" xlink:label="note-289-04" xlink:href="note-289-04a" xml:space="preserve">Oĩa puncta <lb/>cæli ſunt in <lb/>aliquo ſi-<lb/>gno ĩ terria <lb/>acceptione. <lb/>Quarta ac-<lb/>ceptio ſigni.</note> </div> <p style="it"> <s xml:id="echoid-s10680" xml:space="preserve">IAM intelligatur corpus quoddam, cuius baſis ſit ſignum, ſecun- <pb o="254" file="290" n="291" rhead="Comment in 2. Cap. Sphæræ."/> dum quod nunc ultimo accepimus ſignũ, acumen uero eius ſit ſuper axem <lb/>Zodiaci. </s> <s xml:id="echoid-s10681" xml:space="preserve">Tale igitur corpus in quarta ſignificatione dicitur ſignum, ſe-<lb/>cundum quam acceptionem totus mundus diuiditur in duodecim partes <lb/>æquales, quæ dicuntur ſigna. </s> <s xml:id="echoid-s10682" xml:space="preserve">Et ſic, quidquid eſt in mundo, eſt in aliquo <lb/>ſigno.</s> <s xml:id="echoid-s10683" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div532" type="section" level="1" n="176"> <head xml:id="echoid-head183" xml:space="preserve">COMMENTARIS.</head> <p> <s xml:id="echoid-s10684" xml:space="preserve"><emph style="sc">Qvarto</emph> modo capitur ſignum iterum pro cor <lb/> <anchor type="figure" xlink:label="fig-290-01a" xlink:href="fig-290-01"/> pore quodam, veluti in ſecunda acceptione. </s> <s xml:id="echoid-s10685" xml:space="preserve">Si nam-<lb/>que intelligatur corpus aliquod, cuius baſis ſit ſignũ <lb/>in tertia ſignificatione, latera vero planæ ſuperficies <lb/>duorum ſemicirculorum, quorum circumferentiæ in-<lb/>cludunt idem ſignum, ita vt acumen corporis ſit in <lb/>axe Zodiaci, habebitur ſignum in quarta acceptione. <lb/></s> <s xml:id="echoid-s10686" xml:space="preserve">Nam in quarta acceptione ſumitur Zodiacus pro tota <lb/>ſoliditate mundi: </s> <s xml:id="echoid-s10687" xml:space="preserve">Vnde ſi totus mundus in 12. </s> <s xml:id="echoid-s10688" xml:space="preserve">par-<lb/> <anchor type="note" xlink:label="note-290-01a" xlink:href="note-290-01"/> tes æquales diuidatur circulis, qui per polos Zodiaci, <lb/>& </s> <s xml:id="echoid-s10689" xml:space="preserve">initia ſignorum incedunt, ſeſeq́; </s> <s xml:id="echoid-s10690" xml:space="preserve">mutuo ſecant in <lb/>axe Zodiaci, effecta erunt 12. </s> <s xml:id="echoid-s10691" xml:space="preserve">ſigna in quarta acceptio-<lb/>ne. </s> <s xml:id="echoid-s10692" xml:space="preserve">Quare iuxta hanc ſigni acceptionem nihil erit <lb/>in vniuerſo mundo, quod non in aliquo ſigno dicatur <lb/> <anchor type="note" xlink:label="note-290-02a" xlink:href="note-290-02"/> eſſe: </s> <s xml:id="echoid-s10693" xml:space="preserve">quoniam hæc 12. </s> <s xml:id="echoid-s10694" xml:space="preserve">ſigna totum vniuerſum conſti-<lb/>tuunt, tanquam partes integrantes, vt nulla ſit par-<lb/>ticula, quantumuis minima in mundo, quæ extra aliquod 12. </s> <s xml:id="echoid-s10695" xml:space="preserve">ſignorum præ-<lb/>dictorum reperiatur.</s> <s xml:id="echoid-s10696" xml:space="preserve"/> </p> <div xml:id="echoid-div532" type="float" level="2" n="1"> <figure xlink:label="fig-290-01" xlink:href="fig-290-01a"> <image file="290-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/290-01"/> </figure> <note position="left" xlink:label="note-290-01" xlink:href="note-290-01a" xml:space="preserve">Quarta ac-<lb/>ceptio Zo-<lb/>diaci.</note> <note position="left" xlink:label="note-290-02" xlink:href="note-290-02a" xml:space="preserve">Omnia q̃ <lb/>ſunt in mũ <lb/>do, ſuntin <lb/>aliquo ſi-<lb/>gno ĩ quar-<lb/>ta acceptio-<lb/>ne.</note> </div> <p> <s xml:id="echoid-s10697" xml:space="preserve"><emph style="sc">Astronomi</emph> nonnulli, quatuor acceptionibus ſigni, & </s> <s xml:id="echoid-s10698" xml:space="preserve">Zodiaciadij-<lb/>ciunt alias duas, ita vt quinto modo dicatur Zodiacus ſola linea ecliptica, <lb/> <anchor type="note" xlink:label="note-290-03a" xlink:href="note-290-03"/> quæ quidem eſt, vt dixim@e, circumferentia circuli, quam Sol, motu annuo <lb/>proprio deſcribit ab occaſu in ortum. </s> <s xml:id="echoid-s10699" xml:space="preserve">Vnde ſi hæc circumferentia ecliptica <lb/>in 12. </s> <s xml:id="echoid-s10700" xml:space="preserve">æquales partes ſecetur, efficientur 12. </s> <s xml:id="echoid-s10701" xml:space="preserve">ſigna in quinta acceptione: </s> <s xml:id="echoid-s10702" xml:space="preserve">ita ſi-<lb/>gnum in quinta ſignificatione non ſit aliud, quàm duodecima pars lineæ ecli <lb/>pticæ. </s> <s xml:id="echoid-s10703" xml:space="preserve">Sexto deinde modo accipitur Zodiacus pro ſupeificie plana circulari, <lb/> <anchor type="note" xlink:label="note-290-04a" xlink:href="note-290-04"/> quam concludit circumferentia ecliptica. </s> <s xml:id="echoid-s10704" xml:space="preserve">Quamobrem, ſi à ſignis in quinta <lb/>acceptione ad centrum mundi rectæ lineæ demittantur, diuidetur totus cir-<lb/>culus eclipticus in 12. </s> <s xml:id="echoid-s10705" xml:space="preserve">ſectores inter ſe æquales, qui 12. </s> <s xml:id="echoid-s10706" xml:space="preserve">ſigna in ſexta acceptio <lb/>ne dabunt. </s> <s xml:id="echoid-s10707" xml:space="preserve">Itaque ſignum in ſexta ſignificatione eſt ſector circuli ecliptici, <lb/>qui ſit duodecima pars e@uſdem circuli.</s> <s xml:id="echoid-s10708" xml:space="preserve"/> </p> <div xml:id="echoid-div533" type="float" level="2" n="2"> <note position="left" xlink:label="note-290-03" xlink:href="note-290-03a" xml:space="preserve">Quinta ac-<lb/>ceptip Zo-<lb/>diaci, & ſi-<lb/>gni.</note> <note position="left" xlink:label="note-290-04" xlink:href="note-290-04a" xml:space="preserve">Sexta acce-<lb/>p@io Zodia-<lb/>ci & ſigni.</note> </div> <p> <s xml:id="echoid-s10709" xml:space="preserve"><emph style="sc">Caetervm</emph> tam varia, ac multiplex ſignificatio, ſeu acceptio Zodiaci, <lb/>& </s> <s xml:id="echoid-s10710" xml:space="preserve">ſigni excogitata fuit ab artificibus, vt commode omnia, quæcunque in mun <lb/>do ſunt, aliquo modo in ſigno aliquo eſſe dicerentur. </s> <s xml:id="echoid-s10711" xml:space="preserve">Verumtamen apud <lb/> <anchor type="note" xlink:label="note-290-05a" xlink:href="note-290-05"/> Aſtronomos peritiores ſatis eſt ſignum in quinta acceptione, vt omnia in ali-<lb/>quo ſigno dicantur eſſe. </s> <s xml:id="echoid-s10712" xml:space="preserve">Si enim per polos Zodiaci, & </s> <s xml:id="echoid-s10713" xml:space="preserve">per quoduis aſtrum, <lb/>ſeu punctum in mundo, intelligatur ſuperficies circuli maximi tranſire, dice-<lb/>tur aſtrum illud, ſeu punctum, in eo ſigno eſſe, ad quod peruenit circumferen <lb/>tia d cti circuli in linea ecliptica, vt apertius docebimus, vbi de latitudine <lb/>ſtellarum verba fecerimus in officijs eclipticæ lineæ.</s> <s xml:id="echoid-s10714" xml:space="preserve"/> </p> <div xml:id="echoid-div534" type="float" level="2" n="3"> <note position="left" xlink:label="note-290-05" xlink:href="note-290-05a" xml:space="preserve">Qũo Aſtro-<lb/>nomi dicãt <lb/>omnia eſſe <lb/>in aliquo ſi-<lb/>gno.</note> </div> <pb o="255" file="291" n="292" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div536" type="section" level="1" n="177"> <head xml:id="echoid-head184" xml:space="preserve">OFFICIA ZODIACI, SEV ECLIPTICÆ.</head> <head xml:id="echoid-head185" xml:space="preserve">I.</head> <p> <s xml:id="echoid-s10715" xml:space="preserve"><emph style="sc">Est</emph> regula, & </s> <s xml:id="echoid-s10716" xml:space="preserve">menſura motus ſecundi, qui eſt ab occaſu in ortum, quem-<lb/> <anchor type="note" xlink:label="note-291-01a" xlink:href="note-291-01"/> admodum Aequator eſt menſura primi motus, qui fit ab ortu in occaſum. </s> <s xml:id="echoid-s10717" xml:space="preserve">Si-<lb/>cut enim per Aequinoctialem circulum cognoſcimus, quantus ſit motus ſtel <lb/>larum dicimus, ita quoque per Zodiacum diſcimus, quanto tempore ſtellę fi-<lb/>xę, & </s> <s xml:id="echoid-s10718" xml:space="preserve">planetę, qui ſecundum obliquitatem Zodiaci feruntur, ſuos motus pro-<lb/>prios ab occidente in orientem abſoluant. </s> <s xml:id="echoid-s10719" xml:space="preserve">Item ſicut Aequator eſt maximus <lb/>circulus deſcriptus motu primo, ſiue diurno, eſtq́; </s> <s xml:id="echoid-s10720" xml:space="preserve">cingulus primi motus ip-<lb/>ſum per ęqualia diuidens, æqualiterq́; </s> <s xml:id="echoid-s10721" xml:space="preserve">ſecundum omnes ſui partes a duobus <lb/>mundi polis ſemotus; </s> <s xml:id="echoid-s10722" xml:space="preserve">ſic etiam Zodiacus eſt maximus circulus motu ſccundo <lb/>deſcriptus; </s> <s xml:id="echoid-s10723" xml:space="preserve">e ſtq́; </s> <s xml:id="echoid-s10724" xml:space="preserve">cingulus ſecundimotus dirimens eundem bifariam, ac ęqua-<lb/>liter diſtans a polis Zodiaci ſecundum omnes ſui partes.</s> <s xml:id="echoid-s10725" xml:space="preserve"/> </p> <div xml:id="echoid-div536" type="float" level="2" n="1"> <note position="right" xlink:label="note-291-01" xlink:href="note-291-01a" xml:space="preserve">Ecliptica <lb/>mẽſura eſt <lb/>motus cęli <lb/>ab occaſu <lb/>in oitum.</note> </div> </div> <div xml:id="echoid-div538" type="section" level="1" n="178"> <head xml:id="echoid-head186" xml:space="preserve">II.</head> <p> <s xml:id="echoid-s10726" xml:space="preserve"><emph style="sc">Svb</emph> ecliptica fiunt eclipſes luminarium, Solis videlicet, atque Lunę: </s> <s xml:id="echoid-s10727" xml:space="preserve">ex <lb/> <anchor type="note" xlink:label="note-291-02a" xlink:href="note-291-02"/> quo eſt ecliptica appellata: </s> <s xml:id="echoid-s10728" xml:space="preserve">Adeo ut quotieſcunque Luna in coniunctione <lb/>cum Sole ſub ecliptica, nel certe propè eclipticam extiterit, contingat eclip-<lb/>ſis Solis: </s> <s xml:id="echoid-s10729" xml:space="preserve">In oppoſitione uero cum Sole, @clipſis Lunę.</s> <s xml:id="echoid-s10730" xml:space="preserve"/> </p> <div xml:id="echoid-div538" type="float" level="2" n="1"> <note position="right" xlink:label="note-291-02" xlink:href="note-291-02a" xml:space="preserve">Ecliptica <lb/>cauſa eſt <lb/>eclipſim.</note> </div> </div> <div xml:id="echoid-div540" type="section" level="1" n="179"> <head xml:id="echoid-head187" xml:space="preserve">III.</head> <p> <s xml:id="echoid-s10731" xml:space="preserve"><emph style="sc">Ecliptica</emph> obliquitate ſua eſt cauſainę qualitatis dierum, & </s> <s xml:id="echoid-s10732" xml:space="preserve">noctium, <lb/> <anchor type="note" xlink:label="note-291-03a" xlink:href="note-291-03"/> immo origo omnis viciſsitudinis temporumanni: </s> <s xml:id="echoid-s10733" xml:space="preserve">Vnde etiam cauſa ſecun-<lb/>dum philoſophos exiſtit generationis, atque corruptionis.</s> <s xml:id="echoid-s10734" xml:space="preserve"/> </p> <div xml:id="echoid-div540" type="float" level="2" n="1"> <note position="right" xlink:label="note-291-03" xlink:href="note-291-03a" xml:space="preserve">Ecliptica <lb/>cauſa eſt in <lb/>æqualitatis <lb/>dierũ; & vi <lb/>ciſsitudinis <lb/>temporum. <lb/>Eclip@ica ſe <lb/>cat cęlũ in <lb/>hemiſphę <lb/>rium borea <lb/>le, & auſtra <lb/>le.</note> </div> </div> <div xml:id="echoid-div542" type="section" level="1" n="180"> <head xml:id="echoid-head188" xml:space="preserve">IIII.</head> <p> <s xml:id="echoid-s10735" xml:space="preserve"><emph style="sc">Dirimit</emph> totum cęlum in duo hemiſphęria, quorum illud, quod inter <lb/>eclipticam, & </s> <s xml:id="echoid-s10736" xml:space="preserve">polum eclipticum Boreum interiicitur, Septentrionale; </s> <s xml:id="echoid-s10737" xml:space="preserve">Aliud <lb/>vero inter eclipticam, & </s> <s xml:id="echoid-s10738" xml:space="preserve">polum eclipticę Auſtralem poſitum, Meridionale no <lb/>minatur. </s> <s xml:id="echoid-s10739" xml:space="preserve">Quamuis enim abſolutè pars illa cœli inter polum Arcticũ, & </s> <s xml:id="echoid-s10740" xml:space="preserve">Aequa <lb/>torem collocata, Septenz<unsure/>rionalis dicatur, reliqua vero Auſtralis, vt ſupra in <lb/>expoſitione officiorum Aequatoris diximus: </s> <s xml:id="echoid-s10741" xml:space="preserve">tamen plauit Aſtronomis idem <lb/>cœlum ab ecliptica diuidi in hemiſphęrium Septentrionale, & </s> <s xml:id="echoid-s10742" xml:space="preserve">Meridionale, <lb/>fortaſſis ꝑꝑ motum ſecundum ab occaſu in ortum. </s> <s xml:id="echoid-s10743" xml:space="preserve">Ita namq; </s> <s xml:id="echoid-s10744" xml:space="preserve">fiet, vt quemad-<lb/>modum vna & </s> <s xml:id="echoid-s10745" xml:space="preserve">eadem ſtella mota a primo mobili motu diurno ſemper eodẽ <lb/>modo eſt Septentrionalis, uel Auſtralis, ita vt propter illum motum non ma-<lb/>gis ad Aequatorem accedat, vel ab eodem recedat: </s> <s xml:id="echoid-s10746" xml:space="preserve">Sic etiam eadem ſtella mo <lb/>ta ab occaſu in ortum motu ſecundo ſit hoc poſteriori modo ſemper eadem <lb/>ratione Septentrionalis, Meridionalisve: </s> <s xml:id="echoid-s10747" xml:space="preserve">Neque enim propter iſtum motum <lb/>vicinior vnquam erit eclipticę ſtella quęcunque, vel remotior ab eadem ecli-<lb/>ptica. </s> <s xml:id="echoid-s10748" xml:space="preserve">Hinc factum eſt, vt Aſtronomi aliquando diuidant ſtellas in ſeptentrio-<lb/> <anchor type="note" xlink:label="note-291-04a" xlink:href="note-291-04"/> nales, & </s> <s xml:id="echoid-s10749" xml:space="preserve">Auſtrales, habita ratione Eclipticæ, & </s> <s xml:id="echoid-s10750" xml:space="preserve">nõ Aequatoris, vt perſpicuum <lb/>eſt ex tabula ſtellarum fixarum, quam in primo cap. </s> <s xml:id="echoid-s10751" xml:space="preserve">deſcripſimus. </s> <s xml:id="echoid-s10752" xml:space="preserve">Hinc etiam <lb/>efficitur, vt Planetæ exiſtentes in ſigno ♋, quod eſt maxime Septentrionale, <lb/>& </s> <s xml:id="echoid-s10753" xml:space="preserve">aliis ſignis Septentrionalibus, dicãtur aliquãdo in tabulis Ephemeridũ Me <lb/>ridionales, quia nimirũ deuiant ab ecliptica in meridiem, quamuis ab Aequa <lb/>tore in Boreã declinent: </s> <s xml:id="echoid-s10754" xml:space="preserve">Similiter exiſtentes in ſigno ♑, maxime Auſtrali, nec <lb/>non in aliis ſignis <emph style="sc">A</emph>uſtralibus, denominentur Septentrionales; </s> <s xml:id="echoid-s10755" xml:space="preserve">quoniam vide-<lb/>licet ab Eclipticain Septentrionem excurrunt, licet ab Aequatore deflectant <lb/>in meridiem, vt in Theoricis planetarũ explicatur. </s> <s xml:id="echoid-s10756" xml:space="preserve">Hac rarione Sol nunquam <pb o="256" file="292" n="293" rhead="Comment. in II Cap. Sphæræ."/> dici poterit Septentrionalis, uel Meridionalis, quia uiam eclipticam nunquæ <lb/>deſerit. </s> <s xml:id="echoid-s10757" xml:space="preserve">Idemq; </s> <s xml:id="echoid-s10758" xml:space="preserve">dicendum eſt de ſtellis fixis, & </s> <s xml:id="echoid-s10759" xml:space="preserve">cæteris planetis, qui ſub Ecli-<lb/>ptica ad amuſſim conſt ituti fuerint. <lb/></s> <s xml:id="echoid-s10760" xml:space="preserve"> <anchor type="note" xlink:label="note-292-01a" xlink:href="note-292-01"/> </s> </p> <div xml:id="echoid-div542" type="float" level="2" n="1"> <note position="right" xlink:label="note-291-04" xlink:href="note-291-04a" xml:space="preserve">Qua ratio-<lb/>ne planetæ <lb/>inſignis bo <lb/>realib. exi-<lb/>ſtentes dici <lb/>poſſint au-<lb/>ſtrales, bo-<lb/>reales vero, <lb/>quando in <lb/>ſignis au-<lb/>ſtralib. exi-<lb/>ſtunt.</note> <note position="left" xlink:label="note-292-01" xlink:href="note-292-01a" xml:space="preserve">Verticalis <lb/>circulus ꝓ-<lb/>prie dictus <lb/>ſecat cœ@ũ <lb/>i hemiſ phæ <lb/>riũ berea-<lb/>le, & auſtra <lb/>le.</note> </div> <p> <s xml:id="echoid-s10761" xml:space="preserve"><emph style="sc">Praeter</emph> duos modos prædictos accipitur adhuc aliter apud Aſtrono-<lb/>mos pars Borealis, atq; </s> <s xml:id="echoid-s10762" xml:space="preserve">Meridionalis. </s> <s xml:id="echoid-s10763" xml:space="preserve">Nã circulus Verticalis ꝓprie dictus, qui <lb/>videlicet per uerticẽ capitis, ſeu Zenith cuiuſcunq; </s> <s xml:id="echoid-s10764" xml:space="preserve">loci, & </s> <s xml:id="echoid-s10765" xml:space="preserve">cõmunes ſectio-<lb/>nes Aequatoris, Horizõtisq́; </s> <s xml:id="echoid-s10766" xml:space="preserve">incedit, eſtq; </s> <s xml:id="echoid-s10767" xml:space="preserve">ad Horizontẽ rectus, diuidit quoq; <lb/></s> <s xml:id="echoid-s10768" xml:space="preserve">vniuerſum cælũ in duo hemiſphæria, quorũ illud, quod à dicto Verticalicir-<lb/>culo in Boreã porrigi tur, Septẽtrionale, alterũ aũt, quod ad Meridiem uer-<lb/>git, Meridionale uocatur. </s> <s xml:id="echoid-s10769" xml:space="preserve">Hoc pacto intelligit partẽ Borealẽ, & </s> <s xml:id="echoid-s10770" xml:space="preserve">Meridionali <lb/> <anchor type="note" xlink:label="note-292-02a" xlink:href="note-292-02"/> Ptolemæus in libello de Analemmate, ipſumq́; </s> <s xml:id="echoid-s10771" xml:space="preserve">ſequuntur omnes Aſtronomi <lb/>qui horologiorũ Solariũ deſcriptiones tradunt. </s> <s xml:id="echoid-s10772" xml:space="preserve">Eſt enim hæc tertia acceptio, <lb/>partis Septentrionalis, Meridionalisq́; </s> <s xml:id="echoid-s10773" xml:space="preserve">cõmodiſſima pro horologiorũ deſcri-<lb/>ptionibus. </s> <s xml:id="echoid-s10774" xml:space="preserve">Itaq; </s> <s xml:id="echoid-s10775" xml:space="preserve">tribus circulis, nẽpe Aequatore, Zodiaco, & </s> <s xml:id="echoid-s10776" xml:space="preserve">Verticali ꝓprie <lb/>dicto tripliciter ſphæra ab Aſtronomis diſtribuitur in hemiſphæriũ Boreale, <lb/>& </s> <s xml:id="echoid-s10777" xml:space="preserve">Auſtrale: </s> <s xml:id="echoid-s10778" xml:space="preserve">quod hoc loco cõmonere lectorẽ uolui, ut attente cõſideret, quã-<lb/>do ſcriptores mentionẽ dictarum partium cæli faciunt, in qua ſignificatione <lb/>intelligant hemiſphęriũ Septẽtrionale, Meridionaleve. </s> <s xml:id="echoid-s10779" xml:space="preserve">Ex hac acceptione ef <lb/>ficitur, ut Sol in ſignis Borealibus decurrens iuxta ortum, & </s> <s xml:id="echoid-s10780" xml:space="preserve">occaſum dicatur <lb/> <anchor type="note" xlink:label="note-292-03a" xlink:href="note-292-03"/> Septentrionalis reliquo uero dieitempore ante, & </s> <s xml:id="echoid-s10781" xml:space="preserve">poſt meridiem, Meridio-<lb/>nalis uocetur. </s> <s xml:id="echoid-s10782" xml:space="preserve">Quod quidem intelligendum eſt in habitatione Boreali.</s> <s xml:id="echoid-s10783" xml:space="preserve"/> </p> <div xml:id="echoid-div543" type="float" level="2" n="2"> <note position="left" xlink:label="note-292-02" xlink:href="note-292-02a" xml:space="preserve">Tripliciter <lb/>cœlũ in he <lb/>miſphæriũ <lb/>boreale, & <lb/>auſtrale di-<lb/>uiditur, nẽ-<lb/>pe ab Ae-<lb/>quatore, E-<lb/>cliptica, & <lb/>Verticali.</note> <note position="left" xlink:label="note-292-03" xlink:href="note-292-03a" xml:space="preserve">Sol quo pa <lb/>cto eodem <lb/>die ſit bo-<lb/>realis, & au <lb/>ſtralis.</note> </div> </div> <div xml:id="echoid-div545" type="section" level="1" n="181"> <head xml:id="echoid-head189" xml:space="preserve">V.</head> <p> <s xml:id="echoid-s10784" xml:space="preserve"><emph style="sc">Ecliptica</emph> eſt terminus, à quo computantur latitudines omnium ſtella-<lb/> <anchor type="note" xlink:label="note-292-04a" xlink:href="note-292-04"/> rum, punctorumque cæli, quemadmodum Aequator omnes declinationes <lb/>aſtrorum terminat. </s> <s xml:id="echoid-s10785" xml:space="preserve">In hoc enim differt latitudo ſtellarum ab earundem decli-<lb/>natione, quòd latitudo eſt diſtantia ab Ecliptica, declinatio uero diſtantia ab <lb/>Aequatore: </s> <s xml:id="echoid-s10786" xml:space="preserve">quamuis nonnulli, inter quos etiam eſt auctor noſter, ſine ullo di <lb/>ſcrimine utramq; </s> <s xml:id="echoid-s10787" xml:space="preserve">diſtantiam interdum appellent declinationem, non tñ ſim-<lb/> <anchor type="note" xlink:label="note-292-05a" xlink:href="note-292-05"/> pliciter. </s> <s xml:id="echoid-s10788" xml:space="preserve">Latitudinem enim dicunt declinationẽ ab Ecliptica; </s> <s xml:id="echoid-s10789" xml:space="preserve">Declinationem <lb/>uero proprie dictã, declinationem ab Aequatore. </s> <s xml:id="echoid-s10790" xml:space="preserve">Sed ſatius eſt cũ alijs <emph style="sc">A</emph>ſtro-<lb/>nomis cuilibet harum diſtantiarum propriũ, ac peculiare attribuere nomen. <lb/></s> <s xml:id="echoid-s10791" xml:space="preserve">Vtraque autem diſtantia eſt duplex, ſecundum quod ſtella quæuis recedit ab <lb/>Ecliptica, uel Aequatore in Boream, aut Meridiem. </s> <s xml:id="echoid-s10792" xml:space="preserve">Nam ſi ſtella ab Ecliptica <lb/>ad Boream uergit, dicitur habere latitudinem Septentrionalẽ: </s> <s xml:id="echoid-s10793" xml:space="preserve">Si uero in me-<lb/> <anchor type="note" xlink:label="note-292-06a" xlink:href="note-292-06"/> ridiem deflectit, latitudinem Meridionalem habere pronunciatur. </s> <s xml:id="echoid-s10794" xml:space="preserve">Eadem ra-<lb/>tione ſtella recedens ab Aquatore uerſus Septen trionẽ habet declinationem <lb/>Septentrionalem ſeu Borealem; </s> <s xml:id="echoid-s10795" xml:space="preserve">Recedens autem in Auſtrum, declinationem <lb/>Auſtralem, Meridionalemve obtinet. </s> <s xml:id="echoid-s10796" xml:space="preserve">Latitudinẽ cuiuſcunque ſtellæ metiun-<lb/>tur Aſtronomi circulo maximo, qui per polos Zodiaci & </s> <s xml:id="echoid-s10797" xml:space="preserve">per centrum ſtellæ <lb/>ducitur. </s> <s xml:id="echoid-s10798" xml:space="preserve">Atque hic circulus dici ſolet circulus latitudinis. </s> <s xml:id="echoid-s10799" xml:space="preserve">Vnde ab Aſtrono-<lb/>mis latitudo ſtellæ ita definitur. </s> <s xml:id="echoid-s10800" xml:space="preserve">Latitudo ſtellæ eſt arcus circuli maximi, qui <lb/> <anchor type="note" xlink:label="note-292-07a" xlink:href="note-292-07"/> per Zodiaci polos, & </s> <s xml:id="echoid-s10801" xml:space="preserve">per centtum ſtellæ incedit, interceptus inter Eclipticam <lb/>& </s> <s xml:id="echoid-s10802" xml:space="preserve">uerum locum ſtellę Gradus autem Eclipticæ, per quem circulus latitudinis <lb/>tranſit, dicitur gradus longitudinis ſtellæ. </s> <s xml:id="echoid-s10803" xml:space="preserve">Oſtendit enim, quot gradus interci <lb/>piantur inter ipſum, & </s> <s xml:id="echoid-s10804" xml:space="preserve">principium ♈, à quo longitudo ſtellæ cuiuſuis ſumi <lb/> <anchor type="note" xlink:label="note-292-08a" xlink:href="note-292-08"/> debet, ſecundum ſucceſſio nem ſignorũ procedendo; </s> <s xml:id="echoid-s10805" xml:space="preserve">Vt longitudo ſtellæ non <lb/>ſit aliud, quàm arcus Eclipticæ ab initio ♈, uſque ad circulum latitudinis <lb/>ſtellæ ſecundum ſignorum ſeriem computatus. </s> <s xml:id="echoid-s10806" xml:space="preserve">Declinatio uero ſtellæ cuiuſli <pb o="257" file="293" n="294" rhead="Ioan. de Sacro Boſco."/> bet menſuratur circulo maximo per polos mundi, & </s> <s xml:id="echoid-s10807" xml:space="preserve">per centrum ſtellæ ince-<lb/>dente. </s> <s xml:id="echoid-s10808" xml:space="preserve">Qui quidem circulus appellari ſolet circulus declinationis. </s> <s xml:id="echoid-s10809" xml:space="preserve">Quotirca <lb/> <anchor type="note" xlink:label="note-293-01a" xlink:href="note-293-01"/> ita ab Aſtronomis definiri conſueuit declinatio ſtellæ cuiuſque, vel etiam pun <lb/>cti cuiuſuis eclipticæ. </s> <s xml:id="echoid-s10810" xml:space="preserve">Declinatio ſtellæ, vel gradus eclipticæ, eſt arcus circuli <lb/>maximi per mundi polos, & </s> <s xml:id="echoid-s10811" xml:space="preserve">centrum ſtellæ, ſeu gradum eclipticæ propoſitum <lb/>incedentis, interceptus inter Aequatorem, & </s> <s xml:id="echoid-s10812" xml:space="preserve">ſtellam, ſeu gradum eclipticæ. <lb/></s> <s xml:id="echoid-s10813" xml:space="preserve">Tam autem latitudo, quàm declinatio ad ſummum eſſe poteſt 90. </s> <s xml:id="echoid-s10814" xml:space="preserve">grad. </s> <s xml:id="echoid-s10815" xml:space="preserve">Nul-<lb/>lum enim punctum cœli ab ecliptica, ſiue ab Aequatore magis recedere põt, <lb/>quàm per quadrantem. </s> <s xml:id="echoid-s10816" xml:space="preserve">Vnde fit, vt maximam latitudinem habeant poli Zo-<lb/>diaci; </s> <s xml:id="echoid-s10817" xml:space="preserve">Maximam autem declinationem poli mundi; </s> <s xml:id="echoid-s10818" xml:space="preserve">quandoquidem poli cu-<lb/>inſuis circuli maximi per quadrantem ab eius circumferentia ſeparantur, vt in <lb/>coroll. </s> <s xml:id="echoid-s10819" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s10820" xml:space="preserve">16. </s> <s xml:id="echoid-s10821" xml:space="preserve">lib. </s> <s xml:id="echoid-s10822" xml:space="preserve">1. </s> <s xml:id="echoid-s10823" xml:space="preserve">Theod. </s> <s xml:id="echoid-s10824" xml:space="preserve">demonſtratum eſt à nobis.</s> <s xml:id="echoid-s10825" xml:space="preserve"/> </p> <div xml:id="echoid-div545" type="float" level="2" n="1"> <note position="left" xlink:label="note-292-04" xlink:href="note-292-04a" xml:space="preserve">Ecliptica <lb/>terminus <lb/>eſt, à quo la <lb/>titudines <lb/>aſtrorũ ſu-<lb/>putantur.</note> <note position="left" xlink:label="note-292-05" xlink:href="note-292-05a" xml:space="preserve">Latitudo <lb/>ſtellarum <lb/>ꝗd, & quo <lb/>modo à de <lb/>clinatione <lb/>difſerat.</note> <note position="left" xlink:label="note-292-06" xlink:href="note-292-06a" xml:space="preserve">Latitudo, <lb/>& declina-<lb/>tio ſtellarũ <lb/>borealis, & <lb/>auſtralis, & <lb/>qua ratio-<lb/>ne utraque <lb/>mẽſuretur.</note> <note position="left" xlink:label="note-292-07" xlink:href="note-292-07a" xml:space="preserve">Circulus <lb/>latitudinis</note> <note position="left" xlink:label="note-292-08" xlink:href="note-292-08a" xml:space="preserve">Longitudo <lb/>ſtellæ quid</note> <note position="right" xlink:label="note-293-01" xlink:href="note-293-01a" xml:space="preserve">Circulus de <lb/>clinationis</note> </div> <p> <s xml:id="echoid-s10826" xml:space="preserve">Ex his, quæ de latitudine, atque declinatione ſtellarum diximus, colligi-<lb/> <anchor type="note" xlink:label="note-293-02a" xlink:href="note-293-02"/> tur primum, ſtellas, ſeu planetas nonnunquam habere declinationem, nullam <lb/>autem latitudinem; </s> <s xml:id="echoid-s10827" xml:space="preserve">cuiuſmodi ſunt ſtellæ quæ extra Aequatorem reperiun-<lb/>tur, & </s> <s xml:id="echoid-s10828" xml:space="preserve">ſub ecliptica præcise collocantur, vt eſt Sol omni tempore, duobus <lb/>æquinoctijs exceptis. </s> <s xml:id="echoid-s10829" xml:space="preserve">Deinde, ſtellas nonnunquam habere latitudinem, nul-<lb/>lam vero declinationem, vt ſunt ſtellæ omnes, quæ extra eclipticam poſitæ ſub <lb/>Aequatore directe conſtituuntur. </s> <s xml:id="echoid-s10830" xml:space="preserve">Tertio, ſtellas nonnunquam carere, & </s> <s xml:id="echoid-s10831" xml:space="preserve">lati-<lb/>tudine, & </s> <s xml:id="echoid-s10832" xml:space="preserve">declinatione; </s> <s xml:id="echoid-s10833" xml:space="preserve">qualis eſt Sol tempore æquinoctiorum. </s> <s xml:id="echoid-s10834" xml:space="preserve">Quarto, ſtel-<lb/>las aliquas habere latitudinem Septentrionalem, & </s> <s xml:id="echoid-s10835" xml:space="preserve">declinationem etiam Se-<lb/>ptentrionalem; </s> <s xml:id="echoid-s10836" xml:space="preserve">quales ſunt ſtellæ, quæ & </s> <s xml:id="echoid-s10837" xml:space="preserve">ab Ecliptica, & </s> <s xml:id="echoid-s10838" xml:space="preserve">ab Aequatore in Bo-<lb/>ream deuiant. </s> <s xml:id="echoid-s10839" xml:space="preserve">Quinto, ſtellas aliquas habere@ & </s> <s xml:id="echoid-s10840" xml:space="preserve">latitudinem, & </s> <s xml:id="echoid-s10841" xml:space="preserve">declinatio-<lb/>nem Auſtralem; </s> <s xml:id="echoid-s10842" xml:space="preserve">cuiuſmodi ſunt ſtellæ, quæ tam ab Ecliptica, quàm ab Aequa-<lb/>tore in Auſtrum recedunt. </s> <s xml:id="echoid-s10843" xml:space="preserve">Sexto aliquas ſtellas habere latitudinem Septrio-<lb/>nalem, & </s> <s xml:id="echoid-s10844" xml:space="preserve">declinationem Auſtralem, vt ſunt ſtellæ poſitæ inter Aequatorem, <lb/>& </s> <s xml:id="echoid-s10845" xml:space="preserve">eam Eclipticæ medietatem, quæ ad Auſtrum vergit. </s> <s xml:id="echoid-s10846" xml:space="preserve">Septimo, @ſtellas ali-<lb/>quas habere latitudinem Auſtralem, & </s> <s xml:id="echoid-s10847" xml:space="preserve">declinationem Septentrionalem, cu-<lb/>iuſmodi ſunt ſtellæ inter Aequatorem, & </s> <s xml:id="echoid-s10848" xml:space="preserve">medietatem Zodiaci Borealcm com <lb/>prehenſæ. <lb/></s> <s xml:id="echoid-s10849" xml:space="preserve"> <anchor type="note" xlink:label="note-293-03a" xlink:href="note-293-03"/> </s> </p> <div xml:id="echoid-div546" type="float" level="2" n="2"> <note position="right" xlink:label="note-293-02" xlink:href="note-293-02a" xml:space="preserve">Variæ habl <lb/>tudines ſtel <lb/>larum, quo-<lb/>ad latitudi-<lb/>nẽ, & decli-<lb/>nationem.</note> <note position="right" xlink:label="note-293-03" xlink:href="note-293-03a" xml:space="preserve">Quæ pun-<lb/>cta eclipticę <lb/>æquales hæ <lb/>beant decli <lb/>nationes, <lb/>quæ maio-<lb/>rẽ, vel mi-<lb/>norem.</note> </div> <p> <s xml:id="echoid-s10850" xml:space="preserve"><emph style="sc">Obiter</emph> etiam hic admonendum eſt, ea puncta Eclipticæ, quæ æquè re-<lb/>mouentur à punctis æquinoctialibus, in quibus videlicet Aequator, & </s> <s xml:id="echoid-s10851" xml:space="preserve">Ecli-<lb/>ptica, ſe mutuo interſecant@, æquales habere declinationes: </s> <s xml:id="echoid-s10852" xml:space="preserve">Punctum vero ab <lb/>alterutro æquinoctiali puncto remotius maiorem declinationem habere: </s> <s xml:id="echoid-s10853" xml:space="preserve">Pun <lb/>ctum deniq; </s> <s xml:id="echoid-s10854" xml:space="preserve">remotiſſimum, nempe medium inter æquinoctialia puncta, quale <lb/>eſt prin@ip@um ♋, & </s> <s xml:id="echoid-s10855" xml:space="preserve">♑, declinationem habere maximam. </s> <s xml:id="echoid-s10856" xml:space="preserve">Ex quo eſſicitur, <lb/>in Ecliptica eſſe duo puncta non declinantia, ipſa ſcilicet æquinoctialia: </s> <s xml:id="echoid-s10857" xml:space="preserve">Qua-<lb/>terna vero puncta vbique æqualiter declinare ab Aequatore, bina videlicet Se <lb/>ptentrionali<unsure/>a, ac bina Auſtralia, quoniam ſemper reperiuntur quatuor puncta, <lb/>quæ æqualiter diſtant à duobus punctis æquinoctialibus. </s> <s xml:id="echoid-s10858" xml:space="preserve">Eodem modo puncta <lb/>Eclipticæ, quæ æquales habent declinationes æqualiter diſtabunt à punctis <lb/>æquinoctialibus: </s> <s xml:id="echoid-s10859" xml:space="preserve">Quod vero punctum maiorem habet declinationem, remo-<lb/>tius erit ab æquinoctij puncto: </s> <s xml:id="echoid-s10860" xml:space="preserve">Quod denique maximam declinationem obti <lb/>net, remotiſsimum erit ab æquinoctiali puncto. </s> <s xml:id="echoid-s10861" xml:space="preserve">Hæc autem omnia facile de-<lb/>monſtrari poſſunt ex elementis ſphæricis Theod. </s> <s xml:id="echoid-s10862" xml:space="preserve">& </s> <s xml:id="echoid-s10863" xml:space="preserve">triangulis ſphæricis.</s> <s xml:id="echoid-s10864" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div548" type="section" level="1" n="182"> <head xml:id="echoid-head190" xml:space="preserve">VI.</head> <note position="right" xml:space="preserve">Ecliptiea <lb/>oſtendit ve <lb/>ra loca ſtel.</note> <p> <s xml:id="echoid-s10865" xml:space="preserve"><emph style="sc">Ostendit</emph> Ecliptica ſtellarum, atque planetarum vera loca in Zo-<lb/>diaco, vt non ſit difficile beneficio Eclipticæ noſſe, in quonam ſigno, & </s> <s xml:id="echoid-s10866" xml:space="preserve">gradu <pb o="258" file="294" n="295" rhead="Comment. in II. Cap. Sphæræ"/> ſigni ſtella, aut planeta quiuis exiſtat. </s> <s xml:id="echoid-s10867" xml:space="preserve">In eo enim gradu dicitur eſſe aſtrum <lb/> <anchor type="note" xlink:label="note-294-01a" xlink:href="note-294-01"/> quodcunque, per quẽ tranſit circulus latitudinis aſtri; </s> <s xml:id="echoid-s10868" xml:space="preserve">ita ut ſi trãſeat v.</s> <s xml:id="echoid-s10869" xml:space="preserve">g. </s> <s xml:id="echoid-s10870" xml:space="preserve">per <lb/>10. </s> <s xml:id="echoid-s10871" xml:space="preserve">grad. </s> <s xml:id="echoid-s10872" xml:space="preserve">♌, dicatur eſſe in 10. </s> <s xml:id="echoid-s10873" xml:space="preserve">grad. </s> <s xml:id="echoid-s10874" xml:space="preserve">♌, &</s> <s xml:id="echoid-s10875" xml:space="preserve">c. </s> <s xml:id="echoid-s10876" xml:space="preserve">Ex quo ſequitur, ſtellas illas, quæ in <lb/>eodem latitudinis ſemicirculo inter duos polos Zodiaci interiecto ſunt poſi-<lb/>tę, exiſtere in eodem omnino gradu Zodiaci, licet una ſit maxime Borealis, & </s> <s xml:id="echoid-s10877" xml:space="preserve"><lb/>altera maxime Auſtralis. </s> <s xml:id="echoid-s10878" xml:space="preserve">Solum pclis Zodiaci non poſſunt aſſignari propria lo <lb/>ca in Zodiaco, cum non ſit maior ratio, cur in hoc potius ſigno dicantur exiſte <lb/>re, quàm in illo, ſed æque bene ad omnia poſſint puncta eclipticæ referri.</s> <s xml:id="echoid-s10879" xml:space="preserve"/> </p> <div xml:id="echoid-div548" type="float" level="2" n="1"> <note position="left" xlink:label="note-294-01" xlink:href="note-294-01a" xml:space="preserve">latũ in Zo-<lb/>diaco, & ꝗd <lb/>ſir uerus 10 <lb/>cus ſtellæ <lb/>cuiuſuis in <lb/>Zodiaco.</note> </div> </div> <div xml:id="echoid-div550" type="section" level="1" n="183"> <head xml:id="echoid-head191" xml:space="preserve">VII.</head> <note position="left" xml:space="preserve">Ecliptica in <lb/>dicãr veros <lb/>mo tus ſtel-<lb/>larum.</note> <p> <s xml:id="echoid-s10880" xml:space="preserve"><emph style="sc">Astronomi</emph> officio eclipticæ inueſtigant ueros motus planetarum, <lb/>omniumq́; </s> <s xml:id="echoid-s10881" xml:space="preserve">ſtellarum fixarum. </s> <s xml:id="echoid-s10882" xml:space="preserve">Eſt enim uerus motus aſtri cuiuſcunque, arcus <lb/>eclipticæ ab initio ♈, ad lineam ueri motus ſecundum ſeriem ſignorum nume <lb/> <anchor type="note" xlink:label="note-294-03a" xlink:href="note-294-03"/> ratus, ut in theoricis explicatur. </s> <s xml:id="echoid-s10883" xml:space="preserve">Linea autem ueri motus eſt ea, quæ à centro <lb/>terræ per ſtellæ centrum ad eclipticam educitur: </s> <s xml:id="echoid-s10884" xml:space="preserve">uel certe, ſi aſtrum in eclipti <lb/>canon fuerit, quæ uſque ad circulum latitudinis ſtellæ extenditur.</s> <s xml:id="echoid-s10885" xml:space="preserve"/> </p> <div xml:id="echoid-div550" type="float" level="2" n="1"> <note position="left" xlink:label="note-294-03" xlink:href="note-294-03a" xml:space="preserve">Verus mo-<lb/>tus, & linea <lb/>ueri motus <lb/>quid ſit.</note> </div> </div> <div xml:id="echoid-div552" type="section" level="1" n="184"> <head xml:id="echoid-head192" style="it" xml:space="preserve">DE DVOBVS COLVRIS.</head> <note position="left" xml:space="preserve">Coluri qd<unsure/> <lb/>officiũ ha-<lb/>beãt, & vn-<lb/>de ſic dican <lb/>tur.</note> <p style="it"> <s xml:id="echoid-s10886" xml:space="preserve">SVNT autem alij duo circuli maiores in ſphæra, qui di-<lb/>cuntur Coluri; </s> <s xml:id="echoid-s10887" xml:space="preserve">quorum officium eſt, diſtinguere ſolſtitia, <lb/>& </s> <s xml:id="echoid-s10888" xml:space="preserve">æquinoctia. </s> <s xml:id="echoid-s10889" xml:space="preserve">Dicitur autem Colurus à κῶλον, Græce, <lb/>quod eſt membrum, et {οὖτ} ρος, quod eſt bos ſilueſter. </s> <s xml:id="echoid-s10890" xml:space="preserve">Quia <lb/>quemadmodum cauda bouis ſilueſtris erecta, quę eſt eius <lb/>membrum, facitſemicirculum, & </s> <s xml:id="echoid-s10891" xml:space="preserve">non perfectum: </s> <s xml:id="echoid-s10892" xml:space="preserve">ita Co <lb/>lurus ſemper apparet nobis imperfectus; </s> <s xml:id="echoid-s10893" xml:space="preserve">quoniam ſolum una eius medie-<lb/>tas apparet, alia uero nobis occultatur.</s> <s xml:id="echoid-s10894" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div553" type="section" level="1" n="185"> <head xml:id="echoid-head193" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s10895" xml:space="preserve"><emph style="sc">TErtio</emph> loco poſt Zodiacum agit auctor de duobus Coluris, <lb/>quoniã hi duo circuli ſunt intrinſeci, & </s> <s xml:id="echoid-s10896" xml:space="preserve">mobiles, alij autem duo, <lb/>videlicet Meridianus atque Horizon, extrinſeci, & </s> <s xml:id="echoid-s10897" xml:space="preserve">immobiles: <lb/></s> <s xml:id="echoid-s10898" xml:space="preserve">Item quia duo Coluri per ſe, & </s> <s xml:id="echoid-s10899" xml:space="preserve">abſolute in cœlo ponuntur, alii <lb/>autem duo conſtituuntur in cœlo, habita ratione habitationis in <lb/>terra, & </s> <s xml:id="echoid-s10900" xml:space="preserve">illi duo manent ſemper idem in omni climate, hi uero mutato clima <lb/>te, mutantur quoque neceſſario. </s> <s xml:id="echoid-s10901" xml:space="preserve">Sunt autẽ duo Coluri circuli maximi in ſphæ <lb/> <anchor type="note" xlink:label="note-294-05a" xlink:href="note-294-05"/> ra, qui per polos mundi, & </s> <s xml:id="echoid-s10902" xml:space="preserve">per quatuor puncta cardinalia Zodiaci ducuntur <lb/>ſeſe mutuo ad angulos rectos ſphęrales interſecantes in ipſi polis, & </s> <s xml:id="echoid-s10903" xml:space="preserve">unà cum <lb/>ſphæra circumuoluuntur. </s> <s xml:id="echoid-s10904" xml:space="preserve">Horum officium ait eſſe, ut diſtinguant ſolſtitia, & </s> <s xml:id="echoid-s10905" xml:space="preserve"><lb/>æquinoctia, hoc eſt, ut indicent, quibus in punctis eclipticę ſolſtitia, & </s> <s xml:id="echoid-s10906" xml:space="preserve">æqui-<lb/>noctia, contingant, ut mox dicetur.</s> <s xml:id="echoid-s10907" xml:space="preserve"/> </p> <div xml:id="echoid-div553" type="float" level="2" n="1"> <note position="left" xlink:label="note-294-05" xlink:href="note-294-05a" xml:space="preserve">Coluri qui <lb/>ſint.</note> </div> <p> <s xml:id="echoid-s10908" xml:space="preserve"><emph style="sc">Addvcit</emph> deinde etymologiam huius nominis, cur uidelicethi duo <lb/>circuli dicantur Coluri, quæ ridicula prorſus exiſtit, & </s> <s xml:id="echoid-s10909" xml:space="preserve">nullius momenti. </s> <s xml:id="echoid-s10910" xml:space="preserve">Pro-<lb/> <anchor type="note" xlink:label="note-294-06a" xlink:href="note-294-06"/> pria enim, ac uera etymologia eſt, ut hi circuli dicãtur Coluri a uocabulo græ <lb/>co κόλ{ου}ρος, quod figuificani mutilum, & </s> <s xml:id="echoid-s10911" xml:space="preserve">imperfectum. </s> <s xml:id="echoid-s10912" xml:space="preserve">Apparent enim hi circu <lb/>li habitantibus in ſphæra obliqua ſemper mutili, imperfectiq́;</s> <s xml:id="echoid-s10913" xml:space="preserve">; ita ut nec ſimul <pb o="259" file="295" n="296" rhead="Ioan. de Sacro Boſco."/> vno tempore, nec ſucceſſiue diuerſis temporibus, omnes illorum partes conſpi <lb/>ci poſſint. </s> <s xml:id="echoid-s10914" xml:space="preserve">Etenim arcus ipſorum oppoſiti utrinque iuxta mundi polos in ſphę <lb/>ra obliqua quacunque ita ſeſe habent, ut ij quidem, qui iuxta polum eleua-<lb/>tum ſupra Horizontem exiſtunt, perpetuo oculis obijciantur, neque unquam <lb/>è conſpectu amoueantur, ſubducanturve: </s> <s xml:id="echoid-s10915" xml:space="preserve">ij uero, qui his opponuntur prope <lb/>polum ſub Horizonte depreſſum, nunquam producantur in conſpectum, ſed <lb/>perpetuo deliteſcant; </s> <s xml:id="echoid-s10916" xml:space="preserve">adeo ut quò obliquior fuerit ſphæra, eo etiam maiores <lb/>exiſtant arcus horum circulorum perpetuo apparentes, perpetuoque latentes: <lb/></s> <s xml:id="echoid-s10917" xml:space="preserve">cum tamen omnes alij circuli mobiles in cælo ita ſint comparati, ut aut ſem-<lb/>per totos, & </s> <s xml:id="echoid-s10918" xml:space="preserve">integros ſupra Horizontem videamus, ut ſunt circuli minores iux <lb/>ta polum conſpicuum; </s> <s xml:id="echoid-s10919" xml:space="preserve">aut penitus nunquam eos intueri liceat, cuiuſmodi ſunt <lb/>circuli minores prope polum occultum oppoſiti prioribus, qui ſemper ſupra <lb/>Horizontem attolluntur; </s> <s xml:id="echoid-s10920" xml:space="preserve">aut certe totos ſucceſſiue ſpacio 24. </s> <s xml:id="echoid-s10921" xml:space="preserve">horarum intuea <lb/>mur, ut ſunt Zodiacus, Aequator, &</s> <s xml:id="echoid-s10922" xml:space="preserve">c. </s> <s xml:id="echoid-s10923" xml:space="preserve">Hi enim circuli quamuis uno, eodemq́ue <lb/>tempore integri non compareant, tamen intra diem, ac noctem toti ſupra Ho-<lb/>rizontem emergunt.</s> <s xml:id="echoid-s10924" xml:space="preserve"/> </p> <div xml:id="echoid-div554" type="float" level="2" n="2"> <note position="left" xlink:label="note-294-06" xlink:href="note-294-06a" xml:space="preserve">@tymolo-<lb/>gia ueia <lb/>Colurorũ.</note> </div> <p> <s xml:id="echoid-s10925" xml:space="preserve">Ex his perſpicuum eſt, omnes circulos maximos mobiles, qui per polos <lb/>mundi incedunt, appellari poſſe Coluros, id eſt, mutilos, ac imperfectos, quia <lb/>nunquam omnes eorum partes ſupra Horizontem in ſphæra quacunque obli-<lb/>qua aſcendunt: </s> <s xml:id="echoid-s10926" xml:space="preserve">Veruntamen hoc nomen tanquam proprium ſi bi uendicarunt <lb/>duo circuli, qui per quatu or puncta Zodiaci cardinalia ducuntur, ſeſeque ad <lb/>angulos rectos in polis mundi diuidunt, ita ut ſolum hi dicantur peculiari no <lb/> <anchor type="note" xlink:label="note-295-01a" xlink:href="note-295-01"/> mine Coluri. </s> <s xml:id="echoid-s10927" xml:space="preserve">Manifeſtum etiam ex dictis relinquitur, in ſphæra recta nullos <lb/>circulos mobiles dici poſſe Coluros, quoniam cum nullum ſit punctum cœli, <lb/>quod non ſupra Horizontem aſcendat motu primi mobilis, nullus erit quoq, <lb/>circulus, qui non totus ſucceſſiue ſpacio 24. </s> <s xml:id="echoid-s10928" xml:space="preserve">horarum ſupra Horizontem con-<lb/>ſpiciatur. </s> <s xml:id="echoid-s10929" xml:space="preserve">Vnde ſi ij, qui in ſphæra recta degunt, nomina circulis cœleſtibus <lb/>impoſuiſſent, nullos Coluros uocaſſent. <lb/></s> <s xml:id="echoid-s10930" xml:space="preserve"> <anchor type="note" xlink:label="note-295-02a" xlink:href="note-295-02"/> </s> </p> <div xml:id="echoid-div555" type="float" level="2" n="3"> <note position="right" xlink:label="note-295-01" xlink:href="note-295-01a" xml:space="preserve">Nulli eireu <lb/>li in ſphæra <lb/>recta dici <lb/>poſſunt C@ <lb/>luri.</note> <note position="right" xlink:label="note-295-02" xlink:href="note-295-02a" xml:space="preserve">Colurus ſol <lb/>ſtitiorum.</note> </div> <p style="it"> <s xml:id="echoid-s10931" xml:space="preserve">COLVRVS igitur diſtinguens Solſtitia tranſit per polos mundi, & </s> <s xml:id="echoid-s10932" xml:space="preserve"><lb/>per polos Zodiaci, & </s> <s xml:id="echoid-s10933" xml:space="preserve">maximas Solis declinationes, hoc eſt, per primos gra-<lb/>dus Cancri, & </s> <s xml:id="echoid-s10934" xml:space="preserve">Capricorni. </s> <s xml:id="echoid-s10935" xml:space="preserve">Vnde primus punctus Cancri, ubi Colurus <lb/>iſte interſecat Zodiacum, dicitur punctus Solſtitij Aeſtiualis; </s> <s xml:id="echoid-s10936" xml:space="preserve">quia quando <lb/>Sol eſt in eo, eſt Solſtitium Aeſtiuale, & </s> <s xml:id="echoid-s10937" xml:space="preserve">non poteſt Sol magis accedere <lb/> <anchor type="note" xlink:label="note-295-03a" xlink:href="note-295-03"/> ad Zenith capitis noſtri. </s> <s xml:id="echoid-s10938" xml:space="preserve">Eſt autem Zenith punctus in firmamento directe <lb/>ſuprapoſitus capitibus noſtris. </s> <s xml:id="echoid-s10939" xml:space="preserve">Arcus uero Coluri, qui intercipitur inter <lb/> <anchor type="note" xlink:label="note-295-04a" xlink:href="note-295-04"/> punctum Solſtitij Aeſtiualis, & </s> <s xml:id="echoid-s10940" xml:space="preserve">Aequinoct alem, appellatur maxima So-<lb/>lis declinatio. </s> <s xml:id="echoid-s10941" xml:space="preserve">Et eſt ſecundum Ptolemęum uiginti trium graduum, & </s> <s xml:id="echoid-s10942" xml:space="preserve"><lb/>unius, & </s> <s xml:id="echoid-s10943" xml:space="preserve">quinquaginta minutorum: </s> <s xml:id="echoid-s10944" xml:space="preserve">Secundum Almeonem uero, uiginti <lb/>trium graduum, & </s> <s xml:id="echoid-s10945" xml:space="preserve">triginta trium minutorum.</s> <s xml:id="echoid-s10946" xml:space="preserve"/> </p> <div xml:id="echoid-div556" type="float" level="2" n="4"> <note position="right" xlink:label="note-295-03" xlink:href="note-295-03a" xml:space="preserve">Zenith ca-<lb/>pitis quid.</note> <note position="right" xlink:label="note-295-04" xlink:href="note-295-04a" xml:space="preserve">Maxima <lb/>Solis decli-<lb/>natio quid.</note> </div> <p> <s xml:id="echoid-s10947" xml:space="preserve">SIMILITER primus punctus Capricorni, ubiidem Colurus ex <lb/>alia parte interſecat Zodiacum, dicitur punctus Solſtitij hyemalis: </s> <s xml:id="echoid-s10948" xml:space="preserve">Et ar-<lb/>cus Coluri interceptus inter punctum illum & </s> <s xml:id="echoid-s10949" xml:space="preserve">Aequinoctialem; </s> <s xml:id="echoid-s10950" xml:space="preserve">dicitur <lb/>alia maxima Solis declinatio, & </s> <s xml:id="echoid-s10951" xml:space="preserve">eſt æqualis priori.</s> <s xml:id="echoid-s10952" xml:space="preserve"/> </p> <pb o="260" file="296" n="297" rhead="Comment. in II. Cap. Sphæræ"/> </div> <div xml:id="echoid-div558" type="section" level="1" n="186"> <head xml:id="echoid-head194" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s10953" xml:space="preserve"><emph style="sc">Diximvs</emph> ſupra duos eſſe Coluros, alterum ſolſtitio rum, æquinoctio-<lb/>rum alterum, quod & </s> <s xml:id="echoid-s10954" xml:space="preserve">auctor inſinuauit, dum dixit officium horum circulorũ <lb/>eſſe, diſtinguere ſolſtitia, & </s> <s xml:id="echoid-s10955" xml:space="preserve">æquinoctia: </s> <s xml:id="echoid-s10956" xml:space="preserve">Ideo utrum que iam ſeorſum explicat, <lb/>incipiens à Coluro ſolſtitiorum. </s> <s xml:id="echoid-s10957" xml:space="preserve">Ait igitur, eum Colurũ diſtinguere ſolſtitia, <lb/>hoc eſt, appellari Colurum ſolſtitiorum, qui & </s> <s xml:id="echoid-s10958" xml:space="preserve">per polos mundi, & </s> <s xml:id="echoid-s10959" xml:space="preserve">per polos <lb/>Zodiaci, nec non per maximas Solis declinationes deſcribitur. </s> <s xml:id="echoid-s10960" xml:space="preserve">Vbi declarat, <lb/> <anchor type="note" xlink:label="note-296-01a" xlink:href="note-296-01"/> principia ♋, & </s> <s xml:id="echoid-s10961" xml:space="preserve">♑, eſſe puncta ſolſtitialia, illud quidem, punctum ſolſtitij æſti-<lb/>ui, hoc uero ſolſtitij hyberni: </s> <s xml:id="echoid-s10962" xml:space="preserve">quoniam Sol exiſtens in primo puncto ♋, facit <lb/>ſolſtitium æftiuum, & </s> <s xml:id="echoid-s10963" xml:space="preserve">non poteſt magis ad Zenith, hoc eſt, ad punctum cœli ca <lb/>piti noſtro ſuprapoſitum, accedere; </s> <s xml:id="echoid-s10964" xml:space="preserve">Exiſtens autem in principio ♑, efficit ſol-<lb/>ſtitium hyemale, & </s> <s xml:id="echoid-s10965" xml:space="preserve">non poteſt magis à nobis recedere. </s> <s xml:id="echoid-s10966" xml:space="preserve">Item duos arcus Colu-<lb/>ri ſolſtitiorum, qui inter dicta puncta ſolſtitialia, & </s> <s xml:id="echoid-s10967" xml:space="preserve">Aequatorem interijciun-<lb/>tur, appellari maximas Solis declinationes, quæ æquales ſunt inter ſe, ut infe-<lb/>rius demonſtrabimus. </s> <s xml:id="echoid-s10968" xml:space="preserve">Verum de hac maxima Solis declinatione, & </s> <s xml:id="echoid-s10969" xml:space="preserve">ſolſtitio <lb/>plura dicemus in officijs horum circulorum.</s> <s xml:id="echoid-s10970" xml:space="preserve"/> </p> <div xml:id="echoid-div558" type="float" level="2" n="1"> <note position="left" xlink:label="note-296-01" xlink:href="note-296-01a" xml:space="preserve">Punctũ ſol-<lb/>ſtitiũ æſtiui <lb/>& hyemalis <lb/>quod.</note> </div> <p style="it"> <s xml:id="echoid-s10971" xml:space="preserve">ALTER quidem Colurus tranſit per polos mundi, & </s> <s xml:id="echoid-s10972" xml:space="preserve">per prima <lb/> <anchor type="note" xlink:label="note-296-02a" xlink:href="note-296-02"/> puncta Arietis, & </s> <s xml:id="echoid-s10973" xml:space="preserve">Libræ, ubi ſunt duo Aequinoctia; </s> <s xml:id="echoid-s10974" xml:space="preserve">Vnde appellatur Co-<lb/>lurus diſtinguens Aequinoctia. </s> <s xml:id="echoid-s10975" xml:space="preserve">Iſti autem duo Coluri interſecant ſeſe ſu-<lb/>per polos mundi ad angulos rectos ſphærales. </s> <s xml:id="echoid-s10976" xml:space="preserve">Signa quidem Solſtitiorum, <lb/>& </s> <s xml:id="echoid-s10977" xml:space="preserve">Aequinoctiorum patent his uerſibus.</s> <s xml:id="echoid-s10978" xml:space="preserve"/> </p> <div xml:id="echoid-div559" type="float" level="2" n="2"> <note position="left" xlink:label="note-296-02" xlink:href="note-296-02a" xml:space="preserve">Colurns æ-<lb/>quinoctio-<lb/>rum,</note> </div> <p> <s xml:id="echoid-s10979" xml:space="preserve">Hæc duo ſolſtitiorum faciunt Cancer, Capricornus; <lb/></s> <s xml:id="echoid-s10980" xml:space="preserve">Sed noctes æquant Aries, & </s> <s xml:id="echoid-s10981" xml:space="preserve">Libra diebus.</s> <s xml:id="echoid-s10982" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div561" type="section" level="1" n="187"> <head xml:id="echoid-head195" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s10983" xml:space="preserve"><emph style="sc">Docet</emph> alterum Colurum, qui per polos mundi, & </s> <s xml:id="echoid-s10984" xml:space="preserve">per initia ♈, & </s> <s xml:id="echoid-s10985" xml:space="preserve"><lb/>♎, tranſit, vocari Colurum æquinoctiorum, ſeu diſtinguentem æquinoctia; <lb/></s> <s xml:id="echoid-s10986" xml:space="preserve">quia Solin dictis punctis exiſtens, efficit diem æqualem nocti. </s> <s xml:id="echoid-s10987" xml:space="preserve">Atque hi duo <lb/>Coluri, inquit, ſe mutuo interſecant in polis mundi ad angulos rectos ſphæ-<lb/>rales. </s> <s xml:id="echoid-s10988" xml:space="preserve">Eſt autem angulus ſphæralis ille, qui efficitur in ſuperficie conuexa ſphę <lb/>ræ ex ſectione circunferẽtiarum duorum circulorum maximorum: </s> <s xml:id="echoid-s10989" xml:space="preserve">Vnde ſi cir-<lb/> <anchor type="note" xlink:label="note-296-03a" xlink:href="note-296-03"/> culus circulum ita ſecet, ut efficiantur utrobique duo anguli æquales, appel-<lb/>labitur uter que angulus rectus ſphæralis; </s> <s xml:id="echoid-s10990" xml:space="preserve">Si uero efficiuntur anguli inæqua-<lb/>les, maior dicetur obtuſus ſphæralis, minor autem acutus. </s> <s xml:id="echoid-s10991" xml:space="preserve">Quod autem Co-<lb/>luri ſeſe mutuo in polis ad angulos rectos interſecent, perſpicuum eſt ex pro-<lb/>poſ. </s> <s xml:id="echoid-s10992" xml:space="preserve">15. </s> <s xml:id="echoid-s10993" xml:space="preserve">lib. </s> <s xml:id="echoid-s10994" xml:space="preserve">1. </s> <s xml:id="echoid-s10995" xml:space="preserve">Theod. </s> <s xml:id="echoid-s10996" xml:space="preserve">& </s> <s xml:id="echoid-s10997" xml:space="preserve">ex proprietate 5. </s> <s xml:id="echoid-s10998" xml:space="preserve">circulorum ſphæræ ſupra allata; </s> <s xml:id="echoid-s10999" xml:space="preserve">cum <lb/>vterque per polos alterius tranſeat. </s> <s xml:id="echoid-s11000" xml:space="preserve">Sunt enim principia ♈, & </s> <s xml:id="echoid-s11001" xml:space="preserve">♎, in quibus <lb/>nimirum Colurus æquinoctiorum, & </s> <s xml:id="echoid-s11002" xml:space="preserve">æquator ſecant ſe mutuo, poli Colur@ <lb/>ſolſtitiorum; </s> <s xml:id="echoid-s11003" xml:space="preserve">Puncta uero, in quibus Colurus ſolſtitiorum, & </s> <s xml:id="echoid-s11004" xml:space="preserve">Aequator ſe m@ <lb/>tuo ſecant, poli Coluri æquinoctiorum, ut conſtat ex definitione poli.</s> <s xml:id="echoid-s11005" xml:space="preserve"/> </p> <div xml:id="echoid-div561" type="float" level="2" n="1"> <note position="left" xlink:label="note-296-03" xlink:href="note-296-03a" xml:space="preserve">Angnlus <lb/>ſphæralis <lb/>q@id.</note> </div> <pb o="261" file="297" n="298" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div563" type="section" level="1" n="188"> <head xml:id="echoid-head196" xml:space="preserve">OFFICIA VTRIVSQVE COLVRI.</head> <head xml:id="echoid-head197" xml:space="preserve">I.</head> <p> <s xml:id="echoid-s11006" xml:space="preserve"><emph style="sc">Demonstrant</emph> duo Coluri quatuor puncta principalia in Zodia-<lb/>co, quæ Cardinalia dicuntur, & </s> <s xml:id="echoid-s11007" xml:space="preserve">in quibus ex motu Solis maximæ temporum <lb/> <anchor type="note" xlink:label="note-297-01a" xlink:href="note-297-01"/> mutationes fieri ſolent, ut Ver, Æffas, Autumnus, & </s> <s xml:id="echoid-s11008" xml:space="preserve">Hyems, qualia ſunt prin-<lb/>cipia ♈, ♋, ♎, & </s> <s xml:id="echoid-s11009" xml:space="preserve">♑. </s> <s xml:id="echoid-s11010" xml:space="preserve">Vnde & </s> <s xml:id="echoid-s11011" xml:space="preserve">totus Zodiacus ab eiſdem Coluris in dictis <lb/>quatuor punctis ſecabitur in quatuor Quadrantes correſpondentes quatuor <lb/>illis anni temporibus; </s> <s xml:id="echoid-s11012" xml:space="preserve">Immo & </s> <s xml:id="echoid-s11013" xml:space="preserve">Aequator ab eiſdem in quatuor Quadrantes <lb/>diſtribuetur, quorum maximus eſt uſus, ut conſtabit ex 3. </s> <s xml:id="echoid-s11014" xml:space="preserve">cap. </s> <s xml:id="echoid-s11015" xml:space="preserve">in ortu & </s> <s xml:id="echoid-s11016" xml:space="preserve">occa-<lb/>ſu ſignorum cognoſcendo. </s> <s xml:id="echoid-s11017" xml:space="preserve">Eadem ratione iidem Coluri omnes circulos pa-<lb/>rallelos, ſeu æquidiſtantes Aequatori in quatuor Quadrantes diriment, ut fa-<lb/>cile demonſtrari poteſt ex ſphæricis elementis Theodoſii.</s> <s xml:id="echoid-s11018" xml:space="preserve"/> </p> <div xml:id="echoid-div563" type="float" level="2" n="1"> <note position="right" xlink:label="note-297-01" xlink:href="note-297-01a" xml:space="preserve">DuoColut@ <lb/>indicãtqua <lb/>tuor pũctæ <lb/>Cardinalia <lb/>diuiduntq́; <lb/>Zodiacum, <lb/>Aequatorẽ <lb/>& omnes <lb/>parallelos <lb/>in quatuor <lb/>quadrãtes.</note> </div> </div> <div xml:id="echoid-div565" type="section" level="1" n="189"> <head xml:id="echoid-head198" xml:space="preserve">II.</head> <p> <s xml:id="echoid-s11019" xml:space="preserve"><emph style="sc">Colvrvs</emph> Solſtitiorum, qui nimirum & </s> <s xml:id="echoid-s11020" xml:space="preserve">Aequatorem, eiusq́ue paralle-<lb/>los omnes, & </s> <s xml:id="echoid-s11021" xml:space="preserve">Zodiacum, ſiue Eclipticam, ad rectos angulos ſecat, per propoſ. <lb/></s> <s xml:id="echoid-s11022" xml:space="preserve">15. </s> <s xml:id="echoid-s11023" xml:space="preserve">lib. </s> <s xml:id="echoid-s11024" xml:space="preserve">1. </s> <s xml:id="echoid-s11025" xml:space="preserve">Theod. </s> <s xml:id="echoid-s11026" xml:space="preserve">cum per horum circulorum polos incedat, oſtendit duo pun-<lb/> <anchor type="note" xlink:label="note-297-02a" xlink:href="note-297-02"/> cta ſolſtitialia, nẽpe prima puncta ♋, & </s> <s xml:id="echoid-s11027" xml:space="preserve">♑, quæ non idcirco ſolſtitialia dicun <lb/>tur, quòd Sol ad ea delatus inſiſtat, & </s> <s xml:id="echoid-s11028" xml:space="preserve">commoretur aliquand u: </s> <s xml:id="echoid-s11029" xml:space="preserve">Hoc enim fal-<lb/>ſum eſt, cum nunquam in Zodiaco conquieſcat, aut curſum ſuum intermittar, <lb/>ut experientia quotidiana teſtatur, ſed quòd, cum, Sole exiſtente prope illa <lb/>puncta, aliquot diebus, nec umbræ meridianæ uarientur, ſed eiuſdem ſint lon <lb/>gitudinis, quoad ſenſum, nec diurna, nocturnaq́; </s> <s xml:id="echoid-s11030" xml:space="preserve">ſpacra notabiliter augeantur, <lb/>uel diminuantur, conſiſtere Sol quodammodo uideatur in dictis punctis. </s> <s xml:id="echoid-s11031" xml:space="preserve">Vel <lb/>etiam, quia cum ea Sol attigerit, nõ prouehitur ulterius, ſed inhibet curſum, <lb/>ſeſeq́; </s> <s xml:id="echoid-s11032" xml:space="preserve">rurſus ad oppoſitum mundi polum conuertit, ita ut in dictis pũctis Sol, <lb/>quantum ad acceſſum, & </s> <s xml:id="echoid-s11033" xml:space="preserve">receſſum ab uno polo ad alterum, ſtare quodammo <lb/>do uideatur, cum ſeſe ad oppoſitam cęli partem conuertat. </s> <s xml:id="echoid-s11034" xml:space="preserve">Vnde ab hac con-<lb/> <anchor type="note" xlink:label="note-297-03a" xlink:href="note-297-03"/> uerſione Solis à Gręcis dicuntur eadem puncta {τρ}οπικὰ. </s> <s xml:id="echoid-s11035" xml:space="preserve">Itaq; </s> <s xml:id="echoid-s11036" xml:space="preserve">ſolſtitium nihil <lb/>erit aliud, quàm finis receſſus Solis ab Æquatore, & </s> <s xml:id="echoid-s11037" xml:space="preserve">principiũ acceſſus ad eun-<lb/>dem. </s> <s xml:id="echoid-s11038" xml:space="preserve">Eſt autem duplex ſolſtitium, æſtiuum videlicet, quod fit Sole exiſtente in <lb/>principio ♋, ſi de hemiſphærio Boreali loquamur, quando nimirũ eſt æſtas, <lb/>& </s> <s xml:id="echoid-s11039" xml:space="preserve">hyemale, quod contingit, Sole commorante in principio ♑, quando uideli-<lb/>cet hyems imminet. </s> <s xml:id="echoid-s11040" xml:space="preserve">In illo Sol uiciniſſimus noſtro uertici capitis exiſtit: </s> <s xml:id="echoid-s11041" xml:space="preserve">in <lb/> <anchor type="note" xlink:label="note-297-04a" xlink:href="note-297-04"/> iſto uero ab eodem remotiſſimus. </s> <s xml:id="echoid-s11042" xml:space="preserve">Item illud abſolute, atque ſimpliciter non-<lb/>nulli Solſtitium dicunt, hoc uero Brumam. </s> <s xml:id="echoid-s11043" xml:space="preserve">Ita appellauit quoque Ouidius <lb/>ſolſtitium hyemale lib. </s> <s xml:id="echoid-s11044" xml:space="preserve">1. </s> <s xml:id="echoid-s11045" xml:space="preserve">de Faſt. </s> <s xml:id="echoid-s11046" xml:space="preserve">cum dixit.</s> <s xml:id="echoid-s11047" xml:space="preserve"/> </p> <div xml:id="echoid-div565" type="float" level="2" n="1"> <note position="right" xlink:label="note-297-02" xlink:href="note-297-02a" xml:space="preserve">Prima pun-<lb/>cta Cancri, <lb/>& Capricor <lb/>ni, cur ſolſti <lb/>tialia dican <lb/>tur.</note> <note position="right" xlink:label="note-297-03" xlink:href="note-297-03a" xml:space="preserve">Primũ pun <lb/>ctũ Cancri, <lb/>& Capricor <lb/>ni cur dicã <lb/>tur etiam <lb/>tropica.</note> <note position="right" xlink:label="note-297-04" xlink:href="note-297-04a" xml:space="preserve">Solſtitium <lb/>quid.</note> </div> <p style="it"> <s xml:id="echoid-s11048" xml:space="preserve">Bruma noui prima eſt, ueteriſ q́ue nouiſſima Solis: <lb/></s> <s xml:id="echoid-s11049" xml:space="preserve">Principium capiunt Phæbus, & </s> <s xml:id="echoid-s11050" xml:space="preserve">annus idem. </s> <s xml:id="echoid-s11051" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-297-05a" xlink:href="note-297-05"/> </s> </p> <div xml:id="echoid-div566" type="float" level="2" n="2"> <note position="right" xlink:label="note-297-05" xlink:href="note-297-05a" xml:space="preserve">Colurus ſol <lb/>ſtitiorũ ſe-<lb/>cat eclipti-<lb/>cã in ſemi-<lb/>circulum <lb/>aſcendentẽ <lb/>& ſemieir-<lb/>culum de-<lb/>ſcendentẽ.</note> </div> </div> <div xml:id="echoid-div568" type="section" level="1" n="190"> <head xml:id="echoid-head199" xml:space="preserve">III.</head> <p> <s xml:id="echoid-s11052" xml:space="preserve"><emph style="sc">Idem</emph> Colurus ſolſtitiorum partitur Zodiacum, ſiue Eclipticam in dues <lb/>ſemicirculos, quorum ille, qui à principio ♑, per ♈, uſque ad finem ♊, porri <lb/>gitur, Aſcendens: </s> <s xml:id="echoid-s11053" xml:space="preserve">alter uero à principio ♋, per ♎, uſquein finem ♐, Deſcen <lb/>dens uocatur, ſi rationem nimirum habeamus habitationis Borealis, ut ſupra <lb/>cum de ordine ſignorum differemus, explicauimus.</s> <s xml:id="echoid-s11054" xml:space="preserve"/> </p> <pb o="262" file="298" n="299" rhead="Comment. in II. Cap. Sphæræ"/> </div> <div xml:id="echoid-div569" type="section" level="1" n="191"> <head xml:id="echoid-head200" xml:space="preserve">IIII.</head> <p> <s xml:id="echoid-s11055" xml:space="preserve"><emph style="sc">Circvlvs</emph> idem diſtinguit duodecim ſigna Zodiaci in duas claſſes: </s> <s xml:id="echoid-s11056" xml:space="preserve">In <lb/> <anchor type="note" xlink:label="note-298-01a" xlink:href="note-298-01"/> prima claſſe continentur ſex ſigna, nempe ♋, ♌, ♍, ♎, ♏, ♐: </s> <s xml:id="echoid-s11057" xml:space="preserve">quæ rectè <lb/>oriuntur in ſphæra obliqua Boreali: </s> <s xml:id="echoid-s11058" xml:space="preserve">In ſecunda claſſe comprehenduntur <lb/>ſigna reliqua ſex, vt, ♑, ♒, ♓, ♈, ♉, ♊, quæ oblique oriuntur, vt in 3. </s> <s xml:id="echoid-s11059" xml:space="preserve">cap. <lb/></s> <s xml:id="echoid-s11060" xml:space="preserve">exponemus.</s> <s xml:id="echoid-s11061" xml:space="preserve"/> </p> <div xml:id="echoid-div569" type="float" level="2" n="1"> <note position="left" xlink:label="note-298-01" xlink:href="note-298-01a" xml:space="preserve">Colurus ſol <lb/>ſtitiorũ di-<lb/>uidit Zo-<lb/>diacum in <lb/>ſex ſigna re <lb/>cte orien-<lb/>tia in ſphæ <lb/>ra obliqua, <lb/>& in ſex ſi-<lb/>gna obli-<lb/>qua orien <lb/>tia.</note> </div> <p> <s xml:id="echoid-s11062" xml:space="preserve"><emph style="sc">Adhvc</emph> circulus hic diſtinguens Solſtitia metitur maximas declinatio-<lb/>nes Solis. </s> <s xml:id="echoid-s11063" xml:space="preserve">Quando enim Sol ad hunc circulum proprio motu ab occaſu in <lb/>ortum peruenit, ſiue ex parte Boreali, vbi eſt principium ♋, ſiue ex parte Au-<lb/>ſtrali, vbi eſt principium ♑, maxime ab Aequatore declinat: </s> <s xml:id="echoid-s11064" xml:space="preserve">Vnde in præfatis <lb/>punctis maximam dicitur habere declinationem, quoniã vltra ea non amplius <lb/> <anchor type="note" xlink:label="note-298-02a" xlink:href="note-298-02"/> excurrit in Boream, Meridiemvè, ſed reuertitur ad Aequatorem: </s> <s xml:id="echoid-s11065" xml:space="preserve">Quam qui-<lb/>dem maximam declinationem determinat Colurus Solſtitiorum: </s> <s xml:id="echoid-s11066" xml:space="preserve">Etenim tan-<lb/>ta eſt maxima Solis declinatio, quantus eſt arcus Coluri Solſtitiorum interce <lb/>ptus inter Aequatorem, & </s> <s xml:id="echoid-s11067" xml:space="preserve">punctum vtriuſlibet Solſtitij.</s> <s xml:id="echoid-s11068" xml:space="preserve"/> </p> <div xml:id="echoid-div570" type="float" level="2" n="2"> <note position="left" xlink:label="note-298-02" xlink:href="note-298-02a" xml:space="preserve">Circulus ſol <lb/>ſtitiorũ me <lb/>titur maxi-<lb/>mas Solis <lb/>declinatio-<lb/>nes.</note> </div> <p> <s xml:id="echoid-s11069" xml:space="preserve"><emph style="sc">Haec</emph> autem maxima declinatio Solis varia reperta fuit ab Aſtronomis <lb/>in temporibus diuerſis, propter motum trepidationis octauæ ſphęræ, quo om <lb/>nes inferiores ſphęræ mouentur, vt dictum eſt in prime cap. <lb/></s> <s xml:id="echoid-s11070" xml:space="preserve"> <anchor type="note" xlink:label="note-298-03a" xlink:href="note-298-03"/> </s> </p> <div xml:id="echoid-div571" type="float" level="2" n="3"> <note position="left" xlink:label="note-298-03" xlink:href="note-298-03a" xml:space="preserve">Variæ ob-<lb/>ſeruationes <lb/>maximę de <lb/>clinationis <lb/>Solis, & <lb/>quã tenen <lb/>dam eſſe <lb/>putemus.</note> </div> <p> <s xml:id="echoid-s11071" xml:space="preserve"><emph style="sc">Nam</emph> Ptolemęus deprehendit maximam Solis declinationem compre-<lb/>hendere gradus 23. </s> <s xml:id="echoid-s11072" xml:space="preserve">min. </s> <s xml:id="echoid-s11073" xml:space="preserve">51. </s> <s xml:id="echoid-s11074" xml:space="preserve">Sec. </s> <s xml:id="echoid-s11075" xml:space="preserve">20. </s> <s xml:id="echoid-s11076" xml:space="preserve">qualem fere auctor noſter aſſeruit ex ſen-<lb/>tentia Ptolemæ@.</s> <s xml:id="echoid-s11077" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11078" xml:space="preserve"><emph style="sc">Mahometes</emph> Aratenſis inuenit eandem grad. </s> <s xml:id="echoid-s11079" xml:space="preserve">23. </s> <s xml:id="echoid-s11080" xml:space="preserve">min. </s> <s xml:id="echoid-s11081" xml:space="preserve">35.</s> <s xml:id="echoid-s11082" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11083" xml:space="preserve"><emph style="sc">Arzael</emph> Hiſpanus eam obſeruauit eſſe grad. </s> <s xml:id="echoid-s11084" xml:space="preserve">23. </s> <s xml:id="echoid-s11085" xml:space="preserve">min. </s> <s xml:id="echoid-s11086" xml:space="preserve">34.</s> <s xml:id="echoid-s11087" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11088" xml:space="preserve"><emph style="sc">Almeon</emph> reperiteandem eſſe grad. </s> <s xml:id="echoid-s11089" xml:space="preserve">23. </s> <s xml:id="echoid-s11090" xml:space="preserve">min. </s> <s xml:id="echoid-s11091" xml:space="preserve">33. </s> <s xml:id="echoid-s11092" xml:space="preserve">vt retulit auctor.</s> <s xml:id="echoid-s11093" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11094" xml:space="preserve"><emph style="sc">Prophativs</emph> Iudæus numerauit eam grad. </s> <s xml:id="echoid-s11095" xml:space="preserve">23. </s> <s xml:id="echoid-s11096" xml:space="preserve">min. </s> <s xml:id="echoid-s11097" xml:space="preserve">32.</s> <s xml:id="echoid-s11098" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11099" xml:space="preserve"><emph style="sc">Ioannes</emph> Regiom. </s> <s xml:id="echoid-s11100" xml:space="preserve">aſſeruit eam eſſe grad. </s> <s xml:id="echoid-s11101" xml:space="preserve">23. </s> <s xml:id="echoid-s11102" xml:space="preserve">min. </s> <s xml:id="echoid-s11103" xml:space="preserve">30.</s> <s xml:id="echoid-s11104" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11105" xml:space="preserve"><emph style="sc">Dominicvs</emph> Maria Italus inquit, eandem habere grad. </s> <s xml:id="echoid-s11106" xml:space="preserve">23. </s> <s xml:id="echoid-s11107" xml:space="preserve">min. </s> <s xml:id="echoid-s11108" xml:space="preserve">29.</s> <s xml:id="echoid-s11109" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11110" xml:space="preserve"><emph style="sc">Ioannes</emph> Vvernerus Norimbergenſis eidem tribuit grad. </s> <s xml:id="echoid-s11111" xml:space="preserve">23. </s> <s xml:id="echoid-s11112" xml:space="preserve">min. </s> <s xml:id="echoid-s11113" xml:space="preserve">28. <lb/></s> <s xml:id="echoid-s11114" xml:space="preserve">ſecun. </s> <s xml:id="echoid-s11115" xml:space="preserve">30.</s> <s xml:id="echoid-s11116" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11117" xml:space="preserve"><emph style="sc">Nicolavs</emph> Copernicus eandem pronunciauit grad. </s> <s xml:id="echoid-s11118" xml:space="preserve">23. </s> <s xml:id="echoid-s11119" xml:space="preserve">min. </s> <s xml:id="echoid-s11120" xml:space="preserve">28. </s> <s xml:id="echoid-s11121" xml:space="preserve">ſe-<lb/>cun. </s> <s xml:id="echoid-s11122" xml:space="preserve">20.</s> <s xml:id="echoid-s11123" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11124" xml:space="preserve"><emph style="sc">Demonstravit</emph> autem Copernicus, hanc maximam Solis Decli-<lb/>nationem regulari motu decreuiſſe, & </s> <s xml:id="echoid-s11125" xml:space="preserve">decreturam eſſe vſque ad 23. </s> <s xml:id="echoid-s11126" xml:space="preserve">grad. </s> <s xml:id="echoid-s11127" xml:space="preserve">& </s> <s xml:id="echoid-s11128" xml:space="preserve"><lb/>28. </s> <s xml:id="echoid-s11129" xml:space="preserve">min. </s> <s xml:id="echoid-s11130" xml:space="preserve">non amplius: </s> <s xml:id="echoid-s11131" xml:space="preserve">Poſtea rurſus eandem accreturam vſque ad grad. </s> <s xml:id="echoid-s11132" xml:space="preserve">23. </s> <s xml:id="echoid-s11133" xml:space="preserve">min. <lb/></s> <s xml:id="echoid-s11134" xml:space="preserve">52. </s> <s xml:id="echoid-s11135" xml:space="preserve">Ita vt maxima hæc ſit, minima vero illa; </s> <s xml:id="echoid-s11136" xml:space="preserve">Differentiaq́; </s> <s xml:id="echoid-s11137" xml:space="preserve">inter maximam & </s> <s xml:id="echoid-s11138" xml:space="preserve"><lb/>minimam complectatur 24. </s> <s xml:id="echoid-s11139" xml:space="preserve">min.</s> <s xml:id="echoid-s11140" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11141" xml:space="preserve"><emph style="sc">Inter</emph> omnes autem prædictas maximas Solis declinationes communis <lb/>ſchola Aſtronomorum retinet eam, quam Ioannes Regiom. </s> <s xml:id="echoid-s11142" xml:space="preserve">ſummus Aſtrono-<lb/>mus obſeruauit, nimirum grad. </s> <s xml:id="echoid-s11143" xml:space="preserve">23. </s> <s xml:id="echoid-s11144" xml:space="preserve">min. </s> <s xml:id="echoid-s11145" xml:space="preserve">30. </s> <s xml:id="echoid-s11146" xml:space="preserve">Quamuis admodum probabile ſit, <lb/>eam fortaſſis eſſe tantum grad. </s> <s xml:id="echoid-s11147" xml:space="preserve">23. </s> <s xml:id="echoid-s11148" xml:space="preserve">min. </s> <s xml:id="echoid-s11149" xml:space="preserve">28. </s> <s xml:id="echoid-s11150" xml:space="preserve">paulo amplius, qualem poſuit Co-<lb/>pernicus. </s> <s xml:id="echoid-s11151" xml:space="preserve">Veruntamen ne à communi ſententia recedere videamur, eandem <lb/>in ſequentibus aſſumens grad. </s> <s xml:id="echoid-s11152" xml:space="preserve">23. </s> <s xml:id="echoid-s11153" xml:space="preserve">min. </s> <s xml:id="echoid-s11154" xml:space="preserve">30. </s> <s xml:id="echoid-s11155" xml:space="preserve">ob eam vel præcipue cauſam quod <lb/>2. </s> <s xml:id="echoid-s11156" xml:space="preserve">min non inducant notabilem differentiam, & </s> <s xml:id="echoid-s11157" xml:space="preserve">quod 30. </s> <s xml:id="echoid-s11158" xml:space="preserve">min. </s> <s xml:id="echoid-s11159" xml:space="preserve">ſint dimidiata <lb/>pars vnius gradus.</s> <s xml:id="echoid-s11160" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11161" xml:space="preserve"><emph style="sc">Modvs</emph>, quo Aſtronomi maximam Solis declinationem obſeruant, inter <lb/> <anchor type="note" xlink:label="note-298-04a" xlink:href="note-298-04"/> alios hic eſt pręcipuus. </s> <s xml:id="echoid-s11162" xml:space="preserve">Obſeruetur circa ſolſtitium æſtiuum, nempe circa diem <lb/>22. </s> <s xml:id="echoid-s11163" xml:space="preserve">Iunij hoc tempore, Solis altitudo Meridiana ſumma diligentia, donec <lb/>ea maxima deprehendatur; </s> <s xml:id="echoid-s11164" xml:space="preserve">In ea enim habet Sol maximam declinationem in <pb o="263" file="299" n="300" rhead="Ioan. de Sacro Boſco."/> æſtate: </s> <s xml:id="echoid-s11165" xml:space="preserve">Deinde idem fiat circa Solſtitium brumale, donec altitudo Solis Meri-<lb/>diana minima inueniatur; </s> <s xml:id="echoid-s11166" xml:space="preserve">in ea enim Sol maxime declinat ab Aequatore in Au <lb/>ſtrum. </s> <s xml:id="echoid-s11167" xml:space="preserve">Si igitur minimam hanc altitudinem meridianam ex maxima illa detra <lb/>hamus, & </s> <s xml:id="echoid-s11168" xml:space="preserve">reliquos gradus bifariam diuiſerimus, habebimus maximã Solis de-<lb/>clinationem ex utraq; </s> <s xml:id="echoid-s11169" xml:space="preserve">parte Aequatoris, quoniam maxima declinatio Borea-<lb/>lis, æqualis eſt maximę Auſtrali, ut mox demõſtrabimus, quod & </s> <s xml:id="echoid-s11170" xml:space="preserve">auctor dixit. <lb/></s> <s xml:id="echoid-s11171" xml:space="preserve">EXEMPLVM. </s> <s xml:id="echoid-s11172" xml:space="preserve">10. </s> <s xml:id="echoid-s11173" xml:space="preserve">Regiomon. </s> <s xml:id="echoid-s11174" xml:space="preserve">Viennæ dep@ehendit circa Solſtitium æſti-<lb/>uum maximam Solis altitudinem meridianam grad. </s> <s xml:id="echoid-s11175" xml:space="preserve">65. </s> <s xml:id="echoid-s11176" xml:space="preserve">min. </s> <s xml:id="echoid-s11177" xml:space="preserve">30. </s> <s xml:id="echoid-s11178" xml:space="preserve">Circa ſolſtitiũ <lb/>vero brumale minimam Solis altitudinem meridianam offendit grad. </s> <s xml:id="echoid-s11179" xml:space="preserve">18. </s> <s xml:id="echoid-s11180" xml:space="preserve">min. </s> <s xml:id="echoid-s11181" xml:space="preserve"><lb/>30. </s> <s xml:id="echoid-s11182" xml:space="preserve">qua ablata à priori, remanent grad. </s> <s xml:id="echoid-s11183" xml:space="preserve">47. </s> <s xml:id="echoid-s11184" xml:space="preserve">quorum medietas dabit maximam <lb/>Solis declinationem gra. </s> <s xml:id="echoid-s11185" xml:space="preserve">23. </s> <s xml:id="echoid-s11186" xml:space="preserve">min. </s> <s xml:id="echoid-s11187" xml:space="preserve">30 Porrò vtriq; </s> <s xml:id="echoid-s11188" xml:space="preserve">altitudini meridianæ, & </s> <s xml:id="echoid-s11189" xml:space="preserve">ma-<lb/>ximæ & </s> <s xml:id="echoid-s11190" xml:space="preserve">minimæ captandæ aptiſſimum erit inſtrumentum. </s> <s xml:id="echoid-s11191" xml:space="preserve">Quadrans eximiæ <lb/>magnitudinis, ut in eo etiam minuta graduum deſignari queant, in quo linea <lb/>fiducię circumuoluatur circa eius centrũ. </s> <s xml:id="echoid-s11192" xml:space="preserve">Si. </s> <s xml:id="echoid-s11193" xml:space="preserve">n. </s> <s xml:id="echoid-s11194" xml:space="preserve">hic quadrans in plano, quod Ho <lb/>rizonti ęquidiſtet, ita ſtatuatur, ut rectus illi plano inſiſtat, & </s> <s xml:id="echoid-s11195" xml:space="preserve">unum latus eius <lb/>directe lineæ meridianæ reſpondeat, centrumq́; </s> <s xml:id="echoid-s11196" xml:space="preserve">eiuſdem Boreã reſpiciat, facil <lb/>limo negotio dictæ altitudines meridianæ reperientur. </s> <s xml:id="echoid-s11197" xml:space="preserve">Conſtur ctionem huius <lb/>quadrãtis inuenies apud Orontium Delphinatem in ſphæra, quã conſcripſit.</s> <s xml:id="echoid-s11198" xml:space="preserve"/> </p> <div xml:id="echoid-div572" type="float" level="2" n="4"> <note position="left" xlink:label="note-298-04" xlink:href="note-298-04a" xml:space="preserve">Qua ratio-<lb/>ne maxima <lb/>Solis decli-<lb/>natio inue-<lb/>ſtigãda ſit.</note> </div> <p> <s xml:id="echoid-s11199" xml:space="preserve"><emph style="sc">Cognita</emph> maxima Solis declinatione, veniemus per doctrinam ſinuum in <lb/>notitiam declinationum omnium punctorum eclipticæ. </s> <s xml:id="echoid-s11200" xml:space="preserve">Quoniam enim, ut à <lb/>nobis demonſtratum eſt in coroll. </s> <s xml:id="echoid-s11201" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s11202" xml:space="preserve">1. </s> <s xml:id="echoid-s11203" xml:space="preserve">lib. </s> <s xml:id="echoid-s11204" xml:space="preserve">1. </s> <s xml:id="echoid-s11205" xml:space="preserve">noſtræ Gnomonices, & </s> <s xml:id="echoid-s11206" xml:space="preserve">alibi. <lb/></s> <s xml:id="echoid-s11207" xml:space="preserve"> <anchor type="note" xlink:label="note-299-01a" xlink:href="note-299-01"/> Item à Ioan. </s> <s xml:id="echoid-s11208" xml:space="preserve">Regiom. </s> <s xml:id="echoid-s11209" xml:space="preserve">in Epit. </s> <s xml:id="echoid-s11210" xml:space="preserve">Almag. </s> <s xml:id="echoid-s11211" xml:space="preserve">lib. </s> <s xml:id="echoid-s11212" xml:space="preserve">1. </s> <s xml:id="echoid-s11213" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s11214" xml:space="preserve">18. </s> <s xml:id="echoid-s11215" xml:space="preserve">Item à Gebro Hiſpalenſi <lb/>lib. </s> <s xml:id="echoid-s11216" xml:space="preserve">2. </s> <s xml:id="echoid-s11217" xml:space="preserve">& </s> <s xml:id="echoid-s11218" xml:space="preserve">à Petro Nonio Luſitano propoſ. </s> <s xml:id="echoid-s11219" xml:space="preserve">2. </s> <s xml:id="echoid-s11220" xml:space="preserve">ſecundæ partis de crepuſculis; </s> <s xml:id="echoid-s11221" xml:space="preserve">Sicut <lb/>ſe habet ſinus totus ad ſinum maximæ declinationis, ita ſe habet, ſinus arcus, <lb/>quo diſtat punctum eclipticæ datum ab alterutro punctorum æquinoctialium <lb/>ad ſiaum declinationis eiuſdem puncti: </s> <s xml:id="echoid-s11222" xml:space="preserve">ſi iuxta regulam proportionum, mul-<lb/>tiplicetur ſinus maximæ declinationis in ſinum arcus, quo datũ punctum ecli-<lb/>pticæ ab alterutro punctorum æquinoctialium remouetur, nempe à viciniori, <lb/>& </s> <s xml:id="echoid-s11223" xml:space="preserve">numerus productus per ſinum totum diuidatur (quod fiet, reijciendo à pro-<lb/>ducto numero quinque figuras ad manum dextram; </s> <s xml:id="echoid-s11224" xml:space="preserve">ſumimus enim nunc ſinũ <lb/>totum eſſe particularum 100000.) </s> <s xml:id="echoid-s11225" xml:space="preserve">proueniet ſinus, cuius arcus inuentus ex ta-<lb/>bula ſinuum offeret illico declinationem puncti propoſiti. </s> <s xml:id="echoid-s11226" xml:space="preserve">EXEMPLVM. <lb/></s> <s xml:id="echoid-s11227" xml:space="preserve">Poſita declinatione maxima Solis grad. </s> <s xml:id="echoid-s11228" xml:space="preserve">23. </s> <s xml:id="echoid-s11229" xml:space="preserve">min. </s> <s xml:id="echoid-s11230" xml:space="preserve">30. </s> <s xml:id="echoid-s11231" xml:space="preserve">libet perueſtigare declina-<lb/>tionem octaui grad. </s> <s xml:id="echoid-s11232" xml:space="preserve">♍, qui quidem recedit ab æquinoctio autumnali grad. </s> <s xml:id="echoid-s11233" xml:space="preserve">22. </s> <s xml:id="echoid-s11234" xml:space="preserve"><lb/>Multiplico igitur ſinum maximæ declinationis poſitæ, nempe 39874. </s> <s xml:id="echoid-s11235" xml:space="preserve">in ſinum <lb/>diſtantiæ propoſitæ, hoc eſt, grad. </s> <s xml:id="echoid-s11236" xml:space="preserve">22. </s> <s xml:id="echoid-s11237" xml:space="preserve">uidelicet in 37460. </s> <s xml:id="echoid-s11238" xml:space="preserve">produceturq́; </s> <s xml:id="echoid-s11239" xml:space="preserve">nume-<lb/>rus 1493680040. </s> <s xml:id="echoid-s11240" xml:space="preserve">a quo reiectis quinque ſiguris ex parte dextra, remanebit ſi-<lb/>nus 14936. </s> <s xml:id="echoid-s11241" xml:space="preserve">cui in tabula ſinuum reſpondet arcus grad. </s> <s xml:id="echoid-s11242" xml:space="preserve">8. </s> <s xml:id="echoid-s11243" xml:space="preserve">min. </s> <s xml:id="echoid-s11244" xml:space="preserve">35. </s> <s xml:id="echoid-s11245" xml:space="preserve">Tantam igitur <lb/>dicemus eſſe declinationem octaui gradus ♍. </s> <s xml:id="echoid-s11246" xml:space="preserve">Et ſic de cæteris.</s> <s xml:id="echoid-s11247" xml:space="preserve"/> </p> <div xml:id="echoid-div573" type="float" level="2" n="5"> <note position="right" xlink:label="note-299-01" xlink:href="note-299-01a" xml:space="preserve">Qua arte <lb/>declinatio-<lb/>nes puncto <lb/>rum eclipti-<lb/>cę ſuppurem <lb/>tur.</note> </div> <p> <s xml:id="echoid-s11248" xml:space="preserve"><emph style="sc">Hac</emph> arte ſupputauimus ſequentem tabulam, in quo continentur decli-<lb/>nationes omnium graduum Zodiaci, unà cùm duodecimis partibus graduum: <lb/></s> <s xml:id="echoid-s11249" xml:space="preserve">ita ut rabula per quinta minuta graduum ſit extenſa. </s> <s xml:id="echoid-s11250" xml:space="preserve">Quoniam uero, ut ſupra <lb/>diximus, in Zodiaco ſemper reperiuntur quaterna puncta, quæ habent ęquales <lb/>declinationes, ſatis erit, ſi computentur declinationes omnium graduum, & </s> <s xml:id="echoid-s11251" xml:space="preserve"><lb/>minutorum unius quadrantis. </s> <s xml:id="echoid-s11252" xml:space="preserve">Nam puncta aliorum trium Quadrantum facile <lb/>huius Quadrantis partibus accommodabuntur, ut in ſphæra materiali uidere <lb/>licet, & </s> <s xml:id="echoid-s11253" xml:space="preserve">perſpicuum eſſe poteſt in ſubſequenti tabula.</s> <s xml:id="echoid-s11254" xml:space="preserve"/> </p> <pb o="264" file="300" n="301" rhead="Comment in II. Cap. Sphæræ"/> <note position="right" xml:space="preserve"> <lb/>########## DECLIN ATIONES PVNCTORVM. \\ Eclipticæ ab Aequatore. <lb/>## Signa # ♈ # ♎ # ♉ # ♏ # ♊ # ♐ # ## Signa <lb/>G # M # G # M # G # M # G # M # G # M <lb/>0 # 0 # 0 # 0 # 11 # 30 # 20 # 12 # 30 # 0 <lb/>0 # 5 # 0 # 2 # 11 # 32 # 20 # 13 # 29 # 55 <lb/>0 # 10 # 0 # 3 # 11 # 34 # 20 # 14 # 29 # 50 <lb/>0 # 15 # 0 # 6 # 11 # 35 # 20 # 15 # 29 # 45 <lb/>0 # 20 # 0 # 8 # 11 # 37 # 20 # 16 # 29 # 40 <lb/>0 # 25 # 0 # 10 # 11 # 39 # 20 # 17 # 29 # 35 <lb/>0 # 30 # 0 # 12 # 11 # 41 # 20 # 18 # 29 # 30 <lb/>0 # 35 # 0 # 14 # 11 # 42 # 20 # 19 # 29 # 25 <lb/>0 # 40 # 0 # 16 # 11 # 44 # 20 # 20 # 29 # 20 <lb/>0 # 45 # 0 # 18 # 11 # 46 # 20 # 22 # 29 # 15 <lb/>0 # 50 # 0 # 20 # 11 # 48 # 20 # 23 # 29 # 10 <lb/>0 # 55 # 0 # 22 # 11 # 49 # 20 # 24 # 29 # 5 <lb/>1 # 0 # 0 # 24 # 11 # 51 # 20 # 25 # 29 # 0 <lb/>1 # 5 # 0 # 26 # 11 # 53 # 20 # 26 # 29 # 55 <lb/>1 # 10 # 0 # 28 # 11 # 55 # 20 # 27 # 28 # 50 <lb/>1 # 15 # 0 # 30 # 11 # 56 # 20 # 28 # 28 # 45 <lb/>1 # 20 # 0 # 32 # 11 # 58 # 20 # 29 # 8 # 40 <lb/>1 # 25 # 0 # 34 # 12 # 0 # 20 # 30 # 28 # 35 <lb/>1 # 30 # 0 # 36 # 12 # 1 # 20 # 31 # 28 # 30 <lb/>1 # 35 # 0 # 38 # 12 # 3 # 20 # 32 # 28 # 25 <lb/>1 # 40 # 0 # 40 # 12 # 5 # 20 # 33 # 28 # 20 <lb/>1 # 45 # 0 # 42 # 12 # 7 # 20 # 34 # 28 # 15 <lb/>1 # 50 # 0 # 44 # 12 # 8 # 20 # 35 # 28 # 10 <lb/>1 # 55 # 0 # 46 # 12 # 10 # 20 # 30 # 28 # 5 <lb/>2 # 0 # 0 # 48 # 12 # 12 # 20 # 37 # 28 # 0 <lb/>2 # 5 # 0 # 50 # 12 # 14 # 20 # 38 # 27 # 55 <lb/>2 # 10 # 0 # 52 # 12 # 15 # 20 # 39 # 27 # 50 <lb/>2 # 15 # 0 # 54 # 12 # 17 # 20 # 40 # 27 # 45 <lb/>2 # 20 # 0 # 56 # 12 # 19 # 20 # 41 # 27 # 40 <lb/>2 # 25 # 0 # 58 # 12 # 21 # 20 # 42 # 27 # 35 <lb/>2 # 30 # 1 # 0 # 12 # 22 # 20 # 43 # 27 # 30 <lb/>2 # 35 # 1 # 2 # 12 # 24 # 20 # 44 # 27 # 25 <lb/>2 # 40 # 1 # 4 # 12 # 26 # 20 # 45 # 27 # 20 <lb/>2 # 45 # 1 # 6 # 12 # 28 # 20 # 46 # 27 # 15 <lb/>2 # 50 # 1 # 8 # 12 # 29 # 20 # 47 # 27 # 10 <lb/>2 # 55 # 1 # 10 # 12 # 31 # 20 # 48 # 27 # 5 <lb/>3 # 0 # 1 # 12 # 12 # 33 # 20 # 49 # 27 # 0 <lb/>3 # 5 # 1 # 14 # 12 # 34 # 20 # 50 # 27 # 55 <lb/>3 # 10 # 1 # 16 # 12 # 36 # 20 # 51 # 27 # 50 <lb/>3 # 15 # 1 # 18 # 12 # 38 # 20 # 52 # 27 # 45 <lb/>## Signa # ♓ # ♍ # ♒ # ♌ # ♑ # ♋ # ## Signa <lb/></note> <pb o="265" file="301" n="302" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve"> <lb/>## Signa # ♈ # ♎ # ♉ # ♏ # ♊ # ♐ # ## Signa <lb/>G # M # G # M # G # M # G # M # G # M <lb/>3 # 20 # 1 # 20 # 12 # 39 # 20 # 53 # 26 # 40 <lb/>3 # 25 # 1 # 22 # 12 # 41 # 20 # 53 # 26 # 35 <lb/>3 # 30 # 1 # 24 # 12 # 43 # 20 # 54 # 26 # 30 <lb/>3 # 35 # 1 # 6 # 12 # 45 # 20 # 55 # 26 # 25 <lb/>3 # 40 # 1 # 28 # 12 # 46 # 20 # 56 # 26 # 20 <lb/>3 # 45 # 1 # 30 # 12 # 48 # 20 # 57 # 26 # 15 <lb/>3 # 50 # 1 # 32 # 12 # 50 # 20 # 58 # 26 # 10 <lb/>4 # 55 # 1 # 34 # 12 # 51 # 20 # 59 # 26 # 5 <lb/>4 # 0 # 1 # 36 # 12 # 53 # 21 # 0 # 26 # 0 <lb/>4 # 5 # 1 # 38 # 12 # 55 # 21 # 1 # 25 # 55 <lb/>4 # 10 # 1 # 40 # 12 # 56 # 21 # 2 # 25 # 50 <lb/>4 # 15 # 1 # 42 # 12 # 58 # 21 # 3 # 25 # 45 <lb/>4 # 20 # 1 # 44 # 13 # 0 # 21 # 4 # 25 # 40 <lb/>4 # 25 # 1 # 46 # 13 # 1 # 21 # 5 # 25 # 35 <lb/>4 # 30 # 1 # 48 # 13 # 3 # 21 # 6 # 25 # 30 <lb/>4 # 35 # 1 # 50 # 13 # 5 # 21 # 7 # 25 # 25 <lb/>4 # 40 # 1 # 52 # 13 # 7 # 21 # 8 # 25 # 20 <lb/>4 # 45 # 1 # 54 # 13 # 8 # 21 # 8 # 25 # 15 <lb/>4 # 50 # 1 # 56 # 13 # 10 # 21 # 9 # 25 # 10 <lb/>4 # 55 # 1 # 58 # 13 # 11 # 21 # 10 # 25 # 5 <lb/>5 # 0 # 2 # 0 # 13 # 13 # 21 # 11 # 25 # 0 <lb/>5 # 5 # 2 # 2 # 13 # 15 # 21 # 12 # 24 # 55 <lb/>5 # 10 # 2 # 4 # 13 # 17 # 21 # 13 # 24 # 50 <lb/>5 # 15 # 2 # 6 # 13 # 18 # 21 # 14 # 24 # 45 <lb/>5 # 20 # 2 # 8 # 13 # 20 # 21 # 15 # 24 # 40 <lb/>5 # 25 # 2 # 9 # 13 # 22 # 21 # 16 # 24 # 35 <lb/>5 # 30 # 2 # 11 # 13 # 23 # 21 # 16 # 24 # 30 <lb/>5 # 5 # 2 # 13 # 13 # 25 # 21 # 17 # 24 # 25 <lb/>5 # 40 # 2 # 15 # 13 # 27 # 21 # 18 # 24 # 20 <lb/>5 # 45 # 2 # 17 # 13 # 28 # 21 # 19 # 24 # 15 <lb/>5 # 50 # 2 # 19 # 13 # 30 # 21 # 20 # 24 # 10 <lb/>6 # 55 # 2 # 21 # 13 # 32 # 21 # 21 # 24 # 5 <lb/>6 # 0 # 2 # 23 # 13 # 33 # 22 # 21 # 24 # 0 <lb/>6 # 5 # 2 # 25 # 13 # 35 # 23 # 21 # 23 # 55 <lb/>6 # 10 # 2 # 27 # 13 # 37 # 23 # 21 # 23 # 50 <lb/>6 # 15 # 2 # 29 # 13 # 38 # 21 # 24 # 23 # 45 <lb/>6 # 20 # 2 # 31 # 13 # 40 # 21 # 25 # 23 # 40 <lb/>6 # 25 # 2 # 33 # 13 # 42 # 21 # 26 # 23 # 35 <lb/>6 # 30 # 2 # 35 # 13 # 43 # 21 # 27 # 23 # 30 <lb/>6 # 35 # 2 # 37 # 13 # 45 # 21 # 28 # 23 # 25 <lb/>6 # 40 # 2 # 39 # 13 # 46 # 21 # 28 # 23 # 20 <lb/>6 # 45 # 2 # 41 # 13 # 48 # 21 # 29 # 23 # 15 <lb/>## Signa # ♓ # ♍ # ♒ # ♌ # ♑ # ♋ # ## Signa <lb/></note> <pb o="266" file="302" n="303" rhead="Comment. in II. Cap. Sphæræ"/> <note position="right" xml:space="preserve"> <lb/>## Signa # ♈ # ♎ # ♉ # ♏ # ♊ # ♐ # ## Signa <lb/>G # M # G # M # G # M # G # M # G # M <lb/>6 # 50 # 2 # 43 # 13 # 50 # 21 # 30 # 23 # 10 <lb/>6 # 55 # 2 # 45 # 13 # 51 # 21 # 31 # 23 # 5 <lb/>7 # 0 # 2 # 47 # 13 # 53 # 21 # 32 # 23 # 0 <lb/>7 # 5 # 2 # 49 # 13 # 55 # 21 # 33 # 22 # 55 <lb/>7 # 10 # 2 # 51 # 13 # 56 # 21 # 34 # 22 # 50 <lb/>7 # 15 # 2 # 53 # 13 # 58 # 21 # 34 # 22 # 45 <lb/>7 # 20 # 2 # 55 # 14 # 0 # 21 # 35 # 22 # 40 <lb/>7 # 25 # 2 # 57 # 14 # 1 # 21 # 36 # 22 # 35 <lb/>7 # 30 # 2 # 59 # 14 # 3 # 21 # 37 # 22 # 30 <lb/>7 # 35 # 3 # 1 # 14 # 5 # 21 # 38 # 22 # 25 <lb/>7 # 40 # 3 # 3 # 14 # 6 # 21 # 38 # 22 # 20 <lb/>7 # 45 # 3 # 5 # 14 # 8 # 21 # 39 # 22 # 15 <lb/>7 # 50 # 3 # 7 # 14 # 9 # 21 # 40 # 22 # 10 <lb/>7 # 55 # 3 # 9 # 14 # 11 # 21 # 41 # 22 # 5 <lb/>8 # 0 # 3 # 11 # 14 # 13 # 21 # 42 # 22 # 0 <lb/>8 # 5 # 3 # 13 # 14 # 14 # 21 # 42 # 21 # 55 <lb/>8 # 10 # 3 # 15 # 14 # 16 # 21 # 43 # 21 # 50 <lb/>8 # 15 # 3 # 17 # 14 # 18 # 21 # 44 # 21 # 45 <lb/>8 # 20 # 3 # 19 # 14 # 19 # 21 # 45 # 21 # 50 <lb/>8 # 25 # 3 # 21 # 14 # 21 # 21 # 46 # 21 # 35 <lb/>8 # 30 # 3 # 23 # 14 # 22 # 21 # 47 # 21 # 30 <lb/>8 # 35 # 3 # 25 # 14 # 24 # 21 # 47 # 21 # 25 <lb/>8 # 40 # 3 # 27 # 14 # 25 # 21 # 48 # 21 # 20 <lb/>8 # 45 # 3 # 29 # 14 # 27 # 21 # 49 # 21 # 15 <lb/>8 # 50 # 3 # 31 # 14 # 29 # 21 # 50 # 21 # 10 <lb/>8 # 55 # 3 # 33 # 14 # 30 # 21 # 51 # 21 # 0 <lb/>9 # 0 # 3 # 35 # 14 # 32 # 21 # 51 # 21 # 5 <lb/>9 # 5 # 3 # 37 # 14 # 34 # 21 # 52 # 20 # 55 <lb/>9 # 10 # 3 # 39 # 14 # 35 # 21 # 53 # 20 # 50 <lb/>9 # 15 # 3 # 40 # 14 # 37 # 21 # 54 # 20 # 45 <lb/>9 # 20 # 3 # 42 # 14 # 38 # 21 # 54 # 20 # 40 <lb/>9 # 25 # 3 # 44 # 14 # 40 # 21 # 55 # 20 # 35 <lb/>9 # 30 # 3 # 46 # 14 # 42 # 21 # 56 # 20 # 30 <lb/>9 # 35 # 3 # 48 # 14 # 43 # 21 # 57 # 20 # 25 <lb/>9 # 40 # 3 # 50 # 14 # 45 # 21 # 57 # 20 # 20 <lb/>9 # 45 # 3 # 52 # 14 # 46 # 21 # 58 # 20 # 15 <lb/>9 # 50 # 3 # 54 # 14 # 48 # 21 # 59 # 20 # 10 <lb/>9 # 55 # 3 # 56 # 14 # 49 # 22 # 0 # 20 # 5 <lb/>10 # 0 # 3 # 58 # 14 # 51 # 22 # 0 # 20 # 0 <lb/>10 # 5 # 4 # 0 # 14 # 55 # 22 # 1 # 19 # 55 <lb/>10 # 10 # 4 # 2 # 14 # 54 # 22 # 2 # 19 # 50 <lb/>10 # 15 # 4 # 4 # 14 # 56 # 22 # 3 # 19 # 45 <lb/>## Signa # ♓ # ♍ # ♒ # ♌ # ♑ # ♋ # ## Signa <lb/></note> <pb o="267" file="303" n="304" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve"> <lb/>## Signa # ♈ # ♎ # ♉ # ♏ # ♊ # ♐ # ## Signa <lb/>G # M # G # M # G # M # G # M # G # M <lb/>10 # 20 # 4 # 6 # 14 # 57 # 22 # 3 # 19 # 40 <lb/>10 # 25 # 4 # 8 # 14 # 59 # 22 # 4 # 19 # 35 <lb/>10 # 30 # 4 # 10 # 15 # 1 # 22 # 5 # 19 # 30 <lb/>10 # 35 # 4 # 12 # 15 # 2 # 22 # 5 # 19 # 25 <lb/>10 # 40 # 4 # 14 # 15 # 4 # 22 # 6 # 19 # 20 <lb/>10 # 45 # 4 # 16 # 15 # 5 # 22 # 7 # 19 # 15 <lb/>10 # 50 # 4 # 18 # 15 # 7 # 22 # 8 # 19 # 10 <lb/>10 # 55 # 4 # 20 # 15 # 8 # 22 # 8 # 19 # 5 <lb/>11 # 0 # 4 # 22 # 15 # 10 # 22 # 9 # 19 # 0 <lb/>11 # 5 # 4 # 24 # 15 # 11 # 22 # 10 # 18 # 55 <lb/>11 # 10 # 4 # 26 # 15 # 13 # 22 # 10 # 18 # 50 <lb/>11 # 15 # 4 # 28 # 15 # 13 # 22 # 11 # 18 # 45 <lb/>11 # 20 # 4 # 30 # 15 # 16 # 22 # 12 # 18 # 40 <lb/>11 # 25 # 4 # 32 # 15 # 18 # 22 # 12 # 18 # 35 <lb/>11 # 30 # 4 # 34 # 15 # 19 # 22 # 13 # 18 # 30 <lb/>11 # 35 # 4 # 36 # 15 # 21 # 22 # 14 # 18 # 25 <lb/>11 # 40 # 4 # 38 # 15 # 22 # 22 # 15 # 18 # 20 <lb/>11 # 45 # 4 # 39 # 15 # 24 # 22 # 15 # 18 # 15 <lb/>11 # 50 # 4 # 41 # 15 # 25 # 22 # 16 # 18 # 10 <lb/>11 # 55 # 4 # 43 # 15 # 27 # 22 # 16 # 18 # 5 <lb/>12 # 0 # 4 # 45 # 15 # 28 # 22 # 17 # 18 # 0 <lb/>12 # 5 # 4 # 47 # 15 # 30 # 22 # 18 # 17 # 55 <lb/>12 # 10 # 4 # 49 # 15 # 32 # 22 # 18 # 17 # 50 <lb/>12 # 15 # 4 # 51 # 15 # 33 # 22 # 19 # 17 # 45 <lb/>12 # 20 # 4 # 53 # 15 # 35 # 22 # 20 # 17 # 40 <lb/>12 # 25 # 4 # 55 # 15 # 36 # 22 # 20 # 17 # 35 <lb/>12 # 30 # 4 # 57 # 15 # 38 # 22 # 21 # 17 # 30 <lb/>12 # 35 # 4 # 59 # 15 # 39 # 22 # 22 # 17 # 25 <lb/>12 # 40 # 5 # 1 # 15 # 41 # 22 # 22 # 17 # 20 <lb/>12 # 45 # 5 # 3 # 15 # 42 # 22 # 23 # 17 # 15 <lb/>12 # 50 # 5 # 5 # 15 # 44 # 22 # 23 # 17 # 10 <lb/>12 # 55 # 5 # 7 # 15 # 45 # 22 # 24 # 17 # 5 <lb/>13 # 0 # 5 # 9 # 15 # 47 # 22 # 25 # 17 # 0 <lb/>13 # 5 # 5 # 11 # 15 # 48 # 22 # 26 # 16 # 55 <lb/>13 # 10 # 5 # 13 # 15 # 50 # 22 # 26 # 16 # 50 <lb/>13 # 15 # 5 # 15 # 15 # 51 # 22 # 27 # 16 # 45 <lb/>13 # 20 # 5 # 17 # 15 # 53 # 22 # 27 # 16 # 40 <lb/>13 # 25 # 5 # 19 # 15 # 54 # 22 # 28 # 16 # 35 <lb/>13 # 30 # 5 # 20 # 15 # 56 # 22 # 29 # 16 # 30 <lb/>13 # 35 # 5 # 22 # 15 # 57 # 22 # 29 # 16 # 25 <lb/>13 # 40 # 5 # 24 # 15 # 59 # 22 # 30 # 16 # 20 <lb/>13 # 45 # 5 # 26 # 15 # 0 # 22 # 3 # 16 # 15 <lb/>## Signa # ♓ # ♍ # ♒ # ♌ # ♑ # ♋ # ## Signa <lb/></note> <pb o="268" file="304" n="305" rhead="Comment. in II. Cap. Sphæræ"/> <note position="right" xml:space="preserve"> <lb/>## Signa # ♈ # ♎ # ♉ # ♏ # ♊ # ♐ # ## Signa <lb/>H # M # G # M # G # M # G # M # G # M <lb/>13 # 50 # 5 # 28 # 16 # 2 # 22 # 31 # 16 # 10 <lb/>13 # 55 # 5 # 30 # 16 # 3 # 22 # 31 # 16 # 5 <lb/>14 # 0 # 5 # 32 # 16 # 5 # 22 # 32 # 16 # 0 <lb/>14 # 5 # 5 # 34 # 16 # 6 # 22 # 33 # 15 # 55 <lb/>14 # 10 # 5 # 36 # 16 # 8 # 22 # 33 # 15 # 50 <lb/>14 # 15 # 5 # 38 # 16 # 9 # 22 # 34 # 15 # 45 <lb/>14 # 20 # 5 # 40 # 16 # 11 # 22 # 35 # 15 # 40 <lb/>14 # 25 # 5 # 42 # 16 # 12 # 22 # 35 # 15 # 35 <lb/>14 # 30 # 5 # 44 # 16 # 14 # 22 # 36 # 15 # 30 <lb/>14 # 35 # 5 # 46 # 16 # 15 # 22 # 36 # 15 # 25 <lb/>14 # 40 # 5 # 48 # 16 # 17 # 22 # 37 # 15 # 20 <lb/>14 # 45 # 5 # 50 # 16 # 18 # 22 # 37 # 15 # 15 <lb/>14 # 50 # 5 # 51 # 16 # 20 # 22 # 37 # 15 # 10 <lb/>14 # 55 # 5 # 53 # 16 # 21 # 22 # 38 # 15 # 5 <lb/>15 # 0 # 5 # 55 # 16 # 23 # 22 # 39 # 15 # 0 <lb/>15 # 5 # 5 # 57 # 16 # 24 # 22 # 39 # 14 # 55 <lb/>15 # 10 # 5 # 59 # 16 # 26 # 22 # 40 # 14 # 50 <lb/>15 # 15 # 6 # 1 # 16 # 27 # 22 # 40 # 14 # 45 <lb/>15 # 20 # 6 # 3 # 16 # 28 # 22 # 41 # 14 # 40 <lb/>15 # 25 # 6 # 5 # 16 # 30 # 22 # 41 # 14 # 35 <lb/>15 # 30 # 6 # 7 # 16 # 31 # 22 # 42 # 14 # 30 <lb/>15 # 35 # 6 # 9 # 16 # 33 # 22 # 42 # 14 # 25 <lb/>15 # 40 # 6 # 11 # 16 # 34 # 22 # 43 # 14 # 20 <lb/>15 # 45 # 6 # 13 # 16 # 36 # 22 # 43 # 14 # 15 <lb/>15 # 50 # 6 # 15 # 16 # 37 # 22 # 44 # 14 # 10 <lb/>15 # 55 # 6 # 17 # 16 # 39 # 22 # 45 # 14 # 5 <lb/>16 # 0 # 6 # 19 # 16 # 40 # 22 # 46 # 14 # 0 <lb/>16 # 5 # 6 # 21 # 16 # 41 # 22 # 46 # 13 # 55 <lb/>16 # 10 # 6 # 22 # 16 # 43 # 22 # 47 # 13 # 50 <lb/>16 # 15 # 6 # 24 # 16 # 44 # 22 # 47 # 13 # 45 <lb/>16 # 20 # 6 # 26 # 16 # 46 # 22 # 48 # 13 # 40 <lb/>16 # 25 # 6 # 28 # 16 # 47 # 22 # 48 # 13 # 35 <lb/>16 # 30 # 6 # 30 # 16 # 49 # 22 # 49 # 13 # 30 <lb/>16 # 35 # 6 # 32 # 16 # 50 # 22 # 49 # 13 # 25 <lb/>16 # 40 # 6 # 34 # 16 # 52 # 22 # 50 # 13 # 20 <lb/>16 # 45 # 6 # 6 # 16 # 53 # 22 # 50 # 13 # 15 <lb/>16 # 50 # 6 # 36 # 16 # 54 # 22 # 51 # 13 # 10 <lb/>16 # 55 # 6 # 40 # 16 # 56 # 22 # 51 # 13 # 5 <lb/>17 # 0 # 6 # 42 # 16 # 57 # 22 # 52 # 13 # 0 <lb/>17 # 5 # 6 # 44 # 16 # 59 # 22 # 52 # 12 # 55 <lb/>17 # 10 # 6 # 46 # 17 # 0 # 22 # 53 # 12 # 50 <lb/>17 # 15 # 6 # 47 # 17 # 2 # 22 # 53 # 12 # 45 <lb/>## Signa # ♓ # ♍ # ♒ # ♌ # ♑ # ♋ # ## Signa <lb/></note> <pb o="269" file="305" n="306" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve"> <lb/>## Signa # ♈ # ♎ # ♉ # ♏ # ♊ # ♐ # ## Signa <lb/>G # M # G # M # G # M # G # M # G # M <lb/>17 # 20 # 6 # 49 # 17 # 3 # 22 # 54 # 12 # 40 <lb/>17 # 25 # 6 # 51 # 17 # 4 # 22 # 54 # 12 # 35 <lb/>17 # 30 # 6 # 53 # 17 # 6 # 22 # 55 # 12 # 30 <lb/>17 # 35 # 6 # 55 # 17 # 7 # 22 # 55 # 12 # 25 <lb/>17 # 40 # 6 # 57 # 17 # 9 # 22 # 56 # 12 # 20 <lb/>17 # 45 # 6 # 59 # 17 # 10 # 22 # 56 # 12 # 15 <lb/>17 # 50 # 7 # 1 # 17 # 11 # 22 # 57 # 12 # 10 <lb/>17 # 55 # 7 # 3 # 17 # 13 # 22 # 57 # 12 # 5 <lb/>18 # 0 # 7 # 5 # 17 # 14 # 22 # 58 # 12 # 0 <lb/>18 # 5 # 7 # 7 # 17 # 16 # 22 # 58 # 11 # 55 <lb/>18 # 10 # 7 # 8 # 17 # 18 # 22 # 58 # 11 # 50 <lb/>18 # 15 # 7 # 10 # 17 # 19 # 22 # 59 # 11 # 45 <lb/>18 # 20 # 7 # 12 # 17 # 20 # 22 # 59 # 11 # 40 <lb/>18 # 25 # 7 # 14 # 17 # 21 # 23 # 0 # 11 # 35 <lb/>18 # 30 # 7 # 16 # 17 # 23 # 23 # 0 # 11 # 30 <lb/>18 # 35 # 7 # 18 # 17 # 24 # 23 # 0 # 11 # 25 <lb/>18 # 40 # 7 # 20 # 17 # 25 # 23 # 1 # 11 # 20 <lb/>18 # 45 # 7 # 22 # 17 # 27 # 23 # 1 # 11 # 15 <lb/>18 # 50 # 7 # 24 # 17 # 28 # 23 # 2 # 11 # 10 <lb/>18 # 55 # 7 # 26 # 17 # 29 # 23 # 2 # 11 # 5 <lb/>19 # 0 # 7 # 28 # 17 # 31 # 23 # 3 # 11 # 0 <lb/>19 # 5 # 7 # 29 # 17 # 32 # 23 # 3 # 10 # 55 <lb/>19 # 10 # 7 # 31 # 17 # 34 # 23 # 3 # 10 # 50 <lb/>19 # 15 # 7 # 33 # 17 # 35 # 23 # 4 # 10 # 45 <lb/>19 # 20 # 7 # 35 # 17 # 36 # 23 # 4 # 10 # 40 <lb/>19 # 25 # 7 # 37 # 17 # 38 # 23 # 5 # 10 # 35 <lb/>19 # 30 # 7 # 39 # 17 # 39 # 23 # 5 # 10 # 30 <lb/>19 # 35 # 7 # 41 # 17 # 40 # 23 # 5 # 10 # 25 <lb/>19 # 40 # 7 # 43 # 17 # 42 # 23 # 6 # 10 # 20 <lb/>19 # 45 # 7 # 45 # 17 # 43 # 23 # 6 # 10 # 15 <lb/>19 # 50 # 7 # 47 # 17 # 44 # 23 # 7 # 10 # 10 <lb/>19 # 55 # 5 # 48 # 17 # 46 # 23 # 7 # 10 # 5 <lb/>20 # 0 # 7 # 50 # 17 # 47 # 23 # 7 # 10 # 0 <lb/>20 # 5 # 7 # 52 # 17 # 48 # 23 # 8 # 9 # 55 <lb/>20 # 10 # 7 # 54 # 17 # 49 # 23 # 8 # 9 # 50 <lb/>20 # 15 # 7 # 56 # 17 # 51 # 23 # 8 # 9 # 45 <lb/>20 # 20 # 7 # 58 # 17 # 52 # 23 # 9 # 9 # 40 <lb/>20 # 25 # 8 # 0 # 17 # 54 # 23 # 9 # 9 # 35 <lb/>20 # 30 # 8 # 2 # 17 # 55 # 23 # 9 # 9 # 30 <lb/>20 # 35 # 8 # 4 # 17 # 57 # 23 # 10 # 9 # 25 <lb/>20 # 40 # 8 # 5 # 17 # 58 # 23 # 10 # 9 # 20 <lb/>20 # 45 # 8 # 7 # 17 # 59 # 23 # 11 # 9 # 15 <lb/>## Signa # ♓ # ♍ # ♒ # ♌ # ♑ # ♋ # ## Signa <lb/></note> <pb o="270" file="306" n="307" rhead="Comment. in II. Cap. Sphæræ"/> <note position="right" xml:space="preserve"> <lb/>## Signa # ♈ # ♎ # ♉ # ♏ # ♊ # ♐ # ## Signa <lb/>G # M # G # M # G # M # G # M # G # M <lb/>20 # 50 # 8 # 9 # 18 # 0 # 23 # 11 # 9 # 10 <lb/>20 # 55 # 8 # 11 # 18 # 2 # 23 # 11 # 9 # 5 <lb/>21 # 0 # 8 # 13 # 18 # 3 # 23 # 12 # 9 # 0 <lb/>21 # 5 # 8 # 15 # 18 # 4 # 23 # 12 # 8 # 55 <lb/>21 # 10 # 8 # 17 # 18 # 6 # 23 # 12 # 8 # 50 <lb/>21 # 15 # 8 # 19 # 18 # 7 # 23 # 13 # 8 # 45 <lb/>21 # 20 # 8 # 20 # 18 # 8 # 23 # 13 # 8 # 40 <lb/>21 # 25 # 8 # 22 # 18 # 10 # 23 # 13 # 8 # 35 <lb/>21 # 30 # 8 # 24 # 18 # 11 # 23 # 14 # 8 # 30 <lb/>21 # 35 # 8 # 26 # 18 # 12 # 23 # 14 # 8 # 25 <lb/>21 # 40 # 8 # 28 # 18 # 14 # 23 # 14 # 8 # 20 <lb/>21 # 45 # 8 # 30 # 18 # 15 # 23 # 15 # 8 # 15 <lb/>21 # 50 # 8 # 32 # 18 # 16 # 23 # 15 # 8 # 10 <lb/>21 # 55 # 8 # 34 # 18 # 17 # 23 # 15 # 8 # 5 <lb/>22 # 0 # 8 # 35 # 18 # 19 # 23 # 15 # 8 # 0 <lb/>22 # 5 # 8 # 37 # 18 # 20 # 23 # 16 # 7 # 55 <lb/>22 # 10 # 8 # 39 # 18 # 21 # 23 # 16 # 7 # 50 <lb/>22 # 15 # 8 # 41 # 18 # 23 # 23 # 16 # 7 # 45 <lb/>22 # 20 # 8 # 43 # 18 # 24 # 23 # 16 # 7 # 40 <lb/>22 # 25 # 8 # 45 # 18 # 25 # 23 # 17 # 7 # 35 <lb/>22 # 30 # 8 # 47 # 18 # 27 # 23 # 17 # 7 # 30 <lb/>22 # 35 # 8 # 48 # 18 # 28 # 23 # 17 # 7 # 25 <lb/>22 # 40 # 8 # 50 # 18 # 29 # 23 # 18 # 7 # 20 <lb/>22 # 45 # 8 # 52 # 18 # 30 # 23 # 18 # 7 # 15 <lb/>22 # 50 # 8 # 54 # 18 # 32 # 23 # 18 # 7 # 10 <lb/>22 # 55 # 8 # 56 # 18 # 33 # 23 # 19 # 7 # 5 <lb/>23 # 0 # 8 # 58 # 18 # 34 # 23 # 19 # 7 # 0 <lb/>23 # 5 # 9 # 0 # 18 # 35 # 23 # 19 # 6 # 55 <lb/>23 # 10 # 9 # 1 # 18 # 37 # 23 # 19 # 6 # 50 <lb/>23 # 15 # 9 # 3 # 18 # 38 # 23 # 20 # 6 # 45 <lb/>23 # 20 # 9 # 5 # 18 # 39 # 23 # 20 # 6 # 40 <lb/>23 # 25 # 9 # 7 # 18 # 40 # 23 # 20 # 6 # 35 <lb/>23 # 30 # 9 # 9 # 18 # 42 # 23 # 20 # 6 # 30 <lb/>23 # 35 # 9 # 11 # 18 # 43 # 23 # 21 # 6 # 25 <lb/>23 # 40 # 9 # 13 # 18 # 44 # 23 # 21 # 6 # 20 <lb/>23 # 45 # 9 # 14 # 18 # 45 # 23 # 21 # 6 # 15 <lb/>23 # 50 # 9 # 16 # 18 # 47 # 23 # 21 # 6 # 10 <lb/>23 # 55 # 9 # 18 # 18 # 48 # 23 # 22 # 6 # 5 <lb/>24 # 0 # 9 # 20 # 18 # 49 # 23 # 22 # 6 # 0 <lb/>24 # 5 # 9 # 22 # 18 # 50 # 23 # 22 # 5 # 55 <lb/>24 # 10 # 9 # 24 # 18 # 52 # 23 # 22 # 5 # 50 <lb/>24 # 15 # 9 # 26 # 18 # 53 # 23 # 22 # 5 # 45 <lb/>## Signa # ♓ # ♍ # ♒ # ♌ # ♑ # ♋ # ## Signa <lb/></note> <pb o="271" file="307" n="308" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve"> <lb/>## Signa # ♈ # ♎ # ♉ # ♏ # ♊ # ♐ # ## Signa <lb/>H # M # G # M # G # M # G # M # G # M <lb/>24 # 20 # 9 # 28 # 18 # 54 # 23 # 23 # 5 # 40 <lb/>24 # 25 # 9 # 30 # 18 # 55 # 23 # 23 # 5 # 35 <lb/>24 # 30 # 9 # 32 # 18 # 57 # 23 # 23 # 5 # 30 <lb/>24 # 35 # 9 # 34 # 18 # 58 # 23 # 23 # 5 # 25 <lb/>24 # 40 # 9 # 35 # 18 # 59 # 23 # 24 # 5 # 20 <lb/>24 # 45 # 9 # 37 # 19 # 0 # 23 # 24 # 5 # 15 <lb/>24 # 50 # 9 # 38 # 19 # 2 # 23 # 24 # 5 # 10 <lb/>24 # 55 # 9 # 40 # 19 # 3 # 23 # 24 # 5 # 5 <lb/>25 # 0 # 9 # 42 # 19 # 4 # 23 # 24 # 5 # 0 <lb/>25 # 5 # 9 # 44 # 19 # 5 # 23 # 24 # 4 # 55 <lb/>25 # 10 # 9 # 46 # 19 # 6 # 23 # 25 # 4 # 50 <lb/>25 # 15 # 9 # 48 # 19 # 8 # 23 # 25 # 4 # 45 <lb/>25 # 20 # 9 # 49 # 19 # 9 # 23 # 25 # 4 # 40 <lb/>25 # 25 # 9 # 51 # 19 # 10 # 23 # 25 # 4 # 35 <lb/>25 # 30 # 9 # 53 # 19 # 11 # 23 # 25 # 4 # 30 <lb/>25 # 35 # 9 # 55 # 19 # 12 # 23 # 26 # 4 # 25 <lb/>25 # 40 # 9 # 57 # 19 # 13 # 23 # 26 # 4 # 20 <lb/>25 # 45 # 9 # 59 # 19 # 15 # 23 # 26 # 4 # 15 <lb/>15 # 50 # 10 # 0 # 19 # 16 # 23 # 26 # 4 # 10 <lb/>25 # 55 # 10 # 2 # 19 # 17 # 23 # 26 # 4 # 5 <lb/>26 # 0 # 10 # 4 # 19 # 18 # 23 # 26 # 4 # 0 <lb/>26 # 5 # 10 # 6 # 19 # 19 # 23 # 26 # 3 # 55 <lb/>26 # 10 # 10 # 8 # 19 # 21 # 23 # 27 # 3 # 50 <lb/>26 # 15 # 10 # 9 # 19 # 22 # 23 # 27 # 3 # 45 <lb/>26 # 20 # 10 # 11 # 19 # 23 # 23 # 27 # 3 # 40 <lb/>26 # 25 # 10 # 13 # 19 # 24 # 23 # 27 # 3 # 35 <lb/>26 # 30 # 10 # 15 # 19 # 25 # 23 # 27 # 3 # 30 <lb/>26 # 35 # 10 # 17 # 19 # 26 # 23 # 27 # 3 # 25 <lb/>26 # 40 # 10 # 19 # 19 # 28 # 23 # 27 # 3 # 20 <lb/>26 # 45 # 10 # 20 # 19 # 29 # 23 # 28 # 3 # 15 <lb/>26 # 50 # 10 # 22 # 19 # 30 # 23 # 28 # 3 # 10 <lb/>26 # 55 # 10 # 24 # 19 # 31 # 23 # 28 # 3 # 5 <lb/>27 # 0 # 10 # 26 # 19 # 32 # 23 # 28 # 3 # 0 <lb/>27 # 5 # 10 # 28 # 19 # 33 # 23 # 28 # 2 # 55 <lb/>27 # 10 # 10 # 29 # 19 # 35 # 23 # 28 # 2 # 50 <lb/>27 # 15 # 10 # 31 # 19 # 36 # 23 # 28 # 2 # 45 <lb/>27 # 20 # 10 # 33 # 19 # 37 # 23 # 28 # 2 # 40 <lb/>27 # 25 # 10 # 35 # 19 # 38 # 23 # 28 # 2 # 35 <lb/>27 # 30 # 10 # 37 # 19 # 39 # 23 # 29 # 2 # 30 <lb/>27 # 35 # 10 # 38 # 19 # 40 # 23 # 29 # 2 # 25 <lb/>37 # 40 # 10 # 40 # 19 # 41 # 23 # 29 # 2 # 20 <lb/>27 # 45 # 10 # 41 # 19 # 42 # 23 # 29 # 2 # 15 <lb/>## Signa # ♓ # ♍ # ♒ # ♌ # ♑ # ♋ # ## Signa <lb/></note> <pb o="272" file="308" n="309" rhead="Comment. in II. Cap. Sphæræ"/> <note position="right" xml:space="preserve"> <lb/>## Signa # ♈ # ♎ # ♉ # ♏ # ♊ # ♐ # ## Signa <lb/>G # M # G # M # G # M # G # M # G # M <lb/>27 # 50 # 10 # 44 # 19 # 44 # 23 # 29 # 2 # 10 <lb/>27 # 55 # 10 # 46 # 19 # 45 # 23 # 29 # 2 # 5 <lb/>28 # 0 # 10 # 47 # 19 # 46 # 23 # 29 # 2 # 0 <lb/>28 # 5 # 10 # 49 # 19 # 47 # 23 # 29 # 1 # 55 <lb/>28 # 10 # 10 # 51 # 19 # 48 # 23 # 29 # 1 # 50 <lb/>28 # 15 # 10 # 53 # 19 # 49 # 23 # 29 # 1 # 45 <lb/>28 # 20 # 10 # 54 # 19 # 50 # 23 # 29 # 1 # 40 <lb/>28 # 25 # 10 # 56 # 19 # 51 # 23 # 29 # 1 # 35 <lb/>28 # 30 # 10 # 58 # 19 # 53 # 23 # 29 # 1 # 30 <lb/>28 # 35 # 12 # 0 # 19 # 54 # 23 # 29 # 1 # 25 <lb/>28 # 40 # 11 # 2 # 19 # 55 # 23 # 30 # 1 # 20 <lb/>28 # 45 # 11 # 3 # 19 # 56 # 23 # 30 # 1 # 15 <lb/>28 # 50 # 11 # 5 # 19 # 57 # 23 # 30 # 1 # 10 <lb/>28 # 55 # 11 # 7 # 19 # 58 # 23 # 30 # 1 # 5 <lb/>29 # 0 # 11 # 9 # 19 # 59 # 23 # 30 # 1 # 0 <lb/>29 # 5 # 11 # 11 # 20 # 0 # 23 # 30 # 0 # 55 <lb/>29 # 10 # 11 # 12 # 20 # 1 # 23 # 30 # 0 # 50 <lb/>29 # 15 # 11 # 14 # 20 # 2 # 23 # 30 # 0 # 45 <lb/>29 # 20 # 11 # 16 # 20 # 3 # 23 # 30 # 0 # 40 <lb/>29 # 25 # 11 # 18 # 20 # 5 # 23 # 30 # 0 # 35 <lb/>29 # 30 # 11 # 19 # 20 # 6 # 23 # 30 # 0 # 30 <lb/>29 # 35 # 11 # 21 # 20 # 7 # 23 # 30 # 0 # 25 <lb/>29 # 40 # 11 # 23 # 20 # 8 # 23 # 30 # 0 # 20 <lb/>29 # 45 # 11 # 25 # 20 # 9 # 23 # 30 # 0 # 15 <lb/>29 # 50 # 11 # 27 # 20 # 10 # 23 # 30 # 0 # 10 <lb/>29 # 55 # 11 # 29 # 20 # 11 # 23 # 30 # 0 # 5 <lb/>30 # 0 # 11 # 30 # 20 # 12 # 23 # 30 # 0 # 0 <lb/>## Signa # ♓ # ♍ # ♒ # ♌ # ♑ # ♋ # ## Signa <lb/></note> </div> <div xml:id="echoid-div575" type="section" level="1" n="192"> <head xml:id="echoid-head201" xml:space="preserve">VSVS TABVLAE DECLINATIONVM.</head> <p> <s xml:id="echoid-s11255" xml:space="preserve"><emph style="sc">Si</emph> ſignum, cuius graduum declinationes deſiderantur, in ſuperiori linea <lb/>tabulæ repertum fuerit, accipiendi erunt gradus, ac minuta in ſiniſtra tabulæ <lb/>parte: </s> <s xml:id="echoid-s11256" xml:space="preserve">Si vero in linea tabulæ inferiori fuerit repoſitum ſignum, in dextra par-<lb/>te erunt gradus ſumendi cum minutis, & </s> <s xml:id="echoid-s11257" xml:space="preserve">illico in communi concurſu ſigni, & </s> <s xml:id="echoid-s11258" xml:space="preserve"><lb/>gradus accepti, offendentur gradus, ac minuta declinationis. </s> <s xml:id="echoid-s11259" xml:space="preserve"><emph style="sc">Exemplvm</emph>. <lb/></s> <s xml:id="echoid-s11260" xml:space="preserve">Scire lubet quantum declinet grad. </s> <s xml:id="echoid-s11261" xml:space="preserve">17. </s> <s xml:id="echoid-s11262" xml:space="preserve">♏, ab Aequatore. </s> <s xml:id="echoid-s11263" xml:space="preserve">In ſiniſtra igitur par <lb/>te tabulæ accipio gradum 17. </s> <s xml:id="echoid-s11264" xml:space="preserve">♏. </s> <s xml:id="echoid-s11265" xml:space="preserve">(Nam hoc ſignum collocatur in ſuperiori <pb o="273" file="309" n="310" rhead="Ioan. de Sacro Boſco."/> parte tabulæ) & </s> <s xml:id="echoid-s11266" xml:space="preserve">in cõmuni angulo ſub ♏. </s> <s xml:id="echoid-s11267" xml:space="preserve">reperio grad. </s> <s xml:id="echoid-s11268" xml:space="preserve">16. </s> <s xml:id="echoid-s11269" xml:space="preserve">min. </s> <s xml:id="echoid-s11270" xml:space="preserve">57. </s> <s xml:id="echoid-s11271" xml:space="preserve">Tãtã igitur <lb/>pronuncio eſſe declinationẽ grad. </s> <s xml:id="echoid-s11272" xml:space="preserve">17. </s> <s xml:id="echoid-s11273" xml:space="preserve">♏. </s> <s xml:id="echoid-s11274" xml:space="preserve">Itẽ inueſtigandum ſit, quantam ha-<lb/>beat declinationẽ grad. </s> <s xml:id="echoid-s11275" xml:space="preserve">23. </s> <s xml:id="echoid-s11276" xml:space="preserve">min. </s> <s xml:id="echoid-s11277" xml:space="preserve">40. </s> <s xml:id="echoid-s11278" xml:space="preserve">♋. </s> <s xml:id="echoid-s11279" xml:space="preserve">Quoniã igitur hoc ſignum eſt in parte <lb/>tabulæ inferiori, inuenio in parte dextra dicto gradui 23. </s> <s xml:id="echoid-s11280" xml:space="preserve">& </s> <s xml:id="echoid-s11281" xml:space="preserve">40. </s> <s xml:id="echoid-s11282" xml:space="preserve">min. </s> <s xml:id="echoid-s11283" xml:space="preserve">ſupra ſi-<lb/>gnum ♋, reſpondere grad. </s> <s xml:id="echoid-s11284" xml:space="preserve">21. </s> <s xml:id="echoid-s11285" xml:space="preserve">min. </s> <s xml:id="echoid-s11286" xml:space="preserve">25. </s> <s xml:id="echoid-s11287" xml:space="preserve">Atq; </s> <s xml:id="echoid-s11288" xml:space="preserve">tanta eſt declinatio quęſita. </s> <s xml:id="echoid-s11289" xml:space="preserve">Quod <lb/>ſi minuta propoſita non reperiantur in tabula prædicta,@ſumendæ erunt decli-<lb/>nationes minutorum proxime maiorũ, & </s> <s xml:id="echoid-s11290" xml:space="preserve">proximæ minorum, & </s> <s xml:id="echoid-s11291" xml:space="preserve">per earũ diffe <lb/>rentiam elicienda pars proportionalis, quę adijciẽda quidem erit declinationi <lb/>minutorũ proxime minorũ, ſi ſignũ propoſitũ fuerit ſuperius: </s> <s xml:id="echoid-s11292" xml:space="preserve">detrahenda vero <lb/>ab eadẽ declinatione minutorum proxime minorum, ſi ſignum inferius fuerit.</s> <s xml:id="echoid-s11293" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11294" xml:space="preserve"><emph style="sc">Exemplvm</emph> utriuſque. </s> <s xml:id="echoid-s11295" xml:space="preserve">Volò declinationũ grad. </s> <s xml:id="echoid-s11296" xml:space="preserve">4. </s> <s xml:id="echoid-s11297" xml:space="preserve">min. </s> <s xml:id="echoid-s11298" xml:space="preserve">27. </s> <s xml:id="echoid-s11299" xml:space="preserve">ſigni ♊. </s> <s xml:id="echoid-s11300" xml:space="preserve">Quouiã <lb/>igitur min. </s> <s xml:id="echoid-s11301" xml:space="preserve">27. </s> <s xml:id="echoid-s11302" xml:space="preserve">non reperiuntur in dicta tabula, accipio differentiam declina-<lb/>tionum, quas habent min. </s> <s xml:id="echoid-s11303" xml:space="preserve">25. </s> <s xml:id="echoid-s11304" xml:space="preserve">& </s> <s xml:id="echoid-s11305" xml:space="preserve">min. </s> <s xml:id="echoid-s11306" xml:space="preserve">30. </s> <s xml:id="echoid-s11307" xml:space="preserve">quarti gradus ſigni ♊, quę differentia <lb/>continet min. </s> <s xml:id="echoid-s11308" xml:space="preserve">1. </s> <s xml:id="echoid-s11309" xml:space="preserve">& </s> <s xml:id="echoid-s11310" xml:space="preserve">per regulam proportionum inuenio minutis 2 (quibus mi-<lb/>nuta 25. </s> <s xml:id="echoid-s11311" xml:space="preserve">ſuperantur à minutis 27.) </s> <s xml:id="echoid-s11312" xml:space="preserve">reſpondere minuta {2/1}. </s> <s xml:id="echoid-s11313" xml:space="preserve">hoc eſt, Sec. </s> <s xml:id="echoid-s11314" xml:space="preserve">24. </s> <s xml:id="echoid-s11315" xml:space="preserve">quan <lb/>doquidem minutis 3.) </s> <s xml:id="echoid-s11316" xml:space="preserve">quibus minuta 25. </s> <s xml:id="echoid-s11317" xml:space="preserve">ſuperantur à minutis 30. </s> <s xml:id="echoid-s11318" xml:space="preserve">reſpondet <lb/>minutum 1. </s> <s xml:id="echoid-s11319" xml:space="preserve">differentiæ. </s> <s xml:id="echoid-s11320" xml:space="preserve">Et quia ſignum ♊, eſt ſuperius, adijcienda erunt Sec. <lb/></s> <s xml:id="echoid-s11321" xml:space="preserve">24. </s> <s xml:id="echoid-s11322" xml:space="preserve">declinationi grad. </s> <s xml:id="echoid-s11323" xml:space="preserve">4. </s> <s xml:id="echoid-s11324" xml:space="preserve">Min. </s> <s xml:id="echoid-s11325" xml:space="preserve">25. </s> <s xml:id="echoid-s11326" xml:space="preserve">♊, quæ continet grad. </s> <s xml:id="echoid-s11327" xml:space="preserve">21. </s> <s xml:id="echoid-s11328" xml:space="preserve">min. </s> <s xml:id="echoid-s11329" xml:space="preserve">5. </s> <s xml:id="echoid-s11330" xml:space="preserve">Atque ita <lb/>declinatio grad. </s> <s xml:id="echoid-s11331" xml:space="preserve">2. </s> <s xml:id="echoid-s11332" xml:space="preserve">min. </s> <s xml:id="echoid-s11333" xml:space="preserve">27. </s> <s xml:id="echoid-s11334" xml:space="preserve">ſigni ♊, complectetur grad. </s> <s xml:id="echoid-s11335" xml:space="preserve">21. </s> <s xml:id="echoid-s11336" xml:space="preserve">min. </s> <s xml:id="echoid-s11337" xml:space="preserve">5. </s> <s xml:id="echoid-s11338" xml:space="preserve">Sec. </s> <s xml:id="echoid-s11339" xml:space="preserve">24. </s> <s xml:id="echoid-s11340" xml:space="preserve">Pari <lb/>ratione uolo declinationem grad. </s> <s xml:id="echoid-s11341" xml:space="preserve">25. </s> <s xml:id="echoid-s11342" xml:space="preserve">min. </s> <s xml:id="echoid-s11343" xml:space="preserve">32. </s> <s xml:id="echoid-s11344" xml:space="preserve">ſigni ♑. </s> <s xml:id="echoid-s11345" xml:space="preserve">Quoniam igitur ſignum <lb/>propoſitum eſt, inferius detraho eandem partem proportionalem, uidelicet <lb/>Sec. </s> <s xml:id="echoid-s11346" xml:space="preserve">24. </s> <s xml:id="echoid-s11347" xml:space="preserve">ex declinatione grad. </s> <s xml:id="echoid-s11348" xml:space="preserve">25. </s> <s xml:id="echoid-s11349" xml:space="preserve">min. </s> <s xml:id="echoid-s11350" xml:space="preserve">30. </s> <s xml:id="echoid-s11351" xml:space="preserve">♑, hoc eſt, ex grad. </s> <s xml:id="echoid-s11352" xml:space="preserve">21. </s> <s xml:id="echoid-s11353" xml:space="preserve">min. </s> <s xml:id="echoid-s11354" xml:space="preserve">6. </s> <s xml:id="echoid-s11355" xml:space="preserve">remane-<lb/>bitque declinttio propoſita graduum 21. </s> <s xml:id="echoid-s11356" xml:space="preserve">min. </s> <s xml:id="echoid-s11357" xml:space="preserve">5. </s> <s xml:id="echoid-s11358" xml:space="preserve">Sec. </s> <s xml:id="echoid-s11359" xml:space="preserve">36.</s> <s xml:id="echoid-s11360" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11361" xml:space="preserve"><emph style="sc">Porro</emph> maxima Solis de <lb/> <anchor type="figure" xlink:label="fig-309-01a" xlink:href="fig-309-01"/> <anchor type="note" xlink:label="note-309-01a" xlink:href="note-309-01"/> clinatio Borea ęqualis eſt <lb/>maximę declinationi Auſtra <lb/>li, ut auctor dixit; </s> <s xml:id="echoid-s11362" xml:space="preserve">qđ quidẽ <lb/>facile hac rõne demonſtrari <lb/>poteſt. </s> <s xml:id="echoid-s11363" xml:space="preserve">Sumatur aliqua ſphæ <lb/>ra, in qua Colurus Solſtitio-<lb/>rũ ſit ABCD; </s> <s xml:id="echoid-s11364" xml:space="preserve">Æquator AC; <lb/></s> <s xml:id="echoid-s11365" xml:space="preserve">Zodiacus ſiue Ecliptica EI; </s> <s xml:id="echoid-s11366" xml:space="preserve"><lb/>Tropicus ♋, FG; </s> <s xml:id="echoid-s11367" xml:space="preserve">Tropicus <lb/>♑, HI; </s> <s xml:id="echoid-s11368" xml:space="preserve">Maximæ Solis decli-<lb/>nationes, AF, Borea, CI, Au-<lb/>@trina. </s> <s xml:id="echoid-s11369" xml:space="preserve">Quoniã igitur ſemicir <lb/>culus ABC, ſemicirculo FBI, <lb/>ęqualis eſt; </s> <s xml:id="echoid-s11370" xml:space="preserve">dẽpto cõi arcu-<lb/>EBC, erit AF, maxima Solis <lb/>declinatio Borea æqualis ar-<lb/>cui CI, hoc eſt, maximæ de-<lb/>clinationi Solis Auſtrinę, <lb/>quod eſt propoſitum.</s> <s xml:id="echoid-s11371" xml:space="preserve"/> </p> <div xml:id="echoid-div575" type="float" level="2" n="1"> <figure xlink:label="fig-309-01" xlink:href="fig-309-01a"> <image file="309-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/309-01"/> </figure> <note position="right" xlink:label="note-309-01" xlink:href="note-309-01a" xml:space="preserve">Maximam <lb/>Solis decli-<lb/>nationem <lb/>boreã ęqu@ <lb/>lẽ eſſe ma-<lb/>ximę decl@ <lb/>nationi So-<lb/>lis auſtrali</note> </div> </div> <div xml:id="echoid-div577" type="section" level="1" n="193"> <head xml:id="echoid-head202" xml:space="preserve">VI.</head> <note position="right" xml:space="preserve">Colur@ ſol. <lb/>ſtitiorũ m@ <lb/>titur diſtã-<lb/>tias polorũ <lb/>Zodiaci à <lb/>polis mũ@i.</note> <p> <s xml:id="echoid-s11372" xml:space="preserve"><emph style="sc">Solstitiorvm</emph> Colurus menſurat quoque diſtantias polorum <lb/>Zodiaci à polis mundi. </s> <s xml:id="echoid-s11373" xml:space="preserve">Eſt enim hæc diſtantia tanta, quantus eſt arcus Colu-<lb/>ri Solſtitiorum inter duos polos, nempe polum mundi, & </s> <s xml:id="echoid-s11374" xml:space="preserve">polum Zodiaci, in-<lb/>terceptus. </s> <s xml:id="echoid-s11375" xml:space="preserve">Sunt autem duę hæ diſtantię polorum Zodiaci à mundi polis ęqua- <pb o="274" file="310" n="311" rhead="Comment. in II. Cap. Sphæræ"/> les maxim is declinationibus Solis. </s> <s xml:id="echoid-s11376" xml:space="preserve">Repetatur enim ſphæra, in qua poli mun-<lb/>di B, D; </s> <s xml:id="echoid-s11377" xml:space="preserve">poli Zodiaci K, I; </s> <s xml:id="echoid-s11378" xml:space="preserve">Maximę Solis decli-<lb/> <anchor type="figure" xlink:label="fig-310-01a" xlink:href="fig-310-01"/> <anchor type="note" xlink:label="note-310-01a" xlink:href="note-310-01"/> clinationes A E, C H. </s> <s xml:id="echoid-s11379" xml:space="preserve">Quoniam igitur qua-<lb/>drans A B, quadranti EK, eſt æqualis; </s> <s xml:id="echoid-s11380" xml:space="preserve">abla-<lb/>to communi arcu EB, remanebit arcus AE, nẽ-<lb/>pe maxima declinatio Solis, arcui BK, uideli-<lb/>cet diſtantiæ unius poli ab altero, ęqualis. <lb/></s> <s xml:id="echoid-s11381" xml:space="preserve">Eadem ratione erit CH, altera maxima Solis <lb/>declinatio æqualis arcui DL, ſcilicet alteri di-<lb/>ſtantiæ poli Zodiaci à polo mundi, ſi nimirum <lb/>aſſumantur duo Quadrantes C D, HL. </s> <s xml:id="echoid-s11382" xml:space="preserve">Vnde <lb/>manifeſtum eſt, tantum diſtare polum Zodiaci <lb/>Boreum à polo mundi Boreo, quantum rece-<lb/>dit à polo mundi Auſtrali Auſtralis polus Zo-<lb/>diaci, propterea quòd utraque diſtantia æqua-<lb/>lis eſt utrique maximæ declinationi Solis. </s> <s xml:id="echoid-s11383" xml:space="preserve">Quod etiam ita oſtendetur. </s> <s xml:id="echoid-s11384" xml:space="preserve">Quo-<lb/>niam ſemicirculi BCD, KHL, ęquales ſunt; </s> <s xml:id="echoid-s11385" xml:space="preserve">ſi auferatur communis arcus KD, <lb/>æquales relinquetur arcus BK, DL, hoc eſt, diſtantiæ polorum Zodiaci à po-<lb/>lis mundi.</s> <s xml:id="echoid-s11386" xml:space="preserve"/> </p> <div xml:id="echoid-div577" type="float" level="2" n="1"> <figure xlink:label="fig-310-01" xlink:href="fig-310-01a"> <image file="310-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/310-01"/> </figure> <note position="left" xlink:label="note-310-01" xlink:href="note-310-01a" xml:space="preserve">Diſtantias <lb/>polorũ Zo-<lb/>diaci à po-<lb/>lis mundi <lb/>ęquales eſſe <lb/>maximis <lb/>declinatio-<lb/>@ibus Solis.</note> </div> </div> <div xml:id="echoid-div579" type="section" level="1" n="194"> <head xml:id="echoid-head203" xml:space="preserve">VII.</head> <p> <s xml:id="echoid-s11387" xml:space="preserve"><emph style="sc">Colvrvs</emph> Aequino<unsure/> ctiorum, qui uidelicet Aequatorem ad angulos re-<lb/> <anchor type="note" xlink:label="note-310-02a" xlink:href="note-310-02"/> ctos, ac Eclipticam ad angulos obliquos ſecat, (cum per illius polos, & </s> <s xml:id="echoid-s11388" xml:space="preserve">nõ per <lb/>huius incedat) demonſtrat duo puncta ęquinoctialia, nempe principium ♈, & </s> <s xml:id="echoid-s11389" xml:space="preserve"><lb/>♎, in quibus contingunt ęquinoctia, ut dictum eſt.</s> <s xml:id="echoid-s11390" xml:space="preserve"/> </p> <div xml:id="echoid-div579" type="float" level="2" n="1"> <note position="left" xlink:label="note-310-02" xlink:href="note-310-02a" xml:space="preserve">Colurus æ-<lb/>quinoctio-<lb/>rũ indicat <lb/>duo puncta <lb/>ęquinoctia-<lb/>lia.</note> </div> <p> <s xml:id="echoid-s11391" xml:space="preserve"><emph style="sc">Caetervm</emph> Aequinoctia, & </s> <s xml:id="echoid-s11392" xml:space="preserve">Solſtitia non ſemper eodem anni tempo-<lb/>re contigerunt, ſed perpetuo ſedes ſuas mutarunt uerſus initia menſiũ in Ca-<lb/> <anchor type="note" xlink:label="note-310-03a" xlink:href="note-310-03"/> lendario. </s> <s xml:id="echoid-s11393" xml:space="preserve">Nam olim Hipparchus anno fere 145. </s> <s xml:id="echoid-s11394" xml:space="preserve">ante Chriſtum deprehendit <lb/>Vernum æquinoctiũ fieri propemodũ circa diem 23. </s> <s xml:id="echoid-s11395" xml:space="preserve">Martii:</s> <s xml:id="echoid-s11396" xml:space="preserve"><unsure/> Autumnale uero <lb/>circa diem 26. </s> <s xml:id="echoid-s11397" xml:space="preserve">Septembris fere. </s> <s xml:id="echoid-s11398" xml:space="preserve">Solſtitium autem æſtiuum incidebat tunc in <lb/>diem ſere 24. </s> <s xml:id="echoid-s11399" xml:space="preserve">Iunii; </s> <s xml:id="echoid-s11400" xml:space="preserve">& </s> <s xml:id="echoid-s11401" xml:space="preserve">Hybernum in diem 24. </s> <s xml:id="echoid-s11402" xml:space="preserve">Decembris. </s> <s xml:id="echoid-s11403" xml:space="preserve">At uero Ptolemæus <lb/>anno Domini 140. </s> <s xml:id="echoid-s11404" xml:space="preserve">æquinoctium Vernum obſeruauit fieri propemodum circa <lb/>diẽ 22. </s> <s xml:id="echoid-s11405" xml:space="preserve">Martij: </s> <s xml:id="echoid-s11406" xml:space="preserve">Autumnale uero quaſi circa diem 25. </s> <s xml:id="echoid-s11407" xml:space="preserve">Septembris. </s> <s xml:id="echoid-s11408" xml:space="preserve">Solſtitium au-<lb/>tem æſtiuum circa diem 25. </s> <s xml:id="echoid-s11409" xml:space="preserve">Iunij, & </s> <s xml:id="echoid-s11410" xml:space="preserve">Hybernum circa diem 23. </s> <s xml:id="echoid-s11411" xml:space="preserve">Decembris con <lb/>tingebat. </s> <s xml:id="echoid-s11412" xml:space="preserve">Vt vehementer mirer, quòd plerique, qui nuper de anni correctio-<lb/>ne ſcripſerunt, tam pertinaciter contendere uoluerint, æquinoctium Vernum <lb/>reducendum eſſe ad diem 25. </s> <s xml:id="echoid-s11413" xml:space="preserve">Martij, propterea quòd, ut ipſi aſſerunt, tempo-<lb/>re Chriſti, aut Iulii Cęſaris, eo die tunc contingebat. </s> <s xml:id="echoid-s11414" xml:space="preserve">Hoc enim omnino fal-<lb/>ſum eſt. </s> <s xml:id="echoid-s11415" xml:space="preserve">Quoniam enim tempore Ptolemæi æquinoctium Vernũ anticipabat <lb/>unum diem in Calendario ſpatio 322. </s> <s xml:id="echoid-s11416" xml:space="preserve">annorum, ut ipſe diligentiſſime obſer-<lb/>uauit, fit ut in annis 200. </s> <s xml:id="echoid-s11417" xml:space="preserve">qui fere inter Iuliũ Cæſarem, & </s> <s xml:id="echoid-s11418" xml:space="preserve">Ptolemæũ inciderũt, <lb/>anticiparit tantũmodo hor. </s> <s xml:id="echoid-s11419" xml:space="preserve">16. </s> <s xml:id="echoid-s11420" xml:space="preserve">nẽpe {2/3}. </s> <s xml:id="echoid-s11421" xml:space="preserve">unius diei. </s> <s xml:id="echoid-s11422" xml:space="preserve">Quare cum Ptolemęus ip <lb/>ſum deprehenderit circa diem 22. </s> <s xml:id="echoid-s11423" xml:space="preserve">Martii quodammodo, neceſſe eſt, idem tem-<lb/>pore Iulii Cęſaris cõtigiſſe non ſerius, quàm die 23. </s> <s xml:id="echoid-s11424" xml:space="preserve">Martii. </s> <s xml:id="echoid-s11425" xml:space="preserve">Quare rectius Gre <lb/>gorius XIII. </s> <s xml:id="echoid-s11426" xml:space="preserve">Pontifex Opt. </s> <s xml:id="echoid-s11427" xml:space="preserve">Max. </s> <s xml:id="echoid-s11428" xml:space="preserve">idem anno 1582. </s> <s xml:id="echoid-s11429" xml:space="preserve">reduxit ad diem 21. </s> <s xml:id="echoid-s11430" xml:space="preserve">Martii, <lb/>quo nimirum contingebat tẽpore concilii Niceni, hoc eſt, anno 325. </s> <s xml:id="echoid-s11431" xml:space="preserve">Ita enim <lb/>nihil prorſus immutandum fuit in Breuiarii, ac Miſſalibus, permanſueruntque <lb/>iidem termini paſchales, quos Sancti illi Patres in cõcilio Nicęno cõſtituerũt.</s> <s xml:id="echoid-s11432" xml:space="preserve"/> </p> <div xml:id="echoid-div580" type="float" level="2" n="2"> <note position="left" xlink:label="note-310-03" xlink:href="note-310-03a" xml:space="preserve">Aequino-<lb/>ctia & Sol <lb/>ſtitia ſedes <lb/>mutant in <lb/>Calẽdario.</note> </div> <p> <s xml:id="echoid-s11433" xml:space="preserve"><emph style="sc">Cavsa</emph> autem huius anticipationis eſt, quòd Iulius Cæſar, quem Ec- <pb o="275" file="311" n="312" rhead="Ioan. de Sacro Boſco."/> @eſia Romana eſt ſecuta, plus æquo tribuit quanticati unius auni. </s> <s xml:id="echoid-s11434" xml:space="preserve">Conſtituit <lb/> <anchor type="note" xlink:label="note-311-01a" xlink:href="note-311-01"/> enim annum Solarem dierum 365. </s> <s xml:id="echoid-s11435" xml:space="preserve">& </s> <s xml:id="echoid-s11436" xml:space="preserve">6. </s> <s xml:id="echoid-s11437" xml:space="preserve">horarũ: </s> <s xml:id="echoid-s11438" xml:space="preserve">Vnde quoniam in anno omitte <lb/>bat ſex illas horas, quæ in quatuor annis diem integrum efficiebat, decreuit, <lb/>vt quolibet quarto anno intercalaretur dies integer ex 24. </s> <s xml:id="echoid-s11439" xml:space="preserve">horis conflatus, <lb/>quem annum Biſſextum uocabat, conſtantem diebus 366. </s> <s xml:id="echoid-s11440" xml:space="preserve">Annus autem So-<lb/>laris tantus non eſt, ſed ſecundum calculum Alphonſiaorum continet dunta <lb/>xat dies 365. </s> <s xml:id="echoid-s11441" xml:space="preserve">horas 5. </s> <s xml:id="echoid-s11442" xml:space="preserve">min. </s> <s xml:id="echoid-s11443" xml:space="preserve">49. </s> <s xml:id="echoid-s11444" xml:space="preserve">Sec. </s> <s xml:id="echoid-s11445" xml:space="preserve">16. </s> <s xml:id="echoid-s11446" xml:space="preserve">ita ut annus Romanus, quo Eccleſia uti-<lb/>tur, ſuperet annum uerum iuxta calculum Alphonſi regis Hiſpaniæ, min. </s> <s xml:id="echoid-s11447" xml:space="preserve">10. <lb/></s> <s xml:id="echoid-s11448" xml:space="preserve">unius horæ & </s> <s xml:id="echoid-s11449" xml:space="preserve">ſecundis 44. </s> <s xml:id="echoid-s11450" xml:space="preserve">Hinc f<unsure/>it, ut totidem minutis, Secundisq́; </s> <s xml:id="echoid-s11451" xml:space="preserve">quolibet <lb/>anno Aequinoctia, & </s> <s xml:id="echoid-s11452" xml:space="preserve">Solſtitia anticipent ſedes ſuas, quia quando Sol ad idẽ <lb/>punctum Aequinoctij, aut Solſtitij reuertitur, deſunt ad annum Romanum <lb/>complendum dicta min. </s> <s xml:id="echoid-s11453" xml:space="preserve">10. </s> <s xml:id="echoid-s11454" xml:space="preserve">Sec. </s> <s xml:id="echoid-s11455" xml:space="preserve">44. </s> <s xml:id="echoid-s11456" xml:space="preserve">unius horæ. </s> <s xml:id="echoid-s11457" xml:space="preserve">Sequitur quoque, ut Aequino <lb/>ctia, & </s> <s xml:id="echoid-s11458" xml:space="preserve">Solſtitia in annis 400. </s> <s xml:id="echoid-s11459" xml:space="preserve">præcurrant ſedes ſuas diebus integris fere tribus. </s> <s xml:id="echoid-s11460" xml:space="preserve"><lb/>Quocirca, ne in poſterum Aequinoctia, & </s> <s xml:id="echoid-s11461" xml:space="preserve">Solſtitia amplius dies in Calenda-<lb/>rio annotatos anteuertant, neceſſarium erit, (vt Gregorius XIII. </s> <s xml:id="echoid-s11462" xml:space="preserve">ſtatuit) in an-<lb/>nis 400. </s> <s xml:id="echoid-s11463" xml:space="preserve">tres annos Biſſextos omittere, hoc eſt, tres annos, qui deberent eſſe <lb/>Biſſexti, dierum ſcilicet 366. </s> <s xml:id="echoid-s11464" xml:space="preserve">cenſere pro communibus, dierũ nimirum 365. </s> <s xml:id="echoid-s11465" xml:space="preserve">Ita <lb/>enim fiet, ut tres illi dies integri reſtituantur. </s> <s xml:id="echoid-s11466" xml:space="preserve">Quod ſi anni quãtitas ad amuſ-<lb/>ſim congrueret motui annuo Solis, nulla cerneretur anticipatio Aequino-<lb/>ctiorum, & </s> <s xml:id="echoid-s11467" xml:space="preserve">Solſtitiorũ, ſed eiſdem ſemper anni diebus recurrerent: </s> <s xml:id="echoid-s11468" xml:space="preserve">quemadmo <lb/>dum etiam uidemus feſtos dies immobiles ſtatis ſemper diebus redire. </s> <s xml:id="echoid-s11469" xml:space="preserve">Et niſi <lb/>Calendarium correctum fuiſſet, contingeret, ut in ſpatio annorum 24500. </s> <s xml:id="echoid-s11470" xml:space="preserve">Ae-<lb/>quinoctia, & </s> <s xml:id="echoid-s11471" xml:space="preserve">Solſtitia uiciſſim inter ſe permutarent ſedes, ita ut Ver incideret <lb/>in Septembrẽ, Autumnus in Martiũ, Brumale frigus in Iuniũ, & </s> <s xml:id="echoid-s11472" xml:space="preserve">æſtiui calores <lb/>in Decembrem, quando Chriſtus natus eſt: </s> <s xml:id="echoid-s11473" xml:space="preserve">In ſpatio tamen annorum 49000. </s> <s xml:id="echoid-s11474" xml:space="preserve"><lb/>ex ſententia Alphonſinorum, reſtituerentur tam Solſtitia, quam æquinoctia <lb/>ad priſtinas ſedes. </s> <s xml:id="echoid-s11475" xml:space="preserve">Hac noſtra tempeſtate, ante æquinoctij reſtitutionem ad diẽ <lb/>21. </s> <s xml:id="echoid-s11476" xml:space="preserve">Martij receſſerant Aequinoctia, & </s> <s xml:id="echoid-s11477" xml:space="preserve">Solſtitia à ſedibus antiquis tempore Iu-<lb/>lij Cæſaris notatis uerſus initia menſium per dies ferme 12. </s> <s xml:id="echoid-s11478" xml:space="preserve">Nam uernũ æqui <lb/> <anchor type="note" xlink:label="note-311-02a" xlink:href="note-311-02"/> nocti<unsure/>ũ cadebat in diẽ 11. </s> <s xml:id="echoid-s11479" xml:space="preserve">Martij, autumnale uero in diem 14. </s> <s xml:id="echoid-s11480" xml:space="preserve">Septembris: </s> <s xml:id="echoid-s11481" xml:space="preserve">Sol-<lb/>ſtitiũ autem æſtiuũ in diem 12. </s> <s xml:id="echoid-s11482" xml:space="preserve">Iunij, & </s> <s xml:id="echoid-s11483" xml:space="preserve">hybernum in diem 12. </s> <s xml:id="echoid-s11484" xml:space="preserve">Decebris: </s> <s xml:id="echoid-s11485" xml:space="preserve">Poſt <lb/>reſtitutionem uero à Gregorio X I I I. </s> <s xml:id="echoid-s11486" xml:space="preserve">factam cadunt hoc tempore æquino-<lb/>ctia in 21. </s> <s xml:id="echoid-s11487" xml:space="preserve">Martii, & </s> <s xml:id="echoid-s11488" xml:space="preserve">24. </s> <s xml:id="echoid-s11489" xml:space="preserve">Septembris: </s> <s xml:id="echoid-s11490" xml:space="preserve">Solſtitia uero in 22. </s> <s xml:id="echoid-s11491" xml:space="preserve">Iunii, & </s> <s xml:id="echoid-s11492" xml:space="preserve">Decembris.</s> <s xml:id="echoid-s11493" xml:space="preserve"/> </p> <div xml:id="echoid-div581" type="float" level="2" n="3"> <note position="right" xlink:label="note-311-01" xlink:href="note-311-01a" xml:space="preserve">Cauſa anti-<lb/>cipationis <lb/>Aequino-<lb/>rum, & Sol <lb/>ſtitiorum <lb/>in Calenda <lb/>rio.</note> <note position="right" xlink:label="note-311-02" xlink:href="note-311-02a" xml:space="preserve">Quibus die <lb/>bus æquino <lb/>ctia, & ſol-<lb/>ſt@tia cõtin <lb/>gebant an-<lb/>te Calenda <lb/>rij correctio <lb/>nem & qui <lb/>bus nunc <lb/>poſt corre-<lb/>ctionem cõ <lb/>tingant.</note> </div> <p> <s xml:id="echoid-s11494" xml:space="preserve"><emph style="sc">Qvoniam</emph> vero de diebus æquinoctiorum, ac ſolſtitiorum poſt Ca-<lb/>lendarii correctionem uerba fecimus, non abs re erit, ſi tabellam hic propo-<lb/>nam, in qua cõtineatur ingreſſus Solis in omnia ſigna Zodiaci. </s> <s xml:id="echoid-s11495" xml:space="preserve">Ad mul@a enim <lb/>r<unsure/>es hæc conducit in rebus aſtronomicis. </s> <s xml:id="echoid-s11496" xml:space="preserve">Quãuis autẽ accuratius hoc cogno-<lb/>ſci poſſit ex ephemeridibus, aut tabulis Aſtronomicis, tamen quia non ſem-<lb/>per eas in promptu habemus, ſatius eſſe iudicamus, idem rudi quadam Miner-<lb/>ua cognoſcere, quam omnino ignorare; </s> <s xml:id="echoid-s11497" xml:space="preserve">præſertim cum nullus error notabilis <lb/>inde oriatur in Mathematicorum inſtrumentis, e@iamſi non omnino ſciatur <lb/>præciſe ingreſſus Solis inſigna Zodiaci: </s> <s xml:id="echoid-s11498" xml:space="preserve">ſed uel uno die citius aliquando ponà<unsure/> <lb/>tur illa ingredi, quàm uere ingrediatur, uel uno die aliquando ſerius. </s> <s xml:id="echoid-s11499" xml:space="preserve">Nam in <lb/>uno die ſenſibiliter declinatio Solis nõ augetur, ut ex ſuperiori tabula mani-<lb/>feſtum eſt. </s> <s xml:id="echoid-s11500" xml:space="preserve">Id quod etiam de gradu, in quo Sol ponitur, intelligendum eſt. <lb/></s> <s xml:id="echoid-s11501" xml:space="preserve">Quamuis enim, Sole exiſtente in certo aliquo gradu, ponamus eũ eſſe in alio <lb/>proxime uel minori, uel maiori, nihil tamen intereſt, ob cauſam iam dictam. </s> <s xml:id="echoid-s11502" xml:space="preserve"><lb/>Ita autem tabella ſe habet.</s> <s xml:id="echoid-s11503" xml:space="preserve"/> </p> <pb o="276" file="312" n="313" rhead="Comment. in I. cap. Sphæræ"/> <note position="right" xml:space="preserve"> <lb/>###### Ingreſſus Solis in 12. ſigna Zodlaci. <lb/>♈ # ♉ # ♊ # ♋ # ♌ # ♍ <lb/>21. Ma@tij # 21. Apr<unsure/>i is # 21. Maij # 22. Iunij # 24. Iulij # 24. Auguſti <lb/>♎ # ♏ # ♐ # ♑ # ♒ # ♓ <lb/>24. Septé<unsure/>brn # 24. Octobris # 23. Nouemb. # 22. Decemb. # 21. Ianuar. # 19. Febr. <lb/></note> <p> <s xml:id="echoid-s11504" xml:space="preserve"><emph style="sc">Hinc</emph> facile inuenies, in quo gradu Zodiaci Sol quouis die plus minus <lb/> <anchor type="note" xlink:label="note-312-02a" xlink:href="note-312-02"/> reperiatur, tribuendo ſingulis diebus ſingulos gradus. </s> <s xml:id="echoid-s11505" xml:space="preserve">@Vt quoniam Sol die 24. <lb/></s> <s xml:id="echoid-s11506" xml:space="preserve">Septẽbris eſt in primo grad. </s> <s xml:id="echoid-s11507" xml:space="preserve">♎, erit die 25. </s> <s xml:id="echoid-s11508" xml:space="preserve">in gradu 2. </s> <s xml:id="echoid-s11509" xml:space="preserve">♎. </s> <s xml:id="echoid-s11510" xml:space="preserve">Die au@ẽ 30. </s> <s xml:id="echoid-s11511" xml:space="preserve">in gradu <lb/>7. </s> <s xml:id="echoid-s11512" xml:space="preserve">♎, & </s> <s xml:id="echoid-s11513" xml:space="preserve">die 9. </s> <s xml:id="echoid-s11514" xml:space="preserve">Octobris in gradu 16. </s> <s xml:id="echoid-s11515" xml:space="preserve">♎, exiſtet, & </s> <s xml:id="echoid-s11516" xml:space="preserve">ſic de cęteris. </s> <s xml:id="echoid-s11517" xml:space="preserve">Nam licet hac <lb/>ratione uno die aliquando à uero loco Solis aberremus, error tamen notabi-<lb/>lis inde non ſequetur, u<unsure/>t diximus.</s> <s xml:id="echoid-s11518" xml:space="preserve"/> </p> <div xml:id="echoid-div582" type="float" level="2" n="4"> <note position="left" xlink:label="note-312-02" xlink:href="note-312-02a" xml:space="preserve">Quomodo <lb/>@ognoſca-<lb/><gap/> quo <lb/>gradu Zo-<unsure/> <lb/>diac@ @ol <lb/>ſit quo<unsure/>uis <lb/>die.</note> </div> </div> <div xml:id="echoid-div584" type="section" level="1" n="195"> <head xml:id="echoid-head204" xml:space="preserve">VIII.</head> <p> <s xml:id="echoid-s11519" xml:space="preserve"><emph style="sc">Idem</emph> Colurus Aequin<unsure/>octiorum ſecat Eclipticam in duos Semicirculos, <lb/> <anchor type="note" xlink:label="note-312-03a" xlink:href="note-312-03"/> Borealem ſcilicet, & </s> <s xml:id="echoid-s11520" xml:space="preserve">Auſtralem. </s> <s xml:id="echoid-s11521" xml:space="preserve">De quibus ſupra.</s> <s xml:id="echoid-s11522" xml:space="preserve"/> </p> <div xml:id="echoid-div584" type="float" level="2" n="1"> <note position="left" xlink:label="note-312-03" xlink:href="note-312-03a" xml:space="preserve">G<unsure/>olurus æ-<unsure/> <lb/>quinoctio@ <lb/>r<unsure/>um parti-<lb/>@ur Eclipti-<lb/>cam in ſe-<lb/>micircu@ũ<unsure/> <lb/>borealẽ, & <lb/>auſtralem. <lb/>Meridia-<lb/>nus quid.</note> </div> </div> <div xml:id="echoid-div586" type="section" level="1" n="196"> <head xml:id="echoid-head205" style="it" xml:space="preserve">DE MERIDIANO.</head> <p style="it"> <s xml:id="echoid-s11523" xml:space="preserve"><emph style="sc">SVnt</emph> iterum duo alij circuli maiores in ſphęra, ſcili-<lb/>cet Meridianus, & </s> <s xml:id="echoid-s11524" xml:space="preserve">Horizon. </s> <s xml:id="echoid-s11525" xml:space="preserve">Eſt autem Meridianus, <lb/>circulus quidam tranſiens per polos mundi, & </s> <s xml:id="echoid-s11526" xml:space="preserve">per Ze <lb/>nith capitis noſtri. </s> <s xml:id="echoid-s11527" xml:space="preserve">Et dicitur Meridianus, quia ubi-<lb/>cunque ſit homo, & </s> <s xml:id="echoid-s11528" xml:space="preserve">in quocunque tempore anni, quan-<lb/> <anchor type="note" xlink:label="note-312-04a" xlink:href="note-312-04"/> do Sol motu firmamẽti peruenit ad ſuum Meridianum, <lb/>eſt illi meridies. </s> <s xml:id="echoid-s11529" xml:space="preserve">Conſimili ratione dicitur circulus medij diei.</s> <s xml:id="echoid-s11530" xml:space="preserve"/> </p> <div xml:id="echoid-div586" type="float" level="2" n="1"> <note position="left" xlink:label="note-312-04" xlink:href="note-312-04a" xml:space="preserve">Meridian@ <lb/>cur ſic diea <lb/>@ur, & circu <lb/>lus medij <lb/>di@i@</note> </div> </div> <div xml:id="echoid-div588" type="section" level="1" n="197"> <head xml:id="echoid-head206" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s11531" xml:space="preserve"><emph style="sc">EXplicatis</emph> quatuor circulis maioribus, qui dicuntur intrin-<lb/>ſeci, ſeu mobiles, agit nunc de reliquis duobus maioribus circu-<lb/>lis, qui extrinſeci, immobilesve appellantur, nempe de Meridiano <lb/>atq; </s> <s xml:id="echoid-s11532" xml:space="preserve">Horizonte. </s> <s xml:id="echoid-s11533" xml:space="preserve">Prius autem exponit Meridianũ circulũ, quia di-<lb/>gnior eſt, ac nobilior, tum quia eſt in medio hemiſphærio, ubi a-<lb/>f<unsure/>tra maximas habent eleuationes, & </s> <s xml:id="echoid-s11534" xml:space="preserve">uirtutes, ut mox dicemus: </s> <s xml:id="echoid-s11535" xml:space="preserve">tum quia ab hoc<unsure/> <lb/>circulo Aſtronomi dies inchoant, non autem ab Horizonte, ut uulgus eos cõ-<lb/>ſueuit inchoare. </s> <s xml:id="echoid-s11536" xml:space="preserve">Definit igitur circulum Meridianũ, dicens eũ tranſire per mũ <lb/>di polos, & </s> <s xml:id="echoid-s11537" xml:space="preserve">Zenith, ſiue uerticem capitis: </s> <s xml:id="echoid-s11538" xml:space="preserve">qualis eſt ille, qui in materiali ſphæ <lb/>ra omnibus ſupereminet, ſuſtinetq́; </s> <s xml:id="echoid-s11539" xml:space="preserve">axem mundi, circa quem reliqui uertun-<lb/>tur. </s> <s xml:id="echoid-s11540" xml:space="preserve">Deinde docet, hunc circulum uocari Meridianum à meridie, quia uideli-<lb/>cet Sol motu primi mobilis ad eum delatus quocunque anni tempore efficit <lb/>meridiem, ſiue medium diem. </s> <s xml:id="echoid-s11541" xml:space="preserve">Vnde eandem ob rationem ait, eum appellari cir <lb/>culum medij diei, quia nimirũ diuidit diẽ artificialẽ in duas partes æquales.</s> <s xml:id="echoid-s11542" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11543" xml:space="preserve"><emph style="sc">Solet</emph> etiam hic circulus ab Aſtronomis nuncupari linea medii cœli@ <lb/> <anchor type="note" xlink:label="note-312-05a" xlink:href="note-312-05"/> uel medii diei: </s> <s xml:id="echoid-s11544" xml:space="preserve">Cuſpis regalis: </s> <s xml:id="echoid-s11545" xml:space="preserve">Cardo regius: </s> <s xml:id="echoid-s11546" xml:space="preserve">principiu@ decimi domicilii cęle <lb/>ſtis: </s> <s xml:id="echoid-s11547" xml:space="preserve">medium cęli, & </s> <s xml:id="echoid-s11548" xml:space="preserve">aliis huiuſmodi nominibus. </s> <s xml:id="echoid-s11549" xml:space="preserve">Eſt autem hic circulus conci-<lb/>piendus in cęlo immobilis prorſus, & </s> <s xml:id="echoid-s11550" xml:space="preserve">ſemper fixus in eodem loco. </s> <s xml:id="echoid-s11551" xml:space="preserve">Cum enim <lb/>neceſ<unsure/>ſario tranſire debeat per uerticem illius loci, cuius Meridianus dicitu@, <pb o="277" file="313" n="314" rhead="Ioan. de Sacro Boſco."/> vertex autem non mutetur in eodẽ loco; </s> <s xml:id="echoid-s11552" xml:space="preserve">ſi aliquãtiſper moueretur, diſcederet <lb/>à locivertice, & </s> <s xml:id="echoid-s11553" xml:space="preserve">ſic nõ diuideret diẽ artificialẽ in duas partes ęquales, neq; </s> <s xml:id="echoid-s11554" xml:space="preserve">Ho <lb/>rizontẽ ad angulos rectos ſecaret: </s> <s xml:id="echoid-s11555" xml:space="preserve">quæ tamẽ omnia in Meridiano requirũ<unsure/>tur.</s> <s xml:id="echoid-s11556" xml:space="preserve"/> </p> <div xml:id="echoid-div588" type="float" level="2" n="1"> <note position="left" xlink:label="note-312-05" xlink:href="note-312-05a" xml:space="preserve">Alia nomi <lb/>@a Mer<unsure/>idia <lb/>ni.</note> </div> <p style="it"> <s xml:id="echoid-s11557" xml:space="preserve"><emph style="sc">Et</emph> notandum, quòd ciuitates, quarum una magis accedit ad orien-<lb/> <anchor type="note" xlink:label="note-313-01a" xlink:href="note-313-01"/> tem, quàm alia, habent diuerſos Meridianos.</s> <s xml:id="echoid-s11558" xml:space="preserve"/> </p> <div xml:id="echoid-div589" type="float" level="2" n="2"> <note position="right" xlink:label="note-313-01" xlink:href="note-313-01a" xml:space="preserve">Ciu itates, <lb/>quarũ una <lb/>eſt<unsure/> alia oriẽ <lb/>talior, di-<lb/>ueiſos ha-<lb/>bent Meri-<lb/>dianos.</note> </div> </div> <div xml:id="echoid-div591" type="section" level="1" n="198"> <head xml:id="echoid-head207" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s11559" xml:space="preserve"><emph style="sc">Qvoniam</emph> d@xerat, Meridianũ per Zenith, ſeu uerticẽ capitis tranſire, <lb/>ex quo efficitur, ut quemadmodum nõ omnia loca terræ eidẽ pũcto cæli ſubij <lb/>ciũtur, ita quoq; </s> <s xml:id="echoid-s11560" xml:space="preserve">nõ omnia eundẽ habere poſsint Meridianũ, docet nũc Meri-<lb/>dianos uariari in diuerſis ciuitatibus, quarum vna orientalior eſt, quã altera.</s> <s xml:id="echoid-s11561" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11562" xml:space="preserve"><emph style="sc">Hinc</emph> manifeſtum eſt, tot eſſe concipiendos Meridianos diuerſos, quot <lb/>ſunt Zenith, ſeu pũcta Verticalia in aliquo circulo parallelo ab ortu in occa-<lb/>ſum, qui tamen omnes ſeſe interſecabunt in polis mundi: </s> <s xml:id="echoid-s11563" xml:space="preserve">@Qua ratione una ea <lb/>demque ciuitas plures continebit Meridianos. </s> <s xml:id="echoid-s11564" xml:space="preserve">Locus enim quo magis fuerit <lb/>Orientalis, eo etiã Meridianum habebit magis orientalem, ſi pręciſe, @ac Geo-<lb/> <anchor type="note" xlink:label="note-313-02a" xlink:href="note-313-02"/> metrice loquamur. </s> <s xml:id="echoid-s11565" xml:space="preserve">Veruntamen ſi ſenſus iudicium conſulere uelimus, in 300. <lb/></s> <s xml:id="echoid-s11566" xml:space="preserve">fere ſtadiorum ſpatio ab ortu in occaſum, ut auctor eſt Proclus in ſphęra, quæ <lb/>eſſiciunt millaria Italica 37 {1/2}. </s> <s xml:id="echoid-s11567" xml:space="preserve">in circulo maximo, comprehenduntq́ue min. </s> <s xml:id="echoid-s11568" xml:space="preserve"><lb/>36. </s> <s xml:id="echoid-s11569" xml:space="preserve">uix ulla accidit Meridiani uariatio ſenſibilis. </s> <s xml:id="echoid-s11570" xml:space="preserve">Nam in tanto ſpatio, ait, diſcer <lb/>ni ſenſibiliter incipiunt puncta Verticalia. </s> <s xml:id="echoid-s11571" xml:space="preserve">Vnde cũ totus Aequator comprehẽ <lb/>dat min. </s> <s xml:id="echoid-s11572" xml:space="preserve">21600. </s> <s xml:id="echoid-s11573" xml:space="preserve">& </s> <s xml:id="echoid-s11574" xml:space="preserve">quilibet Meridianus per duo minuta e diametro oppoſita <lb/>incedat, erunt in toto ambitu cæli conſtituendi Meridiani 300. </s> <s xml:id="echoid-s11575" xml:space="preserve">Ita enim inter <lb/>quoſcunque duos proximos intercedent min. </s> <s xml:id="echoid-s11576" xml:space="preserve">36. </s> <s xml:id="echoid-s11577" xml:space="preserve">quæ conſtitunt millaria Ita-<lb/>lica 37 {1/2}. </s> <s xml:id="echoid-s11578" xml:space="preserve">ſiue ſtadia 300. </s> <s xml:id="echoid-s11579" xml:space="preserve">ut uult Proclus. </s> <s xml:id="echoid-s11580" xml:space="preserve">Hoc igitur modo non ſolum una <lb/>& </s> <s xml:id="echoid-s11581" xml:space="preserve">eadem ciuitas eundem habebit Meridianum, quoad iudicium ſenſus: </s> <s xml:id="echoid-s11582" xml:space="preserve">Verũ <lb/>etiam duæ ciuitates, uel etiam plures, dummodo una non ſit 36. </s> <s xml:id="echoid-s11583" xml:space="preserve">minutis ma-<lb/>gis orientalis, quàm alia.</s> <s xml:id="echoid-s11584" xml:space="preserve"/> </p> <div xml:id="echoid-div591" type="float" level="2" n="1"> <note position="right" xlink:label="note-313-02" xlink:href="note-313-02a" xml:space="preserve">Qnanto <lb/>ſpatio te@-<lb/>ræ ab ortu <lb/>in occaſum <lb/>Meridiani <lb/>@utentu@, <lb/>quoad or-<lb/>tus, & occa-<lb/>ſus ſtellarũ <lb/>Quot Me-<lb/>rldiani con-<lb/>ſtituendi <lb/>ſint, quan-<lb/>tum ad iu-<lb/>dicium ſen <lb/>ſus.</note> </div> <p> <s xml:id="echoid-s11585" xml:space="preserve"><emph style="sc">Cosmographi</emph> vero cum Ptolemęo per polos mundi, & </s> <s xml:id="echoid-s11586" xml:space="preserve">ſingulos gra <lb/> <anchor type="note" xlink:label="note-313-03a" xlink:href="note-313-03"/> dus Aequatoris Meridianos circulos deſcribunt. </s> <s xml:id="echoid-s11587" xml:space="preserve">Quo fit, ut in uniuerſum ſint <lb/>Meridiani 180. </s> <s xml:id="echoid-s11588" xml:space="preserve">quoniam quilibet tranſit per 2. </s> <s xml:id="echoid-s11589" xml:space="preserve">grad. </s> <s xml:id="echoid-s11590" xml:space="preserve">oppo@itos. </s> <s xml:id="echoid-s11591" xml:space="preserve">Primus Meri-<lb/>dianus tranſit per inſulas Fortunatas, quæ nunc Canarię dicuntur, ſuntq́ue ini <lb/>Oceano occidentali prope Africam, & </s> <s xml:id="echoid-s11592" xml:space="preserve">Luſitaniam, à quibus longitudines ciu <lb/>tatum initium ſumunt apud Coſmographos, ut paulo inexplicabitur; </s> <s xml:id="echoid-s11593" xml:space="preserve">Se-<lb/>cundus uero per primum gradum Aequatoris, qui primum Meridianum ſequi-<lb/>tur, uerſus ortum progrediendo. </s> <s xml:id="echoid-s11594" xml:space="preserve">Tertius deinde per ſecnndum gradum, & </s> <s xml:id="echoid-s11595" xml:space="preserve">cæ-<lb/> <anchor type="note" xlink:label="note-313-04a" xlink:href="note-313-04"/> teri eodem modo deinceps. </s> <s xml:id="echoid-s11596" xml:space="preserve">In globo autem Coſmographico, & </s> <s xml:id="echoid-s11597" xml:space="preserve">in deſcriptio-<lb/>nibus orbis, quæ Mappæ mundi dici ſolent, deſcribuntur à Coſmographis Me <lb/>ridiani duntaxat 12 qui totum terræ circuitum in 24. </s> <s xml:id="echoid-s11598" xml:space="preserve">partes æquales diuidũt, <lb/>eam fortaſſ<unsure/>is ob cauſam, ut inter quoslibet duos proximos intercipiantur <lb/>grad. </s> <s xml:id="echoid-s11599" xml:space="preserve">15. </s> <s xml:id="echoid-s11600" xml:space="preserve">qui efficiunt unam horam. </s> <s xml:id="echoid-s11601" xml:space="preserve">Ita enim facile cognoſcetur, quot horis vni <lb/>ciuitati citius meridies efficiatur, quam alteri. </s> <s xml:id="echoid-s11602" xml:space="preserve">Nam ſi una ciuitas ab altera re <lb/>moueatur tribus Meridianis uerſus ortum, habebit tribus horis prius meri-<lb/>diem, &</s> <s xml:id="echoid-s11603" xml:space="preserve">c.</s> <s xml:id="echoid-s11604" xml:space="preserve"/> </p> <div xml:id="echoid-div592" type="float" level="2" n="2"> <note position="right" xlink:label="note-313-03" xlink:href="note-313-03a" xml:space="preserve">Quot Meri-<lb/>diani ſint <lb/>ſecun dum <lb/>Pr<unsure/>olemæũ, <lb/>& Coſmo-<lb/>graphos, & <lb/>vnde initiũ <lb/>ſumant.</note> <note position="right" xlink:label="note-313-04" xlink:href="note-313-04a" xml:space="preserve">In glob@ <lb/>Coſmogra-<lb/>phico, & <lb/>mappis de <lb/>ſcribuntnr <lb/>Meridiani <lb/>24.</note> </div> <p style="it"> <s xml:id="echoid-s11605" xml:space="preserve"><emph style="sc">Arcvs</emph> uero Aequinoctialis interceptus inter duos Meridianos, di-<lb/> <anchor type="note" xlink:label="note-313-05a" xlink:href="note-313-05"/> citur longitudo ciuitatum. </s> <s xml:id="echoid-s11606" xml:space="preserve">Si autem duæ ciuitates eundem habeant Meridia <lb/>num, tunc æqualiter diſtant ab Oriente, & </s> <s xml:id="echoid-s11607" xml:space="preserve">Occidente.</s> <s xml:id="echoid-s11608" xml:space="preserve"/> </p> <div xml:id="echoid-div593" type="float" level="2" n="3"> <note position="right" xlink:label="note-313-05" xlink:href="note-313-05a" xml:space="preserve">@Longitudo <lb/>ciuitatum <lb/>quid.</note> </div> <pb o="278" file="314" n="315" rhead="Comment. in II. Cap. Sphæræ"/> </div> <div xml:id="echoid-div595" type="section" level="1" n="199"> <head xml:id="echoid-head208" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s11609" xml:space="preserve"><emph style="sc">Obiter</emph> explicat, occaſione ſumpta à Meridiano circulo, quid ſit ciui-<lb/>tatum longitudo, dicens eam eſſe arcũ Aequato<unsure/>ris interceptũ inter duos Me-<lb/>ridianos duarum ciuitatum. </s> <s xml:id="echoid-s11610" xml:space="preserve">Quod intelligendum eſt ſi Meridianus alter tran-<lb/>ſeat per inſulas Fortunatas, à quo longitudo ciuitatum ſumitur. </s> <s xml:id="echoid-s11611" xml:space="preserve">Nã<unsure/> arcus in <lb/>ter quoſuis duos Meridianos dicitur differentia longitudinũ. </s> <s xml:id="echoid-s11612" xml:space="preserve">De qua re paulo <lb/>poſt plura uerba faciemus. </s> <s xml:id="echoid-s11613" xml:space="preserve">Quod ſi duæ ciuitates eũdẽ obtineãt Meridianũ, di <lb/>centur ęqualiter diſtare ab oriẽte, & </s> <s xml:id="echoid-s11614" xml:space="preserve">occidẽte, eandẽq́; </s> <s xml:id="echoid-s11615" xml:space="preserve">habere longitudinẽ.</s> <s xml:id="echoid-s11616" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div596" type="section" level="1" n="200"> <head xml:id="echoid-head209" xml:space="preserve">OFFICIA MERIDIANI.</head> <head xml:id="echoid-head210" xml:space="preserve">I.</head> <p> <s xml:id="echoid-s11617" xml:space="preserve"><emph style="sc">Meridianvs</emph> circulus determinat tempus ſemidiurnum, & </s> <s xml:id="echoid-s11618" xml:space="preserve">ſemi-<lb/> <anchor type="note" xlink:label="note-314-01a" xlink:href="note-314-01"/> nocturnum diei, noctisq́ artificialis, oſtendendo puncta meridiei, ac mediæ no <lb/>ctis. </s> <s xml:id="echoid-s11619" xml:space="preserve">Diuidit enim Meridianus dies, & </s> <s xml:id="echoid-s11620" xml:space="preserve">noctes in ſpatia æqualia, diem quemcun <lb/>que in tempus antemeridianum, ſeu matutiuum, & </s> <s xml:id="echoid-s11621" xml:space="preserve">in pomeridianum, ſiue ue <lb/>ſpertinum; </s> <s xml:id="echoid-s11622" xml:space="preserve">Noctem quoq. </s> <s xml:id="echoid-s11623" xml:space="preserve">in horas, quæ mediam noctem antecedũt, & </s> <s xml:id="echoid-s11624" xml:space="preserve">in eas, <lb/>quæ conſequuntur.</s> <s xml:id="echoid-s11625" xml:space="preserve"/> </p> <div xml:id="echoid-div596" type="float" level="2" n="1"> <note position="left" xlink:label="note-314-01" xlink:href="note-314-01a" xml:space="preserve">Meri dian@ <lb/>determi<unsure/>nat <lb/>@e<unsure/>mo<unsure/>us ſe-<lb/>mid@rn ũ. <lb/>& ſemino-<lb/>cturnum.</note> </div> </div> <div xml:id="echoid-div598" type="section" level="1" n="201"> <head xml:id="echoid-head211" xml:space="preserve">II.</head> <note position="left" xml:space="preserve">Aſ<unsure/>tra in <lb/>Meridiano <lb/>maximas <lb/>habent al-<lb/>titudines, <lb/>& uires.</note> <p> <s xml:id="echoid-s11626" xml:space="preserve"><emph style="sc">In</emph> eo omnia aſtra maximam, quam habere poſſunt, altitudinẽ ſiue eleua-<lb/>tionem ſupra Horizontem ſortiuntur, habentq́<unsure/>. </s> <s xml:id="echoid-s11627" xml:space="preserve">intenſiſsimum uigorẽ, ac po-<lb/>tentiam, cum in eo conſtituta agãt in hæc inſeri<unsure/>ora per lineas, quæ magis re-<lb/>ctos, ſiue minus obliquos angulos e<unsure/>fficiunt@ut experimur luce clarius in Sole, <lb/>qui in Meridiano circulo poſitus ue hemẽtius inferiora hæc calefacit, ac deſie <lb/>cat, vaporesq́ue conſumit, quam in ulla alia cæli parte,</s> </p> </div> <div xml:id="echoid-div599" type="section" level="1" n="202"> <head xml:id="echoid-head212" xml:space="preserve">III.</head> <note position="left" xml:space="preserve">Meridianus <lb/>metitur a-<lb/>ſtrorum di-<lb/>ſtantias à <lb/>uertice ca-<lb/>pitis, & pa <lb/>rellelorum <lb/>inter ſe.</note> <p> <s xml:id="echoid-s11628" xml:space="preserve"><emph style="sc">In</emph> eodem collocatur Zenith, ſeu uertex cuiuſque regionis, à quo facile per <lb/>Meridianum metiemur aſtrorum diſtantias, quando in Meridiano conſt<unsure/>itut<unsure/>a <lb/>fuerint: </s> <s xml:id="echoid-s11629" xml:space="preserve">Eodemq́ue modo menſurabimus interualla omnium circulorum pa-<lb/>rallelorum & </s> <s xml:id="echoid-s11630" xml:space="preserve">à noſtro uertice, & </s> <s xml:id="echoid-s11631" xml:space="preserve">inter ſeſe.</s> <s xml:id="echoid-s11632" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div600" type="section" level="1" n="203"> <head xml:id="echoid-head213" xml:space="preserve">IIII.</head> <p> <s xml:id="echoid-s11633" xml:space="preserve"><emph style="sc">Indicat</emph> nobis, quanta ſit Solis, aliorumque ſiderum altitudo meri-<lb/>diana, quam habẽt in Meridiano circulo poſita, cuius maximus eſt uſus apud <lb/> <anchor type="note" xlink:label="note-314-04a" xlink:href="note-314-04"/> Aſtronomos. </s> <s xml:id="echoid-s11634" xml:space="preserve">Eſt enim altitudo ſtellæ cuiusſlibet meridiana, arcus Meridiani <lb/>circuli interceptus inter Horizontem & </s> <s xml:id="echoid-s11635" xml:space="preserve">ſtellam in Meridiano circulo cõſtitu <lb/>tam, dummodo arcus ille Quadrantem non ſuperet, ſed uel ſit præciſe Qua-<lb/>drans, ut ſi ſtella in uertice capitis conſtiterit, uel certe Quadrante mi<unsure/>nor, ut <lb/>dum ſtella inter Horizontem, & </s> <s xml:id="echoid-s11636" xml:space="preserve">uerticem fuerit inferiecta.</s> <s xml:id="echoid-s11637" xml:space="preserve"/> </p> <div xml:id="echoid-div600" type="float" level="2" n="1"> <note position="left" xlink:label="note-314-04" xlink:href="note-314-04a" xml:space="preserve">Altitudo <lb/>meridiana <lb/>ſtellarum <lb/>quid, & quo <lb/>pacto, eam <lb/>Meridian@ <lb/>metiatur.</note> </div> </div> <div xml:id="echoid-div602" type="section" level="1" n="204"> <head xml:id="echoid-head214" xml:space="preserve">V.</head> <p> <s xml:id="echoid-s11638" xml:space="preserve"><emph style="sc">Astronomi</emph> initium diei naturalis, quæ eſt integra Solis reuolu-<lb/> <anchor type="note" xlink:label="note-314-05a" xlink:href="note-314-05"/> tio, ſtatuunt in circulo Meridiano, & </s> <s xml:id="echoid-s11639" xml:space="preserve">non cũ vulgo in Horizonte. </s> <s xml:id="echoid-s11640" xml:space="preserve">Varia enim <lb/>fuerunt diei initia apud varias gentes, nationesque. </s> <s xml:id="echoid-s11641" xml:space="preserve">B@bilonu namque, quos <lb/>nunc imitantur Inſulæ Baleares, quæ dicuntur Maiorica & </s> <s xml:id="echoid-s11642" xml:space="preserve">Minorica, diem <lb/>inchoabant ab ortu Solis ad alterum ortum: </s> <s xml:id="echoid-s11643" xml:space="preserve">Atheni<unsure/>enſes, quos Adhuc Itali <lb/>omnes ſequuntur, diem numerabant ab occaſu Solis ad alte@um occaſum: <lb/></s> <s xml:id="echoid-s11644" xml:space="preserve">Aegyptij, & </s> <s xml:id="echoid-s11645" xml:space="preserve">Sacerdotes Romani à media nocte in alteram mediam noctẽ, quæ <lb/> <anchor type="note" xlink:label="note-314-06a" xlink:href="note-314-06"/> coniuetudo adhuc in Eccleſia Romana permanſit: </s> <s xml:id="echoid-s11646" xml:space="preserve">Vulgus diem computat ab <lb/>ortu Solis ad eius occaſum. </s> <s xml:id="echoid-s11647" xml:space="preserve">Aſtronomi deni<unsure/>que à meridie ad alterum meridiẽ <lb/>diem computant@ Maluerunt autem Aſtronomi à Meridiano circulo diem in-<lb/>choare, quam ab Horizo nte, quoniã, ut in tertio cap. </s> <s xml:id="echoid-s11648" xml:space="preserve">docebimus, Sol & </s> <s xml:id="echoid-s11649" xml:space="preserve">aſtra <pb o="279" file="315" n="316" rhead="Ioan. de Sacro Boſco."/> eodem ſemper modo ſe habent re@pectu Meridiani in omni regione; </s> <s xml:id="echoid-s11650" xml:space="preserve">non au-<lb/> <anchor type="note" xlink:label="note-315-01a" xlink:href="note-315-01"/> tem reſpectu Horizõtis, qui nimirũ in modum uariatur ratione maioris, & </s> <s xml:id="echoid-s11651" xml:space="preserve">mi <lb/>n<unsure/>oris eleuationis poli ſupra Horizontem. </s> <s xml:id="echoid-s11652" xml:space="preserve">Vnde ualde inæquales redd untur <lb/>dies naturales, ut ſuo loco dicetur.</s> <s xml:id="echoid-s11653" xml:space="preserve"/> </p> <div xml:id="echoid-div602" type="float" level="2" n="1"> <note position="left" xlink:label="note-314-05" xlink:href="note-314-05a" xml:space="preserve">Meridianus <lb/>determinat <lb/>principium <lb/>diei apud <lb/>Aſtro no-<lb/>mos.</note> <note position="left" xlink:label="note-314-06" xlink:href="note-314-06a" xml:space="preserve">Variainitia <lb/>die<unsure/>i apudva <lb/>@ias gen@es.</note> <note position="right" xlink:label="note-315-01" xlink:href="note-315-01a" xml:space="preserve">Aſtron<unsure/>om@ <lb/>cur à Me@i<unsure/> <lb/>diano po-<lb/>tius diẽ @@ <lb/>choent, quã <lb/>ab Horizon<unsure/> <lb/>te.</note> </div> </div> <div xml:id="echoid-div604" type="section" level="1" n="205"> <head xml:id="echoid-head215" xml:space="preserve">VI.</head> <p> <s xml:id="echoid-s11654" xml:space="preserve"><emph style="sc">Inventa</emph>, beneficio Meridiani circuli, altitudine Solis meridiana, depre-<lb/> <anchor type="note" xlink:label="note-315-02a" xlink:href="note-315-02"/> henditur facillime poli eleuatio in quacunq. </s> <s xml:id="echoid-s11655" xml:space="preserve">regione, & </s> <s xml:id="echoid-s11656" xml:space="preserve">ſphæræ hab@tudo, ſi-<lb/>ue poſitio, ſine qua uix ulla obſeruatio Aſtronomorũ alicuius eſt momenti. <lb/></s> <s xml:id="echoid-s11657" xml:space="preserve">Cum enim à Zenith, ſeu uertice cuiuslibet regionis ad Horizontem interij-<lb/>ciatur Quadr<unsure/>ans circuli, hoc eſt 90. </s> <s xml:id="echoid-s11658" xml:space="preserve">grad. </s> <s xml:id="echoid-s11659" xml:space="preserve">ſi Sole exiſtente in alterutro puncto-<lb/>rum ęquinoctialium, altitudinẽ meridianam ipſius ex 90. </s> <s xml:id="echoid-s11660" xml:space="preserve">grad. </s> <s xml:id="echoid-s11661" xml:space="preserve">auferamus, relin <lb/>quetur diſtantia inter Zenith, & </s> <s xml:id="echoid-s11662" xml:space="preserve">Aequinoctialem circulũ: </s> <s xml:id="echoid-s11663" xml:space="preserve">At hæc diſtantia, <lb/>ut paulo infra demonſtrabimus ex auctore, quando de Hotizonte aget, æqua-<lb/>l<unsure/>is eſt eleuationi poli, ideſt, arcui Meridiani circuli inter polum mundi eleua@ <lb/>tum, & </s> <s xml:id="echoid-s11664" xml:space="preserve">Horizontẽ interpoſito. </s> <s xml:id="echoid-s11665" xml:space="preserve">@gitur conſtabit eleuatio poli ex altitudine me <lb/>ridiana Solis nota rempore æquinoctiorum. </s> <s xml:id="echoid-s11666" xml:space="preserve"><emph style="sc">Exemplvn</emph>. </s> <s xml:id="echoid-s11667" xml:space="preserve">Romæ tempore ęqui-<lb/>noctiorum Solis altitudo meridiana deprehenditur eſſe ferme grad. </s> <s xml:id="echoid-s11668" xml:space="preserve">48. </s> <s xml:id="echoid-s11669" xml:space="preserve">qua <lb/>ablata ex Quadrante, ſuperſunt 42. </s> <s xml:id="echoid-s11670" xml:space="preserve">fere grad. </s> <s xml:id="echoid-s11671" xml:space="preserve">Tanta igitur erit diſtantia uerti-<lb/> <anchor type="note" xlink:label="note-315-03a" xlink:href="note-315-03"/> cis, ſeu Zenith Romani ab Aequatore, ſeu eleuatio poli Romæ.</s> <s xml:id="echoid-s11672" xml:space="preserve"/> </p> <div xml:id="echoid-div604" type="float" level="2" n="1"> <note position="right" xlink:label="note-315-02" xlink:href="note-315-02a" xml:space="preserve">Meridiani <lb/>circuli be-<lb/>neſicio in@ <lb/>uenitur al-<lb/>titudo po-<lb/>li, tempore <lb/>ęquinoctij.</note> <note position="right" xlink:label="note-315-03" xlink:href="note-315-03a" xml:space="preserve">Altitudo <lb/>meridiana <lb/>Solis, uel <lb/>alia quæcũ <lb/>que quo p@ <lb/>cto depre-<lb/>hendatur.</note> </div> <p> <s xml:id="echoid-s11673" xml:space="preserve"><emph style="sc">Dvobvs</emph> autem modis obtineri poteſt altitudo Solis meridiana, immo <lb/>quæcunque altitudo etiam citra, uel ultra meridiem. </s> <s xml:id="echoid-s11674" xml:space="preserve">Vno modo uſitatiſſimo <lb/>& </s> <s xml:id="echoid-s11675" xml:space="preserve">facillimo per aliquod inſtru mentum Mathematicum, quale eſt Aſtrolabiũ, <lb/>Quadrans, Annulus, &</s> <s xml:id="echoid-s11676" xml:space="preserve">c. </s> <s xml:id="echoid-s11677" xml:space="preserve">Alio modo, ſed difficiliori, & </s> <s xml:id="echoid-s11678" xml:space="preserve">certiori, per umbram <lb/>alicuius gnominis, ſiue ſtyli, qui rectus inſiſtat Horizonti. </s> <s xml:id="echoid-s11679" xml:space="preserve">Si enim quocunque <lb/>tempore, ut v. </s> <s xml:id="echoid-s11680" xml:space="preserve">g in meridie, umbra gnominis æqualis fuerit ipſi gnomoni, (ut <lb/>accidit Venetijs, Mediolani, ac Lugduni in meridie tempore ęquinoctiorum) <lb/>erit altitudo Solis ad amuſſim 45. </s> <s xml:id="echoid-s11681" xml:space="preserve">grad. </s> <s xml:id="echoid-s11682" xml:space="preserve">vt in noſtro Aſtrolabio, & </s> <s xml:id="echoid-s11683" xml:space="preserve">Quadrato <lb/>Geometrico demonſtrauimus. </s> <s xml:id="echoid-s11684" xml:space="preserve">Si uero umbra maior fuerit ipſo gnomone, (ut <lb/>contingit in Germania, & </s> <s xml:id="echoid-s11685" xml:space="preserve">alijs partibus Septent@ionalioribus, quàm 45. </s> <s xml:id="echoid-s11686" xml:space="preserve">grad. <lb/></s> <s xml:id="echoid-s11687" xml:space="preserve">tempore æquinoctiorum in meridie) erit alt<unsure/>itudo Solis minor, quã 45. </s> <s xml:id="echoid-s11688" xml:space="preserve">grad. </s> <s xml:id="echoid-s11689" xml:space="preserve"><lb/>Si denique umbra ſuerit minor ipſo gnomone, (ut fit Romæ, & </s> <s xml:id="echoid-s11690" xml:space="preserve">alijs parti<unsure/>bus, <lb/>quæ minus Septentrionales ſunt, quàm 45. </s> <s xml:id="echoid-s11691" xml:space="preserve">grad. </s> <s xml:id="echoid-s11692" xml:space="preserve">in meridie tempore æquino-<lb/>ctij) erit altitudo Solis maior, quam 45. </s> <s xml:id="echoid-s11693" xml:space="preserve">grad. </s> <s xml:id="echoid-s11694" xml:space="preserve">Quo modo autem ex umbra no-<lb/>ta, & </s> <s xml:id="echoid-s11695" xml:space="preserve">gnomone, meridiana altitudo Solis eliciatur, alibi demonſtrauimus: </s> <s xml:id="echoid-s11696" xml:space="preserve">Nũc <lb/>contenti erimus ſimplici præcepto, atq. </s> <s xml:id="echoid-s11697" xml:space="preserve">exemplo. </s> <s xml:id="echoid-s11698" xml:space="preserve">Apud Montem regiũ Pruſ-<lb/>ſiæ ęquinoctij tẽpore deprehenſa eſt umbra partium 16. </s> <s xml:id="echoid-s11699" xml:space="preserve">qualium gnomon eſt <lb/>1@. </s> <s xml:id="echoid-s11700" xml:space="preserve">Quadratũ vmbrę, @t 256. </s> <s xml:id="echoid-s11701" xml:space="preserve">adiungo ad quadratũ gnomonis, nẽpe ad 144. </s> <s xml:id="echoid-s11702" xml:space="preserve">& </s> <s xml:id="echoid-s11703" xml:space="preserve">ef <lb/>ficio 40. </s> <s xml:id="echoid-s11704" xml:space="preserve">Per huius numeri radicem quadratã, uidelicet, per 20 diuido produ-<lb/>ctũ ex gnomone, nimirũ ex 12. </s> <s xml:id="echoid-s11705" xml:space="preserve">in ſinũ totũ ſcilicet in 100000. </s> <s xml:id="echoid-s11706" xml:space="preserve">qđ eſt 1200000. </s> <s xml:id="echoid-s11707" xml:space="preserve"><lb/>proueniuntq́; </s> <s xml:id="echoid-s11708" xml:space="preserve">60000. </s> <s xml:id="echoid-s11709" xml:space="preserve">pro ſinu altitudinis Solis, cui reſpondent grad. </s> <s xml:id="echoid-s11710" xml:space="preserve">37. </s> <s xml:id="echoid-s11711" xml:space="preserve">fere; </s> <s xml:id="echoid-s11712" xml:space="preserve"><lb/>quibus ablatis ex 90. </s> <s xml:id="echoid-s11713" xml:space="preserve">grad remanebit altitudo poli in dicta ciuitate ferme <lb/>grad. </s> <s xml:id="echoid-s11714" xml:space="preserve">53.</s> <s xml:id="echoid-s11715" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11716" xml:space="preserve"><emph style="sc">Caetervm</emph> hac ratione ſolum tempore æquinoctij ex umbra Solis <lb/> <anchor type="note" xlink:label="note-315-04a" xlink:href="note-315-04"/> meridiana, altitudo poli inuenitur; </s> <s xml:id="echoid-s11717" xml:space="preserve">Tunc enim ſolum detracta altitudine meri <lb/>diana Solis à Quadrante, ideſt, à 90. </s> <s xml:id="echoid-s11718" xml:space="preserve">grad. </s> <s xml:id="echoid-s11719" xml:space="preserve">relinquitur diſtantia Zenith ab Ae <lb/>qualore, quæ quidem æqualis eſt eleuationi poli. </s> <s xml:id="echoid-s11720" xml:space="preserve">Quod ſi quouis tempore an-<lb/>ni, atq. </s> <s xml:id="echoid-s11721" xml:space="preserve">die ex altitudine Solis meridiana eleuationem poli placuerit inue<unsure/>ſti@ <lb/>gare, neceſſe eſt ex Ephemeridibus, aut aliũde, accurate perdiſcere locum So- <pb o="280" file="316" n="317" rhead="Comment. in II. Cap. Sphæræ"/> lis in Ecliptica ad diem propoſitum, eiusq́. </s> <s xml:id="echoid-s11722" xml:space="preserve">declinationẽ ex tabula ſuprap oſita. <lb/></s> <s xml:id="echoid-s11723" xml:space="preserve">Nám Solis declinatio, ſi fuerit Borealis, vt quando Sol in ſignis Borealibus <lb/>♈, ♉, ♊, ♋, ♌, & </s> <s xml:id="echoid-s11724" xml:space="preserve">♍, exiſtit, detrahenda erit ab altitudine meridiana Solis, <lb/>vt habeatur altitudo A equatoris, ſeu@ (quod idẽ eſt) altitudo meridiana Solis, <lb/>quam haberet in æquinoctijs: </s> <s xml:id="echoid-s11725" xml:space="preserve">Hac enim dempta ex 90. </s> <s xml:id="echoid-s11726" xml:space="preserve">grad. </s> <s xml:id="echoid-s11727" xml:space="preserve">relinquetur eleuæ <lb/>tio poli. </s> <s xml:id="echoid-s11728" xml:space="preserve">Vt Romæ anno M D L X I X. </s> <s xml:id="echoid-s11729" xml:space="preserve">& </s> <s xml:id="echoid-s11730" xml:space="preserve">die XX. </s> <s xml:id="echoid-s11731" xml:space="preserve">Iulij, exiſtente Sole in grad. </s> <s xml:id="echoid-s11732" xml:space="preserve"><lb/>6. </s> <s xml:id="echoid-s11733" xml:space="preserve">min. </s> <s xml:id="echoid-s11734" xml:space="preserve">40. </s> <s xml:id="echoid-s11735" xml:space="preserve">♌, quæ quidem declinant in Boream ab Aequatore grad. </s> <s xml:id="echoid-s11736" xml:space="preserve">18. </s> <s xml:id="echoid-s11737" xml:space="preserve">min. </s> <s xml:id="echoid-s11738" xml:space="preserve"><lb/>39. </s> <s xml:id="echoid-s11739" xml:space="preserve">ut ex tabula declinationum cõ@tat; </s> <s xml:id="echoid-s11740" xml:space="preserve">inueni in meridie altitudinem Solis cõ <lb/>tinere grad. </s> <s xml:id="echoid-s11741" xml:space="preserve">66. </s> <s xml:id="echoid-s11742" xml:space="preserve">min. </s> <s xml:id="echoid-s11743" xml:space="preserve">39. </s> <s xml:id="echoid-s11744" xml:space="preserve">De traho ex hac declinationem, nempe gr. </s> <s xml:id="echoid-s11745" xml:space="preserve">18. </s> <s xml:id="echoid-s11746" xml:space="preserve">min. </s> <s xml:id="echoid-s11747" xml:space="preserve">39. </s> <s xml:id="echoid-s11748" xml:space="preserve"><lb/>remanent 48. </s> <s xml:id="echoid-s11749" xml:space="preserve">gr. </s> <s xml:id="echoid-s11750" xml:space="preserve">pro altitudine Aequatoris, qua ablata ex 90. </s> <s xml:id="echoid-s11751" xml:space="preserve">grad. </s> <s xml:id="echoid-s11752" xml:space="preserve">relinquitur <lb/>altitudo poli gr. </s> <s xml:id="echoid-s11753" xml:space="preserve">42. </s> <s xml:id="echoid-s11754" xml:space="preserve">Si vero declinatio Solis fuerit Auſtralis, ut quando Sol <lb/>ſigna Auſtralia ♎, ♏, ♐, ♑, ♒, & </s> <s xml:id="echoid-s11755" xml:space="preserve">♓, percurrit, eritea adijcienda altitudini <lb/>Solis meridianæ, ut inueniatur altitudo Aequatoris; </s> <s xml:id="echoid-s11756" xml:space="preserve">Nam hac ablata ex 90. </s> <s xml:id="echoid-s11757" xml:space="preserve"><lb/>grad. </s> <s xml:id="echoid-s11758" xml:space="preserve">remanebit eleuatio poli, ut prius. </s> <s xml:id="echoid-s11759" xml:space="preserve">Vt Romæ eadem anno M D L X I X. </s> <s xml:id="echoid-s11760" xml:space="preserve">ac <lb/>die XXI. </s> <s xml:id="echoid-s11761" xml:space="preserve">Nouembris, Sole commorante in grad. </s> <s xml:id="echoid-s11762" xml:space="preserve">9. </s> <s xml:id="echoid-s11763" xml:space="preserve">& </s> <s xml:id="echoid-s11764" xml:space="preserve">min. </s> <s xml:id="echoid-s11765" xml:space="preserve">20. </s> <s xml:id="echoid-s11766" xml:space="preserve">♐, quæ diſcedunt <lb/>ab Aequatore in Auſtrum, ut docet tabula declinationum, gr. </s> <s xml:id="echoid-s11767" xml:space="preserve">21. </s> <s xml:id="echoid-s11768" xml:space="preserve">min. </s> <s xml:id="echoid-s11769" xml:space="preserve">54. </s> <s xml:id="echoid-s11770" xml:space="preserve">de-<lb/>prehendi altitudinem Solis meridianam grad. </s> <s xml:id="echoid-s11771" xml:space="preserve">26. </s> <s xml:id="echoid-s11772" xml:space="preserve">min. </s> <s xml:id="echoid-s11773" xml:space="preserve">6. </s> <s xml:id="echoid-s11774" xml:space="preserve">cui ſi addatur declinæ <lb/>tio, puta grad. </s> <s xml:id="echoid-s11775" xml:space="preserve">21. </s> <s xml:id="echoid-s11776" xml:space="preserve">min. </s> <s xml:id="echoid-s11777" xml:space="preserve">54. </s> <s xml:id="echoid-s11778" xml:space="preserve">colligetur altitudo Aequatoris grad. </s> <s xml:id="echoid-s11779" xml:space="preserve">48. </s> <s xml:id="echoid-s11780" xml:space="preserve">ex qua iterũ <lb/>inuenitur ele@a tio poli 42. </s> <s xml:id="echoid-s11781" xml:space="preserve">grad. </s> <s xml:id="echoid-s11782" xml:space="preserve">Aliam rationem inueniendæ altitudinis poli <lb/>ex Analemmate quolibet die, etiamſi declinatio Solis ignota ſit, tradidi in ſe-<lb/>cundo ſcholio. </s> <s xml:id="echoid-s11783" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s11784" xml:space="preserve">28. </s> <s xml:id="echoid-s11785" xml:space="preserve">lib. </s> <s xml:id="echoid-s11786" xml:space="preserve">1. </s> <s xml:id="echoid-s11787" xml:space="preserve">Gnomonices.</s> <s xml:id="echoid-s11788" xml:space="preserve"/> </p> <div xml:id="echoid-div605" type="float" level="2" n="2"> <note position="right" xlink:label="note-315-04" xlink:href="note-315-04a" xml:space="preserve">Inuentio <lb/>altitudinis <lb/>poli ex alti <lb/>tu dine me-<lb/>ridiana So-<lb/>lis extra rẽ <lb/>pus ęquino <lb/>ctij.</note> </div> <p> <s xml:id="echoid-s11789" xml:space="preserve"><emph style="sc">Qvoniam</emph> vero, ut recte inueniatur altitudo poli, præciſe in puncto <lb/> <anchor type="note" xlink:label="note-316-01a" xlink:href="note-316-01"/> meridiei accipienda eſt altitudo Solis, quòd tum demum fiet, cum umbra <lb/>gnomonis præciſe in lineam meridianam proijcietur, nõ abs re fuerit, paucis <lb/>indicare, qua arte linea meridiana indagari debeat: </s> <s xml:id="echoid-s11790" xml:space="preserve">quoniam ad multas obſer-<lb/>uationes Aſtronomorum neceſſaria eſt. </s> <s xml:id="echoid-s11791" xml:space="preserve">In plano igitur ad libellam cõſtructo, <lb/>quod nimirum Horizonti ſit parallelum, deſcribantur plurimi circuli ex eo-<lb/>dem cẽtro E, in quo erigatur ſtylus, ſeu gnomon E F, ad angulos rectos, quod <lb/>tum fiet, quando eius cacumen F, æqualiter remotum fuerit à circunferentia <lb/>cuiuslibet circuli in plano propoſito ex centro E, deſcripti. </s> <s xml:id="echoid-s11792" xml:space="preserve">Erit aurem æqua-<lb/>liter remotũ, ſi à tribus ſaltem punctis circumferentiæ æqualiter diſtiterit, ut <lb/>lib. </s> <s xml:id="echoid-s11793" xml:space="preserve">4. </s> <s xml:id="echoid-s11794" xml:space="preserve">Gnomonices propoſ. </s> <s xml:id="echoid-s11795" xml:space="preserve">12. </s> <s xml:id="echoid-s11796" xml:space="preserve">demonſtrauimus. </s> <s xml:id="echoid-s11797" xml:space="preserve">Deinde ante meridiem obſer-<lb/>uetur extremitas umbræ, donec ad amuſſim circumferentiam alicuius circuli <lb/>tãgat, qualis eſt umbra E G, cuius extremitas præciſe in circumferentiam ter-<lb/>tij circuli cadit. </s> <s xml:id="echoid-s11798" xml:space="preserve">Rurſus poſt meridiem notetur umbræ extremitas, donec in <lb/>circumferentiam eiuſdem circuli cadat præciſe, cuiuſmodi eſt umbra E H. <lb/></s> <s xml:id="echoid-s11799" xml:space="preserve">Vt autem ſcias, qua hora poſt meridiem umbræ extremitas circumferentiam <lb/>eiuſdem circuli @angere poſſit, (ne fruſtra ad Solem accedas) obſeruandæ <lb/>erunttot horæ poſt meridiem, quot horis ante meridiem umbram notaſti. </s> <s xml:id="echoid-s11800" xml:space="preserve">Nã <lb/>@i v. </s> <s xml:id="echoid-s11801" xml:space="preserve">g. </s> <s xml:id="echoid-s11802" xml:space="preserve">tertia hora ante meridiem extremitas umbræ tang it pręciſe circunferẽ-<lb/>tiã alicuius circuli, neceſſe eſt, ut tertia hora poſt meridiem eiuſdem circuli <lb/>circumferentiã contingat umbræ extremitas. </s> <s xml:id="echoid-s11803" xml:space="preserve">Quod quidẽ multo certius ſcies <lb/>hac ratione. </s> <s xml:id="echoid-s11804" xml:space="preserve">Quãdo umbræ extremum cadit ante meridiẽ præciſe in circum-<lb/>ferentiam alicuius circuli, inueſtigetur aliquo inſtrumento altitudo Solis@ quę <lb/>diligenter notata, quando poſt meridiem eandem Sol obtinebit altitudinem, <lb/>certiſſime tibi perſuadeas, tunc umbrã extremã eiuſdem circuli circumferen-<lb/>tiam attingere: </s> <s xml:id="echoid-s11805" xml:space="preserve">Quoniam eadem proportione poſt meridiem altitudo Solis di <lb/>minuitur, qua accreſcit ante meridiẽ, & </s> <s xml:id="echoid-s11806" xml:space="preserve">idcirco qua proportione umbra gn@- <pb o="281" file="317" n="318" rhead="Ioan. de Sacro Boſco."/> <anchor type="figure" xlink:label="fig-317-01a" xlink:href="fig-317-01"/> monis ante meridiem decreſcit, eadem poſt meridiem augeatur, neceſſe eſt, <lb/>vt facile demonſtrari poteſt ex ſphæricis elementis. </s> <s xml:id="echoid-s11807" xml:space="preserve">His itaque duobus pũctis <lb/>G, & </s> <s xml:id="echoid-s11808" xml:space="preserve">H, quorum illud eodem interuallo ante meridiem, quo hoc poſt meri-<lb/>diem diſtat, ſumma diligentia habitis, diuidendus erit arcus GH, bifariã linea <lb/>recta B D, quæ per centrum E, extenditur. </s> <s xml:id="echoid-s11809" xml:space="preserve">Hæc enim linea erit meridiana, in <lb/>quam ſi umbra ſtyli proijciatur, meridiem inſtare dubium non eſt. </s> <s xml:id="echoid-s11810" xml:space="preserve">Erit igitur <lb/>recta B D, communis ſectio Horizontis, & </s> <s xml:id="echoid-s11811" xml:space="preserve">meridiani circuli. </s> <s xml:id="echoid-s11812" xml:space="preserve">Quod ſi hanc <lb/>ad angulos rectos ſe cuerimus linea recta A C, indicabit punctum A, punctum <lb/>ortus tempore æquinoctij, punctum vero C, puuctum occaſus, ut ſi recta A C, <lb/>communis ſectio Horizontis, & </s> <s xml:id="echoid-s11813" xml:space="preserve">Verticalis proprie dicti. </s> <s xml:id="echoid-s11814" xml:space="preserve">Sunt quidem multæ <lb/>aliæ rationes non minus certæ ad inueniendam lineam meridianam, qualis eſt <lb/>illa, quam ex Analemmate tradidi in ſcholio propoſ. </s> <s xml:id="echoid-s11815" xml:space="preserve">23. </s> <s xml:id="echoid-s11816" xml:space="preserve">lib. </s> <s xml:id="echoid-s11817" xml:space="preserve">1. </s> <s xml:id="echoid-s11818" xml:space="preserve">Gnomonices, <lb/>quæ omnium, meo iudicio, certiſſima eſt; </s> <s xml:id="echoid-s11819" xml:space="preserve">ſed hæc, quam explicaui, multo expe <lb/>ditior eſt cæteris omnibus, & </s> <s xml:id="echoid-s11820" xml:space="preserve">ab Aſtronomis magis vſurpata.</s> <s xml:id="echoid-s11821" xml:space="preserve"/> </p> <div xml:id="echoid-div606" type="float" level="2" n="3"> <note position="left" xlink:label="note-316-01" xlink:href="note-316-01a" xml:space="preserve">Meridiana <lb/>linea, qua <lb/>arte inue <lb/>niat@r.</note> <figure xlink:label="fig-317-01" xlink:href="fig-317-01a"> <image file="317-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/317-01"/> </figure> </div> <p> <s xml:id="echoid-s11822" xml:space="preserve"><emph style="sc">Inventa</emph> autem tanto labore ſemel linea meridiana in dicto plano, <lb/>reperiemus ſumma facilitate alias innumeras lineas meridianas in alijs planis <lb/> <anchor type="note" xlink:label="note-317-01a" xlink:href="note-317-01"/> hoc modo. </s> <s xml:id="echoid-s11823" xml:space="preserve">Obſeruetur tempus meridiei, hoc eſt, quando umbra gnomonis in <lb/>lineam metidianam iam inuentã incidit præciſe; </s> <s xml:id="echoid-s11824" xml:space="preserve">Si enim tũcin quolibe@ alio <lb/>plano filum ſubtile cũ perpendiculo manu ſuſtinueris,@ eiuſq; </s> <s xml:id="echoid-s11825" xml:space="preserve">umbrã in plano <lb/>duobus punctis notaueris, erit linea recta, quæ p@r hæc duo puncta educetur, <pb o="282" file="318" n="319" rhead="Comment. in II. Cap. Sphæræ"/> meridiana linea: </s> <s xml:id="echoid-s11826" xml:space="preserve">quoniam uidelicet tempore meridiei @am umbra Solis <lb/>effecit.</s> <s xml:id="echoid-s11827" xml:space="preserve"/> </p> <div xml:id="echoid-div607" type="float" level="2" n="4"> <note position="right" xlink:label="note-317-01" xlink:href="note-317-01a" xml:space="preserve">Qua arte e@ <lb/>@na linea <lb/>meridiana <lb/>inue@ta in-<lb/>numeręalię <lb/>inueniãtur.</note> </div> </div> <div xml:id="echoid-div609" type="section" level="1" n="206"> <head xml:id="echoid-head216" xml:space="preserve">VII.</head> <note position="left" xml:space="preserve">Meridianus <lb/>in omni re <lb/>gione eſt in <lb/>ſtar Horizõ <lb/>tis.</note> <p> <s xml:id="echoid-s11828" xml:space="preserve"><emph style="sc">Praestat</emph> hic circulus in qualibet ſphæra obliquaidem, quod Horizo@ <lb/>rectus in ſphæra recta. </s> <s xml:id="echoid-s11829" xml:space="preserve">Nam ſicut ſe habet quoduis punctum eclipticę, ſeu ſtel-<lb/>la ad Horizontem rectum, ita prorſus ſeſe habeat, neceſſe eſt ad Meridianum <lb/>cuiuslibet ciuitatis, quantum ad ortum, & </s> <s xml:id="echoid-s11830" xml:space="preserve">occaſum, hoc eſt, ad tranſitum per <lb/>Meridianum: </s> <s xml:id="echoid-s11831" xml:space="preserve">quia tam Meridianus, quàm Horizon rectus per utrumq; </s> <s xml:id="echoid-s11832" xml:space="preserve">mundi <lb/>polum incidit. </s> <s xml:id="echoid-s11833" xml:space="preserve">Atque hac de cauſa Aſtronomi dies naturales inchoant a me-<lb/>ridiano circulo, & </s> <s xml:id="echoid-s11834" xml:space="preserve">non ab Horizonte, quoniam cum ipſi in ſuis obſeruationi-<lb/>bus requirant @empora maxime ęqualia, certiſſimo iudicio, ac demonſtratione <lb/>animad uerterunt, Zodiacum in ſuo ortu & </s> <s xml:id="echoid-s11835" xml:space="preserve">occaſu non tantam admittere va-<lb/>rietatem reſpectu Meridiani, quantam reſpectu Horizontis obliqui. </s> <s xml:id="echoid-s11836" xml:space="preserve">Nam quò <lb/>obliquior fuerit Horizon, etiam maior uarietas cernitur in ortu, & </s> <s xml:id="echoid-s11837" xml:space="preserve">occaſu par <lb/>tium Zodiaci. </s> <s xml:id="echoid-s11838" xml:space="preserve">Sed hæc melius percipientur in 3. </s> <s xml:id="echoid-s11839" xml:space="preserve">cap.</s> <s xml:id="echoid-s11840" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div610" type="section" level="1" n="207"> <head xml:id="echoid-head217" xml:space="preserve">VIII.</head> <p> <s xml:id="echoid-s11841" xml:space="preserve"><emph style="sc">Meridianvs</emph> circulus inſignem uſum habet in Coſmographia@ officio <lb/> <anchor type="note" xlink:label="note-318-02a" xlink:href="note-318-02"/> enim illius metiuntur Coſmographi, & </s> <s xml:id="echoid-s11842" xml:space="preserve">lõgitudines, & </s> <s xml:id="echoid-s11843" xml:space="preserve">latitudines ciuitatum. <lb/></s> <s xml:id="echoid-s11844" xml:space="preserve">Quod ut intelligatur, pauca dicenda mihi uidentur de longitudine, latitudi-<lb/>nesq́ue ciuitatum. </s> <s xml:id="echoid-s11845" xml:space="preserve">Ptolemæus igitur ut conſtat ex 1. </s> <s xml:id="echoid-s11846" xml:space="preserve">lib. </s> <s xml:id="echoid-s11847" xml:space="preserve">Geographiæ, cap. </s> <s xml:id="echoid-s11848" xml:space="preserve">6. </s> <s xml:id="echoid-s11849" xml:space="preserve"><lb/>quem omnes Coſmographi imitantur, uidens terram habitabilem magis por-<lb/>rigi ab occaſu in ortum, quàm à Septentriones in Auſtrum, appellat tractum <lb/> <anchor type="note" xlink:label="note-318-03a" xlink:href="note-318-03"/> terræ ab occaſu in ortum, longitudinem, à Septentrione uero in Auſtrum, la-<lb/>titudinem; </s> <s xml:id="echoid-s11850" xml:space="preserve">quemadmodum etiam in quacunque re quanta maiorem diſtan-<lb/>tiam appellare ſolemus longitudinem, & </s> <s xml:id="echoid-s11851" xml:space="preserve">minori diſtantiæ latitudinem tribui <lb/>mus. </s> <s xml:id="echoid-s11852" xml:space="preserve">Vel etiam quia, ut idem ait, motus planetarum ab occaſu in ortum lon-<lb/>gior eſt, quàm à Septentrione in Auſtrum. </s> <s xml:id="echoid-s11853" xml:space="preserve">Hic enim includitur inter duo@ <lb/>tropicos tantum, quorum diſtantia continet grad. </s> <s xml:id="echoid-s11854" xml:space="preserve">47. </s> <s xml:id="echoid-s11855" xml:space="preserve">Ille uero complecti-<lb/>tur grad. </s> <s xml:id="echoid-s11856" xml:space="preserve">360.</s> <s xml:id="echoid-s11857" xml:space="preserve"/> </p> <div xml:id="echoid-div610" type="float" level="2" n="1"> <note position="left" xlink:label="note-318-02" xlink:href="note-318-02a" xml:space="preserve">Meridianus <lb/>metitur lon <lb/>gitudines, et <lb/>latitudines <lb/>@iuitatum.</note> <note position="left" xlink:label="note-318-03" xlink:href="note-318-03a" xml:space="preserve">Cur Ptole-<lb/>@æus appel <lb/>let tractum <lb/>terię ab oc <lb/>@aſu in or@ũ <lb/>lõgitudinẽ, <lb/>à ſep@entrio <lb/>ne uero in <lb/>@uſtrum, la-<lb/>@itudinem.</note> </div> <p> <s xml:id="echoid-s11858" xml:space="preserve"><emph style="sc">Est</emph> autem duplex oriens, atque occidens, abſolutum ſcilicet, & </s> <s xml:id="echoid-s11859" xml:space="preserve">reſpecti-<lb/>uum. </s> <s xml:id="echoid-s11860" xml:space="preserve">Oriens abſolutum dicitur finis terræ habitabilis ex parte orientis, qua-<lb/> <anchor type="note" xlink:label="note-318-04a" xlink:href="note-318-04"/> lis eſt Ptolemæo Sinarum regio, quæ hodie Mangi dicitur, regi Tartarorum <lb/>olim ſubdita, nunc autem regi potentiſſimo Sinarum. </s> <s xml:id="echoid-s11861" xml:space="preserve">Procedenti enim ab <lb/>occaſu ad ortum poſt dictam regionem ſtatim occurrit mare. </s> <s xml:id="echoid-s11862" xml:space="preserve">Occidens abſo-<lb/> <anchor type="note" xlink:label="note-318-05a" xlink:href="note-318-05"/> lutum dicitur finis terræ ex parte occidentis, cuiuſmodi ſunt Inſulæ Fortu-<lb/>natæ, quę in occidente iacent poſt extrema Europæ, & </s> <s xml:id="echoid-s11863" xml:space="preserve">Africæ littora. </s> <s xml:id="echoid-s11864" xml:space="preserve">Oriens <lb/>reſpectiuũ, & </s> <s xml:id="echoid-s11865" xml:space="preserve">occidens ſumitur, habita ratione cuiuſcun que habitationis par-<lb/> <anchor type="note" xlink:label="note-318-06a" xlink:href="note-318-06"/> ticularis, ſeu Horizontis: </s> <s xml:id="echoid-s11866" xml:space="preserve">Quo pacto quælibet ciuitas habere dicitur ſuum <lb/>oriens, ſuumq; </s> <s xml:id="echoid-s11867" xml:space="preserve">occidens. </s> <s xml:id="echoid-s11868" xml:space="preserve">& </s> <s xml:id="echoid-s11869" xml:space="preserve">hoc poſteriori modo Meridianus quilibet æquali-<lb/>ter diſtare dicitur ab ortu & </s> <s xml:id="echoid-s11870" xml:space="preserve">occaſu. </s> <s xml:id="echoid-s11871" xml:space="preserve">Tantum enim temporis conſumit Sol ab <lb/>ortu uſq; </s> <s xml:id="echoid-s11872" xml:space="preserve">ad meridiem, quantum à meridie ad occaſum uſq;</s> <s xml:id="echoid-s11873" xml:space="preserve">: Vel quia in om-<lb/>nibus regionibus in Aequatore, quomodocunque reuoluatur, exiſtunt 90. <lb/></s> <s xml:id="echoid-s11874" xml:space="preserve">gradus inter Horizontem, ac Meridianum. </s> <s xml:id="echoid-s11875" xml:space="preserve">Priori uero modo accipiunt <lb/>Geographi longitudinem terræ, ita ut longitudo cuiuslibet ciuitatis, di-<lb/> <anchor type="note" xlink:label="note-318-07a" xlink:href="note-318-07"/> catur diſtantia ab occaſu, id eſt, ab Inſulis Fortunatis, uerſus ortum, quæ <lb/>ita deſiniri ſolet. </s> <s xml:id="echoid-s11876" xml:space="preserve">Longitudo ciuitatis, aut loci cuiſpiam eſt arcus Aequa-<lb/>toris inter Meridianum dictæ ciuitatis, locive, & </s> <s xml:id="echoid-s11877" xml:space="preserve">Meridianum Inſularum <lb/>Fortunatarum interiectus: </s> <s xml:id="echoid-s11878" xml:space="preserve">Vel arcu paralleli per locum tranſeuntis interce- <pb o="283" file="319" n="320" rhead="Ioan. de Sacro Boſco."/> ptus inter eoſdem duos Meridianos. </s> <s xml:id="echoid-s11879" xml:space="preserve">Eſt etenim hic arcus paralleli ſimilis om <lb/>nino arcui illi Aequatoris, ut conſtat ex propoſ. </s> <s xml:id="echoid-s11880" xml:space="preserve">10. </s> <s xml:id="echoid-s11881" xml:space="preserve">lib. </s> <s xml:id="echoid-s11882" xml:space="preserve">2. </s> <s xml:id="echoid-s11883" xml:space="preserve">Theodoſij. </s> <s xml:id="echoid-s11884" xml:space="preserve">Quoniam <lb/>enim omnes circuli à Septentrione in auſtrum porrecti mouentur ad motum <lb/>cæliab ortu ad occaſum, non potuit ab ullo eorum initium longitudinis fie-<lb/>ri; </s> <s xml:id="echoid-s11885" xml:space="preserve">ſed confugien dum fuit ad Meridianum, qui per inſulas maximè occidenta-<lb/>les tunc cognitas ducitur, quales ſunt Fortunatæ, dicunturq́ue propterea col-<lb/>locari in occidente abſoluto. </s> <s xml:id="echoid-s11886" xml:space="preserve">Pari ratione regio illa Mangi, quia maxime o-<lb/>rientalis eſt, Oriens abſolutum dicitur occupare. </s> <s xml:id="echoid-s11887" xml:space="preserve">Ex quo manifeſtum eſt, lon-<lb/>gitudinem cuiuſque ciuitatis menſurari non poſſe ſine Meridiano. </s> <s xml:id="echoid-s11888" xml:space="preserve">Quot enim <lb/>gradus continebit arcus Ae quatoris, ſeu paralleli inter Meridianum primum, <lb/>qui per inſulas Fortunatas incedit, & </s> <s xml:id="echoid-s11889" xml:space="preserve">Meridianũ ipſius ciuitatis poſitus, tan-<lb/>ta dicitur eſſe eius longitudo. </s> <s xml:id="echoid-s11890" xml:space="preserve">Vt longitudo Romæ continet grad. </s> <s xml:id="echoid-s11891" xml:space="preserve">36. </s> <s xml:id="echoid-s11892" xml:space="preserve">min. <lb/></s> <s xml:id="echoid-s11893" xml:space="preserve"> <anchor type="note" xlink:label="note-319-01a" xlink:href="note-319-01"/> 30. </s> <s xml:id="echoid-s11894" xml:space="preserve">fere Arcus autem Æquatoris, uel paralleli cuiuslibet ciuitatis interiectus <lb/>inter Meridianum proprium, & </s> <s xml:id="echoid-s11895" xml:space="preserve">Meridianum alterius cuiuſpiam ciuitatis, qui <lb/>non t@anſeat per Inſulas Fortunatas, ſeu Canarias, uocatur Differentia lon-<lb/>gitudinum.</s> <s xml:id="echoid-s11896" xml:space="preserve"/> </p> <div xml:id="echoid-div611" type="float" level="2" n="2"> <note position="left" xlink:label="note-318-04" xlink:href="note-318-04a" xml:space="preserve">O@iens abſo <lb/>lutũ quod.</note> <note position="left" xlink:label="note-318-05" xlink:href="note-318-05a" xml:space="preserve">Occidensab <lb/>ſolutũ qd.</note> <note position="left" xlink:label="note-318-06" xlink:href="note-318-06a" xml:space="preserve">Oriẽs, & oc <lb/>@idẽs reſpe-<lb/>@tiuũ quod.</note> <note position="left" xlink:label="note-318-07" xlink:href="note-318-07a" xml:space="preserve">Longitudo <lb/>ciuitatum <lb/>quid.</note> <note position="right" xlink:label="note-319-01" xlink:href="note-319-01a" xml:space="preserve">D@ſſerẽtia <lb/>lõgitudin@ <lb/>quid.</note> </div> <p> <s xml:id="echoid-s11897" xml:space="preserve"><emph style="sc">Latitvdi@is</emph> initium ſtatuitur in Aequatore, quia nullo modo à Borea <lb/>in auſtrum, uel econtrario, mouetur ſed eundem ſemper ſitum reſpectu terræ <lb/> <anchor type="note" xlink:label="note-319-02a" xlink:href="note-319-02"/> habet: </s> <s xml:id="echoid-s11898" xml:space="preserve">ita ut ciuitas quęlibet tantam dicatur habere latitudinem, quantũ ab <lb/>Aequatore ſiue in Boream, ſiue in Auſtrum recedit, Quam quidem metimur <lb/>per Meridianũ. </s> <s xml:id="echoid-s11899" xml:space="preserve">Nam latitudo ciuitatis cuiuſuis eſt arcus Meridiani concluſus <lb/>inter Aequatorem, & </s> <s xml:id="echoid-s11900" xml:space="preserve">parallelum præfalæ ciuitatis. </s> <s xml:id="echoid-s11901" xml:space="preserve">Qa ratione Roma dicitur <lb/> <anchor type="note" xlink:label="note-319-03a" xlink:href="note-319-03"/> habere latitudinem ferme 42. </s> <s xml:id="echoid-s11902" xml:space="preserve">grad. </s> <s xml:id="echoid-s11903" xml:space="preserve">Arcus autem Meridiani interpoſitus inter <lb/>duos parallelos duarum ciuitatum, quarum neutra ſub Aequatore iacet, appel <lb/>latur D@fferentia latitudinum.</s> <s xml:id="echoid-s11904" xml:space="preserve"/> </p> <div xml:id="echoid-div612" type="float" level="2" n="3"> <note position="right" xlink:label="note-319-02" xlink:href="note-319-02a" xml:space="preserve">Latitudo @ <lb/>uitarũ qd.</note> <note position="right" xlink:label="note-319-03" xlink:href="note-319-03a" xml:space="preserve">Differentia <lb/>latitudinũ <lb/>quid.</note> </div> <p> <s xml:id="echoid-s11905" xml:space="preserve"><emph style="sc">Itaqve</emph> ut ſtellarum longitudines, ab Ariete uerſus ſigna orientalia, <lb/>declinationes autem ab Aequatore uerſus alterutrum polorũ computantur, <lb/>ita etiam ciuitatũ longitudines à Meridiano per inſulas Canarias, ſiue For-<lb/> <anchor type="note" xlink:label="note-319-04a" xlink:href="note-319-04"/> tunatas incedente uerſus orientales partes, latitudines uero ab Aequatore <lb/>uerſus utrumuis polum numerantur. </s> <s xml:id="echoid-s11906" xml:space="preserve">Vnde ſicut declinationes ſtellarum, ita <lb/>quoque latitudines ciuitatum duplices erunt, Septentrionales nimirum, ac <lb/>Auſtrales, prout ab Aequatore uel in Boream, Septentrionemve, uel in Auſtrũ <lb/>recedunt. </s> <s xml:id="echoid-s11907" xml:space="preserve">Hac ratio ae loca terræ ſub Aequatore poſitanullam habebunt la-<lb/> <anchor type="note" xlink:label="note-319-05a" xlink:href="note-319-05"/> titudinem: </s> <s xml:id="echoid-s11908" xml:space="preserve">Quę uero ſub polis directe ſunt conſtituta, ſortientur latitudinem <lb/>grad. </s> <s xml:id="echoid-s11909" xml:space="preserve">90. </s> <s xml:id="echoid-s11910" xml:space="preserve">Item loca, quorum uertices uel in eodem parallelo, uel in ęqualibus <lb/>parallelis fuerint conſtituti, eandem obtinebunt latitudinrm. </s> <s xml:id="echoid-s11911" xml:space="preserve">Hinc ſit, Anti-<lb/>podas noſtros eandem habere latitudinem nobiſcum, diuerſi tamen nominis. <lb/></s> <s xml:id="echoid-s11912" xml:space="preserve">Noſtra enim eſt Borea, illorum uero Auſtrina. </s> <s xml:id="echoid-s11913" xml:space="preserve">Rurſus ciuitates, quæ ſub eo-<lb/>dem ſemicirculo Meridiani per inſulas Fortunatas tranſeuntis inter polos <lb/>mundi comprehenſo ponuntur, ſub quo ſitæ ſunt prædictæ inſulę, carebunt <lb/>omni longitudine: </s> <s xml:id="echoid-s11914" xml:space="preserve">Quæ vero ſub oppoſito ſemicirculo ſitæ erunt, poſſidebũt <lb/>longitudinem 180. </s> <s xml:id="echoid-s11915" xml:space="preserve">grad. </s> <s xml:id="echoid-s11916" xml:space="preserve">Pari ratione ciuitates collocatæ ſub uno, eodemque <lb/>ſemicirculo inter duos polos interiecto cuiuſcunque Meridiani, eandem ha-<lb/>bebunt longitudinem: </s> <s xml:id="echoid-s11917" xml:space="preserve">Quæ autem ſub diuerſis ſemicirculis eiuſdem Meri-<lb/>diani conſtitutæ fuerint, habebunt differentiam longitudinalẽ 180. </s> <s xml:id="echoid-s11918" xml:space="preserve">grad. </s> <s xml:id="echoid-s11919" xml:space="preserve">Hęc <lb/>omnia facile intelligentur ex globo aliquo Coſmographico, in quo circuli <lb/>maximi per polos ducti indicant longitudines ciuitatum, circuli uero Aequa <lb/>tori ęquidiſtantes earundem latitudines; </s> <s xml:id="echoid-s11920" xml:space="preserve">Vel certe ex mappa aliqua mundi <pb o="284" file="320" n="321" rhead="Comment. in II. Cap. Sphæræ"/> vniuerſali, in qua linea recta in gradus diuiſa, & </s> <s xml:id="echoid-s11921" xml:space="preserve">à polo in polum porrecta in <lb/>medio mappę refert primum Meridianum, alię uero lineę circulares ad utrã-<lb/>que partem illius ductæ (quę quidem in nonnullis mappis rectę lineæ ſunt) a-<lb/>lios Meridianos ſignificant: </s> <s xml:id="echoid-s11922" xml:space="preserve">Lineę uero rectę Aequatori parallelæ, & </s> <s xml:id="echoid-s11923" xml:space="preserve">à ſiniſtra <lb/>in dextram extenſæ (quæ in quibuſdam mappis ſunt circulares) repręſentant <lb/>parallelos, uellatitudines ciuitatum. </s> <s xml:id="echoid-s11924" xml:space="preserve">Ex quibus facile apparebit, quæ ciuitates <lb/>eandem habeant longitudinem, latitudinemve, aut diuerſam, & </s> <s xml:id="echoid-s11925" xml:space="preserve">quantam.</s> <s xml:id="echoid-s11926" xml:space="preserve"/> </p> <div xml:id="echoid-div613" type="float" level="2" n="4"> <note position="right" xlink:label="note-319-04" xlink:href="note-319-04a" xml:space="preserve">Latitudo <lb/>ciuitatũ du <lb/>plex: Borea <lb/>lis, vel Au-<lb/>ſtralis.</note> <note position="right" xlink:label="note-319-05" xlink:href="note-319-05a" xml:space="preserve">Quæ ciuit@ <lb/>tes eandem <lb/>habeant la <lb/>titudinẽvel <lb/>lõgitudinẽ.</note> </div> <p> <s xml:id="echoid-s11927" xml:space="preserve"><emph style="sc">Philosophi</emph> uero, ut conſtat apud Ariſtotelem lib. </s> <s xml:id="echoid-s11928" xml:space="preserve">2. </s> <s xml:id="echoid-s11929" xml:space="preserve">de cœlo, cap. </s> <s xml:id="echoid-s11930" xml:space="preserve">2. </s> <s xml:id="echoid-s11931" xml:space="preserve">aliter <lb/> <anchor type="note" xlink:label="note-320-01a" xlink:href="note-320-01"/> loquuntur de longitudine, latitudineq́ue totius mundi. </s> <s xml:id="echoid-s11932" xml:space="preserve">Habita enim ratione <lb/>differentiarum poſitionum, quas in cœlo confingunt, appellant Oriens, dextrũ <lb/>cœli; </s> <s xml:id="echoid-s11933" xml:space="preserve">Occidens, ſiniſtrum; </s> <s xml:id="echoid-s11934" xml:space="preserve">Polum Auſtralem, ſiue antarcticum, Superum; </s> <s xml:id="echoid-s11935" xml:space="preserve">Polũ <lb/>Septentrionalem, Inferum. </s> <s xml:id="echoid-s11936" xml:space="preserve">Namque imaginantur hominem per axem mundi <lb/>extenſum, cuius caput in polo Antarctico, pedes in Arctico, manus dextra in <lb/>oriente, ſiniſtra in occidente ſtatuatur. </s> <s xml:id="echoid-s11937" xml:space="preserve">Vnde quemadmodum hominis cuiuſ-<lb/>libet longitudo ſumitur à capite ad pedes, uel uiceuerſa; </s> <s xml:id="echoid-s11938" xml:space="preserve">latitudo autem à dex <lb/>tra in ſiniſtram, uel contra, ita conſequens eſt, eos longitudinem mundi metiri <lb/>à<unsure/> polo ad polum, latitudinem autem ab ortu in occaſum. </s> <s xml:id="echoid-s11939" xml:space="preserve">At Coſmographi <lb/>conſiderantes, ut diximus, terram, prout habitatur, definiunt latitudinem ab <lb/>Aequatore uerſus polos, longitudinem uero ab occaſu in ortum.</s> <s xml:id="echoid-s11940" xml:space="preserve"/> </p> <div xml:id="echoid-div614" type="float" level="2" n="5"> <note position="left" xlink:label="note-320-01" xlink:href="note-320-01a" xml:space="preserve">Philoſophi <lb/>qũo ſumãt <lb/>lõgitu dinẽ <lb/>& latitudi <lb/>nem in Vni <lb/>@erſo.</note> </div> <note position="left" xml:space="preserve">Longitudi-<lb/>nes ciuita-<lb/>@ũ excclipſi <lb/>bus Lunæ <lb/>certiſſi mèĩ<unsure/> <lb/>u@niuntur.</note> <p> <s xml:id="echoid-s11941" xml:space="preserve"><emph style="sc">Longitvdines</emph> ciuitatum certiſſime inueniri poſſunt ex eclipſi-<lb/>ſius Lunæ, quamuis ſint alij modi, ut in Coſmographia docuimus'. </s> <s xml:id="echoid-s11942" xml:space="preserve">Cognito <lb/>enim uni ciuitati duabus horis citius initium eclipſis eſſe factum, quàm inſu-<lb/>lis Fortunatis, colligitur euidenter, eam ciuitatem recedere ab inſulis dictis <lb/>orientem uerſus 30. </s> <s xml:id="echoid-s11943" xml:space="preserve">grad. </s> <s xml:id="echoid-s11944" xml:space="preserve">& </s> <s xml:id="echoid-s11945" xml:space="preserve">ſic do cæteris. </s> <s xml:id="echoid-s11946" xml:space="preserve">Latitudines uero ciuitatum eædem <lb/>ſunt, quę eleuationes poli. </s> <s xml:id="echoid-s11947" xml:space="preserve">Vnde inuenta eleuatione poli in qualibet ciuitate, <lb/>habebitur eius latitudo. </s> <s xml:id="echoid-s11948" xml:space="preserve">Quoniam uero ad multa conducit notitia longitudi-<lb/>num, nec non latitudinum ciuitatum, rem gratam ſtudioſis me facturum arbi <lb/>tror, ſi pręcipuarum ciuitatum longitudines, atque latitudines in ſequentem <lb/>tabulam referam. </s> <s xml:id="echoid-s11949" xml:space="preserve">In qua, ut facilius ciuitas quęuis inueniatur, ſecutus ſum <lb/>ordinem alphabeti.</s> <s xml:id="echoid-s11950" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11951" xml:space="preserve"><emph style="sc">Desvmpsi</emph> autem tam longitudines, quàm latitudines ex Geogra-<lb/>phia ptolemæi, ut plurimum: </s> <s xml:id="echoid-s11952" xml:space="preserve">In paucis admodum ciuitatibus, quarum lon-<lb/>gitudines, & </s> <s xml:id="echoid-s11953" xml:space="preserve">latitudines mihi notæ ſuerunt ex obſeruatio nibus aliorum <lb/>Aſtronomorum, cum Ptolemæo non conuenio. </s> <s xml:id="echoid-s11954" xml:space="preserve">Non enim omni <lb/>ex parte fides habenda eſt, ut ſupra monui, tabulis longitu-<lb/>dinum, & </s> <s xml:id="echoid-s11955" xml:space="preserve">latitudinum: </s> <s xml:id="echoid-s11956" xml:space="preserve">Sæpe enim uno, aut altero gra-<lb/>du maior, minorve longitudo, & </s> <s xml:id="echoid-s11957" xml:space="preserve">latitudo inue-<lb/>nitur. </s> <s xml:id="echoid-s11958" xml:space="preserve">Vnde expedit, ut quilibet in eo <lb/>loco, in quo eſt, inueſtiget longi-<lb/>tudinem, & </s> <s xml:id="echoid-s11959" xml:space="preserve">latitudinem, an-<lb/>tequam ad alias obſer-<lb/>uationes ſeſe <lb/>confe-<lb/>rat.</s> <s xml:id="echoid-s11960" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div616" type="section" level="1" n="208"> <head xml:id="echoid-head218" style="it" xml:space="preserve">SEQVITVR TABVLA LONGITV DINVM, <lb/>& latitudinem Ciuitatum.</head> <pb o="285" file="321" n="322" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve"> <lb/>##### TABVLA CONTINENS \\ LONGITVDINES, LATITVDI- \\ NESQVE CIVITATVM. <lb/>CIVITATVM # ## Longitudo # ## Latitud. <lb/>PRÆCIPVARVM # G. # M. # G. # M. <lb/>Adrianopolis Thraciæ # 53 # 0 # 43 # 0 <lb/>Aetna mons Siciliæ # 39 # 0 # 38 # 20 <lb/>Alba Græca. Beldrago # 45 # 0 # 47 # 40 <lb/>Alexandria # 60 # 30 # 30 # 0 <lb/>Algerium Africæ # 22 # 0 # 32 # 30 <lb/>Amberga # 32 # 40 # 49 # 30 <lb/>Ancona # 38 # 30 # 43 # 40 <lb/>Antuerpia # 24 # 30 # 51 # 48 <lb/>Aquila # 34 # 30 # 43 # 20 <lb/>Aquileia # 34 # 0 # 45 # 12 <lb/>Aquiſgranum. Achen # 27 # 15 # 51 # 10 <lb/>Arelatum. Arles # 22 # 45 # 43 # 20 <lb/>Aretium. Arezo # 34 # 40 # 42 # 50 <lb/>Argentina. Strasburg # 27 # 50 # 48 # 44 <lb/>Argentoratum # 27 # 50 # 48 # 44 <lb/>Ariminum # 35 # 0 # 43 # 50 <lb/>Aſſiſium # 35 # 20 # 42 # 55 <lb/>Athenæ # 52 # 45 # 37 # 15 <lb/>Algerium Sardiniæ # 30 # 20 # 38 # 0 <lb/>Auenio. Auignon # 23 # 0 # 43 # 52 <lb/>Auguſta. Augſpurg # 32 # 30 # 48 # 20 <lb/>Auguſtodunum # 23 # 4 # 46 # 30 <lb/>Aurea Cherſoneſus. Malacha # 161 # 0 # 2 # 0 <lb/>Badaioz # 5 # 20 # 39 # 0 <lb/>BAMBERGA # 31 # 45 # 49 # 56 <lb/>Barcinona # 17 # 15 # 41 # 35 <lb/>Baſilea # 28 # 0 # 47 # 30 <lb/>Belgradum. Alba græca # 45 # 0 # 47 # 40 <lb/>Beneuentum # 41 # 0 # 42 # 0 <lb/>Boſa in Sardinia # 30 # 20 # 37 # 50 <lb/>Bergamum # 32 # 0 # 45 # 0 <lb/>Braga Portugalliæ # 6 # 0 # 43 # 0 <lb/>Brema # 31 # 30 # 52 # 20 <lb/>Brixia. Breſcia # 32 # 30 # 44 # 30 <lb/>Brunduſium # 42 # 30 # 40 # 0 <lb/>Brunſuiga # 32 # 40 # 52 # 30 <lb/></note> <pb o="286" file="322" n="323" rhead="Comment. in II. Cap. Sphæræ"/> <note position="right" xml:space="preserve"> <lb/>CIVITATVM # ## Longitudo # ## Latitud. <lb/>PRÆCIPVARVM # G. # M. # G. # M. <lb/>Buda # 42 # 0 # 47 # 0 <lb/>Bononia # 33 # 30 # 44 # 16 <lb/>Burgos Hiſpaniæ # 12 # 0 # 42 # 48 <lb/>Byzantium. Conſtantinopolis # 56 # 0 # 43 # 5 <lb/>Cæſarauguſta. Saragozza # 14 # 15 # 41 # 45 <lb/>Calicut Indiæ # 112 # 0 # 17 # 0 <lb/>Caliz Hiſpaniæ # 5 # 10 # 37 # 0 <lb/>Calaris in Sardinia # 31 # 30 # 36 # 30 <lb/>Camerinum # 36 # 0 # 43 # 0 <lb/>Candia in Inſula Candiæ # 54 # 10 # 35 # 15 <lb/>Cantuaria # 21 # 0 # 53 # 40 <lb/>Capua # 40 # 0 # 41 # 10 <lb/>Caput uiride # 13 # 0 # 8 # 0 <lb/>Carthago Africæ # 34 # 50 # 32 # 20 <lb/>Carthago noua Hiſpaniæ: Cartagena # 12 # 15 # 38 # 0 <lb/>Catania Siciliæ # 40 # 30 # 37 # 40 <lb/>Cephaludium Siciliæ # 37 # 30 # 37 # 30 <lb/>Coburgum # 31 # 30 # 50 # 20 <lb/>Colonia Agrippinenſis # 27 # 40 # 51 # 0 <lb/>Complutum. Alcala de Henares # 10 # 30 # 41 # 40 <lb/>Compoſtella. S. Iacobus # 7 # 15 # 44 # 15 <lb/>Comum # 31 # 0 # 44 # 30 <lb/>Confluentia. Coblenz # 27 # 30 # 50 # 30 <lb/>Conſtantia. Coſtniz # 28 # 30 # 47 # 30 <lb/>Conſtantinopolis # 56 # 0 # 43 # 5 <lb/>Cracouia # 42 # 40 # 50 # 12 <lb/>Cremona # 33 # 0 # 44 # 0 <lb/>Corduba # 9 # 40 # 37 # 50 <lb/>Conimbrica # 5 # 45 # 40 # 30 <lb/>Damaſcus # 69 # 0 # 33 # 0 <lb/>Dantiſcum. Dantzig # 45 # 0 # 54 # 50 <lb/>Drepanum # 37 # 0 # 37 # 0 <lb/>Dyrracchium # 45 # 0 # 40 # 50 <lb/>Ebora # 6 # 15 # 38 # 0 <lb/>Eboracum # 20 # 0 # 57 # 20 <lb/>Edenburgum # 27 # 15 # 59 # 20 <lb/>Erfordia # 34 # 30 # 51 # 10 <lb/>Florentia # 34 # 0 # 43 # 60 <lb/>Forcheim # 31 # 30 # 49 # 45 <lb/>Francofordia ad Moenum # 30 # 0 # 50 # 30 <lb/>Francofordia ad Oderam # 34 # 0 # 52 # 30 <lb/>Forum Liuij. Forli # 33 # 30 # 43 # 40 <lb/>Fundi # 38 # 10 # 41 # 30 <lb/></note> <pb o="287" file="323" n="324" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve"> <lb/>CIVITATVM # ## Longitudo # ## Latitud. <lb/>PRÆCIPVARVM # G. # M. # G. # M. <lb/>Forum Iulij. Friuli # 32 # 50 # 45 # 12 <lb/>Fauentia. Faenza # 35 # 20 # 43 # 30 <lb/>Genua # 30 # 0 # 43 # 50 <lb/>Granata # 11 # 0 # 37 # 50 <lb/>Gandauum # 20 # 0 # 51 # 30 <lb/>Goſſaria # 32 # 40 # 52 # 0 <lb/>Halberſtadium # 32 # 40 # 52 # 10 <lb/>Hamburgum # 33 # 0 # 54 # 30 <lb/>Herbipolis. Vvirtzburg # 30 # 10 # 49 # 57 <lb/>Heydelberga # 28 # 0 # 49 # 35 <lb/>Hieroſolyma # 66 # 0 # 31 # 40 <lb/>Hiſpalis. Seuilla # 7 # 15 # 37 # 0 <lb/>Imola # 34 # 15 # 43 # 30 <lb/>InſprucK # 32 # 50 # 46 # 55 <lb/>Ingolſtadium # 32 # 10 # 48 # 40 <lb/>Ioachimi vallis Germaniæ # 30 # 20 # 50 # 20 <lb/>Laubinga patria Alberti Magui # 29 # 20 # 48 # 30 <lb/>Lubecum # 31 # 20 # 54 # 48 <lb/>Luneburgum # 34 # 50 # 54 # 0 <lb/>Leontium # 38 # 0 # 38 # 0 <lb/>Lerida # 15 # 56 # 41 # 30 <lb/>Lisbona # 5 # 10 # 39 # 38 <lb/>Liburnus. Liuorno # 33 # 30 # 42 # 30 <lb/>Londinum. Londres # 20 # 0 # 52 # 30 <lb/>Luca # 33 # 0 # 43 # 30 <lb/>Lugdunum. Lion # 23 # 15 # 45 # 10 <lb/>Lutetia. Paris # 23 # 30 # 48 # 40 <lb/>Lipſia # 30 # 30 # 51 # 20 <lb/>Leodium # 22 # 0 # 50 # 50 <lb/>Leopolis Ruſſiæ. Leoburgum # 43 # 15 # 50 # 30 <lb/>Louanium # 20 # 36 # 51 # 0 <lb/>Landishutum # 31 # 0 # 48 # 20 <lb/>Maguntia. Mentz # 27 # 30 # 50 # 30 <lb/>Mantua # 32 # 45 # 44 # 30 <lb/>Madeburgum # 31 # 20 # 52 # 20 <lb/>Maſſilia # 24 # 30 # 43 # 10 <lb/>Mediolanum # 31 # 0 # 45 # 6 <lb/>Melite Inſula, & ciuitas # 38 # 4 # 34 # 40 <lb/>Meroe Ægypti # 61 # 30 # 16 # 20 <lb/>Meſſana # 40 # 30 # 38 # 30 <lb/>Metis. Metz # 25 # 30 # 47 # 30 <lb/>Monachium. Munchen # 32 # 50 # 48 # 0 <lb/>Monaſterium. Munſter # 28 # 10 # 52 # 0 <lb/></note> <pb o="288" file="324" n="325" rhead="Comment. in II. Cap. Sphæræ"/> <note position="right" xml:space="preserve"> <lb/>CIVITATVM # ## Longitudo # ## Latitud. <lb/>PRÆCIPVARVM # G. # M. # G. # M. <lb/>Mons Peſſulanus. Monpellier # 22 # 15 # 43 # 10 <lb/>Mons regius Franconiæ. Patria 10. Regiomontani # 31 # 10 # 50 # 15 <lb/>Miſna. Meyſen # 38 # 10 # 51 # 10 <lb/>Mecha # 65 # 36 # 29 # 20 <lb/>Narbona # 21 # 0 # 43 # 0 <lb/>Narnia # 36 # 30 # 42 # 30 <lb/>Neapolis Campaniæ # 39 # 30 # 41 # 0 <lb/>Niza # 28 # 0 # 43 # 30 <lb/>Norimberga # 31 # 30 # 49 # 30 <lb/>Nouiomagus # 18 # 0 # 47 # 0 <lb/>Olmuntza in Morauia # 41 # 0 # 49 # 30 <lb/>Orcades Inſulæ # 30 # 0 # 61 # 50 <lb/>Orliens. Aurelia # 20 # 40 # 47 # 10 <lb/>Ormuz Inſula # 92 # 0 # 19 # 0 <lb/>Oxonium # 19 # 0 # 54 # 15 <lb/>Oriſtaneum in Sardinia # 30 # 30 # 37 # 10 <lb/>Oppenheym # 27 # 30 # 50 # 0 <lb/>Patauium. Padua # 32 # 50 # 44 # 50 <lb/>Patauia. Paſſau # 33 # 50 # 48 # 40 <lb/>Panhormus. Palermo # 37 # 0 # 38 # 0 <lb/><emph style="sc">Pervsivm</emph> # 35 # 20 # 42 # 56 <lb/>Papia. Pauia # 31 # 0 # 44 # 50 <lb/>Piſaurum. Peſaro # 35 # 10 # 43 # 45 <lb/>Pyſæ in Hetruria # 33 # 30 # 43 # 0 <lb/>Praga # 39 # 15 # 50 # 10 <lb/>Preſſau # 40 # 0 # 51 # 10 <lb/>Pariſium # 24 # 30 # 48 # 40 <lb/>Ratisbona. Regenſpurg # 32 # 15 # 48 # 59 <lb/>Rauenna # 35 # 0 # 44 # 20 <lb/>Rhodus inſula # 58 # 0 # 35 # 0 <lb/>ROMA # 36 # 30 # 41 # 56 <lb/>Raguſia # 44 # 40 # 42 # 30 <lb/>Rocchelle # 16 # 30 # 47 # 10 <lb/>Roſtochium # 39 # 0 # 54 # 30 <lb/>Rothomagus. Roan # 22 # 40 # 49 # 0 <lb/>Saguntum # 14 # 36 # 39 # 40 <lb/>Salmantica # 8 # 50 # 40 # 15 <lb/>Saſſarum in Sardinia # 31 # 30 # 38 # 50 <lb/>Salernum # 40 # 0 # 40 # 40 <lb/>Salisburgum. Saltzburg # 35 # 40 # 47 # 40 <lb/>Samos. Inſula # 52 # 40 # 41 # 15 <lb/>Sauona # 29 # 20 # 43 # 40 <lb/>Senæ. Siena # 34 # 20 # 42 # 50 <lb/></note> <pb o="289" file="325" n="326" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve"> <lb/>CIVITATVM # ## Lõgitudo # ## Latitudo <lb/>PRÆCIPVARVM # G. # M. # G. # M. <lb/>Siguenza # 13 # 30 # 40 # 50 <lb/>Sipontum # 42 # 50 # 40 # 30 <lb/>Spira # 27 # 40 # 49 # 20 <lb/>Spoletum # 36 # 20 # 42 # 45 <lb/>Strasburg # 27 # 50 # 48 # 44 <lb/>Syracuſanæ in Sicilia # 40 # 30 # 37 # 30 <lb/>Strigonium # 42 # 30 # 48 # 0 <lb/>Tarentum # 45 # 30 # 40 # 0 <lb/>Tarracona # 16 # 20 # 41 # 0 <lb/>Taurinum # 30 # 30 # 44 # 0 <lb/>Taurus mons # 66 # 0 # 38 # 0 <lb/>Tybur # 36 # 40 # 42 # 0 <lb/>Ticinum. Pauia # 31 # 0 # 44 # 50 <lb/>Toletum # 10 # 0 # 40 # 0 <lb/>Toloſa # 20 # 30 # 43 # 20 <lb/>Tornacum. Tornay # 25 # 15 # 51 # 40 <lb/>Traiectum in Germania # 26 # 30 # 53 # 20 <lb/>Tridentum. Trento. Trient # 33 # 40 # 45 # 20 <lb/>Treueris. Trier # 26 # 0 # 49 # 30 <lb/>Trutauia. Forcheim # 31 # 30 # 49 # 45 <lb/>Tubinga # 30 # 30 # 48 # 40 <lb/>Turonia. Tours # 14 # 30 # 43 # 30 <lb/>Tunetum. Tunes # 33 # 0 # 32 # 30 <lb/>Valentia in Gallia. Valence # 23 # 0 # 44 # 30 <lb/>Valentia Hiſpaniæ # 14 # 0 # 39 # 30 <lb/>Vallis oletana. Valladolit # 10 # 10 # 42 # 0 <lb/>VENETIÆ # 34 # 0 # 45 # 0 <lb/>Vienna Auſtriæ # 37 # 45 # 48 # 20 <lb/>Vienna Galliæ # 23 # 0 # 45 # 0 <lb/>Vilna Lithuaniæ # 52 # 0 # 53 # 30 <lb/>Verdunum # 25 # 30 # 47 # 30 <lb/>Vlma # 42 # 30 # 48 # 20 <lb/>Vratiſlauia. Preſlau # 40 # 0 # 41 # 10 <lb/>Vuirtzburg # 30 # 10 # 49 # 57 <lb/>Vuormatia. Vuorms # 28 # 0 # 49 # 45 <lb/>Vlyſippo. Lisboa # 5 # 10 # 39 # 38 <lb/>Vuitemberga # 37 # 30 # 51 # 50 <lb/>Velitrum # 37 # 0 # 41 # 30 <lb/>Velona # 45 # 6 # 40 # 10 <lb/>Verona # 33 # 0 # 44 # 0 <lb/>Vicenza # 32 # 10 # 44 # 30 <lb/>Vſtica. Inſula, & ciuitas. # 37 # 30 # 38 # 45 <lb/></note> <pb o="290" file="326" n="327" rhead="Comment. in II. Cap. Sphæræ"/> </div> <div xml:id="echoid-div617" type="section" level="1" n="209"> <head xml:id="echoid-head219" style="it" xml:space="preserve">QVOMODO INVESTIG AND A SIT DIST AN-<lb/>tiu duarum ciuitatum inter ſe, quarum utriuſque longitudo, <lb/>atque latitudo explorata habeatur.</head> <p> <s xml:id="echoid-s11961" xml:space="preserve"><emph style="sc">QVamvis</emph> proprie ad Coſmographiã pertineat docere, qua ratio-<lb/>ne interualla itinerũ inter quaſcunq; </s> <s xml:id="echoid-s11962" xml:space="preserve">ciuitates indagari debeãt, <lb/>non tñ iniucundũ fore exiſtimaui, ſi paucis id ipſum hos loco ex-<lb/> <anchor type="note" xlink:label="note-326-01a" xlink:href="note-326-01"/> plicem. </s> <s xml:id="echoid-s11963" xml:space="preserve">Sumuntur aũt omnes diſtantiæ in terra, ſicut etiã in quo-<lb/>uis alio globo, ſeu ſphæra, ſecundũ circulos maximos, ut in Coſ-<lb/>mographia demonſtrauimus: </s> <s xml:id="echoid-s11964" xml:space="preserve">adeo ut tanta dicat̃ eſſe diſtantia unius loci ab <lb/>alio, quantus eſt arcus circuli maximi per vtrumque locum deſcripti. </s> <s xml:id="echoid-s11965" xml:space="preserve">Nã hic <lb/>arcus maximi circuli eſt omnium linearum circularium, quæ ex uno loco ad <lb/>alium duci poſſunt in ſuperficie conuexa terræ, minimus. </s> <s xml:id="echoid-s11966" xml:space="preserve">Quamobrem nihil <lb/>hil erit aliud inquirere diſtantiam duorum locorum inter ſe, quam perſcru-<lb/>tari, quot gradus aut minuta ſiue milliaria dictus arcus comprehendat.</s> <s xml:id="echoid-s11967" xml:space="preserve"/> </p> <div xml:id="echoid-div617" type="float" level="2" n="1"> <note position="left" xlink:label="note-326-01" xlink:href="note-326-01a" xml:space="preserve">Diftãtiæ lo <lb/>corũ in ter-<lb/>ra ſumũtur <lb/>ſecundum <lb/>circulũ ma-<lb/>ximum.</note> </div> <p> <s xml:id="echoid-s11968" xml:space="preserve"><emph style="sc">Qvando</emph> igitur duæ ciuitates eandem habuerint longitudinem, hoc eſt, <lb/> <anchor type="note" xlink:label="note-326-02a" xlink:href="note-326-02"/> ſub eodẽ ſemicirculo Meridiani inter duos mundi polos interiecto ſitæ fue-<lb/>rint, & </s> <s xml:id="echoid-s11969" xml:space="preserve">utraq; </s> <s xml:id="echoid-s11970" xml:space="preserve">vel in Boream, uel in Auſtrum declinauerit: </s> <s xml:id="echoid-s11971" xml:space="preserve">Detrahenda eſt mi <lb/>nor latitudo à maiore, ut habeatur differentia latitudinũ. </s> <s xml:id="echoid-s11972" xml:space="preserve">Si enim hanc diffe-<lb/>rentiam ad milliaria reuocaueris, tribuendo cuilibet gradui milliaria 62 {1/2}. <lb/></s> <s xml:id="echoid-s11973" xml:space="preserve">cuilibet uero minuto milliari. </s> <s xml:id="echoid-s11974" xml:space="preserve">{1/24}. </s> <s xml:id="echoid-s11975" xml:space="preserve">habebis interuallum inter illas ciuitates. </s> <s xml:id="echoid-s11976" xml:space="preserve"><lb/><emph style="sc">Exemplvm</emph>. </s> <s xml:id="echoid-s11977" xml:space="preserve">Roma, & </s> <s xml:id="echoid-s11978" xml:space="preserve">Salisburgum in Germania habent eandem ferme lon <lb/>gitudinem: </s> <s xml:id="echoid-s11979" xml:space="preserve">Detracta latitudine Romæ, uidelicet gra. </s> <s xml:id="echoid-s11980" xml:space="preserve">41. </s> <s xml:id="echoid-s11981" xml:space="preserve">min. </s> <s xml:id="echoid-s11982" xml:space="preserve">56. </s> <s xml:id="echoid-s11983" xml:space="preserve">à latitudine <lb/>Salisburgi, nempe à gr. </s> <s xml:id="echoid-s11984" xml:space="preserve">47. </s> <s xml:id="echoid-s11985" xml:space="preserve">min. </s> <s xml:id="echoid-s11986" xml:space="preserve">40. </s> <s xml:id="echoid-s11987" xml:space="preserve">Inuenietur differeutia latitudinem grad. </s> <s xml:id="echoid-s11988" xml:space="preserve"><lb/>5. </s> <s xml:id="echoid-s11989" xml:space="preserve">min. </s> <s xml:id="echoid-s11990" xml:space="preserve">44. </s> <s xml:id="echoid-s11991" xml:space="preserve">quæ reducta ad milliaria, exhibet milliaria 358. </s> <s xml:id="echoid-s11992" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s11993" xml:space="preserve">diſtantiam ni-<lb/>mirum urbis Romæ à Salisburgo.</s> <s xml:id="echoid-s11994" xml:space="preserve"/> </p> <div xml:id="echoid-div618" type="float" level="2" n="2"> <note position="left" xlink:label="note-326-02" xlink:href="note-326-02a" xml:space="preserve">Diſtãtiæ lo <lb/>corũ in ter-<lb/>ra quo pa-<lb/>cto inueſti-<lb/>guntur, qũ<unsure/> <lb/>vterq; loc <lb/>eſt borealis <lb/>vel auſtra-<lb/>lis, eſtq́; ea-<lb/>dẽ longitu-<lb/>do vtriuſq;</note> </div> <p> <s xml:id="echoid-s11995" xml:space="preserve"><emph style="sc">Item</emph> Genua, & </s> <s xml:id="echoid-s11996" xml:space="preserve">Francofordia ad Mœnum, nobiliſſimum Germaniæ em-<lb/>porium, ſunt ſub eodem Meridiani ſemicirculo poſitæ, & </s> <s xml:id="echoid-s11997" xml:space="preserve">diſſerentia latitudi-<lb/>num continet gr. </s> <s xml:id="echoid-s11998" xml:space="preserve">6. </s> <s xml:id="echoid-s11999" xml:space="preserve">min. </s> <s xml:id="echoid-s12000" xml:space="preserve">40. </s> <s xml:id="echoid-s12001" xml:space="preserve">quæ efficit milliaria 376. </s> <s xml:id="echoid-s12002" xml:space="preserve">fere. </s> <s xml:id="echoid-s12003" xml:space="preserve">Tantam igitur pro-<lb/>nunciabo eſſe diſtantiam unius ciuitatis ab altera.</s> <s xml:id="echoid-s12004" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12005" xml:space="preserve"><emph style="sc">Qvod</emph> ſi duo loca eandem quidem habuerint longitudinẽ, ſed unius la-<lb/> <anchor type="note" xlink:label="note-326-03a" xlink:href="note-326-03"/> titudo Borealis, alterius autem Meridionalis fuerit, cõiungenda erit latitudo <lb/>vnius cũ latitudine alterius, ut habeatur diſtantia eorum. </s> <s xml:id="echoid-s12006" xml:space="preserve"><emph style="sc">Exemplvm</emph>. </s> <s xml:id="echoid-s12007" xml:space="preserve">Con-<lb/>ſtantinopolis, & </s> <s xml:id="echoid-s12008" xml:space="preserve">Caput bonæ ſpei ſunt eiuſdem ferme longitudinis, habetq̃-<lb/>Conſtantinopolis latitudinem Septentrionalẽ grad. </s> <s xml:id="echoid-s12009" xml:space="preserve">43. </s> <s xml:id="echoid-s12010" xml:space="preserve">fere. </s> <s xml:id="echoid-s12011" xml:space="preserve">Caput uero bo-<lb/>næ ſpei in Auſtrum declinat grad. </s> <s xml:id="echoid-s12012" xml:space="preserve">35. </s> <s xml:id="echoid-s12013" xml:space="preserve">fere, qui appoſiti ad latitudinem Con-<lb/>ſtantinopolis efficiunt grad. </s> <s xml:id="echoid-s12014" xml:space="preserve">78. </s> <s xml:id="echoid-s12015" xml:space="preserve">hoc eſt, milliaria 4875. </s> <s xml:id="echoid-s12016" xml:space="preserve">Tantum eſt itineris <lb/>ſpatium inter Conſtantinopolim, & </s> <s xml:id="echoid-s12017" xml:space="preserve">Caput bonæ ſpei.</s> <s xml:id="echoid-s12018" xml:space="preserve"/> </p> <div xml:id="echoid-div619" type="float" level="2" n="3"> <note position="left" xlink:label="note-326-03" xlink:href="note-326-03a" xml:space="preserve">Qñ loca <lb/>eandẽ ha-<lb/>bent lõgitu <lb/>dinẽ, ſed v-<lb/>@us eſt bo-<lb/>realis, & al-<lb/>ter auſtra-<lb/>lis.</note> </div> <p> <s xml:id="echoid-s12019" xml:space="preserve"><emph style="sc">St</emph> duæ ciuitates ſub diuerſis ſemicirculis eiuſdẽ Meridiani collocatæ ſ<unsure/>ue <lb/> <anchor type="note" xlink:label="note-326-04a" xlink:href="note-326-04"/> rint, quod tum demum continget, ſi earum differentia longitudinem compre <lb/>henderit grad. </s> <s xml:id="echoid-s12020" xml:space="preserve">180. </s> <s xml:id="echoid-s12021" xml:space="preserve">tunc ſi utraq; </s> <s xml:id="echoid-s12022" xml:space="preserve">latitudinem habuerit uel Borealem, uel Au <lb/>ſtralem; </s> <s xml:id="echoid-s12023" xml:space="preserve">congeries latitudinum à ſemicirculo detracta relinquet diſtantiã ea-<lb/>rum. </s> <s xml:id="echoid-s12024" xml:space="preserve"><emph style="sc">Exemplvm</emph>. </s> <s xml:id="echoid-s12025" xml:space="preserve">Granata Hiſpaniæ, & </s> <s xml:id="echoid-s12026" xml:space="preserve">Quinſay ciuitas in prouincia Man-<lb/>gi ultra Chinam, ſunt quaſi ſub eodem Meridiano, ſed ſub diuerſis ſemicir-<lb/>culis, habetq́. </s> <s xml:id="echoid-s12027" xml:space="preserve">utraque latitudinem Septentrionalem, illa quidem gr. </s> <s xml:id="echoid-s12028" xml:space="preserve">37. </s> <s xml:id="echoid-s12029" xml:space="preserve">min. <lb/></s> <s xml:id="echoid-s12030" xml:space="preserve">50. </s> <s xml:id="echoid-s12031" xml:space="preserve">hæc vero gr. </s> <s xml:id="echoid-s12032" xml:space="preserve">37. </s> <s xml:id="echoid-s12033" xml:space="preserve">min. </s> <s xml:id="echoid-s12034" xml:space="preserve">40. </s> <s xml:id="echoid-s12035" xml:space="preserve">Si igitur aggregatum ex utraque latitudine, nẽpe <pb o="291" file="327" n="328" rhead="Ioan. de Sacro Boſco."/> g@ad. </s> <s xml:id="echoid-s12036" xml:space="preserve">75. </s> <s xml:id="echoid-s12037" xml:space="preserve">min. </s> <s xml:id="echoid-s12038" xml:space="preserve">30. </s> <s xml:id="echoid-s12039" xml:space="preserve">detrahatur ex ſemicirculo, nimirum ex grad. </s> <s xml:id="echoid-s12040" xml:space="preserve">180. </s> <s xml:id="echoid-s12041" xml:space="preserve">relinquetur <lb/>diſtantia inter dictas ciuitates grad. </s> <s xml:id="echoid-s12042" xml:space="preserve">104. </s> <s xml:id="echoid-s12043" xml:space="preserve">min. </s> <s xml:id="echoid-s12044" xml:space="preserve">30. </s> <s xml:id="echoid-s12045" xml:space="preserve">hoc eſt, milliariorum 6500.</s> <s xml:id="echoid-s12046" xml:space="preserve"/> </p> <div xml:id="echoid-div620" type="float" level="2" n="4"> <note position="left" xlink:label="note-326-04" xlink:href="note-326-04a" xml:space="preserve">Qñ differen <lb/>tiæ lõgitu-<lb/>dinũ l<unsure/>oco-<lb/>rũ cõprehẽ-<lb/>dit gra. 180. <lb/>& vterque <lb/>eft borealis <lb/>vel auſtra-<lb/>lis.</note> </div> <p> <s xml:id="echoid-s12047" xml:space="preserve"><emph style="sc">Si vero</emph> duo loca ſub diuerſis eiuſdem Meridiani ſemicirculis extite-<lb/> <anchor type="note" xlink:label="note-327-01a" xlink:href="note-327-01"/> rint, & </s> <s xml:id="echoid-s12048" xml:space="preserve">unus in Boreã, alter uero in Auſtrum receſſerit ab Aequatore, auferẽ-<lb/>da erit differentia latitudinum à ſemicirculo, ut obtineatur ſpatium inter ip-<lb/>ſa interpoſicum. </s> <s xml:id="echoid-s12049" xml:space="preserve"><emph style="sc">Exemplvm</emph>. </s> <s xml:id="echoid-s12050" xml:space="preserve">Cantaon portus nobiliſſimus Chinæ, & </s> <s xml:id="echoid-s12051" xml:space="preserve"><lb/>Oſtia fluuij argentei, quem Hiſpani dicunt Rio della Plata, in Peru, ſunt fere <lb/>in eiuſdem Meridiani ſemicirculis diuerſis, eſtq́. </s> <s xml:id="echoid-s12052" xml:space="preserve">latitudo Cantaon Septentrio <lb/>nalis gr. </s> <s xml:id="echoid-s12053" xml:space="preserve">19. </s> <s xml:id="echoid-s12054" xml:space="preserve">fere; </s> <s xml:id="echoid-s12055" xml:space="preserve">Oſtia autem fluuij argentei latitudinem Auſtralem habent <lb/>gr. </s> <s xml:id="echoid-s12056" xml:space="preserve">36. </s> <s xml:id="echoid-s12057" xml:space="preserve">ferme; </s> <s xml:id="echoid-s12058" xml:space="preserve">Differentia latitudinum eſt 17. </s> <s xml:id="echoid-s12059" xml:space="preserve">fere gr. </s> <s xml:id="echoid-s12060" xml:space="preserve">quæ ablata ex 180. </s> <s xml:id="echoid-s12061" xml:space="preserve">nempe <lb/>ex ſemicirculo, relinquit gr. </s> <s xml:id="echoid-s12062" xml:space="preserve">163. </s> <s xml:id="echoid-s12063" xml:space="preserve">qui efficiunt milliaria 10197 {1/2}. </s> <s xml:id="echoid-s12064" xml:space="preserve">Tanta eſt <lb/> <anchor type="note" xlink:label="note-327-02a" xlink:href="note-327-02"/> igitur diſtãtia inter Cantaon, & </s> <s xml:id="echoid-s12065" xml:space="preserve">Oſtia fluuij argentei. </s> <s xml:id="echoid-s12066" xml:space="preserve">Hinc efficitur, ſi duarũ <lb/>ciuitatũ in diuerſis ſemicirculis Meridiani exiſtentiũ unius latitudo Borealis <lb/>ſuerit æqualis latitudini Auſtrali alterius, vnã ab altera pręciſe diſtare ſemi-<lb/>circulo: </s> <s xml:id="echoid-s12067" xml:space="preserve">quoniã<unsure/> videlicet differentia latitudinum nihil eſt, vnde nihil ex ſemi-<lb/>circulo demitur. </s> <s xml:id="echoid-s12068" xml:space="preserve">Perſpicuum etiã eſt, iter directum duorum locorũ ſub diuer <lb/>ſis ſemicirculis eiuſdem Meridiani poſitorum fieri per alterum polorũ, nempe <lb/>per Meridianum circulum, qui per vtrumq. </s> <s xml:id="echoid-s12069" xml:space="preserve">locũ incedit. </s> <s xml:id="echoid-s12070" xml:space="preserve">Illud quoq. </s> <s xml:id="echoid-s12071" xml:space="preserve">obiter <lb/> <anchor type="note" xlink:label="note-327-03a" xlink:href="note-327-03"/> hic eſt notandum, ſi duarum ciuitatum, quarum differentia longitudinũ con-<lb/>tinet ad amuſſim Quadrante, hoc eſt, 90. </s> <s xml:id="echoid-s12072" xml:space="preserve">gr. </s> <s xml:id="echoid-s12073" xml:space="preserve">vna ſita ſit ſub Aequatore, altera <lb/>vero latitudinem quamcunque ſiue Borealem, ſiue Auſtralem, & </s> <s xml:id="echoid-s12074" xml:space="preserve">quantamcun <lb/>que habeat, unam ab altera præciſe diſſi dere ſpatio unius Quadrantis. </s> <s xml:id="echoid-s12075" xml:space="preserve">Atque <lb/>hęc omnia facile ex ſphæricis elementis Theodoſij oſtendi poſſunt, & </s> <s xml:id="echoid-s12076" xml:space="preserve">luce cla <lb/>r<unsure/>ius demonſtrari in ſphæra materiali.</s> <s xml:id="echoid-s12077" xml:space="preserve"/> </p> <div xml:id="echoid-div621" type="float" level="2" n="5"> <note position="right" xlink:label="note-327-01" xlink:href="note-327-01a" xml:space="preserve">Qñ differen <lb/>t@a longitu-<lb/>dinũ lcco-<lb/>rũ cõprehen <lb/>dia gr. 180. <lb/>ſed unus lo <lb/>cus eſt bo-<lb/>realis, & al. <lb/>ter auſtralis.</note> <note position="right" xlink:label="note-327-02" xlink:href="note-327-02a" xml:space="preserve">Quæ ciuita-<lb/>tes diſtent <lb/>ſemicircul@ <lb/>inter ſe.</note> <note position="right" xlink:label="note-327-03" xlink:href="note-327-03a" xml:space="preserve">Quæ ciuita-<lb/>tes diſtent <lb/>Quadrante.</note> </div> <note position="right" xml:space="preserve">Quando ci-<lb/>uitates ſub <lb/>A equatore <lb/>fitæ ſunt.</note> <p> <s xml:id="echoid-s12078" xml:space="preserve"><emph style="sc">Qvando</emph> duæ ciuitates neq. </s> <s xml:id="echoid-s12079" xml:space="preserve">eandem habuerint longitudinem, neq. </s> <s xml:id="echoid-s12080" xml:space="preserve">diffe-<lb/>rentia longitudinum earum fuerit grad. </s> <s xml:id="echoid-s12081" xml:space="preserve">180. </s> <s xml:id="echoid-s12082" xml:space="preserve">hoc eſt, neq. </s> <s xml:id="echoid-s12083" xml:space="preserve">ſub eodcm ſemicir-<lb/>culo Meridiani, neq. </s> <s xml:id="echoid-s12084" xml:space="preserve">ſub diuerſis eiuſdem Meridiani ſemicirculis, collocatę fue <lb/>rint, & </s> <s xml:id="echoid-s12085" xml:space="preserve">vtraque latitudine caruerit, id eſt, ſub Aequatore conſtituta fuerit, diffe <lb/>rentia longitudinum earum diſtantiam manifeſtabit, ſi ea ſemicirculo maior <lb/>non extiterit: </s> <s xml:id="echoid-s12086" xml:space="preserve">Alias hæc differentia ablata à circulo integro dabit optatam di <lb/>ſtantiam. </s> <s xml:id="echoid-s12087" xml:space="preserve">Nam tunc iter ſumendum eſt penes æquinoctialem circulum.</s> <s xml:id="echoid-s12088" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12089" xml:space="preserve"><emph style="sc">Cvmdeniqve</emph> duo loca nullo prædictorum modorum ſeſe habue-<lb/> <anchor type="note" xlink:label="note-327-05a" xlink:href="note-327-05"/> rint, ſiue unus ſub Aequatore ſit poſitus, ſiue neuter, & </s> <s xml:id="echoid-s12090" xml:space="preserve">quaſcunque habeant <lb/>latitudines, explorabimus earum diſtantiam itinerariam artificio F R A N-<lb/>CISCI MAVROLYCI ABBATIS, nempe beneficio tantummo-<lb/>do circini, hoc modo. </s> <s xml:id="echoid-s12091" xml:space="preserve">Deſcribatur circulus A B C D, ex centro E, ſitque pri-<lb/>mum differentia longitudinum duorum locorum arcus A B, ſemicirculo <lb/>minor, & </s> <s xml:id="echoid-s12092" xml:space="preserve">a punctis A, & </s> <s xml:id="echoid-s12093" xml:space="preserve">B, ducantur duæ diametri A E C, B E D: </s> <s xml:id="echoid-s12094" xml:space="preserve">Pona-<lb/> <anchor type="note" xlink:label="note-327-06a" xlink:href="note-327-06"/> tur deinde latitudo loci A, æqualis arcui A F, loci uero B, latitudo æqualis <lb/>arcui B G: </s> <s xml:id="echoid-s12095" xml:space="preserve">demittanturq́ue ad proprias diametros perpendiculares FH, GI. <lb/></s> <s xml:id="echoid-s12096" xml:space="preserve">Poſt hæc, ad ductam rectam H I, educantur ex H, & </s> <s xml:id="echoid-s12097" xml:space="preserve">I, ad eaſdem partes per-<lb/>pendiculares HK, IL, perpendicularibus H F, I G, æquales, ſingulę ſingulis, <lb/>hoc eſt, H K, æqualis rectæ H F, & </s> <s xml:id="echoid-s12098" xml:space="preserve">I L, æqualis rectæ I G. </s> <s xml:id="echoid-s12099" xml:space="preserve">Nam recta li-<lb/>nea coniungens puncta K, & </s> <s xml:id="echoid-s12100" xml:space="preserve">L, erit chorda arcus diſtantiæ unius loci ab alte <lb/>ro. </s> <s xml:id="echoid-s12101" xml:space="preserve">Quare ſi per 1. </s> <s xml:id="echoid-s12102" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s12103" xml:space="preserve">4. </s> <s xml:id="echoid-s12104" xml:space="preserve">lib. </s> <s xml:id="echoid-s12105" xml:space="preserve">Euclid. </s> <s xml:id="echoid-s12106" xml:space="preserve">in circulo coaptaueris rectam D N, æ-<lb/>qualem rectæ K L, erit D N, arcus diſtantia inter duo loca propoſita. </s> <s xml:id="echoid-s12107" xml:space="preserve">Vnde co-<lb/>gnito, quot gradus contineat arcus DN, facile in cognitionẽ diſtantiæ quæſi-<lb/>tæ perueniemus, tribuendo cuilibet gradu milliaria 62 {1/2}. </s> <s xml:id="echoid-s12108" xml:space="preserve">Hæc autem re- <pb o="292" file="328" n="329" rhead="Comment. in II. Cap. Sphæræ"/> <anchor type="figure" xlink:label="fig-328-01a" xlink:href="fig-328-01"/> gula intelligẽda eſt, qñ <lb/>uterq. </s> <s xml:id="echoid-s12109" xml:space="preserve">locus uel in Bo-<lb/>reã, vel in Auſtrum ab <lb/>Aequatore recedit. </s> <s xml:id="echoid-s12110" xml:space="preserve">Nã <lb/>ſi alter eorũ, nẽpe A, in <lb/>Auſtrũ vergat, & </s> <s xml:id="echoid-s12111" xml:space="preserve">alter, <lb/>videlicet B, in Boreã, <lb/>ducẽdæ erũt perpendi-<lb/>culai es ex pũctis H, & </s> <s xml:id="echoid-s12112" xml:space="preserve"><lb/>I, ad rectã H I, ĩ<unsure/> diuer-<lb/>ſas partes, quales ſunt <lb/>I L, & </s> <s xml:id="echoid-s12113" xml:space="preserve">H M, ita tñ, ut <lb/>rurſus I L, æqualis ſit <lb/>rectæ I G, & </s> <s xml:id="echoid-s12114" xml:space="preserve">HM, rectæ <lb/>HF. </s> <s xml:id="echoid-s12115" xml:space="preserve">Nã recta LM, con-<lb/>iungens pũcta L, & </s> <s xml:id="echoid-s12116" xml:space="preserve">M, <lb/>erit iterũ chorda arcus <lb/>diſtãtiæ unius loci ab <lb/>altero. </s> <s xml:id="echoid-s12117" xml:space="preserve">Itaque ſi coap-<lb/>tetur in circulo recta <lb/>DO, ęqualis rectę LM, <lb/>erit arcus DO, diſtan-<lb/>tia duorum locorum propoſitorum.</s> <s xml:id="echoid-s12118" xml:space="preserve"/> </p> <div xml:id="echoid-div622" type="float" level="2" n="6"> <note position="right" xlink:label="note-327-05" xlink:href="note-327-05a" xml:space="preserve">Quando e<unsure/>i-<lb/>uitates ha-<lb/>bent diuer-<lb/>ſam & lati-<lb/>tudinem, & <lb/>longitud@nẽ</note> <note position="right" xlink:label="note-327-06" xlink:href="note-327-06a" xml:space="preserve">Qua arte <lb/>beneficio <lb/>circini di-<lb/>ſtantiæ lo-<lb/>corũ inue-<lb/>niantur.</note> <figure xlink:label="fig-328-01" xlink:href="fig-328-01a"> <image file="328-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/328-01"/> </figure> </div> <p> <s xml:id="echoid-s12119" xml:space="preserve"><emph style="sc">Sit</emph> deinde dr̃ia lõgitudinũ arcus ABD, ſemicirculo maior, (Nã qñ hæc dif <lb/>ſerẽtia, ſemicirculus eſt; </s> <s xml:id="echoid-s12120" xml:space="preserve">dictũ eſt ſupra, qua rõne inueſtigãda ſit diſtãtia loco-<lb/>rũ) & </s> <s xml:id="echoid-s12121" xml:space="preserve">a pũctis A, & </s> <s xml:id="echoid-s12122" xml:space="preserve">D, ducant̃ diametri AEC, DEB: </s> <s xml:id="echoid-s12123" xml:space="preserve">Ponat̃ deinde latitudo loci <lb/>A, æqualis arcui AF, & </s> <s xml:id="echoid-s12124" xml:space="preserve">loci D, latitudo ęqualis arcui DR, demittãturq́. </s> <s xml:id="echoid-s12125" xml:space="preserve">ad ꝓ-<lb/>prias diametros ꝑpẽdiculares FH, RQ. </s> <s xml:id="echoid-s12126" xml:space="preserve">Poſt hæc, ad ductã rectã Q H, ad eaſdẽ <lb/>partes, ſi vterq. </s> <s xml:id="echoid-s12127" xml:space="preserve">locus borealis ẽ, vel auſtralis, ꝑpẽdiculares ducãtur QT, HS, ꝑ-<lb/>pẽdicularib. </s> <s xml:id="echoid-s12128" xml:space="preserve">QR, HF, æquales, ſingulæ ſingulis, hoc eſt, QT, ipſi QR, & </s> <s xml:id="echoid-s12129" xml:space="preserve">HS, ipſi <lb/>HF, æqua, lis. </s> <s xml:id="echoid-s12130" xml:space="preserve">Nã recta cõiũgẽs pũcta T, S, erit chorda arc<unsure/>us diſtãtiæ unius loci <lb/>ab altero. </s> <s xml:id="echoid-s12131" xml:space="preserve">Quare ſi accõmodetur in circulo recta DP, rectæ TS, ęqualis, erit ar <lb/>cus DP, diſtãtia ꝓpoſitorũ locorũ, ut prius. </s> <s xml:id="echoid-s12132" xml:space="preserve">Si uero locus A, fuerit v.</s> <s xml:id="echoid-s12133" xml:space="preserve">g. </s> <s xml:id="echoid-s12134" xml:space="preserve">borea-<lb/>lis, & </s> <s xml:id="echoid-s12135" xml:space="preserve">D, auſtralis, ducẽde erũt ex Q. </s> <s xml:id="echoid-s12136" xml:space="preserve">H, ꝑpẽdiculares ad QH, in di<unsure/>uerſas par-<lb/>tes ẽt, quales ſunt QT, HV, ita tñ, vt rurſus QT, ipſi QR, & </s> <s xml:id="echoid-s12137" xml:space="preserve">HV, ipſi HF, ſit æ-<lb/>qualis. </s> <s xml:id="echoid-s12138" xml:space="preserve">Nã recta TV, erit chorda arcus diſtãtię unius loci ab alten<unsure/>o: </s> <s xml:id="echoid-s12139" xml:space="preserve">ac ꝓinde ſi <lb/>aptetur in circulo recta DX, rectæ TV, æqualis, erit arcus DX, diſtãtia locorũ <lb/>propoſitorũ. </s> <s xml:id="echoid-s12140" xml:space="preserve">Demonſtrationẽ huius operationis, q̃ quidẽ pulcherrima eſt, ac <lb/>breuiſſima, ignorare nõ poterit is, qui vel mediocriter uerſatus fueritĩ doctri <lb/>na ſinuũ, & </s> <s xml:id="echoid-s12141" xml:space="preserve">rẽ diligẽtius introſpexerit in ſphæra aliqua materiali. </s> <s xml:id="echoid-s12142" xml:space="preserve">Nã circulus <lb/>ABCD, referet Aequatorẽ: </s> <s xml:id="echoid-s12143" xml:space="preserve">Diametri AC, BD, cões ſectiones Aequatoris cũ <lb/>Meridianis locorum propoſitorum: </s> <s xml:id="echoid-s12144" xml:space="preserve">Puncta H, & </s> <s xml:id="echoid-s12145" xml:space="preserve">I, in Aequatoris plano, erunt <lb/>ea, in quæ incidunt ſinus recti latitudinũ dictorum locorum. </s> <s xml:id="echoid-s12146" xml:space="preserve">Vnde ſi a punctis <lb/>H, & </s> <s xml:id="echoid-s12147" xml:space="preserve">I, erigantur ad planũ Aequatoris perpendiculares, erunt eæ ipſæ ſinus re-<lb/>cti latitudinũ, perueniẽtq́. </s> <s xml:id="echoid-s12148" xml:space="preserve">ad ipſa loca in ſuperficie ſphæræ, æqualesq́. </s> <s xml:id="echoid-s12149" xml:space="preserve">omnino <lb/>erunt rectis HK, IL, ut conſtat. </s> <s xml:id="echoid-s12150" xml:space="preserve">Quocirca recta KL, æqualis erit chordæ arcus, <lb/>qui inter dicta loca interponitur: </s> <s xml:id="echoid-s12151" xml:space="preserve">Nã rectæ HK, IL, ſunt ęquales ſinubus re-<lb/>ctis, latitudinũ. </s> <s xml:id="echoid-s12152" xml:space="preserve">Hœc eadẽ præcepta inſeruiunt ad inueſtigandã diſtantiã inter <pb o="293" file="329" n="330" rhead="Ioan. de Sacro Boſco."/> quaſcunque duas ſtellas Firmamẽti, dummodo loco Meridiani accipiatur cir <lb/>culus longitudinis ſtellarum, qui nimirum incedit per polos eclipticę, vt per-<lb/>ſpicuum eſt. </s> <s xml:id="echoid-s12153" xml:space="preserve">Verum de his, & </s> <s xml:id="echoid-s12154" xml:space="preserve">de longitudine, latitudineque ci@itatum plura <lb/>diximusin Coſmographia: </s> <s xml:id="echoid-s12155" xml:space="preserve">Satis eſt, hoc loco pauca hæc attigiſſe.</s> <s xml:id="echoid-s12156" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12157" xml:space="preserve"><emph style="sc">Sed</emph> omniũ commodiſſima via eſt, & </s> <s xml:id="echoid-s12158" xml:space="preserve">facillima per globum Coſmographi-<lb/>cum, ſi adſit, accuratè delineatum. </s> <s xml:id="echoid-s12159" xml:space="preserve">Nam ſi circino incuruo ſumatur in eo diſtan <lb/>tia unius loci ab altero, & </s> <s xml:id="echoid-s12160" xml:space="preserve">hæc in Aequinoctialem circulum transferatur, il-<lb/>lico gradus inter pedes circini indicabunt, diſtantiam vnius loci ab altero.</s> <s xml:id="echoid-s12161" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12162" xml:space="preserve"><emph style="sc">Non</emph> tamẽ abs re erit, ex omnibus mo dis illum hoc loco adducere, quẽ <lb/>Petrus Nonius lib. </s> <s xml:id="echoid-s12163" xml:space="preserve">2. </s> <s xml:id="echoid-s12164" xml:space="preserve">de arte nauigandi, demonſtrauit, & </s> <s xml:id="echoid-s12165" xml:space="preserve">quem clarius nos in <lb/>Coſmographia, demonſtrabim us. </s> <s xml:id="echoid-s12166" xml:space="preserve">Is autem eſt eiuſmodi. </s> <s xml:id="echoid-s12167" xml:space="preserve">Quando duo loca da <lb/> <anchor type="note" xlink:label="note-329-01a" xlink:href="note-329-01"/> ta fuerint borealia, uel auſtralia; </s> <s xml:id="echoid-s12168" xml:space="preserve">Fiat, vt quadratum ſinus totius ad rectangulũ <lb/>contentum ſub ſinubus complementorum latitudinum locorũ, ita ſinus uer-<lb/>ſus differentiæ longitudinum eorundem locorum (quæ differentia, ſi ſemicir-<lb/>culum ſuperet, detrahenda eſt ex toto circulo, & </s> <s xml:id="echoid-s12169" xml:space="preserve">eius, quod reliquũ eſt, ſinus <lb/>verſus accipiendus, tanquã differentiæ longitudinũ breuioris, hoc eſt, breuio-<lb/>ris diſtantiæ inter Meridianos datorũ locorum) ad aliud. </s> <s xml:id="echoid-s12170" xml:space="preserve">Inuenietur enim nu-<lb/>merus, ex quo diſtantiã locorum inueſtigabimus hac induſtria. </s> <s xml:id="echoid-s12171" xml:space="preserve">Conferatur nu <lb/>merus inuentus cum ſinu complementi differẽtię latitudinum datorum, loco <lb/>rum. </s> <s xml:id="echoid-s12172" xml:space="preserve">Nã ſi inuentus numerus æqualis fuerit ſinui illius complementi, comple-<lb/>ctetur diſtãtia locorum Quadrantem circuli maximi; </s> <s xml:id="echoid-s12173" xml:space="preserve">At vero ſi minor fuerit, <lb/>detracto hoc ex illo, relinquetur ſinus complementi diſtantiæ locorum; </s> <s xml:id="echoid-s12174" xml:space="preserve">atq. <lb/></s> <s xml:id="echoid-s12175" xml:space="preserve">adeo ſi complementum hoc ex quadrante dematur, reliqua erit locorũ diſtan <lb/>tia: </s> <s xml:id="echoid-s12176" xml:space="preserve">Si denique numerus inuentus maior fuerit ſinu complementi differentiæ <lb/>latitudinum datorum locorum, detracto hoc ex illo, reliquus erit ſinus, cuius <lb/>arcus Quadranti adiectus dabit itinerariam diſtantiã propoſitorum locorum. </s> <s xml:id="echoid-s12177" xml:space="preserve"><lb/>Quando autem unus locus borealis fuerit, & </s> <s xml:id="echoid-s12178" xml:space="preserve">auſtralis alter, accipiendus erit lo <lb/>cus per diametrum uni eorum oppoſitus, qui eandem habeat latitudinem, li-<lb/>cet oppoſitam, ut habeãtur duo loca eiuſdem denominationis, borealia nimi-<lb/>rum, uel auſtrlia: </s> <s xml:id="echoid-s12179" xml:space="preserve">Deinde in quirendum, ut docuimus, itinerariũ interuallum <lb/>inter hęc duo loca eiuſdẽ denominationis, dummodo loco differentiæ longi <lb/>tudinum datorum locorum ſumatur id, quod relinquitur, ſi ea differe@tia ex <lb/>ſemicirculo detrahatur, ut habeatur differentia longitudinũ illorum duorum <lb/>locorum eiuſdẽ denominationis. </s> <s xml:id="echoid-s12180" xml:space="preserve">Nã ſi hoc interuallũ itinerarium ſubducatur <lb/>ex ſemicirculo, nota relinquetur diſtãtia datorũ locorũ, quorum nnus borealis <lb/>eſt, & </s> <s xml:id="echoid-s12181" xml:space="preserve">alter auſtralis. </s> <s xml:id="echoid-s12182" xml:space="preserve">Sed exempla nonnulla proponamus, vt res planior fiat.</s> <s xml:id="echoid-s12183" xml:space="preserve"/> </p> <div xml:id="echoid-div623" type="float" level="2" n="7"> <note position="right" xlink:label="note-329-01" xlink:href="note-329-01a" xml:space="preserve">Quo pacto <lb/>ex ſinubus <lb/>interuallũ <lb/>itinerariũ <lb/>inter duo <lb/>loca inuc-<lb/>niatur.</note> </div> <p> <s xml:id="echoid-s12184" xml:space="preserve"><emph style="sc">Explorandvm</emph> ſit ſpatiũ itinerarium inter Romam, cuius longitu-<lb/>do continet grad. </s> <s xml:id="echoid-s12185" xml:space="preserve">36. </s> <s xml:id="echoid-s12186" xml:space="preserve">min. </s> <s xml:id="echoid-s12187" xml:space="preserve">30. </s> <s xml:id="echoid-s12188" xml:space="preserve">latitudo uero borealis grad. </s> <s xml:id="echoid-s12189" xml:space="preserve">41. </s> <s xml:id="echoid-s12190" xml:space="preserve">min. </s> <s xml:id="echoid-s12191" xml:space="preserve">56. </s> <s xml:id="echoid-s12192" xml:space="preserve">& </s> <s xml:id="echoid-s12193" xml:space="preserve">Con-<lb/>ſtantinopolim, cuius longitudo cõplectitur grad. </s> <s xml:id="echoid-s12194" xml:space="preserve">56. </s> <s xml:id="echoid-s12195" xml:space="preserve">min. </s> <s xml:id="echoid-s12196" xml:space="preserve">o. </s> <s xml:id="echoid-s12197" xml:space="preserve">latitudo uero bo-<lb/>realis quoq; </s> <s xml:id="echoid-s12198" xml:space="preserve">grad. </s> <s xml:id="echoid-s12199" xml:space="preserve">43. </s> <s xml:id="echoid-s12200" xml:space="preserve">min. </s> <s xml:id="echoid-s12201" xml:space="preserve">5. </s> <s xml:id="echoid-s12202" xml:space="preserve">Fiat, ut 10000000000. </s> <s xml:id="echoid-s12203" xml:space="preserve">quadratũ ſinus totius ad <lb/>5433294112. </s> <s xml:id="echoid-s12204" xml:space="preserve">rectangulum contentum ſub 74392. </s> <s xml:id="echoid-s12205" xml:space="preserve">ſinu complementi latitudi <lb/>nis grad. </s> <s xml:id="echoid-s12206" xml:space="preserve">41. </s> <s xml:id="echoid-s12207" xml:space="preserve">min. </s> <s xml:id="echoid-s12208" xml:space="preserve">56. </s> <s xml:id="echoid-s12209" xml:space="preserve">& </s> <s xml:id="echoid-s12210" xml:space="preserve">ſub 73036. </s> <s xml:id="echoid-s12211" xml:space="preserve">ſinu cõplementi latitudinis grad. </s> <s xml:id="echoid-s12212" xml:space="preserve">43. </s> <s xml:id="echoid-s12213" xml:space="preserve">min. </s> <s xml:id="echoid-s12214" xml:space="preserve">5. <lb/></s> <s xml:id="echoid-s12215" xml:space="preserve">ita 5736. </s> <s xml:id="echoid-s12216" xml:space="preserve">ſinus uerſus differentiæ longitudinũ, quæ comprehẽdit grad. </s> <s xml:id="echoid-s12217" xml:space="preserve">19. </s> <s xml:id="echoid-s12218" xml:space="preserve">mi. </s> <s xml:id="echoid-s12219" xml:space="preserve"><lb/>30. </s> <s xml:id="echoid-s12220" xml:space="preserve">ad aliud, inuenieturq́. </s> <s xml:id="echoid-s12221" xml:space="preserve">hic fere numerus 3116. </s> <s xml:id="echoid-s12222" xml:space="preserve">quẽ, quoniã minor eſt, quã <lb/>99979. </s> <s xml:id="echoid-s12223" xml:space="preserve">ſinus complementi differẽtiæ latitudinũ datorum locotũ, quæ comple <lb/>ctitur gr. </s> <s xml:id="echoid-s12224" xml:space="preserve">1. </s> <s xml:id="echoid-s12225" xml:space="preserve">min. </s> <s xml:id="echoid-s12226" xml:space="preserve">9. </s> <s xml:id="echoid-s12227" xml:space="preserve">auferemus ex 99979. </s> <s xml:id="echoid-s12228" xml:space="preserve">ſinu complemẽti differẽtiæ latitudinũ <lb/>locorũ, remanebuntq́. </s> <s xml:id="echoid-s12229" xml:space="preserve">96863. </s> <s xml:id="echoid-s12230" xml:space="preserve">pro ſinu complementi diſtantiæ datorũ locorũ, <lb/>Continebit ergo complementũ hoc gr. </s> <s xml:id="echoid-s12231" xml:space="preserve">75. </s> <s xml:id="echoid-s12232" xml:space="preserve">min. </s> <s xml:id="echoid-s12233" xml:space="preserve">37. </s> <s xml:id="echoid-s12234" xml:space="preserve">atque adeo diſtantia gr. </s> <s xml:id="echoid-s12235" xml:space="preserve">14.</s> <s xml:id="echoid-s12236" xml:space="preserve"> <pb o="294" file="330" n="331" rhead="Comment. in II. Cap. Sphæræ"/> min. </s> <s xml:id="echoid-s12237" xml:space="preserve">23. </s> <s xml:id="echoid-s12238" xml:space="preserve">complectetur, hoc eſt, milliaria Italica 898 {23/24}. </s> <s xml:id="echoid-s12239" xml:space="preserve">tribuendo ſingulis <lb/>grad@bus milliaria 62 {1/2}. </s> <s xml:id="echoid-s12240" xml:space="preserve">& </s> <s xml:id="echoid-s12241" xml:space="preserve">ſingulis minutis milliar. </s> <s xml:id="echoid-s12242" xml:space="preserve">1 {1/24}</s> </p> <p> <s xml:id="echoid-s12243" xml:space="preserve"><emph style="sc">Rvrsvs</emph> inueſtiganda ſit diſtantia itineraria inter Romã, & </s> <s xml:id="echoid-s12244" xml:space="preserve">Malacham, <lb/>in aurea Cherſoneſo, cuius longitudo habet gr. </s> <s xml:id="echoid-s12245" xml:space="preserve">161. </s> <s xml:id="echoid-s12246" xml:space="preserve">min. </s> <s xml:id="echoid-s12247" xml:space="preserve">0. </s> <s xml:id="echoid-s12248" xml:space="preserve">latitudo aũt borea <lb/>lis quoq;</s> <s xml:id="echoid-s12249" xml:space="preserve">, ſicut & </s> <s xml:id="echoid-s12250" xml:space="preserve">latitudo Romæ borealis ẽ, gr. </s> <s xml:id="echoid-s12251" xml:space="preserve">2. </s> <s xml:id="echoid-s12252" xml:space="preserve">mi. </s> <s xml:id="echoid-s12253" xml:space="preserve">2. </s> <s xml:id="echoid-s12254" xml:space="preserve">Fiat, ut 10000000000. <lb/></s> <s xml:id="echoid-s12255" xml:space="preserve">quadratũ finus totius, ad 7434662088. </s> <s xml:id="echoid-s12256" xml:space="preserve">rectãgulũ contentũ ſub 74392. </s> <s xml:id="echoid-s12257" xml:space="preserve">ſinu cõ <lb/>plementi latitudinis Romæ, quæ cõtinet gr. </s> <s xml:id="echoid-s12258" xml:space="preserve">41. </s> <s xml:id="echoid-s12259" xml:space="preserve">min. </s> <s xml:id="echoid-s12260" xml:space="preserve">56. </s> <s xml:id="echoid-s12261" xml:space="preserve">& </s> <s xml:id="echoid-s12262" xml:space="preserve">ſub 99939. </s> <s xml:id="echoid-s12263" xml:space="preserve">ſinu cõple <lb/>mẽti latitudinis Malachæ, quæ habet gr. </s> <s xml:id="echoid-s12264" xml:space="preserve">2. </s> <s xml:id="echoid-s12265" xml:space="preserve">min. </s> <s xml:id="echoid-s12266" xml:space="preserve">0. </s> <s xml:id="echoid-s12267" xml:space="preserve">ita 156640. </s> <s xml:id="echoid-s12268" xml:space="preserve">ſinus uerſus diffe <lb/>rẽtiæ longitudinũ, quæ cõplectitur gr. </s> <s xml:id="echoid-s12269" xml:space="preserve">124. </s> <s xml:id="echoid-s12270" xml:space="preserve">min. </s> <s xml:id="echoid-s12271" xml:space="preserve">30. </s> <s xml:id="echoid-s12272" xml:space="preserve">ad aliud, inuenieturq́. </s> <s xml:id="echoid-s12273" xml:space="preserve">fere <lb/>hic numerus 116456. </s> <s xml:id="echoid-s12274" xml:space="preserve">a quo, qm̃ maior eſt, quàm 76679. </s> <s xml:id="echoid-s12275" xml:space="preserve">ſinus cõplementi diffe <lb/>rẽtię latitudinũ locorũ, quæ cõtinet gr. </s> <s xml:id="echoid-s12276" xml:space="preserve">39. </s> <s xml:id="echoid-s12277" xml:space="preserve">min. </s> <s xml:id="echoid-s12278" xml:space="preserve">56. </s> <s xml:id="echoid-s12279" xml:space="preserve">auferemus 76679. </s> <s xml:id="echoid-s12280" xml:space="preserve">ſuũ com-<lb/>plementi differentię latitudinum locorũ, remanebitq; </s> <s xml:id="echoid-s12281" xml:space="preserve">ſinus 39777. </s> <s xml:id="echoid-s12282" xml:space="preserve">cuius ar-<lb/>cus gr. </s> <s xml:id="echoid-s12283" xml:space="preserve">23. </s> <s xml:id="echoid-s12284" xml:space="preserve">min. </s> <s xml:id="echoid-s12285" xml:space="preserve">26. </s> <s xml:id="echoid-s12286" xml:space="preserve">additus quadrãti efficit gr. </s> <s xml:id="echoid-s12287" xml:space="preserve">113. </s> <s xml:id="echoid-s12288" xml:space="preserve">min. </s> <s xml:id="echoid-s12289" xml:space="preserve">26. </s> <s xml:id="echoid-s12290" xml:space="preserve">hoc eſt, milliaria Ita-<lb/>lica 7089. </s> <s xml:id="echoid-s12291" xml:space="preserve">{7/12}. </s> <s xml:id="echoid-s12292" xml:space="preserve">pro diſtantia inter Romam, & </s> <s xml:id="echoid-s12293" xml:space="preserve">Malachã in aurea Cherſoneſo.</s> <s xml:id="echoid-s12294" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12295" xml:space="preserve"><emph style="sc">Sit</emph> quoq. </s> <s xml:id="echoid-s12296" xml:space="preserve">inquirendũ ſpatium itinerariũ inter Romã, & </s> <s xml:id="echoid-s12297" xml:space="preserve">Mexicũ in India <lb/>occidẽtali, cuius longitudinẽ Ioſephus Moletius in tabula noua Hiſpaniæ no <lb/>uę in commentarijs in Geographiã Ptolemæi ponit ferme gr. </s> <s xml:id="echoid-s12298" xml:space="preserve">272. </s> <s xml:id="echoid-s12299" xml:space="preserve">min. </s> <s xml:id="echoid-s12300" xml:space="preserve">30. </s> <s xml:id="echoid-s12301" xml:space="preserve">la <lb/>titudinẽ uero borealem grad. </s> <s xml:id="echoid-s12302" xml:space="preserve">20. </s> <s xml:id="echoid-s12303" xml:space="preserve">min. </s> <s xml:id="echoid-s12304" xml:space="preserve">20. </s> <s xml:id="echoid-s12305" xml:space="preserve">(ut & </s> <s xml:id="echoid-s12306" xml:space="preserve">Romæ latitudo borealis eſt) <lb/>quãuis alij aliã eius longitudinẽ, ac latitudinẽ faciãt. </s> <s xml:id="echoid-s12307" xml:space="preserve">Fiat, vt 10000000000. <lb/></s> <s xml:id="echoid-s12308" xml:space="preserve">ad 6975589059. </s> <s xml:id="echoid-s12309" xml:space="preserve">rectangulũ contentũ ſub 74392. </s> <s xml:id="echoid-s12310" xml:space="preserve">ſinu complemẽti latitudinis <lb/>Romæ, quæ eſt gr. </s> <s xml:id="echoid-s12311" xml:space="preserve">41. </s> <s xml:id="echoid-s12312" xml:space="preserve">min. </s> <s xml:id="echoid-s12313" xml:space="preserve">56. </s> <s xml:id="echoid-s12314" xml:space="preserve">& </s> <s xml:id="echoid-s12315" xml:space="preserve">ſub 93768. </s> <s xml:id="echoid-s12316" xml:space="preserve">ſinu cõplementi latitudinis Mexi-<lb/>canæ, quæ poſita eſt gr. </s> <s xml:id="echoid-s12317" xml:space="preserve">20. </s> <s xml:id="echoid-s12318" xml:space="preserve">min. </s> <s xml:id="echoid-s12319" xml:space="preserve">20. </s> <s xml:id="echoid-s12320" xml:space="preserve">ita 158778. </s> <s xml:id="echoid-s12321" xml:space="preserve">ſinus uerſus differentiæ longitu <lb/>dinũ, (quæ eſt gr. </s> <s xml:id="echoid-s12322" xml:space="preserve">234. </s> <s xml:id="echoid-s12323" xml:space="preserve">min. </s> <s xml:id="echoid-s12324" xml:space="preserve">0. </s> <s xml:id="echoid-s12325" xml:space="preserve">quę quoniã ſemicirculum ſuperat, detrahenda eſt <lb/>ex circulo integro, ut remaneãt gr. </s> <s xml:id="echoid-s12326" xml:space="preserve">126. </s> <s xml:id="echoid-s12327" xml:space="preserve">min. </s> <s xml:id="echoid-s12328" xml:space="preserve">0. </s> <s xml:id="echoid-s12329" xml:space="preserve">pro differentia longitudinũ bre <lb/>uiori, nempe breuior diſtãtia inter Meridianos locorũ propoſitorum cuius ſi-<lb/>nus uerſus eſt 158778.) </s> <s xml:id="echoid-s12330" xml:space="preserve">ad aliud, inuenieturq́; </s> <s xml:id="echoid-s12331" xml:space="preserve">hic ꝓpemodũ numerus 110757. </s> <s xml:id="echoid-s12332" xml:space="preserve"><lb/>a quo, quoniam maior eſt, quàm 92977. </s> <s xml:id="echoid-s12333" xml:space="preserve">ſinus complementi differentiæ latitu <lb/>dinum locorum, quæ gr. </s> <s xml:id="echoid-s12334" xml:space="preserve">21. </s> <s xml:id="echoid-s12335" xml:space="preserve">min. </s> <s xml:id="echoid-s12336" xml:space="preserve">36. </s> <s xml:id="echoid-s12337" xml:space="preserve">complectitur, auferemus 92977. </s> <s xml:id="echoid-s12338" xml:space="preserve">ſinũ com <lb/>plementi differentiæ latitudinum, remanebitq́; </s> <s xml:id="echoid-s12339" xml:space="preserve">ſinus 17780. </s> <s xml:id="echoid-s12340" xml:space="preserve">cuius arcus gr. </s> <s xml:id="echoid-s12341" xml:space="preserve">10. </s> <s xml:id="echoid-s12342" xml:space="preserve"><lb/>min. </s> <s xml:id="echoid-s12343" xml:space="preserve">15. </s> <s xml:id="echoid-s12344" xml:space="preserve">quaſi, additus quadranti conficit gr. </s> <s xml:id="echoid-s12345" xml:space="preserve">100. </s> <s xml:id="echoid-s12346" xml:space="preserve">min. </s> <s xml:id="echoid-s12347" xml:space="preserve">15. </s> <s xml:id="echoid-s12348" xml:space="preserve">id eſt, milliaria Itali-<lb/>ca 6265 {5/8}. </s> <s xml:id="echoid-s12349" xml:space="preserve">pro diſtantia inter Romam, & </s> <s xml:id="echoid-s12350" xml:space="preserve">Mexicum in India occidentali.</s> <s xml:id="echoid-s12351" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12352" xml:space="preserve"><emph style="sc">Postremo</emph> proponatur explorãda diſtantia itineraria inter Romam, <lb/>& </s> <s xml:id="echoid-s12353" xml:space="preserve">Cuſchum Metropolim prouinciæ Peru in occidentali India nobiliſſimæ, ac <lb/>ditiſſimæ, cuius lõgitudinẽ Ioſephus Moletius in tabula noua terræ nouę ſta-<lb/>tuit gr. </s> <s xml:id="echoid-s12354" xml:space="preserve">305. </s> <s xml:id="echoid-s12355" xml:space="preserve">min. </s> <s xml:id="echoid-s12356" xml:space="preserve">40. </s> <s xml:id="echoid-s12357" xml:space="preserve">fere, latitudinẽ autẽ auſtralẽ gr. </s> <s xml:id="echoid-s12358" xml:space="preserve">18. </s> <s xml:id="echoid-s12359" xml:space="preserve">min. </s> <s xml:id="echoid-s12360" xml:space="preserve">40. </s> <s xml:id="echoid-s12361" xml:space="preserve">fere, quàmuis <lb/>alij ſcriptores aliter ſentiant. </s> <s xml:id="echoid-s12362" xml:space="preserve">Et quia Roma uergit in Boreã, & </s> <s xml:id="echoid-s12363" xml:space="preserve">Cuſchum in <lb/>Auſtrum, ſumens locũ borealẽ Coſcho oppoſitũ per diametrũ, qui nimirum <lb/>latitudinẽ habeat borealẽ gr. </s> <s xml:id="echoid-s12364" xml:space="preserve">18. </s> <s xml:id="echoid-s12365" xml:space="preserve">min. </s> <s xml:id="echoid-s12366" xml:space="preserve">40. </s> <s xml:id="echoid-s12367" xml:space="preserve">Deinde differentiã longitudinũ Ro <lb/>mæ, & </s> <s xml:id="echoid-s12368" xml:space="preserve">Cuſchi, quæ eſt gr. </s> <s xml:id="echoid-s12369" xml:space="preserve">269. </s> <s xml:id="echoid-s12370" xml:space="preserve">min. </s> <s xml:id="echoid-s12371" xml:space="preserve">10. </s> <s xml:id="echoid-s12372" xml:space="preserve">ſuperatq́. </s> <s xml:id="echoid-s12373" xml:space="preserve">ſemicirculũ, auferemus ex toto <lb/>circulo, relinqueturq́ differentia lõgitudinũ breuior, hoc eſt, breuior diſtãtia <lb/>inter Meridianos datorum locorum, gr. </s> <s xml:id="echoid-s12374" xml:space="preserve">80. </s> <s xml:id="echoid-s12375" xml:space="preserve">min. </s> <s xml:id="echoid-s12376" xml:space="preserve">50. </s> <s xml:id="echoid-s12377" xml:space="preserve">Hãc rurſus ex ſemicirculo <lb/>ſubtrahemus, ut habeamus differentiã longitudinalem inter Romã, & </s> <s xml:id="echoid-s12378" xml:space="preserve">locũ il <lb/>Ium Cuſcho oppoſitũ, id eſt, diſtantiã inter Meridianum Romæ, & </s> <s xml:id="echoid-s12379" xml:space="preserve">Meridianũ <lb/>dicti loci, gr. </s> <s xml:id="echoid-s12380" xml:space="preserve">99. </s> <s xml:id="echoid-s12381" xml:space="preserve">min. </s> <s xml:id="echoid-s12382" xml:space="preserve">10. </s> <s xml:id="echoid-s12383" xml:space="preserve">His poſitis, ſi fiat, ut 10000000000. </s> <s xml:id="echoid-s12384" xml:space="preserve">quadratũ ſinus to-<lb/>tius ad 7047823688. </s> <s xml:id="echoid-s12385" xml:space="preserve">rectãgulum cõtentum ſub 74392. </s> <s xml:id="echoid-s12386" xml:space="preserve">ſinu cõplementi latitu <lb/>dinis Romæ, quæ eſt gr. </s> <s xml:id="echoid-s12387" xml:space="preserve">41. </s> <s xml:id="echoid-s12388" xml:space="preserve">min. </s> <s xml:id="echoid-s12389" xml:space="preserve">56. </s> <s xml:id="echoid-s12390" xml:space="preserve">& </s> <s xml:id="echoid-s12391" xml:space="preserve">ſub 94739. </s> <s xml:id="echoid-s12392" xml:space="preserve">ſinu cõplemẽti latitudinis lo <lb/>ci, qui Cuſcho opponitur, quę gr. </s> <s xml:id="echoid-s12393" xml:space="preserve">18. </s> <s xml:id="echoid-s12394" xml:space="preserve">min. </s> <s xml:id="echoid-s12395" xml:space="preserve">40. </s> <s xml:id="echoid-s12396" xml:space="preserve">cõtinet, ita 115 930. </s> <s xml:id="echoid-s12397" xml:space="preserve">ſinus uerſus <lb/>differentiæ longitudinum, (quã diximus comprehendere grad. </s> <s xml:id="echoid-s12398" xml:space="preserve">99. </s> <s xml:id="echoid-s12399" xml:space="preserve">min. </s> <s xml:id="echoid-s12400" xml:space="preserve">10.) </s> <s xml:id="echoid-s12401" xml:space="preserve">ad <pb o="295" file="331" n="332" rhead="Ioan. de Sacro Boſco."/> aliud, reperietur hic quaſi numerus 81705. </s> <s xml:id="echoid-s12402" xml:space="preserve">quẽ, quia minor eſt, quàm 91867. <lb/></s> <s xml:id="echoid-s12403" xml:space="preserve">ſinus cõplementi differentiæ latitudinem locorum datorum, quæ complecti-<lb/>tur grad. </s> <s xml:id="echoid-s12404" xml:space="preserve">23. </s> <s xml:id="echoid-s12405" xml:space="preserve">min. </s> <s xml:id="echoid-s12406" xml:space="preserve">16. </s> <s xml:id="echoid-s12407" xml:space="preserve">ſubtrahemus à 91867. </s> <s xml:id="echoid-s12408" xml:space="preserve">ſinu complementi differentiæ lati-<lb/>tudinem, relinquenturq́; </s> <s xml:id="echoid-s12409" xml:space="preserve">10162. </s> <s xml:id="echoid-s12410" xml:space="preserve">pro ſinu complementi diſtãtiæ Romæ ab il-<lb/>lo loco, qui Cuſcho obijcitur. </s> <s xml:id="echoid-s12411" xml:space="preserve">Hoc autem complementum in tabula ſinuum <lb/>continet grad. </s> <s xml:id="echoid-s12412" xml:space="preserve">5. </s> <s xml:id="echoid-s12413" xml:space="preserve">min. </s> <s xml:id="echoid-s12414" xml:space="preserve">50. </s> <s xml:id="echoid-s12415" xml:space="preserve">Ipſa ergo diſtantia comprehendet gr. </s> <s xml:id="echoid-s12416" xml:space="preserve">84. </s> <s xml:id="echoid-s12417" xml:space="preserve">min. </s> <s xml:id="echoid-s12418" xml:space="preserve">10. </s> <s xml:id="echoid-s12419" xml:space="preserve">quã <lb/>ſi ex ſemicirculo demamus, relinquetur diſtantia inter Romam, & </s> <s xml:id="echoid-s12420" xml:space="preserve">Cuſchum <lb/>gr. </s> <s xml:id="echoid-s12421" xml:space="preserve">95. </s> <s xml:id="echoid-s12422" xml:space="preserve">min. </s> <s xml:id="echoid-s12423" xml:space="preserve">50. </s> <s xml:id="echoid-s12424" xml:space="preserve">nimirum milliariorum Italicorum {7/12}</s> </p> </div> <div xml:id="echoid-div625" type="section" level="1" n="210"> <head xml:id="echoid-head220" xml:space="preserve">DEHORIZONTE.</head> <p style="it"> <s xml:id="echoid-s12425" xml:space="preserve">HORIZON uero eſt circulus diuidens inferius hemiſphæ <lb/> <anchor type="note" xlink:label="note-331-01a" xlink:href="note-331-01"/> rium à ſuperiori. </s> <s xml:id="echoid-s12426" xml:space="preserve">Vnde appellatur Horizon, id eſt, termi-<lb/>nator uiſus. </s> <s xml:id="echoid-s12427" xml:space="preserve">Dicitur etiam Horizon, circulus hemiſphærij <lb/>eadem de cauſa.</s> <s xml:id="echoid-s12428" xml:space="preserve"/> </p> <div xml:id="echoid-div625" type="float" level="2" n="1"> <note position="right" xlink:label="note-331-01" xlink:href="note-331-01a" xml:space="preserve">Horizon @ <lb/>ſit, & cur <lb/>ſic dicatur.</note> </div> </div> <div xml:id="echoid-div627" type="section" level="1" n="211"> <head xml:id="echoid-head221" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s12429" xml:space="preserve"><emph style="sc">VLtimo</emph> loco inter circulos maximos agit de Horizonte, quem <lb/>in ſphęra dicit eſſe eum circulum, intellige maximũ, qui diuidit <lb/>hemiſphæriũ inferius à ſuperiori hemiſphærio. </s> <s xml:id="echoid-s12430" xml:space="preserve">Quãuis. </s> <s xml:id="echoid-s12431" xml:space="preserve">n. </s> <s xml:id="echoid-s12432" xml:space="preserve">qui-<lb/>libet circulus maximus ſphærã in duo hemiſphæria diuidat æ-<lb/>qualia, peculiari @@ ratioue, & </s> <s xml:id="echoid-s12433" xml:space="preserve">ſimpliciter hemiſphærium dici <lb/>conſueuit pars cœli uiſa, uel non uiſa, in quas partes, præter Horizontẽ, nul-<lb/>lus circulus maximus diſtribuit cœlum, niſi quando munere Horizontis fun <lb/>gitur, qualis eſt Aequator reſpectu illorum, qui ſub polis mundi habitant.</s> <s xml:id="echoid-s12434" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12435" xml:space="preserve"><emph style="sc">Docet</emph> deinde hunc circulũ appellari Horizontẽ, quaſi terminatorẽ uiſus, <lb/> <anchor type="note" xlink:label="note-331-02a" xlink:href="note-331-02"/> à<unsure/> uerbo nimirum græco ὁρίζομ{αι}, quod ſignificat determino, ꝓpterea quòd <lb/>ſeparat partem cœli uiſam à non viſa. </s> <s xml:id="echoid-s12436" xml:space="preserve">Eandem ob cauſam ait, eundẽ dici circu <lb/>lum hemiſphærij, propter uiſum ſcilicet hemiſphærium, ac non uiſum. </s> <s xml:id="echoid-s12437" xml:space="preserve">Solet <lb/>quuq; </s> <s xml:id="echoid-s12438" xml:space="preserve">hic circulus uocari gyrus hemiſphærij, & </s> <s xml:id="echoid-s12439" xml:space="preserve">a Latinis Finitor, ſiue Finiẽs.</s> <s xml:id="echoid-s12440" xml:space="preserve"/> </p> <div xml:id="echoid-div627" type="float" level="2" n="1"> <note position="right" xlink:label="note-331-02" xlink:href="note-331-02a" xml:space="preserve">Varia n@@a <lb/>Horizõtis.</note> </div> <p> <s xml:id="echoid-s12441" xml:space="preserve"><emph style="sc">Est</emph> autem Horizon in cęlo concipiendus immobilis prorſus, ſicut & </s> <s xml:id="echoid-s12442" xml:space="preserve">Me-<lb/> <anchor type="note" xlink:label="note-331-03a" xlink:href="note-331-03"/> ridianus. </s> <s xml:id="echoid-s12443" xml:space="preserve">Debet enim neceſſario eſſe rectus ad Meridianum in omni climatè; <lb/></s> <s xml:id="echoid-s12444" xml:space="preserve">Perſpicuum autem eſt, Horizontem non ſemper poſſe eſſe rectum ad Meri-<lb/>dianum, ſi moueatur, hoc manente immobili. </s> <s xml:id="echoid-s12445" xml:space="preserve">Ex quo efficitur, tot eſſe Hori-<lb/>zontes ab ortu in occaſum ſub eodem parallelo procedendo diſtinctos, quot <lb/> <anchor type="note" xlink:label="note-331-04a" xlink:href="note-331-04"/> fuperius diximus eſſe Meridianos, ſi ſenſus iudiciũ ſequamur, nẽpe 300. </s> <s xml:id="echoid-s12446" xml:space="preserve">Con <lb/>ſequuntur enim ſeſe mutuo Meridianus, atq; </s> <s xml:id="echoid-s12447" xml:space="preserve">Horizon, ita ut uno mutato, ne <lb/>ceſſario alter quoque mutetur: </s> <s xml:id="echoid-s12448" xml:space="preserve">ut mirum ſit, cur Proclus in ſphæra aſſerue-<lb/>rit Meridianũ mutari ſenſibiliter in ſpatio 300. </s> <s xml:id="echoid-s12449" xml:space="preserve">ſtadiorum, quę cõſtituunt mil <lb/>liaria 37. </s> <s xml:id="echoid-s12450" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s12451" xml:space="preserve">ut ſupra diximus: </s> <s xml:id="echoid-s12452" xml:space="preserve">Horizontẽ uero in ſpatio 400. </s> <s xml:id="echoid-s12453" xml:space="preserve">ſtadiorũ, quæ effi <lb/>ciunt milliaria 50. </s> <s xml:id="echoid-s12454" xml:space="preserve">niſi forte mutationem Horizontum intelligat non ab or-<lb/>tu in occaſum, ſed à Septentrione in meridiem. </s> <s xml:id="echoid-s12455" xml:space="preserve">Mutantur enim Horizontes <lb/>non ſolum ab ortu in occaſum, ſicut & </s> <s xml:id="echoid-s12456" xml:space="preserve">Meridiani, uerum etiam à polo ad po <lb/>lum, ita ut impoſſibile ſit omnino, in terra duas ciuitates eundẽ poſſe habere <lb/>Horizontem, ſi Geometricè loqui uelimus, ſiue una ab altera in ortum occa-<lb/>ſumve, ſiue in Boream, Meridiemve remoueatur. </s> <s xml:id="echoid-s12457" xml:space="preserve">At uero plurimæ ciuitates, <lb/>omnes uidelicet, quæ eandem habent longitudinem, uel etiam, quarum dif- <pb o="296" file="332" n="333" rhead="Comment. in II. Cap. Sphæræ"/> ferentia longitudinum cõtinet ſemicirculum, hoc eſt, grad. </s> <s xml:id="echoid-s12458" xml:space="preserve">180. </s> <s xml:id="echoid-s12459" xml:space="preserve">eundem obti-<lb/>nere poſſunt Meridianum, etiã Geometrice loquendo. </s> <s xml:id="echoid-s12460" xml:space="preserve">Quæ cum ita ſint, vo-<lb/>luit fortaſſe Proclus Meridianum, & </s> <s xml:id="echoid-s12461" xml:space="preserve">ex conſequenti Horizontem ab ortu in <lb/>occaſum ſenſibiliter variari in ſpatio 300. </s> <s xml:id="echoid-s12462" xml:space="preserve">ſtadiorum, quod nimirum attinet <lb/>ad ortum & </s> <s xml:id="echoid-s12463" xml:space="preserve">occaſum ſiderum: </s> <s xml:id="echoid-s12464" xml:space="preserve">At vero Horizontem à polo ad polum uaria-<lb/>tionem ſenſibilem ſuſcipere, quod attinet ad eleuationem poli, in ſpatio 400. <lb/></s> <s xml:id="echoid-s12465" xml:space="preserve">ſtadiorum. </s> <s xml:id="echoid-s12466" xml:space="preserve">Nam una & </s> <s xml:id="echoid-s12467" xml:space="preserve">eadem eleuatio poli inſeruire poteſt tanto ſpatio in <lb/>terra, ut oſtendunt horologia ſol aria. </s> <s xml:id="echoid-s12468" xml:space="preserve">Verumtamen neque in mutatione Me-<lb/>ridianorũ, neque Horizontum, quomodocunque loquamur, certa lex præſcri <lb/>bi poteſt. </s> <s xml:id="echoid-s12469" xml:space="preserve">Nam iuxta æquatorem mutatio unius gradus, uel duo rum in eleua <lb/>tione poli, quæ fit ex mutatione Horizontum à polo ad polum, nullum ſen-<lb/>fibilem errorem inducit, quancũ ad incrementũ, & </s> <s xml:id="echoid-s12470" xml:space="preserve">decrementum dierum, no-<lb/>ctiumq́.</s> <s xml:id="echoid-s12471" xml:space="preserve">, & </s> <s xml:id="echoid-s12472" xml:space="preserve">uarietatem umbrarũ: </s> <s xml:id="echoid-s12473" xml:space="preserve">At iuxta polos, unius tantũmodo gradus mu-<lb/>tatio maximam inducit differentiam in phænomenis Aſtronomorum. </s> <s xml:id="echoid-s12474" xml:space="preserve">Idemq́; </s> <s xml:id="echoid-s12475" xml:space="preserve"><lb/>proportione quadam dices de Meridianis, qui mutantur ab ortu in occaſum. </s> <s xml:id="echoid-s12476" xml:space="preserve"><lb/>Verum hæc omnia Geometricè poſſunt demonſtrari ex ſphæricis elementis <lb/>Theodoſij, ac Menelai, eademque certiſſime docet calculus ſinuum.</s> <s xml:id="echoid-s12477" xml:space="preserve"/> </p> <div xml:id="echoid-div628" type="float" level="2" n="2"> <note position="right" xlink:label="note-331-03" xlink:href="note-331-03a" xml:space="preserve">Horizon <lb/>concipien-<lb/>dus eſt im-<lb/>mobilis.</note> <note position="right" xlink:label="note-331-04" xlink:href="note-331-04a" xml:space="preserve">Tot eſſe ho <lb/>rizontes ab <lb/>ortu in oc-<lb/>casũ, quot <lb/>meridiani.</note> </div> <p> <s xml:id="echoid-s12478" xml:space="preserve"><emph style="sc">Proclvs</emph>, Albertus magnus, & </s> <s xml:id="echoid-s12479" xml:space="preserve">plerique alij ſcriptores duplicem Hori-<lb/>zontem conſtituunt. </s> <s xml:id="echoid-s12480" xml:space="preserve">Dicunt enim unum eſſe ratione perceptum, quem ap-<lb/>pellant Rationalem, Naturalemve: </s> <s xml:id="echoid-s12481" xml:space="preserve">Alterum ſenſu eſſe perceptum, quem uo-<lb/>cant Senſibilem, Apparentemve. </s> <s xml:id="echoid-s12482" xml:space="preserve">Rationalis eſt, qui diuidit totum cœlum in <lb/> <anchor type="note" xlink:label="note-332-01a" xlink:href="note-332-01"/> duo hemiſphæria æqualia, ſegregatq́; </s> <s xml:id="echoid-s12483" xml:space="preserve">partem cœli uiſam à nõ uiſa, cuius poli <lb/>in ſphæra ſunt uertex capitis, ſeu Zenith, & </s> <s xml:id="echoid-s12484" xml:space="preserve">pũctu m oppoſitum, quod Nadit <lb/>appellant; </s> <s xml:id="echoid-s12485" xml:space="preserve">centrum uero idem quod centrum terræ. </s> <s xml:id="echoid-s12486" xml:space="preserve">Nam quod vulgo dici ſo-<lb/>let, Horizontem, de quo Aſtronomi diſputant, eſſe planam ſuperficiẽ circula-<lb/> <anchor type="figure" xlink:label="fig-332-01a" xlink:href="fig-332-01"/> rem incumbentem ſu-<lb/>perficiei terræ, attingen <lb/>temq́. </s> <s xml:id="echoid-s12487" xml:space="preserve">cœlum undique, <lb/>ita ut diuidat ipſum in <lb/>duas partes æquales; </s> <s xml:id="echoid-s12488" xml:space="preserve">in-<lb/>telligendũ eſt duntaxat <lb/>ſecundum iudicium ſen <lb/>ſuum. </s> <s xml:id="echoid-s12489" xml:space="preserve">Geometricè enim <lb/>loquendo, huiuſmodi <lb/>ſuperficies non diuidit <lb/>cœlum bifariã, cum non <lb/>tranſeat per eius cen-<lb/>trum: </s> <s xml:id="echoid-s12490" xml:space="preserve">Tamen quia di-<lb/>ſtantia à ſuperficie ter-<lb/>ræ uſque ad centrũ eius <lb/>tanta non eſt, quæ effi-<lb/>cere poſſit, ut oculus in <lb/>terræ globo cõſtitutus, <lb/>ſublatis alijsimpedimen <lb/>tis, montium uidelicer, <lb/>& </s> <s xml:id="echoid-s12491" xml:space="preserve">uallium, mediam par <lb/>tem cœli non conſpiciat; </s> <s xml:id="echoid-s12492" xml:space="preserve">Immo fieri poteſt, ut quis in excelſo aliquo monte <lb/>exiſtens plus, quàm mediã partem cœli conſpiciat: </s> <s xml:id="echoid-s12493" xml:space="preserve">factum eſt, ut ſuperficies il <pb o="297" file="333" n="334" rhead="Ioan. de Sacro Boſco."/> la circularis ſuperficiei terræ incũbens pro Horizonte capiatur. </s> <s xml:id="echoid-s12494" xml:space="preserve">Vt enim ꝑlu <lb/>rimis experimentis in 1. </s> <s xml:id="echoid-s12495" xml:space="preserve">ca. </s> <s xml:id="echoid-s12496" xml:space="preserve">comprobauimus, hæc ſuperficies ſenſibiliter cœlũ <lb/>in duas medietates diſſecat, quãuis Geometrice loquendo tãtummodo ſuper-<lb/>ficies per centrum terræ educta cęlum bifariam ſecet, quæ Horizon rationa-<lb/>lis à prædictis auctoribus uocatur, quòd ſola ratione ſit collectus. </s> <s xml:id="echoid-s12497" xml:space="preserve">Neq; </s> <s xml:id="echoid-s12498" xml:space="preserve">enim <lb/>acies oculorum ad extremum uſq; </s> <s xml:id="echoid-s12499" xml:space="preserve">cęlum excurrit, ut cęli diuiſionem in par-<lb/>tes æquales percipiat, ſed ex phænomenis uarijs, quæ ſenſu percipiuntur, mẽs <lb/>ratiocinando colligit, rem ita ſeſe habere. </s> <s xml:id="echoid-s12500" xml:space="preserve">Eadem de cauſa uocatur à nonnul-<lb/> <anchor type="note" xlink:label="note-333-01a" xlink:href="note-333-01"/> lis Artificialis, eo quod beneficio artis Aſtronomicæ ſit inuentus. </s> <s xml:id="echoid-s12501" xml:space="preserve">De hoc igi <lb/>tur Horizonte rationali diſſerit hoc loco @oannes de Sacroboſco, eiq; </s> <s xml:id="echoid-s12502" xml:space="preserve">æqui-<lb/>diſtat omne pauimentum ad libellam conſtructum. </s> <s xml:id="echoid-s12503" xml:space="preserve">Item quæuis ſuperficies <lb/>conuexa aquæ, quatenus nimirum ſenſui plana eſſe uidetur.</s> <s xml:id="echoid-s12504" xml:space="preserve"/> </p> <div xml:id="echoid-div629" type="float" level="2" n="3"> <note position="left" xlink:label="note-332-01" xlink:href="note-332-01a" xml:space="preserve">Horizon <lb/>Rationalis <lb/>quid.</note> <figure xlink:label="fig-332-01" xlink:href="fig-332-01a"> <image file="332-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/332-01"/> </figure> <note position="right" xlink:label="note-333-01" xlink:href="note-333-01a" xml:space="preserve">Horizon@ <lb/>artificialis <lb/>quid.</note> </div> <p> <s xml:id="echoid-s12505" xml:space="preserve"><emph style="sc">Horizon</emph> ſenſibilis nuncupatur illud ſpacium in ſuperficie terræ, mariſ-<lb/> <anchor type="note" xlink:label="note-333-02a" xlink:href="note-333-02"/> ue, quod acies oculorum circumducta conſpicere poteſt, ſublatis omnibus <lb/>impedimentis. </s> <s xml:id="echoid-s12506" xml:space="preserve">Quoniam enim terra rotunda eſt, non poteſt oculus in eius ſu <lb/>perficie conſtitutus maius ſpatium intueri, quàm quod auferunt lineæ rectæ <lb/>ab oculo egrediẽtes, quæ globi terreſtris ſuperficiem contingãt, ut apud Per-<lb/>ſpectiuos manifeſtum eſt. </s> <s xml:id="echoid-s12507" xml:space="preserve">Hoc autem ſpacium non eiuſdem quantitatis om-<lb/>nes auctores faciunt. </s> <s xml:id="echoid-s12508" xml:space="preserve">Ex ſententia enim Macrobij eius ſemidiameter comple <lb/>ctitur ſtadia 180. </s> <s xml:id="echoid-s12509" xml:space="preserve">hoc eſt, milliaria 22 {1/2}. </s> <s xml:id="echoid-s12510" xml:space="preserve">Eratoſthenes eandem ſtatuit ſtadio-<lb/>rum 350. </s> <s xml:id="echoid-s12511" xml:space="preserve">quæ milliaria ferme efficiunt 44. </s> <s xml:id="echoid-s12512" xml:space="preserve">Albertus Magnus aſſerit eandem <lb/>continere ſtadia 1000. </s> <s xml:id="echoid-s12513" xml:space="preserve">id eſt, milliaria 125. </s> <s xml:id="echoid-s12514" xml:space="preserve">Proclus autem eandẽ facit ſtadio-<lb/>rum 2000. </s> <s xml:id="echoid-s12515" xml:space="preserve">quæ efficiunt milliaria 250. </s> <s xml:id="echoid-s12516" xml:space="preserve">Apud pleroſque uero reperies eandẽ <lb/>continere, tanquã iuxta ueriorem ſentẽtiam, ſtadia 500. </s> <s xml:id="echoid-s12517" xml:space="preserve">duntaxat, ſeu millia-<lb/>ria 62 {1/2}. </s> <s xml:id="echoid-s12518" xml:space="preserve">Quantumcumque denique hoc ſpatiũ exiſtat, (difficile enim deter <lb/>minari poteſt) ſatis nobis ſit, illud appellari Horizontem ſenſibilem.</s> <s xml:id="echoid-s12519" xml:space="preserve"/> </p> <div xml:id="echoid-div630" type="float" level="2" n="4"> <note position="right" xlink:label="note-333-02" xlink:href="note-333-02a" xml:space="preserve">Horizon <lb/>ſenſibilis <lb/>quid.</note> </div> <p style="it"> <s xml:id="echoid-s12520" xml:space="preserve">EST autem duplex Horizon, rectus, & </s> <s xml:id="echoid-s12521" xml:space="preserve">obliquus ſiue declinis. </s> <s xml:id="echoid-s12522" xml:space="preserve">Re-<lb/> <anchor type="note" xlink:label="note-333-03a" xlink:href="note-333-03"/> ctum Horizontem, & </s> <s xml:id="echoid-s12523" xml:space="preserve">ſphæram rectam habent illi, quorum Zenith eſt in <lb/>Aequinoctiali, quia illorum Horizon eſt circulus tranſiens per polos <lb/>mundi, diuidens Aequinoctialem ad angulos rectos ſphærales: </s> <s xml:id="echoid-s12524" xml:space="preserve">Vnde di-<lb/> <anchor type="note" xlink:label="note-333-04a" xlink:href="note-333-04"/> citur Horizonrectus, & </s> <s xml:id="echoid-s12525" xml:space="preserve">ſphæra recta. </s> <s xml:id="echoid-s12526" xml:space="preserve">Obliquum Horizontem, ſiue de-<lb/>cliuem habent illi, quibus polus mundi eleuatur ſupra Horizontem: </s> <s xml:id="echoid-s12527" xml:space="preserve">Et <lb/>quoniam illorum Horizon interſecat Aequinoctialem ad angolus im-<lb/>pares & </s> <s xml:id="echoid-s12528" xml:space="preserve">obliquos, dicitur Horizon obliquus, & </s> <s xml:id="echoid-s12529" xml:space="preserve">ſphęra obliqua, ſiue <lb/>decliuis.</s> <s xml:id="echoid-s12530" xml:space="preserve"/> </p> <div xml:id="echoid-div631" type="float" level="2" n="5"> <note position="right" xlink:label="note-333-03" xlink:href="note-333-03a" xml:space="preserve">Horizon <lb/>rectus, & <lb/>obliquus.</note> <note position="right" xlink:label="note-333-04" xlink:href="note-333-04a" xml:space="preserve">Qui habeã@ <lb/>Horizõtem <lb/>rectum vel <lb/>obliquum.</note> </div> </div> <div xml:id="echoid-div633" type="section" level="1" n="212"> <head xml:id="echoid-head222" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s12531" xml:space="preserve"><emph style="sc">Dividit</emph> Horizontem in rectum, & </s> <s xml:id="echoid-s12532" xml:space="preserve">obliquum, docetque rectum appel-<lb/>lari quoque ſphæram rectam, obliquum autem ſphæram obliquam. </s> <s xml:id="echoid-s12533" xml:space="preserve">Qua de <lb/>re plura ſcripſi in primo cap. </s> <s xml:id="echoid-s12534" xml:space="preserve">Nunc ſatis erit utrumque Horizontẽ, ſeu ſphæ-<lb/>ram proprijs figuris ob oculos ponere.</s> <s xml:id="echoid-s12535" xml:space="preserve"/> </p> <pb o="298" file="334" n="335" rhead="Comment. in II. Cap. Sphæræ."/> </div> <div xml:id="echoid-div634" type="section" level="1" n="213"> <head xml:id="echoid-head223" xml:space="preserve">SCHEMA ORIZONTIS RECTI <lb/>ET OBLIQVI.</head> <figure> <image file="334-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/334-01"/> </figure> <p style="it"> <s xml:id="echoid-s12536" xml:space="preserve">ZENITH autem capitis noſtri ſemper eſt polus Horizontis. </s> <s xml:id="echoid-s12537" xml:space="preserve">Vn-<lb/> <anchor type="note" xlink:label="note-334-01a" xlink:href="note-334-01"/> de ex his patet, quòd quanta eſt eleuatio poli mundi ſupra Horizontem, <lb/>tanta eſt diſtantia Zenith ab Aequinoctiali, quod ſic patet. </s> <s xml:id="echoid-s12538" xml:space="preserve">Cum in quo-<lb/>libet die naturali uterque Colurus bis iungatur Meridiano, ſiue idem ſit <lb/>quod Meridianus, quidquid de uno probatur, & </s> <s xml:id="echoid-s12539" xml:space="preserve">de reliquo. </s> <s xml:id="echoid-s12540" xml:space="preserve">Sumatur igi-<lb/>tur quarta pars Coluri diſtinguentis Solſtitia, quæ eſt ab Aequinoctiali <lb/> <anchor type="note" xlink:label="note-334-02a" xlink:href="note-334-02"/> uſque ad polum mundi: </s> <s xml:id="echoid-s12541" xml:space="preserve">Sumatur iterum quarta pars eiuſdem Coluri, quę <lb/>eſt à Zcnith uſque ad Horizontem, cum Zenith ſi polus Horizontis. </s> <s xml:id="echoid-s12542" xml:space="preserve">Iſtæ <lb/>duę quartę, cum ſint quartæ eiuſdem circuli, inter ſe ſunt æquales: </s> <s xml:id="echoid-s12543" xml:space="preserve">Sed ſi <lb/>ab ęqualibus æqualia demantur, uel idem commune, reſidua ſunt ęqua-<lb/>lia. </s> <s xml:id="echoid-s12544" xml:space="preserve">Dempto communi igitur arcu, ſcilicet, qui eſt inter Zenith, & </s> <s xml:id="echoid-s12545" xml:space="preserve">polum <lb/>mundi, reſidua erunt æqualia, ſcilicet eleuatio poli mundi ſupra Horizon-<lb/>tem, & </s> <s xml:id="echoid-s12546" xml:space="preserve">diſtantia Zenith ab Aequinoctiali.</s> <s xml:id="echoid-s12547" xml:space="preserve"/> </p> <div xml:id="echoid-div634" type="float" level="2" n="1"> <note position="left" xlink:label="note-334-01" xlink:href="note-334-01a" xml:space="preserve">Zenith ca-<lb/>pitis eſſe po <lb/>lum Hori-<lb/>zontis.</note> <note position="left" xlink:label="note-334-02" xlink:href="note-334-02a" xml:space="preserve">Eleuatio <lb/>poli ſupra <lb/>Horizõtem <lb/>æqualis eſt <lb/>diſtãtiæ Ze <lb/>nith ab Ae-<lb/>quatore.</note> </div> </div> <div xml:id="echoid-div636" type="section" level="1" n="214"> <head xml:id="echoid-head224" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s12548" xml:space="preserve"><emph style="sc">Ex</emph> <emph style="sc">Eo</emph> quod Zenith, ſeu uertex capitis noſtri perpetuo polus eſt Hori-<lb/> <anchor type="figure" xlink:label="fig-334-02a" xlink:href="fig-334-02"/> zontis, ita ut à Zenith quaqua uerſus ad Horizo-<lb/>tem uſque ſit Quadrans circuli, demonſtrat hoc <lb/>loco auctor, tantam eſſe eleuationem poli ſupra <lb/>Horizontẽ, quanta eſt diſtantia Zenith ab Aequa-<lb/>tore; </s> <s xml:id="echoid-s12549" xml:space="preserve">quod nos ſupra in Meridiano circulo, ut no-<lb/>tum, aſſumpſimus. </s> <s xml:id="echoid-s12550" xml:space="preserve">Demonſtratio uero aucto-<lb/>ris culibet perſpicua eſſe poteſt in hac figura, in <lb/>qua circulus A B C D, ſit Colurus ſolſtitio-<lb/>rum idem, qui Meridianus, Horizon, A E C; <lb/></s> <s xml:id="echoid-s12551" xml:space="preserve">Aequator B E I; </s> <s xml:id="echoid-s12552" xml:space="preserve">poli mundi, G, H; </s> <s xml:id="echoid-s12553" xml:space="preserve">Zenith <lb/>F; </s> <s xml:id="echoid-s12554" xml:space="preserve">Quadrans ab Aequatore per Zenith uſque ad <pb o="299" file="335" n="336" rhead="Ioan. de Sacro Boſco."/> polum arcus BFG; </s> <s xml:id="echoid-s12555" xml:space="preserve">Quadrans a Zenith per polum ad Horizontem uſque ar-<lb/>cus F G C: </s> <s xml:id="echoid-s12556" xml:space="preserve">Cum igitur Quadrantes BG, FC, ſint æquales, perſpicuum eſt, dẽ-<lb/>pto communi arcu F G, reliquum arcum GC, nempe eleuationem poli ſupra <lb/> <anchor type="note" xlink:label="note-335-01a" xlink:href="note-335-01"/> Horizontem, æqualem eſſe arcui reliquo FB, nimirum diſtantiæ Zenit ab Ae-<lb/>quatore. </s> <s xml:id="echoid-s12557" xml:space="preserve">Hinc perſpicuum eſt, altitudinem poli in quacunque ciuitate æqua <lb/>lem eſſe latitudini eiuſdem loci, cum tanta ſit latitudo loci, quanta eſt diſtan <lb/>tia Zenith ab Aequatore.</s> <s xml:id="echoid-s12558" xml:space="preserve"/> </p> <div xml:id="echoid-div636" type="float" level="2" n="1"> <figure xlink:label="fig-334-02" xlink:href="fig-334-02a"> <image file="334-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/334-02"/> </figure> <note position="right" xlink:label="note-335-01" xlink:href="note-335-01a" xml:space="preserve">Latitudo lo <lb/>ci cuiuſuis <lb/>æqualis eſt <lb/>altitudini <lb/>poli ſupra <lb/>Horizon@ẽ.</note> </div> </div> <div xml:id="echoid-div638" type="section" level="1" n="215"> <head xml:id="echoid-head225" xml:space="preserve">OFFICIA HORIZONTIS.</head> <head xml:id="echoid-head226" xml:space="preserve">I.</head> <p> <s xml:id="echoid-s12559" xml:space="preserve"><emph style="sc">Dividit</emph> cælum in duo hemiſphęria æqualia, ſuperum ſeu uiſum alte-<lb/> <anchor type="note" xlink:label="note-335-02a" xlink:href="note-335-02"/> rum, alterum uero inferum ſeu occultum.</s> <s xml:id="echoid-s12560" xml:space="preserve"/> </p> <div xml:id="echoid-div638" type="float" level="2" n="1"> <note position="right" xlink:label="note-335-02" xlink:href="note-335-02a" xml:space="preserve">Horizon ſe <lb/>cat cælum <lb/>@ hemiſphæ <lb/>rium uisũ, <lb/>uel ſuperũ, <lb/>& nõ uisũ, <lb/>uel inferũ.</note> </div> </div> <div xml:id="echoid-div640" type="section" level="1" n="216"> <head xml:id="echoid-head227" xml:space="preserve">II.</head> <p> <s xml:id="echoid-s12561" xml:space="preserve"><emph style="sc">Est</emph> cauſa rectæ, & </s> <s xml:id="echoid-s12562" xml:space="preserve">obliquæ ſphæræ. </s> <s xml:id="echoid-s12563" xml:space="preserve">Quo enim Horizon aliquis polum <lb/>mundi magis eleuatum habet, eo etiam magis obliquam ſphæram habebũt il-<lb/>li, qui in tali Horizonte habitant, & </s> <s xml:id="echoid-s12564" xml:space="preserve">quo minus eleuatum polum habet Hori-<lb/>zon quiſpiam, eo quoque minus obliquam ſphæram nanciſcẽtur degentes in <lb/> <anchor type="note" xlink:label="note-335-03a" xlink:href="note-335-03"/> tali Horizonte; </s> <s xml:id="echoid-s12565" xml:space="preserve">adeo ut ubi maxime alter polorum ſupra Horizontem extol <lb/>litur, ibi maxime obliqua exiſtat ſphæra, ut contingit habitantibus ſub mun-<lb/>di polis; </s> <s xml:id="echoid-s12566" xml:space="preserve">Vbi uero nulla eſt eleuatio ſupra Horizontem, ut degentibus ſub Ae <lb/>quatore directe accidit, ibi nulla ſit ſphæræ obliquitas, ſed omnino ſphæra re <lb/>cta exiſtat.</s> <s xml:id="echoid-s12567" xml:space="preserve"/> </p> <div xml:id="echoid-div640" type="float" level="2" n="1"> <note position="right" xlink:label="note-335-03" xlink:href="note-335-03a" xml:space="preserve">Horizõ cau <lb/>ſa eſt rectæ, <lb/>& obliquæ <lb/>ſphæræ.</note> </div> </div> <div xml:id="echoid-div642" type="section" level="1" n="217"> <head xml:id="echoid-head228" xml:space="preserve">III.</head> <note position="right" xml:space="preserve">Horizon <lb/>determinat <lb/>diem, & no <lb/>ctem artifi-<lb/>cialem.</note> <p> <s xml:id="echoid-s12568" xml:space="preserve"><emph style="sc">Penes</emph>. </s> <s xml:id="echoid-s12569" xml:space="preserve">Horizontem ſumitur quantitas cuiuslibet diei, & </s> <s xml:id="echoid-s12570" xml:space="preserve">noctis artifi-<lb/>cialis. </s> <s xml:id="echoid-s12571" xml:space="preserve">Definitur enim Dies artificialis eſſe mora Solis ſupra Horizontẽ: </s> <s xml:id="echoid-s12572" xml:space="preserve">Nox <lb/>uero, mora eiuſdem Solis infra Horizontem. </s> <s xml:id="echoid-s12573" xml:space="preserve">Hæc autem mora cognoſcitur <lb/>tantummodo ex arcubus parallelorum ſupra, uel infra Horizontem, quos Sol <lb/> <anchor type="note" xlink:label="note-335-05a" xlink:href="note-335-05"/> ad motum diurnum deſcribit: </s> <s xml:id="echoid-s12574" xml:space="preserve">Ita ut ſi Horizon diuidat omnes parallelos <lb/>per æqualia, ut fit in ſphæra recta, perpetuo dies noctibus ſint æquales: </s> <s xml:id="echoid-s12575" xml:space="preserve">ſi uero <lb/>per inæqualia, diebus noctes ſint inæquales: </s> <s xml:id="echoid-s12576" xml:space="preserve">Sed de his plura in 3. </s> <s xml:id="echoid-s12577" xml:space="preserve">cap. </s> <s xml:id="echoid-s12578" xml:space="preserve">Ex quo <lb/>facile colligitur, Horizontem ſolum eſſe cauſam inęqualitatis dierum, ac no-<lb/>ctium artificialium.</s> <s xml:id="echoid-s12579" xml:space="preserve"/> </p> <div xml:id="echoid-div642" type="float" level="2" n="1"> <note position="right" xlink:label="note-335-05" xlink:href="note-335-05a" xml:space="preserve">Dies & nox <lb/>artificialis <lb/>quid.</note> </div> </div> <div xml:id="echoid-div644" type="section" level="1" n="218"> <head xml:id="echoid-head229" xml:space="preserve">IIII.</head> <p> <s xml:id="echoid-s12580" xml:space="preserve"><emph style="sc">Ostendit</emph> moram omnium ſtellarum ſupra Horizontem, & </s> <s xml:id="echoid-s12581" xml:space="preserve">infra eũ-<lb/> <anchor type="note" xlink:label="note-335-06a" xlink:href="note-335-06"/> dem. </s> <s xml:id="echoid-s12582" xml:space="preserve">Quando enim Horizon omnes parallellos, qui ad motum diurnum de-<lb/>ſcribuntur, diuidit bifariam, ut contingit in ſphæra recta, quælibet ſtella tan-<lb/>tum temporis ſpacium conſumit ſupra Horizontẽ, quantũ infra eundẽ: </s> <s xml:id="echoid-s12583" xml:space="preserve">Quã-<lb/>do uero Horizon parallelos nõ bifariam ſecat, ut fit in ſphæra obliqua, ſtellæ <lb/>ab Aequatore uerſus polum conſpicuum declinantes maiorem trahunt morã <lb/>ſupra, quàm infra Horizontem: </s> <s xml:id="echoid-s12584" xml:space="preserve">cuiuſmodi ſunt nobis in Europa degentibus <lb/>omnes ſtellæ in hemiſphærio Boreali conſtitutæ: </s> <s xml:id="echoid-s12585" xml:space="preserve">Declinantes autem ad po-<lb/>lum occultum minus temporis conſumunt ſupra Horizontem, quã infra, qua-<lb/>les ſunt in noſtro Horizõte omnes ſtellæ poſitæ in hemiſphærio Auſtrali. </s> <s xml:id="echoid-s12586" xml:space="preserve">Quę <lb/>omnia facile demonſtrantur ex ſphæricis elementis Theodoſij. </s> <s xml:id="echoid-s12587" xml:space="preserve">Immo quædã <lb/>ſtellæ in ſphæra quacunq. </s> <s xml:id="echoid-s12588" xml:space="preserve">obliqua non aſcendunt ſupra Horizontem, ſed ſub <lb/>eo perpetuo deliteſcunt: </s> <s xml:id="echoid-s12589" xml:space="preserve">quædam uero non infra ipſum deſcendunt, ſed ſem-<lb/>per conſpicuæ ſupra Horizontem exiſtunt, ut mox dicemus.</s> <s xml:id="echoid-s12590" xml:space="preserve"/> </p> <div xml:id="echoid-div644" type="float" level="2" n="1"> <note position="right" xlink:label="note-335-06" xlink:href="note-335-06a" xml:space="preserve">Horizon in-<lb/>dicat mo-<lb/>rã omnium <lb/>ſtellarumſu <lb/>pra Hori-<lb/>zontem.</note> </div> <pb o="300" file="336" n="337" rhead="Comment. in II. Cap. Sphæræ"/> <note position="left" xml:space="preserve">Horizon <lb/>oſtẽdit pũ-<lb/>cta ortus & <lb/>occaſus ſi-<lb/>derum, & <lb/>quantũ eo <lb/>rum ortus <lb/>& occaſus <lb/>ab æquino-<lb/>ctiali ortu, <lb/>& occaſu <lb/>diſter.</note> </div> <div xml:id="echoid-div646" type="section" level="1" n="219"> <head xml:id="echoid-head230" xml:space="preserve">V.</head> <p> <s xml:id="echoid-s12591" xml:space="preserve"><emph style="sc">Manifestat</emph> puncta ortus, & </s> <s xml:id="echoid-s12592" xml:space="preserve">occaſus omnium ſiderum, & </s> <s xml:id="echoid-s12593" xml:space="preserve">quan-<lb/>tum eorum ortus, occaſusq́; </s> <s xml:id="echoid-s12594" xml:space="preserve">diſtet á vero, & </s> <s xml:id="echoid-s12595" xml:space="preserve">æquinoctiali ortu, cuius rei ratio <lb/>nem maximam habent Aſtronomi, præcipue in quantitatibus vmbrarum prę-<lb/>niendis. </s> <s xml:id="echoid-s12596" xml:space="preserve">Appellatur ortus uerus ſiue aequinoctialis, punctũ illud, in quo Ae-<lb/>quator Horizontẽ fecat ex parte orientis; </s> <s xml:id="echoid-s12597" xml:space="preserve">occaſus autem verus, æquinoctia-<lb/>lisve, dicitur illud punctum, in quo Aequator eundẽ Horizontem interſecat <lb/>ex parte occidentis. </s> <s xml:id="echoid-s12598" xml:space="preserve">Quando igitur aſtrũ nõ oritur, aut occidit in tali puncto, <lb/>dicitur ab Aſtronomis habere latitu dinẽ ortiuã, uel occiduã; </s> <s xml:id="echoid-s12599" xml:space="preserve">Ita ut Latitudo, <lb/>ſeu amplitude ortiua, occiduave cuiuſcunque aſtri, ſit arcus Horizontis in-<lb/> <anchor type="note" xlink:label="note-336-02a" xlink:href="note-336-02"/> terceptus inter punctum ortus, uel occaſus dicti aſtri, & </s> <s xml:id="echoid-s12600" xml:space="preserve">punctum ueriortus, <lb/>uel occaſus. </s> <s xml:id="echoid-s12601" xml:space="preserve">Et autem in omni climate amplitudo ſeu latitudo ortiua cuiufli <lb/>bet altri æqualis amplitudini, ſeu latitudini occiduæ eiuſdem aſtri. </s> <s xml:id="echoid-s12602" xml:space="preserve">Item duo <lb/> <anchor type="note" xlink:label="note-336-03a" xlink:href="note-336-03"/> aſtra æqualiter ab Aequatore remota, unum quidem in Boream, alterum ve <lb/>ro in Auſtrum, uel etiam utrum que in Boream, uel in Auſtrum, habent ęqua <lb/>les amplitudines ortiuas, & </s> <s xml:id="echoid-s12603" xml:space="preserve">occiduas; </s> <s xml:id="echoid-s12604" xml:space="preserve">Vt facile ex elementis ſphæricis Theo-<lb/>doſij, & </s> <s xml:id="echoid-s12605" xml:space="preserve">Menelai poteſt deduci. </s> <s xml:id="echoid-s12606" xml:space="preserve">Ex quo fit, amplitudines ortiuas, & </s> <s xml:id="echoid-s12607" xml:space="preserve">occiduas <lb/>punctorum unius Quadrãtis Eclipticæ, ęquales eſſe omnibus amplitudinibus <lb/>ortiuis & </s> <s xml:id="echoid-s12608" xml:space="preserve">occiduis punctorum omnium, quæ in alijs Quadrantibus reperiun <lb/>tur, ita ut ſemper exiſtant quaterna puncta Eclipticæ, quorum æquales ſint <lb/>amplitudines ortiuę, atque occiduę, quemadmodum ſupra de declinationi <lb/>bus punctorum Eclipticæ diximus.</s> <s xml:id="echoid-s12609" xml:space="preserve"/> </p> <div xml:id="echoid-div646" type="float" level="2" n="1"> <note position="left" xlink:label="note-336-02" xlink:href="note-336-02a" xml:space="preserve">Ortus uel <lb/>occaſus ue-<lb/>rus, æquino <lb/>ctialiſve ꝗd</note> <note position="left" xlink:label="note-336-03" xlink:href="note-336-03a" xml:space="preserve">Latitudo <lb/>ortiua uel <lb/>occidua ſtel <lb/>læ qũid.</note> </div> <p> <s xml:id="echoid-s12610" xml:space="preserve"><emph style="sc">Imve nietvr</emph> amplitudo ortiua ſiue occidua cuiuſuis puncti Ecli-<lb/> <anchor type="note" xlink:label="note-336-04a" xlink:href="note-336-04"/> pticæ, uel etiam ſtellę cuiuſlibet, ex doctrina ſinuũ hac ratione. </s> <s xml:id="echoid-s12611" xml:space="preserve">Multiplicetur <lb/>ſinus declinationis ſtellæ, punctiue Eclipticæ propoſiti in ſinum totũ, produ-<lb/>ctusq; </s> <s xml:id="echoid-s12612" xml:space="preserve">numerus per ſinum complementi latitudinis loci, in quo amplitudinẽ <lb/>inquiris, (Appellamus complementũ alicuius arcus, id quod illi deeſt ad Qua <lb/>drãtem complendum. </s> <s xml:id="echoid-s12613" xml:space="preserve">Vt complementum 30. </s> <s xml:id="echoid-s12614" xml:space="preserve">graduum erit arcus 60. </s> <s xml:id="echoid-s12615" xml:space="preserve">grad. </s> <s xml:id="echoid-s12616" xml:space="preserve">& </s> <s xml:id="echoid-s12617" xml:space="preserve"><lb/>ſic de@reliquis arcubus.) </s> <s xml:id="echoid-s12618" xml:space="preserve">diuidatur. </s> <s xml:id="echoid-s12619" xml:space="preserve">Exibit enim ſinus, cuius arcus ex tabula ſi-<lb/>nuum inuẽtus dabit amplitudinem quæſitam. </s> <s xml:id="echoid-s12620" xml:space="preserve">Nam ut demõſtrant Geber lib. <lb/></s> <s xml:id="echoid-s12621" xml:space="preserve">2. </s> <s xml:id="echoid-s12622" xml:space="preserve">& </s> <s xml:id="echoid-s12623" xml:space="preserve">Ioan. </s> <s xml:id="echoid-s12624" xml:space="preserve">Regiom. </s> <s xml:id="echoid-s12625" xml:space="preserve">lib. </s> <s xml:id="echoid-s12626" xml:space="preserve">2. </s> <s xml:id="echoid-s12627" xml:space="preserve">Epitomes propoſ. </s> <s xml:id="echoid-s12628" xml:space="preserve">2. </s> <s xml:id="echoid-s12629" xml:space="preserve">& </s> <s xml:id="echoid-s12630" xml:space="preserve">ut a nobis demonſtratũ eſt lib. </s> <s xml:id="echoid-s12631" xml:space="preserve"><lb/>1. </s> <s xml:id="echoid-s12632" xml:space="preserve">Gnomonices propoſ. </s> <s xml:id="echoid-s12633" xml:space="preserve">34. </s> <s xml:id="echoid-s12634" xml:space="preserve">Sicut ſe habet ſinus complementi altitudinis poli, <lb/>ſeu latitudinis cuiuſcunq; </s> <s xml:id="echoid-s12635" xml:space="preserve">loci, ad ſinum declinationis ſtellæ, ſeu puncti Ecli <lb/>ptieæ, ita ſe ſe habet ſinus totus ad ſinũ amplitudinis ortiuæ, occiduæve pro-<lb/>poſitæ ſtellæ, uel puncti Eclipticæ. </s> <s xml:id="echoid-s12636" xml:space="preserve"><emph style="sc">Exemplvm</emph>. </s> <s xml:id="echoid-s12637" xml:space="preserve">Sole exiſtente in prin-<lb/>cipio ♋. </s> <s xml:id="echoid-s12638" xml:space="preserve">Multiplico ſinũ declinationis, quę eſt grad. </s> <s xml:id="echoid-s12639" xml:space="preserve">23. </s> <s xml:id="echoid-s12640" xml:space="preserve">min. </s> <s xml:id="echoid-s12641" xml:space="preserve">30. </s> <s xml:id="echoid-s12642" xml:space="preserve">nẽpe. </s> <s xml:id="echoid-s12643" xml:space="preserve">39874 <lb/>in ſinum totum, ut in 100000. </s> <s xml:id="echoid-s12644" xml:space="preserve">& </s> <s xml:id="echoid-s12645" xml:space="preserve">prodictum numerũ, uidelicet 3987400000. </s> <s xml:id="echoid-s12646" xml:space="preserve"><lb/>diuido per 74314. </s> <s xml:id="echoid-s12647" xml:space="preserve">nempe per ſinum complementi latitudinis Romæ, quã nũc <lb/>ponimus grad. </s> <s xml:id="echoid-s12648" xml:space="preserve">42. </s> <s xml:id="echoid-s12649" xml:space="preserve">ut uitemus Minuta, exitq; </s> <s xml:id="echoid-s12650" xml:space="preserve">ſinus amplitudinis q̃ſitę 53656. </s> <s xml:id="echoid-s12651" xml:space="preserve"><lb/>cui in tabula ſinũ reſpõdet arcus grad. </s> <s xml:id="echoid-s12652" xml:space="preserve">32. </s> <s xml:id="echoid-s12653" xml:space="preserve">min. </s> <s xml:id="echoid-s12654" xml:space="preserve">27. </s> <s xml:id="echoid-s12655" xml:space="preserve">Tãta igitur eſt amplitudo <lb/>ortiua, ſeu occidua, Sole exiſtẽte in principio ♋, ubi polus eleuatur grad. </s> <s xml:id="echoid-s12656" xml:space="preserve">42. </s> <s xml:id="echoid-s12657" xml:space="preserve"><lb/>quemadmodum fere Romæ contingit. </s> <s xml:id="echoid-s12658" xml:space="preserve">Eademq; </s> <s xml:id="echoid-s12659" xml:space="preserve">eſt ratio de cæteris punctis.</s> <s xml:id="echoid-s12660" xml:space="preserve"/> </p> <div xml:id="echoid-div647" type="float" level="2" n="2"> <note position="left" xlink:label="note-336-04" xlink:href="note-336-04a" xml:space="preserve">Latitudo <lb/>ortiua, & <lb/>occidua <lb/>quomodo <lb/>ꝑ ſinus ſup <lb/>ꝑutetur.</note> </div> </div> <div xml:id="echoid-div649" type="section" level="1" n="220"> <head xml:id="echoid-head231" xml:space="preserve">VI.</head> <note position="left" xml:space="preserve">Morizon in-<lb/>dicatgradũ <lb/>Eclipticæ, <lb/>cũ quo ſtel-<lb/>la quælibet <lb/>oritur.</note> <p> <s xml:id="echoid-s12661" xml:space="preserve"><emph style="sc">Demonstrat</emph> gradum Eclipticæ, cum quo quælibet ſtella oria-<lb/>tur, & </s> <s xml:id="echoid-s12662" xml:space="preserve">occidat. </s> <s xml:id="echoid-s12663" xml:space="preserve">Poſita namq; </s> <s xml:id="echoid-s12664" xml:space="preserve">ſtella in Horizõte ex parte orientis, notetur gra <lb/>dus Eclipticæ, qui tunc Horizontem contingit. </s> <s xml:id="echoid-s12665" xml:space="preserve">Nã cum eo ſtella illa oriri di-<lb/>citur. </s> <s xml:id="echoid-s12666" xml:space="preserve">Poſita rurſus eadem ſtella in Horizonte ex parte occidentis, obſerue- <pb o="301" file="337" n="338" rhead="Ioan. de Sacro Boſco."/> tur gradus Eclipticæ, qui tunc Horizontem contingit; </s> <s xml:id="echoid-s12667" xml:space="preserve">Cum eo enim occi-<lb/>det ſtella prædicta.</s> <s xml:id="echoid-s12668" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div650" type="section" level="1" n="221"> <head xml:id="echoid-head232" xml:space="preserve">VII.</head> <note position="right" xml:space="preserve">Horizon <lb/>oſtenditſtel <lb/>las orientes <lb/>occidentes <lb/>que, & per-<lb/>pe@uo appa <lb/>rentesque.</note> <p> <s xml:id="echoid-s12669" xml:space="preserve"><emph style="sc">Indicat</emph>, quænam ſtellæ ſint perpetuæ apparitionis in quocunq; </s> <s xml:id="echoid-s12670" xml:space="preserve">cli-<lb/>mate, & </s> <s xml:id="echoid-s12671" xml:space="preserve">quæ perpetuæ occultationis, quæ denique oriri, atque occidere dicã <lb/>tur. </s> <s xml:id="echoid-s12672" xml:space="preserve">Si enim Horizon per polos mundi incedit, qualis eſt Horizon rectus, di-<lb/>uidet omnes parallelos, quos ad motum diurnũ deſcribunt ſtellæ, bifariã, ut <lb/>cõſtat ex propoſ. </s> <s xml:id="echoid-s12673" xml:space="preserve">15. </s> <s xml:id="echoid-s12674" xml:space="preserve">lib. </s> <s xml:id="echoid-s12675" xml:space="preserve">1. </s> <s xml:id="echoid-s12676" xml:space="preserve">Theod. </s> <s xml:id="echoid-s12677" xml:space="preserve">quod & </s> <s xml:id="echoid-s12678" xml:space="preserve">ſupra in 5. </s> <s xml:id="echoid-s12679" xml:space="preserve">proprietate circulorum <lb/>ſphæræ aſſeruimus. </s> <s xml:id="echoid-s12680" xml:space="preserve">Quare in huiuſmodi Horizõte, videlicet in ſphæra recta, <lb/>omnes ſtellæ orientur, occidẽtq́ue. </s> <s xml:id="echoid-s12681" xml:space="preserve">Si uero Horizon minime per mũdi polos <lb/>tranſeat, qualis eſt omnis Horizon obliquus, non diuidet ullum parallelũ bi <lb/>fariam, præ@erquam Aequatorem: </s> <s xml:id="echoid-s12682" xml:space="preserve">immo quoſdam @uxta polosnequaquã di-<lb/>uidet. </s> <s xml:id="echoid-s12683" xml:space="preserve">Vnde ſtellæ deſcribentes parallelos, qui ab Horizonte non d@uidun-<lb/>tur, neque orientur, neque occident, ſed aut perpetuo ſupra Horizontem at-<lb/>tollentur, ſi nimirum iuxta polum conſpicuum exiſtũt, aut perpetuo, ſub eo-<lb/>dem deprimentur, ſi uidelicet prope alterum polũ occultum ſunt collocatę: <lb/></s> <s xml:id="echoid-s12684" xml:space="preserve">Stellę uero, quarum paralleli diuiduntur ab Horizonte, orientur, & </s> <s xml:id="echoid-s12685" xml:space="preserve">occidẽt. </s> <s xml:id="echoid-s12686" xml:space="preserve"><lb/>Cognoſcuntur ſtellæ, quæ ſunt ſempiternæ apparitionis, per circulũ ęquidi-<lb/>ſtantẽ Aequatori, qui Horizontẽ prope polum conſpicuum contingit. </s> <s xml:id="echoid-s12687" xml:space="preserve">Om-<lb/>nes etenim ſtellę, quæ intra polum eleuatũ, & </s> <s xml:id="echoid-s12688" xml:space="preserve">dictũ parallelum comprehen-<lb/>duntur, perpetuo ſupra Horizontẽ conſpiciuntur, ut facile uidere eſt in ſphę <lb/>ra materiali: </s> <s xml:id="echoid-s12689" xml:space="preserve">Stellæ uero, quæ ſemper occultantur ſub Horizonte, diſcernun <lb/>tut alio circulo ęquidiſtãte Aequatori, qui cum priori ſit ęqualis, Horizon-<lb/>tem contingit ad partes poli occulti. </s> <s xml:id="echoid-s12690" xml:space="preserve">Nam omnes ſtellæ, quæ intra polum oc <lb/>cultũ, & </s> <s xml:id="echoid-s12691" xml:space="preserve">dictũ parailelem includũtur, nunquam in conſpectũ uenire poſſunt, <lb/>ſed ſempiternę ſunt occultationis. </s> <s xml:id="echoid-s12692" xml:space="preserve">Hi autẽ duo circuli paralleli, (quorũ ille <lb/> <anchor type="note" xlink:label="note-337-02a" xlink:href="note-337-02"/> dicitur ab Aſtronomis Maximus ſemper apparentiũ, quod omnium paralle-<lb/>lorũ, qui ſemper apparẽt, ſit maximos, hic uero Maximus ſemper occultorũ, <lb/>eo quod omniũ parallelorum ſemper deliteſcentiũ maximus ſit,) tanto maio <lb/>res exiſtunt, & </s> <s xml:id="echoid-s12693" xml:space="preserve">inter ſe uiciniores, pluresq́; </s> <s xml:id="echoid-s12694" xml:space="preserve">includunt ſtellas, quanto Hori-<lb/>rizon obliquior exiſtit, ſeu polus magis ſupra Horizontẽ extollitur; </s> <s xml:id="echoid-s12695" xml:space="preserve">adeo ut <lb/> <anchor type="note" xlink:label="note-337-03a" xlink:href="note-337-03"/> degentibus ſub alterutro polorũ dicti circuli prorſus in unum coeant, coinci <lb/>dãtq; </s> <s xml:id="echoid-s12696" xml:space="preserve">cũ Aequatore, eiſdemq; </s> <s xml:id="echoid-s12697" xml:space="preserve">nulla ſtella fixa oriatur, atq; </s> <s xml:id="echoid-s12698" xml:space="preserve">occidat, ſed me-<lb/>dia pars earum perpetuo appareat, media uero pars altera ſemper deliteſcat: <lb/></s> <s xml:id="echoid-s12699" xml:space="preserve">Quãuis planetæ omnes per dimidiam partem temporis, quo proprios motus <lb/>conficiunt in Zodiaco, ſemper appareant, per reliquum uero temporis ſpa-<lb/>cium occultentur, quia nimirum continue alter ſemicirculus Zodiaci ſupra <lb/>Horizontem conſpicitur, alter uero infsa eundem deliteſcit. </s> <s xml:id="echoid-s12700" xml:space="preserve">Habitantibus <lb/>porro ſub circulis polaribus officium dictorum circulorum exhibebunt duo <lb/>circuli tropici; </s> <s xml:id="echoid-s12701" xml:space="preserve">Et uiciſſim, habitantibus ſub duobus tropicis circuli polares <lb/>fungentur munere eorundem duorum parallelorum. </s> <s xml:id="echoid-s12702" xml:space="preserve">Sunt enim ſemper in <lb/>omni regione dicti paralleli inter ſe ęquales, & </s> <s xml:id="echoid-s12703" xml:space="preserve">qualiter ab Aequatore remo <lb/>ti, ut conſtat ex proproſ 6. </s> <s xml:id="echoid-s12704" xml:space="preserve">lib. </s> <s xml:id="echoid-s12705" xml:space="preserve">2. </s> <s xml:id="echoid-s12706" xml:space="preserve">Theod. </s> <s xml:id="echoid-s12707" xml:space="preserve">uel etiam ex 7. </s> <s xml:id="echoid-s12708" xml:space="preserve">proptietate circulorũ <lb/>ſphęrę, Idemq́ue perſpicuum cuius eſſe poteſt in ſphęra materiali Stellę de-<lb/>nique reliquę inter Aequatorem, & </s> <s xml:id="echoid-s12709" xml:space="preserve">dictos duos parallelos collocatę oriun-<lb/>tur, atque occidunt.</s> <s xml:id="echoid-s12710" xml:space="preserve"/> </p> <div xml:id="echoid-div650" type="float" level="2" n="1"> <note position="right" xlink:label="note-337-02" xlink:href="note-337-02a" xml:space="preserve">Parallelorũ <lb/>ſemper ap-<lb/>parentium, <lb/>uel ſemper <lb/>latentium <lb/>maximus <lb/>quid.</note> <note position="right" xlink:label="note-337-03" xlink:href="note-337-03a" xml:space="preserve">Variæ habi-<lb/>tudines pa-<lb/>rallelo@um <lb/>ſemper ap-<lb/>paren@um <lb/>ſemperq́ue <lb/>latent@um <lb/>maximorũ.</note> </div> <p> <s xml:id="echoid-s12711" xml:space="preserve"><emph style="sc">Caetervm</emph> ex cognita declinatione cuiuslibet ſtellę, & </s> <s xml:id="echoid-s12712" xml:space="preserve">latitudin@ <lb/>loti, ſeu altitudine poli, quod idem eſt, facile deprehendetur, nũ ipſa oriatur, <pb o="302" file="338" n="339" rhead="Comment. in II. Cap. Sphæræ"/> occidatque, an potius perpetuo appareat, perpetuove deliteſcat, hacnimi-<lb/> <anchor type="note" xlink:label="note-338-01a" xlink:href="note-338-01"/> rum arte. </s> <s xml:id="echoid-s12713" xml:space="preserve">Coniungatur altitudo poli, ſiue latitudo loci cũ ſtellæ declinatio-<lb/>ne, ſi quam habet. </s> <s xml:id="echoid-s12714" xml:space="preserve">Nam ſi aggregatum Quadrãte minus fuerit, hoc eſt, 90. </s> <s xml:id="echoid-s12715" xml:space="preserve">gra <lb/>dibus, ftella orietur, occiderque: </s> <s xml:id="echoid-s12716" xml:space="preserve">Si uero Quadrantem, ideſt, 90. </s> <s xml:id="echoid-s12717" xml:space="preserve">gradus ſupe <lb/>rauerit, ſtella declinans in Boream perpetuo apparebit, & </s> <s xml:id="echoid-s12718" xml:space="preserve">non orietur, neque <lb/>occidet; </s> <s xml:id="echoid-s12719" xml:space="preserve">Stella autem in Auſtrum urgens perpetuo occultabitur, & </s> <s xml:id="echoid-s12720" xml:space="preserve">nunquam <lb/>in conſpectum ſupra Horizontem uenire poterit. </s> <s xml:id="echoid-s12721" xml:space="preserve">Quod ſi dictum aggregatũ <lb/>Quadranti æquale extiterit, tanget ſtella, & </s> <s xml:id="echoid-s12722" xml:space="preserve">quodammodo radeo Horizontẽ <lb/>ſiue ex parte Septentrionis, ſi habuerit declinationem Borealem, ſiue ex par-<lb/>te Meridiei, ſi declinatio fuerit Auſtralis. </s> <s xml:id="echoid-s12723" xml:space="preserve">Quæ omnia conſpicua ſunt in ſphę <lb/>ra meteriali.</s> <s xml:id="echoid-s12724" xml:space="preserve"/> </p> <div xml:id="echoid-div651" type="float" level="2" n="2"> <note position="left" xlink:label="note-338-01" xlink:href="note-338-01a" xml:space="preserve">Quomodo <lb/>cognoſcatur <lb/>an ſtella pro <lb/>poſita oria-<lb/>tur, necne, <lb/>& an ſit per-<lb/>petuo appa-<lb/>rẽs uel per-<lb/>petuo latẽs.</note> </div> <p> <s xml:id="echoid-s12725" xml:space="preserve">IDEM hac ratione couſequemur. </s> <s xml:id="echoid-s12726" xml:space="preserve">Si complementum declinationis ſtel-<lb/>læ altitudine poli fuerit maius, orietur, & </s> <s xml:id="echoid-s12727" xml:space="preserve">occidet ſtella: </s> <s xml:id="echoid-s12728" xml:space="preserve">Si autem altitudine <lb/>poli minus fuerit, perpetuo apparebit ſtella Borealis, auſtralis uero perpetuo <lb/>latebit. </s> <s xml:id="echoid-s12729" xml:space="preserve">Si deniq; </s> <s xml:id="echoid-s12730" xml:space="preserve">altitudini poli æquale fuerit, ſtella ſiue borealis, ſiue auſtra <lb/>lis Horizontem continget. </s> <s xml:id="echoid-s12731" xml:space="preserve">Vt in ſphæra materiali apparet.</s> <s xml:id="echoid-s12732" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12733" xml:space="preserve">IDEM hoc etiam modo obtinebimus. </s> <s xml:id="echoid-s12734" xml:space="preserve">Si ſtellæ declinatio minor fuerit <lb/>complemẽto altitudinis poli, orietur ipſa ſtella, & </s> <s xml:id="echoid-s12735" xml:space="preserve">occidet: </s> <s xml:id="echoid-s12736" xml:space="preserve">Si autẽ maior fue <lb/>rit, perpetuo apparebit, uel occultabitur: </s> <s xml:id="echoid-s12737" xml:space="preserve">ſi deniq; </s> <s xml:id="echoid-s12738" xml:space="preserve">æqualis fuerit, Horizontẽ <lb/>tanget. </s> <s xml:id="echoid-s12739" xml:space="preserve">Vt ex eadem ſphæra materiali perſpicuum eſt, ſi pro ſtellis borealibus <lb/>ſumatur arcus Meridiani infra Horizontem ex parte poli arctici inter Hori-<lb/>zontẽ & </s> <s xml:id="echoid-s12740" xml:space="preserve">Aequatorẽ, & </s> <s xml:id="echoid-s12741" xml:space="preserve">declinatio ſtellæ in eodẽ arcu numeretur ab Aequato <lb/>re uerſus Horizontem; </s> <s xml:id="echoid-s12742" xml:space="preserve">Pro ſtellis uero auſtralib us accipitur arcus Meridiani <lb/>ſupra Horizontem ex parte auſtrali inter Horizontem, & </s> <s xml:id="echoid-s12743" xml:space="preserve">Aequatorem, & </s> <s xml:id="echoid-s12744" xml:space="preserve">de <lb/>clinatio ſtellæ in eodem arcu numeretur ab Aequatore uerſus Horizontem.</s> <s xml:id="echoid-s12745" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div653" type="section" level="1" n="222"> <head xml:id="echoid-head233" xml:space="preserve">VIII.</head> <p> <s xml:id="echoid-s12746" xml:space="preserve">MAGNAM commoditatem affert Horizon Coſmographis, ſiue Geo-<lb/> <anchor type="note" xlink:label="note-338-02a" xlink:href="note-338-02"/> graphis. </s> <s xml:id="echoid-s12747" xml:space="preserve">Nam ad hunc referuntur altitudines poli, quas latitudinibus loco-<lb/>rum demonſtrauimus eſſe æquales, & </s> <s xml:id="echoid-s12748" xml:space="preserve">quarum maximam habent rationẽ Coſ <lb/>mographi. </s> <s xml:id="echoid-s12749" xml:space="preserve">Hinc rurſus cognita altitudine poli, ſeu latitudine loci, cognoſce-<lb/>tur altitudo Aequatoris. </s> <s xml:id="echoid-s12750" xml:space="preserve">Cum enim à Zenith per Aequatorem ad Herizon <lb/> <anchor type="note" xlink:label="note-338-03a" xlink:href="note-338-03"/> tem uſque ſit integer Quadrans Meridiani, ſi latitudo loci, hoc eſt, diſtantia <lb/>Zenith ab Aequatore, auferatur ex Quadrante, relinquetur altitudo Aequa <lb/>toris. </s> <s xml:id="echoid-s12751" xml:space="preserve">Vt ſi grad. </s> <s xml:id="echoid-s12752" xml:space="preserve">41. </s> <s xml:id="echoid-s12753" xml:space="preserve">Min. </s> <s xml:id="echoid-s12754" xml:space="preserve">56. </s> <s xml:id="echoid-s12755" xml:space="preserve">(latitudo uidelicet Romæ) auferantur ex 90. </s> <s xml:id="echoid-s12756" xml:space="preserve">gr. <lb/></s> <s xml:id="echoid-s12757" xml:space="preserve">remanebit altitudo Aequatoris grad. </s> <s xml:id="echoid-s12758" xml:space="preserve">48. </s> <s xml:id="echoid-s12759" xml:space="preserve">Min. </s> <s xml:id="echoid-s12760" xml:space="preserve">4. </s> <s xml:id="echoid-s12761" xml:space="preserve">quot nimirum comprehen-<lb/> <anchor type="figure" xlink:label="fig-338-01a" xlink:href="fig-338-01"/> dit arcus Meridiani inter Aequatorem, & </s> <s xml:id="echoid-s12762" xml:space="preserve">Hori-<lb/>zontem interceptus. </s> <s xml:id="echoid-s12763" xml:space="preserve">Eſt autem altitudo Aequa-<lb/> <anchor type="note" xlink:label="note-338-04a" xlink:href="note-338-04"/> toris perpetuo æqualis complemento altitudinis <lb/>poli, ſeu latitudinis loci, hoc eſt, diſtantiæ <lb/>Zenith à polo mundi. </s> <s xml:id="echoid-s12764" xml:space="preserve">Quoniam uidelicet lati-<lb/>tudo Aequatoris eſt complementum latitudinis <lb/>loci, ut patet, latitudo autem loci æqualis eſt <lb/>altitudini poli. </s> <s xml:id="echoid-s12765" xml:space="preserve">Quod etiam hac ratione demon-<lb/>ſtrabitur. </s> <s xml:id="echoid-s12766" xml:space="preserve">Repetatur proxime ptæcedens figura. <lb/></s> <s xml:id="echoid-s12767" xml:space="preserve">In qua cum Quadrans A F, æqualis ſit Quadran-<lb/>ti B G, dempto communi arcu B F, remanebit ar <lb/>cus AB, nempe altitudo Aequatoris, æqualis ar-<lb/>cui FG, uidelicet complemento altitudinis poli.</s> <s xml:id="echoid-s12768" xml:space="preserve"/> </p> <div xml:id="echoid-div653" type="float" level="2" n="1"> <note position="left" xlink:label="note-338-02" xlink:href="note-338-02a" xml:space="preserve">Horizon in <lb/>ſeruit Coſ-<lb/>mographis.</note> <note position="left" xlink:label="note-338-03" xlink:href="note-338-03a" xml:space="preserve">Altitudo <lb/>Aequatoris <lb/>quo pacto <lb/>cognoſca <lb/>tur.</note> <figure xlink:label="fig-338-01" xlink:href="fig-338-01a"> <image file="338-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/338-01"/> </figure> <note position="left" xlink:label="note-338-04" xlink:href="note-338-04a" xml:space="preserve">Altitudo <lb/>Aequatoris <lb/>æqualis eſt <lb/>complemẽ-<lb/>to altitudi-<lb/>nis poli.</note> </div> <pb o="303" file="339" n="340" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div655" type="section" level="1" n="223"> <head xml:id="echoid-head234" style="it" xml:space="preserve">DEQVATVOR CIRCVLIS MINORIBVS.</head> <p style="it"> <s xml:id="echoid-s12769" xml:space="preserve">DICTO de ſex circulis maioribus, dicedum eſt de qua-<lb/> <anchor type="note" xlink:label="note-339-01a" xlink:href="note-339-01"/> tuor minoribus. </s> <s xml:id="echoid-s12770" xml:space="preserve">Notandum igitur, quod Sol exiſtẽs in <lb/>primo puncto Cancri, ſiue in primo puncto ſolſtitij eſti-<lb/>ualis, raptu Firmamenti deſcribit quendam circulum, <lb/>qui ultimo deſcriptus eſt à Sole ex parte poli Arctici, <lb/>unde appellatur circulus ſolſtitij ęſtiualis, ratione ſu-<lb/>perius dicta: </s> <s xml:id="echoid-s12771" xml:space="preserve">Vel tropicus æſtiualis, à τροπὴ, quod eſt conuerſio: </s> <s xml:id="echoid-s12772" xml:space="preserve">quia tunc <lb/>Sol incipit ſe conuertere ad inferius hemiſphærium, & </s> <s xml:id="echoid-s12773" xml:space="preserve">recedere à nobis.</s> <s xml:id="echoid-s12774" xml:space="preserve"/> </p> <div xml:id="echoid-div655" type="float" level="2" n="1"> <note position="right" xlink:label="note-339-01" xlink:href="note-339-01a" xml:space="preserve">Tropici <lb/>quomodo <lb/>deſcriban-<lb/>tur.</note> </div> <p style="it"> <s xml:id="echoid-s12775" xml:space="preserve">SOL iterum exiſtens in primo puncto Capricorni, ſiue Solſtitij hye-<lb/>malis, raptu Firmamenti deſcribit quendam circulum, qui ultimo deſcri-<lb/>bitur à Sole ex parte poli Antarctici, under appellatur circulus ſolſtitij <lb/>hyemali@, ſiue tropicus hyemalis, quia tunc Sol conuertitur ad nos.</s> <s xml:id="echoid-s12776" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div657" type="section" level="1" n="224"> <head xml:id="echoid-head235" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s12777" xml:space="preserve"><emph style="sc">FInita</emph> tractatione ſex circulorum, qui in ſphæra ſunt maximi, <lb/>agit hoc loco de quatuor minoribus, ſeu non maximis, & </s> <s xml:id="echoid-s12778" xml:space="preserve">pri-<lb/>mo de duobus, qui raptu primi mobilis deſcribuntur à primo <lb/>grad. </s> <s xml:id="echoid-s12779" xml:space="preserve">♋, & </s> <s xml:id="echoid-s12780" xml:space="preserve">♑, & </s> <s xml:id="echoid-s12781" xml:space="preserve">conſequenter ab Aequatore remouentur grad. <lb/></s> <s xml:id="echoid-s12782" xml:space="preserve">23. </s> <s xml:id="echoid-s12783" xml:space="preserve">Min. </s> <s xml:id="echoid-s12784" xml:space="preserve">20. </s> <s xml:id="echoid-s12785" xml:space="preserve">quemadmodum & </s> <s xml:id="echoid-s12786" xml:space="preserve">principia ♋, & </s> <s xml:id="echoid-s12787" xml:space="preserve">♑. </s> <s xml:id="echoid-s12788" xml:space="preserve">Hi autem <lb/>duo circuli inter ſe æquales ſunt, contingitq́ue uterque unico tantum pun-<lb/>cto Eclipticam, ut ex 2. </s> <s xml:id="echoid-s12789" xml:space="preserve">lib. </s> <s xml:id="echoid-s12790" xml:space="preserve">Theodoſij colligitur: </s> <s xml:id="echoid-s12791" xml:space="preserve">Item ſunt ultimi, ac mini-<lb/>mi, quos Sol motu diurno deſcribit. </s> <s xml:id="echoid-s12792" xml:space="preserve">Nam uſq; </s> <s xml:id="echoid-s12793" xml:space="preserve">ad illos euagatur huc, illucq; </s> <s xml:id="echoid-s12794" xml:space="preserve"><lb/>ab Aequatore Sol; </s> <s xml:id="echoid-s12795" xml:space="preserve">quàm primum autem ad eos peruenerit, mox ad Aequato-<lb/>rem rurſus iter ſuum dirigit. </s> <s xml:id="echoid-s12796" xml:space="preserve">Qua de re ait, ipſos uocari Tropicos à nomine <lb/> <anchor type="note" xlink:label="note-339-02a" xlink:href="note-339-02"/> græco, τροπὴ, quod ſignificat conuerſionem, quia in illis exiſtens Sol iterum <lb/>ſe conuertit ad Aequatorem. </s> <s xml:id="echoid-s12797" xml:space="preserve">Ille quidem, qui à primo puncto ♋, deſcribi-<lb/>tur, appellatur Tropicus Cancri: </s> <s xml:id="echoid-s12798" xml:space="preserve">Hic uero, qui deſcribitur ab initio ♑, Tro-<lb/>picus Capricorni dici conſueuit. </s> <s xml:id="echoid-s12799" xml:space="preserve">Pari ratione Tropicus Cancri appellari ſo <lb/>@et Tropicus æſt@ualis: </s> <s xml:id="echoid-s12800" xml:space="preserve">Tropicus ſeu circul<emph style="sub">9</emph> Solſtitij æſtiui, quod intellige in <lb/> <anchor type="note" xlink:label="note-339-03a" xlink:href="note-339-03"/> hamiſphærio Boreali: </s> <s xml:id="echoid-s12801" xml:space="preserve">Tropicus Septentrionalis: </s> <s xml:id="echoid-s12802" xml:space="preserve">circulus uerſilis Cancri. </s> <s xml:id="echoid-s12803" xml:space="preserve">Itẽ <lb/>Tropicus Capricorni uocatur Tropicus hyemalis: </s> <s xml:id="echoid-s12804" xml:space="preserve">Tropicus, ſeu circulus <lb/>Solſtitij hyemalis: </s> <s xml:id="echoid-s12805" xml:space="preserve">Tropicus Auſtralis, & </s> <s xml:id="echoid-s12806" xml:space="preserve">id genus alijs plurimis nominibus <lb/>uterque nominari ſolet à ſcriptoribus.</s> <s xml:id="echoid-s12807" xml:space="preserve"/> </p> <div xml:id="echoid-div657" type="float" level="2" n="1"> <note position="right" xlink:label="note-339-02" xlink:href="note-339-02a" xml:space="preserve">Tropicus <lb/>cancri, & <lb/>tropicus ca <lb/>pricorni.</note> <note position="right" xlink:label="note-339-03" xlink:href="note-339-03a" xml:space="preserve">Varia no-<lb/>mina Tro-<lb/>picorum.</note> </div> <p style="it"> <s xml:id="echoid-s12808" xml:space="preserve">CVM autem Zodiacus declinet ab Aequinoctiali, & </s> <s xml:id="echoid-s12809" xml:space="preserve">polus Zodiaci <lb/> <anchor type="note" xlink:label="note-339-04a" xlink:href="note-339-04"/> declinabit à polo mundi. </s> <s xml:id="echoid-s12810" xml:space="preserve">Cum igitur moueatur octaua ſphæra, & </s> <s xml:id="echoid-s12811" xml:space="preserve">Zodia-<lb/>cus, qui eſt pars octauæ ſphæræ, mouebitur circa axem mundi, & </s> <s xml:id="echoid-s12812" xml:space="preserve">polus <lb/>Zodiaci mouebitur cir capolum mundi. </s> <s xml:id="echoid-s12813" xml:space="preserve">Iſte igitur circulus, quem deſcri-<lb/>bit polus Zodiaci circa polum mundi Arcticum, dicitur circulus Arcti-<lb/>cus: </s> <s xml:id="echoid-s12814" xml:space="preserve">Ille uero circulus, quem deſcribit alter polus Zodiaci circa polum <lb/>mundi Antarcticum, dicitur circulus Antarcticus.</s> <s xml:id="echoid-s12815" xml:space="preserve"/> </p> <div xml:id="echoid-div658" type="float" level="2" n="2"> <note position="right" xlink:label="note-339-04" xlink:href="note-339-04a" xml:space="preserve">Arcticus <lb/>circulus, & <lb/>Antarcticus</note> </div> <pb o="304" file="340" n="341" rhead="Comment. in II. Cap. Sphæræ"/> </div> <div xml:id="echoid-div660" type="section" level="1" n="225"> <head xml:id="echoid-head236" xml:space="preserve">COMMENTARIS.</head> <p> <s xml:id="echoid-s12816" xml:space="preserve"><emph style="sc">Explicat</emph> hic duos circulos polares: </s> <s xml:id="echoid-s12817" xml:space="preserve">Arcticum ſcilicet, & </s> <s xml:id="echoid-s12818" xml:space="preserve">Antarcticum, <lb/> <anchor type="note" xlink:label="note-340-01a" xlink:href="note-340-01"/> qui deſcribuntur motu primi mobilis à poli Zodiaci circa polos mundi. </s> <s xml:id="echoid-s12819" xml:space="preserve">Vn-<lb/>de quoniam diſtantia polorum Zodiaci à polismundi æqualis eſt maximæ <lb/>Solis declinationi, vt paulo ſuperius demonſtrauimus, efficitur, ut uterque <lb/> <anchor type="note" xlink:label="note-340-02a" xlink:href="note-340-02"/> circulus polaris tantum abſit à polis mundi, (Arcticus quidem à polo Arcti-<lb/>cto, Antarcticus uero ab Antarctico) quantum ab Æquatore reced unt duo <lb/>Tropici, nimirum grad. </s> <s xml:id="echoid-s12820" xml:space="preserve">23. </s> <s xml:id="echoid-s12821" xml:space="preserve">Min. </s> <s xml:id="echoid-s12822" xml:space="preserve">30.</s> <s xml:id="echoid-s12823" xml:space="preserve"/> </p> <div xml:id="echoid-div660" type="float" level="2" n="1"> <note position="left" xlink:label="note-340-01" xlink:href="note-340-01a" xml:space="preserve">Circuli po-<lb/>lares ꝗ ſin@.</note> <note position="left" xlink:label="note-340-02" xlink:href="note-340-02a" xml:space="preserve">Polares cir-<lb/>culi quan-<lb/>tum à polis <lb/>mundi ab <lb/>ſint.</note> </div> <p> <s xml:id="echoid-s12824" xml:space="preserve"><emph style="sc">Graeci</emph>, vt videre licet apud Proclum, & </s> <s xml:id="echoid-s12825" xml:space="preserve">Cleomedem, multo aliter in-<lb/>telligunt duos circulos polares. </s> <s xml:id="echoid-s12826" xml:space="preserve">Non enim cum Latinis circulos polares ap-<lb/> <anchor type="note" xlink:label="note-340-03a" xlink:href="note-340-03"/> pellant eos, qui à Zodiaci polis deſcribũtur, ſed apud ipſos duo circuli dicun <lb/>tur polares, quorũ alter eſt maximus parallelorũ ſemper apparentiũ, alter ue-<lb/>ro maximus ſemper deliteſcentiũ de quibus in officio 7. </s> <s xml:id="echoid-s12827" xml:space="preserve">Horizontis egimus. <lb/></s> <s xml:id="echoid-s12828" xml:space="preserve">Maluerunt autẽ Græci potius hoc modo definire circulos polares, ut per ip-<lb/>ſos cognoſcantur omnes ſtellæ, quæ nunquam oriuntur, & </s> <s xml:id="echoid-s12829" xml:space="preserve">occidunt, ſed uel <lb/>perpetuo apparent, ut ſunt illæ, quas Arcticus includit, uel perpetuo latent, <lb/>quales ſunt eæ, quas comprehendit Antarcticus. </s> <s xml:id="echoid-s12830" xml:space="preserve">Ex quibus perſpicuum eſt, <lb/>apud Græcos duos circulos polares non eſſe eiuſdem quantitatis in omnibus <lb/>regionibus, quemadmodum apud Lations, ſed quo obliquior ſphæra fuerit, eo <lb/>etiam maiores eos effici, ut ſupra de maximo paralle lorum ſemper apparen-<lb/>tium, & </s> <s xml:id="echoid-s12831" xml:space="preserve">maximo ſemper occultorum dictum eſt.</s> <s xml:id="echoid-s12832" xml:space="preserve"/> </p> <div xml:id="echoid-div661" type="float" level="2" n="2"> <note position="left" xlink:label="note-340-03" xlink:href="note-340-03a" xml:space="preserve">Polares cir-<lb/>culi quomo <lb/>do à Græ-<lb/>cis ſumãtur</note> </div> <p> <s xml:id="echoid-s12833" xml:space="preserve"><emph style="sc">Caetervm</emph> quatuor prædicti circuli minores: </s> <s xml:id="echoid-s12834" xml:space="preserve">tropici uidelicet, atque po-<lb/>lares, æquidiſtant Aequatori, ut conſtat ex propoſ. </s> <s xml:id="echoid-s12835" xml:space="preserve">2. </s> <s xml:id="echoid-s12836" xml:space="preserve">lib. </s> <s xml:id="echoid-s12837" xml:space="preserve">2. </s> <s xml:id="echoid-s12838" xml:space="preserve">Theod. </s> <s xml:id="echoid-s12839" xml:space="preserve">propterea, <lb/>quod eoſdem polos poſſident, quos Aequator, nempe polos mundi, ex qui-<lb/>bus deſcribũ tur. </s> <s xml:id="echoid-s12840" xml:space="preserve">Et quamuis quiuis circulus in ſphæra maximus ſuos habeat <lb/>parallelos, ut initio huius cap. </s> <s xml:id="echoid-s12841" xml:space="preserve">diximus, præcipua tamen apud Aſtronomos ra <lb/>tio habetur parallelofũ Aequatoris, & </s> <s xml:id="echoid-s12842" xml:space="preserve">Zodiaci. </s> <s xml:id="echoid-s12843" xml:space="preserve">Nam ſingulæ ſtellæ, punctave <lb/>cœli Aequatori ſingulos circulos æquidiſtantes deſcribunt ad motum diur-<lb/>num primi mobilis: </s> <s xml:id="echoid-s12844" xml:space="preserve">Ad motum uero nonæ ſphæræ ab occaſu in ortum de-<lb/>lineant circulos æquidiſtantes Zodiaco. </s> <s xml:id="echoid-s12845" xml:space="preserve">Inter omnes autem circulos paral-<lb/>lelos Aequatoris inſigniti ſunt peculiaribus nominibus quatuor hi minores, <lb/>quos auctor noſter explicauit.</s> <s xml:id="echoid-s12846" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12847" xml:space="preserve"><emph style="sc">Qvemadmodvm</emph> autem Aequator, ſeu circulus quilibet maximus in <lb/>ſphæra diſtribuitur in 360. </s> <s xml:id="echoid-s12848" xml:space="preserve">grad. </s> <s xml:id="echoid-s12849" xml:space="preserve">ita etiam, ut ſupra monuimus, circulus qui-<lb/>cunque minor in totidem gradus ſecatur, qui omnino ſimiles ſunt gradibus <lb/>maximi circuli, ut ex propoſ. </s> <s xml:id="echoid-s12850" xml:space="preserve">10. </s> <s xml:id="echoid-s12851" xml:space="preserve">lib. </s> <s xml:id="echoid-s12852" xml:space="preserve">2. </s> <s xml:id="echoid-s12853" xml:space="preserve">Theod. </s> <s xml:id="echoid-s12854" xml:space="preserve">colligitur, ita ut quàm propor-<lb/>tionem habet circulus maximus ad circulum non maximum, eandem ſeruent <lb/>ſinguli gradus maximi circuli ad ſingulos gradus circuli non maximi.</s> <s xml:id="echoid-s12855" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12856" xml:space="preserve"><emph style="sc">Habebitvr</emph> autem ex do ctrina ſinuum proportio circuli maximi ad cir <lb/> <anchor type="note" xlink:label="note-340-04a" xlink:href="note-340-04"/> culum nõ maximum, cuius declinatio nota fuerit, hac ratione. </s> <s xml:id="echoid-s12857" xml:space="preserve">Multiplicetur <lb/>ſinus complemẽti declinationis circuli non maximi per circulum integrum, <lb/>hoc eſt, per grad. </s> <s xml:id="echoid-s12858" xml:space="preserve">360. </s> <s xml:id="echoid-s12859" xml:space="preserve">& </s> <s xml:id="echoid-s12860" xml:space="preserve">numerus productus diuidatur in ſinũ totum, habebi-<lb/>turq; </s> <s xml:id="echoid-s12861" xml:space="preserve">numerus graduum circuli non maximi, qualium 360. </s> <s xml:id="echoid-s12862" xml:space="preserve">cõtinet maximus <lb/>circulus. </s> <s xml:id="echoid-s12863" xml:space="preserve">Vt enim in Coſmographia oſtendimus, quemadmodum ſe habet ſi-<lb/>nus totus ad ſinum cõplementi declinationis cuiuſuis paralleli, ita ſe habet <lb/>circulus maximus ad propoſitum circulum non maximum. </s> <s xml:id="echoid-s12864" xml:space="preserve"><emph style="sc">Exempivm</emph>. </s> <s xml:id="echoid-s12865" xml:space="preserve">Pro-<lb/>poſitum ſit perquirere, quam proportionem habeat Aequator ad parallelũ, <pb o="305" file="341" n="342" rhead="Ioan. de Sacro Boſco."/> qui tranſit per punctum Verticale Romæ, cuius declinatio ponatur grad. </s> <s xml:id="echoid-s12866" xml:space="preserve">41. <lb/></s> <s xml:id="echoid-s12867" xml:space="preserve">Multiplico ſinum complementi huius declinationis, hoc eſt, ſinum 48. </s> <s xml:id="echoid-s12868" xml:space="preserve">grad. </s> <s xml:id="echoid-s12869" xml:space="preserve"><lb/>videlicet 74314. </s> <s xml:id="echoid-s12870" xml:space="preserve">per 360. </s> <s xml:id="echoid-s12871" xml:space="preserve">productumq; </s> <s xml:id="echoid-s12872" xml:space="preserve">numerũ 2753040. </s> <s xml:id="echoid-s12873" xml:space="preserve">partior per 100000. </s> <s xml:id="echoid-s12874" xml:space="preserve"><lb/>ſinum totum, & </s> <s xml:id="echoid-s12875" xml:space="preserve">inuenio gradus 267 {1/2}. </s> <s xml:id="echoid-s12876" xml:space="preserve">fere. </s> <s xml:id="echoid-s12877" xml:space="preserve">Habebit igitur Aequator ad pa-<lb/>rallelum, qui per uerticem Romæ incedit, uel etiam unus gradus Aequatoris <lb/>ad unũ gradum dicti paralleli, proportionem, quam 360. </s> <s xml:id="echoid-s12878" xml:space="preserve">grad. </s> <s xml:id="echoid-s12879" xml:space="preserve">ad grad. </s> <s xml:id="echoid-s12880" xml:space="preserve">267 {1/2}. </s> <s xml:id="echoid-s12881" xml:space="preserve"><lb/>fere, hoc eſt, fere ſeſquitertiam, qualis eſt 4. </s> <s xml:id="echoid-s12882" xml:space="preserve">ad 3. </s> <s xml:id="echoid-s12883" xml:space="preserve">&</s> <s xml:id="echoid-s12884" xml:space="preserve">c.</s> <s xml:id="echoid-s12885" xml:space="preserve"/> </p> <div xml:id="echoid-div662" type="float" level="2" n="3"> <note position="left" xlink:label="note-340-04" xlink:href="note-340-04a" xml:space="preserve">proportio <lb/>circuli ma-<lb/>@ imi ad nõ <lb/>maximum <lb/>qua ratione <lb/>ex ſinubus <lb/>@ognoſca-<lb/>tur.</note> </div> <p style="it"> <s xml:id="echoid-s12886" xml:space="preserve">QVANTA eſt etiam maxima Solis declinatio, ſe<unsure/>ilicet ab Aequi <lb/> <anchor type="note" xlink:label="note-341-01a" xlink:href="note-341-01"/> noctiali, tanta eſt diſtantia poli mundi à polo Zodiaci, quod ſic patet. </s> <s xml:id="echoid-s12887" xml:space="preserve">Su <lb/>matur Colurus diſtinguens Solſtitia, quitranſit per polos mundi, & </s> <s xml:id="echoid-s12888" xml:space="preserve">per <lb/>polos Zodiaci Cum igitur omnes quartæ unius, & </s> <s xml:id="echoid-s12889" xml:space="preserve">eiuſdem circuli inter <lb/>ſe ſint æquales, quarta huius Coluri, quę eſt ab Aequinoctiali uſque ad <lb/>polum mundi, erit æqualis quartæ eiuſdem Coluri, quæ eſt à primo puncto <lb/>Cancri uſque ad polum Zodiaci. </s> <s xml:id="echoid-s12890" xml:space="preserve">Igitur ab illis ęqualibus dempto commu-<lb/>ni arcu, qui eſt à primo puncto Cancri uſque ad polum mundi, reſidua <lb/>erunt æqualia, ſcilicet maxima Solis declinatio, & </s> <s xml:id="echoid-s12891" xml:space="preserve">diſtantia poli mundi <lb/>à polo Zodiaci.</s> <s xml:id="echoid-s12892" xml:space="preserve"/> </p> <div xml:id="echoid-div663" type="float" level="2" n="4"> <note position="right" xlink:label="note-341-01" xlink:href="note-341-01a" xml:space="preserve">Diſtanti@ <lb/>poli zodia-<lb/>ci à polo <lb/>mũ di æqua <lb/>lis eſt maxi <lb/>mæ Solis <lb/>declinati@-<lb/>ni.</note> </div> </div> <div xml:id="echoid-div665" type="section" level="1" n="226"> <head xml:id="echoid-head237" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s12893" xml:space="preserve"><emph style="sc">Probat</emph>, tanto ſpatio polos Zo-<lb/> <anchor type="figure" xlink:label="fig-341-01a" xlink:href="fig-341-01"/> diaci à polis mundi recedere, quanta eſt <lb/>utrauis maxima declinatio Solis: </s> <s xml:id="echoid-s12894" xml:space="preserve">Quod <lb/>quidem demonſtrat eodem modo, quo nos <lb/>idem oſtendimus in 6. </s> <s xml:id="echoid-s12895" xml:space="preserve">officio Colurorum, <lb/>ut perſpicuũ eſt in hac figura, in qua cir-<lb/>culus A B C D, eſt Colurus Solſtitiorum; <lb/></s> <s xml:id="echoid-s12896" xml:space="preserve">A B, quarta ab Aequinoctiali A C, vſque <lb/> <anchor type="note" xlink:label="note-341-02a" xlink:href="note-341-02"/> ad mundi polum B; </s> <s xml:id="echoid-s12897" xml:space="preserve">E K, quarta à primo <lb/>puncto ♋, vſque ad polum Zodiaci K; <lb/></s> <s xml:id="echoid-s12898" xml:space="preserve">A E, maxima Solis declinatio; </s> <s xml:id="echoid-s12899" xml:space="preserve">B K, di-<lb/>ſtantia poli mundi a polo Zodiaci, &</s> <s xml:id="echoid-s12900" xml:space="preserve">c.</s> <s xml:id="echoid-s12901" xml:space="preserve"/> </p> <div xml:id="echoid-div665" type="float" level="2" n="1"> <figure xlink:label="fig-341-01" xlink:href="fig-341-01a"> <image file="341-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/341-01"/> </figure> <note position="right" xlink:label="note-341-02" xlink:href="note-341-02a" xml:space="preserve">Quomodo <lb/>intelligen-<lb/>dũ ſit, diſtã <lb/>tiam polo-<lb/>rũ zodiaci <lb/>à polis mũ <lb/>d@ ęqualem <lb/>eſſe maxi-<lb/>mæ declina <lb/>tioni Solis.</note> </div> <p> <s xml:id="echoid-s12902" xml:space="preserve"><emph style="sc">Qvoniam</emph> vero ſupra diximus, maxi-<lb/>mam Solis declinationem uariari propter <lb/>motum trepidationis octauæ ſphæræ, efficitur, vt hæc ratio tantum conclu-<lb/>dat, maximam declinationem Eclipticæ nonæ ſphæræ æqualem eſſe diſtantiæ <lb/>polorum Eclipticæ eiuſdem ſphæræ a polis mundi, quoniam hæc ſphæra mo-<lb/>tu trepidationis non citetur. </s> <s xml:id="echoid-s12903" xml:space="preserve">Non enim declinatio maxima Solis, cum va-<lb/>rietur, æqualis eſſe poterit diſtantiæ poli Zodiaci a polo mundi, quæ in nona <lb/> <anchor type="note" xlink:label="note-341-03a" xlink:href="note-341-03"/> ſphæra ſumitur, permanetq́ue ſemper eadem.</s> <s xml:id="echoid-s12904" xml:space="preserve"/> </p> <div xml:id="echoid-div666" type="float" level="2" n="2"> <note position="right" xlink:label="note-341-03" xlink:href="note-341-03a" xml:space="preserve">Quãtus ſit <lb/>arcus Colu <lb/>ri inter tro <lb/>picum Ca@ <lb/>cri, & circu <lb/>lum arcti-<lb/>cum.</note> </div> <p style="it"> <s xml:id="echoid-s12905" xml:space="preserve">CVM autem circulus Arcticus ſecundum quamlibet ſui partem <lb/>æque diſtet à polo mũdi, patet, quòd illa pars Coluri, quę eſt inter primum <lb/>punctum Cancri, & </s> <s xml:id="echoid-s12906" xml:space="preserve">circulum Arcticum, fere eſt dupla ad maximam So- <pb o="306" file="342" n="343" rhead="Comment in II. Cap. Sphæræ"/> lis declinationem, ſiue ad arcum eiuſdem Coluri, qui intercipitur inter cir-<lb/>culum Arcticum, & </s> <s xml:id="echoid-s12907" xml:space="preserve">polum mundi Arcticum, qui etiam arcus ęqualis eſt <lb/>maximę Solis declinationi. </s> <s xml:id="echoid-s12908" xml:space="preserve">Cum enim Colurus iſte, ſicut alij circuli in-<lb/>ſphęra, ſit 360. </s> <s xml:id="echoid-s12909" xml:space="preserve">grad. </s> <s xml:id="echoid-s12910" xml:space="preserve">quarta eius erit 90. </s> <s xml:id="echoid-s12911" xml:space="preserve">grad. </s> <s xml:id="echoid-s12912" xml:space="preserve">Cum igitur maxima So-<lb/>lis declinatio ſecundum Ptolemæum ſit 23. </s> <s xml:id="echoid-s12913" xml:space="preserve">grad. </s> <s xml:id="echoid-s12914" xml:space="preserve">& </s> <s xml:id="echoid-s12915" xml:space="preserve">51. </s> <s xml:id="echoid-s12916" xml:space="preserve">minutorum, & </s> <s xml:id="echoid-s12917" xml:space="preserve"><lb/>totidem graduum ſit arcus, qui eſt inter circulum Arcticum, & </s> <s xml:id="echoid-s12918" xml:space="preserve">polum <lb/>mundi Arcticum, ſi iſta duo ſimul iuncta, quæ fere faciunt 48. </s> <s xml:id="echoid-s12919" xml:space="preserve">gradus, <lb/>ſubtrahantur à 90. </s> <s xml:id="echoid-s12920" xml:space="preserve">reſiduum erunt 42. </s> <s xml:id="echoid-s12921" xml:space="preserve">gradus, quantus eſt arcus Coluri, <lb/>qui eſt inter primum punctum Cancri, & </s> <s xml:id="echoid-s12922" xml:space="preserve">circulum Arcticũ: </s> <s xml:id="echoid-s12923" xml:space="preserve">Et ſic patet, <lb/>quòd ille arcus fere duplus eſt ad maximam Solis declinationem.</s> <s xml:id="echoid-s12924" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div668" type="section" level="1" n="227"> <head xml:id="echoid-head238" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s12925" xml:space="preserve"><emph style="sc">Colligit</emph> ex ijs, quæ dicta ſunt, arcum Coluri interceptum inter Tro-<lb/>picum ♋, & </s> <s xml:id="echoid-s12926" xml:space="preserve">circulum Arcticum, duplum fere eſſe maximæ declinationis <lb/>Solis, ſiue diſtantiæ poli zodiaci a polo mundi. </s> <s xml:id="echoid-s12927" xml:space="preserve">Cum enim, iuxta Ptolemæi <lb/>ſententiam, maxima Solis declinatio ſit grad. </s> <s xml:id="echoid-s12928" xml:space="preserve">23. </s> <s xml:id="echoid-s12929" xml:space="preserve">min. </s> <s xml:id="echoid-s12930" xml:space="preserve">51. </s> <s xml:id="echoid-s12931" xml:space="preserve">erit arcus ille ferme <lb/>grad. </s> <s xml:id="echoid-s12932" xml:space="preserve">42. </s> <s xml:id="echoid-s12933" xml:space="preserve">Iuxta tamen communem ſententiam hoc tempore maxima declina-<lb/>tio Solis eſt grad. </s> <s xml:id="echoid-s12934" xml:space="preserve">23. </s> <s xml:id="echoid-s12935" xml:space="preserve">min. </s> <s xml:id="echoid-s12936" xml:space="preserve">30. </s> <s xml:id="echoid-s12937" xml:space="preserve">Arcus autem dictus grad. </s> <s xml:id="echoid-s12938" xml:space="preserve">43.</s> <s xml:id="echoid-s12939" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div669" type="section" level="1" n="228"> <head xml:id="echoid-head239" xml:space="preserve">DE CIRCVLO LACTEO.</head> <p> <s xml:id="echoid-s12940" xml:space="preserve"><emph style="sc">Porro</emph> quia præter hos decem ſphæræ circulos Proclus etiam agit de cir <lb/>culo lacteo, qui & </s> <s xml:id="echoid-s12941" xml:space="preserve">Galaxia dicitur, non abs re erit, paucis explicare hoc loco, <lb/>quidnam ſit circulus lacteus, & </s> <s xml:id="echoid-s12942" xml:space="preserve">per quas conſtellationes in cœlo incedat. </s> <s xml:id="echoid-s12943" xml:space="preserve">Cir-<lb/> <anchor type="note" xlink:label="note-342-01a" xlink:href="note-342-01"/> culus igitur lacteus eſt maximus in cœlo latitudinem, & </s> <s xml:id="echoid-s12944" xml:space="preserve">ſplendõ<unsure/>rem habens <lb/>varium, ita ut in una parte maiorem habeat latitudinem, quã in alia; </s> <s xml:id="echoid-s12945" xml:space="preserve">Itẽ ma-<lb/>iorem candorem in una parte, quàm in alia, incedens per Geminos, & </s> <s xml:id="echoid-s12946" xml:space="preserve">Sagitta <lb/> <anchor type="note" xlink:label="note-342-02a" xlink:href="note-342-02"/> rium, ut copioſiſſime explicat Ptolemæus Dict. </s> <s xml:id="echoid-s12947" xml:space="preserve">8. </s> <s xml:id="echoid-s12948" xml:space="preserve">cap.</s> <s xml:id="echoid-s12949" xml:space="preserve">2. </s> <s xml:id="echoid-s12950" xml:space="preserve">Candor vero eius, a <lb/>quo lactei nomen habet, prouenit, ut nonnullis placet, ex multitudine nimia <lb/>ſtellarum exiguarum, quæ in ipſo continentur, & </s> <s xml:id="echoid-s12951" xml:space="preserve">ad noſtrũ uiſum diſtincte nõ <lb/>perueniunt, ſicut cæteræ ſtellæ. </s> <s xml:id="echoid-s12952" xml:space="preserve">Ego tamen cum alijs probabilius exiſtimo, La <lb/>cteum circulum eſſe partem Firmamenti continua, & </s> <s xml:id="echoid-s12953" xml:space="preserve">denſiorem alijs partibus <lb/>cœli, ita ut lumen Solis recipere poſſit, non tamen ſicut aliæ ſtellæ, quæ ſunt <lb/> <anchor type="note" xlink:label="note-342-03a" xlink:href="note-342-03"/> partes Firmamenti multo denſiores, & </s> <s xml:id="echoid-s12954" xml:space="preserve">inter ſe diſtantes; </s> <s xml:id="echoid-s12955" xml:space="preserve">quid quid fabulentur <lb/>Poetæ de lacte Iunonis, & </s> <s xml:id="echoid-s12956" xml:space="preserve">combuſtione, quam Sol effecit. </s> <s xml:id="echoid-s12957" xml:space="preserve">Itaque lacteus cir-<lb/>culus uere exiſtit in Firmamento, non autem in regione aeris, ut Ariſtoteles <lb/>uolebat. </s> <s xml:id="echoid-s12958" xml:space="preserve">Nã hac ratione nõ cerneretur in quacunq; </s> <s xml:id="echoid-s12959" xml:space="preserve">orbis terreni parte tran-<lb/>ſire præciſe per eaſdem ſtellas Firmamenti, quemadmodum neq; </s> <s xml:id="echoid-s12960" xml:space="preserve">Cometa, qui <lb/>in aere exiſtit, in omnibus regionibus ſub eadem ſtella fixa conſpicitur, quod <lb/>falſum eſt. </s> <s xml:id="echoid-s12961" xml:space="preserve">Incedit enim lacteus circulus perpetuo, ut uidere eſt apud Pt<unsure/>ole-<lb/> <anchor type="note" xlink:label="note-342-04a" xlink:href="note-342-04"/> mæum loco citato, & </s> <s xml:id="echoid-s12962" xml:space="preserve">experientia docet, per Caſſiopeiam, Cygnum, Aquilam <lb/>volantem, ſagittam Sagittarij, & </s> <s xml:id="echoid-s12963" xml:space="preserve">caudam Scorpij, Centaurum, Argonauem, <lb/>pedes Geminorum, Heniochum, ſiue Aurigam, & </s> <s xml:id="echoid-s12964" xml:space="preserve">Perſeum, ut clariſſime con- <pb o="307" file="343" n="344" rhead="Ioan. de Sacro Boſco."/> ſtat in globo aliquo aſtronomico. </s> <s xml:id="echoid-s12965" xml:space="preserve">Quod quidem Manilius perpulchre his car-<lb/>minibus declarat. </s> <s xml:id="echoid-s12966" xml:space="preserve">Poſtquam enim de Zodiaco uerba fecit, ita de lact eo circu-<lb/>lo ſcribit.</s> <s xml:id="echoid-s12967" xml:space="preserve"/> </p> <div xml:id="echoid-div669" type="float" level="2" n="1"> <note position="left" xlink:label="note-342-01" xlink:href="note-342-01a" xml:space="preserve">E<unsure/>acteus cir <lb/>culus.</note> <note position="left" xlink:label="note-342-02" xlink:href="note-342-02a" xml:space="preserve">Vnde pro-<lb/>ueniat can-<lb/>dor in la-<lb/>cteo circu-<lb/>lo.</note> <note position="left" xlink:label="note-342-03" xlink:href="note-342-03a" xml:space="preserve">Lacteũ cir-<lb/>culum exi-<lb/>ſtere in Fir <lb/>ma mento, <lb/>non aũt in <lb/>aere.</note> <note position="left" xlink:label="note-342-04" xlink:href="note-342-04a" xml:space="preserve">Per quas <lb/>cõſtellatio-<lb/>nes circulus <lb/>@cteus. in-<lb/>@edat.</note> </div> <p style="it"> <s xml:id="echoid-s12968" xml:space="preserve">Alter in aduerſum poſitas ſuccedit ad Arctos, <lb/>Et paulum à Boreæ gyro ſua fila reducit, <lb/>Tranſitq́; </s> <s xml:id="echoid-s12969" xml:space="preserve">inuerſæ per ſidera Casſiopeiæ, <lb/>Inde per obliquum deſcendens tangit Olorem, <lb/>Aeſtiu@sq́; </s> <s xml:id="echoid-s12970" xml:space="preserve">ſecat fines, Aquilamq́; </s> <s xml:id="echoid-s12971" xml:space="preserve">ſupinam; <lb/></s> <s xml:id="echoid-s12972" xml:space="preserve">Temporaq́; </s> <s xml:id="echoid-s12973" xml:space="preserve">æquantem gyrum, zonamq́; </s> <s xml:id="echoid-s12974" xml:space="preserve">ferentem <lb/>Solis equos, intra caudam qua Scorpius ardet, <lb/>Extremamq́; </s> <s xml:id="echoid-s12975" xml:space="preserve">Sagittari læuam, atque ſagittam. </s> <s xml:id="echoid-s12976" xml:space="preserve"><lb/>Inde ſuos ſinuat flexus per crura pedesq́. </s> <s xml:id="echoid-s12977" xml:space="preserve"><lb/>Centauri alterius; </s> <s xml:id="echoid-s12978" xml:space="preserve">Rurſusq́ aſcendere cælum <lb/>Incipit, Argiuamq́. </s> <s xml:id="echoid-s12979" xml:space="preserve">ratem per paluſtria ſumma, <lb/>Et medium mundi gyrum, Geminosq per imum <lb/>Signa ſecat: </s> <s xml:id="echoid-s12980" xml:space="preserve">ſubit Heniochum: </s> <s xml:id="echoid-s12981" xml:space="preserve">te q. </s> <s xml:id="echoid-s12982" xml:space="preserve">inde profectus <lb/>Caſsiopeia petens ſuper ipſum Perſea tranſit, <lb/>Orbemq́. </s> <s xml:id="echoid-s12983" xml:space="preserve">ex illa cœptum concludit in illa: </s> <s xml:id="echoid-s12984" xml:space="preserve"><lb/>Tresq́. </s> <s xml:id="echoid-s12985" xml:space="preserve">ſecat medios Gyros, & </s> <s xml:id="echoid-s12986" xml:space="preserve">ſigna ferentem <lb/>Partibus @ binis, quoties præciditur ipſe. </s> <s xml:id="echoid-s12987" xml:space="preserve"><lb/>Nec quærendus erit, uiſus incurrit in ipſos <lb/>Sponte ſua ſeq́. </s> <s xml:id="echoid-s12988" xml:space="preserve">ipſe docet cogitq́. </s> <s xml:id="echoid-s12989" xml:space="preserve">notari. </s> <s xml:id="echoid-s12990" xml:space="preserve"><lb/>Namque in cæruleo candens nitet orbita mundo.</s> <s xml:id="echoid-s12991" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12992" xml:space="preserve"><emph style="sc">Lactevm</emph> circulum uocat Ouidius iter, quo ſuperi ad Iouem accede-<lb/>bant, his uerſibus in 1. </s> <s xml:id="echoid-s12993" xml:space="preserve">lib. </s> <s xml:id="echoid-s12994" xml:space="preserve">Metamorph.</s> <s xml:id="echoid-s12995" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s12996" xml:space="preserve">Eſt uia ſublimis cælo manifeſta ſereno, <lb/>(Lactea nomen habet) candore notabilis ipſo. <lb/></s> <s xml:id="echoid-s12997" xml:space="preserve">Hac iter eſt ſuperis ad magni regna Tonantis, <lb/>Re galemq́. </s> <s xml:id="echoid-s12998" xml:space="preserve">domum &</s> <s xml:id="echoid-s12999" xml:space="preserve">c.</s> <s xml:id="echoid-s13000" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13001" xml:space="preserve"><emph style="sc">Qvi</emph> plura de hoc circulo deſiderat, legat Ptolemæum loco citato, & </s> <s xml:id="echoid-s13002" xml:space="preserve">præ-<lb/>cipue commentarios Steflerini in ſphæram Pocli. </s> <s xml:id="echoid-s13003" xml:space="preserve">Ibi enim varias opiniones <lb/>circa hunc circulum extitiſſe reperiet.</s> <s xml:id="echoid-s13004" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div671" type="section" level="1" n="229"> <head xml:id="echoid-head240" xml:space="preserve">OFFICIA CIRCVLORVM PARALLEL ORVM.</head> <note position="right" xml:space="preserve">Tropici in <lb/>cludũt uiã <lb/>Solis.</note> </div> <div xml:id="echoid-div672" type="section" level="1" n="230"> <head xml:id="echoid-head241" xml:space="preserve">I.</head> <p> <s xml:id="echoid-s13005" xml:space="preserve"><emph style="sc">Tropici</emph> includunt uiam Solis. </s> <s xml:id="echoid-s13006" xml:space="preserve">Sunt enim ueluti limites includentes <lb/> <anchor type="note" xlink:label="note-343-02a" xlink:href="note-343-02"/> in cœlo regionem, extra quam Sol nunquam euagatur, ſed in ea perpetuo de <lb/>fertur. </s> <s xml:id="echoid-s13007" xml:space="preserve">Vnde ijdem indicant in Ecliptica duo puncta, in quibus Solſtitia contin <lb/>gunt, & </s> <s xml:id="echoid-s13008" xml:space="preserve">in quibus Sol maximam habet declinationem.</s> <s xml:id="echoid-s13009" xml:space="preserve"/> </p> <div xml:id="echoid-div672" type="float" level="2" n="1"> <note position="right" xlink:label="note-343-02" xlink:href="note-343-02a" xml:space="preserve">Polares cir <lb/>culi inclu-<lb/>dunt regio-<lb/>nes uerſus <lb/>polos, quæ <lb/>maximum <lb/>diẽ habent <lb/>maiorem, <lb/>quàm 24. <lb/>hor.</note> </div> </div> <div xml:id="echoid-div674" type="section" level="1" n="231"> <head xml:id="echoid-head242" xml:space="preserve">II.</head> <p> <s xml:id="echoid-s13010" xml:space="preserve"><emph style="sc">Polares</emph> circuli determinant diſtantiam polorum Zodiaci a polis <lb/>mundi, includuntque uerſus polos mundi regiones, in quibus maxima dies an <lb/>ni, maxim aque nox ſuperat 24. </s> <s xml:id="echoid-s13011" xml:space="preserve">horas, conficiturque ex pluribus diebus, ut in 3. <lb/></s> <s xml:id="echoid-s13012" xml:space="preserve">cap. </s> <s xml:id="echoid-s13013" xml:space="preserve">do cebitur.</s> <s xml:id="echoid-s13014" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">Tropici, & <lb/>polares cir <lb/>culi conſti-<lb/>tuunt quin <lb/>que<unsure/> zonas.</note> </div> <div xml:id="echoid-div675" type="section" level="1" n="232"> <head xml:id="echoid-head243" xml:space="preserve">III.</head> <p> <s xml:id="echoid-s13015" xml:space="preserve"><emph style="sc">Dvo</emph> Tropici, & </s> <s xml:id="echoid-s13016" xml:space="preserve">duo polares circuli tam in cœlo, quàm in terra quinque <lb/>Zonas conſtituunt, ut mox dicemus.</s> <s xml:id="echoid-s13017" xml:space="preserve"/> </p> <pb o="308" file="344" n="345" rhead="Comment. in II. Cap. Sphæræ"/> </div> <div xml:id="echoid-div676" type="section" level="1" n="233"> <head xml:id="echoid-head244" xml:space="preserve">IIII.</head> <note position="left" xml:space="preserve">Patalleli <lb/>circuli in-<lb/>dicãt æqua <lb/>litatem die <lb/>rum & no-<lb/>ctiũ in ſphę <lb/>ra recta, in <lb/>æqualitatẽ <lb/>uero in ob <lb/>liqua.</note> <p> <s xml:id="echoid-s13018" xml:space="preserve"><emph style="sc">Paralleli</emph> circuli, quos deſcribit Sol ad motum primi mobilis, nu-<lb/>mero 182. </s> <s xml:id="echoid-s13019" xml:space="preserve">fere, vt in 3. </s> <s xml:id="echoid-s13020" xml:space="preserve">cap. </s> <s xml:id="echoid-s13021" xml:space="preserve">dicemus, cauſam aperiunt perpetuæ æqualitatis die <lb/>rum & </s> <s xml:id="echoid-s13022" xml:space="preserve">noctium in ſphæra recta, inæqualita tis uero eorundem dierum & </s> <s xml:id="echoid-s13023" xml:space="preserve">no-<lb/>ctium, in ſphæra obliqua.</s> <s xml:id="echoid-s13024" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div677" type="section" level="1" n="234"> <head xml:id="echoid-head245" xml:space="preserve">V.</head> <p> <s xml:id="echoid-s13025" xml:space="preserve"><emph style="sc">Paralleli</emph> per Verticalia puncta omnium locorum incedentes pro-<lb/>ponunt ob oculos per totum circuitum cœli limites latitudinum ciuitatum, <lb/>& </s> <s xml:id="echoid-s13026" xml:space="preserve">in eiſdem longitudines locorum numerantur ab occaſu in ortum, vt dictum <lb/> <anchor type="note" xlink:label="note-344-02a" xlink:href="note-344-02"/> eſt ſupra.</s> <s xml:id="echoid-s13027" xml:space="preserve"/> </p> <div xml:id="echoid-div677" type="float" level="2" n="1"> <note position="left" xlink:label="note-344-02" xlink:href="note-344-02a" xml:space="preserve">Parelleli <lb/>circuli de-<lb/>terminant <lb/>latitudines <lb/>locorum, & <lb/>in illis nu-<lb/>merantur <lb/>longitudi-<lb/>nes.</note> </div> </div> <div xml:id="echoid-div679" type="section" level="1" n="235"> <head xml:id="echoid-head246" xml:space="preserve">VI.</head> <p> <s xml:id="echoid-s13028" xml:space="preserve"><emph style="sc">Paralleli</emph>, quos planetæ, uel ſtellæ fixæ motu diurno ab ortu in <lb/>occaſum deſcribunt, terminos pręfigunt declinationum omnium aſtrorum ab <lb/>Aequatore; </s> <s xml:id="echoid-s13029" xml:space="preserve">Quos vero delineant ab occaſu in ortum reſpectu Eclipticæ, latitu <lb/>dinum ab Ecliptica fines deſignant.</s> <s xml:id="echoid-s13030" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div680" type="section" level="1" n="236"> <head xml:id="echoid-head247" xml:space="preserve">VII.</head> <note position="left" xml:space="preserve">Paralleli <lb/>circuli indi <lb/>cant decli-<lb/>nationes <lb/>ſtellarũ, & <lb/>altitudines</note> <p> <s xml:id="echoid-s13031" xml:space="preserve"><emph style="sc">Circvli</emph> paralleli magnum uſum habent apud Coſmographos. </s> <s xml:id="echoid-s13032" xml:space="preserve">Nam <lb/>per illos in terra diſiungunt ſpatia tanto interuallo, ut maximi dies artificia-<lb/>les ſeſe mutuo ſuperent quadrante unius horæ. </s> <s xml:id="echoid-s13033" xml:space="preserve">Atque per eoſdem varia clima <lb/>ta conſtituuntur, vt ex 3. </s> <s xml:id="echoid-s13034" xml:space="preserve">cap. </s> <s xml:id="echoid-s13035" xml:space="preserve">parebit.</s> <s xml:id="echoid-s13036" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">Paralleli <lb/>circuli in <lb/>uſu ſunt a-<lb/>pud Coſmo <lb/>graphos.</note> </div> <div xml:id="echoid-div681" type="section" level="1" n="237"> <head xml:id="echoid-head248" style="it" xml:space="preserve">DE QVINQVE ZONIS.</head> <p style="it"> <s xml:id="echoid-s13037" xml:space="preserve">AEQ VINOCTI ALIS cum quatuor circulis minori-<lb/> <anchor type="note" xlink:label="note-344-05a" xlink:href="note-344-05"/> bus dicuntur quinque paralleli, quaſi æquidiſtantes: </s> <s xml:id="echoid-s13038" xml:space="preserve">non quia <lb/>quantum primus diſtat à ſecundo, tantum ſecund{us} diſtet à <lb/>tertio, quia hoc falſum eſt, ſicut iam patuit; </s> <s xml:id="echoid-s13039" xml:space="preserve">Sed, quia qui-<lb/>libet duo circuli per ſe ſumpti ſecundum quamlibet ſui partem æquidi-<lb/>ſtant ab inuicem; </s> <s xml:id="echoid-s13040" xml:space="preserve">& </s> <s xml:id="echoid-s13041" xml:space="preserve">dicuntur parallel{us} Aequinoctialis, parallelus Sol-<lb/>ſtitij ęſtiualis, parallelus Solſtitij hyemalis, & </s> <s xml:id="echoid-s13042" xml:space="preserve">parallel{us} Arctic{us}, & </s> <s xml:id="echoid-s13043" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-344-06a" xlink:href="note-344-06"/> parallel{us} Antarcticus.</s> <s xml:id="echoid-s13044" xml:space="preserve"/> </p> <div xml:id="echoid-div681" type="float" level="2" n="1"> <note position="left" xlink:label="note-344-05" xlink:href="note-344-05a" xml:space="preserve">Quinque <lb/>paralleli in <lb/>ſphæra qui <lb/>ſint.</note> <note position="left" xlink:label="note-344-06" xlink:href="note-344-06a" xml:space="preserve">Quatuor <lb/>paralleli <lb/>minoras di <lb/>ſtinguunt <lb/>in cœlo & <lb/>terra quin-<lb/>que zonas.</note> </div> <p style="it"> <s xml:id="echoid-s13045" xml:space="preserve">NOT ANDVM etiam, quod quatuor paralleli minores, ſcilicet <lb/>duo Tropici, & </s> <s xml:id="echoid-s13046" xml:space="preserve">parallel{us} Arctic{us}, & </s> <s xml:id="echoid-s13047" xml:space="preserve">parallel{us} Antarcticus, diſtin-<lb/>guunt in cœlo quinque Zonas, ſiue regiones. </s> <s xml:id="echoid-s13048" xml:space="preserve">Vnde Virgilius in 1. </s> <s xml:id="echoid-s13049" xml:space="preserve">Georg.</s> <s xml:id="echoid-s13050" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13051" xml:space="preserve">Quinque tenent cœlum Zonæ, quarum una coruſco <lb/>Semper Sole rubens, & </s> <s xml:id="echoid-s13052" xml:space="preserve">torrida ſemper ab igne. <lb/></s> <s xml:id="echoid-s13053" xml:space="preserve">Quam circum extremæ dextra, læuaq́ue trahuntur <lb/>Cærulea glacie concretæ, atque imbribus atris. </s> <s xml:id="echoid-s13054" xml:space="preserve"><lb/>Has inter, mediamque duæ mortalibus ægris <lb/>Munere conceſſæ Diuum, & </s> <s xml:id="echoid-s13055" xml:space="preserve">via ſecta per ambas, <lb/>Obliquus qua ſe ſignorum verteret ordo,</s> </p> <pb o="309" file="345" n="346" rhead="Ioan. de Sacro Boſco."/> <p style="it"> <s xml:id="echoid-s13056" xml:space="preserve">DISTINGVV NTVR etiam totidem plagæ in terra directe <lb/>prædictis Zonis ſuppoſitæ. </s> <s xml:id="echoid-s13057" xml:space="preserve">Vnde Ouid. </s> <s xml:id="echoid-s13058" xml:space="preserve">1. </s> <s xml:id="echoid-s13059" xml:space="preserve">Metamorph.</s> <s xml:id="echoid-s13060" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13061" xml:space="preserve">Vtque duæ dextra cœlum, totidemq́ue ſiniſtra <lb/>Parte ſecant Zonę, quinta eſt ardentior illis: <lb/></s> <s xml:id="echoid-s13062" xml:space="preserve">Sic onus incluſum numero diſtinxit eodem <lb/>Cura Dei, totidemq́ue plagæ tellure premuntur. </s> <s xml:id="echoid-s13063" xml:space="preserve"><lb/>Quarum quæ media eſt, non eſt habitabilis æſtu: </s> <s xml:id="echoid-s13064" xml:space="preserve"><lb/>Nix tegit alta duas: </s> <s xml:id="echoid-s13065" xml:space="preserve">totidem inter vtramque locauit, <lb/>Temperiemq́ue dedit, miſta cum frigore flamma.</s> <s xml:id="echoid-s13066" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s13067" xml:space="preserve">ILLA igitur zona, quæ eſt inter duos Tropicos, dicitur inhabita-<lb/> <anchor type="note" xlink:label="note-345-01a" xlink:href="note-345-01"/> bilis, propter calorem Solis diſcurrentis ſemper inter tropicos. </s> <s xml:id="echoid-s13068" xml:space="preserve">Simili-<lb/>ter plaga terræ illi directe ſuppoſita dicitur inhabitabilis propter calo-<lb/>rem Solis diſcurrentis ſuper illam. </s> <s xml:id="echoid-s13069" xml:space="preserve">Illę uero duæ zonæ, quæ circumſcri-<lb/>buntur à ci@culo Arctico, & </s> <s xml:id="echoid-s13070" xml:space="preserve">circulo Antarctico circa polos mundi, in-<lb/>habitabiles ſunt, propter nimiam frigiditatem, quia Sol ab eis maxime <lb/>remonetur. </s> <s xml:id="echoid-s13071" xml:space="preserve">Similiter inte lligendum eſt de plagis terrę illis directe ſup-<lb/>poſitis. </s> <s xml:id="echoid-s13072" xml:space="preserve">Illæ autem duæ zonæ, quarum una eſt inter Tropicum æſtiua-<lb/>lem, & </s> <s xml:id="echoid-s13073" xml:space="preserve">circulum Arcticum, & </s> <s xml:id="echoid-s13074" xml:space="preserve">reliqua, quæ eſt inter Tropicum hyema-<lb/>lem & </s> <s xml:id="echoid-s13075" xml:space="preserve">circulum Antarcticum, habitabiles ſunt, & </s> <s xml:id="echoid-s13076" xml:space="preserve">temperatæ caliditate <lb/>torridæ zonæ exiſtentis inter Tropicos, & </s> <s xml:id="echoid-s13077" xml:space="preserve">frigiditate zonarum extrema-<lb/>rum, quæ ſunt circa polos mundi. </s> <s xml:id="echoid-s13078" xml:space="preserve">Idem intellige de plagis terræ illis dire-<lb/>cte ſuppoſitis.</s> <s xml:id="echoid-s13079" xml:space="preserve"/> </p> <div xml:id="echoid-div682" type="float" level="2" n="2"> <note position="right" xlink:label="note-345-01" xlink:href="note-345-01a" xml:space="preserve">Quæ Zonæ <lb/>dicantu in <lb/>habitabiles <lb/>& quæ ha-<lb/>bitabiles.</note> </div> </div> <div xml:id="echoid-div684" type="section" level="1" n="238"> <head xml:id="echoid-head249" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s13080" xml:space="preserve"><emph style="sc">AGit</emph> in tertia hac parte <lb/> <anchor type="figure" xlink:label="fig-345-01a" xlink:href="fig-345-01"/> cap. </s> <s xml:id="echoid-s13081" xml:space="preserve">da quinque Zonis, <lb/>quas ait in cœlo diſtin-<lb/>gui per quatuor circulos <lb/>minores, ita ut media, <lb/>quæ torrida dicitur, comprehendatur <lb/> <anchor type="note" xlink:label="note-345-02a" xlink:href="note-345-02"/> inter duos Tropicos. </s> <s xml:id="echoid-s13082" xml:space="preserve">Duę uero dictæ <lb/>temperatę inter utrumq. </s> <s xml:id="echoid-s13083" xml:space="preserve">Tropicũ, & </s> <s xml:id="echoid-s13084" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-345-03a" xlink:href="note-345-03"/> circulum polarem; </s> <s xml:id="echoid-s13085" xml:space="preserve">Reliquæ denique <lb/> <anchor type="note" xlink:label="note-345-04a" xlink:href="note-345-04"/> duę, quæ frigidæ uocãtur, inter duos <lb/>circulos polares, & </s> <s xml:id="echoid-s13086" xml:space="preserve">polos mundi, vt in <lb/>hac figura conſpicis. </s> <s xml:id="echoid-s13087" xml:space="preserve">Deinde docet, <lb/>totidem eſſe Zonas in terra illis cœ-<lb/>leſtibus directe ſuppoſitas. </s> <s xml:id="echoid-s13088" xml:space="preserve">In teſtimo-<lb/>nium Zonarum cœleſtium adducit <lb/>carmina quædã Vi@gilij ex 1. </s> <s xml:id="echoid-s13089" xml:space="preserve">Georg. <lb/></s> <s xml:id="echoid-s13090" xml:space="preserve">In confirma tionem vero terreſtrium <pb o="310" file="346" n="347" rhead="Comment. in III. Cap. Sphæræ"/> citat carmina Ouidij ex 1. </s> <s xml:id="echoid-s13091" xml:space="preserve">Metamorph. </s> <s xml:id="echoid-s13092" xml:space="preserve">aſſignatq́; </s> <s xml:id="echoid-s13093" xml:space="preserve">cauſam, propter quam Zo-<lb/>na omniũ media dicatur torrida, extremæ uero frigidæ, & </s> <s xml:id="echoid-s13094" xml:space="preserve">reliquæ inter tor-<lb/>ridam, & </s> <s xml:id="echoid-s13095" xml:space="preserve">frig idas temperatæ. </s> <s xml:id="echoid-s13096" xml:space="preserve">Quæ omnia perſpicua ſunt in auctore.</s> <s xml:id="echoid-s13097" xml:space="preserve"/> </p> <div xml:id="echoid-div684" type="float" level="2" n="1"> <figure xlink:label="fig-345-01" xlink:href="fig-345-01a"> <image file="345-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/345-01"/> </figure> <note position="right" xlink:label="note-345-02" xlink:href="note-345-02a" xml:space="preserve">Zona torĩ<unsure/>-<lb/>da.</note> <note position="right" xlink:label="note-345-03" xlink:href="note-345-03a" xml:space="preserve">Zonę tem-<lb/>peratæ.</note> <note position="right" xlink:label="note-345-04" xlink:href="note-345-04a" xml:space="preserve">Zonæ fri-<lb/>gidæ</note> </div> <note position="left" xml:space="preserve">Pars dextra, <lb/>& ſiniſtra <lb/>cæli apud <lb/>ph@loſo-<lb/>phos, & Coſ <lb/>mogr<unsure/>aphos. <lb/>quæ.</note> <p> <s xml:id="echoid-s13098" xml:space="preserve"><emph style="sc">Solvm</emph> obiter hoc loco animadnertendum eſt, quoniam uterq; </s> <s xml:id="echoid-s13099" xml:space="preserve">Poeta <lb/>ab Auctore adductus mentionẽ fecit dextrę & </s> <s xml:id="echoid-s13100" xml:space="preserve">ſiniſtrę partis in cęlo, nõ eodẽ <lb/>modo apud omnes accipi dextrum, ac ſiniſtrũ in corporibus cæleſtibus. </s> <s xml:id="echoid-s13101" xml:space="preserve">Plato <lb/>enim, Ariſtoteles, cæteriq́; </s> <s xml:id="echoid-s13102" xml:space="preserve">philoſophi, nec non Geographi, partes orientales <lb/>Dextras appellant, & </s> <s xml:id="echoid-s13103" xml:space="preserve">occidentales Siniſtras. </s> <s xml:id="echoid-s13104" xml:space="preserve">Ariſtoteles quidẽ, & </s> <s xml:id="echoid-s13105" xml:space="preserve">philoſophi <lb/>propterea quòd ab oriente motus cælorum incipit, quemadmodum & </s> <s xml:id="echoid-s13106" xml:space="preserve">in ani <lb/>malibus motus initiũ ſumit ex parte dextra: </s> <s xml:id="echoid-s13107" xml:space="preserve">Geographi autem, (loquor de <lb/>Geographis citra Aequatorẽ) quia uolentes indagare altitudinẽ poli, ut ter-<lb/>rę ſitum rectius depingant, faciem ſuã vertunt ad polum Arcticum; </s> <s xml:id="echoid-s13108" xml:space="preserve">Vnde ne-<lb/>ceſſario Oriens erit illis ad dextram, Occidens uero ad ſiniſtram poſitũ. </s> <s xml:id="echoid-s13109" xml:space="preserve">Hinc <lb/>fit, ut omnes mappæ mundi, & </s> <s xml:id="echoid-s13110" xml:space="preserve">regionum tabulæ ita fere deſcribãtur à Coſmo <lb/> <anchor type="note" xlink:label="note-346-02a" xlink:href="note-346-02"/> graphis, (vt uidere licet apud Ptolemæum, & </s> <s xml:id="echoid-s13111" xml:space="preserve">alios) vt intuẽti mappas, ſiue ta <lb/>bulas, oriẽs ex parte dextra, occidẽs autẽ ex parte ſiniſtra collocetur. </s> <s xml:id="echoid-s13112" xml:space="preserve">Aſtrono <lb/>mi uero contra, occidẽtales partes cęli dextras, & </s> <s xml:id="echoid-s13113" xml:space="preserve">orientales ſiniſtras uocant, <lb/>eo quòd citra Aequatorem degentes faciem ſuã conuertãt ad Auſtrũ, uerſus <lb/>nimirum Aequinoctialẽ circulũ, ubi uelociſſimus exiſtit motus, ut accuratius <lb/>ſiderum curſus obſeruẽt. </s> <s xml:id="echoid-s13114" xml:space="preserve">Ex quo fit, ut à dextris habeant Occidẽs, à ſiniſtris <lb/>uero Oriens Poetæ deniq; </s> <s xml:id="echoid-s13115" xml:space="preserve">partes cęli Septentrionales dextras, Auſtrales ue-<lb/> <anchor type="note" xlink:label="note-346-03a" xlink:href="note-346-03"/> rc ſiniſtras appellant; </s> <s xml:id="echoid-s13116" xml:space="preserve">quia uidelicet obſeruantes occaſus aſtrorũ faciẽ eõuer-<lb/>tunt ad cccaſum, & </s> <s xml:id="echoid-s13117" xml:space="preserve">ſic Septentrio ponitur ad dextrã, Auſter uero ad ſiniſtrã. <lb/></s> <s xml:id="echoid-s13118" xml:space="preserve">Sententiam hanc Poetarũ conſirmant Aſtronomi, ut nimirũ pars Septẽtriona <lb/>lis in cælo dicatur Dextra, & </s> <s xml:id="echoid-s13119" xml:space="preserve">Auſtralis ſiniſtra, quoniã uidelicet in quocunq; </s> <s xml:id="echoid-s13120" xml:space="preserve"><lb/>climate Sol oriens ſupra Horizontem Septẽtrionẽ habet à dextris, Auſtrum <lb/>vero à ſiniſtris, ſuntq́; </s> <s xml:id="echoid-s13121" xml:space="preserve">plures ſtellæ prope polũ borealem, quàm prope auſtra-<lb/>lem, ut ſupra dictum eſt. </s> <s xml:id="echoid-s13122" xml:space="preserve">Ex his igitur cõſtat Virgilium, & </s> <s xml:id="echoid-s13123" xml:space="preserve">Ouidium nomine <lb/>partis dextræ, ac ſiniſtræ intellexiſſe Septẽtrionem, & </s> <s xml:id="echoid-s13124" xml:space="preserve">Auſtrum. </s> <s xml:id="echoid-s13125" xml:space="preserve">Ita quoq; </s> <s xml:id="echoid-s13126" xml:space="preserve">in-<lb/>tellexit partem dextram, atque ſiniſtram Lucanus lib. </s> <s xml:id="echoid-s13127" xml:space="preserve">3. </s> <s xml:id="echoid-s13128" xml:space="preserve">quando dicit.</s> <s xml:id="echoid-s13129" xml:space="preserve"/> </p> <div xml:id="echoid-div685" type="float" level="2" n="2"> <note position="left" xlink:label="note-346-02" xlink:href="note-346-02a" xml:space="preserve">Pars dextra <lb/>& ſiniſtra <lb/>cæli apud <lb/>aſtronomos <lb/>quę.</note> <note position="left" xlink:label="note-346-03" xlink:href="note-346-03a" xml:space="preserve">Pars dextra <lb/>& ſiniſtra <lb/>cæli apud <lb/>Poetas qu ę.</note> </div> <p style="it"> <s xml:id="echoid-s13130" xml:space="preserve">Ignotum vobis Arabes veniſtis in orbem, <lb/>Vmbras mirati nemorum non ire ſiniſtras.</s> <s xml:id="echoid-s13131" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13132" xml:space="preserve">Voluit enim ſignificare, Arabes ueniſſe citra tropicũ ♋, ubi perpetuo umbræ <lb/>corporũ in meridie uerſus ſeptentrionẽ, hoc eſt, ad dextram partẽ mũdi, pro-<lb/>ijciuntur; </s> <s xml:id="echoid-s13133" xml:space="preserve">& </s> <s xml:id="echoid-s13134" xml:space="preserve">non uerſus Auſtrum, id eſt, ad ſiniſtrã partẽ, ut in 3. </s> <s xml:id="echoid-s13135" xml:space="preserve">cap. </s> <s xml:id="echoid-s13136" xml:space="preserve">dicemus.</s> <s xml:id="echoid-s13137" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13138" xml:space="preserve"><emph style="sc">Dicvntvr</emph> Zonæ interdum ab auctoribus Faſciæ, cinguli, Plagę, & </s> <s xml:id="echoid-s13139" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-346-04a" xlink:href="note-346-04"/> à Cicerone in Somnio Scipionis Maculæ. </s> <s xml:id="echoid-s13140" xml:space="preserve">Porro cum duo ſint genera Zona-<lb/>rum, unum cæleſtium, a@terreſtriũ alterũ. </s> <s xml:id="echoid-s13141" xml:space="preserve">Cęleſtes primariæ ſunt, & </s> <s xml:id="echoid-s13142" xml:space="preserve">terreſtriũ <lb/>cauſæ; </s> <s xml:id="echoid-s13143" xml:space="preserve">non quòd illæ cæleſtes calidæ ſint, uel frigidæ, uel tẽperatæ: </s> <s xml:id="echoid-s13144" xml:space="preserve">lõge enim <lb/>abſunt huiuſmodi qualitates à corporibus cæleſtibus, ſed quòd Sol ob uariã <lb/>radiorũ reflexionẽ, directã uidelicet, aut obliquã, terreſtres Zonas aut reddat <lb/>omnino frigidas propter nimiã obliquitatem radiorũ, ut accidit in duabus ex <lb/>tremis Zonis iuxta polos mundi: </s> <s xml:id="echoid-s13145" xml:space="preserve">aut omnino incendat, ob rectitudinẽ radio-<lb/>rum, ut fit in Zona media omniũ inter duos Tropicos; </s> <s xml:id="echoid-s13146" xml:space="preserve">aut denique in illis tem <lb/>peratum calorẽ, & </s> <s xml:id="echoid-s13147" xml:space="preserve">frigus inducat, quando nimirũ radij Solares nec nimis di-<lb/>recti, nec nimis obliqui exiſtunt, ſed medio ſe habent modo, ut contingit in <lb/>Zonis temperatis, quæ collocantur inter Tropicos, & </s> <s xml:id="echoid-s13148" xml:space="preserve">circulos polares.</s> <s xml:id="echoid-s13149" xml:space="preserve"/> </p> <div xml:id="echoid-div686" type="float" level="2" n="3"> <note position="left" xlink:label="note-346-04" xlink:href="note-346-04a" xml:space="preserve">Varia nomi <lb/>@a Zonarũ.</note> </div> <p> <s xml:id="echoid-s13150" xml:space="preserve">ID vero, quod Poetæ fabulãtur, frigidas Zonas ob nimium frigus, & </s> <s xml:id="echoid-s13151" xml:space="preserve">tor- <pb o="311" file="347" n="348" rhead="Ioan. de Sacro Boſco."/> ridam ob nimium æſtum eſſe in habitabiles, uerum non eſt. </s> <s xml:id="echoid-s13152" xml:space="preserve">Experientia enim, <lb/>& </s> <s xml:id="echoid-s13153" xml:space="preserve">nauigatione Luſitanorum, Hiſpanorumq; </s> <s xml:id="echoid-s13154" xml:space="preserve">ſatis conſtat, ſub Aequatore, hoc <lb/>eſt, ſub medio Zonæ torridæ, plurimos populos habitare. </s> <s xml:id="echoid-s13155" xml:space="preserve">Item ſub polis, ſal-<lb/>tem ſub polo Arctico, id eſt, ſub medio frigidatũ Zonarum, ut refert Magnus <lb/>Olaus Gothus. </s> <s xml:id="echoid-s13156" xml:space="preserve">Immo omnes, qui eò nauigarunt, affirmant, optimam eſſe ſub <lb/>Æquatore habitationem, cuius rei cauſas longũ eſſet hoc loco recitare. </s> <s xml:id="echoid-s13157" xml:space="preserve">Nam <lb/>quidquid ſit de frigore, & </s> <s xml:id="echoid-s13158" xml:space="preserve">calore, credendũ eſt, Naturam, quæ regiones calore, <lb/>ac frigore diſtinxit, homines quoq; </s> <s xml:id="echoid-s13159" xml:space="preserve">& </s> <s xml:id="echoid-s13160" xml:space="preserve">cętera aĩalia ad locorũ patiẽtiã quoque <lb/>generaſſe, pręſertim cũ uideamus & </s> <s xml:id="echoid-s13161" xml:space="preserve">Luſitanos, & </s> <s xml:id="echoid-s13162" xml:space="preserve">Hiſpanos tãdẽ aſſueuiſſe fer <lb/>re intem periẽ Zonæ torridæ, cum multi hoc tempore ſub Aequatore degant.</s> <s xml:id="echoid-s13163" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13164" xml:space="preserve">Qvo aũt pacto terreſtres Zonæ cæleſtibus ſint directe ſuppoſitæ, dilucide <lb/>explicat ſubiecta figura, in qua ex omnibus quatuor circulis minoribus cæli <lb/>ad centrum terræ deductæ ſunt lineæ rectæ. </s> <s xml:id="echoid-s13165" xml:space="preserve">Vbi enim hæ ſuperficiem terræ <lb/>interſecant, ibi ijdem circuli in terra deſcribuntur, ita ut omnes circuli in ter-<lb/>ra ad perpendicu<unsure/>lum ſubijciantur circulis cæleſtibus. </s> <s xml:id="echoid-s13166" xml:space="preserve">Ita enim fiet, ut facile ex <lb/>vltima propoſ. </s> <s xml:id="echoid-s13167" xml:space="preserve">lib. </s> <s xml:id="echoid-s13168" xml:space="preserve">6. </s> <s xml:id="echoid-s13169" xml:space="preserve">Euclid. </s> <s xml:id="echoid-s13170" xml:space="preserve">colligi poteſt, cum cęlum & </s> <s xml:id="echoid-s13171" xml:space="preserve">terra idem habent <lb/>centrum, ſegmenta a terrę, quæ dictis circulis includuntur, eſſe ſimilia ſegmẽ-<lb/>tis cęli inter eoſdem circulos cæleſtes comprehenſis.</s> <s xml:id="echoid-s13172" xml:space="preserve"/> </p> <figure> <image file="347-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/347-01"/> </figure> <p> <s xml:id="echoid-s13173" xml:space="preserve"><emph style="sc">Vnde</emph> ſi à dictis parallelis cæleſtibus perpendicula demitterentur ad ſu-<lb/>per<unsure/>ſiciem terræ, quæ ad centrum mundi neceſſario uergerent, deſcriberentur <lb/>ab illis in terræ ſuperficie circuli ijdem directe cæleſtibus illis reſpondentes.</s> <s xml:id="echoid-s13174" xml:space="preserve"/> </p> <pb o="312" file="348" n="349" rhead="Comment. in II. Cap. Sphæræ"/> <p> <s xml:id="echoid-s13175" xml:space="preserve"><emph style="sc">Qvaelibet</emph> Zona eſt eiuſdem ſemper latitudinis à Borea in Auſtrum, <lb/>vndecunque in cipias, propterea quòd inter duos circulos æquidiſtantes conti <lb/> <anchor type="note" xlink:label="note-348-01a" xlink:href="note-348-01"/> netur, non autem eiuſdem longitudinis ab ortu in occaſum. </s> <s xml:id="echoid-s13176" xml:space="preserve">Nã partes cuiuſ-<lb/>libet Zonæ, quò viciniores fuerint Aequatori, eò etiam longitudinẽ habebũt <lb/>maiorem, quò uero polis propinquiores, eò minorem, cum paralleli uerſus po <lb/>los ſemper minores fiant, ut ſupra dictũ eſt. </s> <s xml:id="echoid-s13177" xml:space="preserve">Habebitur autem facile ex dictis <lb/>latitudo cuiuſuis Zonæ. </s> <s xml:id="echoid-s13178" xml:space="preserve">Quoniam enim uterque Tropicus diſtat ab Aequa-<lb/>tore grad. </s> <s xml:id="echoid-s13179" xml:space="preserve">23. </s> <s xml:id="echoid-s13180" xml:space="preserve">min. </s> <s xml:id="echoid-s13181" xml:space="preserve">30. </s> <s xml:id="echoid-s13182" xml:space="preserve">erit latitudo totius Zonæ torridæ grad. </s> <s xml:id="echoid-s13183" xml:space="preserve">47. </s> <s xml:id="echoid-s13184" xml:space="preserve">qui efficiunt <lb/>milliaria 2937 {1/2}. </s> <s xml:id="echoid-s13185" xml:space="preserve">Rurſus quia vterque circulus polaris à polo mundi vicino <lb/> <anchor type="note" xlink:label="note-348-02a" xlink:href="note-348-02"/> recedit grad. </s> <s xml:id="echoid-s13186" xml:space="preserve">23. </s> <s xml:id="echoid-s13187" xml:space="preserve">min. </s> <s xml:id="echoid-s13188" xml:space="preserve">30. </s> <s xml:id="echoid-s13189" xml:space="preserve">tanta erit latitudo utriuſlibet Zonæ frigidæ à polo <lb/>ad circulum polarem, hoc eſt, continebit milliaria 1468 {3/4}. </s> <s xml:id="echoid-s13190" xml:space="preserve">tota autem latitu-<lb/>do ſecundũ diametrum ſumpta complectetur gr. </s> <s xml:id="echoid-s13191" xml:space="preserve">47. </s> <s xml:id="echoid-s13192" xml:space="preserve">hoc eſt, milliaria 2937 {1/2}. <lb/></s> <s xml:id="echoid-s13193" xml:space="preserve">Denique ſi ex 90. </s> <s xml:id="echoid-s13194" xml:space="preserve">grad. </s> <s xml:id="echoid-s13195" xml:space="preserve">ſubtrahas diſtantiam circuli polaris à polo, & </s> <s xml:id="echoid-s13196" xml:space="preserve">Tropici <lb/>ab Aequatore, uidelicet grad. </s> <s xml:id="echoid-s13197" xml:space="preserve">47. </s> <s xml:id="echoid-s13198" xml:space="preserve">remanebit latitudo utriuſuis Zonæ tempera <lb/>tæ, grad. </s> <s xml:id="echoid-s13199" xml:space="preserve">33. </s> <s xml:id="echoid-s13200" xml:space="preserve">quibus conueniunt milliaria 2687 {1/2}. </s> <s xml:id="echoid-s13201" xml:space="preserve">Longitudinem quoque cu-<lb/> <anchor type="note" xlink:label="note-348-03a" xlink:href="note-348-03"/> iuſque Zonæ obtinebimus tam in principio, quàm in medio, ac fine, ſi prius <lb/>per ea, quæ docuimus ſupra, inueſtigemus proportionem Aequatoris ad quẽ-<lb/>cunque parallelum, hoc eſt, quot gradus, ſeu partes quilibet parallelus com-<lb/>prehendat ex ijs, quarum 360. </s> <s xml:id="echoid-s13202" xml:space="preserve">continet Aequator. </s> <s xml:id="echoid-s13203" xml:space="preserve">Vt quia parallelus per Ro-<lb/>mam tranſiens continet tales partes 267 {1/2}. </s> <s xml:id="echoid-s13204" xml:space="preserve">fere, habebit longitudo tempera-<lb/>tæ Zonæ in eo parallelo, qui per Romam incedit grad. </s> <s xml:id="echoid-s13205" xml:space="preserve">267. </s> <s xml:id="echoid-s13206" xml:space="preserve">min. </s> <s xml:id="echoid-s13207" xml:space="preserve">30. </s> <s xml:id="echoid-s13208" xml:space="preserve">nimirum <lb/>milliaria ferme 16719. </s> <s xml:id="echoid-s13209" xml:space="preserve">&</s> <s xml:id="echoid-s13210" xml:space="preserve">c.</s> <s xml:id="echoid-s13211" xml:space="preserve"/> </p> <div xml:id="echoid-div687" type="float" level="2" n="4"> <note position="left" xlink:label="note-348-01" xlink:href="note-348-01a" xml:space="preserve">Zona quæ-<lb/>uis eſt eiuſ <lb/>dem latitu <lb/>dinis, ſed <lb/>non eiuſdẽ <lb/>lõgitudinis <lb/>quoad om-<lb/>nes partes.</note> <note position="left" xlink:label="note-348-02" xlink:href="note-348-02a" xml:space="preserve">Latitudi-<lb/>nes Zonar<unsure/>ũ <lb/>quãtæ ſint.</note> <note position="left" xlink:label="note-348-03" xlink:href="note-348-03a" xml:space="preserve">Longitu di-<lb/>nes Zonarũ <lb/>qua arte de <lb/>prehendan <lb/>tur tam in <lb/>principio <lb/>quã in me-<lb/>dio, & fine.</note> </div> <p> <s xml:id="echoid-s13212" xml:space="preserve"><emph style="sc">Proposita</emph> etiam quacunque ciuitate, facillimo negotio cognoſcemus, <lb/> <anchor type="note" xlink:label="note-348-04a" xlink:href="note-348-04"/> in quanam Zona ſit repoſita, ſi diligenter inſpiciamus globum aliquem Coſ-<lb/>mographicum, uel etiam Mappam uniuerſalem totius mundi. </s> <s xml:id="echoid-s13213" xml:space="preserve">Cum enim ſiue <lb/>in globo, ſiue in Mappa depingantur circuli paralleli diſtinguentes totã ter-<lb/>ram in quinque ſupradictas Zonas, omnes ciuitates, quæ reperient̃ intra duos <lb/>Tropicos, ſitæ erunt in zona torrida: </s> <s xml:id="echoid-s13214" xml:space="preserve">Quæ uero inter alterutrũ Tropicorum, <lb/>& </s> <s xml:id="echoid-s13215" xml:space="preserve">polarem circulum uicinum, in zona temperata: </s> <s xml:id="echoid-s13216" xml:space="preserve">Quæ denique inter circulũ. <lb/></s> <s xml:id="echoid-s13217" xml:space="preserve">quemuis polarem, & </s> <s xml:id="echoid-s13218" xml:space="preserve">polum mũdi propinquum, in zona frigida conſtituẽtur <lb/>Quod ſi nulla adſit copia globi Coſmographici, aut Mappæ, ita conijcienda <lb/>erit zona cuiuſcunq; </s> <s xml:id="echoid-s13219" xml:space="preserve">ciuitatis. </s> <s xml:id="echoid-s13220" xml:space="preserve">Omnis ciuitas latitudinem habẽs minorẽ quã <lb/>gr. </s> <s xml:id="echoid-s13221" xml:space="preserve">23. </s> <s xml:id="echoid-s13222" xml:space="preserve">min. </s> <s xml:id="echoid-s13223" xml:space="preserve">30. </s> <s xml:id="echoid-s13224" xml:space="preserve">ſita erit in zona torrida, cum uterq; </s> <s xml:id="echoid-s13225" xml:space="preserve">Tropicorũ declinet ab Ae-<lb/>quatore grad. </s> <s xml:id="echoid-s13226" xml:space="preserve">23. </s> <s xml:id="echoid-s13227" xml:space="preserve">min. </s> <s xml:id="echoid-s13228" xml:space="preserve">30. </s> <s xml:id="echoid-s13229" xml:space="preserve">Quod ſi ciuitatis oblatæ latitudo præciſe fuerit gr. </s> <s xml:id="echoid-s13230" xml:space="preserve"><lb/>23. </s> <s xml:id="echoid-s13231" xml:space="preserve">min. </s> <s xml:id="echoid-s13232" xml:space="preserve">30. </s> <s xml:id="echoid-s13233" xml:space="preserve">& </s> <s xml:id="echoid-s13234" xml:space="preserve">ſita uerſus Septẽtrionem, collocabitur præciſe ſub Tropico ♋, <lb/>qui finis eſt torridæ zonæ, & </s> <s xml:id="echoid-s13235" xml:space="preserve">initium temperatæ Septentrionalis: </s> <s xml:id="echoid-s13236" xml:space="preserve">Si autem ſi-<lb/>ta fuerit uerſus auſtrum, erit ſub Tropico ♑, qui finis etiam eſt zonæ torri-<lb/>dæ, & </s> <s xml:id="echoid-s13237" xml:space="preserve">principium temperatæ Meridionalis. </s> <s xml:id="echoid-s13238" xml:space="preserve">Omnis uero ciuitas latitudinem <lb/>habens maiorem quidem, quàm grad. </s> <s xml:id="echoid-s13239" xml:space="preserve">23. </s> <s xml:id="echoid-s13240" xml:space="preserve">min. </s> <s xml:id="echoid-s13241" xml:space="preserve">30. </s> <s xml:id="echoid-s13242" xml:space="preserve">minorem autem quàm gra. </s> <s xml:id="echoid-s13243" xml:space="preserve"><lb/>66. </s> <s xml:id="echoid-s13244" xml:space="preserve">min. </s> <s xml:id="echoid-s13245" xml:space="preserve">40. </s> <s xml:id="echoid-s13246" xml:space="preserve">habebit Zonã temperatam Borealem, ſi uerſus Septẽtrionem uer-<lb/>gat: </s> <s xml:id="echoid-s13247" xml:space="preserve">Si enim in Auſtrum declinet, erit in Zona temperata Auſtrali. </s> <s xml:id="echoid-s13248" xml:space="preserve">Quod ſi ci <lb/>ui tatis latitudo fuerit præciſe grad. </s> <s xml:id="echoid-s13249" xml:space="preserve">66. </s> <s xml:id="echoid-s13250" xml:space="preserve">min. </s> <s xml:id="echoid-s13251" xml:space="preserve">30. </s> <s xml:id="echoid-s13252" xml:space="preserve">collocabitur directe ſub circu-<lb/>lo Arctico, uel Antarctico, prout in Septentrionem, uel Meridiem declinaue-<lb/>rit. </s> <s xml:id="echoid-s13253" xml:space="preserve">Omnis denique ciuitas, cuius latitudo excedit grad. </s> <s xml:id="echoid-s13254" xml:space="preserve">66. </s> <s xml:id="echoid-s13255" xml:space="preserve">min. </s> <s xml:id="echoid-s13256" xml:space="preserve">30. </s> <s xml:id="echoid-s13257" xml:space="preserve">obtinebit <lb/>Zonam frigidam, uel Septentrionalem, uel Meridionalem. </s> <s xml:id="echoid-s13258" xml:space="preserve">Quod ſi præciſe <lb/>altitudo fuerit grad. </s> <s xml:id="echoid-s13259" xml:space="preserve">90. </s> <s xml:id="echoid-s13260" xml:space="preserve">erit directe illa ciuitas poſita ſub altero polorum <lb/>mundi. </s> <s xml:id="echoid-s13261" xml:space="preserve">Ex his omnibus perſpicuũ eſt, ſi cognita fuerit loci alicuius latitudo, <lb/>in quanam Zona contineri dicatur.</s> <s xml:id="echoid-s13262" xml:space="preserve"/> </p> <div xml:id="echoid-div688" type="float" level="2" n="5"> <note position="left" xlink:label="note-348-04" xlink:href="note-348-04a" xml:space="preserve">Quanã in <lb/>Zona ciui-<lb/>@as propo-<lb/>ſita ſit, quo <lb/>pacto co-<lb/>@noſcatur.</note> </div> <pb o="313" file="349" n="350" rhead="Ioan. de Sacro Boſco."/> <p> <s xml:id="echoid-s13263" xml:space="preserve"><emph style="sc">Iilvd</emph> quoque minime uidetur eſſe prætereundum, apud ſcriptores va-<lb/>rios, præſertim Aſtronomos & </s> <s xml:id="echoid-s13264" xml:space="preserve">Coſmographos, populos illos, qui alterutram-<lb/>zonarum frigidarum incolunt, appellari Periſcos, quòd umbræ eorũ uelut in <lb/>orbem, molarum more, circumagantur in plano Horizontis certis anni tẽpo-<lb/>ribus. </s> <s xml:id="echoid-s13265" xml:space="preserve">Sol enim ad ea loca tranſmittit radios quodammodo æquidiſtantes Ho <lb/>rizontis plano, ut ex ſphæra materiali conſtat, qui in gyrum ſemper feruntur. <lb/></s> <s xml:id="echoid-s13266" xml:space="preserve">Eos autem, qui temperatarum alterutram zonam obtinent, dici Heteroſcios, <lb/>quòd uerſus unum tantum mundi polum umbras meridianas proijciant, <lb/>Boreales quidem ad polum Arcticum, Auſtrales uero ad Antarcti-<lb/>cum. </s> <s xml:id="echoid-s13267" xml:space="preserve">Nam Sol nunquam eorum uertices attingit. </s> <s xml:id="echoid-s13268" xml:space="preserve">Illos deni-<lb/>que, qui torridam zonam inhabitãt, uocari Amphiſcios, <lb/>quòd eorum umbræ meridianæ diuerſis anni tem-<lb/>poribus nunc uerſus polum Arcticum, nunc <lb/>verſus Antarcticum porrigantur: </s> <s xml:id="echoid-s13269" xml:space="preserve">quo-<lb/>niam uidelicet. </s> <s xml:id="echoid-s13270" xml:space="preserve">Sol aliquando <lb/>vertices eorum tranſcendit, <lb/>vt perſpicuum eſt <lb/>in ſphæra ma-<lb/>teriali.</s> <s xml:id="echoid-s13271" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div690" type="section" level="1" n="239"> <head xml:id="echoid-head250" xml:space="preserve">SECVNDI CAPITIS FINIS.</head> <figure> <image file="349-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/349-01"/> </figure> <pb o="314" file="350" n="351"/> </div> <div xml:id="echoid-div691" type="section" level="1" n="240"> <head xml:id="echoid-head251" xml:space="preserve">CAPVT TERTIVM <lb/>DE ORTV, ET OCCASV SIGNORVM. <lb/>De diuerſitate dierum, & noctium, & de <lb/>diuiſione climatum.</head> <note position="left" xml:space="preserve">Ortus & oc <lb/>caſus ſide-<lb/>rum ſecun <lb/>dum Poetas <lb/>@riplex.</note> <p style="it"> <s xml:id="echoid-s13272" xml:space="preserve">SIGNORVM autem ortus, & </s> <s xml:id="echoid-s13273" xml:space="preserve">occaſus dupliciter <lb/>accipitur, quoniam quantum ad poetas, & </s> <s xml:id="echoid-s13274" xml:space="preserve">quantum <lb/>ad Aſtronomos. </s> <s xml:id="echoid-s13275" xml:space="preserve">Eſt igitur ortus & </s> <s xml:id="echoid-s13276" xml:space="preserve">occaſus ſigno@ũ, <lb/>quoad Poetas, triplex, ſcilicet Coſmicus, Chronicus, <lb/>& </s> <s xml:id="echoid-s13277" xml:space="preserve">Heliacus.</s> <s xml:id="echoid-s13278" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s13279" xml:space="preserve">COSMICVS enim ortus, ſiue mundanus eſt, <lb/> <anchor type="note" xlink:label="note-350-02a" xlink:href="note-350-02"/> quando ſignum, uel ſtella ſuper Horizontẽ ex parte orientis de die aſcen-<lb/>dit. </s> <s xml:id="echoid-s13280" xml:space="preserve">Et licet in qualibet die artiſiciali ſex ſigna ſic oriantur, tamen Anto-<lb/>nomaſtice ſignum illud dicitur Coſmice oriri, cum quo, & </s> <s xml:id="echoid-s13281" xml:space="preserve">in quo Sol ma-<lb/>ne oritur. </s> <s xml:id="echoid-s13282" xml:space="preserve">Et ſic ortus proprius, & </s> <s xml:id="echoid-s13283" xml:space="preserve">principalis, & </s> <s xml:id="echoid-s13284" xml:space="preserve">quotidianus dicitur. <lb/></s> <s xml:id="echoid-s13285" xml:space="preserve">De hoc ortu exemplum in 1. </s> <s xml:id="echoid-s13286" xml:space="preserve">Georg. </s> <s xml:id="echoid-s13287" xml:space="preserve">habetur, ubi docetur ſatio fabarum, <lb/>& </s> <s xml:id="echoid-s13288" xml:space="preserve">milij in Vere, Sole exiſtente in Tauro, ſic.</s> <s xml:id="echoid-s13289" xml:space="preserve"/> </p> <div xml:id="echoid-div691" type="float" level="2" n="1"> <note position="left" xlink:label="note-350-02" xlink:href="note-350-02a" xml:space="preserve">Ortus Coſ-<lb/>@icus q d.</note> </div> </div> <div xml:id="echoid-div693" type="section" level="1" n="241"> <head xml:id="echoid-head252" xml:space="preserve">Candidus auratis aperit cum cornibus annum <lb/>Taurus, &c.</head> <p style="it"> <s xml:id="echoid-s13290" xml:space="preserve">OCC ASVS uero Coſmicus eſt reſpectu oppoſitionis, ſcilicet quan-<lb/> <anchor type="note" xlink:label="note-350-03a" xlink:href="note-350-03"/> do Sol oritur cum aliquo ſigno, cuius ſigni ſignum oppoſitum occidit Coſ-<lb/>mice. </s> <s xml:id="echoid-s13291" xml:space="preserve">De hoc occaſu dicitur in Georg. </s> <s xml:id="echoid-s13292" xml:space="preserve">ubi docetur ſatio frumenti in fine <lb/>Autumni, Sole exiſtente in Scorpione, qui cum oriatur cum Sole, Taurus <lb/>ſigni eius oppoſitum, ubi ſunt Pleiades, occidit; </s> <s xml:id="echoid-s13293" xml:space="preserve">ſic.</s> <s xml:id="echoid-s13294" xml:space="preserve"/> </p> <div xml:id="echoid-div693" type="float" level="2" n="1"> <note position="left" xlink:label="note-350-03" xlink:href="note-350-03a" xml:space="preserve">Oce<unsure/>aſus <lb/>Coſmicus <lb/>quid.</note> </div> </div> <div xml:id="echoid-div695" type="section" level="1" n="242"> <head xml:id="echoid-head253" xml:space="preserve">Ante tibi Eoæ Atlantides abſcondantur, <lb/>Debita quam ſulcis committas ſemina, quamq́; <lb/>Inuitæ properes anni ſpem credere terræ.</head> <note position="left" xml:space="preserve">Ortus chro <lb/>nicus @ d.</note> <p style="it"> <s xml:id="echoid-s13295" xml:space="preserve">CHRONICVS ortus, ſiue temporalis eſt, quando ſignum, uel <lb/>ſtella poſt Solis occaſum ſupra Horizontẽ ex parte orientis emergit chro-<lb/>nice, ſcilicet de nocte; </s> <s xml:id="echoid-s13296" xml:space="preserve">Et dicitur temporalis, quia tempus Mathematico-<lb/>rum naſcitur cum Solis occaſu. </s> <s xml:id="echoid-s13297" xml:space="preserve">De hoc ortu habemus in Ouidio lib. </s> <s xml:id="echoid-s13298" xml:space="preserve">1. </s> <s xml:id="echoid-s13299" xml:space="preserve">de <lb/>Ponto, ubi conqueritur moram exilij ſui, dicens.</s> <s xml:id="echoid-s13300" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div696" type="section" level="1" n="243"> <head xml:id="echoid-head254" xml:space="preserve">Quatuor autumnos Pleias orta facit.</head> <p style="it"> <s xml:id="echoid-s13301" xml:space="preserve">Significat enim per quatuor Autumnos, quatuor annos transijſſe, poſtquã <lb/>mißus erat in exilium. </s> <s xml:id="echoid-s13302" xml:space="preserve">Sed Virgilius uoluit in Autumno Pleiades occi-<lb/>dere; </s> <s xml:id="echoid-s13303" xml:space="preserve">ergo contrarij uidentur. </s> <s xml:id="echoid-s13304" xml:space="preserve">Sed ratio huius eſt, quod ſecundum Vir-<lb/>gilium occidunt Coſmice, ſecundum Ouidium oriuntur Chronice, quod <lb/>bene poteſt contingere eodem die, ſed differenter tamen, quia Coſmicus <pb o="315" file="351" n="352" rhead="Ioan. de Sacro Boſco."/> occaſus eſt reſpectu temporis matutini. </s> <s xml:id="echoid-s13305" xml:space="preserve">Chronicus uero ortus reſpectu ue-<lb/>ſpertini eſt.</s> <s xml:id="echoid-s13306" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s13307" xml:space="preserve"><emph style="sc">Chronicvs</emph> occaſus eſt reſpectu oppoſitionis. </s> <s xml:id="echoid-s13308" xml:space="preserve">Vnde Lucanus <lb/> <anchor type="note" xlink:label="note-351-01a" xlink:href="note-351-01"/> lib. </s> <s xml:id="echoid-s13309" xml:space="preserve">4. </s> <s xml:id="echoid-s13310" xml:space="preserve">inquit.</s> <s xml:id="echoid-s13311" xml:space="preserve"/> </p> <div xml:id="echoid-div696" type="float" level="2" n="1"> <note position="right" xlink:label="note-351-01" xlink:href="note-351-01a" xml:space="preserve">Occaſus <lb/>chronicus <lb/>quid.</note> </div> <p> <s xml:id="echoid-s13312" xml:space="preserve">Nox tum Theſſalicas vrgebat parua ſagittas.</s> <s xml:id="echoid-s13313" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s13314" xml:space="preserve"><emph style="sc">Heliacvs</emph> ortus, ſiue Solaris eſt, quando ſignum, uel ſtella uide-<lb/> <anchor type="note" xlink:label="note-351-02a" xlink:href="note-351-02"/> ri poteſt per elongationem Solis ab illo, quod prius uideri non poterat So-<lb/>lis propinquitate. </s> <s xml:id="echoid-s13315" xml:space="preserve">Exemplum huius ponit Ouid. </s> <s xml:id="echoid-s13316" xml:space="preserve">lib. </s> <s xml:id="echoid-s13317" xml:space="preserve">2. </s> <s xml:id="echoid-s13318" xml:space="preserve">de Faſt. </s> <s xml:id="echoid-s13319" xml:space="preserve">ſic.</s> <s xml:id="echoid-s13320" xml:space="preserve"/> </p> <div xml:id="echoid-div697" type="float" level="2" n="2"> <note position="right" xlink:label="note-351-02" xlink:href="note-351-02a" xml:space="preserve">Ortus He-<lb/>liacus quid.<unsure/></note> </div> <p> <s xml:id="echoid-s13321" xml:space="preserve">Iam leuis obliqua ſubſedit Aquarius vrna.</s> <s xml:id="echoid-s13322" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s13323" xml:space="preserve"><emph style="sc">Et</emph> Virgilius in Georg. </s> <s xml:id="echoid-s13324" xml:space="preserve">lib. </s> <s xml:id="echoid-s13325" xml:space="preserve">1.</s> <s xml:id="echoid-s13326" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13327" xml:space="preserve">Gnoſiaq́; </s> <s xml:id="echoid-s13328" xml:space="preserve">ardentis decedat ſtella coronæ.</s> <s xml:id="echoid-s13329" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s13330" xml:space="preserve">Quæ iuxta Scorpionem exiſtens non uidebatur, dum Sol erat in Scor-<lb/>pione.</s> <s xml:id="echoid-s13331" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s13332" xml:space="preserve"><emph style="sc">Occasvs</emph> Heliacus eſt, quando Sol ad ſignum accedit, & </s> <s xml:id="echoid-s13333" xml:space="preserve">illud <lb/> <anchor type="note" xlink:label="note-351-03a" xlink:href="note-351-03"/> ſua præſentia, & </s> <s xml:id="echoid-s13334" xml:space="preserve">luminoſitate uideri non permittit. </s> <s xml:id="echoid-s13335" xml:space="preserve">Huius exemplum eſt <lb/>apud Virg. </s> <s xml:id="echoid-s13336" xml:space="preserve">in Georg. </s> <s xml:id="echoid-s13337" xml:space="preserve">lib. </s> <s xml:id="echoid-s13338" xml:space="preserve">1.</s> <s xml:id="echoid-s13339" xml:space="preserve"/> </p> <div xml:id="echoid-div698" type="float" level="2" n="3"> <note position="right" xlink:label="note-351-03" xlink:href="note-351-03a" xml:space="preserve">Occaſus He <lb/>liacus quid</note> </div> <p> <s xml:id="echoid-s13340" xml:space="preserve">. </s> <s xml:id="echoid-s13341" xml:space="preserve">. </s> <s xml:id="echoid-s13342" xml:space="preserve">. </s> <s xml:id="echoid-s13343" xml:space="preserve">Et aduerſo cedens Canis occidit aſtro.</s> <s xml:id="echoid-s13344" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div700" type="section" level="1" n="244"> <head xml:id="echoid-head255" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s13345" xml:space="preserve"><emph style="sc">EXplicatis</emph> in 2. </s> <s xml:id="echoid-s13346" xml:space="preserve">capit. </s> <s xml:id="echoid-s13347" xml:space="preserve">omnibus decem circulis, ex quibus <lb/> <anchor type="note" xlink:label="note-351-04a" xlink:href="note-351-04"/> ſphæra materialis componitur, & </s> <s xml:id="echoid-s13348" xml:space="preserve">illa cæleſtis componi intelligi-<lb/>tur, agit iam auctor in hoc 3. </s> <s xml:id="echoid-s13349" xml:space="preserve">cap. </s> <s xml:id="echoid-s13350" xml:space="preserve">de diuerſis apparentijs, quæ fiũt <lb/>ratione motus primi mobilis, & </s> <s xml:id="echoid-s13351" xml:space="preserve">Solis in Zodiaco. </s> <s xml:id="echoid-s13352" xml:space="preserve">Poteſt autem <lb/>hoc caput diuidi in quatuor particulas. </s> <s xml:id="echoid-s13353" xml:space="preserve">In prima agit de ortu & </s> <s xml:id="echoid-s13354" xml:space="preserve"><lb/>occaſu ſiderum: </s> <s xml:id="echoid-s13355" xml:space="preserve">In ſecunda de diebus naturalibus, & </s> <s xml:id="echoid-s13356" xml:space="preserve">artificialibus: </s> <s xml:id="echoid-s13357" xml:space="preserve">In tertia <lb/>aſſ@gnat propria quædam, quæ conueniunt hominibus ratione diuerſæ habita <lb/>tionis in terra: </s> <s xml:id="echoid-s13358" xml:space="preserve">In quarta denique diſputat de climatibus mundi.</s> <s xml:id="echoid-s13359" xml:space="preserve"/> </p> <div xml:id="echoid-div700" type="float" level="2" n="1"> <note position="right" xlink:label="note-351-04" xlink:href="note-351-04a" xml:space="preserve">Argumenti <lb/>in tertij ca-<lb/>pitis, eiuſ-<lb/>dẽq́ue diui <lb/>ſio.</note> </div> <p> <s xml:id="echoid-s13360" xml:space="preserve"><emph style="sc">Est</emph> autem ortus cuiuſlibet aſtri, eleuatio, ſeu aſcenſio eius ſupra Hori-<lb/> <anchor type="note" xlink:label="note-351-05a" xlink:href="note-351-05"/> zontem, vel certe apparitio eiuſdẽ, quod antea ob vicinitatem Solis non con-<lb/> <anchor type="note" xlink:label="note-351-06a" xlink:href="note-351-06"/> ſpiciebatur. </s> <s xml:id="echoid-s13361" xml:space="preserve">Occaſus vero eſt depreſſio, ſiue deſcẽſio aſtri infra Horizontem, <lb/>uel certe occultatio eius, ita ut amplius cerni nequeat propter Solis propin-<lb/>quitatem. </s> <s xml:id="echoid-s13362" xml:space="preserve">Itaque ortus omnis aſtrorum, occaſus ſumitur uel comparatione <lb/>Horizontis, uel comparatione Solis. </s> <s xml:id="echoid-s13363" xml:space="preserve">Hinc fit, vt apud Poetas, ſicut auctor di-<lb/>cit, triplex ſit ortus occaſusq́; </s> <s xml:id="echoid-s13364" xml:space="preserve">ſiderũ, nimirum Coſmicus, Chronicus, qui duo <lb/>penes Horizontem ſumuntur, & </s> <s xml:id="echoid-s13365" xml:space="preserve">Heliacus, qui ad Solem refertur.</s> <s xml:id="echoid-s13366" xml:space="preserve"/> </p> <div xml:id="echoid-div701" type="float" level="2" n="2"> <note position="right" xlink:label="note-351-05" xlink:href="note-351-05a" xml:space="preserve">Ortus aſtr@ <lb/>quid.</note> <note position="right" xlink:label="note-351-06" xlink:href="note-351-06a" xml:space="preserve">Occaſus a-<lb/>ſtri quid. <lb/>Penes quid <lb/>ſumatur o@ <lb/>tus, & occa <lb/>ſas ſiderũ.</note> </div> <p> <s xml:id="echoid-s13367" xml:space="preserve"><emph style="sc">Signvm</emph> illud uel aſtrum proprie Coſmice dicitur oriri, quod unà cum <lb/>Sole ſupra Horizontem matutino tempore aſcendit: </s> <s xml:id="echoid-s13368" xml:space="preserve">Improprie autem omne <lb/>aſtrum, quod in die eleuatur ſupra Horizontẽ; </s> <s xml:id="echoid-s13369" xml:space="preserve">quo pacto ſingulis diebus ſex <lb/>ſigna Zodiaci Coſmice dicuntur oriri, quamuis ob ſplendorem Solis minime <lb/>poſſint uideri. </s> <s xml:id="echoid-s13370" xml:space="preserve">Ortum Coſmicum proprie dictum inteHexit Virgil. </s> <s xml:id="echoid-s13371" xml:space="preserve">1. </s> <s xml:id="echoid-s13372" xml:space="preserve">Georg <lb/>@armine illo, quod auctor retulit, videlicet.</s> <s xml:id="echoid-s13373" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s13374" xml:space="preserve">Candidus auratis aperit cum cornibus annum <lb/>Taurus, &</s> <s xml:id="echoid-s13375" xml:space="preserve">c.</s> <s xml:id="echoid-s13376" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13377" xml:space="preserve">Voluit enim ſignificare menſem Aprilem, in quo mane vnà cum Sole Taurus <pb o="316" file="352" n="353" rhead="Comment. in III. Cap. Sphæræ"/> ſupra Horizontem emergit, cum eo tempore in Tauro Sol exiſtat.</s> <s xml:id="echoid-s13378" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13379" xml:space="preserve"><emph style="sc">Pari</emph> ratione ſignum illud, uel aſtrum proprie Coſmice dicitur occide-<lb/>re, quòd tempore matutino, Sole oriente, ſub Horizontem deſcendit; </s> <s xml:id="echoid-s13380" xml:space="preserve">Impro-<lb/>prie uerò omne aſtrum, quod in die infra Horizontem labitur. </s> <s xml:id="echoid-s13381" xml:space="preserve">Itaque orien-<lb/>te ſigno quocunque, ſeu ſtella Coſmice, neceſſe ſignum, ſtellamve per diame-<lb/>trum oppoſitam, immo vero & </s> <s xml:id="echoid-s13382" xml:space="preserve">omnes ſtellas, quæ tunc Horizontem ex parte <lb/>occidentis contingunt, Coſmice occidere. </s> <s xml:id="echoid-s13383" xml:space="preserve">De hoc occaſu Coſmico loquitur <lb/>Virgil. </s> <s xml:id="echoid-s13384" xml:space="preserve">1. </s> <s xml:id="echoid-s13385" xml:space="preserve">Georg. </s> <s xml:id="echoid-s13386" xml:space="preserve">in his carminibus.</s> <s xml:id="echoid-s13387" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s13388" xml:space="preserve">Ante tibi Eoæ Atlantides abſcondantur, <lb/>Debita quàm ſulcis committas ſemina, quamq́; <lb/></s> <s xml:id="echoid-s13389" xml:space="preserve">Inuitæ properes anni ſpem credere terræ.</s> <s xml:id="echoid-s13390" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13391" xml:space="preserve">Intelligit etenim tempus Autumni, in quo, Sole exiſtente in Scorpio, Pleia-<lb/>des in Tauro ſigno oppoſito conſtitutæ mane occidunt, hoc eſt, Coſmice.</s> <s xml:id="echoid-s13392" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13393" xml:space="preserve"><emph style="sc">Chronice</emph>, ſeu potius, ſecundum aliquos, Achronyce oriri ſignum, <lb/>vel aſtrum proptie dicitur, quod veſpertino tempore, Sole infra Horizontem <lb/>deſcendente, ex parte orientis ſupra Horizontem emergit; </s> <s xml:id="echoid-s13394" xml:space="preserve">Improprie uero <lb/>quodcunque in nocte ſupra Horizontem aſcendit: </s> <s xml:id="echoid-s13395" xml:space="preserve">quo pacto qualibet nocte <lb/>ſex ſigna dici poſſunt oriri chronice. </s> <s xml:id="echoid-s13396" xml:space="preserve">De ortu Chronico ſcribit Ouid. </s> <s xml:id="echoid-s13397" xml:space="preserve">lib. </s> <s xml:id="echoid-s13398" xml:space="preserve">1. </s> <s xml:id="echoid-s13399" xml:space="preserve">de <lb/>Ponto. </s> <s xml:id="echoid-s13400" xml:space="preserve">Elegia 9.</s> <s xml:id="echoid-s13401" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s13402" xml:space="preserve">Vt careo uobis Scythicas detruſus in oras, <lb/>Quatuor Autumnos Pleias orta facit.</s> <s xml:id="echoid-s13403" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13404" xml:space="preserve">Tempore enim Autumni, Sole videlicet exiſtente in Scorpio, oriuntur Pleia-<lb/>des veſperi ſub Solis occaſum, id eſt, Chronice.</s> <s xml:id="echoid-s13405" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13406" xml:space="preserve"><emph style="sc">Chronice</emph> occidere dicitur proprie illud aſtrum, ſi ue ſignum, quod <lb/>vnà cum Sole ſub Horizontem deſcendit; </s> <s xml:id="echoid-s13407" xml:space="preserve">Improprie autem omne ſignũ, quod <lb/>nocturno tempore infra Horizontem deprimitur; </s> <s xml:id="echoid-s13408" xml:space="preserve">qua ratione ſingulis nocti-<lb/>bus ſex ſigna Zodiaci dicuntur Chronice occidere. </s> <s xml:id="echoid-s13409" xml:space="preserve">Itaque oriente aſtro quo-<lb/>cunque, ſeu ſigno Chronice, occidet neceſſario ſignũ, ſiue aſtrum oppoſitum <lb/>Chronice. </s> <s xml:id="echoid-s13410" xml:space="preserve">Quod etiam de omnibus ſtellis, quæ tunc Horizontem ex parte oc <lb/>cidentis tangunt, ac proinde cum Sole occidunt, intelligendum eſt. </s> <s xml:id="echoid-s13411" xml:space="preserve">De occa-<lb/>ſu Chronico ſecundum auctorem lucutus eſt Lucanus lib. </s> <s xml:id="echoid-s13412" xml:space="preserve">4.</s> <s xml:id="echoid-s13413" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s13414" xml:space="preserve">-------Nam Sol Ledæa tenebat <lb/>Sidera, vicino cum lux altiſſima Cancro eſt; <lb/></s> <s xml:id="echoid-s13415" xml:space="preserve">Nox tum Theſſalicas vrgebat parua ſagittas.</s> <s xml:id="echoid-s13416" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13417" xml:space="preserve">Indicare enim uoluit tempus prope auroram, Sole exiſtente prope finem Ge-<lb/>minorum; </s> <s xml:id="echoid-s13418" xml:space="preserve">unde paulo ante ortum Solis neceſſe eſt Sagittarium, qui Geminis <lb/>opponitur, occidere improprie Chronice. </s> <s xml:id="echoid-s13419" xml:space="preserve">Sed fortaſſe Lucanus in eo loco <lb/>nullum genus occaſus intellexit, ſed ſolum ſignificare uoluit tempus illud <lb/>ante Solis ortum, quo Sagittarius occumbit. </s> <s xml:id="echoid-s13420" xml:space="preserve">At Ouid. </s> <s xml:id="echoid-s13421" xml:space="preserve">de hoc occaſu ſcribit <lb/>lib. </s> <s xml:id="echoid-s13422" xml:space="preserve">2. </s> <s xml:id="echoid-s13423" xml:space="preserve">de Faſt.</s> <s xml:id="echoid-s13424" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s13425" xml:space="preserve">Quem modo cęlatum ſtellis Delphina videbas <lb/>Is fugiet uiſus nocte ſequente tuos.</s> <s xml:id="echoid-s13426" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13427" xml:space="preserve">Loquitur enim de tertio die Februarij, ante quem poſt Solis occaſum appare-<lb/>bat Delphinus ſupra Horizontẽ, ſed tertio die unà cum Sole occidebat Chro <lb/> <anchor type="note" xlink:label="note-352-01a" xlink:href="note-352-01"/> nice, cũ exiſtat in Aquario, in quo tunc Sol commorabatur. </s> <s xml:id="echoid-s13428" xml:space="preserve">Hinc perſpicuum <lb/>eſt, vnum idemq́; </s> <s xml:id="echoid-s13429" xml:space="preserve">ſignum, in quo exiſtit Sol, mane oriri Coſmice, & </s> <s xml:id="echoid-s13430" xml:space="preserve">veſpere oc <lb/>cidere Chronice: </s> <s xml:id="echoid-s13431" xml:space="preserve">Item ſignum oppoſitum Soli ueſpere oriri Chronice; </s> <s xml:id="echoid-s13432" xml:space="preserve">& </s> <s xml:id="echoid-s13433" xml:space="preserve">ma <lb/>ne occidere Coſmice; </s> <s xml:id="echoid-s13434" xml:space="preserve">ut mirum non ſit Virgilium dixiſſe; </s> <s xml:id="echoid-s13435" xml:space="preserve">Pleiades occidere <pb o="317" file="353" n="354" rhead="Ioan. de Sacro Boſco."/> in Autumno, nempe Coſmice; </s> <s xml:id="echoid-s13436" xml:space="preserve">Ouid autem docuiſſe, eaſdem eodem tempore <lb/>oriri, nempe Chronice, quod veriſſimum eſt. </s> <s xml:id="echoid-s13437" xml:space="preserve">Vnde extant duo verſiculi.</s> <s xml:id="echoid-s13438" xml:space="preserve"/> </p> <div xml:id="echoid-div702" type="float" level="2" n="3"> <note position="left" xlink:label="note-352-01" xlink:href="note-352-01a" xml:space="preserve">Signum <lb/>Chronice <lb/>oriens occi-<lb/>dit Coſmi-<lb/>@c, & cõtra.</note> </div> <p style="it"> <s xml:id="echoid-s13439" xml:space="preserve">Coſmice deſcendit ſignum, quod Chronice ſurgit. <lb/></s> <s xml:id="echoid-s13440" xml:space="preserve">Chronice deſcendit ſignum, quod Coſmice ſurgit.</s> <s xml:id="echoid-s13441" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13442" xml:space="preserve">Hoc tamen de ſtellis extra eclipticam poſitis uerum non eſt in ſphæra obli-<lb/>qua. </s> <s xml:id="echoid-s13443" xml:space="preserve">Nulla enim talis ſtella, quæ ſimul cum Sole oritur, cum eodem occidere <lb/>poteſt, aut quæ cum eo occidit, cum codem oriri: </s> <s xml:id="echoid-s13444" xml:space="preserve">ſed ſtella, quæ borealior eſt <lb/>puncto eclipticæ, cum quo ſimul oritur, poſterius occidit, quàm punctum illud <lb/>eclipticæ: </s> <s xml:id="echoid-s13445" xml:space="preserve">cum quo vero puncto eclipticæ ſimul occidit, prius oritur, quam il-<lb/>lud punctum. </s> <s xml:id="echoid-s13446" xml:space="preserve">Contrarium intelligatur de ſtella, quæ auſtralior eſt puncto da-<lb/>to eclipticæ. </s> <s xml:id="echoid-s13447" xml:space="preserve">Ex quo fit, ſtellam borealiorem, auſtralioremve dato puncto ecli-<lb/>pticæ, ſi cum eo oriatur coſmicè, non poſſe cum eodem occidere chronicè, ſi <lb/>uero cum eo occidat chronicè, non poſſe cum eodem coſmice oriri, aut con-<lb/>tra. </s> <s xml:id="echoid-s13448" xml:space="preserve">Stellę tamen in ecliptica poſitæ in Horizonte quocunque obliquo, & </s> <s xml:id="echoid-s13449" xml:space="preserve">ſtel-<lb/>læ omnes in ſphæra recta cum eiſdem punctis eclipticę oriuntur & </s> <s xml:id="echoid-s13450" xml:space="preserve">occidunt. <lb/></s> <s xml:id="echoid-s13451" xml:space="preserve">Quocirca quæ coſmice oriuntur, occidunt chronice: </s> <s xml:id="echoid-s13452" xml:space="preserve">& </s> <s xml:id="echoid-s13453" xml:space="preserve">quæ oriuntur chroni-<lb/>cè, occidunt coſmicè, & </s> <s xml:id="echoid-s13454" xml:space="preserve">contra. </s> <s xml:id="echoid-s13455" xml:space="preserve">Vt manifeſtum eſt in ſphæra materiali, vel glo-<lb/>bo Aſtronomico.</s> <s xml:id="echoid-s13456" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13457" xml:space="preserve"><emph style="sc">Heliace</emph> dicitur oriri aſtrũ illud, quod ſeſe profert in conſpectum, cum <lb/>aatea uicini Solis radijs tectum latuerit. </s> <s xml:id="echoid-s13458" xml:space="preserve">De hoc ortu canit Ouid. </s> <s xml:id="echoid-s13459" xml:space="preserve">lib. </s> <s xml:id="echoid-s13460" xml:space="preserve">2. </s> <s xml:id="echoid-s13461" xml:space="preserve">de Faſt.</s> <s xml:id="echoid-s13462" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s13463" xml:space="preserve">Iam leuis obliqua ſubſedit Aquarius vrna; <lb/></s> <s xml:id="echoid-s13464" xml:space="preserve">Proximus æthereos excipe Piſcis equos.</s> <s xml:id="echoid-s13465" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13466" xml:space="preserve">In Februario etenim Sol exiſtens in Aquario, illum nimio ſplendore occulta <lb/>bat, ſed circa finem Februarij, ingrediente Sole Piſces, apparebat Aquarius ma <lb/>ne ante Solis exortum, atque ita Heliace oriebatur. </s> <s xml:id="echoid-s13467" xml:space="preserve">Eundem ortum Heliacum <lb/>intellexit Virg. </s> <s xml:id="echoid-s13468" xml:space="preserve">in 1. </s> <s xml:id="echoid-s13469" xml:space="preserve">Georg. </s> <s xml:id="echoid-s13470" xml:space="preserve">ita ſcribens de Gnoſia, ſtella uidelicet coronæ Se-<lb/>ptentrionalis.</s> <s xml:id="echoid-s13471" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s13472" xml:space="preserve">Ante tibi Eoæ Atlantides abſcondantur, <lb/>Gnoſiaq́; </s> <s xml:id="echoid-s13473" xml:space="preserve">ardentis decedat ſtella coronæ, <lb/>Debita quàm ſulcis committas ſemina, &</s> <s xml:id="echoid-s13474" xml:space="preserve">c.</s> <s xml:id="echoid-s13475" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13476" xml:space="preserve">Quando namq́. </s> <s xml:id="echoid-s13477" xml:space="preserve">Pleiades occidunt coſmice, nempe in Autumno, oritur corona <lb/>Septentrionalis, quæ exiſtebat olim prope finem Libræ, Heliace tempore matu <lb/>tino ante Solis ortum in Scorpio.</s> <s xml:id="echoid-s13478" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13479" xml:space="preserve"><emph style="sc">Occidere</emph> Heliace dicitur aſtrum, quod nimio ſplendore Solis offu-<lb/>ſcatur, ita ut cum antea apparuerit, iam amplius conſpici nequeat. </s> <s xml:id="echoid-s13480" xml:space="preserve">De hoc oc-<lb/>caſu loquitur Virg. </s> <s xml:id="echoid-s13481" xml:space="preserve">in vltimo horum duorum carminum.</s> <s xml:id="echoid-s13482" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s13483" xml:space="preserve">Candidus auratis aperit cum cornibus annum <lb/>Taurus, & </s> <s xml:id="echoid-s13484" xml:space="preserve">aduerſo cedens Canis occidit aſtro.</s> <s xml:id="echoid-s13485" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13486" xml:space="preserve">Nam cum olim Canis maior exiſteret in Geminis, occidebat Heliace, quando <lb/>Pleiades occidebant Coſmice, Sole nimirum exiſtente in Tauro iuxta Pleia-<lb/>des. </s> <s xml:id="echoid-s13487" xml:space="preserve">Quantum uero debeat aſtrum quodcunq; </s> <s xml:id="echoid-s13488" xml:space="preserve">præcedere Solem, aut eundem <lb/>ſubſequi, ut oriatur, uel occidat Heliace, certo deſiniri nequit, cum nec omnes <lb/>ſtellæ eiuſdem ſint magnitudinis, nec eandem habeant latitudinem ab Eclipti-<lb/>ca@ Certum autem eſt, minores ſtellas, & </s> <s xml:id="echoid-s13489" xml:space="preserve">viciniores eclipticæ tardius oriri He-<lb/>liace, & </s> <s xml:id="echoid-s13490" xml:space="preserve">citius occidere, quàm maiores, remotioresq́; </s> <s xml:id="echoid-s13491" xml:space="preserve">ab ecliptica.</s> <s xml:id="echoid-s13492" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13493" xml:space="preserve"><emph style="sc">Qvoniam</emph> autem motus Solis uelocior eſt ab occaſu in ortum, quàm <lb/>motus ſtellarũ fixarum, efficitur, ut ſtellæ fixæ, quando è radijs ſolaribus egre-<lb/>diuntur, relinquantur liberæ a Sole verſus partes cœli occidentales, oriãturq́;</s> <s xml:id="echoid-s13494" xml:space="preserve"> <pb o="318" file="354" n="355" rhead="Comment in III. Cap. Sphæræ"/> Heliace matutino tempore prope Horizontem ex parte orientis, ante ortum <lb/>Solis; </s> <s xml:id="echoid-s13495" xml:space="preserve">Tunc enim primo incipiunt apparere, cum ante ob uicinitatem Solis, <lb/> <anchor type="note" xlink:label="note-354-01a" xlink:href="note-354-01"/> qui iam ab ipſis orientem verſus receſſit, occultæ latuerint. </s> <s xml:id="echoid-s13496" xml:space="preserve">Eadem de cauſa <lb/>eædem ſtellæ occidant Heliace neceſſe eſt, veſpertino tempore prope Hori-<lb/>zontem ex parte occidentis, poſtquam Sol infra Horizontem deſcendit. </s> <s xml:id="echoid-s13497" xml:space="preserve">Nam <lb/>cum antea ſemper apparuerint poſt occaſum Solis, tunc primum ob propin-<lb/>quitatem Solis, qui ad ipſas accedit, deliteſcere incipiunt. </s> <s xml:id="echoid-s13498" xml:space="preserve">Idem prorſus di-<lb/>cendum eſt de Saturno, Ioue, ac Marte, quia tardiores habent motus pro-<lb/>prios, quàm Sol. </s> <s xml:id="echoid-s13499" xml:space="preserve">Cõtrarium autem intelligendum eſt de Luna. </s> <s xml:id="echoid-s13500" xml:space="preserve">Cum enim ve-<lb/>locius proprio motu incedat, quàm Sol, fit, vt non Sol ab ipſa recedat ſicut à <lb/>ſtellis fixis, ſed potius ipſa à Sole remoueatur verſus orientem. </s> <s xml:id="echoid-s13501" xml:space="preserve">Vnde Helia-<lb/>ce orietur veſpere ex parte occidentis poſt Solis occaſum, vt contingere vide-<lb/>mus poſt Nouilunia, quia Luna poſt Nouilunium quodlibet ſ@atim à So-<lb/>le recedit in orientem. </s> <s xml:id="echoid-s13502" xml:space="preserve">Occidet autẽ Heliace ex parte orientis matutino tem-<lb/>pore ante ortum Solis, vt cernimus ante Nouilunia, quia ſemper Soli appro-<lb/>pinquat verſus orientem. </s> <s xml:id="echoid-s13503" xml:space="preserve">Hæc eſt cauſa, cur poſt Nouilunia paulatim Lunam <lb/> <anchor type="note" xlink:label="note-354-02a" xlink:href="note-354-02"/> creſcere, & </s> <s xml:id="echoid-s13504" xml:space="preserve">ante Nouilunia eandem decreſcere conſpiciamus. </s> <s xml:id="echoid-s13505" xml:space="preserve">Deniq; </s> <s xml:id="echoid-s13506" xml:space="preserve">Venus <lb/>atq; </s> <s xml:id="echoid-s13507" xml:space="preserve">Mercurius, cum nunc Solẽ anteuertant, nunc ſubſequantur, aliquando <lb/>orientur Heliace iuxta orientem, & </s> <s xml:id="echoid-s13508" xml:space="preserve">occident iuxta occidentem; </s> <s xml:id="echoid-s13509" xml:space="preserve">aliquando ve <lb/>ro orientur Heliace iuxta occidentem, & </s> <s xml:id="echoid-s13510" xml:space="preserve">occident iuxta orientẽ. </s> <s xml:id="echoid-s13511" xml:space="preserve">Sed de his <lb/>omnibus plura dicenda ſunt in Theoricis Planetarũ. </s> <s xml:id="echoid-s13512" xml:space="preserve">Inde effectũ eſt, vt Venus <lb/>modo dicatur Lucifer, quando videlicet mane ante Solem oritur, modo He-<lb/>ſperus, quando ſcilicet poſt Solis occaſum iuxta occidentem conſpicitur.</s> <s xml:id="echoid-s13513" xml:space="preserve"/> </p> <div xml:id="echoid-div703" type="float" level="2" n="4"> <note position="left" xlink:label="note-354-01" xlink:href="note-354-01a" xml:space="preserve">In qua par <lb/>te cœli pla <lb/>netæ, & ſt<unsure/>el <lb/>læ oriãtur, <lb/>& occidant <lb/>Heliace.</note> <note position="left" xlink:label="note-354-02" xlink:href="note-354-02a" xml:space="preserve">Venus quã <lb/>do dicatur <lb/>Lucifer, & <lb/>quando He <lb/>ſperus.</note> </div> <p> <s xml:id="echoid-s13514" xml:space="preserve"><emph style="sc">Qvo</emph> vero tempore anni quæuis ſtella hac tempeſtate oriatur Coſmice, <lb/> <anchor type="note" xlink:label="note-354-03a" xlink:href="note-354-03"/> Chronice, aut Heliace, vel etiã occidat, pulchre indicat globus cæleſtis, vel <lb/>Aſtrolabium quodcunque. </s> <s xml:id="echoid-s13515" xml:space="preserve">Poſito etenim globo in propria eleuatione, ſtatua <lb/>tur ſtella quæuis in Horizonte ex parte Orientis, noteturq; </s> <s xml:id="echoid-s13516" xml:space="preserve">gradus Eclipticæ <lb/>Horizontem tangens in oriente: </s> <s xml:id="echoid-s13517" xml:space="preserve">Quando nãque Sol gradum illum Eclipticę <lb/>obtinebit, orietur dicta ſtella Coſmice: </s> <s xml:id="echoid-s13518" xml:space="preserve">quando vero Sol gradum eclipticæ op <lb/>poſitum occupabit, orietur eadem ſtella chronice. </s> <s xml:id="echoid-s13519" xml:space="preserve">Poſita item ſtella in Hori-<lb/>zonte ex parte occidentis, notetur gradus Eclipticæ Horizontem tangens in <lb/>occidente. </s> <s xml:id="echoid-s13520" xml:space="preserve">Quando enim poſſidebit Sol gradum illum Eclipticæ; </s> <s xml:id="echoid-s13521" xml:space="preserve">occidet eadẽ <lb/>ſtella Chronice: </s> <s xml:id="echoid-s13522" xml:space="preserve">quando vero in gradu eclipticæ oppoſito Sol extiterit, occi-<lb/>det ſtella eadẽ coſmice. </s> <s xml:id="echoid-s13523" xml:space="preserve">Ortus vero Heliacus, & </s> <s xml:id="echoid-s13524" xml:space="preserve">occaſus plus minus dignoſce <lb/>tur, ſi cognitum fue<unsure/>rit, in quonã gradu Eclipticæ ſtella quælibet cõſtituatur.</s> <s xml:id="echoid-s13525" xml:space="preserve"/> </p> <div xml:id="echoid-div704" type="float" level="2" n="5"> <note position="left" xlink:label="note-354-03" xlink:href="note-354-03a" xml:space="preserve">Quomodo <lb/>cognoſca-<lb/>tur, quãdo <lb/>ſtella quæ <lb/>uis oriatur <lb/>Coſmice, <lb/>Chronice, <lb/>vel Helia-<lb/>ce.</note> </div> <p> <s xml:id="echoid-s13526" xml:space="preserve"><emph style="sc">Astonomi</emph> ortum ſtellarum, & </s> <s xml:id="echoid-s13527" xml:space="preserve">occaſum diuidunt in Verum, & </s> <s xml:id="echoid-s13528" xml:space="preserve">Ap-<lb/> <anchor type="note" xlink:label="note-354-04a" xlink:href="note-354-04"/> parentem. </s> <s xml:id="echoid-s13529" xml:space="preserve">Verus ortus, & </s> <s xml:id="echoid-s13530" xml:space="preserve">occaſus eſt, quando uere ſtella ſupra Horizon-<lb/>tem aſcendit, vel infra eundem deſcendit. </s> <s xml:id="echoid-s13531" xml:space="preserve">Atque hic duplex eſt, Matutinus <lb/>videlicet, quando, Sole oriente, ſtella aliqua oritur, uel occidit; </s> <s xml:id="echoid-s13532" xml:space="preserve">quem <lb/>poetæ dicunt Coſmicum ortum, & </s> <s xml:id="echoid-s13533" xml:space="preserve">occaſum; </s> <s xml:id="echoid-s13534" xml:space="preserve">& </s> <s xml:id="echoid-s13535" xml:space="preserve">Veſpertinus, quando, So-<lb/>le occumbente, ſtella aliqua oritur uel occidit, quia Poetis dicitur ortus, <lb/>& </s> <s xml:id="echoid-s13536" xml:space="preserve">occaſus Chronieus. </s> <s xml:id="echoid-s13537" xml:space="preserve">O@tus uero, & </s> <s xml:id="echoid-s13538" xml:space="preserve">occaſus apparens eſt ille, quem poetæ uo <lb/>cant Heliacum; </s> <s xml:id="echoid-s13539" xml:space="preserve">Atque hunc quoque diſtinguunt in matutinum, & </s> <s xml:id="echoid-s13540" xml:space="preserve">ueſper-<lb/>@inum, prout ſtella liberata à radijs ſolaribus mane, uel ueſpere incipit appa-<lb/>rere, vt dictum eſt.</s> <s xml:id="echoid-s13541" xml:space="preserve"/> </p> <div xml:id="echoid-div705" type="float" level="2" n="6"> <note position="left" xlink:label="note-354-04" xlink:href="note-354-04a" xml:space="preserve">Ortus & oc <lb/>caſus verus <lb/>& apparẽs. <lb/>Item Matu <lb/>tinus, & Ve <lb/>ſpertinus <lb/>quid.</note> </div> <note position="left" xml:space="preserve">Quomodo <lb/>Pto@emæus <lb/>ortus & oc-<lb/>caſus ſtella-<lb/>rum vocet.</note> <p> <s xml:id="echoid-s13542" xml:space="preserve"><emph style="sc">Ptolemaevs</emph> Dict. </s> <s xml:id="echoid-s13543" xml:space="preserve">8. </s> <s xml:id="echoid-s13544" xml:space="preserve">cap. </s> <s xml:id="echoid-s13545" xml:space="preserve">4. </s> <s xml:id="echoid-s13546" xml:space="preserve">vocat ortus ſtellarum, aſpectus earum <lb/>ad Solem, recitatque nouem Differẽtias, quarum quælibet adhuc multiplex <lb/>eſt; </s> <s xml:id="echoid-s13547" xml:space="preserve">ita vt in uniuerſum ſint aſpectus uigintquatuor. </s> <s xml:id="echoid-s13548" xml:space="preserve">Sed de hac re lege Ptole- <pb o="319" file="355" n="356" rhead="Ioan. de Sacro Boſco."/> mæum loco citato, & </s> <s xml:id="echoid-s13549" xml:space="preserve">Ioan. </s> <s xml:id="echoid-s13550" xml:space="preserve">Regiom. </s> <s xml:id="echoid-s13551" xml:space="preserve">in Epit. </s> <s xml:id="echoid-s13552" xml:space="preserve">lib. </s> <s xml:id="echoid-s13553" xml:space="preserve">8. </s> <s xml:id="echoid-s13554" xml:space="preserve">cap. </s> <s xml:id="echoid-s13555" xml:space="preserve">5. </s> <s xml:id="echoid-s13556" xml:space="preserve">Longum enim foret <lb/>omnes aſpectus hoc loco recenſere.</s> <s xml:id="echoid-s13557" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">Ad quid <lb/>cõducat or-<lb/>tus & occa-<lb/>ſus. Poet@-<lb/>cus.</note> <p> <s xml:id="echoid-s13558" xml:space="preserve"><emph style="sc">Porro</emph> cognitio ortus, & </s> <s xml:id="echoid-s13559" xml:space="preserve">occaſus Poetici plurimum conducit ad vete-<lb/>rum tum Poetarum, tum Hiſtoricorum uolumina intelligenda. </s> <s xml:id="echoid-s13560" xml:space="preserve">Sepiſſime <lb/>enim tempus aliquod certum exprimere conantur per aliquem ortum ſtellæ <lb/>cuiuſpiam, ut ex adductis exemplis perſpicuum eſſe poteſt.</s> <s xml:id="echoid-s13561" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div707" type="section" level="1" n="245"> <head xml:id="echoid-head256" style="it" xml:space="preserve">DE ORTV, ET OCCASV SIGNORVM <lb/>ſecundum Aſtrologos, ſeu de aſcenſionibus, & deſcenſioni-<lb/>bus ſignorum & rectis & obliquis.</head> <p style="it"> <s xml:id="echoid-s13562" xml:space="preserve"><emph style="sc">Seqvitvr</emph> de ortu & </s> <s xml:id="echoid-s13563" xml:space="preserve">occaſu ſignorum, prout ſumunt Aſtro-<lb/>nomi, & </s> <s xml:id="echoid-s13564" xml:space="preserve">prius in ſphęra recta.</s> <s xml:id="echoid-s13565" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div708" type="section" level="1" n="246"> <head xml:id="echoid-head257" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s13566" xml:space="preserve"><emph style="sc">Postqvam</emph> explicauit auctor ortum, & </s> <s xml:id="echoid-s13567" xml:space="preserve">occaſum ſiderum iuxta Poe-<lb/>tas, agit iam de ortu, & </s> <s xml:id="echoid-s13568" xml:space="preserve">occaſu ſignorum ſecundum Aſtronomos, quem or-<lb/>tum, & </s> <s xml:id="echoid-s13569" xml:space="preserve">occaſum Aſtronomicũ dicere ſolent aſcenſiones, deſcenſionesq; </s> <s xml:id="echoid-s13570" xml:space="preserve">ſigno-<lb/>rum, habetq́ue tractatio hæc de aſcenſionibus, deſcenſionibusq́ue ſignorum <lb/>plurimas, & </s> <s xml:id="echoid-s13571" xml:space="preserve">inſignes utilitates. </s> <s xml:id="echoid-s13572" xml:space="preserve">Nam maxima pars Doctrinæ primi mobilis <lb/>ex his depèndere uidetur. </s> <s xml:id="echoid-s13573" xml:space="preserve">Tria autem explicat auctor hac in parte; </s> <s xml:id="echoid-s13574" xml:space="preserve">Primum, <lb/>quid ſit ortus, & </s> <s xml:id="echoid-s13575" xml:space="preserve">occaſus ſecundum Aſtronomos, & </s> <s xml:id="echoid-s13576" xml:space="preserve">quotuplex; </s> <s xml:id="echoid-s13577" xml:space="preserve">Deinde quo-<lb/>modo ſigna oriantur, & </s> <s xml:id="echoid-s13578" xml:space="preserve">occidant in ſphæra recta; </s> <s xml:id="echoid-s13579" xml:space="preserve">Tertio demum, quo pacto <lb/>ſeſe habeant ſigna, quantum ad ortum, & </s> <s xml:id="echoid-s13580" xml:space="preserve">occaſum Aſtronomicum in ſphæ-<lb/> <anchor type="note" xlink:label="note-355-02a" xlink:href="note-355-02"/> ra quacunq; </s> <s xml:id="echoid-s13581" xml:space="preserve">obiqua. </s> <s xml:id="echoid-s13582" xml:space="preserve">Sed ante omnia explicandum eſt breuiter diſcrimen in-<lb/>ter ortum & </s> <s xml:id="echoid-s13583" xml:space="preserve">occaſum ſignorum iuxta poetas, & </s> <s xml:id="echoid-s13584" xml:space="preserve">Aſtronomos; </s> <s xml:id="echoid-s13585" xml:space="preserve">Illud autem hu <lb/>iuſmodi eſt. </s> <s xml:id="echoid-s13586" xml:space="preserve">Poetę in ortu, & </s> <s xml:id="echoid-s13587" xml:space="preserve">occaſu ſignorum obſeruant qualitatem temporis, <lb/>an uidelicet ſignũ aliquod oriatur in Vere, an in Aeſtate, an uero in Autun-<lb/>no, uel in Hyeme. </s> <s xml:id="echoid-s13588" xml:space="preserve">Item an matutino tempore, an uero ueſpertino: </s> <s xml:id="echoid-s13589" xml:space="preserve">Aſtronomi <lb/>uero quantitatem temporis conſiderant in ortu, & </s> <s xml:id="echoid-s13590" xml:space="preserve">occaſu ſignorum, quanto <lb/>nimirum tẽpore hoc ſignum, uel illud oriatur, occidatve in hac uel illa obli-<lb/>quitate ſphæræ, ſiue hoc fiat in Vere, uel in Aeſtate, &</s> <s xml:id="echoid-s13591" xml:space="preserve">c. </s> <s xml:id="echoid-s13592" xml:space="preserve">& </s> <s xml:id="echoid-s13593" xml:space="preserve">ſiue tempore diur-<lb/>no, ſiue nocturno. </s> <s xml:id="echoid-s13594" xml:space="preserve">Vnde apud Aſtronomos non diuiditur ortus & </s> <s xml:id="echoid-s13595" xml:space="preserve">occaſus in <lb/>Coſmicum, ſeu Matutinum, & </s> <s xml:id="echoid-s13596" xml:space="preserve">in Chronicum, ſeu Temporalem, ut Poetæ fa-<lb/>ciunt, ſed in rectum, & </s> <s xml:id="echoid-s13597" xml:space="preserve">obliquum, ut mox dicetur.</s> <s xml:id="echoid-s13598" xml:space="preserve"/> </p> <div xml:id="echoid-div708" type="float" level="2" n="1"> <note position="right" xlink:label="note-355-02" xlink:href="note-355-02a" xml:space="preserve">Diſcrimen@ <lb/>inter ortũ <lb/>& occaſum <lb/>quoad Poe-<lb/>tas, & quo-<lb/>ad Aſtrono <lb/>mos.</note> </div> <p style="it"> <s xml:id="echoid-s13599" xml:space="preserve"><emph style="sc">Sciendvm</emph> eſt, quòd tam in ſphęrarecta, quàm obliqua aſcendit <lb/> <anchor type="note" xlink:label="note-355-03a" xlink:href="note-355-03"/> A@quinoctialis circulus ſemper uniformiter, ſcilicet in temporibus ęqua-<lb/>libus ęquales arcus aſcendunt. </s> <s xml:id="echoid-s13600" xml:space="preserve">Motus enim cęli uniformis eſt; </s> <s xml:id="echoid-s13601" xml:space="preserve">Et angu-<lb/>lus, quem facit Aequinoctialis circulus cum Horizonte, non diuerſifica-<lb/>tur in aliquibus horis.</s> <s xml:id="echoid-s13602" xml:space="preserve"/> </p> <div xml:id="echoid-div709" type="float" level="2" n="2"> <note position="right" xlink:label="note-355-03" xlink:href="note-355-03a" xml:space="preserve">Aequator <lb/>vniformi-<lb/>ter aſcẽdit <lb/>ſupra quẽ-<lb/>cunq; Hori-<lb/>zontem.</note> </div> </div> <div xml:id="echoid-div711" type="section" level="1" n="247"> <head xml:id="echoid-head258" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s13603" xml:space="preserve"><emph style="sc">Anteqvam</emph> declaret<unsure/>, quid ſit ortus uel occaſus iuxta Aſtronomos, & </s> <s xml:id="echoid-s13604" xml:space="preserve"><lb/>quotuplex, demonſtrat prius duas concluſiones, quarum prior eſt. </s> <s xml:id="echoid-s13605" xml:space="preserve">Aequino-<lb/>ctialis circulus uniformiter ſupra Horizontem tam rectũ, quàm obliquũ quẽ <lb/>cunque eleuatur ſecundum omnes ſui partes, ita ut in temporibus æqualibus <lb/>æquales arcus Aequatoris ſupra Horizontem aſcendant. </s> <s xml:id="echoid-s13606" xml:space="preserve">Hanc concluſionem <pb o="320" file="356" n="357" rhead="Comment in III. Cap. Sphæræ"/> probat dupliciter: </s> <s xml:id="echoid-s13607" xml:space="preserve">Primũ, quia motus cęli diurnus uniformis eſt in omni Ho-<lb/>rizonte, & </s> <s xml:id="echoid-s13608" xml:space="preserve">regularis: </s> <s xml:id="echoid-s13609" xml:space="preserve">Non enim aliquando citeriori motu fertur, & </s> <s xml:id="echoid-s13610" xml:space="preserve">aliquãdo <lb/>remiſſiori. </s> <s xml:id="echoid-s13611" xml:space="preserve">Cum igitur Aequator ſit menſura, ac regula primi motus, mouea-<lb/>turq; </s> <s xml:id="echoid-s13612" xml:space="preserve">circa eoſdem polos, circa quos totum cęlum circumuertitur, nempe cir-<lb/>ca polos mũdi, neceſſe eſt, ut in qualibet ſphæra uniformiter ſupra Horizon-<lb/>tem emergat ſecundũ omnes ſui partes. </s> <s xml:id="echoid-s13613" xml:space="preserve">Deinde quia Aequator perpetuo eoſ-<lb/>dem angulos cum Horizõte efficit, cum recto quidem rectos, & </s> <s xml:id="echoid-s13614" xml:space="preserve">cum obliquo <lb/>obliquos: </s> <s xml:id="echoid-s13615" xml:space="preserve">fit, ut uniformiter ſecundum omnes ſui partes eleuetur ſupra Hori-<lb/>zontem quemcunque. </s> <s xml:id="echoid-s13616" xml:space="preserve">Teſtantur idem phænomena clariſſima Aſtronomorũ. <lb/></s> <s xml:id="echoid-s13617" xml:space="preserve">Deprehenſum eſt enim in quacunque ſphęra, ſingulis horis gradus quindecim <lb/>Aequatoris ſupra Horizontem aſcendere, totidemq́. </s> <s xml:id="echoid-s13618" xml:space="preserve">infra eundem deſcende-<lb/>re. </s> <s xml:id="echoid-s13619" xml:space="preserve">Spatio vero quatuor Minutorũ unius horæ eleuari, & </s> <s xml:id="echoid-s13620" xml:space="preserve">deprimi vnũ gradum <lb/>Aequatoris, &</s> <s xml:id="echoid-s13621" xml:space="preserve">c. </s> <s xml:id="echoid-s13622" xml:space="preserve">Quod minime fieret, ſi non regulariter, & </s> <s xml:id="echoid-s13623" xml:space="preserve">uniformiter aſcen-<lb/>deret<unsure/> Aequator ſupra Horizontem.</s> <s xml:id="echoid-s13624" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s13625" xml:space="preserve">PARTES uero Zodiaci non de neceſſitate habent æquales aſcen-<lb/>ſiones in utraque ſphæra; </s> <s xml:id="echoid-s13626" xml:space="preserve">Quia quanto aliqua Zodiaci pars rectius oritur, <lb/>tanto plus temporis ponitur in ſuo ortu. </s> <s xml:id="echoid-s13627" xml:space="preserve">Huius ſignum eſt, quia ſex ſigna <lb/>oriuntur in longa, uel in breui die artificiali, ſimiliter & </s> <s xml:id="echoid-s13628" xml:space="preserve">in nocte.</s> <s xml:id="echoid-s13629" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div712" type="section" level="1" n="248"> <head xml:id="echoid-head259" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s13630" xml:space="preserve"><emph style="sc">Posterior</emph> concluſio eſt, Zodiacus tam in ſphæra recta, quàm in obli-<lb/>qua, non aſcẽdit ſecundum omnes ſui partes ſupra Horizontem uniformiter. <lb/></s> <s xml:id="echoid-s13631" xml:space="preserve">Quam quidem hac ratione uidetur confirmare. </s> <s xml:id="echoid-s13632" xml:space="preserve">Cum Zodiacus circa alienos <lb/>polos feratur motu diurno, à quibus alibi longius, alibi minus abeſt, fit, ut ali <lb/>quæ eius partes cũ quolibet Horizonte eſſiciant angulos obliquiores, aliquæ <lb/>minus obliquos. </s> <s xml:id="echoid-s13633" xml:space="preserve">Quocirca pars illa, quæ rectiores cũ Horizonte angulos con-<lb/>ſ<unsure/>tituit, & </s> <s xml:id="echoid-s13634" xml:space="preserve">idcirco rectius oritur, tardiori motu ſupra Horizontem eleuabitur. </s> <s xml:id="echoid-s13635" xml:space="preserve"><lb/>atq; </s> <s xml:id="echoid-s13636" xml:space="preserve">plus tẽporis in ſuo ortu requiret, quã quę minus rectos angulos cũ Hori <lb/>zonte efficit, ut experientia docet in ſphæra quacunq; </s> <s xml:id="echoid-s13637" xml:space="preserve">materiali, quoniã quo <lb/>aliquis arcus rectius exoritur, eo etiã magis ſucceſſiue partes eius aſcendunt. </s> <s xml:id="echoid-s13638" xml:space="preserve"><lb/>Eandẽ concluſionẽ comprobat experimento manifeſto: </s> <s xml:id="echoid-s13639" xml:space="preserve">quia videlicet quali-<lb/>bet die, ſiue nocte artificiali tã longiſſima, quàm breuiſſima, ſex ſigna præciſe <lb/>Zodiaci ſupra Horizontẽ aſcendunt, & </s> <s xml:id="echoid-s13640" xml:space="preserve">infra eundẽ deſcendunt, ita ut quoli-<lb/>bet die medietas Zodiaci exoriatur. </s> <s xml:id="echoid-s13641" xml:space="preserve">Cum enim Zodiacus, & </s> <s xml:id="echoid-s13642" xml:space="preserve">Horizon quicun <lb/>que ſeſe mutuo bifariam ſecent, quò<unsure/>d ſint circuli ſphæræ maximi, fit, ut ea me <lb/>dietas Zodiaci, quæ intercipitur inter ſolem poſitum in oriente, & </s> <s xml:id="echoid-s13643" xml:space="preserve">punctũ op-<lb/>poſitum, procedendo per mediã noctẽ in die exoriatur, ut perſpicue in inſtru-<lb/>mentis apparet. </s> <s xml:id="echoid-s13644" xml:space="preserve">Quapropter Zodiacus uniformiter non orietur ſupra Hori-<lb/>zontem ſecundum omnes ſui partes, quandoquidẽ temporibus inæqualibus, <lb/>nempe diebus & </s> <s xml:id="echoid-s13645" xml:space="preserve">noctibus inæqualibus, ęquales ſemper arcusaſcendunt, nimi <lb/>rum medietates Zodiaci. </s> <s xml:id="echoid-s13646" xml:space="preserve">Quod ſi quælibet medietas Zodiaci, ſecundum om-<lb/>nes ſui partes uniformiter aſcenderet, eſſent omnes dies, ac noctes inter ſe <lb/>æquales, quod eſt contra experientiam. </s> <s xml:id="echoid-s13647" xml:space="preserve">Idem de reliquis partibus ſemicirculo <lb/>minoribus probari poteſt ex doctrina ſphæricorum triangulorum.</s> <s xml:id="echoid-s13648" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s13649" xml:space="preserve">Notandum igitur, quòd ortus, uel occaſus alicuius ſigni, nihil aliud <pb o="321" file="357" n="358" rhead="Ioan. de Sacro Boſco."/> eſt, quam illam partem Aequinoctialis oriri, quæ oritur cum ilio ſigno <lb/> <anchor type="note" xlink:label="note-357-01a" xlink:href="note-357-01"/> oriente, id eſt, aſcendente ſupra Horizontem: </s> <s xml:id="echoid-s13650" xml:space="preserve">Vel illam partem Aequi-<lb/>noctialis occidere, quæ occidit cum illo ſigno occidente, id eſt, tendente <lb/>ad occaſum ſub Horizontem.</s> <s xml:id="echoid-s13651" xml:space="preserve"/> </p> <div xml:id="echoid-div712" type="float" level="2" n="1"> <note position="right" xlink:label="note-357-01" xlink:href="note-357-01a" xml:space="preserve">Ortus, & oe-<lb/>caſus ſecu@ <lb/>dum Aſtro <lb/>nomos @d.</note> </div> </div> <div xml:id="echoid-div714" type="section" level="1" n="249"> <head xml:id="echoid-head260" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s13652" xml:space="preserve"><emph style="sc">Exponit</emph> iam, quid ſit ortus, & </s> <s xml:id="echoid-s13653" xml:space="preserve">occaſus cuiuſq; </s> <s xml:id="echoid-s13654" xml:space="preserve">ſigni, ſiue arcus Zodiaci <lb/>ſecundum Aſtronomos, dicens, oriri aliquod ſignum non eſſe aliud, quàm ar-<lb/>cum illum Aequatoris, qui ſimul cum illo ſigno ſupra Horizontem aſcendit, <lb/>oriri: </s> <s xml:id="echoid-s13655" xml:space="preserve">Occidere uero ſignum aliquod non eſſe aliud, quàm occidere illum ar-<lb/>cum Aequatoris, qui vnà cum illo ſigno infra Horizontem deſcendit. </s> <s xml:id="echoid-s13656" xml:space="preserve">Vnde <lb/>ortus ſigni, uel cuiuſque arcus Zodiaci definitur eſſe arcus Aequatoris, qui cũ <lb/>eo ſi gno, uelarcu cooritur. </s> <s xml:id="echoid-s13657" xml:space="preserve">Occaſus vero ſigni, uel cuiuſ<unsure/>libet arcus Zodiaci <lb/>dicitur arcus Aequatoris, qui cum ſigno, uel arcu infra Horizontem demergi <lb/>tur. </s> <s xml:id="echoid-s13658" xml:space="preserve">Vt quia Romæ v.</s> <s xml:id="echoid-s13659" xml:space="preserve">g. </s> <s xml:id="echoid-s13660" xml:space="preserve">cum toto arcu Arietis cooriuntur grad. </s> <s xml:id="echoid-s13661" xml:space="preserve">17. </s> <s xml:id="echoid-s13662" xml:space="preserve">Min. </s> <s xml:id="echoid-s13663" xml:space="preserve">21. <lb/></s> <s xml:id="echoid-s13664" xml:space="preserve">Aequatoris, ideo arcus Aequatoris continens grad. </s> <s xml:id="echoid-s13665" xml:space="preserve">17. </s> <s xml:id="echoid-s13666" xml:space="preserve">min. </s> <s xml:id="echoid-s13667" xml:space="preserve">21. </s> <s xml:id="echoid-s13668" xml:space="preserve">dicitur ortus <lb/>Arietis Romę. </s> <s xml:id="echoid-s13669" xml:space="preserve">Pari ratione, quia Romæ cum ſigno Arietis deſcendunt infra <lb/>Horizontem grad. </s> <s xml:id="echoid-s13670" xml:space="preserve">38. </s> <s xml:id="echoid-s13671" xml:space="preserve">min. </s> <s xml:id="echoid-s13672" xml:space="preserve">27. </s> <s xml:id="echoid-s13673" xml:space="preserve">propterea arcus Aequatoris complectens grad. </s> <s xml:id="echoid-s13674" xml:space="preserve"><lb/>38. </s> <s xml:id="echoid-s13675" xml:space="preserve">min. </s> <s xml:id="echoid-s13676" xml:space="preserve">27. </s> <s xml:id="echoid-s13677" xml:space="preserve">dicetur occaſus ſigni Arietis, & </s> <s xml:id="echoid-s13678" xml:space="preserve">ſic de cæteris. </s> <s xml:id="echoid-s13679" xml:space="preserve">Hinc factum eſt, ut <lb/>ortus ſigni, uel arcus Zodiaci apud Aſtronomos dicatur Aſcenſio; </s> <s xml:id="echoid-s13680" xml:space="preserve">occaſus ve-<lb/>ro, Decenſio: </s> <s xml:id="echoid-s13681" xml:space="preserve">quia nimirum conſiderant in ortu, uel occaſu cuiuſuis arcus por <lb/>tionem Aequatoris, quæ ſimul aſcendit, uel deſcendit cum illo arcu.</s> <s xml:id="echoid-s13682" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13683" xml:space="preserve"><emph style="sc">Definivnt</emph> autem Aſtronomi ortum, & </s> <s xml:id="echoid-s13684" xml:space="preserve">occaſum cuiuſcũque arcus, <lb/> <anchor type="note" xlink:label="note-357-02a" xlink:href="note-357-02"/> uel ſigni per arcum Aequatoris coaſcendentem; </s> <s xml:id="echoid-s13685" xml:space="preserve">vel condeſcendentem: </s> <s xml:id="echoid-s13686" xml:space="preserve">quo-<lb/>niam cum animaduertiſſent, Zodiacum inæqualiter eleuari ſupra Horizon-<lb/>tem, & </s> <s xml:id="echoid-s13687" xml:space="preserve">ſub eundem deſcendere motu primi mobilis, quippe cum non poſſi-<lb/>deat eoſdem cum primo mobili polos: </s> <s xml:id="echoid-s13688" xml:space="preserve">Aequatorem uero ſecundũ omnes ſui <lb/>partes uniformiter oriri, & </s> <s xml:id="echoid-s13689" xml:space="preserve">occidere, propterea quod eoſdem polos obr<unsure/>inet <lb/>cum primo mobili, ceu in prædictis duabus concluſionibus fuit oſtẽſum: </s> <s xml:id="echoid-s13690" xml:space="preserve">opor <lb/>tuit eos per aliquod uniforme, ac regulare cognoſcere tempus, quod quilibet <lb/>arcus Zodiaci conſumit in ortu ſuo, & </s> <s xml:id="echoid-s13691" xml:space="preserve">occaſu: </s> <s xml:id="echoid-s13692" xml:space="preserve">quod quidem commodiſſime <lb/>factum eſt beneſicio Aequinoctialis circuli. </s> <s xml:id="echoid-s13693" xml:space="preserve">Cum enim ſingulis horis eleuen-<lb/>tur grad. </s> <s xml:id="echoid-s13694" xml:space="preserve">15. </s> <s xml:id="echoid-s13695" xml:space="preserve">Aequatoris in quocunque Horizonte, ſi cum aliquo arcu Zodiaci <lb/>eleuantur v. </s> <s xml:id="echoid-s13696" xml:space="preserve">g. </s> <s xml:id="echoid-s13697" xml:space="preserve">45. </s> <s xml:id="echoid-s13698" xml:space="preserve">grad. </s> <s xml:id="echoid-s13699" xml:space="preserve">Aequatoris ſupra aliquem Horizontem, certiſſime col <lb/>ligitur, talem at cum tribus integris horis totum exoriri, &</s> <s xml:id="echoid-s13700" xml:space="preserve">c.</s> <s xml:id="echoid-s13701" xml:space="preserve"/> </p> <div xml:id="echoid-div714" type="float" level="2" n="1"> <note position="right" xlink:label="note-357-02" xlink:href="note-357-02a" xml:space="preserve">Cur Aſtro-<lb/>nomi ortũ <lb/>& occaſum <lb/>definiant @ <lb/>Aequatorẽ.</note> </div> <p> <s xml:id="echoid-s13702" xml:space="preserve"><emph style="sc">Non solvm</emph> autem aſcenſiones, deſcenſionesq́ue arcum Zodiaci per <lb/>Aequatoris arcus fimul aſcendentes, deſcendentesve definiuntur: </s> <s xml:id="echoid-s13703" xml:space="preserve">Verum <lb/>etiam aſcenſio, & </s> <s xml:id="echoid-s13704" xml:space="preserve">deſcenſio cuiuſlibet puncti Eclipticæ, nec non ſtellæ cu-<lb/>iuſcunque. </s> <s xml:id="echoid-s13705" xml:space="preserve">Nam Aſcenſio ſtellæ cuiuſuis, vel etiam puncti Eclipticæ, eſt <lb/> <anchor type="note" xlink:label="note-357-03a" xlink:href="note-357-03"/> arcus Aequatoris a ſectione Verna, hoc eſt, a principio ♈, ſecundum ſigno-<lb/>rum ordinem uſque ad Horizontem, dum ſtella oritur, computatus. </s> <s xml:id="echoid-s13706" xml:space="preserve">Vt quia <lb/>Romæ poſito gradu tertio ♌, in oriẽte, arcus Aequatoris dictus comprehen-<lb/>dit grad. </s> <s xml:id="echoid-s13707" xml:space="preserve">106. </s> <s xml:id="echoid-s13708" xml:space="preserve">min. </s> <s xml:id="echoid-s13709" xml:space="preserve">40. </s> <s xml:id="echoid-s13710" xml:space="preserve">propterea dictus arcus Aequatoris dicitur aſcenſio ter-<lb/>tij gradus ♌, quia ſimul cum hoc gradu aſcendit. </s> <s xml:id="echoid-s13711" xml:space="preserve">Deſcenſio uero ſtellæ cu <lb/>iuſlibet, uel puncti Eclipticæ, eſt arcus Aequatoris a ſectione Verna, id eſt, a <lb/>principio ♈, ſecundum ſignorum ſeriem ad Horizontem uſque, dum ſtella <lb/>occidit, numeratus. </s> <s xml:id="echoid-s13712" xml:space="preserve">Vt quia Romæ collocato tertio gradu ♌, in occidente, <pb o="322" file="358" n="359" rhead="Comment. in III. Cap. Sphæræ"/> arcus prædictus Aequatoris continet grad. </s> <s xml:id="echoid-s13713" xml:space="preserve">143. </s> <s xml:id="echoid-s13714" xml:space="preserve">min. </s> <s xml:id="echoid-s13715" xml:space="preserve">57. </s> <s xml:id="echoid-s13716" xml:space="preserve">ideo præfatus arcus <lb/>vocatur deſcenſio tertij gradus ♌, quia unà cum eo deſcẽdit, & </s> <s xml:id="echoid-s13717" xml:space="preserve">ſic de cęteris. <lb/></s> <s xml:id="echoid-s13718" xml:space="preserve">Itaq; </s> <s xml:id="echoid-s13719" xml:space="preserve">aſcenſio, ſiue deſcenſio cuiuſlibet puncti Eclipticæ, uel etiã ſtellæ cuiuſ-<lb/>uis, eadẽ eſt, quæ aſcenſio, uel deſcenſio arcus Eclipticæ, qui ab initio ♈, cõpu <lb/>tatur ſecundum ſignorũ ſucceſſionẽ uſq; </s> <s xml:id="echoid-s13720" xml:space="preserve">ad Horizonté, poſita ſtella, uel gra-<lb/>du Eclipticæ in Horizonte præciſe, ex parte quidem orientis ſi de aſcenſione <lb/>ſermo habeatur, ex parte vero occidentis, ſi deſcenſionis habeatur ratio.</s> <s xml:id="echoid-s13721" xml:space="preserve"/> </p> <div xml:id="echoid-div715" type="float" level="2" n="2"> <note position="right" xlink:label="note-357-03" xlink:href="note-357-03a" xml:space="preserve">Aſcenſio & <lb/>Deſcenſio <lb/>ſtellæ cuius <lb/>uis, aut etiã <lb/>puncti cu-<lb/>iuſlibet Ecl@ <lb/>pticę quid.</note> </div> <p style="it"> <s xml:id="echoid-s13722" xml:space="preserve">SIGNVM autem recte oriri dicitur, cum quo maior pars Aequi-<lb/> <anchor type="note" xlink:label="note-358-01a" xlink:href="note-358-01"/> noctialis oritur: </s> <s xml:id="echoid-s13723" xml:space="preserve">oblique uero, cum quo minor. </s> <s xml:id="echoid-s13724" xml:space="preserve">Similiter etiam intelligen <lb/>dum eſt de occaſu.</s> <s xml:id="echoid-s13725" xml:space="preserve"/> </p> <div xml:id="echoid-div716" type="float" level="2" n="3"> <note position="left" xlink:label="note-358-01" xlink:href="note-358-01a" xml:space="preserve">Signum re-<lb/>cte, uel obli <lb/>que oriri, <lb/>aut occide-<lb/>I<unsure/>e quid.</note> </div> </div> <div xml:id="echoid-div718" type="section" level="1" n="250"> <head xml:id="echoid-head261" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s13726" xml:space="preserve"><emph style="sc">Qvoniam</emph> dictum eſt, Aequatorem ſecundum omnes ſui partes unifor <lb/>miter ſupra Horizontem eleuari, non autẽ Zodiacum, fit, ut aliquando cum <lb/>uno arcu Eclipticæ, ſeu Zodiaci maior arcus Aequatoris aſcendat, aliquando <lb/>minor docet iam ſignum illud: </s> <s xml:id="echoid-s13727" xml:space="preserve">ſiue arcum Eclipticæ, cum quo maior arcus <lb/>Aequatoris cooritur, dici oriri recte: </s> <s xml:id="echoid-s13728" xml:space="preserve">cum quo uero minor arcus Aequatoris <lb/>coaſcendit, oriri oblique. </s> <s xml:id="echoid-s13729" xml:space="preserve">Pari ratione ſignum, uel arcum Eclipticæ, cum quo <lb/>maior arcus Aequatoris ſub Horizontem tendit, occidere recte: </s> <s xml:id="echoid-s13730" xml:space="preserve">cum quo ue-<lb/>ro minor, oblique.</s> <s xml:id="echoid-s13731" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13732" xml:space="preserve"><emph style="sc">Exemplvm</emph>. </s> <s xml:id="echoid-s13733" xml:space="preserve">Romæ cum arcu Libræ, qui comprehendit grad. </s> <s xml:id="echoid-s13734" xml:space="preserve">30. </s> <s xml:id="echoid-s13735" xml:space="preserve">a-<lb/>ſcendit arcus Aequatoris continens grad. </s> <s xml:id="echoid-s13736" xml:space="preserve">38. </s> <s xml:id="echoid-s13737" xml:space="preserve">Min. </s> <s xml:id="echoid-s13738" xml:space="preserve">27. </s> <s xml:id="echoid-s13739" xml:space="preserve">Quare ſignum ♎, dice-<lb/>tur oriri recte: </s> <s xml:id="echoid-s13740" xml:space="preserve">At cum arcu Arietis coaſcendunt grad. </s> <s xml:id="echoid-s13741" xml:space="preserve">17. </s> <s xml:id="echoid-s13742" xml:space="preserve">min. </s> <s xml:id="echoid-s13743" xml:space="preserve">21. </s> <s xml:id="echoid-s13744" xml:space="preserve">Aequato-<lb/>ris, idcirco dicetur ſignum ♈, oriri oblique. </s> <s xml:id="echoid-s13745" xml:space="preserve">Similiter quia cum ſigno ♈, de-<lb/>ſcendunt grad. </s> <s xml:id="echoid-s13746" xml:space="preserve">38. </s> <s xml:id="echoid-s13747" xml:space="preserve">min. </s> <s xml:id="echoid-s13748" xml:space="preserve">27. </s> <s xml:id="echoid-s13749" xml:space="preserve">dicetur Aries occidere recte: </s> <s xml:id="echoid-s13750" xml:space="preserve">At Libra dicetur occi-<lb/>dere oblique, quia deſcendunt tantum grad. </s> <s xml:id="echoid-s13751" xml:space="preserve">17. </s> <s xml:id="echoid-s13752" xml:space="preserve">min. </s> <s xml:id="echoid-s13753" xml:space="preserve">21. </s> <s xml:id="echoid-s13754" xml:space="preserve">Aequatoris cum ea <lb/>infra Horizontem, &</s> <s xml:id="echoid-s13755" xml:space="preserve">c.</s> <s xml:id="echoid-s13756" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13757" xml:space="preserve"><emph style="sc">Dicitvr</emph> prior ortus, & </s> <s xml:id="echoid-s13758" xml:space="preserve">occaſus, quando nimirum plures gradus Aequa-<lb/> <anchor type="note" xlink:label="note-358-02a" xlink:href="note-358-02"/> toris cooriuntur, uel ſimul occidunt, rectus, quia tunc rectiores angulos efficit <lb/>arcus ille Zodiaci exoriens, uel deſcendens, cum Horizonte: </s> <s xml:id="echoid-s13759" xml:space="preserve">Poſterior autem <lb/>ortus, & </s> <s xml:id="echoid-s13760" xml:space="preserve">occaſus, quando ſcilicet pauciores gradus Aequatoris aſcendunt ſi-<lb/>mul, uel deſcendunt, uocatur obliquus, quoniam arcus ille Zodiaci emergẽs, <lb/>uel occumbens obliquiores angulos cum Horizonte conſtituit. </s> <s xml:id="echoid-s13761" xml:space="preserve">Quæ omnia <lb/>perſpicua ſunt in ſphæra materiali. </s> <s xml:id="echoid-s13762" xml:space="preserve">Vnde arcus Zodiaci, cum quo æqualis <lb/>arcus Aequatoris peroritur, uel occidit, dici poterit oriri, & </s> <s xml:id="echoid-s13763" xml:space="preserve">occidere medio <lb/>modo: </s> <s xml:id="echoid-s13764" xml:space="preserve">cuiuſmodi ſunt quatuor Quadrantes zodiaci in ſphæra recta. </s> <s xml:id="echoid-s13765" xml:space="preserve">Oriuntur <lb/>enim ſinguli cum ſingulis Quadrantibus Aequatoris, ut ſtatim dicemus.</s> <s xml:id="echoid-s13766" xml:space="preserve"/> </p> <div xml:id="echoid-div718" type="float" level="2" n="1"> <note position="left" xlink:label="note-358-02" xlink:href="note-358-02a" xml:space="preserve">Ortus, & oc <lb/>caſus rect’, <lb/>uel obliqu’ <lb/>cur ſic dica <lb/>tur.</note> </div> <p> <s xml:id="echoid-s13767" xml:space="preserve"><emph style="sc">Ptolemaevs</emph> autem, quem ſequuntur omnes Aſtronomi, Aſcenſiones <lb/> <anchor type="note" xlink:label="note-358-03a" xlink:href="note-358-03"/> rectas uocat eas omnes, quæ fiunt in ſphæra recta: </s> <s xml:id="echoid-s13768" xml:space="preserve">Obliquas autem illas, quæ <lb/>in ſphæra obliqua habentur, ſiue maior arcus Aequatoris, minorve, ſiue æqua <lb/>lis cooriatur. </s> <s xml:id="echoid-s13769" xml:space="preserve">Ita quoq; </s> <s xml:id="echoid-s13770" xml:space="preserve">eas appellant Aſtronomi in tabulis aſcenſionum. </s> <s xml:id="echoid-s13771" xml:space="preserve">Vn-<lb/>de recta aſcenſio alicuius arcus, ſiue gradus Eclipticæ, apud ipſos ſumitur pro <lb/>aſcenſione, quam habet in ſphæra recta, ſiue maior arcus cum eo oriatur, ſi-<lb/>ue minor: </s> <s xml:id="echoid-s13772" xml:space="preserve">obliqua uero aſcenſio cuiuſque arcus intelligitur ea, quam habet <lb/>in ſphæra obliqua, cum quantocunque arcu Aequatoris ipſe coaſcẽdat. </s> <s xml:id="echoid-s13773" xml:space="preserve">Idem <lb/>dicendum eſt de Deſcenſionibus rectis & </s> <s xml:id="echoid-s13774" xml:space="preserve">obliquis.</s> <s xml:id="echoid-s13775" xml:space="preserve"/> </p> <div xml:id="echoid-div719" type="float" level="2" n="2"> <note position="left" xlink:label="note-358-03" xlink:href="note-358-03a" xml:space="preserve">Aſcẽſiones <lb/>rectæ, uel <lb/>obliquæ a-<lb/>pud Ptolo-<lb/>mæũ & A-<lb/>ſtronomos <lb/>quæ.</note> </div> <pb o="323" file="359" n="360" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div721" type="section" level="1" n="251"> <head xml:id="echoid-head262" style="it" xml:space="preserve">DE ORTV, ET OCC ASV SIGNO-<lb/>rum in ſphæra recta.</head> <p style="it"> <s xml:id="echoid-s13776" xml:space="preserve">E T eſt ſciendum, quod in ſphæra recta Quartæ Zodiaci inchoatæ à <lb/> <anchor type="note" xlink:label="note-359-01a" xlink:href="note-359-01"/> quatuor punctis, duobus ſcilicet Solſtitialibus, & </s> <s xml:id="echoid-s13777" xml:space="preserve">duobus ęquinoctiali-<lb/>bus, adæquantur ſuis aſcenſionibus, ideſt quantum temporis conſumit Quin <lb/>ta Zodiaci in ſuo ortu, in tanto tempore Quarta Aequinoctialis illi conter-<lb/>minalis peroritur. </s> <s xml:id="echoid-s13778" xml:space="preserve">Sed tamen partes illarum Quartarum uariantur, neque <lb/>habent æquales aſcenſiones, ſicut iam patebit.</s> <s xml:id="echoid-s13779" xml:space="preserve"/> </p> <div xml:id="echoid-div721" type="float" level="2" n="1"> <note position="right" xlink:label="note-359-01" xlink:href="note-359-01a" xml:space="preserve">Ortus arcu@ <lb/>Zodiaci in <lb/>ſphæra te-<lb/>cta.</note> </div> </div> <div xml:id="echoid-div723" type="section" level="1" n="252"> <head xml:id="echoid-head263" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s13780" xml:space="preserve"><emph style="sc">Tradit</emph> hic duas regulas ad ortum, & </s> <s xml:id="echoid-s13781" xml:space="preserve">occaſum ſignorum cognoſcen-<lb/>dum in ſphęra recta. </s> <s xml:id="echoid-s13782" xml:space="preserve">Prima eſt. </s> <s xml:id="echoid-s13783" xml:space="preserve">Quatuor Zodiaci Quadrantes, qui initium ſu-<lb/>munt a quatuor punctis cardinalibus, in ſphæra recta adæquantur ſuis aſcenſio <lb/>nibus, hoc eſt, cooriuntur præciſe cum Quadrantibus Aequatoris correſpon-<lb/>dentibus, ita ut quilibet eorum conſumat in ortu ſuo ſupra Horizontem 6. </s> <s xml:id="echoid-s13784" xml:space="preserve">ho <lb/>ras integras, quemadmodum & </s> <s xml:id="echoid-s13785" xml:space="preserve">quilibet Quadrans Aequatoris 6. </s> <s xml:id="echoid-s13786" xml:space="preserve">horis ſupra <lb/>Horizontem emergit: </s> <s xml:id="echoid-s13787" xml:space="preserve">Partes tamen dictorum Quadrantum non ſunt æquales <lb/>ſuis aſcenſionibus, hoc eſt, cum partibus eorum modo coaſcendunt arcus Ae-<lb/>quatoris maiores, modo minores, ita ut grad. </s> <s xml:id="echoid-s13788" xml:space="preserve">15. </s> <s xml:id="echoid-s13789" xml:space="preserve">v.</s> <s xml:id="echoid-s13790" xml:space="preserve">g. </s> <s xml:id="echoid-s13791" xml:space="preserve">aliquando plus temporis <lb/>requirant, ut exoriantur ſupra Horizontem, quam horam, aliquando uero mi-<lb/>nus. </s> <s xml:id="echoid-s13792" xml:space="preserve">Nam priores 15. </s> <s xml:id="echoid-s13793" xml:space="preserve">grad. </s> <s xml:id="echoid-s13794" xml:space="preserve">Arietis aſcendunt cum grad. </s> <s xml:id="echoid-s13795" xml:space="preserve">13. </s> <s xml:id="echoid-s13796" xml:space="preserve">min. </s> <s xml:id="echoid-s13797" xml:space="preserve">48. </s> <s xml:id="echoid-s13798" xml:space="preserve">Aequatoris, <lb/>hoc eſt, requirunt minuta 55. </s> <s xml:id="echoid-s13799" xml:space="preserve">Secunda 12. </s> <s xml:id="echoid-s13800" xml:space="preserve">unius horæ, ut ſupra Horizontem <lb/>emergant: </s> <s xml:id="echoid-s13801" xml:space="preserve">At poſteriores 15. </s> <s xml:id="echoid-s13802" xml:space="preserve">grad. </s> <s xml:id="echoid-s13803" xml:space="preserve">Geminorum aſcendunt cum grad. </s> <s xml:id="echoid-s13804" xml:space="preserve">16. </s> <s xml:id="echoid-s13805" xml:space="preserve">min-<lb/>17. </s> <s xml:id="echoid-s13806" xml:space="preserve">Aequatoris, hoc eſt, expoſcunt horam 1. </s> <s xml:id="echoid-s13807" xml:space="preserve">min. </s> <s xml:id="echoid-s13808" xml:space="preserve">5. </s> <s xml:id="echoid-s13809" xml:space="preserve">Sec. </s> <s xml:id="echoid-s13810" xml:space="preserve">8. </s> <s xml:id="echoid-s13811" xml:space="preserve">ut ſupra Horizontem <lb/>aſcendant. </s> <s xml:id="echoid-s13812" xml:space="preserve">Prior pars regulæ huius facile probari poteſt; </s> <s xml:id="echoid-s13813" xml:space="preserve">quia uterque Colu-<lb/>rus, cum per polos mundi tranſeat, coniungitur cum Horizonte recto bis in <lb/>die: </s> <s xml:id="echoid-s13814" xml:space="preserve">Vnde non poterunt Quadrantes prædicti Horizontem extremis ſuis pun-<lb/>ctis attingere, quin eundem alter Colurus per extremitates tranſiens eodem <lb/>temporis momento attingat, & </s> <s xml:id="echoid-s13815" xml:space="preserve">cum Horizonte coniungatur. </s> <s xml:id="echoid-s13816" xml:space="preserve">Quare poſtquam <lb/>Quadrans Zodiaci totus emerſerit ſupra Horizontem, neceſſe eſt, Quadran-<lb/>tem Aequatoris correſpondentem totum quoque aſcendiſſe ſupra Horizon-<lb/>tem. </s> <s xml:id="echoid-s13817" xml:space="preserve">Poſterior pars eiuſdem regulę oſtendi poteſt ex propoſ. </s> <s xml:id="echoid-s13818" xml:space="preserve">10. </s> <s xml:id="echoid-s13819" xml:space="preserve">lib. </s> <s xml:id="echoid-s13820" xml:space="preserve">1. </s> <s xml:id="echoid-s13821" xml:space="preserve">Mene-<lb/>lai ſphæricorum triangulorum, uel ex propoſ. </s> <s xml:id="echoid-s13822" xml:space="preserve">11. </s> <s xml:id="echoid-s13823" xml:space="preserve">noſtrorum triangulorum <lb/>ſphæricorum; </s> <s xml:id="echoid-s13824" xml:space="preserve">quia quælibet pars Eclipticæ, præter dictos Quadrantes, con-<lb/>ſtituit cum Horizonte recto nunc angulum obtuſum, nunc acutum, ut conſtat <lb/>ex Theodoſio, cum non tranſeat Horizon per eius polos: </s> <s xml:id="echoid-s13825" xml:space="preserve">Quare cum per <lb/>prædictas propoſitiones maiori angulo in triangulo ſphęrico maius latus op-<lb/>ponatur, & </s> <s xml:id="echoid-s13826" xml:space="preserve">minori minus, perſpicuum eſt, partes Quadrantum principium ha-<lb/>bentium in punctis æquinoctialibus non adæquari ſuis aſcenſionibus. </s> <s xml:id="echoid-s13827" xml:space="preserve">Quod <lb/>autem neque partes aliorum Quadrantum, qui initium habent in punctis Sol <lb/>ſtitialibus, adæquentur ſuis aſcenſionibus, ita demonſtrari poteſt. </s> <s xml:id="echoid-s13828" xml:space="preserve">Quoniam, <lb/>ut eodem modo probabitur, partes Zodiaci incipientes a punctis æquinoctia-<lb/>libus, quæ maiores ſint Quadrante, inæquales ſunt ſuis aſcenſionibus, ſi aufe-<lb/>rantur æquales Quadrantes, unus quidem Zodiaci ab arcu Zodiaci, alter uero <lb/>Aequatoris ab arcu Aquatoris coaſcendente cum arcu Zodiaci, erunt ad- <pb o="324" file="360" n="361" rhead="Comment. in III. Cap. Sphæræ"/> huc reliqui arcus inæquales, arcus uidelicet Zodiaci, & </s> <s xml:id="echoid-s13829" xml:space="preserve">eius aſcenſio. </s> <s xml:id="echoid-s13830" xml:space="preserve">Verum <lb/>hæc omnia cuius facile intueri licet in ſphæra materiali, manifeſtaq́ue erunt <lb/>ex tabula aſcenſionum rectarum.</s> <s xml:id="echoid-s13831" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">Qui arcus <lb/>Zodiaci ha <lb/>beant in <lb/>ſphæra re <lb/>cta ęquales <lb/>aſcẽſiones.</note> <p style="it"> <s xml:id="echoid-s13832" xml:space="preserve"><emph style="sc">Est enim</emph> regula. </s> <s xml:id="echoid-s13833" xml:space="preserve">Quilibet duo arcus Zodiaci æquales, & </s> <s xml:id="echoid-s13834" xml:space="preserve">æqua-<lb/>liter diſtantes ab aliquo quatuor punctorum iam dictorum, æquales ha-<lb/>bent aſcenſiones.</s> <s xml:id="echoid-s13835" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div724" type="section" level="1" n="253"> <head xml:id="echoid-head264" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s13836" xml:space="preserve"><emph style="sc">Secvnda</emph> regula eſt. </s> <s xml:id="echoid-s13837" xml:space="preserve">Quilibet duo arcus Zodiaci ęquales, & </s> <s xml:id="echoid-s13838" xml:space="preserve">æqualiter <lb/>diſtantes ab aliquo quatuor punctorum Cardinalium, in ſphæra recta æqua-<lb/>les habent aſcenſiones inter ſe. </s> <s xml:id="echoid-s13839" xml:space="preserve">Vt v. </s> <s xml:id="echoid-s13840" xml:space="preserve">g. </s> <s xml:id="echoid-s13841" xml:space="preserve">ſignum ♊, & </s> <s xml:id="echoid-s13842" xml:space="preserve">ſignum ♋, quia ſunt ar-<lb/>cus æquales, & </s> <s xml:id="echoid-s13843" xml:space="preserve">æqualiterq́; </s> <s xml:id="echoid-s13844" xml:space="preserve">remoti a puncto ſolſtitij æſtiui, habent unam, ean <lb/>demq́ue a ſcenſionem; </s> <s xml:id="echoid-s13845" xml:space="preserve">cum utro libet enim ſigno aſcendunt grad. </s> <s xml:id="echoid-s13846" xml:space="preserve">32. </s> <s xml:id="echoid-s13847" xml:space="preserve">min. </s> <s xml:id="echoid-s13848" xml:space="preserve">12. <lb/></s> <s xml:id="echoid-s13849" xml:space="preserve">Aequatoris. </s> <s xml:id="echoid-s13850" xml:space="preserve">Eademq; </s> <s xml:id="echoid-s13851" xml:space="preserve">eſt ratio de ſigno ♉, & </s> <s xml:id="echoid-s13852" xml:space="preserve">♌: </s> <s xml:id="echoid-s13853" xml:space="preserve">Item de ſigno ♈, & </s> <s xml:id="echoid-s13854" xml:space="preserve">♍, & </s> <s xml:id="echoid-s13855" xml:space="preserve">ſic <lb/>de cæteris arcubus æqualibus, dummodo æqualiter remoueantur ab aliquo <lb/>dictorum quatuor punctorum, ut perſpicuum erit ex tabula aſcenſionum re-<lb/>ctarum. </s> <s xml:id="echoid-s13856" xml:space="preserve">Confirmari poteſt hęc regula ex ſphæricis triangulis; </s> <s xml:id="echoid-s13857" xml:space="preserve">quia huiuſmodi <lb/>arcus Eclipticæ, cum æque ab Aequatore extremis punctis declinent, ut ſupra <lb/>dictum eſt, æquales efficiunt angulos cum Horizonte, unde æquales arcus <lb/>Aequatoris ipſis reſpondeant neceſſe eſt, ac propterea æquales habebũt aſcẽ-<lb/>fiones inter ſe.</s> <s xml:id="echoid-s13858" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s13859" xml:space="preserve"><emph style="sc">Et</emph> ex hoc ſequitur, quòd ſigna oppoſita ęquales habent aſcenſiones. <lb/></s> <s xml:id="echoid-s13860" xml:space="preserve">Et hoc eſt, quod dicit Lucanus lib. </s> <s xml:id="echoid-s13861" xml:space="preserve">9. </s> <s xml:id="echoid-s13862" xml:space="preserve">loquens de proceſſu Catonis in Libyã <lb/>uerſus Aequinoctialem.</s> <s xml:id="echoid-s13863" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13864" xml:space="preserve">Deprehenſum eſt hunc eſſe locum, qua circulus alti</s> </p> <p> <s xml:id="echoid-s13865" xml:space="preserve">Solſtitij medium fignorum percutit orbem.</s> <s xml:id="echoid-s13866" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13867" xml:space="preserve">Non obliqua meant, nec <emph style="sc">Tavro</emph> <emph style="sc">Scorpivs</emph> exit</s> </p> <p> <s xml:id="echoid-s13868" xml:space="preserve">Rectior; </s> <s xml:id="echoid-s13869" xml:space="preserve">aut <emph style="sc">Aries</emph> donat ſua tempora <emph style="sc">Librae</emph>;</s> <s xml:id="echoid-s13870" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13871" xml:space="preserve">Aut <emph style="sc">Astraea</emph> iubet lentos deſcendere <emph style="sc">Pisces</emph>;</s> <s xml:id="echoid-s13872" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13873" xml:space="preserve">Par <emph style="sc">Geminis</emph> <emph style="sc">Chiron</emph>; </s> <s xml:id="echoid-s13874" xml:space="preserve">& </s> <s xml:id="echoid-s13875" xml:space="preserve">idem quod <emph style="sc">Carcinvs</emph> ardens.</s> <s xml:id="echoid-s13876" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13877" xml:space="preserve">Humidus <emph style="sc">Aegoceros</emph>; </s> <s xml:id="echoid-s13878" xml:space="preserve">nec plus <emph style="sc">Leo</emph> tollitur <emph style="sc">Vrna</emph>.</s> <s xml:id="echoid-s13879" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s13880" xml:space="preserve"><emph style="sc">Hic</emph> dicit Lucanus, quod exiſtentibusſub Aequinoctiali, ſigna oppo-<lb/>ſita ęquales habent aſcenſiones, & </s> <s xml:id="echoid-s13881" xml:space="preserve">occaſus. </s> <s xml:id="echoid-s13882" xml:space="preserve">Oppoſitio autem ſignorum ha-<lb/>betur per hunc uerſum.</s> <s xml:id="echoid-s13883" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13884" xml:space="preserve">Eſt Lib. </s> <s xml:id="echoid-s13885" xml:space="preserve">Ari. </s> <s xml:id="echoid-s13886" xml:space="preserve">Scor. </s> <s xml:id="echoid-s13887" xml:space="preserve">Tau. </s> <s xml:id="echoid-s13888" xml:space="preserve">Sa. </s> <s xml:id="echoid-s13889" xml:space="preserve">Gemi. </s> <s xml:id="echoid-s13890" xml:space="preserve">Capri. </s> <s xml:id="echoid-s13891" xml:space="preserve">Cancr. </s> <s xml:id="echoid-s13892" xml:space="preserve">A. </s> <s xml:id="echoid-s13893" xml:space="preserve">Le. </s> <s xml:id="echoid-s13894" xml:space="preserve">Piſ. </s> <s xml:id="echoid-s13895" xml:space="preserve">Vir.</s> <s xml:id="echoid-s13896" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div725" type="section" level="1" n="254"> <head xml:id="echoid-head265" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s13897" xml:space="preserve"><emph style="sc">Colligit</emph> ex 2. </s> <s xml:id="echoid-s13898" xml:space="preserve">regula, ſigna oppoſita in ſphæra recta æquales inter <lb/>ſe habere aſcenſiones. </s> <s xml:id="echoid-s13899" xml:space="preserve">Quod confirmat auctoritate Lucani lib. </s> <s xml:id="echoid-s13900" xml:space="preserve">9. </s> <s xml:id="echoid-s13901" xml:space="preserve">ubi deſcri-<lb/>bit aduentum Catonis ſub Aequino ctialem circulum, quem appellat circulũ <lb/>alti ſolſtitij, dicens, omnia ſigna oppoſita habere æquales aſcenſiones, & </s> <s xml:id="echoid-s13902" xml:space="preserve">de-<lb/>ſcenſiones, ita ut nullum ſignum ſuo oppoſito rectius, aut obliquius aſcẽdat, <pb o="325" file="361" n="362" rhead="Ioan. de Sacro Boſco."/> @el deſcendat, ſicut in ſphæra obliqua contingit, ut mox patebit. </s> <s xml:id="echoid-s13903" xml:space="preserve">Non enim uo <lb/>luit eo in loco Lucanus, omnia ſigna in ſphæra recta rectè, & </s> <s xml:id="echoid-s13904" xml:space="preserve">nullum oblique <lb/>oriri, ut perperam explicant Sulpitius, & </s> <s xml:id="echoid-s13905" xml:space="preserve">Omnibonus interpretes Lucani. </s> <s xml:id="echoid-s13906" xml:space="preserve">Hoc <lb/>enim falſum eſt; </s> <s xml:id="echoid-s13907" xml:space="preserve">ſed ſolum uoluit, nullum rectius o<unsure/>riri, uel obliquius ſuo op-<lb/>poſito, quàmuis quædam ibi recte oriantur, quædam uero oblique, ut conſtat <lb/>ex tabula aſcen ſionum rectarum.</s> <s xml:id="echoid-s13908" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">Locus Lu-<lb/>cani eme@ <lb/>datus.</note> <p> <s xml:id="echoid-s13909" xml:space="preserve"><emph style="sc">Vervm</emph> locus hic Lucani mendo non caret. </s> <s xml:id="echoid-s13910" xml:space="preserve">Neq; </s> <s xml:id="echoid-s13911" xml:space="preserve">enim Lucanus vult, <lb/>Catonem ad Aequatorem perueniſſe, ut carmina allata indicare uidentur, ſed <lb/>ad templum Iouis Ammonij, quod Lucanus putabat prope tro picum Cancri <lb/>eſſe ſitum. </s> <s xml:id="echoid-s13912" xml:space="preserve">Id autem ut planius fiat, afferenda ſunt nonnulla carmina Lucani vt <lb/>in uulgatis exemplaribus habentur, ſed ordine præpoſtero: </s> <s xml:id="echoid-s13913" xml:space="preserve">Deinde eadem pro <lb/>prium in ſitum redigenda. </s> <s xml:id="echoid-s13914" xml:space="preserve">Sic igitur, ut nunc legitur, Lucanus naturam illius <lb/>loci deſcribit.</s> <s xml:id="echoid-s13915" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s13916" xml:space="preserve">Hic quoque nil obſtat Phœbo, cum cardine ſummo <lb/>Stat librata dies: </s> <s xml:id="echoid-s13917" xml:space="preserve">truncum uix protegit arbor: <lb/></s> <s xml:id="echoid-s13918" xml:space="preserve">Tam breuis in medium radijs compellitur umbra. </s> <s xml:id="echoid-s13919" xml:space="preserve"><lb/>Deprenſum eſt, hunc eſſe locum, qua circulus alti <lb/>Solſtitij medium ſignorum percutit orbem. </s> <s xml:id="echoid-s13920" xml:space="preserve"><lb/>Non obliqua meant, nec Tauro Scorpius exit <lb/>Rectior: </s> <s xml:id="echoid-s13921" xml:space="preserve">aut Aries donat ſua tempora Libræ: </s> <s xml:id="echoid-s13922" xml:space="preserve"><lb/>Aut Aſtræa iubet lentos deſcendere Piſces. </s> <s xml:id="echoid-s13923" xml:space="preserve"><lb/>Par Geminis Chiron: </s> <s xml:id="echoid-s13924" xml:space="preserve">& </s> <s xml:id="echoid-s13925" xml:space="preserve">idem quod Carcinus ardent, <lb/>Humidus Aegoceros: </s> <s xml:id="echoid-s13926" xml:space="preserve">nec Plus Leo tollitur Vrna. </s> <s xml:id="echoid-s13927" xml:space="preserve"><lb/>At tibi, quæcunque es Lybico gensigne dirempta, <lb/>In Noton umbra cadit, quæ nobis exit in Arcton. </s> <s xml:id="echoid-s13928" xml:space="preserve"><lb/>Te ſegnis Cynoſura ſubit, tu ſicca profundo <lb/>Mergi plauſtra putas, nullumq́; </s> <s xml:id="echoid-s13929" xml:space="preserve">in uertice ſummo <lb/>Sidus habes immune maris, procul axis uterque eſt, <lb/>Et fuga ſignorum medio rapit omnia cœlo.</s> <s xml:id="echoid-s13930" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13931" xml:space="preserve"><emph style="sc">Qvae</emph> carmina ſi hoc ordine a Lucano fuiſſent conſcripta, proculdubio <lb/>per circulum alti ſolſtitij intellexiſſet Aequatorem, cum ea, quæ ſequuntur de <lb/>ortu & </s> <s xml:id="echoid-s13932" xml:space="preserve">occaſu ſignorum, nulli alteriregioni conuenire poſſint, quà<unsure/>m illi, quæ <lb/>directe ſub Aequatore conſtituitur. </s> <s xml:id="echoid-s13933" xml:space="preserve">Sed cur poſtea ſubiunxiſſet, [At tibi quæcun <lb/>que es Lybico gens igne dirempta, & </s> <s xml:id="echoid-s13934" xml:space="preserve">c.</s> <s xml:id="echoid-s13935" xml:space="preserve">] non intelligo, cum ea quoque ſphæræ re-<lb/>ctæ conueniant, ut perſpicuum eſt. </s> <s xml:id="echoid-s13936" xml:space="preserve">Intellexit igitur per circulum alti Solſtitij <lb/>Tropicum cancri, qui medium ſignorum orbem, id eſt, Eclipticam, percutit, id <lb/>eſt, tangit tantummodo. </s> <s xml:id="echoid-s13937" xml:space="preserve">Deinde uero cum dicit, [At tibi quæcunque es, & </s> <s xml:id="echoid-s13938" xml:space="preserve">c.</s> <s xml:id="echoid-s13939" xml:space="preserve">] ſigni <lb/>ficat ſphæram rectam, quę ſub Aequatore ſita eſt, vbi omnes ſtellæ oriuntur, & </s> <s xml:id="echoid-s13940" xml:space="preserve"><lb/>occidunt; </s> <s xml:id="echoid-s13941" xml:space="preserve">ſigna item oppoſita eandem habent aſcenſionem, & </s> <s xml:id="echoid-s13942" xml:space="preserve">deſcenſionem. </s> <s xml:id="echoid-s13943" xml:space="preserve">Vn<unsure/> <lb/>de ita collocanda erunt carmina, ut Petrus Iaconus Hiſpanus uirin omnium <lb/>artium ſubtilitate ſolertiſſimus animaduertit.</s> <s xml:id="echoid-s13944" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s13945" xml:space="preserve">Hic quoque nil obſtat Phœbo, cum cardine ſummo <lb/>Stat librata dies: </s> <s xml:id="echoid-s13946" xml:space="preserve">truncum uix protegit arbor: <lb/></s> <s xml:id="echoid-s13947" xml:space="preserve">Tam breuis in medium radijs compellitur umbra. </s> <s xml:id="echoid-s13948" xml:space="preserve"><lb/>Deprenſum eſt, hunc eſſe locum, qua circulus alti <lb/>Solſtitij medium ſignorumpercutit orbem. </s> <s xml:id="echoid-s13949" xml:space="preserve"><lb/>At tibi, quæcunque es Lybico gens igne dirempta, <lb/>In Noton umbra cadit, quę nobis exit in Arcton.</s> <s xml:id="echoid-s13950" xml:space="preserve"> <pb o="326" file="362" n="363" rhead="Comment. in II. Cap. Sphæræ"/> Te ſegnis Cynoſura ſubit: </s> <s xml:id="echoid-s13951" xml:space="preserve">tu ſicca profundo <lb/>Mergi plauſtra putas: </s> <s xml:id="echoid-s13952" xml:space="preserve">nullumq́; </s> <s xml:id="echoid-s13953" xml:space="preserve">in uertice ſummo. <lb/></s> <s xml:id="echoid-s13954" xml:space="preserve">Sidus habes immune maris, procul axis uterque eſt. </s> <s xml:id="echoid-s13955" xml:space="preserve"><lb/>Et fuga ſignorum medio rapit omnia cælo. </s> <s xml:id="echoid-s13956" xml:space="preserve"><lb/>Non obliqua meant, nec Tauro Scorpius exit <lb/>Rectior; </s> <s xml:id="echoid-s13957" xml:space="preserve">aut Aries donat ſua tempora Libræ; </s> <s xml:id="echoid-s13958" xml:space="preserve"><lb/>Aut Aſtræa iubei lentos deſcendere Piſces: </s> <s xml:id="echoid-s13959" xml:space="preserve"><lb/>Par Geminis Chiron: </s> <s xml:id="echoid-s13960" xml:space="preserve">Et idem quod Carcinus ardens, <lb/>Humidus Aegoceros: </s> <s xml:id="echoid-s13961" xml:space="preserve">Nec plus Leo tollitur Vrna.</s> <s xml:id="echoid-s13962" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13963" xml:space="preserve"><emph style="sc">Ita</emph> enim ab illo loco [At tibi, quæcunqise es & </s> <s xml:id="echoid-s13964" xml:space="preserve">c.</s> <s xml:id="echoid-s13965" xml:space="preserve">] d@ſcribit ſphæram re-<lb/>ctam, cum antea obliquam ſub tropico Cancri deſcripſerit, ut perſpicuum eſt.</s> <s xml:id="echoid-s13966" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13967" xml:space="preserve"><emph style="sc">Qvod</emph> autem ex ſecunda regula ſequatur, ſigna oppoſita in ſphæra recta <lb/>æquales habere aſcenſiones, deſcenſionesq́ue, probari poteſt hac ratione.</s> <s xml:id="echoid-s13968" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13969" xml:space="preserve"><emph style="sc">Qvae@ibet</emph> duo ſigna oppoſita habent conuenientiam quandã cum <lb/>aliquo tertio ſigno, ita ut hoc tertium ſignum, & </s> <s xml:id="echoid-s13970" xml:space="preserve">quodlibet oppoſitorum quo-<lb/>rumcunq; </s> <s xml:id="echoid-s13971" xml:space="preserve">æqualiter diſtent uel ab alterutro punctorum ſolſtitialium, uel ab <lb/>alterutro æquinoctialium. </s> <s xml:id="echoid-s13972" xml:space="preserve">Quare utrumq; </s> <s xml:id="echoid-s13973" xml:space="preserve">eandem habebit aſcenſionẽ, quam <lb/>tertium illud ſignum ex 2. </s> <s xml:id="echoid-s13974" xml:space="preserve">regula, & </s> <s xml:id="echoid-s13975" xml:space="preserve">propterea ipſa oppoſita ſigna ęquales in-<lb/>terſe habebunt aſcenſiones. </s> <s xml:id="echoid-s13976" xml:space="preserve">Exempli cauſa. </s> <s xml:id="echoid-s13977" xml:space="preserve">♈, & </s> <s xml:id="echoid-s13978" xml:space="preserve">♎, ſunt ſigna oppoſita, & </s> <s xml:id="echoid-s13979" xml:space="preserve"><lb/>quia ♈, eandem habet aſcenſionem, quam ♍, cum hæc ſigna æqualiter ſint re-<lb/>mota a ſol@titio æſtiuo; </s> <s xml:id="echoid-s13980" xml:space="preserve">Item ♎, eandem quoque habet aſcenſionem cum ♍, <lb/>quòd æque recedant hęc ſigna ab æquinoctio autumnali: </s> <s xml:id="echoid-s13981" xml:space="preserve">idcirco eandem obti <lb/>nebunt aſcenſionem ♈, & </s> <s xml:id="echoid-s13982" xml:space="preserve">♎. </s> <s xml:id="echoid-s13983" xml:space="preserve">Sic quoque ♉, & </s> <s xml:id="echoid-s13984" xml:space="preserve">♏, ſigna oppoſita conueniunt <lb/>cum, ♌, in aſcenſione: </s> <s xml:id="echoid-s13985" xml:space="preserve">♊ & </s> <s xml:id="echoid-s13986" xml:space="preserve">♐, cum ♋@ ♋, & </s> <s xml:id="echoid-s13987" xml:space="preserve">♑, cum ♊: </s> <s xml:id="echoid-s13988" xml:space="preserve">♌, & </s> <s xml:id="echoid-s13989" xml:space="preserve">♒, cum ♉: <lb/></s> <s xml:id="echoid-s13990" xml:space="preserve">♍, & </s> <s xml:id="echoid-s13991" xml:space="preserve">♓, cum ♈, ut ex ſphæra materiali conſtat. </s> <s xml:id="echoid-s13992" xml:space="preserve">Omniaigitur ſigna oppoſita <lb/>æquales ſortiuntur aſcenſiones in ſphæra recta. </s> <s xml:id="echoid-s13993" xml:space="preserve">Idem etiam ex eo demonſtra-<lb/>ri poteſt, quòd ſigna oppoſita eoſdem cum Horizonte angulos conſtituunt, v-<lb/>num quidem ad partes poli Arctici, alterum uero ad partes poli Antarct ci. </s> <s xml:id="echoid-s13994" xml:space="preserve"><lb/>Hinc enim ex doctrina triangulorum ſphæricorum colligitur, arcus Aequato-<lb/>risilli correſpondentes eſſe æquales. </s> <s xml:id="echoid-s13995" xml:space="preserve">Id ipſum maniſeſtabit tabula aſcenſio-<lb/>num rectarum.</s> <s xml:id="echoid-s13996" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">@@lutio cu <lb/>iuſdam du-<lb/>bij.</note> <p style="it"> <s xml:id="echoid-s13997" xml:space="preserve">ET eſt notandum, quòd non ualet talis argumentatio. </s> <s xml:id="echoid-s13998" xml:space="preserve">Iſti duo arc{us} <lb/>ſunt æquales, & </s> <s xml:id="echoid-s13999" xml:space="preserve">ſimul incipiunt oriri, & </s> <s xml:id="echoid-s14000" xml:space="preserve">ſemper maior pars oritur de uno, <lb/>quàm de reliquo; </s> <s xml:id="echoid-s14001" xml:space="preserve">ergo ille arcus citius peroritur, cuius maior pars ſemper <lb/>oriebatur. </s> <s xml:id="echoid-s14002" xml:space="preserve">Inſtantia huius argumentationis manifeſta eſt in partibus præ-<lb/>dictarum quartarum. </s> <s xml:id="echoid-s14003" xml:space="preserve">Si enim ſumatur quarta pars Zodiaci, quæ eſt à <lb/>principio ♈, uſque ad finem ♊, ſemper maior pars oritur de quarta Zodia-<lb/>ci, quàm de quarta Aequinoctialis ſibi conterminali, & </s> <s xml:id="echoid-s14004" xml:space="preserve">tamenillæ duæ <lb/>quartæ ſimul peroriuntur. </s> <s xml:id="echoid-s14005" xml:space="preserve">Idem intellige de quarta Zodiaci, quæ eſt à prin-<lb/>cipio ♎, uſque ad finem ♐.</s> <s xml:id="echoid-s14006" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s14007" xml:space="preserve">ITEM ſi ſumatur quarta Zodiaci, quæ eſt à principio ♋, uſque ad <lb/>finem ♍, ſemper maior pars oritur de quarta Aequinoctialis, quàm de <lb/>quarta Zodiaci illi conterminali, & </s> <s xml:id="echoid-s14008" xml:space="preserve">tamen illę duæ quartæ ſimul peroriun <lb/>tur. </s> <s xml:id="echoid-s14009" xml:space="preserve">Idem intellige de quarta Zodiaci, quæ eſt à primo puncto ♑, uſque <lb/>a<unsure/>d finem ♓.</s> <s xml:id="echoid-s14010" xml:space="preserve"/> </p> <pb o="327" file="363" n="364" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div726" type="section" level="1" n="255"> <head xml:id="echoid-head266" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s14011" xml:space="preserve"><emph style="sc">Solvit</emph> hic auctor ex ijs, quæ dixit, dubitationem quandam, quæ alicui <lb/>faceſſere poſſet negotium. </s> <s xml:id="echoid-s14012" xml:space="preserve">videlicet, non valere hanc argumentationem: </s> <s xml:id="echoid-s14013" xml:space="preserve">Sunt <lb/>duo arcus in ſphæra omnino æquales inter ſe, qui ſimul eodem temporis mo <lb/>mento incipiunt oriri ſupra Horizontem, ſemperq́. </s> <s xml:id="echoid-s14014" xml:space="preserve">maior pars unius exorta <lb/>eſt, quàm alterius, igitur citius arcus ille totus, cuius ſemper maior pars eſt <lb/>perorta, ſupra Horizontẽ aſcendet, quàm arcus, cuius ſemper minor fuit por-<lb/>tio orta. </s> <s xml:id="echoid-s14015" xml:space="preserve">Soluitur enim hæc argumẽtatio per ea, quæ dicta ſunt in prima regu<unsure/> <lb/>la. </s> <s xml:id="echoid-s14016" xml:space="preserve">Nam quilibet Quadrans Zodiaci initium ſumens ab aliquo quatuor pun-<lb/>ctorum cardinalium, ut diximus, ſimul totus exoritur cum quadrante Aequa-<lb/>toris correſpondente, & </s> <s xml:id="echoid-s14017" xml:space="preserve">@amen, antequam toti Quadrantes peroriantur, ſem-<lb/>per maior pars alicuius eorum eſt exorta, quàm alterius. </s> <s xml:id="echoid-s14018" xml:space="preserve">Semper enim maior <lb/>pars cuiuſlibet quadrantis Zodiaci ab alterutro æquinoctio in cipientis aſcen-<lb/>dit ſupra Horizontem, quàm Quadrantis Aequatoris, initio facto ſemper om <lb/>nium arcuum orientium à puncto æquinoctij, quia ſemper talis arcus Zodiaci <lb/>efficit minorẽ angulum cum Horizonte ad partes Aequatoris, quàm Aequa-<lb/>tor: </s> <s xml:id="echoid-s14019" xml:space="preserve">Vnde per propoſ. </s> <s xml:id="echoid-s14020" xml:space="preserve">10. </s> <s xml:id="echoid-s14021" xml:space="preserve">lib. </s> <s xml:id="echoid-s14022" xml:space="preserve">1. </s> <s xml:id="echoid-s14023" xml:space="preserve">Menelai, uel per propoſ. </s> <s xml:id="echoid-s14024" xml:space="preserve">11. </s> <s xml:id="echoid-s14025" xml:space="preserve">noſtrorum triangu-<lb/>lerum ſphæricorum, minor arcus Aequatoris correſpondebit, donec in fine <lb/>Quadrantum uterque angulus fiat rectus, & </s> <s xml:id="echoid-s14026" xml:space="preserve">conſequenter arcus æquales, per <lb/>propoſ. </s> <s xml:id="echoid-s14027" xml:space="preserve">4. </s> <s xml:id="echoid-s14028" xml:space="preserve">eiuſdem lib. </s> <s xml:id="echoid-s14029" xml:space="preserve">1. </s> <s xml:id="echoid-s14030" xml:space="preserve">Menelai, uel per propoſ. </s> <s xml:id="echoid-s14031" xml:space="preserve">5. </s> <s xml:id="echoid-s14032" xml:space="preserve">noſtrorum triangulorum <lb/>ſphæricornm. </s> <s xml:id="echoid-s14033" xml:space="preserve">Simili modo ſemper maior pars cuiuſlibet Quadrantis Aequa-<lb/>toris initium ſumentis à Coluro ſolſtitiorum, ſupra Horizontem emergit, <lb/>quàm Quadrantis Zodiaci correſpondentis, ut clariſſime deducitur ex trian-<lb/>gulis ſphæricis, & </s> <s xml:id="echoid-s14034" xml:space="preserve">perſpicue apparebit ex tabula aſcenſionum rectarum: </s> <s xml:id="echoid-s14035" xml:space="preserve">quia <lb/>videlicet ſemper talis arcus Aequatoris minorem angulum cõſtituit cum Ho <lb/>rizonte, quàm Zodiacus, &</s> <s xml:id="echoid-s14036" xml:space="preserve">c. </s> <s xml:id="echoid-s14037" xml:space="preserve">Quod autem toti Quadrantes ſimul peroriãtur, <lb/>etiamſi ſemper maior pars unius ſit perorta, quã alterius, inde prouenit, quòd <lb/>non ſemper eadem proportione maior pars unius oriatur, quàm alterius, ſed <lb/>paulatim decreſcatilla proportio, ut manifeſtum eſt ex tabula aſcenſionũ re-<lb/>ctarum, ita ut in fine ſit iam compenſata tota inæqualitas aſcenſionum. </s> <s xml:id="echoid-s14038" xml:space="preserve">Quod <lb/>quidem fieri poſſe, præter exemplum Quadrãtum Zodiaci, & </s> <s xml:id="echoid-s14039" xml:space="preserve">Aequatoris ad-<lb/>ductum, hoc uno exemplo percipi poteſt. </s> <s xml:id="echoid-s14040" xml:space="preserve">Sint duo mobilia A, & </s> <s xml:id="echoid-s14041" xml:space="preserve">B, quæ per <lb/>vnum & </s> <s xml:id="echoid-s14042" xml:space="preserve">idem ſpatium moueantur, incipiendo eodem temporis momẽto, hac <lb/>tamen lege, ut A, quidem ſemper regulariter, & </s> <s xml:id="echoid-s14043" xml:space="preserve">uniformiter incedat, B, vero <lb/>vſq; </s> <s xml:id="echoid-s14044" xml:space="preserve">ad medium ſpatium uelocius, uel tardius feratur, & </s> <s xml:id="echoid-s14045" xml:space="preserve">a medio ad finẽ uſq; <lb/></s> <s xml:id="echoid-s14046" xml:space="preserve">tardius uel uelocius eadem omnino proportione, quaantea vincebat mobile <lb/>A, vel ab eo ſuperabatur. </s> <s xml:id="echoid-s14047" xml:space="preserve">Quo poſito certum eſt, utrumque mobile eodem <lb/>tempore ad finem. </s> <s xml:id="echoid-s14048" xml:space="preserve">ſpatij peruenturũ, quòd illa dicta proportione tota inæqua <lb/>litas compenſetur: </s> <s xml:id="echoid-s14049" xml:space="preserve">nihilominus tamen ante finem ſpatij totius ſemper mobile <lb/>A, antecedet, uel conſequetur mobile B. </s> <s xml:id="echoid-s14050" xml:space="preserve">Alias non una abſoluerent totum <lb/>ſpatium, ut conſtat. </s> <s xml:id="echoid-s14051" xml:space="preserve">Sic igitur intelligendum eſt moueri Quadrantes Zodiaci, <lb/>& </s> <s xml:id="echoid-s14052" xml:space="preserve">Aequatoris, totos quidem eodem tempore exoriri, partes uero eorundem <lb/>temporibus inæqualibus. </s> <s xml:id="echoid-s14053" xml:space="preserve">Nam quadrantes Zodiaci a Coluro æquinoctio-<lb/>rum incipientes velocius exoriuntur circa principium, tardius uero circa fi-<lb/>nem: </s> <s xml:id="echoid-s14054" xml:space="preserve">At Quadrantes a Coluro Solſtitiorum inchoati tardius in principio, <lb/>quàm in fine.</s> <s xml:id="echoid-s14055" xml:space="preserve"/> </p> <pb o="328" file="364" n="365" rhead="Comment. in III. Cap. Sphæræ"/> <p> <s xml:id="echoid-s14056" xml:space="preserve"><emph style="sc">Porro</emph> in ſphæra recta aſcenſio cuiuſlibet ſigni, ſeu arcus Zodiaci, æqua-<lb/> <anchor type="note" xlink:label="note-364-01a" xlink:href="note-364-01"/> lis eſt ſuæ deſcenſioni: </s> <s xml:id="echoid-s14057" xml:space="preserve">quoniam deſcenſio in uno Horizonte recto, eſt aſcen-<lb/>ſio in alio Horizonte recto, (quem nimirum habent antipodes habitantium <lb/>in priori Horizonte) & </s> <s xml:id="echoid-s14058" xml:space="preserve">contra. </s> <s xml:id="echoid-s14059" xml:space="preserve">Certum autem eſt, aſcenſionem unius eiuſ-<lb/>demque arcus Zodiaci eandem eſſe in quolibet Horizonte @ecto, propter æ-<lb/>qualem inclinationem Zodiaci. </s> <s xml:id="echoid-s14060" xml:space="preserve">Eodem pacto aſcenſio cuiuſlibet ſigni æqua-<lb/>lis eſt meditationi cęli eiuſdem, hoc eſt, quanto tempore ſignum aliquod ſu <lb/>pra Horizontem exoritur, tanto etiam præciſe tempore Meridianũ cuiuſcun-<lb/>que loci pertranſit, quia uidelicet Meridianus quilibet Horizon rectus appel-<lb/>lari poteſt, cum per mundi polos tranſeat. </s> <s xml:id="echoid-s14061" xml:space="preserve">Quare omnia, quæ dicta ſunt de <lb/>aſcenſionibus ſignorum, ſiue arcuum Zodiaci, in ſphæra recta, eadem intelli-<lb/>genda ſunt de deſcenſionibus in eadem ſphæra recta, necnon de cęli medita-<lb/>@@onibus tam in ſphæra recta, quàm in obliqua.</s> <s xml:id="echoid-s14062" xml:space="preserve"/> </p> <div xml:id="echoid-div726" type="float" level="2" n="1"> <note position="left" xlink:label="note-364-01" xlink:href="note-364-01a" xml:space="preserve">Aſcenſio cu <lb/>iuſuis @rcus <lb/>Zodiaci in <lb/>ſphæra ar-<lb/>ctæ æqualis <lb/>eſt deſcẽſio <lb/>ni eiuſdem <lb/>in eadem <lb/>ſphęra recta <lb/>& cœli me <lb/>ditationi tã <lb/>@ſphæra re <lb/>cta, quã in <lb/>obliqua.</note> </div> </div> <div xml:id="echoid-div728" type="section" level="1" n="256"> <head xml:id="echoid-head267" xml:space="preserve">QVOMODO ASCENSIO RECTA <lb/>cuiuſlibet arcus Zodiaci a Verna ſectione <lb/>inchoati ſupputetur.</head> <p> <s xml:id="echoid-s14063" xml:space="preserve"><emph style="sc">Demonstravit</emph> Ioan. </s> <s xml:id="echoid-s14064" xml:space="preserve">Regiom. </s> <s xml:id="echoid-s14065" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s14066" xml:space="preserve">ultima lib. </s> <s xml:id="echoid-s14067" xml:space="preserve">1. </s> <s xml:id="echoid-s14068" xml:space="preserve">Epitomes, & </s> <s xml:id="echoid-s14069" xml:space="preserve">Ge-<lb/> <anchor type="note" xlink:label="note-364-02a" xlink:href="note-364-02"/> ber in opere Aſtronomico, & </s> <s xml:id="echoid-s14070" xml:space="preserve">nos etiam in ſcholio propoſ. </s> <s xml:id="echoid-s14071" xml:space="preserve">lib. </s> <s xml:id="echoid-s14072" xml:space="preserve">2. </s> <s xml:id="echoid-s14073" xml:space="preserve">Gnomonices <lb/>demonſtrauimus: </s> <s xml:id="echoid-s14074" xml:space="preserve">Talem eſſe proportionem ſinus complementi declinatio-<lb/>nis puncti arcum Eclipticæ ab alterutro æquino ctio inchoatum terminantis, <lb/>ad ſinum complementi eiuſdem arcus, qualis eſt proportio ſinus totius ad ſi-<lb/>num complementi aſcenſionis rectæ. </s> <s xml:id="echoid-s14075" xml:space="preserve">Quare ſi iuxta regulam proportionum <lb/>ſinus totus in ſinum complemẽti arcus propoſiti multiplicetur, productusque <lb/>numerus diuidatur in ſinum complementi declinationis ultimi puncti arcus, <lb/>inuenietur ſinus complementi aſcenſionis rectæ, ideoq; </s> <s xml:id="echoid-s14076" xml:space="preserve">aſcenſio nota erit. <lb/></s> <s xml:id="echoid-s14077" xml:space="preserve">Quæ cum ita ſint, inuenietur aſcenſiones rectæ omnium arcuum Eclipticæ <lb/>incipientium a ſectione Verna hac ratione.</s> <s xml:id="echoid-s14078" xml:space="preserve"/> </p> <div xml:id="echoid-div728" type="float" level="2" n="1"> <note position="left" xlink:label="note-364-02" xlink:href="note-364-02a" xml:space="preserve">Aſcenſio re <lb/>cta cuiuſuis <lb/>arcus Ecli-<lb/>pticæ qua <lb/>ratione per <lb/>ſinus ſit in <lb/>@@ſtiganda.</note> </div> <p> <s xml:id="echoid-s14079" xml:space="preserve"><emph style="sc">Si</emph> arcus propoſitus Quadrante minorſuerit, dabit documentum iam expo <lb/> <anchor type="note" xlink:label="note-364-03a" xlink:href="note-364-03"/> ſitum aſcenſionem eius rectam. </s> <s xml:id="echoid-s14080" xml:space="preserve"><emph style="sc">Exemplvm</emph>. </s> <s xml:id="echoid-s14081" xml:space="preserve">Sit inuenienda aſcenſio recta <lb/>viceſimi gradus ♊, hoc eſt, arcus continentis grad. </s> <s xml:id="echoid-s14082" xml:space="preserve">80. </s> <s xml:id="echoid-s14083" xml:space="preserve">Multiplicetur ſinus to-<lb/>tus, uidelicet, 100000. </s> <s xml:id="echoid-s14084" xml:space="preserve">per 17364. </s> <s xml:id="echoid-s14085" xml:space="preserve">ſinum complementi dicti arcus, productuſ-<lb/>que numerus 1736400000. </s> <s xml:id="echoid-s14086" xml:space="preserve">diuidatur par 91970. </s> <s xml:id="echoid-s14087" xml:space="preserve">ſinum complementi decli-<lb/>nationis. </s> <s xml:id="echoid-s14088" xml:space="preserve">Nam proueniet ſinus complementi aſcenſionis rectæ 18880. </s> <s xml:id="echoid-s14089" xml:space="preserve">cui re-<lb/>ſpondet in tabula ſinuum arcus grad. </s> <s xml:id="echoid-s14090" xml:space="preserve">10. </s> <s xml:id="echoid-s14091" xml:space="preserve">min. </s> <s xml:id="echoid-s14092" xml:space="preserve">53. </s> <s xml:id="echoid-s14093" xml:space="preserve">quo ablato ex 90. </s> <s xml:id="echoid-s14094" xml:space="preserve">grad. </s> <s xml:id="echoid-s14095" xml:space="preserve">relin-<lb/>quetur aſcenſio recta grad. </s> <s xml:id="echoid-s14096" xml:space="preserve">79. </s> <s xml:id="echoid-s14097" xml:space="preserve">min. </s> <s xml:id="echoid-s14098" xml:space="preserve">7. </s> <s xml:id="echoid-s14099" xml:space="preserve">Quod ſi arcus zodiaci pręciſe Quadrans <lb/>fuerit, erit eius aſcenſio recta Quadrans quoque, nempe grad. </s> <s xml:id="echoid-s14100" xml:space="preserve">90.</s> <s xml:id="echoid-s14101" xml:space="preserve"/> </p> <div xml:id="echoid-div729" type="float" level="2" n="2"> <note position="left" xlink:label="note-364-03" xlink:href="note-364-03a" xml:space="preserve">Quando at <lb/>cus Eclipti <lb/>@æ quadran <lb/>@e minor eſt@</note> </div> <p> <s xml:id="echoid-s14102" xml:space="preserve"><emph style="sc">Si</emph> arcus Quadrante quidem maior, at ſemicirculo minor extiterit, detra-<lb/> <anchor type="note" xlink:label="note-364-04a" xlink:href="note-364-04"/> hendus erit ex ſemicirculo, hoc eſt, ex grad. </s> <s xml:id="echoid-s14103" xml:space="preserve">180. </s> <s xml:id="echoid-s14104" xml:space="preserve">& </s> <s xml:id="echoid-s14105" xml:space="preserve">reliqui incipientis a ſectio-<lb/>ne Autumnali aſcẽſio recta exploranda. </s> <s xml:id="echoid-s14106" xml:space="preserve">Nam ſi ea rurſus a ſemicirculo aufe-<lb/>ratur, remanebit aſcenſio recta arcus propoſiti: </s> <s xml:id="echoid-s14107" xml:space="preserve">quia totus ſemicirculus Zo-<lb/>diaci aſcendit cum toto ſemicirculo Aequatoris. </s> <s xml:id="echoid-s14108" xml:space="preserve"><emph style="sc">Exemplvm</emph>. </s> <s xml:id="echoid-s14109" xml:space="preserve">Quærenda <lb/>ſit aſcenſio recta grad. </s> <s xml:id="echoid-s14110" xml:space="preserve">♋, hoc eſt, arcus continentis grad. </s> <s xml:id="echoid-s14111" xml:space="preserve">100. </s> <s xml:id="echoid-s14112" xml:space="preserve">Detracto hoc <lb/>arcu ex ſemicirculo, remanet arcus grad. </s> <s xml:id="echoid-s14113" xml:space="preserve">80. </s> <s xml:id="echoid-s14114" xml:space="preserve">cuius aſcenſio recta grad. </s> <s xml:id="echoid-s14115" xml:space="preserve">79. <lb/></s> <s xml:id="echoid-s14116" xml:space="preserve">Min. </s> <s xml:id="echoid-s14117" xml:space="preserve">7. </s> <s xml:id="echoid-s14118" xml:space="preserve">ablata a ſemicirculo dabit aſcenſionem propoſiti arcus grad. </s> <s xml:id="echoid-s14119" xml:space="preserve">100.</s> <s xml:id="echoid-s14120" xml:space="preserve"> <pb o="329" file="365" n="366" rhead="Ioan. de Sacro Boſco."/> min 53. </s> <s xml:id="echoid-s14121" xml:space="preserve">Quod ſi arcus Z<unsure/>odiaci præciſe fuerit ſemicirculus, erit & </s> <s xml:id="echoid-s14122" xml:space="preserve">eius aſcenſio <lb/>ſemicirculus, nimirum grad. </s> <s xml:id="echoid-s14123" xml:space="preserve">180.</s> <s xml:id="echoid-s14124" xml:space="preserve"/> </p> <div xml:id="echoid-div730" type="float" level="2" n="3"> <note position="left" xlink:label="note-364-04" xlink:href="note-364-04a" xml:space="preserve">Quando at <lb/>cus Eclipti <lb/>@ę quadran <lb/>@e maior eſt <lb/>minortamẽ <lb/>@emicirculo</note> </div> <p> <s xml:id="echoid-s14125" xml:space="preserve"><emph style="sc">Existente</emph> arcu maiore quidem, quàm ſit ſemicirculus, minore uero, <lb/> <anchor type="note" xlink:label="note-365-01a" xlink:href="note-365-01"/> quàm grad. </s> <s xml:id="echoid-s14126" xml:space="preserve">270. </s> <s xml:id="echoid-s14127" xml:space="preserve">ſubtrahendus erit ex ipſo ſemicirculus, hoc eſt, grad. </s> <s xml:id="echoid-s14128" xml:space="preserve">180. </s> <s xml:id="echoid-s14129" xml:space="preserve">& </s> <s xml:id="echoid-s14130" xml:space="preserve"><lb/>reliqui arcus aſcenſio recta adijcienda rurſus ſemicirculo, ut habeatur aſcen-<lb/>ſio quæſita. </s> <s xml:id="echoid-s14131" xml:space="preserve">E<emph style="sc">XEMPLVM.</emph> Inquirenda ſit aſcenſio recta grad. </s> <s xml:id="echoid-s14132" xml:space="preserve">20. </s> <s xml:id="echoid-s14133" xml:space="preserve">♐, hoc eſt, <lb/>arcus gra. </s> <s xml:id="echoid-s14134" xml:space="preserve">260. </s> <s xml:id="echoid-s14135" xml:space="preserve">Detrahatur ſemicirculus, & </s> <s xml:id="echoid-s14136" xml:space="preserve">remanet arcus gra. </s> <s xml:id="echoid-s14137" xml:space="preserve">80. </s> <s xml:id="echoid-s14138" xml:space="preserve">cuius aſcen <lb/>ſio recta, nempe gra. </s> <s xml:id="echoid-s14139" xml:space="preserve">79. </s> <s xml:id="echoid-s14140" xml:space="preserve">min. </s> <s xml:id="echoid-s14141" xml:space="preserve">7. </s> <s xml:id="echoid-s14142" xml:space="preserve">addita ſemicirculo, dabit aſcenſionem optatam <lb/>grad. </s> <s xml:id="echoid-s14143" xml:space="preserve">259. </s> <s xml:id="echoid-s14144" xml:space="preserve">min. </s> <s xml:id="echoid-s14145" xml:space="preserve">7. </s> <s xml:id="echoid-s14146" xml:space="preserve">Quod ſi arcus Zodiaci præciſe tres Quadrantes conſtituat, <lb/>nimirum grad. </s> <s xml:id="echoid-s14147" xml:space="preserve">270. </s> <s xml:id="echoid-s14148" xml:space="preserve">totidem graduum erit aſcenſio illi debita.</s> <s xml:id="echoid-s14149" xml:space="preserve"/> </p> <div xml:id="echoid-div731" type="float" level="2" n="4"> <note position="right" xlink:label="note-365-01" xlink:href="note-365-01a" xml:space="preserve">Quando at <lb/>cus Eclipti-<lb/>cæ maior <lb/>eſt ſemicir-<lb/>culo, ſed mi <lb/>nor quàm <lb/>grad. 270.</note> </div> <p> <s xml:id="echoid-s14150" xml:space="preserve"><emph style="sc">Qvando</emph> denique arcus tres Quadrantes ſuperauerit, minor tamen in-<lb/> <anchor type="note" xlink:label="note-365-02a" xlink:href="note-365-02"/> tegro circulo extiterit, auferendus erit ex toto circulo, ut a gra. </s> <s xml:id="echoid-s14151" xml:space="preserve">360. </s> <s xml:id="echoid-s14152" xml:space="preserve">& </s> <s xml:id="echoid-s14153" xml:space="preserve">reli-<lb/>qui arcus aſcenſio recta iterum ex circulo integro detrahenda: </s> <s xml:id="echoid-s14154" xml:space="preserve">Relinquetur <lb/>enim quæſita aſcenſio. </s> <s xml:id="echoid-s14155" xml:space="preserve"><emph style="sc">Exemplvm</emph>. </s> <s xml:id="echoid-s14156" xml:space="preserve">Exploranda ſit aſcenſio grad. </s> <s xml:id="echoid-s14157" xml:space="preserve">10. </s> <s xml:id="echoid-s14158" xml:space="preserve">♑, hoc <lb/>eſt, arcus grad. </s> <s xml:id="echoid-s14159" xml:space="preserve">280. </s> <s xml:id="echoid-s14160" xml:space="preserve">Detracto hoc arcu ex grad. </s> <s xml:id="echoid-s14161" xml:space="preserve">360. </s> <s xml:id="echoid-s14162" xml:space="preserve">remanetarcus grad. </s> <s xml:id="echoid-s14163" xml:space="preserve">80. <lb/></s> <s xml:id="echoid-s14164" xml:space="preserve">cuius aſcenſio recta grad. </s> <s xml:id="echoid-s14165" xml:space="preserve">79. </s> <s xml:id="echoid-s14166" xml:space="preserve">min. </s> <s xml:id="echoid-s14167" xml:space="preserve">7. </s> <s xml:id="echoid-s14168" xml:space="preserve">ablata ex 360. </s> <s xml:id="echoid-s14169" xml:space="preserve">manifeſtabit quæſitam aſcen <lb/>ſionem rectam grad. </s> <s xml:id="echoid-s14170" xml:space="preserve">280. </s> <s xml:id="echoid-s14171" xml:space="preserve">min. </s> <s xml:id="echoid-s14172" xml:space="preserve">53. </s> <s xml:id="echoid-s14173" xml:space="preserve">Quod ſi arcus Zodiaci eſt integer circulus, <lb/>aſcendet utiq; </s> <s xml:id="echoid-s14174" xml:space="preserve">cum integro quoque circulo Aequatoris.</s> <s xml:id="echoid-s14175" xml:space="preserve"/> </p> <div xml:id="echoid-div732" type="float" level="2" n="5"> <note position="right" xlink:label="note-365-02" xlink:href="note-365-02a" xml:space="preserve">Quando at <lb/>cus Eclipti <lb/>cę maior eſt <lb/>quàm grad. <lb/>270.</note> </div> <p> <s xml:id="echoid-s14176" xml:space="preserve">Ex his manifeſtum eſt, quanam arte conſtruenda ſit tabula aſcenſionũ re-<lb/> <anchor type="note" xlink:label="note-365-03a" xlink:href="note-365-03"/> ctarum, quæ nimirum in ſphæra recta contingant. </s> <s xml:id="echoid-s14177" xml:space="preserve">Si enim ſupputemus aſcẽſio <lb/>nes omnium arcuum primi Quadrantis Eclipticæ initium ſumentiũ ab ♈, ha-<lb/>bebimus aſcenſiones rectas omnium punctorum primi Quadrantis Eclipticæ. <lb/></s> <s xml:id="echoid-s14178" xml:space="preserve">Quòd ſi ſingulas ex ſemicirculo detrahamur, initio facto a maioribus, ſiue po <lb/>ſterioribus, reliquæ erunt aſcenſiones rectæ omnium punctorũ ſecundi Qua-<lb/>drantis Eclipticæ, initio facto a principio ♈, uſq; </s> <s xml:id="echoid-s14179" xml:space="preserve">ad principium ♎@ Rurſus ſi <lb/>eiuſdem primi Quadrantis aſcenſiones ſemicirculo apponamus, facto initio a <lb/>minoribus, ſiue prioribus, conficiemus aſcenſiones rectas omnium punctorum <lb/>tertij Quadrantis Eclipticæ, initio facto a principio ♈, vſq; </s> <s xml:id="echoid-s14180" xml:space="preserve">ad finem ♐. </s> <s xml:id="echoid-s14181" xml:space="preserve">Si de-<lb/>niq; </s> <s xml:id="echoid-s14182" xml:space="preserve">eaſdem aſcenſiones primi Quadrantis ex toto circulo auferamus, initio <lb/>rurſus facto a maioribus, ſiue poſterioribus, remanebunt aſcenſiones rectæ om <lb/>nium punctorum ultimi Quadrantis Eclipticæ, incipiendo abinitio ♈, vſque <lb/>ad finem ♓, ut conſtat. </s> <s xml:id="echoid-s14183" xml:space="preserve">Itaq; </s> <s xml:id="echoid-s14184" xml:space="preserve">totus labor conſiſtit in eo, ut inquirantur aſcen-<lb/>ſiones ſingulorum arcuum primi Quadrantis Eclipticæ. </s> <s xml:id="echoid-s14185" xml:space="preserve">Hac arte Ioannes Re <lb/>giom. </s> <s xml:id="echoid-s14186" xml:space="preserve">ſupputauit aſcenſiones rectas omnium arcuum Eclipticæ, per ſin-<lb/>gulos gradus procedendo, quam libuit hoc loco apponere, ut ob <lb/>oculos propoſitæ habeantur omnes aſcenſiones arcuum Zodia <lb/>ci, & </s> <s xml:id="echoid-s14187" xml:space="preserve">deſcenſiones ſphæræ rectæ, nec non meditationes <lb/>cœli in qualibet ſphæra. </s> <s xml:id="echoid-s14188" xml:space="preserve">Ad multa enim earum co-<lb/>gnitio utilis eſt, ut ex ijs, quæ in Gnomoni-<lb/>ca noſtra de ſignis aſcendentibus tra-<lb/>didimus, aliqua ex parte per-<lb/>ſpicuum eſſe poteſt.</s> <s xml:id="echoid-s14189" xml:space="preserve"/> </p> <div xml:id="echoid-div733" type="float" level="2" n="6"> <note position="right" xlink:label="note-365-03" xlink:href="note-365-03a" xml:space="preserve">Qua arte t@ <lb/>buia aſcen-<lb/>ſionum re-<lb/>ctarum com <lb/>ſtruatur.</note> </div> <pb o="330" file="366" n="367" rhead="Comment. in III. Cap. Sphæræ"/> </div> <div xml:id="echoid-div735" type="section" level="1" n="257"> <head xml:id="echoid-head268" xml:space="preserve">TABVLA ASCENSIONVM <lb/>Rectarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♈ # ## ♉ # ## ♊ # ## ♋ # ## ♌ # ## ♍ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 0 # 0 # 27 # 54 # 57 # 48 # 90 # 0 # 122 # 12 # 152 # 6 1 # 0 # 55 # 28 # 51 # 58 # 51 # 91 # 6 # 123 # 14 # 153 # 3 2 # 1 # 50 # 29 # 49 # 59 # 54 # 92 # 12 # 124 # 16 # 154 # 0 3 # 2 # 45 # 30 # 46 # 60 # 57 # 93 # 17 # 125 # 18 # 154 # 57 4 # 3 # 40 # 31 # 44 # 62 # 0 # 94 # 22 # 126 # 20 # 155 # 54 5 # 4 # 35 # 32 # 42 # 63 # 3 # 95 # 27 # 127 # 22 # 156 # 51 6 # 5 # 30 # 33 # 40 # 64 # 6 # 96 # 33 # 128 # 24 # 157 # 48 7 # 6 # 25 # 34 # 39 # 65 # 9 # 97 # 38 # 129 # 25 # 158 # 45 8 # 7 # 20 # 35 # 37 # 66 # 13 # 98 # 43 # 130 # 26 # 159 # 41 9 # 8 # 15 # 36 # 36 # 67 # 17 # 99 # 48 # 131 # 27 # 160 # 37 10 # 9 # 11 # 37 # 35 # 68 # 21 # 100 # 53 # 132 # 27 # 161 # 33 11 # 10 # 6 # 38 # 34 # 69 # 25 # 101 # 58 # 133 # 28 # 162 # 29 12 # 11 # 1 # 39 # 33 # 70 # 29 # 103 # 3 # 134 # 29 # 163 # 25 13 # 11 # 57 # 40 # 32 # 71 # 33 # 104 # 8 # 135 # 29 # 164 # 21 14 # 12 # 52 # 41 # 31 # 72 # 38 # 105 # 13 # 136 # 29 # 165 # 17 15 # 13 # 48 # 42 # 31 # 73 # 43 # 106 # 17 # 137 # 29 # 166 # 12 16 # 14 # 43 # 43 # 31 # 74 # 47 # 107 # 22 # 138 # 29 # 167 # 8 17 # 15 # 39 # 44 # 31 # 75 # 52 # 108 # 27 # 139 # 28 # 168 # 3 18 # 16 # 35 # 45 # 31 # 76 # 57 # 109 # 31 # 140 # 27 # 168 # 59 19 # 17 # 31 # 46 # 32 # 78 # 2 # 110 # 35 # 141 # 26 # 169 # 54 20 # 18 # 27 # 47 # 33 # 79 # 7 # 111 # 39 # 142 # 25 # 170 # 49 21 # 19 # 23 # 48 # 33 # 80 # 12 # 112 # 43 # 143 # 24 # 171 # 45 22 # 20 # 19 # 49 # 34 # 81 # 17 # 113 # 47 # 144 # 23 # 172 # 40 23 # 21 # 15 # 50 # 35 # 82 # 22 # 114 # 51 # 145 # 21 # 173 # 35 24 # 22 # 12 # 51 # 36 # 83 # 27 # 115 # 54 # 146 # 20 # 174 # 30 25 # 23 # 9 # 52 # 38 # 84 # 33 # 116 # 57 # 147 # 18 # 175 # 25 26 # 24 # 6 # 53 # 40 # 85 # 38 # 118 # 0 # 148 # 16 # 176 # 20 27 # 25 # 3 # 54 # 42 # 86 # 43 # 119 # 3 # 149 # 14 # 177 # 15 28 # 26 # 0 # 55 # 44 # 87 # 48 # 120 # 6 # 10 # 11 # 178 # 10 29 # 26 # 57 # 56 # 46 # 88 # 54 # 121 # 9 # 151 # 9 # 179 # 5 30 # 27 # 54 # 57 # 48 # 90 # 0 # 122 # 12 # 15<unsure/>2 # 6 # 180 # 0 </note> <pb o="331" file="367" n="368" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div736" type="section" level="1" n="258"> <head xml:id="echoid-head269" xml:space="preserve">RESIDVVM TABVLAE ASCEN <lb/>ſionum rectarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♎ # ## ♏ # ## ♐ # ## ♑ # ## ♒ # ## ♓ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 180 # 0 # 207 # 54 # 237 # 48 # 270 # 0 # 302 # 12 # 332 # 6 1 # 180 # 50 # 208 # 51 # 238 # 51 # 271 # 6 # 303 # 14 # 333 # 3 2 # 181 # 55 # 209 # 49 # 239 # 54 # 272 # 12 # 304 # 16 # 334 # 0 3 # 182 # 45 # 210 # 46 # 240 # 57 # 273 # 17 # 305 # 18 # 334 # 57 4 # 183 # 40 # 211 # 44 # 242 # 0 # 274 # 22 # 306 # 20 # 335 # 54 5 # 184 # 35 # 212 # 42 # 243 # 3 # 275 # 27 # 307 # 22 # 336 # 51 6 # 185 # 30 # 213 # 40 # 244 # 6 # 276 # 33 # 308 # 24 # 337 # 48 7 # 186 # 25 # 214 # 39 # 245 # 9 # 277 # 38 # 309 # 25 # 338 # 45 8 # 187 # 20 # 215 # 37 # 246 # 13 # 278 # 43 # 310 # 26 # 339 # 41 9 # 188 # 15 # 216 # 36 # 247 # 17 # 279 # 48 # 311 # 27 # 340 # 37 10 # 189 # 11 # 117 # 35 # 248 # 21 # 280 # 53 # 312 # 27 # 341 # 33 11 # 190 # 6 # 218 # 34 # 249 # 25 # 281 # 58 # 313 # 28 # 342 # 29 12 # 191 # 1 # 219 # 33 # 250 # 29 # 283 # 3 # 314 # 29 # 343 # 25 13 # 191 # 57 # 220 # 32 # 251 # 33 # 284 # 8 # 315 # 29 # 344 # 21 14 # 192 # 52 # 221 # 31 # 252 # 38 # 285 # 13 # 316 # 29 # 345 # 17 15 # 193 # 48 # 222 # 31 # 253 # 43 # 286 # 17 # 317 # 29 # 346 # 12 16 # 194 # 43 # 223 # 31 # 254 # 47 # 287 # 22 # 318 # 29 # 347 # 8 17 # 195 # 39 # 224 # 31 # 255 # 52 # 288 # 27 # 319 # 28 # 348 # 3 18 # 196 # 35 # 225 # 31 # 256 # 57 # 289 # 31 # 320 # 27 # 348 # 59 19 # 197 # 31 # 226 # 32 # 258 # 2 # 290 # 35 # 321 # 26 # 349 # 54 20 # 198 # 27 # 227 # 33 # 259 # 7 # 291 # 39 # 322 # 25 # 350 # 50 21 # 199 # 23 # 228 # 33 # 260 # 12 # 292 # 43 # 323 # 24 # 351 # 45 22 # 200 # 19 # 229 # 34 # 261 # 17 # 293 # 45 # 324 # 23 # 352 # 40 23 # 201 # 15 # 230 # 35 # 262 # 22 # 294 # 51 # 325 # 21 # 353 # 35 24 # 202 # 12 # 231 # 36 # 263 # 27 # 295 # 54 # 326 # 20 # 354 # 30 25 # 203 # 9 # 232 # 38 # 264 # 33 # 296 # 57 # 327 # 18 # 355 # 25 26 # 204 # 6 # 233 # 40 # 265 # 38 # 298 # 0 # 328 # 16 # 356 # 20 27 # 205 # 3 # 234 # 42 # 266 # 43 # 299 # 3 # 329 # 14 # 357 # 15 28 # 206 # 0 # 235 # 44 # 267 # 48 # 300 # 6 # 330 # 11 # 358 # 10 29 # 206 # 57 # 236 # 46 # 268 # 54 # 301 # 9 # 331 # 9 # 359 # 5 30 # 207 # 54 # 237 # 48 # 270 # 0 # 302 # 12 # 332 # 6 # 360 # 0 </note> <pb o="332" file="368" n="369" rhead="Comment. in III. Cap. Sphæræ"/> </div> <div xml:id="echoid-div737" type="section" level="1" n="259"> <head xml:id="echoid-head270" xml:space="preserve">VSVS TABVLÆ ASCESIONVM <lb/><emph style="sc">RECTARVM</emph>.</head> <p> <s xml:id="echoid-s14190" xml:space="preserve"><emph style="sc">In</emph> capite tabulæ accipiendum eſt ſignum, & </s> <s xml:id="echoid-s14191" xml:space="preserve">in latere ſiniſtro gtadus ſigni. <lb/></s> <s xml:id="echoid-s14192" xml:space="preserve"> <anchor type="note" xlink:label="note-368-01a" xlink:href="note-368-01"/> Nam in communi concurſu ſigni, & </s> <s xml:id="echoid-s14193" xml:space="preserve">gradus propoſiti reperientur gradus, ac <lb/>Minuta Aequatoris. </s> <s xml:id="echoid-s14194" xml:space="preserve">quæ ſimul dato gradu Eclipticæ oriuntur. </s> <s xml:id="echoid-s14195" xml:space="preserve">Sic uides cum <lb/>19. </s> <s xml:id="echoid-s14196" xml:space="preserve">grad. </s> <s xml:id="echoid-s14197" xml:space="preserve">♌, (hoc eſt, cum arcu Eclipticæ inchoato a principio ♈, & </s> <s xml:id="echoid-s14198" xml:space="preserve">termina-<lb/>to in 19. </s> <s xml:id="echoid-s14199" xml:space="preserve">gradu ♌, qui comprehendit gradus 139.) </s> <s xml:id="echoid-s14200" xml:space="preserve">in Horizonte recto coo-<lb/>riri grad. </s> <s xml:id="echoid-s14201" xml:space="preserve">141. </s> <s xml:id="echoid-s14202" xml:space="preserve">min. </s> <s xml:id="echoid-s14203" xml:space="preserve">26. </s> <s xml:id="echoid-s14204" xml:space="preserve">Aequinoctialis circuli. </s> <s xml:id="echoid-s14205" xml:space="preserve">Quod ſi arcui dato minuta adhę <lb/>reant, elicienda erit pars proportionalis, reſpondens oblatis minutis, ut dictũ <lb/>eſt in uſu tabulæ Declinationum, eaq; </s> <s xml:id="echoid-s14206" xml:space="preserve">adijcienda aſcenſioni arcus integrorũ <lb/>graduum proxime minoris. </s> <s xml:id="echoid-s14207" xml:space="preserve"><emph style="sc">Exemplvm</emph>. </s> <s xml:id="echoid-s14208" xml:space="preserve">Quæratur aſcenſio recta arcus Ecli-<lb/>pticæ co ntinentis grad. </s> <s xml:id="echoid-s14209" xml:space="preserve">125. </s> <s xml:id="echoid-s14210" xml:space="preserve">mi<unsure/>n. </s> <s xml:id="echoid-s14211" xml:space="preserve">40. </s> <s xml:id="echoid-s14212" xml:space="preserve">hoc eſt, aſcenſio grad. </s> <s xml:id="echoid-s14213" xml:space="preserve">5. </s> <s xml:id="echoid-s14214" xml:space="preserve">min. </s> <s xml:id="echoid-s14215" xml:space="preserve">40. </s> <s xml:id="echoid-s14216" xml:space="preserve">♌. </s> <s xml:id="echoid-s14217" xml:space="preserve">De-<lb/>traho aſcenſionem grad. </s> <s xml:id="echoid-s14218" xml:space="preserve">5. </s> <s xml:id="echoid-s14219" xml:space="preserve">♌, uidelicet grad. </s> <s xml:id="echoid-s14220" xml:space="preserve">127. </s> <s xml:id="echoid-s14221" xml:space="preserve">min. </s> <s xml:id="echoid-s14222" xml:space="preserve">22. </s> <s xml:id="echoid-s14223" xml:space="preserve">ex aſcenſione gra. <lb/></s> <s xml:id="echoid-s14224" xml:space="preserve">6. </s> <s xml:id="echoid-s14225" xml:space="preserve">♌, nempe ex grad. </s> <s xml:id="echoid-s14226" xml:space="preserve">128. </s> <s xml:id="echoid-s14227" xml:space="preserve">min. </s> <s xml:id="echoid-s14228" xml:space="preserve">24. </s> <s xml:id="echoid-s14229" xml:space="preserve">remanetq; </s> <s xml:id="echoid-s14230" xml:space="preserve">grad. </s> <s xml:id="echoid-s14231" xml:space="preserve">1. </s> <s xml:id="echoid-s14232" xml:space="preserve">min. </s> <s xml:id="echoid-s14233" xml:space="preserve">2. </s> <s xml:id="echoid-s14234" xml:space="preserve">differentia utri<unsure/>uſ-<lb/>que aſcenſionis, quæ conuenit 60. </s> <s xml:id="echoid-s14235" xml:space="preserve">Minutis. </s> <s xml:id="echoid-s14236" xml:space="preserve">Quare ſecundum regulam propor <lb/>tionum Minutis 40. </s> <s xml:id="echoid-s14237" xml:space="preserve">debentur Minuta 41 {1/3}. </s> <s xml:id="echoid-s14238" xml:space="preserve">quæ ſi adijciantur aſcenſioni gra <lb/>5. </s> <s xml:id="echoid-s14239" xml:space="preserve">♌, habebitur aſcenſio propoſiti arcus grad. </s> <s xml:id="echoid-s14240" xml:space="preserve">128. </s> <s xml:id="echoid-s14241" xml:space="preserve">min. </s> <s xml:id="echoid-s14242" xml:space="preserve">3. </s> <s xml:id="echoid-s14243" xml:space="preserve">fere.</s> <s xml:id="echoid-s14244" xml:space="preserve"/> </p> <div xml:id="echoid-div737" type="float" level="2" n="1"> <note position="left" xlink:label="note-368-01" xlink:href="note-368-01a" xml:space="preserve">Quomodo <lb/>ex tabula <lb/>aſcenſionũ <lb/>rectarũ eli-<lb/>ciãtur aſcẽ <lb/>ſiones rectę</note> </div> <p> <s xml:id="echoid-s14245" xml:space="preserve"><emph style="sc">Qvòd</emph> ſi inquirenda ſit aſcenſio arcus Eclipticæ non a princip io ♈, inchoa <lb/>ti, v.</s> <s xml:id="echoid-s14246" xml:space="preserve">g.</s> <s xml:id="echoid-s14247" xml:space="preserve">arcus Zodiaci incipientis a grad. </s> <s xml:id="echoid-s14248" xml:space="preserve">10. </s> <s xml:id="echoid-s14249" xml:space="preserve">♉, & </s> <s xml:id="echoid-s14250" xml:space="preserve">terminati in grad. </s> <s xml:id="echoid-s14251" xml:space="preserve">18. </s> <s xml:id="echoid-s14252" xml:space="preserve">♊, qui <lb/>complectitur grad. </s> <s xml:id="echoid-s14253" xml:space="preserve">38. </s> <s xml:id="echoid-s14254" xml:space="preserve">Detrahenda erit aſcenſio grad. </s> <s xml:id="echoid-s14255" xml:space="preserve">10. </s> <s xml:id="echoid-s14256" xml:space="preserve">♉, nempe grad. </s> <s xml:id="echoid-s14257" xml:space="preserve">37. <lb/></s> <s xml:id="echoid-s14258" xml:space="preserve">mio. </s> <s xml:id="echoid-s14259" xml:space="preserve">35. </s> <s xml:id="echoid-s14260" xml:space="preserve">ab aſcenſione grad. </s> <s xml:id="echoid-s14261" xml:space="preserve">18. </s> <s xml:id="echoid-s14262" xml:space="preserve">♊, videlicet a grad. </s> <s xml:id="echoid-s14263" xml:space="preserve">76. </s> <s xml:id="echoid-s14264" xml:space="preserve">min. </s> <s xml:id="echoid-s14265" xml:space="preserve">57. </s> <s xml:id="echoid-s14266" xml:space="preserve">vt relinquatur <lb/>aſcenſio propoſiti arc us grad. </s> <s xml:id="echoid-s14267" xml:space="preserve">39. </s> <s xml:id="echoid-s14268" xml:space="preserve">min. </s> <s xml:id="echoid-s14269" xml:space="preserve">22.</s> <s xml:id="echoid-s14270" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14271" xml:space="preserve"><emph style="sc">Hac</emph> ratione facile colliges aſcenſionem rectam cuiuſlibet ſigni Zo diaci<unsure/> <lb/>per ſe ſumpti, ueluti in ſequenti formula apparet.</s> <s xml:id="echoid-s14272" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>##### ASCENSIONES SIGNORVM IN \\ ſphæra recta. <lb/>♈ Aries # ♍ Virgo # ♎ Libra # ♓ Piſces # 27. 54 <lb/>♉ Taurus # ♌ Leo # ♏ Scorpius # ♒ Aquarius # 29. 54 <lb/>♊ Gemini # ♋ Cancer # ♐ Sagittarius # ♑ Capricornus # 32. 12 <lb/></note> <p> <s xml:id="echoid-s14273" xml:space="preserve"><emph style="sc">Perspicve</emph> hinc ſequitur, in ſphæra recta quatuor ſigna, quæ duo pun-<lb/> <anchor type="note" xlink:label="note-368-03a" xlink:href="note-368-03"/> cta ſolſtitialia circunſtant, oriri recte, reliqua uero octo oblique. </s> <s xml:id="echoid-s14274" xml:space="preserve">Item arcus. <lb/></s> <s xml:id="echoid-s14275" xml:space="preserve">illos obliquius oriri, qui propinquiores ſunt punctis ęquinoctialibus, rectius <lb/>vero eos, qui punctis Solſtitialibus uiciniores exiſtunt. </s> <s xml:id="echoid-s14276" xml:space="preserve">Idem dices de deſcen <lb/>ſionibus, & </s> <s xml:id="echoid-s14277" xml:space="preserve">cęli<unsure/> meditationi<unsure/>bus. </s> <s xml:id="echoid-s14278" xml:space="preserve">In ſphęra igitur recta quaterna ſemper ſigna <lb/>æquales habent aſcẽſiones, ęqualesq́. </s> <s xml:id="echoid-s14279" xml:space="preserve">deſcenſiones, & </s> <s xml:id="echoid-s14280" xml:space="preserve">cęli meditationes. </s> <s xml:id="echoid-s14281" xml:space="preserve">Quę <lb/>quidem omnia demonſtrari poſſunt ex ſphęricis triangulis.</s> <s xml:id="echoid-s14282" xml:space="preserve"/> </p> <div xml:id="echoid-div738" type="float" level="2" n="2"> <note position="left" xlink:label="note-368-03" xlink:href="note-368-03a" xml:space="preserve">Quæ ſigna <lb/>recte oiian <lb/>tur in ſphę <lb/>ra recta, & <lb/>q̃ @oblique.</note> </div> </div> <div xml:id="echoid-div740" type="section" level="1" n="260"> <head xml:id="echoid-head271" style="it" xml:space="preserve">DE ORTV, ET OCCASV SIGNORVM in ſphæraobliqua.</head> <note position="left" xml:space="preserve">Ortus, & oe <lb/>caſus ſignõ <lb/>rũ in ſphæ-<lb/>ra obliqua.</note> <p style="it"> <s xml:id="echoid-s14283" xml:space="preserve">IN ſphæra autem obliqua, ſiue decliui, duæ medietates Zodiaci ad-<lb/>æquantur ſuis aſcenſionibus. </s> <s xml:id="echoid-s14284" xml:space="preserve">Medietates dico, quæ ſumuntur à duobus <pb o="333" file="369" n="370" rhead="Ioan. de Sacro Boſco."/> punctis ęquinoctialibus, quia medietas Zodiaci, quæ eſt à principio Arietis <lb/>uſq; </s> <s xml:id="echoid-s14285" xml:space="preserve">ad finem V<unsure/>irginis, oritur cum medietate Aequinoctialis ſibi conter-<lb/>minali. </s> <s xml:id="echoid-s14286" xml:space="preserve">Similiter alia medietas Zodiaci oritur cum reliqua medietate Ae <lb/>quinoctialis. </s> <s xml:id="echoid-s14287" xml:space="preserve">Partes autem illarum medietatum uariantur ſecundum ſuas <lb/>aſcenſiones, quoniam in illa mndietate Zodiaci, quę eſt à principio Arie-<lb/>tis uſq; </s> <s xml:id="echoid-s14288" xml:space="preserve">ad finem uirginis, ſem per maior pars oritur de Zodiaco, quàm de <lb/>Aequinoctiali; </s> <s xml:id="echoid-s14289" xml:space="preserve">& </s> <s xml:id="echoid-s14290" xml:space="preserve">tamen illæ medietates ſimul peroriuntur. </s> <s xml:id="echoid-s14291" xml:space="preserve">E conuerſo <lb/>contingit in reliqua medietate Zodiaci, quæ eſt a principio Librę uſque ad <lb/>finem Piſcium: </s> <s xml:id="echoid-s14292" xml:space="preserve">Semper enim maior pars oritur de Aequinoctiali, quàm de <lb/>Zodiaco; </s> <s xml:id="echoid-s14293" xml:space="preserve">& </s> <s xml:id="echoid-s14294" xml:space="preserve">tamen illę medietates ſimul peroriuntur. </s> <s xml:id="echoid-s14295" xml:space="preserve">Vnde hic patet in-<lb/>ſtantia facta manifeſtior contra argumentationem ſuperius dictam.</s> <s xml:id="echoid-s14296" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div741" type="section" level="1" n="261"> <head xml:id="echoid-head272" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s14297" xml:space="preserve"><emph style="sc">Proponit</emph> nunc tres regulas, quibus ortus, & </s> <s xml:id="echoid-s14298" xml:space="preserve">occaſus ſignorum, ſeu <lb/>arcuum Eclipticæ, in quauis obliqua ſphæra cognoſcatur. </s> <s xml:id="echoid-s14299" xml:space="preserve">Prima eſt: </s> <s xml:id="echoid-s14300" xml:space="preserve">Medie-<lb/>tates Zodiaci initiũ ſumentes à punctis æquinoctialibus in quo libet Horizõte <lb/>obliquo adæquantur ſuis aſcenſionibus, hoc eſt, cum ipſis coaſcẽdunt medieta <lb/>tes quoq; </s> <s xml:id="echoid-s14301" xml:space="preserve">Aequatoris, nimirũ gr. </s> <s xml:id="echoid-s14302" xml:space="preserve">180. </s> <s xml:id="echoid-s14303" xml:space="preserve">Ita vt in ſpatio 12. </s> <s xml:id="echoid-s14304" xml:space="preserve">horarũ integre ſupra <lb/>Horizontem emergant<unsure/>: </s> <s xml:id="echoid-s14305" xml:space="preserve">Partes tamen dictarum medietatum non ſunt æqua-<lb/>les ſuis aſcenſionibus, hoc eſt, cum nulla parte ipſarum cooritur pars æqualis <lb/>Aequatoris, ſed vel maior, uel minor, ut de partibus Quadrantum in ſphæra <lb/>recta dictum eſt; </s> <s xml:id="echoid-s14306" xml:space="preserve">quoniam cum ſigno ♈, aſcendunt Romæ grad. </s> <s xml:id="echoid-s14307" xml:space="preserve">17. </s> <s xml:id="echoid-s14308" xml:space="preserve">min. </s> <s xml:id="echoid-s14309" xml:space="preserve">21. </s> <s xml:id="echoid-s14310" xml:space="preserve">At <lb/>cum ſigno ♍, aſcendunt grad. </s> <s xml:id="echoid-s14311" xml:space="preserve">38. </s> <s xml:id="echoid-s14312" xml:space="preserve">min. </s> <s xml:id="echoid-s14313" xml:space="preserve">27. </s> <s xml:id="echoid-s14314" xml:space="preserve">&</s> <s xml:id="echoid-s14315" xml:space="preserve">c. </s> <s xml:id="echoid-s14316" xml:space="preserve">Prior pars regulæ perſpicua eſt, <lb/>quia cum Ecliptica, & </s> <s xml:id="echoid-s14317" xml:space="preserve">Aequator ſe mutuo diuidant bifariam in puncti@ <lb/>ęquinoctialibus, neceſſe eſt, initium utriuſque medietatis eodem tempore Ho <lb/>rizontem quemcunq; </s> <s xml:id="echoid-s14318" xml:space="preserve">attingere; </s> <s xml:id="echoid-s14319" xml:space="preserve">idemq; </s> <s xml:id="echoid-s14320" xml:space="preserve">dices de punctis earundem extremis, <lb/>propterea quòd idem punctum eſt utriuſque initium, idemqne utriuſque ex-<lb/>tremum: </s> <s xml:id="echoid-s14321" xml:space="preserve">Vnde ſimul cooriuntur. </s> <s xml:id="echoid-s14322" xml:space="preserve">Poſterior autem regulæ pars demonſtrari fa <lb/>eile poteſt ex propoſ. </s> <s xml:id="echoid-s14323" xml:space="preserve">10. </s> <s xml:id="echoid-s14324" xml:space="preserve">lib. </s> <s xml:id="echoid-s14325" xml:space="preserve">1. </s> <s xml:id="echoid-s14326" xml:space="preserve">Menelai, uel ex propoſ. </s> <s xml:id="echoid-s14327" xml:space="preserve">11. </s> <s xml:id="echoid-s14328" xml:space="preserve">noſtrorum triang-<lb/>ſphær. </s> <s xml:id="echoid-s14329" xml:space="preserve">quia Zodiaci medietas ab ♈, vſque ad ♎, efficit ſemper minorem an-<lb/>gulum cum Horizonte, quam Aequator. </s> <s xml:id="echoid-s14330" xml:space="preserve">Quate maior pars Zodiaci orietur <lb/>ſemper, quàm Aequatoris: </s> <s xml:id="echoid-s14331" xml:space="preserve">Reliqua vero medietas Zodiaci à ♎, vſque ad ♈, <lb/>maiorem ſemper angulum cum Horizonte conſtituit, quam Aequator. </s> <s xml:id="echoid-s14332" xml:space="preserve">Vnde <lb/>maior pars Aequatoris pero@ietur, quàm Zodiaci. </s> <s xml:id="echoid-s14333" xml:space="preserve">Totæ tamen medietates ſi-<lb/>mul perorientur, ut dictum eſt. </s> <s xml:id="echoid-s14334" xml:space="preserve">Verum hæc omnia perſpicua ſunt in ſphæra <lb/>materiali, manifeſtaque erunt ex tabulis aſcenſionum obliquarum.</s> <s xml:id="echoid-s14335" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14336" xml:space="preserve"><emph style="sc">Colligit</emph> ex his rurſus inſtantiam aduerſus argumentationem ſupe-<lb/>rius add@ctam; </s> <s xml:id="echoid-s14337" xml:space="preserve">videlicet non ualere hanc conſecutionem. </s> <s xml:id="echoid-s14338" xml:space="preserve">Sunt duo arcus <lb/> <anchor type="note" xlink:label="note-369-01a" xlink:href="note-369-01"/> æqual es in ſphæra, & </s> <s xml:id="echoid-s14339" xml:space="preserve">ſemper maior pars unius perorta eſt, quàm alterius: </s> <s xml:id="echoid-s14340" xml:space="preserve">igi-<lb/>tur citius orietur totus ille, quàm totus iſte. </s> <s xml:id="echoid-s14341" xml:space="preserve">Soluitur enim facillime hæc ar-<lb/>gumentatio ex ijs, quæ dicta ſunt in prima hac regula, ut manifeſtum eſt.</s> <s xml:id="echoid-s14342" xml:space="preserve"/> </p> <div xml:id="echoid-div741" type="float" level="2" n="1"> <note position="right" xlink:label="note-369-01" xlink:href="note-369-01a" xml:space="preserve">Compar@-<lb/>tio aſcẽſio@ <lb/>nũ in ſphæ <lb/>ra obliqua <lb/>cum aſcen-<lb/>ſionibus <lb/>in ſpl@ær<gap/> <lb/>recta.</note> </div> <p style="it"> <s xml:id="echoid-s14343" xml:space="preserve"><emph style="sc">Arcvs</emph> autem, qui ſuccedunt Arieti uſque ad finem Virginis, in <lb/>ſphæra obliqua minuunt aſcenſiones ſuas ſupra aſcenſione s eorundem ar- <pb o="334" file="370" n="371" rhead="Comment. in III. Cap. Sphæræ"/> cuum in ſphæra recta, quiaminus oritur de Aequinoctiali. </s> <s xml:id="echoid-s14344" xml:space="preserve">Et arcus, qui <lb/>ſuccedunt Librę uſque ad finem Piſcium, in ſphæra obliqua augent aſcen-<lb/>ſiones ſuas ſupra aſcenſiones eorundem arcuum in ſphæra recta, quia plus <lb/>oritur de Aquinoctiali. </s> <s xml:id="echoid-s14345" xml:space="preserve">Augent, dico, ſecundum tantam quantitatem, in <lb/>quanta arcus ſuccedentes Arieti minuunt.</s> <s xml:id="echoid-s14346" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div743" type="section" level="1" n="262"> <head xml:id="echoid-head273" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s14347" xml:space="preserve"><emph style="sc">Comparat</emph> in hac ſecunda regula ſphæram quamlibet obliquam cum <lb/>ſphæra recta, dicens, arcus Zodiaci f<unsure/>ingulos, ab Ariete incipiendo, uſque ad ſi-<lb/>nem Virginis in ſphæra obliqua habere minores ſingulas aſcenſiones, quã <gap/> <lb/>ſphæra recta: </s> <s xml:id="echoid-s14348" xml:space="preserve">At arcus Zodiaci ſingulos, à Libra incipiendo, uſ ad finem Pi-<lb/>ſcium maiores habere ſingulas aſcenſiones in ſphæra obliqua, quàm in ſphęra <lb/>recta, & </s> <s xml:id="echoid-s14349" xml:space="preserve">tanto maiores, quanto minores ſunt aſcenſiones priorum arcuum, ſi <lb/>nimirũ ęquales arcus utrinq; </s> <s xml:id="echoid-s14350" xml:space="preserve">ſumantur. </s> <s xml:id="echoid-s14351" xml:space="preserve">Verbi gratia. </s> <s xml:id="echoid-s14352" xml:space="preserve">Romæ cũ fine ♉, aſcen-<lb/>dunt grad. </s> <s xml:id="echoid-s14353" xml:space="preserve">38. </s> <s xml:id="echoid-s14354" xml:space="preserve">min. </s> <s xml:id="echoid-s14355" xml:space="preserve">27. </s> <s xml:id="echoid-s14356" xml:space="preserve">In ſphæra recta uerò grad. </s> <s xml:id="echoid-s14357" xml:space="preserve">57. </s> <s xml:id="echoid-s14358" xml:space="preserve">min. </s> <s xml:id="echoid-s14359" xml:space="preserve">48. </s> <s xml:id="echoid-s14360" xml:space="preserve">Vides igitur illam <lb/>aſcenſionem ab hac ſuperari grad. </s> <s xml:id="echoid-s14361" xml:space="preserve">19. </s> <s xml:id="echoid-s14362" xml:space="preserve">Min. </s> <s xml:id="echoid-s14363" xml:space="preserve">21. </s> <s xml:id="echoid-s14364" xml:space="preserve">At Romæ finis ♏, aſcendit cum <lb/>grad. </s> <s xml:id="echoid-s14365" xml:space="preserve">77. </s> <s xml:id="echoid-s14366" xml:space="preserve">min. </s> <s xml:id="echoid-s14367" xml:space="preserve">9. </s> <s xml:id="echoid-s14368" xml:space="preserve">In recta autem ſphęra cum grad. </s> <s xml:id="echoid-s14369" xml:space="preserve">57. </s> <s xml:id="echoid-s14370" xml:space="preserve">min. </s> <s xml:id="echoid-s14371" xml:space="preserve">48. </s> <s xml:id="echoid-s14372" xml:space="preserve">ubi uides, hanc ab <lb/>illa ſuperari quoque grad. </s> <s xml:id="echoid-s14373" xml:space="preserve">19. </s> <s xml:id="echoid-s14374" xml:space="preserve">min. </s> <s xml:id="echoid-s14375" xml:space="preserve">21. </s> <s xml:id="echoid-s14376" xml:space="preserve">& </s> <s xml:id="echoid-s14377" xml:space="preserve">ſic de cæteris. </s> <s xml:id="echoid-s14378" xml:space="preserve">Hcc autem manifeſtum <lb/>eſt ex doctrina triangulorum ſphæricorum, & </s> <s xml:id="echoid-s14379" xml:space="preserve">experientia deprehenditur in <lb/>ſphęra materiali, & </s> <s xml:id="echoid-s14380" xml:space="preserve">ex tabulis aſcenſionum obliquarum.</s> <s xml:id="echoid-s14381" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s14382" xml:space="preserve">EX hoc patet, quod duo arcus ęquales, & </s> <s xml:id="echoid-s14383" xml:space="preserve">oppoſiti in ſphæra decli-<lb/> <anchor type="note" xlink:label="note-370-01a" xlink:href="note-370-01"/> ui habent aſcenſiones ſuas innctas æquales aſcenſionibus eorundem arcuum <lb/>in ſphęra recta ſimul ſumptis. </s> <s xml:id="echoid-s14384" xml:space="preserve">quia quanta eſt diminutio ex u<unsure/>na parte, tan <lb/>ta eſt additio ex altera. </s> <s xml:id="echoid-s14385" xml:space="preserve">Licet enim arcus aſcenſionum inter ſe ſint inæqua-<lb/>les, tamen quantum unus minor eſt, tantum recuperat alius, & </s> <s xml:id="echoid-s14386" xml:space="preserve">ſic patet <lb/>adęquatio.</s> <s xml:id="echoid-s14387" xml:space="preserve"/> </p> <div xml:id="echoid-div743" type="float" level="2" n="1"> <note position="left" xlink:label="note-370-01" xlink:href="note-370-01a" xml:space="preserve">Duo arcus <lb/>oppoſiti, & <lb/>æquales ſi-<lb/>mul habẽt <lb/>ſuas aſcen-<lb/>ẽones æqua <lb/>les aſcenſio <lb/>nibus eorũ <lb/>da in ſphæ <lb/>@a recta.</note> </div> </div> <div xml:id="echoid-div745" type="section" level="1" n="263"> <head xml:id="echoid-head274" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s14388" xml:space="preserve">Ex ſecunda regula manifeſtum eſt, in ſphæra @ obliqua quacunque ſigna <lb/>ſeu arcus oppoſitos non habere aſcenſiones æquales, ſi uidelicet arcus initium <lb/>ſumant ab Aequinoctialibus punctis. </s> <s xml:id="echoid-s14389" xml:space="preserve">Nam cũ arcus oppoſiti æquales in ſphæ-<lb/>ra recta æquales habeant aſcenſiones, in ſphæra autem obliqua quacunque <lb/>minor ſit aſcenſio arcus a principio ♈, inchoati, quàm in ſphæra recta, ma-<lb/>ior autem aſcenſio arcus a principio ♎, incepti in ſphæra eadem obliqua, <lb/>quàm in recta, perſpicuum eſt, arcus oppoſitos habere inæquales aſcenſiones <lb/>in ſphæra obliqua: </s> <s xml:id="echoid-s14390" xml:space="preserve">Idcirco infert auctor ex hac ſecunda regula, arcus hu-<lb/>iuſmodi oppoſitos in ſphæra qualibet obliqua habere aſcenſiones ſimul <lb/>ſumptas æquales aſcenſionibus eorundem in ſphæra recta ſimul ſumptis, quam <lb/>uis inter ſe ſint admodum inæquales; </s> <s xml:id="echoid-s14391" xml:space="preserve">quia uidelicet, quanto maior eſt aſcenſio <lb/>unius in ſphæra obliqua, quã in ſphæra recta, tanto minor eſt aſcenſio alterius <lb/>in eadem ſphæræ obliquitate, quàm in recta ſphæra. </s> <s xml:id="echoid-s14392" xml:space="preserve">Ratio autem huius pen-<lb/>det ex propoſ. </s> <s xml:id="echoid-s14393" xml:space="preserve">3. </s> <s xml:id="echoid-s14394" xml:space="preserve">lib. </s> <s xml:id="echoid-s14395" xml:space="preserve">1. </s> <s xml:id="echoid-s14396" xml:space="preserve">Arithmetices Iordani, ubi demonſtrat, Si duo numeri <lb/>inæquales circa duos numeros æquales ponantur, ita ut maximus inæqua-<lb/>lium eodem numero uincat alterum æqualium, quo minus ab altero ſupe-<lb/>ratur, duos inæquales ſimul æquales eſſe duobus æqualibus ſimul: </s> <s xml:id="echoid-s14397" xml:space="preserve">ut conſtat <pb o="335" file="371" n="372" rhead="Ioan. de Sacro Boſco."/> in his numeris, 4. </s> <s xml:id="echoid-s14398" xml:space="preserve">9. </s> <s xml:id="echoid-s14399" xml:space="preserve">9. </s> <s xml:id="echoid-s14400" xml:space="preserve">14. </s> <s xml:id="echoid-s14401" xml:space="preserve">Item in his, 20. </s> <s xml:id="echoid-s14402" xml:space="preserve">70. </s> <s xml:id="echoid-s14403" xml:space="preserve">70. </s> <s xml:id="echoid-s14404" xml:space="preserve">120. </s> <s xml:id="echoid-s14405" xml:space="preserve">Sic igitur fit in aſcenſioni-<lb/>bus. </s> <s xml:id="echoid-s14406" xml:space="preserve">Nam duæ aſcenſiones duorum arcuum oppoſitorum in ſphæra recta ſunt <lb/>ęquales, quibus circumponuntur aſcenſiones inæquales eorundem arcuum in <lb/>ſphæra@ obliqua, ita vt eodem exceſſu ſuperet maior æqualem alteram, quo mi <lb/>nor ab altera æquali ſuperatur. </s> <s xml:id="echoid-s14407" xml:space="preserve">Vt apparet in his quatuor aſcenſionibus, grad. <lb/></s> <s xml:id="echoid-s14408" xml:space="preserve">17. </s> <s xml:id="echoid-s14409" xml:space="preserve">min. </s> <s xml:id="echoid-s14410" xml:space="preserve">21. </s> <s xml:id="echoid-s14411" xml:space="preserve">grad. </s> <s xml:id="echoid-s14412" xml:space="preserve">27. </s> <s xml:id="echoid-s14413" xml:space="preserve">min. </s> <s xml:id="echoid-s14414" xml:space="preserve">54. </s> <s xml:id="echoid-s14415" xml:space="preserve">grad. </s> <s xml:id="echoid-s14416" xml:space="preserve">27. </s> <s xml:id="echoid-s14417" xml:space="preserve">min. </s> <s xml:id="echoid-s14418" xml:space="preserve">54. </s> <s xml:id="echoid-s14419" xml:space="preserve">grad. </s> <s xml:id="echoid-s14420" xml:space="preserve">38. </s> <s xml:id="echoid-s14421" xml:space="preserve">min. </s> <s xml:id="echoid-s14422" xml:space="preserve">27. </s> <s xml:id="echoid-s14423" xml:space="preserve">Quarum prima <lb/>eſt Arietis aſcenſio Romæ; </s> <s xml:id="echoid-s14424" xml:space="preserve">ſecunda, aſcenſio eiuſdem Ar<unsure/>ietis in ſphæra recta; </s> <s xml:id="echoid-s14425" xml:space="preserve"><lb/>Tertia, aſcenſio Libræ ſigni oppoſiti in ſphęra recta; </s> <s xml:id="echoid-s14426" xml:space="preserve">Quarta denique, aſcenſio <lb/>eiuſdẽ Libræ Romæ; </s> <s xml:id="echoid-s14427" xml:space="preserve">& </s> <s xml:id="echoid-s14428" xml:space="preserve">quia tantũ prima ſuperatur à ſecunda, quantum quarta <lb/>ſuperat tertiã; </s> <s xml:id="echoid-s14429" xml:space="preserve">(eſt enim utrobiq; </s> <s xml:id="echoid-s14430" xml:space="preserve">exceſſus grad. </s> <s xml:id="echoid-s14431" xml:space="preserve">10. </s> <s xml:id="echoid-s14432" xml:space="preserve">min. </s> <s xml:id="echoid-s14433" xml:space="preserve">33.) </s> <s xml:id="echoid-s14434" xml:space="preserve">ideo prima, & </s> <s xml:id="echoid-s14435" xml:space="preserve">quar <lb/>ta ſimul efficiunt tot gradus, & </s> <s xml:id="echoid-s14436" xml:space="preserve">minuta, quot conſtituuntur ex medijs duabus, <lb/>nempe grad. </s> <s xml:id="echoid-s14437" xml:space="preserve">55. </s> <s xml:id="echoid-s14438" xml:space="preserve">min. </s> <s xml:id="echoid-s14439" xml:space="preserve">48. </s> <s xml:id="echoid-s14440" xml:space="preserve">Eademque eſt ratio habenda de cæteris.</s> <s xml:id="echoid-s14441" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14442" xml:space="preserve"><emph style="sc">Rvrsvs</emph> arcus æquales, æqualiterque ab alterutro punctorum ſolſtitia-<lb/> <anchor type="note" xlink:label="note-371-01a" xlink:href="note-371-01"/> lium remoti habent aſcenſiones ſimul ſumptas æquales aſcenſionibus eorun-<lb/>dem in ſphæra recta ſimul ſumptis, nempe ♉, & </s> <s xml:id="echoid-s14443" xml:space="preserve">♌; </s> <s xml:id="echoid-s14444" xml:space="preserve">♓, & </s> <s xml:id="echoid-s14445" xml:space="preserve">♎, &</s> <s xml:id="echoid-s14446" xml:space="preserve">c. </s> <s xml:id="echoid-s14447" xml:space="preserve">ut demonſtrãt <lb/>Geber, & </s> <s xml:id="echoid-s14448" xml:space="preserve">Ioan. </s> <s xml:id="echoid-s14449" xml:space="preserve">Regiom. </s> <s xml:id="echoid-s14450" xml:space="preserve">lib. </s> <s xml:id="echoid-s14451" xml:space="preserve">2. </s> <s xml:id="echoid-s14452" xml:space="preserve">Epitomes propoſ. </s> <s xml:id="echoid-s14453" xml:space="preserve">20.</s> <s xml:id="echoid-s14454" xml:space="preserve"/> </p> <div xml:id="echoid-div745" type="float" level="2" n="1"> <note position="right" xlink:label="note-371-01" xlink:href="note-371-01a" xml:space="preserve">Arcus æqu@ <lb/>les, æquali-<lb/>terq́; ab al-<lb/>terutro pun <lb/>ctorum ſol <lb/>ſtitialiũ re-<lb/>moti habẽt <lb/>in ſphæra <lb/>obliqua a-<lb/>ſcẽſiones ſi-<lb/>mul ſum-<lb/>ptas ęqua-<lb/>les aſcenſio <lb/>nibus eorũ-<lb/>dem ſimul <lb/>ſ@mptis in <lb/>ſphæra re-<lb/>cta.</note> </div> <p> <s xml:id="echoid-s14455" xml:space="preserve"><emph style="sc">Eodem</emph> pacto erunt aſcenſiones quorumlibet duorum arcuũ æqualium <lb/>& </s> <s xml:id="echoid-s14456" xml:space="preserve">oppoſitorum, etiamſi non initium ſumant à punctis ęquinoctiorum, ſimul <lb/>ſumptæ æquales aſcenſionibus eorundem arcuũ in ſphæra recta ſimul ſumptis, <lb/>quamuis inter ſe ſint inęquales: </s> <s xml:id="echoid-s14457" xml:space="preserve">Verum tamen eſt, tunc non ſemper aſcenſio-<lb/>nem obliquam arcus, qui in medietate Zodiaci Borea comprehenditur, mino-<lb/>rem eſſe aſcenſione recta eiuſdem arcus, aſcenſionem uero obliquam arcus in <lb/>medietate Zodiaci Auſtrina contenti maiorem aſcenſione recta eiuſdẽ arcus; <lb/></s> <s xml:id="echoid-s14458" xml:space="preserve">ſed quandoque illam eſſe maiorem, hanc vero minorem, quandoq; </s> <s xml:id="echoid-s14459" xml:space="preserve">vero illam <lb/>minorem, & </s> <s xml:id="echoid-s14460" xml:space="preserve">hanc maiorem. </s> <s xml:id="echoid-s14461" xml:space="preserve">Quæ quidem omnia Geometrice poſſunt oſtendi <lb/>ex doctrina triangulorum ſphæricorum, clariſſimeq́. </s> <s xml:id="echoid-s14462" xml:space="preserve">perſpiciuntur in tabulis <lb/>aſcenſionum obliquar<unsure/>um. </s> <s xml:id="echoid-s14463" xml:space="preserve">Nihilominus hoc ipſum hac ratione confirmatio po <lb/>terit. </s> <s xml:id="echoid-s14464" xml:space="preserve">Sint duo ſigna oppoſita ♌, & </s> <s xml:id="echoid-s14465" xml:space="preserve">♒. </s> <s xml:id="echoid-s14466" xml:space="preserve">Dico aſcenſiones eorum ſimul ſumptas <lb/>æquales eſſe aſcenſionibus eorundem ſimul ſumptis in ſphæra recta. </s> <s xml:id="echoid-s14467" xml:space="preserve">Quoniã <lb/>enim aſcenſio ♌ & </s> <s xml:id="echoid-s14468" xml:space="preserve">aſcenſio ♉, in ſphæra obliqua ſimul ſumptæ æquales ſunt <lb/>aſcenſionibus ſimul ſumptis, quas habent in ſphæra recta, vt dictum eſt, quia <lb/>hæc ſigna ęqualiter recedunt a puncto Solſtitij; </s> <s xml:id="echoid-s14469" xml:space="preserve">Et aſcenſio ♉, in ſphæra obli-<lb/>qua æqualis eſt aſcenſioni ♒, ut ex 3. </s> <s xml:id="echoid-s14470" xml:space="preserve">regula conſtabit, quia hæc ſigna ęquali-<lb/>ter ab æquinoctij puncto remouentur; </s> <s xml:id="echoid-s14471" xml:space="preserve">Erunt aſcenſio ♌, & </s> <s xml:id="echoid-s14472" xml:space="preserve">aſcenſio ♒, ſimul <lb/>æquales eorundem ſignorum aſcenſionibus in ſphæra recta. </s> <s xml:id="echoid-s14473" xml:space="preserve">Quod aliter ita <lb/>quoque confirmabitur. </s> <s xml:id="echoid-s14474" xml:space="preserve">Quoniam aſcenſio arcus a principio ♈, vſque ad ſinem <lb/>♌; </s> <s xml:id="echoid-s14475" xml:space="preserve">& </s> <s xml:id="echoid-s14476" xml:space="preserve">aſcenſio arcus a principio ♎, uſque ad finem ♒, in ſphæra obliqua ſimul <lb/>æquales ſunt aſcenſionibus eorundem arcuum ſimul in ſphæra recta, ut ex <lb/>proximo coroll. </s> <s xml:id="echoid-s14477" xml:space="preserve">patet: </s> <s xml:id="echoid-s14478" xml:space="preserve">Item aſcenſio arcus à principio ♈, uſque ad princi-<lb/>pium ♌; </s> <s xml:id="echoid-s14479" xml:space="preserve">& </s> <s xml:id="echoid-s14480" xml:space="preserve">aſcenſio arcus a principio ♎, uſque ad principium ♒, in ſphæ-<lb/>ra obliqua ſimul ęquales ſunt aſcenſionibus eorundem arcuum ſimul in ſphæ-<lb/>ra recta, ut ex eodem coroll. </s> <s xml:id="echoid-s14481" xml:space="preserve">manifeſtum eſt: </s> <s xml:id="echoid-s14482" xml:space="preserve">fit, ut ſi hæ aſcenſiones poſte-<lb/>riores ex illis prioribus detrahantur, reliquæ aſcenſiones arcuum ♌, & </s> <s xml:id="echoid-s14483" xml:space="preserve">♒, ſi-<lb/>mul in ſphæra obliqua æquales ſint reliquis aſcenſionibus eorundem arcuum <lb/>ſimul in ſphæra recta. </s> <s xml:id="echoid-s14484" xml:space="preserve">Idem dices de quibuſcunque arcubus oppoſitis, & </s> <s xml:id="echoid-s14485" xml:space="preserve">æqua-<lb/>libus, quia ſemper aſcenſio unius eſt æqualis aſcenſioni alicuius arcus æqua-<lb/>lis, qui æqualiter cum reliquo a Solſtitiali puncto diſtat, ut patet. </s> <s xml:id="echoid-s14486" xml:space="preserve">Ex his patet <lb/>ueritas 2. </s> <s xml:id="echoid-s14487" xml:space="preserve">regulæ propoſitæ. </s> <s xml:id="echoid-s14488" xml:space="preserve">Eſt enim eadem ratio arcuum æqualium, & </s> <s xml:id="echoid-s14489" xml:space="preserve">oppoſi- <pb o="336" file="372" n="373" rhead="Comment. in III. Cap. Sphæræ"/> torum, ſiue ab æquinoctialibus punctis initium ſumant, ſiue nõ, vt conſtat. </s> <s xml:id="echoid-s14490" xml:space="preserve">In <lb/>dato tamen exemplo aſcenſio ♌, in ſphæra obliqua Romæ continens grad. <lb/></s> <s xml:id="echoid-s14491" xml:space="preserve">38. </s> <s xml:id="echoid-s14492" xml:space="preserve">min. </s> <s xml:id="echoid-s14493" xml:space="preserve">42. </s> <s xml:id="echoid-s14494" xml:space="preserve">maior eſt aſcenſione eiuſdem ♌, in ſphęra recta, quæ complectitur <lb/>gr. </s> <s xml:id="echoid-s14495" xml:space="preserve">29. </s> <s xml:id="echoid-s14496" xml:space="preserve">min. </s> <s xml:id="echoid-s14497" xml:space="preserve">54. </s> <s xml:id="echoid-s14498" xml:space="preserve">Aſcenſio vero ♒, in eadem ſphæra obliqua cõtinens gr. </s> <s xml:id="echoid-s14499" xml:space="preserve">21. </s> <s xml:id="echoid-s14500" xml:space="preserve">min@ <lb/>6. </s> <s xml:id="echoid-s14501" xml:space="preserve">minor eſt aſcenſione eiuſdem ♒, in ſphæra recta, cum in hac cõprehendat <lb/>gr. </s> <s xml:id="echoid-s14502" xml:space="preserve">29. </s> <s xml:id="echoid-s14503" xml:space="preserve">min. </s> <s xml:id="echoid-s14504" xml:space="preserve">54. </s> <s xml:id="echoid-s14505" xml:space="preserve">Cum tamen ♌, exiſtat in medietate Eclipticæ boreali, & </s> <s xml:id="echoid-s14506" xml:space="preserve">♒, in <lb/>medietate auſtrali. </s> <s xml:id="echoid-s14507" xml:space="preserve">Quod quidem contrarium non eſt ſecundæ regulæ: </s> <s xml:id="echoid-s14508" xml:space="preserve">quia <lb/> <anchor type="note" xlink:label="note-372-01a" xlink:href="note-372-01"/> hæc ſigna non incipiunt à<unsure/> puncti<unsure/>s æquinoctialibus, vt ſecunda regula volebat.</s> <s xml:id="echoid-s14509" xml:space="preserve"/> </p> <div xml:id="echoid-div746" type="float" level="2" n="2"> <note position="left" xlink:label="note-372-01" xlink:href="note-372-01a" xml:space="preserve">A@cus æqua <lb/>les, æquali-<lb/>terq; ab al-<lb/>terutro pun <lb/>ctorũ æqui-<lb/>noctialium <lb/>diſtantes æ-<lb/>quales ha-<lb/>berſt aſcen-<lb/>ſiones in <lb/>ſphæra obli <lb/>qua.</note> </div> <p style="it"> <s xml:id="echoid-s14510" xml:space="preserve">REGVLA quidem eſt in ſphęra obliqua, quòd quilibet duo arcus <lb/>Zodiaci æquales, & </s> <s xml:id="echoid-s14511" xml:space="preserve">æqualiter diſtantes ab alterutro punctorum æquino-<lb/>ctialium, æquales habent aſcenſiones.</s> <s xml:id="echoid-s14512" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div748" type="section" level="1" n="264"> <head xml:id="echoid-head275" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s14513" xml:space="preserve"><emph style="sc">Tertia</emph> regula eſt hæc. </s> <s xml:id="echoid-s14514" xml:space="preserve">Quilibet duo arcus Zodiaci æquales, æqualiter-<lb/>que remoti ab alterutr<unsure/>o punctorum æquinoctialium, ſiue incipiant ab ipſo <lb/>puncto æquinoctij, ſiue non, æquales inter ſe habent aſcenſiones in qualibet <lb/>ſphæra decliui. </s> <s xml:id="echoid-s14515" xml:space="preserve">Vt u<unsure/>erbi gratia Aries, & </s> <s xml:id="echoid-s14516" xml:space="preserve">Piſces; </s> <s xml:id="echoid-s14517" xml:space="preserve">Taurus, & </s> <s xml:id="echoid-s14518" xml:space="preserve">Aquarius, &</s> <s xml:id="echoid-s14519" xml:space="preserve">c. </s> <s xml:id="echoid-s14520" xml:space="preserve">vt con-<lb/>ſtat ex ſphæricorum triangulorum doctrina, demonſtraturq́ue à Gebro, & </s> <s xml:id="echoid-s14521" xml:space="preserve">à <lb/>Ioan. </s> <s xml:id="echoid-s14522" xml:space="preserve">Regiom. </s> <s xml:id="echoid-s14523" xml:space="preserve">in lib. </s> <s xml:id="echoid-s14524" xml:space="preserve">2. </s> <s xml:id="echoid-s14525" xml:space="preserve">Epitom. </s> <s xml:id="echoid-s14526" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s14527" xml:space="preserve">19. </s> <s xml:id="echoid-s14528" xml:space="preserve">Verum uidebitur fortaſſe alicui hæc <lb/> <anchor type="note" xlink:label="note-372-02a" xlink:href="note-372-02"/> regula contraria præcedentia. </s> <s xml:id="echoid-s14529" xml:space="preserve">Dictum eſt enim in 2. </s> <s xml:id="echoid-s14530" xml:space="preserve">regula, arcus medietatis <lb/>Eclipticæ ab ♈, uſque ad ♎, habere minores aſcenſiones in ſphæra obliqua, <lb/>quàm arcus reli<unsure/>quæ medietatis. </s> <s xml:id="echoid-s14531" xml:space="preserve">Cum igitur Aries contineatur in medietate <lb/>priori, & </s> <s xml:id="echoid-s14532" xml:space="preserve">Piſces in poſteriori, qua ratione f<unsure/>ieri poreſt, ut hi arcus habeant aſcen <lb/>ſiones æquales? </s> <s xml:id="echoid-s14533" xml:space="preserve">Reſpondendum tamen eſt, hanc regulam eſſe ueriſſimam, & </s> <s xml:id="echoid-s14534" xml:space="preserve">nõ <lb/>aduerſari præcedenti. </s> <s xml:id="echoid-s14535" xml:space="preserve">Nam præcedens regula intelligebatur de arcubus inci-<lb/>pientibus ab initio ♈, nel ♎: </s> <s xml:id="echoid-s14536" xml:space="preserve">Huiuſmodi autem arcus non ſunt Aries, & </s> <s xml:id="echoid-s14537" xml:space="preserve">Pi-<lb/>ſces. </s> <s xml:id="echoid-s14538" xml:space="preserve">Quamuis enim arcus Arietis initium habeat à primo puncto ♈, non tamẽ <lb/> <anchor type="note" xlink:label="note-372-03a" xlink:href="note-372-03"/> arcus Piſcium incipit à primo gradu ♎.</s> <s xml:id="echoid-s14539" xml:space="preserve"/> </p> <div xml:id="echoid-div748" type="float" level="2" n="1"> <note position="left" xlink:label="note-372-02" xlink:href="note-372-02a" xml:space="preserve">Solutio cu-<lb/>iuſdam du-<lb/>bii.</note> <note position="left" xlink:label="note-372-03" xlink:href="note-372-03a" xml:space="preserve">Aſcenſio cu <lb/>iuslibet ar-<lb/>cus in ſphæ <lb/>ra obliqua <lb/>æqualis eſt <lb/>deſcenſioni <lb/>@@rcus oppo-<lb/>ſiti, & æqua <lb/>lis in eadẽ <lb/>ſphæra.</note> </div> <p> <s xml:id="echoid-s14540" xml:space="preserve"><emph style="sc">Caetervm</emph> in omni ſphæra tam recta, quà m decliui, aſcenſio cuiusli-<lb/>bet arcus, ſen ſigni ęqualis eſt deſcenſioni arcus, ſignive oppoſiti. </s> <s xml:id="echoid-s14541" xml:space="preserve">Cum enim <lb/>Horizon, & </s> <s xml:id="echoid-s14542" xml:space="preserve">Zodiacus ſeſe mutuo ſecent bifariam, quòd ſint circuli maiores, <lb/>ſemper erit media pars Zodiaci ſupra Horizontem. </s> <s xml:id="echoid-s14543" xml:space="preserve">Quare quocunque puncto <lb/>Zodiaci aſcendente ſupra Horizontem, neceſſe eſt, oppoſitum ſub Horizontem <lb/>deſcendere: </s> <s xml:id="echoid-s14544" xml:space="preserve">aliàs aut maior arcus ſemicirculo, aut mi<unsure/>nor Zodiaci ſupra Hori-<lb/>zontem extaret: </s> <s xml:id="echoid-s14545" xml:space="preserve">Atque ita exiſtente initio alicuius ſigni in oriente præciſe, exi <lb/> <anchor type="note" xlink:label="note-372-04a" xlink:href="note-372-04"/> ſtet initium ſigni oppoſiti præciſe in occidente; </s> <s xml:id="echoid-s14546" xml:space="preserve">& </s> <s xml:id="echoid-s14547" xml:space="preserve">exiſtente puncto extremo <lb/>prioris ſigni in oriente, exiſtet extremum punctum poſterioris in occidente: <lb/></s> <s xml:id="echoid-s14548" xml:space="preserve">Quocirca aſcendente vno, alterum neceſſario deſcendet.</s> <s xml:id="echoid-s14549" xml:space="preserve"/> </p> <div xml:id="echoid-div749" type="float" level="2" n="2"> <note position="left" xlink:label="note-372-04" xlink:href="note-372-04a" xml:space="preserve">Aſcenſio & <lb/>deſcẽſio cu <lb/>iuslibet ſi-<lb/>gni ſimul <lb/>æquales sũt <lb/>aſcenſioni, <lb/>& deſcenſio<unsure/> <lb/>ni ſigni op@ <lb/>poſiti ì qua <lb/>libet ſphæ-<lb/>ra.</note> </div> <p> <s xml:id="echoid-s14550" xml:space="preserve"><emph style="sc">Hinc</emph> fit, aſcenſionem, atque deſcenſionem ſigni cuiuslibet ſimul adæ-<lb/>quari aſcenſioni deſcenſioniq́ue ſigni oppoſiti ſimul in quauis ſphæra; </s> <s xml:id="echoid-s14551" xml:space="preserve">quia ſci-<lb/>licet aſcenſio unius ſigni eſt deſcenſio ſigni oppoſiti; </s> <s xml:id="echoid-s14552" xml:space="preserve">& </s> <s xml:id="echoid-s14553" xml:space="preserve">deſcenſio eiuſdem eſt <lb/>aſcenſio oppoſiti: </s> <s xml:id="echoid-s14554" xml:space="preserve">Quare ſi æqualibus æqualia addantur, tota f<unsure/>ient ęqualia. </s> <s xml:id="echoid-s14555" xml:space="preserve">Vt <lb/>aſcenſio ♈, æqualis eſt deſcenſioni ♎, & </s> <s xml:id="echoid-s14556" xml:space="preserve">deſcenſio ♈, æqualis eſt aſcenſio-<lb/>ni ♎, &</s> <s xml:id="echoid-s14557" xml:space="preserve">c.</s> <s xml:id="echoid-s14558" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14559" xml:space="preserve"><emph style="sc">Item</emph> manifeſtum eſt, aſcenſionem cuiuslibet ſigni in ſphæra obliqua in <lb/> <anchor type="note" xlink:label="note-372-05a" xlink:href="note-372-05"/> æqualem eſſe deſcenſioni eiuſdẽ, ita vt ſi recte oriatur, obliquè occidat, & </s> <s xml:id="echoid-s14560" xml:space="preserve">con-<lb/>tra. </s> <s xml:id="echoid-s14561" xml:space="preserve">Cum enim aſcenſio cuiuſq<unsure/>@ ſigni æqualis ſit deſcenſioni ſigni oppoſiti, ſi <pb o="337" file="373" n="374" rhead="Ioan. de Sacro Boſco."/> aſcẽſio huius ſigni poſterioris ęqualis eſſet deſcẽſioni eiuſdẽ, haberẽt ſigna <lb/> <anchor type="note" xlink:label="note-373-01a" xlink:href="note-373-01"/> oppoſita ęquales aſcẽſiones, qđ eſt contra ea, q̃ dicta ſunt in 2. </s> <s xml:id="echoid-s14562" xml:space="preserve">regula. </s> <s xml:id="echoid-s14563" xml:space="preserve">Aſcen-<lb/>ſio tamen cuiuſuis ſigni, & </s> <s xml:id="echoid-s14564" xml:space="preserve">deſcenſio eiuſdem in obliqua ſphæra ſimul ſumptæ <lb/>æquales ſunt aſcenſioni, & </s> <s xml:id="echoid-s14565" xml:space="preserve">deſcenſioni eiuſdem in ſph ęra recta ſimul ſumptis; <lb/></s> <s xml:id="echoid-s14566" xml:space="preserve">quia quanto obliquius, uel rectius aliquod ſignum oritur in ſphæra obliqua, <lb/> <anchor type="note" xlink:label="note-373-02a" xlink:href="note-373-02"/> quàm in recta, tanto rectius, uel obliqui<unsure/>us occidit, ut conſtat ex triangulis ſphę <lb/>ricis, & </s> <s xml:id="echoid-s14567" xml:space="preserve">manifeſtum erit ex tabulis aſcenſionum obliquarum.</s> <s xml:id="echoid-s14568" xml:space="preserve"/> </p> <div xml:id="echoid-div750" type="float" level="2" n="3"> <note position="left" xlink:label="note-372-05" xlink:href="note-372-05a" xml:space="preserve">Aſcenſio cu <lb/>iuslibet ſi-<lb/>gni in ſphę <lb/>@@ obliqua</note> <note position="right" xlink:label="note-373-01" xlink:href="note-373-01a" xml:space="preserve">inęqualis<unsure/> <lb/>eſt deſcẽſi@ <lb/>ni eiuſdem <lb/>ſigni.</note> <note position="right" xlink:label="note-373-02" xlink:href="note-373-02a" xml:space="preserve">@ſcẽſio, &c <lb/>deſcenſio <lb/>eiuſdem ſi-<lb/>gni in ſphę <lb/>ra obliqua <lb/>ſimul æquæ <lb/>les sũt aſe@ <lb/>ſioni, & de-<lb/>ſcenſioni <lb/>eiuſde@@ ſi <lb/>gniſimuli@ <lb/>ſphæra re-<lb/>cta.</note> </div> </div> <div xml:id="echoid-div752" type="section" level="1" n="265"> <head xml:id="echoid-head276" xml:space="preserve">QVA RATIONE ASCENSIO OBLIQVA <lb/>cuiuslibet arcus Zodiaci à Verna ſectione nu-<lb/>merati inueniatur.</head> <p> <s xml:id="echoid-s14569" xml:space="preserve"><emph style="sc">Qvia</emph> dictum eſt in 1. </s> <s xml:id="echoid-s14570" xml:space="preserve">regula, aſcenſiones obliquas arcuum Eclipticæ in <lb/>medietate Septentrionali cõtentorum, initio ſemper facto à primo puncto ♈, <lb/>tanto minores eſſe aſcenſionibus rectis eorundem arcuũ, quanto maiores ſunt <lb/>aſcẽſiones obliquæ arcuũ Eclipticæ in medietate Auſtrali comprehenſorum, <lb/>initio quoque ſemper facto à principio ♎, aſcẽſionibus rectis eorundẽ arcuũ; <lb/></s> <s xml:id="echoid-s14571" xml:space="preserve">Manifeſtũ eſt, ſi ab aſcenſionibus rectis arcũ prioris medietatis Eclipticæ de-<lb/> <anchor type="note" xlink:label="note-373-03a" xlink:href="note-373-03"/> trahantur differentię aſcenſionales, quibus nimir<unsure/>ũ differũt aſcenſiones rectæ <lb/>ab obliquis, relinqui eorundem arcuum aſcenſiones ob liquas; </s> <s xml:id="echoid-s14572" xml:space="preserve">Si uero eædem <lb/>differentiæ aſcenſionales adijciantur aſcenſionibus rectis arcuum Eclipticæ <lb/>poſterioris medietatis, effici aſcenſiones obliquas eorũdem arcuum, initio ſem <lb/>per facto à principijs ♈, & </s> <s xml:id="echoid-s14573" xml:space="preserve">♎. </s> <s xml:id="echoid-s14574" xml:space="preserve">Hanc autem aſcenſionalem differentiã hac arte <lb/>inuenies ex doctrina Sinuũ. </s> <s xml:id="echoid-s14575" xml:space="preserve">Vt demonſtrat Geber, & </s> <s xml:id="echoid-s14576" xml:space="preserve">nos etiam demonſtraui-<lb/>mus in ſcholio propoſ. </s> <s xml:id="echoid-s14577" xml:space="preserve">9. </s> <s xml:id="echoid-s14578" xml:space="preserve">lib. </s> <s xml:id="echoid-s14579" xml:space="preserve">2. </s> <s xml:id="echoid-s14580" xml:space="preserve">Gnomonices, ita ſe habet ſinus complementi <lb/> <anchor type="note" xlink:label="note-373-04a" xlink:href="note-373-04"/> declinationis puncti Eclipticæ propoſiti ad ſinum complementi latitudinis <lb/>ortiuæ, ſiue occiduæ eiuſdem puncti Eclipticæ, ut ſinus totus ad ſinum cõple-<lb/>menti differentiæ aſcenſionalis. </s> <s xml:id="echoid-s14581" xml:space="preserve">Quamobrem ſi ſinus complementi latitudi-<lb/>nis ortiuæ in ſinum totum multiplicetur, & </s> <s xml:id="echoid-s14582" xml:space="preserve">productus numerus in ſinum cõ <lb/>plementi declina<unsure/>tionis puncti propoſiti diuidatur, ut pręcipit regula propor-<lb/>tionũ, habebitur ſinus complementi differentiæ aſcenſionalis. </s> <s xml:id="echoid-s14583" xml:space="preserve">Quare cogno-<lb/>ſcetur ex tabula finuum differentia aſcenſionalis. </s> <s xml:id="echoid-s14584" xml:space="preserve"><emph style="sc">Exemplvm</emph>. </s> <s xml:id="echoid-s14585" xml:space="preserve">Quærenda ſit <lb/>differentia Romæ, qua differt aſcenſ@o obliqua arcus Eclipticæ ab ♈, uſque ad <lb/>finem ♊, ab aſcenſioni recta. </s> <s xml:id="echoid-s14586" xml:space="preserve">Quoniam igitur declinatio puncti extremi ♊, eſt <lb/>grad. </s> <s xml:id="echoid-s14587" xml:space="preserve">23. </s> <s xml:id="echoid-s14588" xml:space="preserve">min. </s> <s xml:id="echoid-s14589" xml:space="preserve">30. </s> <s xml:id="echoid-s14590" xml:space="preserve">& </s> <s xml:id="echoid-s14591" xml:space="preserve">latitudo ortiua grad. </s> <s xml:id="echoid-s14592" xml:space="preserve">32. </s> <s xml:id="echoid-s14593" xml:space="preserve">min. </s> <s xml:id="echoid-s14594" xml:space="preserve">27. </s> <s xml:id="echoid-s14595" xml:space="preserve">Multiplico ſinum comple <lb/>menti latitudinis ortiuę, nempe 84386. </s> <s xml:id="echoid-s14596" xml:space="preserve">in ſinum totum, uidelicet in 100000. <lb/></s> <s xml:id="echoid-s14597" xml:space="preserve">productũ deinde numerum 8438600000. </s> <s xml:id="echoid-s14598" xml:space="preserve">diuido per 91706. </s> <s xml:id="echoid-s14599" xml:space="preserve">ſinum comple-<lb/>menti declinationis extremi puncti ♊, & </s> <s xml:id="echoid-s14600" xml:space="preserve">exibit ſinus complementi differen-<lb/> <anchor type="note" xlink:label="note-373-05a" xlink:href="note-373-05"/> tiæ aſcenſionalis fere 92018. </s> <s xml:id="echoid-s14601" xml:space="preserve">cui reſpondent in tabula ſinuum grad. </s> <s xml:id="echoid-s14602" xml:space="preserve">66. </s> <s xml:id="echoid-s14603" xml:space="preserve">min. <lb/></s> <s xml:id="echoid-s14604" xml:space="preserve">57. </s> <s xml:id="echoid-s14605" xml:space="preserve">Igitur differentia aſcenſionalis erit grad. </s> <s xml:id="echoid-s14606" xml:space="preserve">23. </s> <s xml:id="echoid-s14607" xml:space="preserve">min. </s> <s xml:id="echoid-s14608" xml:space="preserve">3. </s> <s xml:id="echoid-s14609" xml:space="preserve">Quia ablata ex aſcenſio <lb/>ne recta arcus propoſiti, nempe ex grad. </s> <s xml:id="echoid-s14610" xml:space="preserve">90. </s> <s xml:id="echoid-s14611" xml:space="preserve">quia eſt in priori medietate Ecli-<lb/>pticæ, relinquetur aſcenſio obliqua dictiarcus Romæ grad. </s> <s xml:id="echoid-s14612" xml:space="preserve">66. </s> <s xml:id="echoid-s14613" xml:space="preserve">min. </s> <s xml:id="echoid-s14614" xml:space="preserve">57.</s> <s xml:id="echoid-s14615" xml:space="preserve"/> </p> <div xml:id="echoid-div752" type="float" level="2" n="1"> <note position="right" xlink:label="note-373-03" xlink:href="note-373-03a" xml:space="preserve">Quo pact@@ <lb/>ex differe@ <lb/>tijs aſcẽſi@-<lb/>libus repe-<lb/>riãtur aſcẽ-<lb/>ſiones obli<unsure/> <lb/>quæ.</note> <note position="right" xlink:label="note-373-04" xlink:href="note-373-04a" xml:space="preserve">Qua rati@ <lb/>ne ꝑ ſinus <lb/>di<unsure/>fferentiæ <lb/>aſcenſiona. <lb/>les inueni@ <lb/>tur.</note> <note position="right" xlink:label="note-373-05" xlink:href="note-373-05a" xml:space="preserve">Satis eſt, ſ@ <lb/>inueſtigen-<lb/>tur differe@ <lb/>tię aſcẽſio-<lb/>nales pun-<lb/>ctorũ vnius <lb/>quadrantis <lb/>Eclipticæ.</note> </div> <p> <s xml:id="echoid-s14616" xml:space="preserve"><emph style="sc">Qvoniam</emph> vero ſupra docuimus, & </s> <s xml:id="echoid-s14617" xml:space="preserve">declinationes, & </s> <s xml:id="echoid-s14618" xml:space="preserve">latitudines ortiuas <lb/>punctorum oium unius Quadrantis ęquales eſſe declinationibus, latitudini-<lb/>busque, quas habent omnia puncta reliquorũ Quadrantũ, perſpicuum eſt, ſatis <lb/>eſſe, ſi @@ueſtigétur differẽtiæ aſcẽſionales unius dũtaxat Quadr<unsure/>ãtis Eclipticę.</s> <s xml:id="echoid-s14619" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">Quo pacto <lb/>a@ter per <lb/>anus inue-</note> <p> <s xml:id="echoid-s14620" xml:space="preserve"><emph style="sc">Alio</emph> modo reperietur differentia aſcenſionalis cuiusuis arcus, ſeu pun-<lb/>cti Eclipticæ abſq. </s> <s xml:id="echoid-s14621" xml:space="preserve">cognitione latitudinis ortiuæ, uel occiduę, hac arte. </s> <s xml:id="echoid-s14622" xml:space="preserve">Mul- <pb o="338" file="374" n="375" rhead="Comment in III. Cap. Sphæræ"/> tiplicetur ſinus altitudinis poli in ſinum totum, numerusq́; </s> <s xml:id="echoid-s14623" xml:space="preserve">productus per ſi-<lb/> <anchor type="note" xlink:label="note-374-01a" xlink:href="note-374-01"/> num complementi altitudinis poli diuidatur. </s> <s xml:id="echoid-s14624" xml:space="preserve">Exibit enim ſinus, qui in una <lb/>eademque regione nunquam uariabitur unde non immerito ſinus regionis <lb/>dici poterit, qui Romæ talis eſt fere 90041. </s> <s xml:id="echoid-s14625" xml:space="preserve">Deinde quoniã, ut demonſtrat 10. <lb/></s> <s xml:id="echoid-s14626" xml:space="preserve">Regiom. </s> <s xml:id="echoid-s14627" xml:space="preserve">lib. </s> <s xml:id="echoid-s14628" xml:space="preserve">2. </s> <s xml:id="echoid-s14629" xml:space="preserve">Epito. </s> <s xml:id="echoid-s14630" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s14631" xml:space="preserve">22. </s> <s xml:id="echoid-s14632" xml:space="preserve">Talis eſt proportio ſinus complementi decli-<lb/>nationis puncti eclipticę propoſiti, quod nimirum arcum datum terminat, ad <lb/>ſinum declinationis, qualis eſt proportio ſinus, quem regionis diximus, ad ſi-<lb/>num differentiæ aſcen@ionalis propoſiti puncti eclipticæ; </s> <s xml:id="echoid-s14633" xml:space="preserve">Si iuxta præceptum <lb/>regulæ proportionum ſinus declinationis puncti propoſiti multiplicetur in ſi <lb/>num regionis inuentum, productus deinde numerus in ſinum complementi <lb/>declinationis diuidatur, habebitur ſinus differentię aſcenſionalis quæſitæ. </s> <s xml:id="echoid-s14634" xml:space="preserve"><lb/><emph style="sc">Exemplvm</emph>. </s> <s xml:id="echoid-s14635" xml:space="preserve">Romæ quæro differentiam aſcenſionalem primi Quadrantis ecli <lb/>pticæ, nempe ultimi puncti ♊. </s> <s xml:id="echoid-s14636" xml:space="preserve">Multiplico 39874. </s> <s xml:id="echoid-s14637" xml:space="preserve">ſinum deelinationis in ſinũ <lb/>regionis Romæ, 90041. </s> <s xml:id="echoid-s14638" xml:space="preserve">productumq. </s> <s xml:id="echoid-s14639" xml:space="preserve">numerũ 3590294834. </s> <s xml:id="echoid-s14640" xml:space="preserve">diuido per 91706. </s> <s xml:id="echoid-s14641" xml:space="preserve"><lb/>finum complementi declinationis, & </s> <s xml:id="echoid-s14642" xml:space="preserve">proueniet ſinus differentiæ aſcenſionalis <lb/>quæſitæ 39150. </s> <s xml:id="echoid-s14643" xml:space="preserve">cui reſpondet arcus grad. </s> <s xml:id="echoid-s14644" xml:space="preserve">23. </s> <s xml:id="echoid-s14645" xml:space="preserve">min. </s> <s xml:id="echoid-s14646" xml:space="preserve">3. </s> <s xml:id="echoid-s14647" xml:space="preserve">ſicut prius.</s> <s xml:id="echoid-s14648" xml:space="preserve"/> </p> <div xml:id="echoid-div753" type="float" level="2" n="2"> <note position="left" xlink:label="note-374-01" xlink:href="note-374-01a" xml:space="preserve">niãtur dif-<lb/>ferentiæ a-<lb/>ſcenſiona-<lb/>les.</note> </div> <p> <s xml:id="echoid-s14649" xml:space="preserve"><emph style="sc">Hac</emph> arte Ioan. </s> <s xml:id="echoid-s14650" xml:space="preserve">Regiom. </s> <s xml:id="echoid-s14651" xml:space="preserve">ſupputauit differẽtias aſcenſionales omniũ pun-<lb/>ctorũ, quæ declinant ab Aequatore, incipiendo à gradu 1. </s> <s xml:id="echoid-s14652" xml:space="preserve">declinationis uſque <lb/>ad grad. </s> <s xml:id="echoid-s14653" xml:space="preserve">32 Nã nullus Planeta, quorum gratia tabulas conſcripſit, maiorem un <lb/>quam habuit declinationem. </s> <s xml:id="echoid-s14654" xml:space="preserve">Si igitur deſideras aſcenſionalem differentiã cu-<lb/> <anchor type="note" xlink:label="note-374-02a" xlink:href="note-374-02"/> iuſuis arcus eclipticæ, quære in uertice tabulæ differentiarũ aſcenſionaliũ ele-<lb/>uationem poli, & </s> <s xml:id="echoid-s14655" xml:space="preserve">in latere ſiniſtro declinationem extremi puncti arcus pro-<lb/>poſiti. </s> <s xml:id="echoid-s14656" xml:space="preserve">Nam in angulo communis concurſus reperies differentiam quæſitã. </s> <s xml:id="echoid-s14657" xml:space="preserve">Vt <lb/>Romæ, ubi eleuatur polus 42. </s> <s xml:id="echoid-s14658" xml:space="preserve">grad. </s> <s xml:id="echoid-s14659" xml:space="preserve">punctum eclipticæ, quod declinat 18. </s> <s xml:id="echoid-s14660" xml:space="preserve">grad. <lb/></s> <s xml:id="echoid-s14661" xml:space="preserve">ab Aequatore, habet differentiam aſcenſionalem grad. </s> <s xml:id="echoid-s14662" xml:space="preserve">17. </s> <s xml:id="echoid-s14663" xml:space="preserve">min. </s> <s xml:id="echoid-s14664" xml:space="preserve">1. </s> <s xml:id="echoid-s14665" xml:space="preserve">&</s> <s xml:id="echoid-s14666" xml:space="preserve">c.</s> <s xml:id="echoid-s14667" xml:space="preserve"/> </p> <div xml:id="echoid-div754" type="float" level="2" n="3"> <note position="left" xlink:label="note-374-02" xlink:href="note-374-02a" xml:space="preserve">Qũo ex ta-<lb/>bula diffe-<lb/>rentiarum <lb/>aſcenſi@na-<lb/>liũ differẽ-<lb/>tiæ aſceſio-<lb/>nales repe-<lb/>riantur.</note> </div> <p> <s xml:id="echoid-s14668" xml:space="preserve"><emph style="sc">Qvod</emph> ſi declinatio puncti non reperiatur in ſiniſtro latere, quærendus <lb/>eſt exceſſus inter aſcenſionalem differentiam declinationis proxime maioris, <lb/>& </s> <s xml:id="echoid-s14669" xml:space="preserve">differentiam aſcenſionem declinationis proxime minoris. </s> <s xml:id="echoid-s14670" xml:space="preserve">Deinde elicien-<lb/>da pars proportionalis minutis propoſitę declinationis reſpondens. </s> <s xml:id="echoid-s14671" xml:space="preserve">Hęc enim <lb/>adiecta diſſerentiæ aſcenſionali declinationis proxime minoris dabit aſcenſio-<lb/>nalem differentiam quęſitam. </s> <s xml:id="echoid-s14672" xml:space="preserve"><emph style="sc">Exemplvm</emph>. </s> <s xml:id="echoid-s14673" xml:space="preserve">Romæ inuenienda ſit differentia <lb/>aſcenſionalis ultimi puncti ♊, uel primi grad. </s> <s xml:id="echoid-s14674" xml:space="preserve">♋, hoc eft primi Quadrantis <lb/>eclipticę. </s> <s xml:id="echoid-s14675" xml:space="preserve">Quoniam igitur declinatio primi gradus ♋, eſt grad. </s> <s xml:id="echoid-s14676" xml:space="preserve">23. </s> <s xml:id="echoid-s14677" xml:space="preserve">min. </s> <s xml:id="echoid-s14678" xml:space="preserve">30. <lb/></s> <s xml:id="echoid-s14679" xml:space="preserve">Accipio differentiam aſcenſionalem grad. </s> <s xml:id="echoid-s14680" xml:space="preserve">23. </s> <s xml:id="echoid-s14681" xml:space="preserve">declinationis, nempe gr. </s> <s xml:id="echoid-s14682" xml:space="preserve">22. </s> <s xml:id="echoid-s14683" xml:space="preserve">min. </s> <s xml:id="echoid-s14684" xml:space="preserve"><lb/>28. </s> <s xml:id="echoid-s14685" xml:space="preserve">Item differentiam aſcenſionalem debitam declinationi grad. </s> <s xml:id="echoid-s14686" xml:space="preserve">24. </s> <s xml:id="echoid-s14687" xml:space="preserve">nimirum <lb/>grad. </s> <s xml:id="echoid-s14688" xml:space="preserve">23. </s> <s xml:id="echoid-s14689" xml:space="preserve">min. </s> <s xml:id="echoid-s14690" xml:space="preserve">23. </s> <s xml:id="echoid-s14691" xml:space="preserve">quarum differentia eſt grad. </s> <s xml:id="echoid-s14692" xml:space="preserve">1. </s> <s xml:id="echoid-s14693" xml:space="preserve">min. </s> <s xml:id="echoid-s14694" xml:space="preserve">10. </s> <s xml:id="echoid-s14695" xml:space="preserve">quę debetur tunc inte-<lb/>gro gradui declinationis: </s> <s xml:id="echoid-s14696" xml:space="preserve">Igitur iuxta regulam proportionum minutis 30. </s> <s xml:id="echoid-s14697" xml:space="preserve">de-<lb/>bentur min. </s> <s xml:id="echoid-s14698" xml:space="preserve">35. </s> <s xml:id="echoid-s14699" xml:space="preserve">quæ adiecta differentiæ aſcenſionali, quę debetur declinatio-<lb/>ni grad. </s> <s xml:id="echoid-s14700" xml:space="preserve">23. </s> <s xml:id="echoid-s14701" xml:space="preserve">nempe gradibus 22. </s> <s xml:id="echoid-s14702" xml:space="preserve">min. </s> <s xml:id="echoid-s14703" xml:space="preserve">28. </s> <s xml:id="echoid-s14704" xml:space="preserve">habebitur differentia aſcenſionalis <lb/>grad. </s> <s xml:id="echoid-s14705" xml:space="preserve">23. </s> <s xml:id="echoid-s14706" xml:space="preserve">min. </s> <s xml:id="echoid-s14707" xml:space="preserve">3. </s> <s xml:id="echoid-s14708" xml:space="preserve">ueluti prius, debita declinationi grad. </s> <s xml:id="echoid-s14709" xml:space="preserve">23. </s> <s xml:id="echoid-s14710" xml:space="preserve">min. </s> <s xml:id="echoid-s14711" xml:space="preserve">30. </s> <s xml:id="echoid-s14712" xml:space="preserve">nempe princi <lb/>pio ♋. </s> <s xml:id="echoid-s14713" xml:space="preserve">Atque ita cæteris.</s> <s xml:id="echoid-s14714" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14715" xml:space="preserve"><emph style="sc">Constat</emph> igitur ex his, qua arte conſtruenda ſit tabula differentia-<lb/>rum aſcenſionalium ad quamcunque poli eleuationem, & </s> <s xml:id="echoid-s14716" xml:space="preserve">conſequenter ex ta <lb/>bula aſcenſionalium differentiarum tabula aſcenſionum obliquarum. </s> <s xml:id="echoid-s14717" xml:space="preserve">Vt ta-<lb/>men lectorem hoc onere ſubleuarem; </s> <s xml:id="echoid-s14718" xml:space="preserve">ſubiunxi ex Ioan. </s> <s xml:id="echoid-s14719" xml:space="preserve">Regiom. </s> <s xml:id="echoid-s14720" xml:space="preserve">tabulas diffe-<lb/>rentiarũ aſcenſionaliũ ad omnes poli eleuationes incipiendo ab 1. </s> <s xml:id="echoid-s14721" xml:space="preserve">gr. </s> <s xml:id="echoid-s14722" xml:space="preserve">vſq; </s> <s xml:id="echoid-s14723" xml:space="preserve">ad <lb/>60. </s> <s xml:id="echoid-s14724" xml:space="preserve">grad. </s> <s xml:id="echoid-s14725" xml:space="preserve">Item tabulas aſcenſionum obliquarum ad ſingulas quoque poli alti-<lb/>tudines, incipiendo à grad. </s> <s xml:id="echoid-s14726" xml:space="preserve">36. </s> <s xml:id="echoid-s14727" xml:space="preserve">vſq; </s> <s xml:id="echoid-s14728" xml:space="preserve">ad grad. </s> <s xml:id="echoid-s14729" xml:space="preserve">60. </s> <s xml:id="echoid-s14730" xml:space="preserve">quoniam inſignes habent utili- <pb o="339" file="375" n="376" rhead="Ioan. de Sacro Boſco."/> @@tes in rebus Aſtronomicis, ut ex ijs conſtat aliqua ex parte, quæ in Gnomo-<lb/>nica de aſcendentibus ſignis ſcripſimus.</s> <s xml:id="echoid-s14731" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14732" xml:space="preserve"><emph style="sc">Invenies</emph> autem ex hiſce tabulis aſcenſionum obliquarum aſcenſionẽ <lb/> <anchor type="note" xlink:label="note-375-01a" xlink:href="note-375-01"/> obliquam cuiuslibet arcus, non ſecus, ac in uſu tabulæ aſcenſionum rectarum <lb/>expoſitum eſt, ſumendo tamen tabulam aſcenſionum obliquarum illius ele-<lb/>uationis poli, in qua aſcenſiones obliquas perquiris. </s> <s xml:id="echoid-s14733" xml:space="preserve">At uero Deſcenſionem <lb/>cuiuſque arcus ita explorabis in ſphæra quauis obliqua. </s> <s xml:id="echoid-s14734" xml:space="preserve">Nam in recta ſphæra <lb/>æquales ſunt aſcenſio, & </s> <s xml:id="echoid-s14735" xml:space="preserve">deſcenſio eiuſdem arcus. </s> <s xml:id="echoid-s14736" xml:space="preserve">Oſtenſum eſt, aſcenſionem <lb/>cuiuslibet arcus æqualem eſſe de ſcenſioni arcus oppoſiti, & </s> <s xml:id="echoid-s14737" xml:space="preserve">deſcenſionẽ arcus <lb/>cuiuſuis æqualem aſcenſioni arcus oppoſiti, idcirco ſi quæratur deſcẽſio alicu-<lb/>ius arcus, inueſtiganda erit aſcenſio arcus oppoſiti. </s> <s xml:id="echoid-s14738" xml:space="preserve">Nam hæc erit deſcenſio <lb/>propoſiti arcus. </s> <s xml:id="echoid-s14739" xml:space="preserve">EXEMPLVM. </s> <s xml:id="echoid-s14740" xml:space="preserve">Deſideratur deſcenſio arcus ab ♈, uſque <lb/>ad grad 8. </s> <s xml:id="echoid-s14741" xml:space="preserve">♍. </s> <s xml:id="echoid-s14742" xml:space="preserve">Romæ, ubi polus eleuatur 42. </s> <s xml:id="echoid-s14743" xml:space="preserve">grad. </s> <s xml:id="echoid-s14744" xml:space="preserve">Arcus oppoſicus eſt à ♎, vſq; <lb/></s> <s xml:id="echoid-s14745" xml:space="preserve">ad grad. </s> <s xml:id="echoid-s14746" xml:space="preserve">8. </s> <s xml:id="echoid-s14747" xml:space="preserve">♓, & </s> <s xml:id="echoid-s14748" xml:space="preserve">quoniam grad. </s> <s xml:id="echoid-s14749" xml:space="preserve">8. </s> <s xml:id="echoid-s14750" xml:space="preserve">♓, aſcendunt cum Aequatoris grad 347. </s> <s xml:id="echoid-s14751" xml:space="preserve">min. </s> <s xml:id="echoid-s14752" xml:space="preserve"><lb/>29. </s> <s xml:id="echoid-s14753" xml:space="preserve">incipiendo ab ♈, ſi detrahantur 180. </s> <s xml:id="echoid-s14754" xml:space="preserve">grad. </s> <s xml:id="echoid-s14755" xml:space="preserve">nempe ſemicirculus ab ♈, uſque <lb/>ad ♎, remanebit aſcenſio arcus à ♎, uſque ad grad. </s> <s xml:id="echoid-s14756" xml:space="preserve">8. </s> <s xml:id="echoid-s14757" xml:space="preserve">♓, hoc eſt, deſcenſio ar-<lb/>cus ab ♈, @ſque ad grad. </s> <s xml:id="echoid-s14758" xml:space="preserve">8. </s> <s xml:id="echoid-s14759" xml:space="preserve">♍, grad. </s> <s xml:id="echoid-s14760" xml:space="preserve">167. </s> <s xml:id="echoid-s14761" xml:space="preserve">min. </s> <s xml:id="echoid-s14762" xml:space="preserve">29. </s> <s xml:id="echoid-s14763" xml:space="preserve">Similiter quæritur deſcenſio <lb/>arcus ab initio ♏, uſque ad 20. </s> <s xml:id="echoid-s14764" xml:space="preserve">grad. </s> <s xml:id="echoid-s14765" xml:space="preserve">♒, Arcus oppoſitus eſt à ♉, vſque ad gra. </s> <s xml:id="echoid-s14766" xml:space="preserve"><lb/>20. </s> <s xml:id="echoid-s14767" xml:space="preserve">♌. </s> <s xml:id="echoid-s14768" xml:space="preserve">Et quia grad. </s> <s xml:id="echoid-s14769" xml:space="preserve">20. </s> <s xml:id="echoid-s14770" xml:space="preserve">♌, incipiendo à principio ♉, aſcendunt cum Aequa-<lb/>toris gradibus 111. </s> <s xml:id="echoid-s14771" xml:space="preserve">min. </s> <s xml:id="echoid-s14772" xml:space="preserve">15. </s> <s xml:id="echoid-s14773" xml:space="preserve">tantam dicemus eſſe deſcenſionẽ arcus inter prin-<lb/>cipium ♏, & </s> <s xml:id="echoid-s14774" xml:space="preserve">grad. </s> <s xml:id="echoid-s14775" xml:space="preserve">20. </s> <s xml:id="echoid-s14776" xml:space="preserve">♒, comprehenſi. </s> <s xml:id="echoid-s14777" xml:space="preserve">Pari ratione inueſtiganda eſt deſcenſio <lb/>ultimi gradus ♐, hoc eſt arcus inter principium ♈, & </s> <s xml:id="echoid-s14778" xml:space="preserve">gradum ultimum ♐, cõ-<lb/>prehenſi. </s> <s xml:id="echoid-s14779" xml:space="preserve">Huic arcui opponitur arcus contentus inter principium ♎, & </s> <s xml:id="echoid-s14780" xml:space="preserve">finem <lb/>♊. </s> <s xml:id="echoid-s14781" xml:space="preserve">Nam prima puncta dictorum arcuum, nec non extrema, per diametrum in <lb/>ſphæra opponuntur. </s> <s xml:id="echoid-s14782" xml:space="preserve">Aſcendit autem arcus a ♎, uſque ad finem ♓, cum grad. </s> <s xml:id="echoid-s14783" xml:space="preserve"><lb/>180. </s> <s xml:id="echoid-s14784" xml:space="preserve">Aequatoris. </s> <s xml:id="echoid-s14785" xml:space="preserve">& </s> <s xml:id="echoid-s14786" xml:space="preserve">arcus ab ♈, uſque ad finem ♊, cum gr. </s> <s xml:id="echoid-s14787" xml:space="preserve">66. </s> <s xml:id="echoid-s14788" xml:space="preserve">min. </s> <s xml:id="echoid-s14789" xml:space="preserve">57. </s> <s xml:id="echoid-s14790" xml:space="preserve">Aequa-<lb/>toris, quibus ſi addantur 180. </s> <s xml:id="echoid-s14791" xml:space="preserve">grad. </s> <s xml:id="echoid-s14792" xml:space="preserve">habebitur aſcenſio arcus ab initio ♎, uſque <lb/>ad finem ♊, hoc eſt deſcenſio arcus ab initio ♈, uſque ad finem ♐, grad. </s> <s xml:id="echoid-s14793" xml:space="preserve">246. </s> <s xml:id="echoid-s14794" xml:space="preserve"><lb/>min. </s> <s xml:id="echoid-s14795" xml:space="preserve">57. </s> <s xml:id="echoid-s14796" xml:space="preserve">& </s> <s xml:id="echoid-s14797" xml:space="preserve">ſic de cæteris.</s> <s xml:id="echoid-s14798" xml:space="preserve"/> </p> <div xml:id="echoid-div755" type="float" level="2" n="4"> <note position="right" xlink:label="note-375-01" xlink:href="note-375-01a" xml:space="preserve">Qno pact@ <lb/>ex t<unsure/>abulis <lb/>aſeenſionũ@ <lb/>obliquarũ <lb/>aſcenſione, <lb/>obliquæ, & <lb/>deſcẽnones <lb/>inueniatur.</note> </div> <note position="right" xml:space="preserve">Quomod@ <lb/>aliter ex ta-<lb/>bulisaſcẽſio <lb/>nũ obliqua <lb/>rum deſce@ <lb/>ſiones obli-<lb/>quæ inqui-<lb/>rantur.</note> <p> <s xml:id="echoid-s14799" xml:space="preserve"><emph style="sc">Solet</emph> quoque inueſtigari aliter, quàm diximus, deſcenſio cuiuslibet ar-<lb/>cus à principio ♈, incipientis, hac ratione. </s> <s xml:id="echoid-s14800" xml:space="preserve">Auferatur ab aſcenſione pũcti, quod <lb/>per diametrum extremo puncto arcus oppoſiti opponitur, integer ſemicircu-<lb/>lus, hoc eſt, grad. </s> <s xml:id="echoid-s14801" xml:space="preserve">180. </s> <s xml:id="echoid-s14802" xml:space="preserve">Quod ſi detractio fieri nequit, adijciantur prius grad. <lb/></s> <s xml:id="echoid-s14803" xml:space="preserve">360. </s> <s xml:id="echoid-s14804" xml:space="preserve">nempe circulus integer, ad aſcenſionem puncti oppoſiti. </s> <s xml:id="echoid-s14805" xml:space="preserve">Quod enim re-<lb/>linquitur, erit deſcenſio quæſita. </s> <s xml:id="echoid-s14806" xml:space="preserve">EXEMPLVM. </s> <s xml:id="echoid-s14807" xml:space="preserve">Quæritur Romæ deſcen-<lb/>ſio grad. </s> <s xml:id="echoid-s14808" xml:space="preserve">8. </s> <s xml:id="echoid-s14809" xml:space="preserve">♌; </s> <s xml:id="echoid-s14810" xml:space="preserve">Ex aſcenſione grad. </s> <s xml:id="echoid-s14811" xml:space="preserve">8. </s> <s xml:id="echoid-s14812" xml:space="preserve">♒, hoc eſt, ex grad. </s> <s xml:id="echoid-s14813" xml:space="preserve">327. </s> <s xml:id="echoid-s14814" xml:space="preserve">min. </s> <s xml:id="echoid-s14815" xml:space="preserve">45. </s> <s xml:id="echoid-s14816" xml:space="preserve">detraho <lb/>grad. </s> <s xml:id="echoid-s14817" xml:space="preserve">180. </s> <s xml:id="echoid-s14818" xml:space="preserve">remanetq; </s> <s xml:id="echoid-s14819" xml:space="preserve">deſcenſio arcus ab ♈, uſque ad grad. </s> <s xml:id="echoid-s14820" xml:space="preserve">8. </s> <s xml:id="echoid-s14821" xml:space="preserve">♌, graduum 147. </s> <s xml:id="echoid-s14822" xml:space="preserve"><lb/>min. </s> <s xml:id="echoid-s14823" xml:space="preserve">45. </s> <s xml:id="echoid-s14824" xml:space="preserve">Rurſus, Inuenienda eſt deſcenſio grad. </s> <s xml:id="echoid-s14825" xml:space="preserve">20. </s> <s xml:id="echoid-s14826" xml:space="preserve">♏, Adi<unsure/>jcio ad aſcenſionẽ <lb/>grad. </s> <s xml:id="echoid-s14827" xml:space="preserve">20. </s> <s xml:id="echoid-s14828" xml:space="preserve">♉, nempe ad grad. </s> <s xml:id="echoid-s14829" xml:space="preserve">30. </s> <s xml:id="echoid-s14830" xml:space="preserve">min. </s> <s xml:id="echoid-s14831" xml:space="preserve">46. </s> <s xml:id="echoid-s14832" xml:space="preserve">integrum circulum, & </s> <s xml:id="echoid-s14833" xml:space="preserve">à numero compo <lb/>ſito, hoc eſt, grad. </s> <s xml:id="echoid-s14834" xml:space="preserve">390. </s> <s xml:id="echoid-s14835" xml:space="preserve">min. </s> <s xml:id="echoid-s14836" xml:space="preserve">46. </s> <s xml:id="echoid-s14837" xml:space="preserve">auſero ſemicirculum, relinquiturque deſcenſio <lb/>arcus ab ♈, uſque ad grad. </s> <s xml:id="echoid-s14838" xml:space="preserve">20. </s> <s xml:id="echoid-s14839" xml:space="preserve">♏, graduum 210. </s> <s xml:id="echoid-s14840" xml:space="preserve">min. </s> <s xml:id="echoid-s14841" xml:space="preserve">46. </s> <s xml:id="echoid-s14842" xml:space="preserve">&</s> <s xml:id="echoid-s14843" xml:space="preserve">c.</s> <s xml:id="echoid-s14844" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div757" type="section" level="1" n="266"> <head xml:id="echoid-head277" xml:space="preserve">Sequuntur Tabulæ.</head> <pb o="340" file="376" n="377" rhead="Comment. in III. Cap. Sphæræ"/> </div> <div xml:id="echoid-div758" type="section" level="1" n="267"> <head xml:id="echoid-head278" xml:space="preserve">TABVLA DIFFERENTIARVM <lb/>Aſcenſionalium.</head> <note position="right" xml:space="preserve"> <lb/> Eleuatio. # G. # ## 1 # ## 2 # ## 3 # ## 4 # ## 5 # ## 6 # ## 7 # # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # 1 # 0 # 1 # 0 # 2 # 0 # 3 # 0 # 4 # 0 # 5 # 0 # 6 # 0 # 7 # 2 # 0 # 2 # 0 # 4 # 0 # 6 # 0 # 8 # 0 # 10 # 0 # 13 # 0 # 15 # 3 # 0 # 3 # 0 # 6 # 0 # 9 # 0 # 13 # 0 # 16 # 0 # 19 # 0 # 22 # 4 # 0 # 4 # 0 # 8 # 0 # 13 # 0 # 17 # 0 # 21 # 0 # 25 # 0 # 30 # 5 # 0 # 5 # 0 # 10 # 0 # 16 # 0 # 21 # 0 # 26 # 0 # 32 # 0 # 37 # 6 # 0 # 6 # 0 # 13 # 0 # 19 # 0 # 25 # 0 # 32 # 0 # 38 # 0 # 44 # 7 # 0 # 7 # 0 # 15 # 0 # 22 # 0 # 30 # 0 # 37 # 0 # 44 # 0 # 52 # 8 # 0 # 8 # 0 # 17 # 0 # 25 # 0 # 34 # 0 # 42 # 0 # 51 # 0 # 59 # 9 # 0 # 9 # 0 # 19 # 0 # 29 # 0 # 38 # 0 # 48 # 0 # 57 # 1 # 7 # 10 # 0 # 11 # 0 # 21 # 0 # 32 # 0 # 42 # 0 # 53 # 1 # 4 # 1 # 14 # 11 # 0 # 12 # 0 # 23 # 0 # 35 # 0 # 47 # 0 # 58 # 1 # 10 # 1 # 22 # 12 # 0 # 13 # 0 # 25 # 0 # 38 # 0 # 51 # 1 # 4 # 1 # 17 # 1 # 30 # 13 # 0 # 14 # 0 # 28 # 0 # 42 # 0 # 56 # 1 # 9 # 1 # 23 # 1 # 37 # 14 # 0 # 15 # 0 # 30 # 0 # 45 # 1 # 0 # 1 # 15 # 1 # 30 # 1 # 45 # 15 # 0 # 16 # 0 # 32 # 0 # 48 # 1 # 4 # 1 # 21 # 1 # 37 # 1 # 53 # 16 # 0 # 17 # 0 # 34 # 0 # 52 # 1 # 9 # 1 # 26 # 1 # 44 # 2 # 1 # 17 # 0 # 18 # 0 # 37 # 0 # 55 # 1 # 14 # 1 # 32 # 1 # 50 # 2 # 9 # 18 # 0 # 19 # 0 # 39 # 0 # 59 # 1 # 18 # 1 # 38 # 1 # 57 # 2 # 17 # 19 # 0 # 21 # 0 # 41 # 1 # 2 # 1 # 23 # 1 # 44 # 2 # 4 # 2 # 25 # 20 # 0 # 22 # 0 # 44 # 1 # 6 # 1 # 27 # 1 # 49 # 2 # 12 # 2 # 34 # 21 # 0 # 23 # 0 # 46 # 1 # 9 # 1 # 32 # 1 # 55 # 2 # 19 # 2 # 42 # 22 # 0 # 24 # 0 # 49 # 1 # 13 # 1 # 37 # 2 # 2 # 2 # 26 # 2 # 51 # 23 # 0 # 25 # 0 # 51 # 1 # 17 # 1 # 42 # 2 # 8 # 2 # 33 # 2 # 59 # 24 # 0 # 27 # 0 # 53 # 1 # 20 # 1 # 47 # 2 # 14 # 2 # 41 # 3 # 8 # 25 # 0 # 28 # 0 # 56 # 1 # 24 # 1 # 52 # 2 # 20 # 2 # 49 # 3 # 17 # 26 # 0 # 29 # 0 # 59 # 1 # 28 # 1 # 57 # 2 # 27 # 2 # 56 # 3 # 26 # 27 # 0 # 31 # 1 # 1 # 1 # 32 # 2 # 3 # 2 # 33 # 3 # 4 # 3 # 35 # 28 # 0 # 32 # 1 # 4 # 1 # 36 # 2 # 8 # 2 # 40 # 3 # 12 # 3 # 45 # 29 # 0 # 33 # 1 # 7 # 1 # 40 # 2 # 13 # 2 # 47 # 3 # 20 # 3 # 54 # 30 # 0 # 35 # 1 # 9 # 1 # 44 # 2 # 19 # 2 # 54 # 3 # 29 # 4 # 4 # 31 # 0 # 36 # 1 # 12 # 1 # 48 # 2 # 24 # 3 # 1 # 3 # 37 # 4 # 14 # 32 # 0 # 37 # 1 # 15 # 1 # 53 # 2 # 30 # 3 # 8 # 3 # 46 # 4 # 24 </note> <pb o="341" file="377" n="378" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div759" type="section" level="1" n="268"> <head xml:id="echoid-head279" xml:space="preserve">RESIDVVM TABVLAE <lb/>Differentiarum Aſcenſionalium. # Poli</head> <note position="right" xml:space="preserve"> <lb/> # ## 8 # ## 9 # ## 10 # ## 11 # ## 12 # ## 13 # ## 14 # ## 15 G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 1 # 0 # 8 # 0 # 9 # 0 # 11 # 0 # 12 # 0 # 13 # 0 # 14 # 0 # 15 # 0 # 16 2 # 0 # 17 # 0 # 19 # 0 # 21 # 0 # 23 # 0 # 25 # 0 # 28 # 0 # 30 # 0 # 32 3 # 0 # 25 # 0 # 29 # 0 # 32 # 0 # 35 # 0 # 38 # 0 # 42 # 0 # 45 # 0 # 48 4 # 0 # 34 # 0 # 38 # 0 # 42 # 0 # 47 # 0 # 51 # 1 # 56 # 0 # 0 # 0 # 4 5 # 0 # 42 # 0 # 48 # 0 # 53 # 0 # 58 # 1 # 4 # 1 # 9 # 1 # 15 # 1 # 21 6 # 0 # 5@ # 0 # 57 # 1 # 4 # 1 # 10 # 1 # 17 # 1 # 23 # 1 # 30 # 1 # 37 7 # 0 # 59 # 1 # 7 # 1 # 14 # 1 # 22 # 1 # 30 # 1 # 37 # 1 # 45 # 1 # 57 8 # 1 # 8 # 1 # 16 # 1 # 25 # 1 # 34 # 1 # 43 # 1 # 52 # 2 # 0 # 2 # 9 9 # 1 # 16 # 1 # 26 # 1 # 36 # 1 # 46 # 1 # 56 # 2 # 6 # 2 # 16 # 2 # 26 10 # 1 # 25 # 1 # 36 # 1 # 47 # 1 # 58 # 2 # 9 # 2 # 20 # 2 # 31 # 2 # 42 11 # 1 # 34 # 1 # 46 # 1 # 58 # 2 # 10 # 2 # 22 # 2 # 34 # 2 # 47 # 2 # 59 12 # 1 # 43 # 1 # 56 # 2 # 9 # 2 # 22 # 2 # 35 # 2 # 49 # 3 # 2 # 3 # 16 13 # 1 # 52 # 2 # 6 # 2 # 20 # 2 # 34 # 2 # 49 # 3 # 3 # 3 # 18 # 3 # 33 14 # 2 # 0 # 2 # 16 # 2 # 31 # 2 # 47 # 3 # @2 # 3 # 18 # 3 # 34 # 3 # 50 15 # 2 # 10 # 2 # 26 # 2 # 42 # 2 # 59 # 3 # 16 # 3 # 33 # 3 # 50 # 4 # 27 16 # 2 # 19 # 2 # 36 # 2 # 54 # 3 # 12 # 3 # 30 # 3 # 48 # 4 # 6 # 4 # 24 17 # 2 # 28 # 2 # 46 # 3 # 5 # 3 # 24 # 3 # 44 # 3 # 3 # 4 # 22 # 4 # 42 18 # 2 # 37 # 2 # 57 # 3 # 17 # 3 # 37 # 3 # 58 # 4 # 18 # 4 # 39 # 5 # 0 19 # 2 # 46 # 3 # 8 # 3 # 29 # 3 # 50 # 4 # 17 # 4 # 34 # 4 # 55 # 5 # 18 20 # 2 # 56 # 3 # 18 # 3 # 41 # 4 # 3 # 4 # 2@ # 4 # 49 # 5 # 12 # 5 # 36 21 # 3 # 6 # 3 # 29 # 3 # 53 # 4 # 17 # 4 # 41 # 5 # 5 # 5 # 30 # 5 # 45 22 # 3 # 15 # 3 # 40 # 4 # 5 # 4 # 30 # 4 # 56 # 5 # 21 # 5 # 47 # 6 # 31 23 # 3 # 25 # 3 # 51 # 4 # 18 # 4 # 44 # 5 # 11 # 5 # 37 # 6 # 7 # 6 # 32 24 # 3 # 35 # 4 # 3 # 4 # 30 # 4 # 58 # 5 # 26 # 5 # 54 # 6 # 22 # 6 # 51 25 # 3 # 45 # 4 # 14 # 4 # 43 # 5 # 12 # 5 # 41 # 6 # 11 # 6 # 41 # 7 # 11 26 # 3 # 56 # 4 # 26 # 4 # 56 # 5 # 26 # 5 # 57 # 6 # 28 # 6 # 59 # 7 # 31 27 # 4 # 6 # 4 # 38 # 5 # 9 # 5 # 41 # 6 # 13 # 6 # 45 # 7 # 18 # 7 # 51 28 # 4 # 17 # 4 # 50 # 5 # 23 # 5 # 56 # 6 # 29 # 7 # 3 # 7 # 37 # 8 # 11 29 # 4 # 28 # 5 # 2 # 5 # 37 # 6 # 11 # 6 # 46 # 7 # 21 # 7 # 57 # 8 # 32 30 # 4 # 39 # 5 # 15 # 5 # 51 # 6 # 27 # 7 # 3 # 7 # 40 # 8 # 17 # 8 # 54 31 # 4 # 51 # 5 # 28 # 6 # 5 # 6 # 42 # 7 # 20 # 7 # 58 # 8 # 37 # 9 # 16 32 # 5 # 2 # 5 # 41 # 6 # 20 # 6 # 59 # 7 # 38 # 8 # 18 # 8 # 58 # 9 # 38 </note> <pb o="342" file="378" n="379" rhead="Comment. in III. Cap. Sphæræ"/> </div> <div xml:id="echoid-div760" type="section" level="1" n="269"> <head xml:id="echoid-head280" xml:space="preserve">TABVLA DIFFERENTIARVM <lb/>Aſcenſionalium.</head> <note position="right" xml:space="preserve"> <lb/> Eleuatio # # ## 16 # ## 17 # ## 18 # ## 19 # ## 20 # ## 21 # ## 22 # G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # 1 # 0 # 17 # 0 # 18 # 0 # 19 # 0 # 21 # 0 # 22 # 0 # 23 # 0 # 24 # 2 # 0 # 34 # 0 # 37 # 0 # 39 # 0 # 41 # 0 # 44 # 0 # 46 # 0 # 49 # 3 # 0 # 52 # 0 # 55 # 0 # 59 # 1 # 2 # 1 # 6 # 1 # 9 # 1 # 13 # 4 # 1 # 9 # 1 # 14 # 1 # 18 # 1 # 23 # 1 # 27 # 1 # 32 # 1 # 37 # 5 # 1 # 26 # 1 # 32 # 1 # 38 # 1 # 44 # 1 # 49 # 1 # 55 # 2 # 2 # 6 # 1 # 44 # 1 # 50 # 1 # 57 # 2 # 4 # 2 # 12 # 2 # 19 # 2 # 26 # 7 # 2 # 1 # 2 # @ # 2 # 17 # 2 # 25 # 2 # 34 # 2 # 42 # 2 # 51 # 8 # 2 # 19 # 2 # 28 # 2 # 37 # 2 # 46 # 2 # 56 # 3 # 6 # 3 # 15 # 9 # 2 # 39 # 2 # 47 # 2 # 57 # 3 # 8 # 3 # 18 # 3 # 29 # 3 # 40 # 10 # 2 # 54 # 3 # 5 # 3 # 17 # 3 # 29 # 3 # 41 # 3 # 53 # 4 # 5 # 11 # 3 # 12 # 3 # 24 # 3 # 37 # 3 # 50 # 4 # 3 # 4 # 17 # 4 # 30 # 12 # 3 # 30 # 3 # 44 # 3 # 58 # 4 # 12 # 4 # 26 # 4 # 41 # 4 # 56 # 13 # 3 # 48 # 4 # 3 # 4 # 18 # 4 # 34 # 4 # 49 # 5 # 5 # 5 # 21 # 14 # 4 # 6 # 4 # 22 # 4 # 39 # 4 # 55 # 5 # 12 # 5 # 30 # 5 # 47 # 15 # 4 # 24 # 4 # 42 # 5 # 0 # 5 # 18 # 5 # 36 # 5 # 54 # 6 # 13 # 16 # 4 # 43 # 5 # 2 # 5 # 21 # 5 # 40 # 5 # 59 # 6 # 19 # 6 # 39 # 17 # 5 # 2 # 5 # 22 # 5 # 42 # 6 # 2 # 6 # 23 # 6 # 44 # 7 # 6 # 18 # 5 # 21 # 5 # 42 # 6 # 4 # 6 # 25 # 6 # 47 # 7 # 10 # 7 # 33 # 19 # 5 # 40 # 6 # 3 # 6 # 25 # 6 # 49 # 7 # 12 # 7 # 36 # 8 # 0 # 20 # 5 # 59 # 6 # 23 # 6 # 47 # 7 # 12 # 7 # 37 # 8 # 2 # 8 # 27 # 21 # 6 # 19 # 6 # 44 # 7 # 10 # 7 # 36 # 8 # 2 # 8 # 28 # 8 # 55 # 22 # 6 # 39 # 7 # 6 # 7 # 33 # 8 # 0 # 8 # 27 # 8 # 55 # 9 # 24 # 23 # 6 # 59 # 7 # 27 # 7 # 56 # 8 # 24 # 8 # 53 # 9 # 22 # 9 # 53 # 24 # 7 # 20 # 7 # 49 # 8 # 19 # 8 # 49 # 9 # 19 # 9 # 50 # 10 # 22 # 25 # 7 # 41 # 8 # 12 # 8 # 43 # 9 # 14 # 9 # 46 # 10 # 19 # 10 # 52 # 26 # 8 # 2 # 8 # 35 # 9 # 7 # 9 # 40 # 10 # 14 # 10 # 47 # 11 # 22 # 27 # 8 # 24 # 8 # 58 # 9 # 32 # 10 # 6 # 10 # 41 # 11 # 17 # 11 # 53 # 28 # 8 # 46 # 9 # 21 # 9 # 57 # 10 # 33 # 11 # 9 # 11 # 47 # 12 # 24 # 29 # 9 # 9 # 9 # 45 # 10 # 23 # 11 # 10 # 11 # 38 # 12 # 17 # 12 # 56 # 30 # 9 # 32 # 10 # 10 # 10 # 49 # 11 # 28 # 12 # 8 # 12 # 48 # 13 # 29 # 31 # 9 # 55 # 10 # 35 # 11 # 16 # 11 # 56 # 12 # 38 # 13 # 20 # 14 # 3 # 32 # 10 # 19 # 11 # 1 # 11 # 43 # 12 # 25 # 13 # 9 # 13 # 53 # 14 # 37 </note> <pb o="343" file="379" n="380" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div761" type="section" level="1" n="270"> <head xml:id="echoid-head281" xml:space="preserve">RESIDVVM TABVLAE <lb/>Differentiarum Aſcenſionalium.</head> <note position="right" xml:space="preserve"> <lb/> # ## 23 # ## 24 # ## 25 # ## 26 # ## 27 # ## 28 # ## 29 # ## 30 # Poli G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 1 # 0 # 25 # 0 # 27 # 0 # 28 # 0 # 29 # 0 # 31 # 0 # 32 # 0 # 33 # 0 # 35 2 # 0 # 51 # 0 # 53 # 0 # 56 # 0 # 59 # 1 # 1 # 1 # 4 # 1 # 7 # 1 # 9 3 # 1 # 17 # 1 # 20 # 1 # 24 # 1 # 28 # 1 # 32 # 1 # 36 # 1 # 40 # 1 # 44 4 # 1 # 42 # 1 # 47 # 1 # 52 # 1 # 57 # 2 # 3 # 2 # 8 # 2 # 13 # 2 # 19 5 # 2 # 8 # 2 # 14 # 2 # 20 # 2 # 27 # 2 # 33 # 2 # 40 # 2 # 47 # 2 # 54 6 # 2 # 33 # 2 # 41 # 2 # 49 # 2 # 56 # 3 # 4 # 3 # 12 # 3 # 20 # 3 # 29 7 # 2 # 59 # 3 # 8 # 3 # 17 # 3 # 26 # 3 # 35 # 3 # 45 # 3 # 54 # 4 # 4 8 # 3 # 25 # 3 # 35 # 3 # 45 # 3 # 56 # 4 # 6 # 4 # 17 # 4 # 28 # 4 # 39 9 # 3 # 5 # 4 # 3 # 4 # 14 # 4 # 26 # 4 # 38 # 4 # 50 # 5 # 2 # 5 # 15 10 # 4 # 18 # 4 # 30 # 4 # 43 # 4 # 56 # 5 # 9 # 5 # 23 # 5 # 37 # 5 # 51 11 # 4 # 44 # 4 # 58 # 5 # 12 # 5 # 26 # 5 # 41 # 5 # 56 # 6 # 11 # 6 # 27 12 # 5 # 11 # 5 # 26 # 5 # 41 # 5 # 57 # 6 # 13 # 6 # 29 # 6 # 46 # 7 # 3 13 # 5 # 38 # 5 # 54 # 6 # 11 # 6 # 28 # 6 # 45 # 7 # 3 # 7 # 21 # 7 # 40 14 # 6 # 5 # 6 # 22 # 6 # 41 # 6 # 59 # 7 # 18 # 7 # 37 # 7 # 56 # 8 # 17 15 # 6 # 32 # 6 # 51 # 7 # 11 # 7 # 31 # 7 # 51 # 8 # 11 # 8 # 32 # 8 # 54 16 # 6 # 59 # 7 # 20 # 7 # 41 # 8 # 3 # 8 # 24 # 8 # 46 # 9 # 8 # 9 # 32 17 # 7 # 27 # 7 # 49 # 8 # 12 # 8 # 35 # 8 # 58 # 9 # 21 # 9 # 45 # 10 # 10 18 # 7 # 56 # 8 # 19 # 8 # 43 # 9 # 7 # 9 # 32 # 9 # 57 # 10 # 23 # 10 # 49 19 # 8 # 24 # 8 # 49 # 9 # 14 # 9 # 40 # 10 # 6 # 10 # 33 # 11 # 0 # 11 # 28 20 # 8 # 53 # 9 # 19 # 9 # 46 # 10 # 14 # 10 # 41 # 11 # 9 # 11 # 38 # 12 # 8 21 # 9 # 23 # 9 # 50 # 10 # 19 # 10 # 47 # 11 # 17 # 11 # 46 # 12 # 17 # 12 # 48 22 # 9 # 53 # 10 # 22 # 10 # 52 # 11 # 22 # 11 # 53 # 12 # 24 # 12 # 56 # 13 # 29 23 # 10 # 23 # 10 # 54 # 11 # 25 # 11 # 57 # 12 # 29 # 13 # 3 # 13 # 37 # 14 # 11 24 # 10 # 54 # 11 # 26 # 11 # 59 # 12 # 33 # 13 # 7 # 13 # 42 # 14 # 17 # 14 # 54 25 # 11 # 25 # 11 # 59 # 12 # 34 # 13 # 9 # 13 # 45 # 14 # 21 # 14 # 59 # 15 # 37 26 # 11 # 57 # 12 # 33 # 13 # 9 # 13 # 46 # 14 # 23 # 15 # 3 # 15 # 41 # 16 # 21 27 # 12 # 29 # 13 # 7 # 13 # 45 # 14 # 23 # 15 # 3 # 15 # 43 # 16 # 24 # 18 # 6 28 # 13 # 3 # 13 # 42 # 14 # 21 # 15 # 2 # 15 # 43 # 16 # 25 # 17 # 8 # 17 # 53 29 # 13 # 37 # 14 # 17 # 14 # 59 # 15 # 41 # 16 # 24 # 17 # 8 # 17 # 54 # 18 # 40 30 # 14 # 11 # 14 # 54 # 15 # 37 # 16 # 21 # 17 # 6 # 17 # 53 # 18 # 40 # 19 # 28 31 # 14 # 47 # 15 # 31 # 16 # 16 # 17 # 2 # 17 # 50 # 18 # 38 # 19 # 27 # 20 # 18 32 # 15 # 23 # 16 # 9 # 16 # 56 # 17 # 45 # 18 # 34 # 19 # 24 # 20 # 16 # 21 # 9 </note> <pb o="344" file="380" n="381" rhead="Comment. in III. Cap Sphæræ"/> </div> <div xml:id="echoid-div762" type="section" level="1" n="271"> <head xml:id="echoid-head282" xml:space="preserve">RESIDVVM TABVLAE <lb/>Differentiarum Aſcenſionalium.</head> <note position="right" xml:space="preserve"> <lb/> ## Eleuatio # # ## 31 # ## 32 # ## 33 # ## 34 # ## 35 # ## 36 G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # # 1 # 0 # 36 # 0 # 37 # 0 # 39 # 0 # 40 # 0 # 42 # 0 # 44 # 0 # 45 # # 2 # 1 # 12 # 1 # 15 # 1 # 18 # 1 # 21 # 1 # 24 # 1 # 27 # 1 # 31 # # 3 # 1 # 48 # 1 # 53 # 1 # 57 # 2 # 2 # 2 # 6 # 2 # 11 # 2 # 16 # # 4 # 2 # 24 # 2 # 30 # 2 # 36 # 2 # 42 # 2 # 48 # 2 # 55 # 3 # 1 # # 5 # 3 # 1 # 3 # 8 # 3 # 15 # 3 # 23 # 3 # 31 # 3 # 39 # 3 # 47 # # 6 # 3 # 37 # 3 # 46 # 3 # 55 # 4 # 4 # 4 # 13 # 4 # 23 # 4 # 33 # # 7 # 4 # 14 # 4 # 24 # 4 # 34 # 4 # 45 # 4 # 56 # 5 # 7 # 5 # 19 # # 8 # 4 # 51 # 5 # 2 # 5 # 14 # 5 # 26 # 5 # 39 # 5 # 52 # 6 # 5 # # 9 # 5 # 28 # 5 # 41 # 5 # 54 # 6 # 8 # 6 # 22 # 6 # 36 # 6 # 41 # # 10 # 6 # 5 # 6 # 20 # 6 # 35 # 6 # 50 # 7 # 6 # 7 # 22 # 7 # 38 # # 11 # 6 # 42 # 6 # 59 # 7 # 15 # 7 # 32 # 7 # 49 # 8 # 7 # 8 # 25 # # 12 # 7 # 20 # 7 # 38 # 7 # 56 # 8 # 15 # 8 # 34 # 8 # 53 # 9 # 13 # # 13 # 7 # 58 # 8 # 18 # 8 # 37 # 8 # 54 # 9 # 18 # 9 # 39 # 10 # 1 # # 14 # 8 # 7 # 8 # 58 # 9 # 19 # 9 # 41 # 10 # 3 # 10 # 26 # 10 # 50 # # 15 # 9 # 16 # 9 # 38 # 10 # 1 # 10 # 25 # 10 # 49 # 11 # 14 # 11 # 39 # # 16 # 9 # 55 # 10 # 19 # 10 # 44 # 11 # 9 # 11 # 35 # 12 # 2 # 12 # 29 # # 17 # 10 # 35 # 11 # 1 # 11 # 27 # 11 # 54 # 12 # 22 # 12 # 50 # 13 # 19 # # 18 # 11 # 19 # 11 # 43 # 12 # 11 # 13 # 40 # 13 # 9 # 13 # 39 # 14 # 10 # # 19 # 11 # 56 # 12 # 25 # 12 # 55 # 13 # 26 # 13 # 57 # 14 # 29 # 15 # 2 # # 20 # 12 # 38 # 13 # 9 # 13 # 40 # 14 # 13 # 14 # 46 # 15 # 20 # 15 # 55 # # 21 # 13 # 20 # 13 # 53 # 14 # 26 # 15 # 0 # 15 # 36 # 16 # 12 # 61 # 49 # # 22 # 14 # 3 # 14 # 47 # 15 # 13 # 15 # 49 # 16 # 27 # 17 # 5 # 17 # 44 # # 23 # 14 # 47 # 15 # 23 # 16 # 0 # 16 # 38 # 17 # 17 # 17 # 58 # 18 # 39 # # 24 # 15 # 31 # 16 # 9 # 16 # 48 # 17 # 29 # 18 # 10 # 18 # 52 # 19 # 36 # # 25 # 16 # 16 # 16 # 56 # 18 # 38 # 18 # 20 # @9 # 3 # 19 # 48 # 20 # 34 # # 26 # 17 # 2 # 17 # 45 # 18 # 28 # 19 # 12 # 19 # 58 # 20 # 45 # 21 # 34 # # 27 # 17 # 50 # 18 # 34 # 19 # 19 # 20 # 6 # 20 # 54 # 21 # 44 # 22 # 35 # # 28 # 18 # 38 # 19 # 24 # 20 # 12 # 21 # 1 # 21 # 51 # 22 # 43 # 23 # 37 # # 29 # 19 # 27 # 20 # 16 # 21 # 6 # 21 # 57 # 22 # 50 # 23 # 45 # 14 # 41 # # 30 # 20 # 18 # 21 # 9 # 22 # 1 # 22 # 55 # 23 # 51 # 24 # 48 # 25 # 47 # # 31 # 11 # 10 # 22 # 3 # 22 # 38 # 23 # 55 # 24 # 53 # 25 # 53 # 26 # 55 # # 32 # 22 # 3 # 22 # 50 # 23 # 56 # 24 # 56 # 25 # 57 # 27 # 0 # 28 # 5 </note> <pb o="345" file="381" n="382" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div763" type="section" level="1" n="272"> <head xml:id="echoid-head283" xml:space="preserve">RESIDVVM TABVLAE <lb/>Differentiarum Aſcenſionalium.</head> <note position="right" xml:space="preserve"> <lb/> # ## 38 # ## 39 # ## 40 # ## 41 # ## 42 # ## 43 # ## 44 # ## 45 # Poli. G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 1 # 0 # 47 # 0 # 49 # 0 # 50 # 0 # 52 # 0 # 54 # 0 # 56 # 0 # 58 # 1 # 0 2 # 1 # 34 # 1 # 37 # 1 # 41 # 1. # 44 # 1 # 48 # 1 # 52 # 1 # 56 # 2 # 0 3 # 2 # 21 # 2 # 26 # 2 # 31 # 2 # 37 # 2 # 42 # 2 # 48 # 2 # 54 # 3 # 0 4 # 3 # 8 # 3 # 15 # 3 # 22 # 3 # 29 # 3 # 37 # 3 # 44 # 3 # 52 # 4 # 2 5 # 3 # 55 # 4 # 4 # 4 # 13 # 4 # 22 # 4 # 31 # 4 # 41 # 4 # 51 # 5 # 2 6 # 4 # 43 # 4 # 53 # 5 # 4 # 5 # 15 # 5 # 26 # 5 # 37 # 5 # 50 # 6 # 2 7 # 5 # 30 # 5 # 42 # 5 # 55 # 6 # 8 # 6 # 21 # 6 # 34 # 6 # 49 # 7 # 3 9 # 6 # 18 # 6 # 32 # 6 # 46 # 7 # 1 # 7 # 16 # 7 # 32 # 7 # 48 # 8 # 5 8 # 7 # 6 # 7 # 22 # 7 # 38 # 7 # 55 # 8 # 12 # 8 # 30 # 8 # 48 # 9 # 7 10 # 7 # 55 # 8 # 13 # 8 # 30 # 8 # 49 # 9 # 8 # 9 # 28 # 9 # 48 # 10 # 9 11 # 8 # 44 # 9 # 3 # 9 # 23 # 9 # 44 # 10 # 5 # 10 # 27 # 10 # 49 # 11 # 13 12 # 9 # 34 # 9 # 55 # 10 # 16 # 10 # 39 # 11 # 2 # 11 # 26 # 11 # 51 # 12 # 16 13 # 10 # 24 # 10 # 46 # 11 # 10 # 11 # 35 # 12 # 0 # 12 # 26 # 12 # 53 # 13 # 21 14 # 11 # 14 # 11 # 39 # 12 # 5 # 12 # 31 # 12 # 58 # 13 # 27 # 13 # 56 # 14 # 26 15 # 12 # 5 # 12 # 32 # 13 # 0 # 13 # 28 # 13 # 58 # 14 # 28 # 15 # 0 # 15 # 32 16 # 12 # 57 # 13 # 26 # 13 # 55 # 14 # 26 # 14 # 58 # 15 # 31 # 16 # 5 # 16 # 40 17 # 13 # 49 # 14 # 20 # 14 # 52 # 15 # 25 # 15 # 59 # 16 # 34 # 17 # 10 # 17 # 48 18 # 14 # 42 # 15 # 15 # 15 # 49 # 16 # 24 # 17 # 1 # 17 # 38 # 18 # 17 # 18 # 58 19 # 15 # 36 # 16 # 11 # 16 # 48 # 17 # 25 # 18 # 4 # 18 # 44 # 19 # 25 # 20 # 9 20 # 16 # 31 # 17 # 8 # 17 # 47 # 18 # 27 # 19 # 8 # 19 # 50 # 20 # 35 # 21 # 21 21 # 17 # 27 # 18 # 7 # 18 # 47 # 19 # 30 # 20 # 13 # 20 # 59 # 21 # 46 # 22 # 34 22 # 18 # 24 # 19 # 6 # 19 # 49 # 20 # 34 # 21 # 20 # 22 # 8 # 22 # 58 # 23 # 50 23 # 19 # 22 # 20 # 6 # 20 # 52 # 21 # 39 # 22 # 28 # 23 # 19 # 14 # 12 # 25 # 7 24 # 20 # 21 # 21 # 8 # 21 # 56 # 22 # 46 # 23 # 38 # 24 # 32 # 25 # 28 # 26 # 26 25 # 21 # 21 # 22 # 11 # 23 # 2 # 23 # 55 # 24 # 50 # 25 # 47 # 26 # 46 # 27 # 48 26 # 22 # 23 # 23 # 16 # 24 # 10 # 25 # 5 # 25 # 3 # 27 # 3 # 28 # 6 # 29 # 11 27 # 23 # 24 # 24 # 22 # 25 # 19 # 26 # 17 # 27 # 18 # 28 # 22 # 29 # 29 # 30 # 38 28 # 24 # 33 # 25 # 30 # 26 # 30 # 27 # 31 # 28 # 36 # 29 # 44 # 30 # 54 # 32 # 7 29 # 25 # 40 # 26 # 40 # 27 # 43 # 28 # 48 # 29 # 56 # 31 # 8 # 32 # 22 # 33 # 40 30 # 26 # 49 # 27 # 52 # 28 # 59 # 30 # 7 # 31 # 19 # 32 # 35 # 33 # 33 # 35 # 16 31 # 28 # 0 # 29 # 7 # 30 # 17 # 31 # 29 # 32 # 45 # 34 # 5 # 35 # 35 # 36 # 56 32 # 29 # 13 # 30 # 54 # 31 # 31 # 32 # 54 # 34 # 14 # 35 # 38 # 37 # 37 # 38 # 40 </note> <pb o="346" file="382" n="383" rhead="Comment. in III. Cap. Sphæræ"/> </div> <div xml:id="echoid-div764" type="section" level="1" n="273"> <head xml:id="echoid-head284" xml:space="preserve">RESIDVVM TABVLAE <lb/>Differentiarum Aſcenſionalium.</head> <note position="right" xml:space="preserve"> <lb/> # ## 46 # ## 47 # ## 48 # ## 49 # ## 50 # ## 51 # ## 52 G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 1 # 1 # 2 # 1 # 4 # 1 # 7 # 1 # 9 # 1 # 12 # 1 # 14 # 1 # 17 2 # 2 # 4 # 2 # 9 # 2 # 13 # 2 # 18 # 2 # 23 # 2 # 28 # 2 # 34 3 # 3 # 7 # 3 # 13 # 3 # 20 # 3 # 27 # 3 # 35 # 3 # 43 # 3 # 51 4 # 4 # 9 # 4 # 18 # 4 # 27 # 4 # 37 # 4 # 47 # 4 # 57 # 5 # 8 5 # 5 # 12 # 5 # 23 # 5 # 35 # 5 # 47 # 5 # 50 # 6 # 12 # 6 # 26 6 # 6 # 15 # 6 # 28 # 6 # 42 # 6 # 57 # 7 # 12 # 7 # 27 # 7 # 44 7 # 7 # 18 # 7 # 34 # 7 # 50 # 8 # 7 # 8 # 25 # 8 # 43 # 9 # 2 8 # 8 # 22 # 8 # 30 # 8 # 59 # 9 # 18 # 9 # 38 # 10 # 0 # 10 # 22 9 # 9 # 26 # 9 # 47 # 10 # 8 # 10 # 30 # 10 # 53 # 11 # 17 # 11 # 42 10 # 10 # 31 # 10 # 54 # 11 # 18 # 11 # 42 # 12 # 8 # 12 # 35 # 13 # 3 11 # 11 # 37 # 12 # 2 # 12 # 28 # 12 # 55 # 13 # 24 # 13 # 53 # 14 # 24 12 # 12 # 43 # 13 # 11 # 13 # 39 # 14 # 9 # 14 # 40 # 15 # 13 # 15 # 47 13 # 13 # 50 # 14 # 20 # 14 # 51 # 15 # 24 # 15 # 58 # 16 # 34 # 17 # 11 14 # 14 # 58 # 15 # 30 # 16 # 5 # 16 # 40 # 17 # 17 # 17 # 56 # 18 # 37 15 # 16 # 7 # 16 # 42 # 17 # 19 # 17 # 57 # 18 # 39 # 19 # 19 # 20 # 4 16 # 17 # 16 # 17 # 54 # 18 # 34 # 19 # 16 # 19 # 59 # 20 # 44 # 21 # 32 17 # 18 # 27 # 19 # 8 # 19 # 51 # 20 # 36 # 21 # 22 # 22 # 11 # 23 # 2 18 # 19 # 40 # 20 # 23 # 21 # 9 # 21 # 57 # 22 # 47 # 23 # 39 # 24 # 34 19 # 20 # 53 # 21 # 40 # 22 # 29 # 23 # 20 # 14 # 14 # 25 # 10 # 26 # 9 20 # 22 # 8 # 22 # 58 # 23 # 51 # 24 # 45 # 25 # 42 # 26 # 43 # 27 # 46 21 # 23 # 25 # 24 # 18 # 25 # 14 # 26 # 12 # 27 # 14 # 28 # 18 # 29 # 26 22 # 24 # 44 # 25 # 40 # 26 # 40 # 27 # 42 # 28 # 47 # 29 # 56 # 31 # 8 23 # 26 # 5 # 27 # 5 # 28 # 8 # 29 # 14 # 30 # 23 # 31 # 37 # 32 # 54 24 # 27 # 27 # 28 # 31 # 29 # 38 # 30 # 48 # 32 # 3 # 33 # 21 # 34 # 44 25 # 28 # 52 # 30 # 0 # 31 # 12 # 32 # 26 # 33 # 46 # 35 # 10 # 36 # 39 26 # 30 # 20 # 31 # 32 # 32 # 48 # 34 # 8 # 35 # 32 # 37 # 2 # 38 # 38 27 # 31 # 51 # 33 # 7 # 34 # 28 # 35 # 53 # 37 # 23 # 39 # 0 # 40 # 42 28 # 33 # 25 # 34 # 46 # 36 # 12 # 37 # 43 # 39 # 19 # 41 # 2 # 42 # 53 29 # 35 # 2 # 36 # 28 # 38 # 0 # 39 # 47 # 41 # 21 # 43 # 12 # 45 # 12 30 # 36 # 43 # 38 # 15 # 39 # 53 # 41 # 47 # 43 # 29 # 45 # 29 # 47 # 49 31 # 38 # 29 # 40 # 7 # 41 # 52 # 43 # 44 # 45 # 44 # 47 # 54 # 50 # 16 32 # 40 # 19 # 42 # 4 # 43 # 57 # 45 # 57 # 48 # 8 # 50 # 30 # 53 # 7 </note> <pb o="347" file="383" n="384" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div765" type="section" level="1" n="274"> <head xml:id="echoid-head285" xml:space="preserve">RESIDVVM TABVLAE <lb/>Differentiarum Aſcenſionalium.</head> <note position="right" xml:space="preserve"> <lb/> # ## 53 # ## 54 # ## 55 # ## 56 # ## 57 # ## 58 # ## 59 # ## 60 # Poli@ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 1 # 1 # 20 # 1 # 23 # 1 # 26 # 1 # 29 # 1 # 32 # 1 # 36 # 1 # 40 # 1 # 44 2 # 2 # 39 # 2 # 45 # 2 # 52 # 2 # 58 # 3 # 5 # 3 # 12 # 3 # 20 # 3 # 28 3 # 3 # 59 # 4 # 8 # 4 # 17 # 4 # 27 # 4 # 38 # 4 # 49 # 5 # 0 # 5 # 13 4 # 5 # 19 # 5 # 31 # 5 # 44 # 5 # 57 # 6 # 11 # 6 # 25 # 6 # 41 # 6 # 57 5 # 6 # 40 # 6 # 55 # 7 # 11 # 7 # 27 # 7 # 44 # 8 # 3 # 8 # 22 # 8 # 43 6 # 8 # 1 # 8 # 19 # 8 # 38 # 8 # 58 # 9 # 19 # 9 # 41 # 10 # 4 # 10 # 28 7 # 9 # 23 # 9 # 44 # 10 # 6 # 10 # 29 # 10 # 54 # 11 # 20 # 11 # 47 # 12 # 17 8 # 10 # 45 # 11 # 9 # 11 # 39 # 12 # 1 # 12 # 30 # 13 # 0 # 13 # 32 # 14 # 5 9 # 12 # 8 # 12 # 35 # 13 # 4 # 13 # 35 # 14 # 7 # 14 # 41 # 15 # 17 # 15 # 55 10 # 13 # 32 # 14 # 3 # 14 # 35 # 15 # 9 # 15 # 45 # 16 # 23 # 17 # 4 # 17 # 47 11 # 14 # 57 # 15 # 31 # 16 # 7 # 16 # 45 # 17 # 25 # 18 # 8 # 18 # 53 # 19 # 41 12 # 16 # 23 # 17 # 0 # 17 # 40 # 18 # 22 # 19 # 6 # 19 # 53 # 20 # 43 # 21 # 36 13 # 17 # 50 # 18 # 32 # 19 # 15 # 20 # 1 # 20 # 50 # 21 # 41 # 22 # 36 # 23 # 34 14 # 19 # 19 # 20 # 4 # 20 # 52 # 21 # 42 # 22 # 35 # 23 # 31 # 24 # 31 # 25 # 35 15 # 20 # 50 # 21 # 38 # 22 # 30 # 23 # 24 # 24 # 22 # 25 # 23 # 2@ # 29 # 27 # 39 16 # 22 # 22 # 23 # 15 # 24 # 10 # 25 # 9 # 26 # 12 # 27 # 19 # 28 # 30 # 31 # 47 17 # 23 # 56 # 24 # 53 # 25 # 53 # 26 # 57 # 28 # 5 # 29 # 18 # 30 # 35 # 31 # 59 18 # 25 # 33 # 26 # 34 # 27 # 39 # 28 # 48 # 30 # 1 # 31 # 20 # 32 # 44 # 34 # 19 19 # 27 # 11 # 28 # 17 # 29 # 27 # 30 # 41 # 32 # 1 # 33 # 26 # 34 # 58 # 36 # 37 20 # 28 # 53 # 30 # 4 # 31 # 19 # 32 # 39 # 34 # 5 # 35 # 37 # 37 # 17 # 40 # 5 21 # 30 # 37 # 31 # 54 # 33 # 15 # 34 # 41 # 36 # 14 # 37 # 54 # 39 # 42 # 41 # 40 22 # 32 # 25 # 33 # 47 # 35 # 14 # 36 # 48 # 38 # 28 # 40 # 17 # 42 # 15 # 44 # 25 23 # 34 # 17 # 35 # 45 # 37 # 19 # 39 # 0 # 40 # 49 # 42 # 47 # 44 # 57 # 47 # 20 24 # 36 # 13 # 37 # 48 # 39 # 29 # 41 # 18 # 43 # 17 # 45 # 26 # 47 # 49 # 50 # 27 25 # 38 # 14 # 39 # 59 # 41 # 45 # 43 # 44 # 45 # 54 # 48 # 16 # 50 # 54 # 53 # 52 26 # 40 # 20 # 42 # 10 # 44 # 9 # 46 # 18 # 48 # 41 # 51 # 19 # 54 # 16 # 57 # 39 27 # 42 # 33 # 44 # 32 # 46 # 41 # 49 # 4 # 31 # 41 # 54 # 38 # 58 # 0 # 61 # 57 28 # 44 # 53 # 47 # 2 # 49 # 24 # 52 # 1 # 54 # 58 # 58 # 19 # 62 # 14 # 67 # 4 29 # 47 # 21 # 49 # 44 # 52 # 20 # 55 # 16 # 58 # 36 # 62 # 31 # 67 # 18 # 73 # 46 30 # 50 # @1 # 52 # 37 # 55 # 32 # 58 # 52 # 62 # 45 # 67 # 31 # 73 # 5@ # 90 # 0 31 # 52 # 53 # 55 # 48 # 59 # 6 # 62 # 58 # 67 # 42 # 74 # 4 # 90 # 0 # 90 # 0 32 # 56 # 2 # 59 # 19 # 63 # 10 # 67 # 53 # 74 # 12 # 90 # 0 # 90 # 0 # 90 # 0 </note> <pb o="348" file="384" n="385" rhead="Comment. in III. Cap Sphæræ"/> </div> <div xml:id="echoid-div766" type="section" level="1" n="275"> <head xml:id="echoid-head286" xml:space="preserve">TABVLA ASCENSIONVM <lb/>Obliquarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♈ # ## ♉ # ## ♊ # ## ♋ # ## ♌ # ## ♍ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 0 # 0 # 19 # 24 # 42 # 18 # 71 # 35 # 106 # 42 # 143 # 36 1 # 0 # 37 # 20 # 5 # 43 # 10 # 72 # 41 # 107 # 55 # 144 # 50 2 # 1 # 15 # 20 # 46 # 44 # 2 # 73 # 47 # 109 # 9 # 146 # 3 3 # 1 # 52 # 21 # 28 # 44 # 55 # 74 # 53 # 110 # 22 # 147 # 17 4 # 2 # 30 # 22 # 10 # 45 # 48 # 76 # 0 # 111 # 36 # 48 # 30 5 # 3 # 8 # 22 # 25 # 46 # 42 # 77 # 7 # 112 # 50 # 149 # 43 6 # 3 # 46 # 23 # 35 # 47 # 36 # 78 # 15 # 114 # 3 # 150 # 57 7 # 4 # 24 # 24 # 18 # 48 # 30 # 79 # 23 # 115 # 17 # 152 # 10 8 # 5 # 2 # 25 # 1 # 49 # 25 # 80 # 31 # 116 # 30 # 153 # 23 9 # 5 # 40 # 25 # 45 # 50 # 20 # 81 # 40 # 117 # 44 # 154 # 36 10 # 6 # 18 # 26 # 29 # 51 # 16 # 82 # 49 # 118 # 58 # 155 # 49 11 # 6 # 56 # 27 # 13 # 5 # 12 # 83 # 58 # 120 # 12 # 157 # 2 12 # 7 # 34 # 27 # 57 # 53 # 9 # 85 # 8 # 111 # 20 # 158 # 15 13 # 8 # 14 # 28 # 41 # 54 # 7 # 86 # 18 # 122 # 40 # 159 # 28 14 # 8 # 50 # 29 # 26 # 55 # 5 # 87 # 28 # 123 # 55 # 160 # 41 15 # 9 # 29 # 30 # 11 # 56 # 4 # 88 # 38 # 125 # 9 # 161 # 53 16 # 10 # 7 # 30 # 57 # 57 # 3 # 89 # 49 # 126 # 23 # 163 # 6 17 # 10 # 49 # 31 # 43 # 58 # 2 # 91 # 0 # 127 # 37 # 164 # 19 18 # 11 # 25 # 32 # 30 # 59 # 2 # 92 # 11 # 128 # 5@ # 165 # 31 19 # 12 # 4 # 33 # 17 # 60 # 2 # 93 # 22 # 130 # 5 # 166 # 44 20 # 12 # 43 # 34 # 4 # 61 # 3 # 94 # 34 # 131 # 19 # 167 # 56 21 # 13 # 22 # 34 # 52 # 62 # 4 # 95 # 46 # 132 # 33 # 169 # 9 22 # 14 # 1 # 35 # 40 # 63 # 6 # 96 # 58 # 133 # 47 # 170 # 21 23 # 14 # 41 # 36 # 28 # 64 # 8 # 98 # 10 # 135 # 1 # 171 # 34 24 # 15 # 21 # 37 # 17 # 65 # 10 # 99 # 23 # 136 # 15 # 172 # 46 25 # 16 # 1 # 38 # 6 # 66 # 13 # 100 # 36 # 137 # 28 # 173 # 58 26 # 16 # 41 # 38 # 56 # 67 # 16 # 101 # 49 # 138 # 42 # 175 # 11 27 # 17 # 24 # 39 # 46 # 68 # 20 # 103 # 2 # 139 # 56 # 176 # 23 28 # 18 # 2 # 40 # 36 # 69 # 24 # 104 # 15 # 141 # 9 # 177 # 36 29 # 18 # 43 # 41 # 27 # 70 # 29 # 105 # 28 # 142 # 23 # 178 # 40 30 # 19 # 24 # 42 # 18 # 71 # 35 # 106 # 42 # 143 # 36 # 180 # 0 </note> <pb o="349" file="385" n="386" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div767" type="section" level="1" n="276"> <head xml:id="echoid-head287" xml:space="preserve">AD LATITV DINEM <lb/>Graduum 36.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♎ # ## ♏ # ## ♐ # ## ♑ # ## ♒ # ## ♓ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 180 # 0 # 216 # 24 # 253 # 18 # 288 # 25 # 317 # 42 # 340 # 36 1 # 181 # 12 # 217 # 37 # 254 # 32 # 289 # 31 # 318 # 33 # 341 # 17 2 # 182 # 24 # 218 # 51 # 255 # 45 # 290 # 36 # 319 # 24 # 341 # 58 3 # 183 # 37 # 220 # 4 # 256 # 58 # 291 # 40 # 320 # 14 # 342 # 39 4 # 184 # 49 # 221 # 18 # 258 # 11 # 292 # 44 # 321 # 4 # 343 # 19 5 # 186 # 2 # 222 # 32 # 259 # 24 # 293 # 47 # 231 # 54 # 343 # 59 6 # 187 # 14 # 223 # 45 # 260 # 37 # 294 # 50 # 322 # 43 # 344 # 39 7 # 188 # 26 # 224 # 59 # 261 # 50 # 295 # 52 # 323 # 32 # 345 # 19 8 # 189 # 39 # 226 # 13 # 263 # 2 # 296 # 54 # 324 # 20 # 545 # 59 9 # 190 # 51 # 227 # 27 # 264 # 14 # 297 # 56 # 325 # 8 # 346 # 38 10 # 192 # 4 # 228 # 41 # 265 # 26 # 298 # 57 # 325 # 56 # 347 # 17 11 # 293 # 16 # 229 # 55 # 266 # 38 # 299 # 58 # 326 # 43 # 347 # 56 12 # 194 # 29 # 131 # 9 # 267 # 49 # 300 # 58 # 327 # 30 # 348 # 35 13 # 195 # 41 # 132 # 23 # 269 # 0 # 201 # 58 # 328 # 17 # 349 # 14 14 # 196 # 54 # 233 # 37 # 270 # 11 # 302 # 57 # 329 # 3 # 349 # 53 15 # 198 # 7 # 234 # 51 # 271 # 22 # 303 # 56 # 329 # 49 # 350 # 31 16 # 199 # 19 # 236 # 5 # 272 # 32 # 304 # 55 # 330 # 34 # 351 # 10 17 # 200 # 32 # 237 # 20 # 273 # 42 # 305 # 53 # 331 # 19 # 351 # 48 18 # 201 # 45 # 238 # 34 # 274 # 52 # 306 # 51 # 332 # 3 # 352 # 26 19 # 202 # 58 # 239 # 48 # 276 # 2 # 307 # 58 # 332 # 47 # 353 # 4 20 # 204 # 11 # 241 # 2 # 277 # 11 # 308 # 44 # 333 # 31 # 353 # 41 21 # 205 # 24 # 242 # 16 # 278 # 20 # 309 # 0 # 334 # 15 # 354 # 20 22 # 206 # 37 # 243 # 30 # 279 # 29 # 310 # 35 # 334 # 59 # 359 # 58 23 # 207 # 50 # 244 # 43 # 280 # 39 # 311 # 30 # 335 # 42 # 355 # 36 24 # 209 # 3 # 345 # 57 # 281 # 45 # 312 # 24 # 336 # 25 # 356 # 14 25 # 210 # 17 # 247 # 10 # 282 # 53 # 313 # 18 # 337 # 8 # 356 # 52 36 # 211 # 30 # 248 # 24 # 284 # 0 # 314 # 12 # 337 # 50 # 357 # 30 27 # 212 # 43 # 249 # 38 # 285 # 7 # 315 # 5 # 338 # 32 # 358 # 8 28 # 213 # 57 # 250 # 51 # 286 # 13 # 315 # 58 # 339 # 14 # 358 # 45 29 # 215 # 10 # 252 # 5 # 267 # 19 # 316 # 50 # 339 # 55 # 399 # 23 30 # 216 # 24 # 253 # 18 # 288 # 25 # 317 # 42 # 340 # 36 # 360 # 0 </note> <pb o="350" file="386" n="387" rhead="Comment in III. Cap Sphæræ"/> </div> <div xml:id="echoid-div768" type="section" level="1" n="277"> <head xml:id="echoid-head288" xml:space="preserve">TABVLA ASCENSIONVM <lb/>Obliquarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♈ # ## ♉ # ## ♊ # ## ♋ # ## ♌ # ## ♍ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M 0 # 0 # 0 # 19 # 5 # 41 # 42 # 70 # 52 # 106 # 6 # 143 # 17 1 # 0 # 37 # 19 # 46 # 42 # 34 # 71 # 58 # 107 # 20 # 144 # 31 2 # 1 # 14 # 20 # 27 # 43 # 26 # 73 # 4 # 108 # 34 # 145 # 45 3 # 1 # 51 # 21 # 8 # 44 # 18 # 74 # 11 # 109 # 48 # 146 # 59 4 # 2 # 28 # 21 # 49 # 45 # 11 # 75 # 18 # 111 # 2 # 148 # 13 5 # 3 # 5 # 22 # 30 # 46 # 4 # 76 # 25 # 112 # 16 # 149 # 27 6 # 3 # 42 # 23 # 12 # 46 # 58 # 77 # 31 # 113 # 30 # 150 # 41 7 # 4 # 19 # 23 # 54 # 47 # 52 # 78 # 41 # 114 # 44 # 151 # 55 8 # 4 # 56 # 24 # 37 # 48 # 47 # 79 # 49 # 115 # 59 # 153 # 19 9 # 5 # 33 # 25 # 20 # 49 # 42 # 80 # 58 # 117 # 13 # 154 # 23 10 # 6 # 11 # 26 # 3 # 50 # 37 # 82 # 7 # 118 # 28 # 155 # 36 11 # 6 # 48 # 26 # 46 # 51 # 33 # 83 # 16 # 119 # 42 # 156 # 50 12 # 7 # 26 # 27 # 30 # 52 # 30 # 84 # 26 # 120 # 57 # 158 # 3 13 # 8 # 3 # 28 # 14 # 53 # 27 # 85 # 36 # 122 # 11 # 159 # 17 14 # 8 # 41 # 28 # 58 # 54 # 25 # 86 # 46 # 123 # 26 # 160 # 30 15 # 9 # 19 # 29 # 43 # 55 # 23 # 87 # 57 # 124 # 41 # 161 # 43 16 # 9 # 57 # 30 # 28 # 56 # 22 # 89 # 8 # 115 # 56 # 162 # 57 17 # 10 # 35 # 31 # 14 # 57 # 21 # 90 # 19 # 127 # 10 # 164 # 10 18 # 11 # 13 # 32 # 0 # 58 # 21 # 91 # 31 # 128 # 25 # 165 # 23 19 # 11 # 51 # 33 # 47 # 59 # 21 # 92 # 43 # 129 # 39 # 166 # 36 20 # 12 # 30 # 22 # 34 # 60 # 21 # 93 # 55 # 130 # 53 # 167 # 49 21 # @3 # 9 # 34 # 21 # 61 # 22 # 95 # 7 # 132 # 8 # 169 # 3 22 # 13 # 48 # 35 # 8 # 62 # 24 # 96 # 19 # 133 # 23 # 170 # 16 23 # 14 # 27 # 35 # 56 # 63 # 26 # 97 # 32 # 134 # 37 # 171 # 29 24 # 15 # 6 # 36 # 44 # 64 # 28 # 98 # 45 # 135 # 52 # 172 # 18 25 # 15 # 45 # 37 # 32 # 65 # 31 # 99 # 58 # 137 # 6 # 173 # 55 26 # 16 # 25 # 38 # 21 # 66 # 34 # 101 # 11 # 138 # 21 # 175 # 8 27 # 17 # 5 # 39 # 10 # 67 # 38 # 102 # 24 # 139 # 35 # 176 # 21 28 # 17 # 45 # 40 # 0 # 68 # 24 # 103 # 38 # 140 # 49 # 177 # 34 29 # 18 # 25 # 40 # 51 # 69 # 47 # 104 # 52 # 142 # 3 # 178 # 47 30 # 19 # 5 # 41 # 41 # 70 # 52 # 106 # 6 # 143 # 17 # 180 # 9 </note> <pb o="351" file="387" n="388" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div769" type="section" level="1" n="278"> <head xml:id="echoid-head289" xml:space="preserve">AD LATITVDINEM <lb/>Graduum 37.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♎ # ## ♏ # ## ♐ # ## ♑ # ## ♒ # ## ♓ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 180 # 0 # 216 # 43 # 253 # 54 # 289 # 8 # 318 # 18 # 340 # 55 1 # 181 # 13 # 217 # 57 # 255 # 8 # 290 # 13 # 319 # 9 # 341 # 35 2 # 182 # 26 # 219 # 11 # 256 # 22 # 291 # 18 # 320 # 0 # 342 # 15 4 # 183 # 39 # 220 # 25 # 257 # 36 # 292 # 22 # 320 # 50 # 342 # 55 3 # 184 # 52 # 221 # 39 # 258 # 49 # 293 # 26 # 321 # 39 # 343 # 35 5 # 186 # 5 # 222 # 54 # 260 # 2 # 294 # 29 # 322 # 28 # 344 # 15 6 # 187 # 18 # 224 # 8 # 261 # 15 # 295 # 32 # 323 # 16 # 344 # 54 7 # 188 # 31 # 225 # 23 # 262 # 28 # 296 # 34 # 324 # 4 # 345 # 33 8 # 189 # 44 # 226 # 37 # 263 # 41 # 297 # 36 # 324 # 52 # 346 # 12 9 # 190 # 57 # 227 # 52 # 264 # 53 # 298 # 38 # 325 # 39 # 346 # 51 10 # 192 # 11 # 229 # 7 # 265 # 5 # 299 # 39 # 326 # 26 # 347 # 30 11 # 193 # 24 # 230 # 21 # 266 # 17 # 300 # 39 # 327 # 13 # 348 # 9 12 # 194 # 37 # 231 # 35 # 268 # 29 # 301 # 39 # 328 # 0 # 348 # 47 13 # 195 # 50 # 232 # 50 # 269 # 41 # 302 # 39 # 328 # 46 # 349 # 25 14 # 197 # 3 # 234 # 4 # 270 # 52 # 303 # 38 # 329 # 32 # 350 # 3 15 # 198 # 17 # 235 # 19 # 272 # 3 # 304 # 37 # 330 # 17 # 350 # 41 16 # 199 # 30 # 236 # 34 # 273 # 14 # 305 # 35 # 331 # 2 # 351 # 19 17 # 200 # 43 # 237 # 49 # 274 # 24 # 306 # 33 # 331 # 46 # 351 # 57 18 # 201 # 57 # 239 # 3 # 275 # 34 # 307 # 30 # 332 # 30 # 352 # 34 19 # 203 # 10 # 240 # 18 # 276 # 44 # 308 # 27 # 333 # 14 # 353 # 12 20 # 204 # 24 # 241 # 32 # 277 # 53 # 309 # 23 # 333 # 57 # 353 # 49 21 # 205 # 37 # 242 # 47 # 279 # 2 # 310 # 18 # 334 # 40 # 354 # 27 22 # 206 # 51 # 244 # 1 # 280 # 11 # 311 # 13 # 335 # 23 # 355 # 4 23 # 208 # 5 # 245 # 16 # 281 # 19 # 312 # 8 # 336 # 6 # 355 # 41 24 # 209 # 19 # 246 # 30 # 282 # 27 # 313 # 2 # 336 # 48 # 356 # 18 25 # 210 # 33 # 247 # 44 # 283 # 35 # 313 # 56 # 337 # 30 # 356 # 55 26 # 211 # 47 # 248 # 58 # 284 # 42 # 314 # 49 # 338 # 11 # 357 # 32 27 # 213 # 1 # 250 # 12 # 285 # 49 # 315 # 42 # 338 # 52 # 358 # 9 28 # 214 # 15 # 251 # 26 # 286 # 56 # 316 # 34 # 339 # 53 # 358 # 46 29 # 215 # 29 # 252 # 40 # 288 # 2 # 317 # 26 # 340 # 14 # 359 # 23 30 # 216 # 43 # 253 # 54 # 289 # 8 # 318 # 18 # 340 # 55 # 360 # 0 </note> <pb o="352" file="388" n="389" rhead="Comment. in III. Cap. Sphæræ"/> </div> <div xml:id="echoid-div770" type="section" level="1" n="279"> <head xml:id="echoid-head290" xml:space="preserve">TABVLA ASCENSIONVM <lb/>Obliquarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♈ # ## ♉ # ## ♊ # ## ♋ # ## ♌ # ## ♍ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 0 # 0 # 18 # 45 # 41 # 6 # 70 # 8 # 105 # 30 # 142 # 57 1 # 0 # 36 # 19 # 25 # 41 # 57 # 71 # 14 # 106 # 44 # 144 # 12 2 # 1 # 12 # 20 # 5 # 42 # 48 # 72 # 20 # 107 # 58 # 145 # 27 3 # 1 # 49 # 20 # 45 # 43 # 40 # 73 # 27 # 109 # 13 # 146 # 41 4 # 2 # 25 # 21 # 26 # 44 # 32 # 74 # 34 # 110 # 27 # 147 # 56 5 # 3 # 2 # 22 # 7 # 45 # 25 # 75 # 41 # 111 # 42 # 149 # 10 6 # 3 # 38 # 22 # 49 # 46 # 18 # 76 # 49 # 112 # 56 # 150 # 25 7 # 4 # 14 # 23 # 31 # 47 # 12 # 77 # 53 # 114 # 11 # 151 # 40 8 # 4 # 51 # 24 # 13 # 48 # 6 # 79 # 6 # 115 # 26 # 152 # 54 9 # 5 # 27 # 24 # 55 # 49 # 1 # 80 # 15 # 116 # 41 # 154 # 9 10 # 6 # 4 # 25 # 38 # 49 # 57 # 81 # 24 # 117 # 56 # 155 # 23 11 # 6 # 41 # 26 # 21 # 50 # 53 # 82 # 34 # 119 # 11 # 156 # 37 12 # 7 # 18 # 27 # 4 # 51 # 49 # 83 # 44 # 120 # 27 # 157 # 51 13 # 7 # 55 # 27 # 47 # 52 # 46 # 84 # 54 # 121 # 43 # 159 # 5 14 # 8 # 32 # 28 # 31 # 53 # 43 # 86 # 4 # 122 # 58 # 160 # 19 15 # 9 # 9 # 29 # 15 # 54 # 41 # 87 # 15 # 124 # 13 # 161 # 33 16 # 9 # 46 # 30 # 0 # 55 # 39 # 88 # 26 # 125 # 28 # 162 # 47 17 # 10 # 24 # 30 # 45 # 56 # 38 # 89 # 38 # 126 # 43 # 164 # 1 18 # 11 # 1 # 31 # 30 # 57 # 37 # 90 # 50 # 127 # 58 # 165 # 15 19 # 11 # 39 # 32 # 16 # 58 # 37 # 92 # 2 # 129 # 13 # 166 # 29 20 # 12 # 17 # 33 # 2 # 59 # 38 # 93 # 15 # 130 # 28 # 167 # 42 21 # 12 # 55 # 33 # 48 # 60 # 39 # 94 # 27 # 131 # 43 # 168 # 56 22 # 13 # 33 # 34 # 35 # 61 # 40 # 95 # 40 # 132 # 58 # 170 # 10 23 # 14 # 11 # 35 # 22 # 62 # 42 # 96 # 53 # 134 # 13 # 171 # 11 24 # 14 # 49 # 36 # 10 # 63 # 44 # 98 # 6 # 135 # 28 # 172 # 38 25 # 15 # 28 # 36 # 58 # 64 # 47 # 99 # 19 # 136 # 43 # 173 # 52 26 # 16 # 8 # 37 # 47 # 65 # 50 # 100 # 33 # 137 # 58 # 175 # 6 27 # 16 # 46 # 38 # 36 # 66 # 54 # 101 # 47 # 139 # 13 # 176 # 20 28 # 17 # 25 # 39 # 26 # 67 # 58 # 103 # 1 # 140 # 28 # 177 # 33 29 # 18 # 5 # 40 # 16 # 69 # 3 # 104 # 15 # 141 # 43 # 178 # 47 30 # 18 # 45 # 41 # 6 # 70 # 8 # 105 # 30 # 142 # 57 # 180 # 0 </note> <pb o="353" file="389" n="390" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div771" type="section" level="1" n="280"> <head xml:id="echoid-head291" xml:space="preserve">AD LATITVDINEM <lb/>Graduum 38.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♎ # ## ♏ # ## ♐ # ## ♑ # ## ♒ # ## ♓ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M 0 # 180 # 0 # 217 # 3 # 254 # 30 # 289 # 52 # 318 # 54 # 341 # 15 1 # 181 # 13 # 218 # 17 # 255 # 45 # 290 # 57 # 319 # 44 # 341 # 55 2 # 182 # 27 # 219 # 32 # 256 # 59 # 292 # 2 # 320 # 34 # 342 # 53 3 # 183 # 40 # 220 # 47 # 258 # 13 # 293 # 6 # 321 # 24 # 343 # 14 4 # 184 # 54 # 222 # 2 # 259 # 27 # 294 # 10 # 322 # 13 # 343 # 53 5 # 186 # 8 # 223 # 17 # 260 # 41 # 295 # 13 # 323 # 2 # 345 # 32 6 # 187 # 22 # 224 # 32 # 261 # 54 # 296 # 16 # 323 # 50 # 345 # 11 7 # 188 # 36 # 225 # 47 # 263 # 7 # 297 # 18 # 324 # 38 # 345 # 49 8 # 189 # 50 # 227 # 2 # 264 # 20 # 298 # 20 # 325 # 25 # 346 # 27 9 # 191 # 4 # 228 # 17 # 265 # 33 # 299 # 21 # 326 # 12 # 347 # 5 10 # 192 # 18 # 229 # 32 # 266 # 45 # 300 # 22 # 326 # 58 # 347 # 43 11 # 193 # 31 # 230 # 47 # 267 # 58 # 301 # 23 # 327 # 44 # 348 # 21 12 # 194 # 45 # 232 # 2 # 269 # 10 # 302 # 23 # 328 # 30 # 348 # 59 13 # 195 # 59 # 233 # 17 # 270 # 22 # 303 # 22 # 329 # 15 # 349 # 36 14 # 197 # 13 # 234 # 32 # 271 # 34 # 304 # 21 # 330 # 0 # 350 # 14 15 # 198 # 27 # 235 # 47 # 272 # 45 # 305 # 19 # 330 # 45 # 350 # 51 16 # 199 # 41 # 237 # 2 # 273 # 56 # 306 # 17 # 331 # 29 # 351 # 28 17 # 200 # 55 # 238 # 17 # 275 # 6 # 307 # 14 # 332 # 13 # 352 # 5 18 # 202 # 9 # 239 # 33 # 276 # 16 # 308 # 11 # 332 # 56 # 352 # 42 19 # 203 # 23 # 240 # 49 # 277 # 26 # 309 # 7 # 333 # 39 # 353 # 19 20 # 204 # 37 # 242 # 4 # 278 # 36 # 310 # 3 # 334 # 22 # 353 # 56 21 # 205 # 51 # 243 # 19 # 279 # 45 # 310 # 59 # 335 # 5 # 354 # 33 22 # 207 # 6 # 244 # 34 # 280 # 54 # 311 # 54 # 335 # 47 # 355 # 9 23 # 208 # 20 # 245 # 49 # 282 # 3 # 312 # 48 # 336 # 29 # 355 # 46 24 # 209 # 35 # 247 # 4 # 283 # 11 # 313 # 42 # 337 # 11 # 356 # 22 25 # 210 # 50 # 248 # 18 # 284 # 19 # 314 # 35 # 337 # 53 # 356 # 58 26 # 212 # 4 # 249 # 33 # 285 # 26 # 315 # 28 # 338 # 34 # 357 # 35 27 # 213 # 19 # 250 # 47 # 286 # 33 # 316 # 20 # 339 # 15 # 358 # 11 28 # 214 # 33 # 252 # 2 # 287 # 70 # 317 # 12 # 339 # 55 # 358 # 48 29 # 215 # 48 # 253 # 16 # 288 # 46 # 318 # 3 # 340 # 35 # 359 # 24 30 # 217 # 3 # 254 # 30 # 289 # 52 # 318 # 54 # 341 # 15 # 360 # 0 </note> <pb o="354" file="390" n="391" rhead="Comment. in III. Cap. Sphæræ"/> </div> <div xml:id="echoid-div772" type="section" level="1" n="281"> <head xml:id="echoid-head292" xml:space="preserve">TABVLA ASCENSIONVM <lb/>Obliquarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♈ # ## ♉ # ## ♊ # ## ♋ # ## ♌ # ## ♍ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 0 # 0 # 18 # 25 # 40 # 28 # 69 # 23 # 104 # 52 # 142 # 37 1 # 0 # 35 # 19 # 4 # 41 # 19 # 70 # 29 # 106 # 7 # 143 # 53 2 # 1 # 11 # 19 # 44 # 42 # 10 # 71 # 35 # 107 # 22 # 145 # 8 3 # 1 # 46 # 20 # 24 # 43 # 2 # 72 # 42 # 108 # 37 # 146 # 24 4 # 2 # 22 # 21 # 4 # 43 # 54 # 73 # 49 # 109 # 52 # 147 # 39 5 # 2 # 58 # 21 # 44 # 44 # 46 # 74 # 56 # 111 # 7 # 148 # 54 6 # 3 # 34 # 22 # 25 # 45 # 39 # 76 # 4 # 112 # 22 # 150 # 9 7 # 4 # 10 # 23 # 6 # 46 # 32 # 77 # 12 # 113 # 37 # 151 # 24 8 # 4 # 46 # 23 # 47 # 47 # 26 # 78 # 21 # 114 # 53 # 152 # 39 9 # 5 # 22 # 24 # 29 # 48 # 20 # 79 # 30 # 116 # 8 # 153 # 54 10 # 5 # 58 # 25 # 11 # 49 # 15 # 80 # 39 # 117 # 24 # 155 # 9 11 # 6 # 34 # 25 # 53 # 50 # 10 # 81 # 59 # 118 # 39 # 156 # 24 12 # 7 # 10 # 26 # 26 # 51 # 6 # 82 # 69 # 119 # 55 # 157 # 39 13 # 7 # 46 # 27 # 19 # 52 # 3 # 84 # 10 # 121 # 11 # 158 # 54 14 # 8 # 22 # 28 # 2 # 53 # 0 # 85 # 21 # 122 # 27 # 160 # 9 15 # 8 # 59 # 28 # 45 # 53 # 58 # 86 # 32 # 123 # 43 # 161 # 23 16 # 9 # 35 # 29 # 29 # 54 # 56 # 87 # 44 # 124 # 59 # 162 # 38 17 # 10 # 12 # 30 # 13 # 55 # 55 # 88 # 56 # 126 # 15 # 163 # 53 18 # 10 # 49 # 30 # 58 # 56 # 54 # 90 # 8 # 127 # 30 # 165 # 7 19 # 11 # 26 # 31 # 44 # 57 # 53 # 91 # 20 # 128 # 46 # 166 # 22 20 # 12 # 3 # 32 # 30 # 58 # 53 # 92 # 33 # 130 # 1 # 167 # 36 21 # 12 # 40 # 33 # 16 # 59 # 54 # 93 # 46 # 131 # 17 # 168 # 51 22 # 13 # 18 # 34 # 2 # 60 # 55 # 94 # 59 # 132 # 33 # 170 # 5 23 # 13 # 56 # 34 # 49 # 61 # 57 # 96 # 12 # 133 # 49 # 171 # 20 24 # 14 # 34 # 35 # 36 # 62 # 59 # 97 # 26 # 135 # 5 # 172 # 34 25 # 15 # 12 # 36 # 23 # 64 # 2 # 98 # 40 # 136 # 20 # 173 # 48 26 # 15 # 50 # 37 # 11 # 65 # 5 # 99 # 54 # 137 # 36 # 175 # 3 27 # 16 # 28 # 37 # 59 # 66 # 9 # 101 # 8 # 138 # 51 # 176 # 17 28 # 17 # 7 # 38 # 48 # 67 # 13 # 102 # 22 # 140 # 7 # 177 # 32 29 # 17 # 46 # 39 # 38 # 68 # 18 # 103 # 37 # 141 # 22 # 178 # 46 30 # 18 # 25 # 40 # 28 # 69 # 23 # 104 # 52 # 142 # 37 # 180 # 0 </note> <pb o="355" file="391" n="392" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div773" type="section" level="1" n="282"> <head xml:id="echoid-head293" xml:space="preserve">AD LATITVDINEM <lb/>Graduum 39.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♎ # ## ♏ # ## ♐ # ## ♑ # ## ♒ # ## ♓ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M 0 # 180 # 0 # 217 # 23 # 255 # 8 # 290 # 37 # 319 # 32 # 341 # 35 1 # 181 # 14 # 218 # 38 # 256 # 23 # 291 # 42 # 320 # 22 # 342 # 14 2 # 182 # 28 # 219 # 53 # 257 # 38 # 292 # 47 # 321 # 12 # 342 # 53 3 # 183 # 43 # 221 # 9 # 258 # 52 # 293 # 51 # 322 # 1 # 343 # 32 4 # 184 # 57 # 222 # 24 # 260 # 6 # 294 # 55 # 322 # 49 # 344 # 10 5 # 186 # 11 # 223 # 40 # 261 # 20 # 295 # 58 # 323 # 37 # 344 # 48 6 # 187 # 26 # 224 # 55 # 262 # 34 # 297 # 1 # 324 # 24 # 345 # 26 7 # 188 # 40 # 226 # 11 # 263 # 48 # 298 # 3 # 325 # 11 # 346 # 4 8 # 189 # 55 # 227 # 27 # 265 # 1 # 299 # 5 # 325 # 58 # 346 # 42 9 # 191 # 9 # 228 # 43 # 266 # 14 # 300 # 6 # 326 # 44 # 347 # 20 10 # 192 # 24 # 229 # 59 # 267 # 27 # 301 # 7 # 327 # 30 # 347 # 57 11 # 193 # 38 # 231 # 14 # 268 # 40 # 302 # 7 # 328 # 16 # 348 # 34 12 # 194 # 53 # 232 # 30 # 269 # 52 # 303 # 6 # 329 # 2 # 349 # 11 13 # 196 # 7 # 233 # 45 # 271 # 4 # 304 # 5 # 329 # 47 # 349 # 47 14 # 197 # 22 # 235 # 1 # 272 # 16 # 305 # 4 # 330 # 31 # 350 # 25 15 # 198 # 37 # 236 # 17 # 273 # 28 # 306 # 2 # 331 # 15 # 351 # 1 16 # 199 # 51 # 237 # 33 # 274 # 39 # 307 # 0 # 331 # 58 # 351 # 38 17 # 201 # 6 # 238 # 49 # 275 # 50 # 307 # 57 # 332 # 41 # 352 # 14 18 # 202 # 21 # 240 # 5 # 277 # 1 # 308 # 54 # 333 # 14 # 352 # 50 19 # 23 # 36 # 241 # 21 # 278 # 11 # 309 # 50 # 334 # 7 # 353 # 26 20 # 204 # 51 # 242 # 36 # 279 # 21 # 310 # 45 # 334 # 49 # 354 # 2 21 # 206 # 6 # 243 # 52 # 280 # 3 # 311 # 40 # 335 # 31 # 354 # 38 22 # 207 # 21 # 245 # 7 # 281 # 39 # 312 # 34 # 336 # 13 # 355 # 14 23 # 208 # 36 # 246 # 23 # 282 # 48 # 313 # 28 # 336 # 54 # 355 # 50 24 # 209 # 51 # 247 # 38 # 283 # 56 # 314 # 21 # 337 # 35 # 356 # 26 25 # 211 # 6 # 248 # 53 # 285 # 4 # 315 # 14 # 338 # 16 # 357 # 2 26 # 212 # 21 # 250 # 8 # 286 # 11 # 316 # 6 # 338 # 56 # 357 # 38 27 # 213 # 36 # 251 # 23 # 287 # 18 # 316 # 58 # 339 # 36 # 358 # 14 28 # 214 # 52 # 252 # 38 # 288 # 25 # 317 # 50 # 340 # 16 # 58 # 48 29 # 216 # 7 # 253 # 53 # 289 # 31 # 318 # 41 # 340 # 56 # 359 # 25 30 # 217 # 23 # 255 # 8 # 290 # 37 # 319 # 32 # 341 # 35 # 360 # 0 </note> <pb o="356" file="392" n="393" rhead="Comment in III. Cap. Sphæræ."/> </div> <div xml:id="echoid-div774" type="section" level="1" n="283"> <head xml:id="echoid-head294" xml:space="preserve">TABVLA ASCENSIONVM <lb/>Obliquarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♈ # ## ♉ # ## ♊ # ## ♋ # ## ♌ # ## ♍ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 0 # 0 # 18 # 4 # 39 # 49 # 68 # 36 # 104 # 13 # 142 # 16 1 # 0 # 35 # 18 # 43 # 40 # 39 # 69 # 41 # 105 # 28 # 143 # 32 2 # 1 # 10 # 19 # 22 # 41 # 30 # 70 # 54 # 106 # 44 # 144 # 48 3 # 1 # 45 # 20 # 1 # 42 # 21 # 71 # 57 # 107 # 59 # 146 # 4 4 # 2 # 20 # 20 # 40 # 43 # 12 # 73 # 1 # 109 # 15 # 147 # 20 5 # 2 # 55 # 21 # 20 # 44 # 4 # 74 # 9 # 110 # 31 # 148 # 36 6 # 3 # 30 # 22 # 0 # 44 # 56 # 75 # 17 # 111 # 46 # 149 # 52 7 # 4 # 5 # 22 # 41 # 45 # 49 # 76 # 25 # 113 # 2 # 151 # 8 8 # 4 # 40 # 23 # 22 # 46 # 43 # 77 # 34 # 114 # 28 # 152 # 23 9 # 5 # 15 # 24 # 3 # 47 # 37 # 78 # 43 # 115 # 34 # 153 # 39 10 # 5 # 51 # 24 # 44 # 48 # 32 # 79 # 53 # 116 # 50 # 154 # 54 11 # 6 # 26 # 25 # 26 # 49 # 27 # 81 # 3 # 118 # 6 # 156 # 10 12 # 7 # 1 # 26 # 8 # 50 # 23 # 82 # 13 # 119 # 22 # 157 # 26 13 # 7 # 37 # 26 # 50 # 51 # 19 # 83 # 24 # 120 # 39 # 158 # 41 14 # 8 # 12 # 27 # 32 # 52 # 16 # 84 # 35 # 121 # 55 # 159 # 57 15 # 8 # 48 # 28 # 14 # 53 # 13 # 85 # 47 # 123 # 12 # 161 # 12 16 # 9 # 24 # 28 # 57 # 54 # 11 # 86 # 59 # 124 # 28 # 162 # 28 17 # 10 # 0 # 29 # 41 # 55 # 9 # 88 # 12 # 125 # 45 # 163 # 43 18 # 10 # 36 # 30 # 26 # 56 # 8 # 89 # 24 # 127 # 2 # 164 # 59 19 # 11 # 12 # 31 # 11 # 57 # 7 # 90 # 37 # 128 # 18 # 166 # 14 20 # 11 # 48 # 31 # 56 # 58 # 7 # 91 # 50 # 129 # 34 # 167 # 29 21 # 12 # 25 # 32 # 41 # 59 # 7 # 93 # 3 # 130 # 51 # 168 # 45 22 # 13 # 2 # 33 # 27 # 60 # 8 # 94 # 17 # 132 # 7 # 170 # 0 23 # 13 # 39 # 34 # 13 # 61 # 10 # 95 # 30 # 133 # 24 # 171 # 15 24 # 14 # 16 # 35 # 0 # 62 # 12 # 96 # 44 # 134 # 40 # 172 # 30 25 # 14 # 54 # 35 # 47 # 63 # 15 # 97 # 58 # 135 # 56 # 173 # 45 26 # 15 # 32 # 36 # 34 # 64 # 18 # 99 # 13 # 137 # 12 # 175 # 0 27 # 16 # 10 # 37 # 22 # 65 # 22 # 100 # 28 # 138 # 28 # 176 # 15 28 # 16 # 48 # 38 # 10 # 66 # 26 # 101 # 43 # 139 # 44 # 177 # 30 29 # 17 # 26 # 38 # 29 # 67 # 31 # 102 # 58 # 141 # 0 # 178 # 45 30 # 18 # 4 # 39 # 49 # 68 # 36 # 103 # 13 # 142 # 16 # 180 # 0 </note> <pb o="357" file="393" n="394" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div775" type="section" level="1" n="284"> <head xml:id="echoid-head295" xml:space="preserve">AD LATITVDINEM <lb/>Graduum 40.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♎ # ## ♏ # ## ♐ # ## ♑ # ## ♒ # ## ♓ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 180 # 0 # 217 # 44 # 255 # 47 # 291 # 24 # 320 # 11 # 341 # 56 1 # 181 # 15 # 219 # 0 # 257 # 2 # 292 # 29 # 321 # 1 # 342 # 34 2 # 182 # 30 # 220 # 16 # 258 # 17 # 293 # 34 # 321 # 50 # 343 # 12 3 # 183 # 45 # 221 # 32 # 259 # 32 # 294 # 38 # 322 # 38 # 343 # 50 4 # 185 # 0 # 222 # 48 # 260 # 47 # 295 # 42 # 323 # 26 # 344 # 28 5 # 186 # 15 # 224 # 4 # 262 # 2 # 296 # 45 # 324 # 13 # 345 # 6 6 # 187 # 30 # 225 # 20 # 263 # 16 # 297 # 48 # 325 # 0 # 345 # 44 7 # 188 # 45 # 226 # 36 # 264 # 30 # 298 # 50 # 325 # 47 # 346 # 21 8 # 190 # 0 # 227 # 53 # 265 # 43 # 299 # 52 # 326 # 33 # 346 # 58 9 # 191 # 15 # 229 # 9 # 266 # 57 # 300 # 53 # 327 # 19 # 347 # 35 10 # 192 # 31 # 230 # 26 # 268 # 10 # 301 # 53 # 328 # 4 # 348 # 12 11 # 193 # 46 # 231 # 42 # 269 # 23 # 302 # 53 # 328 # 49 # 348 # 48 12 # 195 # 1 # 232 # 58 # 270 # 36 # 303 # 52 # 329 # 34 # 349 # 24 13 # 196 # 17 # 234 # 15 # 271 # 48 # 304 # 51 # 330 # 19 # 350 # 0 14 # 197 # 32 # 235 # 32 # 273 # 1 # 305 # 49 # 331 # 3 # 350 # 36 15 # 198 # 48 # 136 # 48 # 274 # 13 # 306 # 47 # 331 # 46 # 351 # 12 16 # 200 # 3 # 238 # 5 # 275 # 25 # 307 # 44 # 332 # 28 # 351 # 48 17 # 201 # 19 # 239 # 21 # 276 # 36 # 308 # 41 # 333 # 10 # 352 # 23 18 # 202 # 34 # 240 # 38 # 277 # 47 # 309 # 37 # 333 # 52 # 352 # 59 19 # 203 # 50 # 241 # 54 # 378 # 57 # 310 # 33 # 334 # 34 # 353 # 34 20 # 205 # 6 # 243 # 10 # 280 # 7 # 311 # 28 # 335 # 16 # 354 # 9 21 # 206 # 21 # 244 # 26 # 281 # 17 # 312 # 23 # 335 # 57 # 354 # 45 22 # 207 # 37 # 245 # 42 # 182 # 26 # 313 # 17 # 336 # 38 # 355 # 20 23 # 208 # 52 # 246 # 58 # 283 # 35 # 314 # 11 # 337 # 19 # 355 # 55 24 # 210 # 8 # 248 # 14 # 284 # 43 # 315 # 4 # 338 # 0 # 356 # 30 25 # 211 # 24 # 249 # 29 # 285 # 51 # 315 # 56 # 338 # 40 # 357 # 5 26 # 212 # 40 # 250 # 45 # 286 # 59 # 316 # 48 # 339 # 20 # 357 # 40 27 # 213 # 56 # 252 # 1 # 288 # 6 # 317 # 39 # 339 # 50 # 358 # 15 28 # 215 # 22 # 253 # 16 # 289 # 13 # 318 # 30 # 340 # 38 # 358 # 50 29 # 216 # 28 # 254 # 32 # 290 # 19 # 319 # 21 # 34 # 17 # 359 # 25 30 # 217 # 44 # 255 # 47 # 291 # 24 # 320 # 11 # 341 # 56 # 360 # 0 </note> <pb o="358" file="394" n="395" rhead="Comment in III. Cap. Sphæræ."/> </div> <div xml:id="echoid-div776" type="section" level="1" n="285"> <head xml:id="echoid-head296" xml:space="preserve">TABVLA ASCENSIONVM <lb/>Obliquarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♈ # ## ♉ # ## ♊ # ## ♋ # ## ♌ # ## ♍ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 0 # 0 # 17 # 43 # 39 # 9 # 67 # 47 # 103 # 33 # 141 # 55 1 # 0 # 34 # 18 # 21 # 39 # 58 # 68 # 53 # 104 # 49 # 143 # 12 2 # 1 # 8 # 18 # 59 # 40 # 48 # 69 # 59 # 106 # 5 # 144 # 29 3 # 1 # 42 # 19 # 38 # 41 # 39 # 71 # 6 # 107 # 21 # 145 # 45 4 # 2 # 16 # 20 # 16 # 42 # 30 # 72 # 13 # 108 # 37 # 147 # 2 5 # 2 # 1 # 20 # 55 # 43 # 22 # 73 # 21 # 109 # 53 # 148 # 18 6 # 3 # 25 # 21 # 34 # 44 # 14 # 74 # 29 # 111 # 9 # 149 # 35 7 # 3 # 29 # 22 # 14 # 45 # 7 # 75 # 38 # 112 # 25 # 150 # 52 8 # 4 # 34 # 22 # 54 # 46 # 0 # 76 # 47 # 113 # 42 # 152 # 8 9 # 5 # 8 # 23 # 34 # 46 # 53 # 77 # 56 # 114 # 58 # 153 # 25 10 # 5 # 43 # 24 # 15 # 47 # 47 # 79 # 6 # 116 # 15 # 154 # 41 11 # 6 # 18 # 24 # 56 # 48 # 42 # 80 # 7 # 117 # 32 # 155 # 58 12 # 6 # 53 # 25 # 38 # 49 # 38 # 81 # 28 # 118 # 49 # 157 # 14 13 # 7 # 28 # 26 # 19 # 50 # 34 # 82 # 39 # 120 # 6 # 158 # 30 14 # 8 # 3 # 27 # 1 # 51 # 30 # 83 # 49 # 121 # 23 # 159 # 46 15 # 8 # 38 # 27 # 43 # 52 # 27 # 85 # 1 # 122 # 40 # 161 # 2 16 # 9 # 13 # 28 # 26 # 53 # 25 # 86 # 13 # 123 # 57 # 162 # 18 17 # 9 # 48 # 29 # 10 # 54 # 23 # 87 # 26 # 125 # 14 # 163 # 34 18 # 10 # 24 # 29 # 53 # 55 # 22 # 88 # 39 # 126 # 31 # 164 # 50 19 # 10 # 59 # 30 # 37 # 56 # 21 # 89 # 52 # 127 # 48 # 166 # 6 20 # 11 # 35 # 31 # 21 # 57 # 20 # 91 # 5 # 129 # 5 # 167 # 21 21 # 12 # 11 # 32 # 6 # 58 # 20 # 92 # 19 # 130 # 22 # 166 # 37 22 # 12 # 47 # 32 # 52 # 59 # 21 # 93 # 33 # 131 # 39 # 168 # 53 23 # 13 # 23 # 33 # 37 # 60 # 22 # 94 # 47 # 332 # 57 # 171 # 9 24 # 13 # 59 # 34 # 23 # 61 # 24 # 96 # 1 # 134 # 14 # 172 # 25 25 # 14 # 35 # 35 # 9 # 62 # 27 # 97 # 16 # 135 # 31 # 173 # 41 26 # 15 # 13 # 35 # 56 # 63 # 30 # 98 # 31 # 136 # 48 # 174 # 57 27 # 15 # 50 # 36 # 44 # 64 # 34 # 99 # 46 # 138 # 5 # 176 # 13 28 # 16 # 28 # 37 # 32 # 65 # 38 # 101 # 2 # 139 # 22 # 177 # 29 29 # 17 # 5 # 38 # 20 # 66 # 42 # 102 # 17 # 140 # 39 # 178 # 45 30 # 17 # 43 # 39 # 9 # 67 # 47 # 103 # 33 # 141 # 55 # 180 # 0 </note> <pb o="359" file="395" n="396" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div777" type="section" level="1" n="286"> <head xml:id="echoid-head297" xml:space="preserve">AD LATITVDINEM <lb/>Graduum 41.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♎ # ## ♏ # ## ♐ # ## ♑ # ## ♒ # ## ♓ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 180 # 0 # 218 # 5 # 256 # 27 # 292 # 13 # 320 # 51 # 342 # 17 1 # 181 # 15 # 219 # 21 # 257 # 43 # 293 # 18 # 321 # 40 # 342 # 55 2 # 182 # 31 # 220 # 38 # 258 # 58 # 294 # 22 # 322 # 28 # 343 # 32 3 # 183 # 47 # 221 # 55 # 260 # 14 # 295 # 26 # 323 # 16 # 344 # 10 4 # 185 # 3 # 223 # 12 # 261 # 29 # 296 # 30 # 324 # 4 # 344 # 47 5 # 186 # 19 # 224 # 29 # 262 # 44 # 297 # 33 # 324 # 51 # 345 # 24 6 # 187 # 35 # 225 # 46 # 263 # 59 # 298 # 36 # 325 # 37 # 346 # 1 7 # 188 # 51 # 227 # 3 # 265 # 13 # 299 # 38 # 326 # 23 # 346 # 37 8 # 190 # 7 # 228 # 21 # 266 # 27 # 300 # 39 # 327 # 8 # 347 # 13 9 # 191 # 23 # 229 # 38 # 267 # 41 # 301 # 40 # 327 # 54 # 347 # 49 10 # 192 # 39 # 230 # 55 # 268 # 55 # 302 # 40 # 328 # 39 # 348 # 25 11 # 193 # 54 # 232 # 12 # 270 # 8 # 303 # 39 # 329 # 23 # 349 # 1 12 # 195 # 10 # 233 # 29 # 271 # 11 # 304 # 38 # 330 # 7 # 349 # 36 13 # 196 # 26 # 234 # 46 # 272 # 34 # 305 # 37 # 330 # 50 # 350 # 12 14 # 197 # 42 # 236 # 3 # 273 # 47 # 306 # 35 # 331 # 34 # 350 # 47 15 # 198 # 58 # 237 # 20 # 274 # 59 # 307 # 33 # 332 # 17 # 351 # 22 16 # 200 # 14 # 238 # 37 # 276 # 11 # 308 # 30 # 332 # 59 # 351 # 57 17 # 201 # 30 # 239 # 54 # 277 # 21 # 309 # 26 # 333 # 41 # 352 # 32 18 # 202 # 46 # 241 # 11 # 278 # 32 # 31 # 22 # 334 # 22 # 353 # 7 19 # 204 # 2 # 242 # 28 # 279 # 43 # 311 # 18 # 335 # 4 # 353 # 42 20 # 205 # 19 # 243 # 45 # 280 # 54 # 312 # 13 # 535 # 45 # 354 # 17 21 # 206 # 53 # 245 # 2 # 282 # 4 # 313 # 7 # 336 # 26 # 354 # 52 22 # 207 # 52 # 246 # 18 # 283 # 13 # 314 # 0 # 337 # 6 # 355 # 26 23 # 209 # 8 # 247 # 35 # 284 # 22 # 314 # 53 # 337 # 46 # 356 # 1 24 # 210 # 25 # 248 # 51 # 285 # 31 # 315 # 46 # 338 # 36 # 356 # 35 25 # 211 # 42 # 250 # 7 # 286 # 39 # 316 # 38 # 339 # 5 # 357 # 9 26 # 212 # 58 # 251 # 23 # 287 # 47 # 317 # 30 # 339 # 44 # 357 # 44 27 # 214 # 15 # 252 # 39 # 288 # 54 # 318 # 21 # 340 # 22 # 358 # 18 28 # 215 # 31 # 253 # 55 # 190 # 1 # 319 # 12 # 341 # 1 # 358 # 52 29 # 216 # 48 # 255 # 11 # 291 # 7 # 320 # 2 # 341 # 59 # 359 # 26 30 # 218 # 5 # 256 # 27 # 292 # 13 # 320 # 51 # 342 # 17 # 360 # 0 </note> <pb o="360" file="396" n="397" rhead="Comment in III. Cap. Sphæræ."/> </div> <div xml:id="echoid-div778" type="section" level="1" n="287"> <head xml:id="echoid-head298" xml:space="preserve">TABVLA ASCENSIONVM <lb/>Obliquarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♈ # ## ♉ # ## ♊ # ## ♋ # ## ♌ # ## ♍ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 0 # 0 # 17 # 21 # 38 # 27 # 66 # 57 # 102 # 51 # 141 # 33 1 # 0 # 33 # 17 # 58 # 39 # 16 # 68 # 3 # 104 # 7 # 142 # 51 2 # 1 # 6 # 18 # 36 # 40 # 6 # 69 # 9 # 105 # 24 # 144 # 8 3 # 1 # 40 # 19 # 31 # 40 # 56 # 70 # 16 # 106 # 40 # 145 # 26 4 # 2 # 13 # 19 # 51 # 41 # 46 # 71 # 23 # 107 # 57 # 146 # 43 5 # 2 # 47 # 20 # 29 # 42 # 37 # 72 # 31 # 109 # 14 # 148 # 0 6 # 3 # 20 # 21 # 8 # 43 # 28 # 73 # 39 # 110 # 31 # 149 # 18 7 # 3 # 54 # 21 # 48 # 44 # 20 # 74 # 47 # 111 # 48 # 150 # 35 8 # 4 # 28 # 22 # 27 # 45 # 13 # 75 # 56 # 113 # 5 # 151 # 52 9 # 5 # 2 # 23 # 6 # 46 # 7 # 77 # 4 # 114 # 22 # 153 # 9 10 # 5 # 36 # 23 # 46 # 47 # 1 # 78 # 16 # 115 # 40 # 154 # 26 11 # 6 # 10 # 24 # 26 # 47 # 56 # 79 # 27 # 116 # 57 # 155 # 43 12 # 6 # 44 # 25 # 7 # 48 # 51 # 80 # 38 # 118 # 15 # 157 # 0 13 # 7 # 18 # 25 # 48 # 49 # 47 # 81 # 50 # 119 # 32 # 158 # 17 14 # 7 # 52 # 26 # 29 # 50 # 43 # 83 # 1 # 120 # 50 # 159 # 34 15 # 8 # 26 # 27 # 10 # 51 # 39 # 84 # 13 # 122 # 8 # 160 # 50 16 # 9 # 0 # 27 # 52 # 51 # 36 # 85 # 26 # 123 # 25 # 162 # 7 17 # 9 # 35 # 28 # 35 # 53 # 34 # 86 # 39 # 124 # 43 # 163 # 24 18 # 10 # 10 # 29 # 13 # 54 # 30 # 87 # 52 # 126 # 0 # 164 # 41 19 # 10 # 45 # 30 # 2 # 55 # 31 # 89 # 5 # 127 # 18 # 165 # 58 20 # 11 # 20 # 30 # 46 # 56 # 30 # 90 # 19 # 128 # 36 # 167 # 24 21 # 11 # 55 # 31 # 30 # 57 # 30 # 91 # 33 # 129 # 54 # 168 # 31 22 # 12 # 31 # 32 # 15 # 58 # 31 # 92 # 47 # 131 # 12 # 169 # 48 23 # 13 # 6 # 33 # 0 # 59 # 32 # 94 # 2 # 132 # 30 # 171 # 4 24 # 13 # 42 # 33 # 45 # 60 # 34 # 95 # 16 # 133 # 48 # 172 # 21 25 # 14 # 18 # 34 # 30 # 61 # 37 # 96 # 31 # 135 # 5 # 173 # 37 26 # 14 # 54 # 35 # 16 # 62 # 40 # 97 # 47 # 136 # 23 # 174 # 54 27 # 15 # 31 # 36 # 3 # 63 # 44 # 99 # 3 # 137 # 41 # 176 # 11 28 # 16 # 7 # 36 # 50 # 64 # 48 # 100 # 19 # 138 # 58 # 177 # 27 29 # 16 # 44 # 37 # 38 # 65 # 52 # 101 # 35 # 140 # 16 # 178 # 44 30 # 17 # 21 # 38 # 27 # 66 # 57 # 102 # 51 # 141 # 33 # 180 # 0 </note> <pb o="361" file="397" n="398" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div779" type="section" level="1" n="288"> <head xml:id="echoid-head299" xml:space="preserve">AD LATITVDINEM <lb/>Graduum 42.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♎ # ## ♏ # ## ♐ # ## ♑ # ## ♒ # ## ♓ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 180 # 0 # 218 # 27 # 257 # 9 # 293 # 3 # 321 # 33 # 342 # 39 1 # 181 # 16 # 219 # 44 # 258 # 25 # 294 # 8 # 322 # 22 # 343 # 16 2 # 182 # 33 # 221 # 2 # 259 # 41 # 295 # 12 # 323 # 10 # 343 # 53 3 # 183 # 49 # 222 # 19 # 260 # 57 # 296 # 16 # 323 # 57 # 344 # 29 4 # 185 # 6 # 223 # 37 # 262 # 13 # 297 # 20 # 324 # 44 # 345 # 6 5 # 186 # 23 # 224 # 55 # 263 # 29 # 298 # 23 # 325 # 30 # 345 # 42 6 # 187 # 39 # 226 # 12 # 264 # 44 # 299 # 26 # 326 # 15 # 346 # 18 7 # 188 # 56 # 227 # 30 # 265 # 58 # 300 # 28 # 327 # 0 # 346 # 54 8 # 190 # 12 # 228 # 48 # 267 # 13 # 301 # 29 # 327 # 45 # 347 # 29 9 # 191 # 29 # 230 # 6 # 268 # 27 # 302 # 30 # 328 # 30 # 348 # 5 10 # 192 # 46 # 231 # 24 # 269 # 41 # 303 # 30 # 329 # 14 # 348 # 40 11 # 194 # 2 # 232 # 42 # 270 # 55 # 304 # 29 # 329 # 58 # 349 # 15 12 # 195 # 19 # 234 # 0 # 272 # 8 # 305 # 28 # 330 # 42 # 349 # 50 13 # 196 # 36 # 23 # 17 # 273 # 21 # 306 # 26 # 331 # 25 # 350 # 25 14 # 197 # 53 # 236 # 35 # 274 # 34 # 307 # 24 # 332 # 8 # 351 # 0 15 # 199 # 10 # 237 # 52 # 275 # 47 # 308 # 21 # 332 # 50 # 351 # 34 16 # 200 # 26 # 239 # 10 # 276 # 59 # 309 # 17 # 333 # 31 # 352 # 8 17 # 201 # 43 # 240 # 28 # 278 # 10 # 310 # 13 # 334 # 12 # 352 # 42 18 # 203 # 0 # 241 # 45 # 279 # 22 # 311 # 9 # 334 # 53 # 353 # 16 19 # 204 # 17 # 243 # 3 # 280 # 33 # 312 # 4 # 335 # 34 # 353 # 50 20 # 205 # 34 # 244 # 20 # 281 # 44 # 312 # 59 # 336 # 14 # 354 # 24 21 # 206 # 51 # 245 # 38 # 282 # 54 # 313 # 53 # 336 # 54 # 354 # 58 22 # 208 # 8 # 246 # 55 # 284 # 4 # 314 # 47 # 337 # 33 # 355 # 32 23 # 209 # 25 # 248 # 12 # 285 # 13 # 315 # 40 # 338 # 12 # 356 # 6 24 # 210 # 42 # 249 # 29 # 286 # 21 # 316 # 32 # 338 # 52 # 356 # 40 25 # 212 # 0 # 250 # 46 # 287 # 29 # 317 # 23 # 339 # 31 # 357 # 13 26 # 213 # 17 # 252 # 3 # 288 # 37 # 318 # 14 # 340 # 9 # 357 # 47 27 # 214 # 34 # 353 # 20 # 289 # 44 # 319 # 4 # 340 # 48 # 358 # 20 28 # 215 # 52 # 254 # 36 # 290 # 51 # 319 # 54 # 341 # 24 # 358 # 54 29 # 217 # 9 # 255 # 53 # 291 # 57 # 320 # 44 # 342 # 2 # 359 # 20 30 # 218 # 27 # 257 # 9 # 293 # 3 # 321 # 33 # 342 # 39 # 360 # 0 </note> <pb o="362" file="398" n="399" rhead="Comment. in III. Cap. Sphæræ"/> </div> <div xml:id="echoid-div780" type="section" level="1" n="289"> <head xml:id="echoid-head300" xml:space="preserve">TABVLA ASCENSIONVM <lb/>Obliquarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♈ # ## ♉ # ## ♊ # ## ♋ # ## ♌ # ## ♍ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 0 # 0 # 16 # 58 # 37 # 44 # 66 # 5 # 102 # 8 # 141 # 10 1 # 0 # 32 # 17 # 35 # 38 # 32 # 67 # 5 # 103 # 25 # 142 # 29 2 # 1 # 5 # 18 # 12 # 39 # 22 # 68 # 17 # 104 # 42 # 143 # 47 3 # 1 # 38 # 18 # 49 # 40 # 12 # 69 # 24 # 105 # 59 # 145 # 5 4 # 2 # 11 # 19 # 26 # 41 # 2 # 70 # 31 # 107 # 16 # 146 # 23 5 # 2 # 44 # 20 # 3 # 41 # 52 # 71 # 39 # 108 # 34 # 147 # 41 6 # 3 # 16 # 20 # 41 # 42 # 43 # 72 # 47 # 109 # 51 # 148 # 59 7 # 3 # 49 # 21 # 20 # 43 # 35 # 73 # 55 # 111 # 9 # 150 # 17 8 # 4 # 22 # 21 # 58 # 44 # 27 # 75 # 4 # 112 # 27 # 151 # 35 9 # 4 # 55 # 22 # 37 # 45 # 20 # 76 # 14 # 113 # 45 # 152 # 53 10 # 5 # 28 # 23 # 16 # 46 # 13 # 77 # 25 # 115 # 3 # 154 # 10 11 # 6 # 1 # 23 # 56 # 47 # 7 # 78 # 36 # 116 # 21 # 155 # 28 12 # 6 # 34 # 24 # 36 # 48 # 2 # 79 # 48 # 117 # 39 # 156 # 46 13 # 7 # 8 # 25 # 16 # 48 # 57 # 80 # 59 # 118 # 58 # 158 # 4 14 # 7 # 41 # 25 # 56 # 49 # 53 # 82 # 11 # 120 # 16 # 159 # 22 15 # 8 # 15 # 26 # 37 # 50 # 49 # 83 # 23 # 121 # 35 # 160 # 39 16 # 8 # 48 # 27 # 19 # 51 # 46 # 84 # 36 # 122 # 53 # 161 # 56 17 # 9 # 22 # 28 # 1 # 52 # 44 # 85 # 50 # 124 # 11 # 163 # 13 18 # 9 # 56 # 28 # 44 # 53 # 42 # 87 # 4 # 125 # 29 # 164 # 31 19 # 10 # 30 # 29 # 26 # 54 # 40 # 88 # 17 # 126 # 47 # 165 # 48 20 # 11 # 4 # 30 # 9 # 55 # 39 # 89 # 31 # 128 # 6 # 167 # 6 21 # 11 # 39 # 30 # 53 # 56 # 39 # 90 # 46 # 129 # 25 # 168 # 23 22 # 12 # 14 # 31 # 37 # 57 # 40 # 92 # 1 # 130 # 43 # 169 # 41 23 # 12 # 49 # 32 # 21 # 58 # 41 # 93 # 16 # 132 # 2 # 170 # 58 24 # 13 # 24 # 33 # 5 # 59 # 43 # 94 # 31 # 133 # 21 # 172 # 16 25 # 13 # 54 # 33 # 50 # 60 # 45 # 95 # 46 # 134 # 39 # 173 # 34 26 # 14 # 34 # 34 # 35 # 61 # 48 # 97 # 2 # 135 # 58 # 174 # 51 27 # 15 # 10 # 35 # 21 # 62 # 51 # 98 # 18 # 137 # 16 # 176 # 8 28 # 15 # 46 # 36 # 8 # 63 # 55 # 99 # 35 # 138 # 34 # 177 # 25 29 # 16 # 22 # 36 # 56 # 65 # 0 # 100 # 51 # 139 # 52 # 178 # 42 30 # 16 # 58 # 37 # 44 # 66 # 5 # 102 # 8 # 140 # 10 # 180 # 0 </note> <pb o="363" file="399" n="400" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div781" type="section" level="1" n="290"> <head xml:id="echoid-head301" xml:space="preserve">AD LATITVDINEM <lb/>Graduum 43.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♎ # ## ♏ # ## ♐ # ## ♑ # ## ♒ # ## ♓ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 180 # 0 # 218 # 50 # 257 # 52 # 293 # 55 # 322 # 16 # 343 # 2 1 # 181 # 18 # 220 # 8 # 259 # 9 # 295 # 0 # 323 # 4 # 343 # 38 2 # 182 # 35 # 221 # 26 # 260 # 25 # 296 # 5 # 323 # 52 # 344 # 14 3 # 183 # 52 # 222 # 44 # 261 # 42 # 297 # 9 # 324 # 39 # 344 # 50 4 # 185 # 9 # 224 # 2 # 262 # 58 # 298 # 12 # 325 # 25 # 345 # 26 5 # 186 # 26 # 225 # 21 # 264 # 14 # 299 # 15 # 326 # 10 # 346 # 1 6 # 187 # 44 # 226 # 39 # 265 # 29 # 300 # 17 # 326 # 55 # 346 # 36 7 # 189 # 2 # 227 # 58 # 266 # 44 # 301 # 19 # 327 # 39 # 347 # 11 8 # 190 # 19 # 229 # 17 # 267 # 59 # 302 # 20 # 328 # 23 # 347 # 46 9 # 191 # 37 # 230 # 35 # 269 # 14 # 303 # 21 # 329 # 7 # 348 # 21 10 # 192 # 54 # 231 # 54 # 270 # 29 # 304 # 21 # 329 # 51 # 348 # 56 11 # 194 # 12 # 233 # 1@ # 271 # 43 # 305 # 20 # 330 # 34 # 349 # 30 12 # 195 # 29 # 234 # 31 # 272 # 56 # 306 # 18 # 331 # 16 # 350 # 4 13 # 196 # 47 # 235 # 49 # 274 # 10 # 307 # 16 # 331 # 59 # 350 # 38 14 # 198 # 4 # 237 # 7 # 275 # 24 # 308 # 14 # 332 # 41 # 351 # 12 15 # 199 # 21 # 238 # 25 # 276 # 37 # 309 # 11 # 333 # 23 # 351 # 45 16 # 200 # 38 # 239 # 40 # 277 # 49 # 310 # 7 # 334 # 4 # 352 # 19 17 # 201 # 56 # 241 # @2 # 279 # 1 # 311 # 3 # 334 # 44 # 352 # 52 18 # 203 # 14 # 242 # 21 # 280 # 12 # 311 # 58 # 335 # 24 # 353 # 26 19 # 204 # 32 # 243 # 39 # 281 # 24 # 312 # 53 # 336 # 4 # 353 # 59 20 # 205 # 50 # 244 # 57 # 282 # 35 # 313 # 47 # 336 # 44 # 354 # 32 21 # 207 # 7 # 246 # 15 # 283 # 46 # 314 # 40 # 337 # 23 # 355 # 5 22 # 208 # 25 # 247 # 33 # 284 # 56 # 315 # 33 # 338 # 2 # 355 # 38 23 # 209 # 43 # 248 # 51 # 286 # 5 # 316 # 25 # 338 # 40 # 356 # 11 24 # 211 # 1 # 250 # 9 # 287 # 13 # 317 # 17 # 339 # 19 # 356 # 44 25 # 212 # 19 # 251 # 26 # 288 # 21 # 318 # 8 # 339 # 57 # 357 # 16 26 # 213 # 37 # 252 # 44 # 289 # 29 # 318 # 58 # 340 # 34 # 357 # 49 27 # 214 # 55 # 254 # 1 # 290 # 36 # 319 # 48 # 341 # 11 # 358 # 22 28 # 216 # 13 # 255 # 18 # 291 # 43 # 320 # 38 # 341 # 48 # 358 # 55 29 # 217 # 31 # 256 # 35 # 292 # 49 # 321 # 27 # 342 # 25 # 359 # 28 30 # 218 # 50 # 357 # 52 # 293 # 55 # 322 # 16 # 343 # 2 # 360 # 0 </note> <pb o="364" file="400" n="401" rhead="Comment. in III. Cap. Sphæræ."/> </div> <div xml:id="echoid-div782" type="section" level="1" n="291"> <head xml:id="echoid-head302" xml:space="preserve">TABVLA ASCENSIONVM <lb/>Obliquarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♈ # ## ♉ # ## ♊ # ## ♋ # ## ♌ # ## ♍ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 0 # 0 # 16 # 34 # 36 # 56 # 65 # 10 # 101 # 23 # 140 # 46 1 # 0 # 32 # 17 # 10 # 37 # 47 # 66 # 15 # 102 # 40 # 142 # 5 2 # 1 # 4 # 17 # 46 # 38 # 36 # 67 # 21 # 103 # 56 # 143 # 24 3 # 1 # 36 # 18 # 22 # 39 # 25 # 68 # 28 # 105 # 16 # 144 # 43 4 # 2 # 8 # 18 # 58 # 40 # 14 # 69 # 36 # 106 # 34 # 146 # 2 5 # 2 # 40 # 19 # 35 # 41 # 4 # 70 # 44 # 107 # 52 # 147 # 21 6 # 3 # 12 # 20 # 12 # 41 # 55 # 71 # 53 # 109 # 10 # 148 # 40 7 # 3 # 44 # 20 # 50 # 42 # 46 # 73 # 2 # 110 # 28 # 149 # 59 8 # 4 # 16 # 21 # 28 # 43 # 38 # 74 # 12 # 111 # 47 # 151 # 18 9 # 4 # 48 # 22 # 6 # 44 # 30 # 75 # 22 # 113 # 5 # 152 # 37 10 # 5 # 20 # 22 # 45 # 45 # 23 # 76 # 32 # 114 # 24 # 153 # 55 11 # 5 # 52 # 23 # 14 # 46 # 17 # 77 # 43 # 115 # 43 # 155 # 14 12 # 6 # 35 # 24 # 3 # 47 # 11 # 78 # 54 # 117 # 2 # 156 # 32 13 # 6 # 57 # 24 # 43 # 48 # 6 # 80 # 6 # 118 # 21 # 157 # 51 14 # 7 # 30 # 25 # 22 # 49 # 1 # 81 # 18 # 119 # 41 # 159 # 9 15 # 8 # 3 # 26 # 2 # 49 # 57 # 82 # 31 # 121 # 0 # 160 # 27 16 # 8 # 36 # 26 # 43 # 50 # 53 # 83 # 44 # 122 # 19 # 161 # 46 17 # 9 # 9 # 27 # 25 # 51 # 50 # 84 # 58 # 123 # 38 # 163 # 4 18 # 9 # 42 # 28 # 6 # 52 # 48 # 86 # 12 # 124 # 57 # 164 # 22 19 # 10 # 15 # 28 # 48 # 53 # 47 # 87 # 26 # 126 # 16 # 165 # 40 20 # 10 # 49 # 29 # 30 # 54 # 46 # 88 # 41 # 127 # 35 # 166 # 58 21 # 11 # 23 # 30 # 13 # 55 # 45 # 89 # 56 # 128 # 54 # 168 # 17 22 # 11 # 57 # 30 # 57 # 56 # 45 # 91 # 11 # 130 # 13 # 169 # 35 23 # 12 # 31 # 31 # 40 # 57 # 46 # 92 # 27 # 131 # 33 # 170 # 54 24 # 13 # 5 # 32 # 24 # 58 # 48 # 93 # 42 # 133 # 52 # 172 # 12 25 # 13 # 39 # 33 # 8 # 59 # 50 # 94 # 58 # 134 # 11 # 173 # 30 26 # 14 # 14 # 33 # 53 # 60 # 53 # 96 # 15 # 135 # 30 # 174 # 48 27 # 14 # 49 # 34 # 39 # 61 # 58 # 97 # 32 # 136 # 49 # 176 # 6 28 # 15 # 24 # 35 # 25 # 63 # 1 # 98 # 46 # 138 # 8 # 177 # 24 29 # 15 # 59 # 36 # 12 # 94 # 6 # 100 # 6 # 139 # 27 # 178 # 42 30 # 16 # 34 # 36 # 56 # 65 # 10 # 101 # 23 # 140 # 46 # 180 # 0 </note> <pb o="365" file="401" n="402" rhead="Ioan de Sacro Boſco."/> </div> <div xml:id="echoid-div783" type="section" level="1" n="292"> <head xml:id="echoid-head303" xml:space="preserve">AD LATITVDINEM <lb/>Graduum 44</head> <note position="right" xml:space="preserve"> <lb/> # ## ♎ # ## ♏ # ## ♐ # ## ♑ # ## ♒ # ## ♓ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 180 # 0 # 219 # 14 # 258 # 37 # 294 # 50 # 323 # 1 # 343 # 26 1 # 181 # 18 # 220 # 33 # 259 # 54 # 295 # 55 # 323 # 48 # 344 # 1 2 # 182 # 36 # 221 # 52 # 261 # 11 # 296 # 59 # 324 # 35 # 344 # 36 3 # 183 # 54 # 223 # 11 # 262 # 28 # 298 # 3 # 325 # 21 # 345 # 11 4 # 185 # 12 # 224 # 30 # 263 # 45 # 299 # 7 # 326 # 7 # 345 # 46 5 # 186 # 30 # 225 # 49 # 265 # 2 # 300 # 10 # 326 # 52 # 346 # 21 6 # 187 # 48 # 227 # 8 # 266 # 18 # 301 # 12 # 327 # 36 # 346 # 55 7 # 189 # 6 # 228 # 27 # 267 # 33 # 302 # 14 # 328 # 20 # 347 # 29 8 # 190 # 25 # 229 # 47 # 268 # 49 # 303 # 15 # 329 # 3 # 348 # 3 9 # 191 # 43 # 231 # 6 # 270 # 4 # 304 # 15 # 329 # 47 # 348 # 37 10 # 193 # 2 # 232 # 25 # 271 # 19 # 305 # 14 # 330 # 30 # 349 # 11 11 # 194 # 20 # 233 # 44 # 272 # 34 # 306 # 13 # 331 # 12 # 349 # 45 12 # 195 # 38 # 235 # 3 # 273 # 48 # 307 # 12 # 331 # 54 # 350 # 18 13 # 196 # 56 # 236 # 23 # 275 # 2 # 308 # 10 # 332 # 35 # 350 # 51 14 # 198 # 14 # 237 # 41 # 276 # 16 # 309 # 7 # 333 # 17 # 351 # 24 15 # 199 # 33 # 239 # 0 # 277 # 29 # 310 # 3 # 333 # 58 # 351 # 57 16 # 200 # 51 # 240 # 19 # 278 # 42 # 310 # 59 # 334 # 38 # 352 # 30 17 # 202 # 9 # 241 # 39 # 279 # 54 # 311 # 54 # 335 # 17 # 353 # 3 18 # 203 # 28 # 242 # 58 # 281 # 6 # 312 # 49 # 335 # 57 # 353 # 35 19 # 204 # 46 # 244 # 17 # 282 # 17 # 313 # 43 # 336 # 36 # 354 # 8 20 # 206 # 5 # 245 # 36 # 283 # 28 # 314 # 37 # 337 # 15 # 354 # 40 21 # 207 # 23 # 246 # 55 # 284 # 38 # 315 # 30 # 337 # 54 # 355 # 12 22 # 208 # 42 # 248 # 13 # 185 # 48 # 316 # 22 # 338 # 32 # 355 # 44 23 # 210 # 1 # 249 # 32 # 286 # 58 # 317 # 14 # 339 # 10 # 356 # 16 24 # 211 # 20 # 250 # 50 # 288 # 7 # 318 # 5 # 339 # 48 # 356 # 48 25 # 212 # 39 # 252 # 8 # 289 # 16 # 318 # 56 # 340 # 25 # 357 # 20 26 # 213 # 58 # 253 # 26 # 290 # 24 # 319 # 46 # 341 # 2 # 357 # @2 27 # 215 # 17 # 254 # 44 # 291 # 32 # 320 # 35 # 341 # 38 # 358 # 24 28 # 216 # 36 # 256 # 2 # 292 # 39 # 321 # 24 # 342 # 14 # 358 # 56 29 # 217 # 55 # 257 # 20 # 293 # 45 # 322 # 13 # 342 # 50 # 359 # 28 30 # 219 # 14 # 258 # 37 # 294 # 50 # 323 # 1 # 343 # 26 # 360 # 0 </note> <pb o="366" file="402" n="403" rhead="Comment. in III. Cap. Sphæræ"/> </div> <div xml:id="echoid-div784" type="section" level="1" n="293"> <head xml:id="echoid-head304" xml:space="preserve">TABVLA ASCENSIONVM <lb/>Obliquarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♈ # ## ♉ # ## ♊ # ## ♋ # ## ♌ # ## ♍ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 0 # 0 # 16 # 10 # 36 # 13 # 64 # 14 # 100 # 37 # 140 # 22 1 # 0 # 31 # 16 # 45 # 37 # 0 # 65 # 20 # 101 # 55 # 141 # 42 2 # 1 # 2 # 17 # 20 # 37 # 48 # 66 # 26 # 103 # 13 # 143 # 2 3 # 1 # 33 # 17 # 56 # 38 # 36 # 67 # 33 # 104 # 32 # 144 # 21 4 # 2 # 4 # 18 # 31 # 39 # 25 # 68 # 40 # 105 # 50 # 145 # 41 5 # 2 # 35 # 19 # 7 # 40 # 15 # 69 # 48 # 107 # 9 # 147 # 0 6 # 3 # 6 # 19 # 43 # 41 # 5 # 70 # 56 # 108 # 28 # 148 # 20 7 # 3 # 37 # 20 # 20 # 41 # 56 # 72 # 5 # 109 # 47 # 149 # 40 8 # 4 # 9 # 20 # 57 # 42 # 47 # 73 # 15 # 111 # 6 # 150 # 59 9 # 4 # 40 # 21 # 34 # 43 # 39 # 74 # 28 # 112 # 25 # 152 # 19 10 # 5 # 12 # 22 # 12 # 44 # 31 # 75 # 36 # 113 # 44 # 153 # 38 11 # 5 # 43 # 22 # 50 # 45 # 24 # 76 # 48 # 115 # 3 # 154 # 58 12 # 6 # 15 # 23 # 29 # 46 # 18 # 78 # 0 # 116 # 23 # 156 # 17 13 # 6 # 47 # 24 # 8 # 47 # 12 # 79 # 12 # 117 # 42 # 157 # 37 14 # 7 # 19 # 24 # 47 # 48 # 7 # 80 # 24 # 119 # 2 # 158 # 56 15 # 7 # 51 # 25 # 26 # 49 # 3 # 81 # 37 # 120 # 22 # 160 # 15 16 # 8 # 33 # 26 # 6 # 49 # 59 # 82 # 51 # 121 # 42 # 161 # 34 17 # 8 # 55 # 26 # 47 # 50 # 56 # 84 # 5 # 123 # 2 # 162 # 53 18 # 9 # 27 # 27 # 28 # 51 # 53 # 85 # 20 # 124 # 22 # 164 # 12 19 # 9 # 59 # 28 # 9 # 52 # 51 # 86 # 34 # 125 # 42 # 165 # 31 20 # 10 # 32 # 28 # 50 # 53 # 50 # 87 # 49 # 127 # 2 # 166 # 50 21 # 11 # 5 # 29 # 32 # 54 # 49 # 89 # 4 # 128 # 22 # 168 # 9 22 # 11 # 38 # 30 # 15 # 55 # 49 # 90 # 20 # 129 # 42 # 169 # 28 23 # 12 # 11 # 30 # 58 # 56 # 50 # 91 # 36 # 131 # 3 # 170 # 47 24 # 12 # 44 # 31 # 41 # 57 # 52 # 92 # 52 # 132 # 23 # 172 # 6 25 # 13 # 18 # 32 # 25 # 58 # 54 # 94 # 9 # 133 # 43 # 173 # 25 26 # 13 # 52 # 33 # 10 # 59 # 57 # 95 # 26 # 135 # 3 # 174 # 44 27 # 14 # 26 # 33 # 56 # 61 # 0 # 96 # 44 # 136 # 23 # 176 # 3 28 # 15 # 1 # 34 # 41 # 62 # 4 # 98 # 1 # 137 # 43 # 177 # 22 29 # 15 # 35 # 35 # 21 # 63 # 9 # 99 # 19 # 139 # 3 # 178 # 41 30 # 16 # 10 # 36 # 13 # 64 # 14 # 100 # 37 # 140 # 22 # 180 # 0 </note> <pb o="367" file="403" n="404" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div785" type="section" level="1" n="294"> <head xml:id="echoid-head305" xml:space="preserve">AD LATITVDINEM <lb/>Graduum 45.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♎ # ## ♏ # ## ♐ # ## ♑ # ## ♒ # ## ♓ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 180 # @0 # 219 # 38 # 259 # 23 # 295 # 46 # 323 # 47 # 343 # 50 1 # 181 # 19 # 220 # 5@ # 260 # 41 # 296 # 51 # 324 # 33 # 344 # 25 2 # 182 # 38 # 222 # 17 # 261 # 59 # 297 # 56 # 325 # 19 # 344 # 59 3 # 183 # 57 # 223 # 37 # 263 # 16 # 299 # 0 # 326 # 4 # 345 # 34 4 # 185 # 16 # 224 # 57 # 264 # 34 # 300 # 3 # 326 # 50 # 346 # 8 5 # 186 # 35 # 226 # 17 # 265 # 51 # 301 # 6 # 327 # 35 # 346 # 42 6 # 187 # 54 # 227 # 37 # 267 # 8 # 302 # 8 # 328 # 19 # 347 # 16 7 # 189 # 13 # 228 # 57 # 268 # 24 # 303 # 10 # 329 # 2 # 347 # 49 8 # 190 # 32 # 230 # 18 # 269 # 40 # 304 # 11 # 329 # 45 # 348 # 22 9 # 191 # 51 # 231 # 38 # 270 # 56 # 305 # 11 # 330 # 28 # 348 # 55 10 # 193 # 10 # 232 # 58 # 272 # 11 # 306 # 10 # 331 # 10 # 349 # 28 11 # 194 # 29 # 234 # 18 # 273 # 26 # 307 # 9 # 331 # 51 # 350 # 1 12 # 195 # 48 # 235 # 38 # 274 # 40 # 308 # 7 # 332 # 32 # 350 # 33 13 # 197 # 7 # 236 # 58 # 275 # 55 # 309 # 4 # 333 # 13 # 351 # 5 14 # 198 # 26 # 238 # 18 # 277 # 9 # 310 # 1 # 333 # 54 # 351 # 37 15 # 199 # 45 # 239 # 38 # 278 # 23 # 310 # 57 # 334 # 34 # 352 # 9 16 # 201 # 4 # 240 # 58 # 279 # 36 # 311 # 53 # 335 # 13 # 352 # 41 17 # 202 # 23 # 242 # 18 # 280 # 48 # 312 # 48 # 335 # 52 # 353 # 13 18 # 203 # 43 # 243 # 37 # 282 # 0 # 313 # 42 # 336 # 31 # 353 # 45 19 # 205 # 2 # 244 # 57 # 283 # 12 # 314 # 36 # 337 # 10 # 354 # 17 20 # 206 # 22 # 246 # 16 # 284 # 24 # 315 # 29 # 337 # 48 # 354 # 48 21 # 207 # 41 # 247 # 35 # 285 # 35 # 316 # 21 # 338 # 26 # 355 # 20 22 # 209 # 1 # 248 # 54 # 286 # 45 # 317 # 13 # 339 # 3 # 355 # 51 23 # 210 # 20 # 250 # 13 # 287 # 55 # 318 # 4 # 339 # 40 # 356 # 23 24 # 211 # 40 # 251 # 32 # 289 # 4 # 318 # 55 # 340 # 17 # 356 # 54 25 # 213 # 0 # 252 # 51 # 290 # 12 # 319 # 45 # 340 # 53 # 357 # 25 26 # 214 # 19 # 254 # 10 # 291 # 20 # 320 # 35 # 341 # 29 # 357 # 56 27 # 215 # 39 # 255 # 28 # 192 # 27 # 321 # 24 # 342 # 4 # 358 # 27 28 # 216 # 58 # 256 # 47 # 293 # 34 # 322 # 12 # 342 # 40 # 358 # 58 29 # 218 # 18 # 258 # 5 # 294 # 40 # 323 # 0 # 343 # 15 # 359 # 29 30 # 219 # 38 # 359 # 23 # 295 # 46 # 323 # 47 # 343 # 50 # 360 # 0 </note> <pb o="368" file="404" n="405" rhead="Comment. in III. Cap. Sphæræ"/> </div> <div xml:id="echoid-div786" type="section" level="1" n="295"> <head xml:id="echoid-head306" xml:space="preserve">TABVLA ASCENSIONVM <lb/>Obliquarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♈ # ## ♉ # ## ♊ # ## ♋ # ## ♌ # ## ♍ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 0 # 0 # 15 # 44 # 35 # 24 # 63 # 14 # 99 # 48 # 139 # 56 1 # 0 # 30 # 16 # 18 # 36 # 11 # 64 # 20 # 101 # 7 # 141 # 17 2 # 1 # 0 # 16 # 53 # 36 # 58 # 65 # 27 # 102 # 26 # 142 # 38 3 # 1 # 30 # 17 # 27 # 37 # 46 # 66 # 34 # 103 # 45 # 143 # 58 4 # 2 # 0 # 18 # 2 # 38 # 34 # 67 # 41 # 105 # 4 # 145 # 19 5 # 2 # 31 # 18 # 37 # 39 # 23 # 68 # 49 # 106 # 24 # 146 # 39 6 # 3 # 1 # 19 # 13 # 40 # 12 # 69 # 58 # 108 # 43 # 148 # 0 7 # 3 # 32 # 19 # 49 # 41 # 2 # 71 # 8 # 109 # 3 # 149 # 20 8 # 4 # 2 # 20 # 26 # 41 # 53 # 72 # 18 # 110 # 23 # 150 # 41 9 # 4 # 33 # 21 # 2 # 42 # 45 # 73 # 28 # 111 # 43 # 152 # 1 10 # 5 # 4 # 21 # 39 # 43 # 37 # 74 # 39 # 113 # 3 # 153 # 21 11 # 5 # 34 # 22 # 16 # 44 # 30 # 75 # 51 # 114 # 23 # 154 # 42 12 # 6 # 5 # 22 # 54 # 45 # 24 # 77 # 3 # 115 # 44 # 156 # 2 13 # 6 # 36 # 23 # 32 # 46 # 18 # 78 # 16 # 117 # 4 # 157 # 22 14 # 7 # 7 # 24 # 10 # 47 # 12 # 79 # 28 # 118 # 25 # 158 # 42 15 # 7 # 38 # 24 # 47 # 48 # 7 # 80 # 41 # 119 # 46 # 160 # 2 16 # 8 # 9 # 25 # 27 # 49 # 3 # 81 # 55 # 121 # 6 # 161 # 22 17 # 8 # 40 # 26 # 7 # 50 # 0 # 83 # 10 # 122 # 27 # 162 # 42 18 # 9 # 12 # 26 # 47 # 50 # 57 # 84 # 25 # 123 # 47 # 164 # 2 19 # 9 # 43 # 27 # 28 # 51 # 55 # 85 # 40 # 125 # 8 # 165 # 22 20 # 10 # 15 # 28 # 9 # 52 # 53 # 86 # 55 # 126 # 29 # 166 # 42 21 # 10 # 47 # 28 # 51 # 53 # 52 # 88 # 11 # 127 # 50 # 168 # 2 22 # 11 # 19 # 29 # 33 # 54 # 52 # 89 # 27 # 129 # 10 # 169 # 22 23 # 11 # 52 # 30 # 15 # 55 # 52 # 90 # 44 # 130 # 31 # 170 # 42 24 # 12 # 24 # 30 # 57 # 56 # 53 # 92 # 0 # 131 # 52 # 172 # 2 25 # 12 # 57 # 31 # 40 # 57 # 55 # 93 # 17 # 133 # 13 # 173 # 21 26 # 13 # 30 # 32 # 23 # 58 # 57 # 94 # 35 # 134 # 34 # 174 # 41 27 # 14 # 3 # 33 # 7 # 60 # 0 # 95 # 53 # 135 # 55 # 176 # 1 28 # 14 # 37 # 33 # 52 # 61 # 4 # 97 # 11 # 137 # 15 # 177 # 21 29 # 15 # 10 # 34 # 38 # 62 # 9 # 98 # 29 # 138 # 36 # 178 # 41 30 # 13 # 44 # 35 # 24 # 63 # 14 # 99 # 48 # 139 # 56 # 180 # 0 </note> <pb o="369" file="405" n="406" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div787" type="section" level="1" n="296"> <head xml:id="echoid-head307" xml:space="preserve">AD LATITVDINEM <lb/>Graduum 46.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♎ # ## ♏ # ## ♐ # ## ♑ # ## ♒ # ## ♓ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 180 # 0 # 220 # 4 # 260 # 12 # 296 # 46 # 324 # 36 # 344 # 16 1 # 181 # 19 # 221 # 24 # 261 # 31 # 297 # 51 # 325 # 22 # 344 # 50 2 # 182 # 39 # 222 # 45 # 262 # 49 # 298 # 56 # 326 # 8 # 345 # 23 3 # 183 # 59 # 224 # 5 # 264 # 7 # 300 # 0 # 326 # 43 # 345 # 57 4 # 185 # 19 # 225 # 26 # 265 # 25 # 301 # 3 # 327 # 37 # 346 # 30 5 # 186 # 39 # 226 # 47 # 266 # 43 # 302 # 5 # 328 # 20 # 347 # 3 6 # 187 # 58 # 228 # 8 # 268 # 0 # 303 # 7 # 329 # 3 # 347 # 36 7 # 189 # 18 # 229 # 29 # 269 # 16 # 304 # 8 # 329 # 45 # 348 # 8 8 # 190 # 38 # 238 # 50 # 270 # 33 # 305 # 8 # 330 # 27 # 348 # 41 9 # 191 # 58 # 232 # 10 # 271 # 49 # 306 # 8 # 331 # 9 # 349 # 13 10 # 193 # 18 # 233 # 31 # 273 # 5 # 307 # 7 # 331 # 51 # 349 # 45 11 # 194 # 38 # 234 # 52 # 274 # 20 # 308 # 5 # 332 # 32 # 350 # 17 12 # 195 # 58 # 236 # 13 # 275 # 35 # 309 # 3 # 333 # 13 # 350 # 48 13 # 197 # 18 # 237 # 33 # 276 # 50 # 310 # 0 # 333 # 53 # 351 # 20 14 # 198 # 38 # 238 # 54 # 278 # 5 # 310 # 57 # 334 # 33 # 351 # 51 15 # 199 # 58 # 240 # 14 # 279 # 19 # 311 # 53 # 335 # 12 # 352 # 22 16 # 201 # 18 # 241 # 35 # 280 # 32 # 312 # 48 # 335 # 50 # 352 # 53 17 # 202 # 38 # 242 # 56 # 281 # 44 # 313 # 42 # 336 # 28 # 353 # 24 18 # 203 # 58 # 244 # 16 # 282 # 57 # 314 # 36 # 337 # 6 # 353 # 55 19 # 205 # 18 # 245 # 37 # 284 # 9 # 315 # 30 # 337 # 44 # 354 # 26 20 # 206 # 39 # 246 # 57 # 285 # @1 # 316 # 23 # 338 # 21 # 354 # 56 21 # 207 # 59 # 248 # 17 # 286 # 32 # 317 # 15 # 338 # 58 # 355 # 27 22 # 209 # 19 # 249 # 37 # 287 # 42 # 318 # 7 # 339 # 34 # 355 # 58 23 # 210 # 40 # 250 # 57 # 288 # 52 # 318 # 58 # 340 # 11 # 356 # 28 24 # 212 # 0 # 252 # 17 # 290 # 2 # 319 # 48 # 340 # 47 # 356 # 59 25 # 213 # 21 # 253 # 36 # 291 # 11 # 320 # 37 # 341 # 23 # 357 # 29 26 # 214 # 41 # 254 # 56 # 292 # 19 # 321 # 26 # 341 # 58 # 358 # 0 27 # 216 # 2 # 256 # 15 # 293 # 26 # 322 # 14 # 342 # 33 # 358 # 30 28 # 217 # 22 # 257 # 34 # 294 # 33 # 323 # 2 # 343 # 7 # 359 # 0 29 # 218 # 43 # 258 # 53 # 295 # 40 # 323 # 49 # 343 # 42 # 359 # 30 30 # 220 # 4 # 260 # 12 # 296 # 46 # 324 # 36 # 344 # 16 # 360 # 0 </note> <pb o="370" file="406" n="407" rhead="Comment. in III. Cap Sphæræ"/> </div> <div xml:id="echoid-div788" type="section" level="1" n="297"> <head xml:id="echoid-head308" xml:space="preserve">TABVLA ASCENSIONVM <lb/>Obliquarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♈ # ## ♉ # ## ♊ # ## ♋ # ## ♌ # ## ♍ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 0 # 0 # 15 # 18 # 34 # 34 # 62 # 12 # 98 # 58 # 139 # 30 1 # 0 # 29 # 15 # 51 # 35 # 20 # 63 # 18 # 100 # 17 # 140 # 52 2 # 0 # 58 # 16 # 25 # 36 # 7 # 64 # 25 # 101 # 37 # 142 # 13 3 # 1 # 28 # 16 # 58 # 36 # 54 # 65 # 32 # 102 # 57 # 143 # 35 4 # 1 # 57 # 17 # 32 # 37 # 41 # 66 # 40 # 104 # 17 # 144 # 56 5 # 2 # 27 # 18 # 6 # 38 # 29 # 67 # 48 # 105 # 27 # 146 # 17 6 # 2 # 56 # 18 # 41 # 39 # 18 # 68 # 57 # 106 # 57 # 147 # 39 7 # 3 # 26 # 19 # 17 # 40 # 8 # 70 # 6 # 108 # 18 # 149 # 0 8 # 3 # 55 # 19 # 52 # 40 # 58 # 71 # 16 # 109 # 38 # 150 # 22 9 # 4 # 25 # 20 # 28 # 41 # 49 # 72 # 27 # 110 # 59 # 151 # 43 10 # 4 # 55 # 21 # 4 # 42 # 40 # 73 # 38 # 112 # 20 # 153 # 4 11 # 5 # 25 # 21 # 40 # 43 # 32 # 74 # 50 # 113 # 41 # 154 # 25 12 # 5 # 55 # 22 # 17 # 44 # 25 # 76 # 2 # 115 # 2 # 155 # 46 13 # 6 # 25 # 22 # 54 # 45 # 19 # 77 # 15 # 116 # 24 # 157 # 7 14 # 6 # 55 # 23 # 31 # 46 # 13 # 78 # 28 # 117 # 45 # 158 # 28 15 # 7 # 25 # 24 # 9 # 47 # 8 # 79 # 42 # 119 # 7 # 159 # 49 16 # 7 # 55 # 24 # 47 # 48 # 3 # 80 # 56 # 120 # 28 # 161 # 10 17 # 8 # 26 # 25 # 26 # 48 # 50 # 82 # 11 # 121 # 49 # 162 # 31 18 # 8 # 56 # 26 # 5 # 49 # 56 # 83 # 26 # 123 # 11 # 163 # 52 19 # 9 # 27 # 26 # 45 # 50 # 54 # 84 # 42 # 124 # 32 # 165 # 13 20 # 9 # 58 # 27 # 26 # 51 # 52 # 85 # 58 # 125 # 54 # 166 # 33 21 # 10 # 29 # 28 # 7 # 52 # 51 # 87 # 41 # 127 # 15 # 167 # 54 22 # 11 # 0 # 28 # 48 # 53 # 51 # 88 # 31 # 128 # 37 # 169 # 15 23 # 11 # 32 # 29 # 30 # 54 # 51 # 89 # 48 # 129 # 58 # 170 # 36 24 # 12 # 3 # 30 # 11 # 55 # 52 # 91 # 5 # 131 # 20 # 171 # 57 25 # 12 # 35 # 30 # 53 # 56 # 54 # 92 # 23 # 132 # 42 # 173 # 17 26 # 13 # 7 # 31 # 36 # 57 # 56 # 93 # 42 # 134 # 4 # 174 # 38 27 # 13 # 40 # 32 # 20 # 58 # 59 # 95 # 1 # 135 # 26 # 175 # 59 28 # 14 # 12 # 33 # 4 # 60 # 3 # 96 # 20 # 136 # 47 # 177 # 19 29 # 14 # 45 # 33 # 49 # 61 # 7 # 97 # 39 # 138 # 9 # 178 # 40 30 # 15 # 18 # 34 # 34 # 62 # 12 # 98 # 58 # 139 # 30 # 180 # 0 </note> <pb o="371" file="407" n="408" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div789" type="section" level="1" n="298"> <head xml:id="echoid-head309" xml:space="preserve">AD LAVITVDINEM <lb/>Graduum 47.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♎ # ## ♏ # ## ♐ # ## ♑ # ## ♒ # ## ♓ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 180 # 0 # 220 # 30 # 261 # 2 # 297 # 48 # 325 # 26 # 344 # 42 1 # 181 # 20 # 221 # 51 # 262 # 21 # 298 # 53 # 326 # 11 # 345 # 15 2 # 182 # 41 # 223 # 13 # 263 # 40 # 299 # 57 # 326 # 56 # 345 # 48 3 # 184 # 1 # 224 # 34 # 264 # 59 # 301 # 1 # 327 # 40 # 346 # 20 4 # 185 # 22 # 225 # 5@ # 266 # 18 # 302 # 4 # 328 # 24 # 346 # 53 5 # 186 # 43 # 227 # 18 # 267 # 37 # 303 # 6 # 329 # 7 # 347 # 25 6 # 188 # 3 # 228 # 40 # 268 # 55 # 304 # 8 # 329 # 49 # 347 # 57 7 # 189 # 24 # 230 # 2 # 270 # 12 # 305 # 9 # 330 # 30 # 348 # 28 8 # 190 # 45 # 231 # 23 # 271 # 29 # 306 # 9 # 331 # 12 # 349 # 0 9 # 192 # 6 # 232 # 45 # 272 # 46 # 307 # 9 # 331 # 53 # 349 # 31 10 # 193 # 27 # 234 # 6 # 274 # 2 # 308 # 8 # 332 # 34 # 350 # 2 11 # 194 # 47 # 235 # 28 # 175 # 18 # 309 # 6 # 333 # 15 # 350 # 33 12 # 196 # 8 # 236 # 49 # 276 # 34 # 310 # 4 # 333 # 55 # 351 # 4 13 # 197 # 29 # 238 # 11 # 277 # 49 # 311 # 1 # 334 # 34 # 351 # 34 14 # 198 # 50 # 239 # 32 # 279 # 4 # 311 # 57 # 335 # 13 # 352 # 5 15 # 200 # 11 # 240 # 53 # 280 # 18 # 312 # 52 # 335 # 51 # 352 # 35 16 # 201 # 32 # 242 # 15 # 281 # 32 # 313 # 47 # 336 # 29 # 353 # 5 17 # 202 # 53 # 243 # 36 # 282 # 45 # 314 # 41 # 337 # 6 # 353 # 35 18 # 204 # 14 # 244 # 58 # 283 # 58 # 315 # 35 # 337 # 43 # 354 # 5 19 # 205 # 35 # 246 # 19 # 285 # 10 # 316 # 28 # 338 # 20 # 354 # 35 20 # 206 # 56 # 247 # 40 # 286 # 22 # 317 # 20 # 338 # 56 # 355 # 5 21 # 208 # 17 # 249 # 1 # 287 # 33 # 318 # 11 # 339 # 32 # 355 # 35 22 # 209 # 38 # 250 # 22 # 288 # 44 # 319 # 2 # 340 # 8 # 356 # 5 23 # 211 # 0 # 251 # 42 # 289 # 54 # 319 # 52 # 340 # 43 # 356 # 34 24 # 212 # 21 # 253 # 3 # 291 # 3 # 320 # 42 # 341 # 19 # 357 # 4 25 # 213 # 43 # 254 # 23 # 292 # 12 # 321 # 31 # 341 # 54 # 357 # 33 26 # 215 # 4 # 255 # 43 # 293 # 20 # 322 # 19 # 342 # 28 # 358 # 3 27 # 216 # 25 # 257 # 3 # 294 # 28 # 323 # 6 # 343 # 2 # 358 # 32 28 # 217 # 47 # 258 # 23 # 295 # 35 # 323 # 53 # 343 # 35 # 359 # 2 29 # 219 # 8 # 259 # 43 # 296 # 42 # 324 # 40 # 344 # 9 # 359 # 31 30 # 220 # 30 # 261 # 3 # 297 # 48 # 325 # 26 # 344 # 42 # 360 # 0 </note> <pb o="372" file="408" n="409" rhead="Comment. in III. Cap. Sphæræ"/> </div> <div xml:id="echoid-div790" type="section" level="1" n="299"> <head xml:id="echoid-head310" xml:space="preserve">TABVLA ASCENSIONVM <lb/>Obliquarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♈ # ## ♉ # ## ♊ # ## ♋ # ## ♌ # ## ♍ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 0 # 0 # 14 # 50 # 33 # 41 # 61 # 7 # 98 # 5 # 139 # 2 1 # 0 # 28 # 15 # 23 # 34 # 26 # 62 # 13 # 99 # 25 # 140 # 25 2 # 0 # 56 # 15 # 56 # 35 # 12 # 63 # 20 # 100 # 46 # 141 # 47 3 # 1 # 25 # 16 # 29 # 35 # 58 # 64 # 27 # 102 # 6 # 143 # 10 4 # 1 # 53 # 17 # 2 # 36 # 45 # 65 # 35 # 103 # 27 # 144 # 32 5 # 2 # 22 # 17 # 35 # 37 # 33 # 66 # 43 # 104 # 48 # 145 # 54 6 # 2 # 50 # 18 # 9 # 38 # 22 # 67 # 51 # 106 # 9 # 147 # 17 7 # 3 # 19 # 18 # 43 # 39 # 12 # 69 # 1 # 107 # 30 # 148 # 39 8 # 3 # 48 # 19 # 18 # 40 # 1 # 70 # 11 # 108 # 52 # 150 # 1 9 # 4 # 17 # 19 # 52 # 40 # 51 # 71 # 22 # 110 # 13 # 151 # 23 10 # 4 # 56 # 20 # 27 # 41 # 41 # 72 # 34 # 111 # 35 # 152 # 45 11 # 5 # 15 # 21 # 2 # 42 # 32 # 73 # 46 # 112 # 57 # 154 # 7 12 # 5 # 44 # 21 # 38 # 43 # 24 # 74 # 59 # 114 # 19 # 155 # 29 13 # 6 # 13 # 22 # 14 # 44 # 17 # 76 # 12 # 115 # 41 # 156 # 51 14 # 6 # 42 # 22 # 51 # 45 # 11 # 77 # 26 # 117 # 3 # 158 # 13 15 # 7 # 11 # 23 # 28 # 46 # 6 # 78 # 40 # 118 # 26 # 159 # 35 16 # 7 # 40 # 24 # 6 # 47 # 1 # 79 # 55 # 119 # 48 # 160 # 57 17 # 8 # 10 # 24 # 45 # 47 # 57 # 81 # 10 # 121 # 10 # 162 # 19 18 # 8 # 39 # 25 # 23 # 48 # 53 # 82 # 26 # 122 # 32 # 163 # 41 19 # 9 # 9 # 26 # 2 # 49 # 50 # 83 # 42 # 123 # 54 # 165 # 3 20 # 9 # 39 # 26 # 41 # 50 # 48 # 84 # 59 # 125 # 17 # 166 # 24 21 # 10 # 9 # 27 # 21 # 51 # 47 # 86 # 16 # 126 # 40 # 167 # 46 22 # 10 # 40 # 28 # 2 # 52 # 47 # 87 # 34 # 128 # 3 # 169 # 8 23 # 11 # 10 # 28 # 42 # 53 # 47 # 88 # 51 # 129 # 26 # 170 # 29 24 # 11 # 41 # 29 # 23 # 54 # 48 # 90 # 9 # 130 # 49 # 171 # 51 25 # 12 # 12 # 30 # 4 # 55 # 49 # 91 # 27 # 132 # 11 # 173 # 12 26 # 12 # 43 # 30 # 46 # 56 # 51 # 92 # 46 # 133 # 34 # 174 # 34 27 # 13 # 15 # 31 # 29 # 57 # 54 # 94 # 6 # 134 # 57 # 175 # 56 28 # 13 # 46 # 32 # 12 # 58 # 58 # 95 # 25 # 136 # 18 # 177 # 17 29 # 14 # 18 # 32 # 56 # 60 # 2 # 96 # 45 # 137 # 40 # 178 # 39 30 # 14 # 50 # 33 # 41 # 61 # 7 # 98 # 5 # 139 # 2 # 180 # 0 </note> <pb o="373" file="409" n="410" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div791" type="section" level="1" n="300"> <head xml:id="echoid-head311" xml:space="preserve">AD LATITVDINEM <lb/>Graduum 48.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♎ # ## ♏ # ## ♐ # ## ♑ # ## ♒ # ## ♓ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 180 # 0 # 220 # 58 # 261 # 55 # 298 # 53 # 326 # 19 # 345 # 10 1 # 181 # 21 # 222 # 20 # 263 # 15 # 299 # 58 # 327 # 4 # 345 # 42 2 # 182 # 43 # 223 # 42 # 264 # 35 # 301 # 2 # 327 # 48 # 346 # 14 3 # 184 # 4 # 225 # 4 # 265 # 54 # 302 # 6 # 328 # 31 # 346 # 45 4 # 185 # 26 # 226 # 26 # 267 # 14 # 303 # 9 # 329 # 14 # 347 # 17 5 # 186 # 48 # 227 # 49 # 268 # 33 # 304 # 11 # 329 # 56 # 347 # 48 6 # 188 # 9 # 229 # 11 # 269 # 51 # 305 # 12 # 330 # 37 # 348 # 19 7 # 189 # 31 # 230 # 34 # 271 # 9 # 306 # 13 # 331 # 18 # 348 # 50 8 # 190 # 52 # 231 # 57 # 272 # 26 # 307 # 13 # 331 # 58 # 349 # 20 9 # 192 # 14 # 233 # 20 # 273 # 44 # 308 # 13 # 332 # 39 # 349 # 51 10 # 193 # 36 # 234 # 43 # 275 # 1 # 309 # 12 # 333 # 19 # 350 # 21 11 # 194 # 57 # 236 # 6 # 276 # 18 # 310 # 10 # 333 # 58 # 350 # 3<unsure/>1 12 # 196 # 19 # 237 # 28 # 277 # 34 # 311 # 7 # 334 # 37 # 351 # 21 13 # 197 # 41 # 238 # 50 # 278 # 50 # 312 # 3 # 335 # 15 # 351 # 50 14 # 199 # 3 # 140 # 12 # 280 # 5 # 312 # 59 # 335 # 54 # 352 # 20 15 # 200 # 25 # 241 # 34 # 281 # 20 # 313 # 54 # 336 # 32 # 352 # 49 16 # 201 # 47 # 242 # 57 # 282 # 34 # 314 # 49 # 337 # 9 # 353 # 18 17 # 203 # 9 # 244 # 19 # 283 # 48 # 315 # 43 # 337 # 46 # 353 # 47 18 # 204 # 31 # 245 # 41 # 285 # 1 # 316 # 36 # 338 # 22 # 354 # 16 19 # 205 # 53 # 247 # 3 # 286 # 14 # 317 # 28 # 338 # 58 # 354 # 45 20 # 207 # 15 # 248 # 25 # 287 # 26 # 318 # 19 # 339 # 33 # 355 # 14 21 # 208 # 37 # 249 # 47 # 288 # 38 # 319 # 9 # 340 # 8 # 355 # 43 22 # 209 # 59 # 251 # 8 # 289 # 49 # 319 # 59 # 340 # 42 # 356 # 12 23 # 211 # 21 # 252 # 30 # 290 # 59 # 320 # 48 # 341 # 17 # 356 # 41 24 # 212 # 43 # 253 # 51 # 292 # 8 # 321 # 38 # 341 # 51 # 357 # 10 25 # 214 # 6 # 255 # 12 # 293 # 17 # 322 # 27 # 342 # 25 # 357 # 38 26 # 215 # 28 # 256 # 33 # 294 # 25 # 323 # 15 # 342 # 58 # 358 # 7 27 # 216 # 50 # 257 # 54 # 295 # 33 # 324 # 2 # 343 # 31 # 358 # 35 28 # 218 # 13 # 259 # 14 # 296 # 40 # 324 # 48 # 344 # 4 # 359 # 4 29 # 219 # 35 # 260 # 35 # 297 # 47 # 325 # 34 # 344 # 37 # 359 # 32 30 # 220 # 58 # 261 # 55 # 298 # 53 # 326 # 19 # 345 # 10 # 360 # 0 </note> <pb o="374" file="410" n="411" rhead="Comment. in III. Cap Sphæræ"/> </div> <div xml:id="echoid-div792" type="section" level="1" n="301"> <head xml:id="echoid-head312" xml:space="preserve">TABVLA ASCENSIONVM <lb/>Obliquarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♈ # ## ♉ # ## ♊ # ## ♋ # ## ♌ # ## ♍ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 0 # 0 # 14 # 22 # 32 # 45 # 59 # 59 # 97 # 9 # 138 # 34 1 # 0 # 27 # 14 # 53 # 33 # 30 # 61 # 5 # 98 # 30 # 139 # 58 2 # 0 # 55 # 15 # 25 # 34 # 15 # 62 # 11 # 99 # 51 # 141 # 21 3 # 1 # 22 # 15 # 57 # 35 # 1 # 63 # 13 # 101 # 13 # 142 # 44 4 # 1 # 50 # 16 # 29 # 35 # 47 # 64 # 26 # 102 # 34 # 144 # 7 5 # 2 # 18 # 17 # 1 # 36 # 34 # 65 # 35 # 103 # 56 # 145 # 30 6 # 2 # 45 # 17 # 34 # 37 # 22 # 66 # 44 # 105 # 18 # 146 # 54 7 # 3 # 13 # 18 # 8 # 38 # 10 # 67 # 54 # 106 # 40 # 148 # 17 8 # 3 # 40 # 18 # 41 # 38 # 59 # 69 # 5 # 108 # 3 # 149 # 40 9 # 4 # 8 # 19 # 15 # 39 # 49 # 70 # 16 # 109 # 25 # 151 # 3 10 # 4 # 36 # 19 # 40 # 40 # 39 # 71 # 28 # 110 # 48 # 152 # 26 11 # 5 # 4 # 20 # 24 # 41 # 30 # 72 # 40 # 112 # 11 # 153 # 49 12 # 5 # 32 # 21 # 0 # 42 # 22 # 73 # 53 # 113 # 34 # 155 # 12 13 # 6 # 0 # 21 # 35 # 43 # 14 # 75 # 6 # 114 # 57 # 156 # 35 14 # 6 # 28 # 22 # 10 # 44 # 7 # 76 # 20 # 116 # 20 # 157 # 58 15 # 6 # 57 # 22 # 46 # 45 # 1 # 77 # 35 # 117 # 44 # 159 # 21 16 # 7 # 25 # 23 # 23 # 45 # 56 # 78 # 51 # 119 # 7 # 160 # 44 17 # 7 # 54 # 24 # 1 # 46 # 52 # 80 # 7 # 120 # 30 # 162 # 7 18 # 8 # 22 # 24 # 38 # 47 # 48 # 81 # 24 # 121 # 53 # 163 # 29 19 # 8 # 51 # 25 # 16 # 48 # 45 # 82 # 40 # 123 # 16 # 164 # 52 20 # 9 # 20 # 25 # 54 # 49 # 42 # 83 # 57 # 124 # 39 # 166 # 14 21 # 9 # 49 # 26 # 33 # 50 # 40 # 85 # 14 # 126 # 2 # 167 # 37 22 # 10 # 19 # 27 # 13 # 51 # 39 # 86 # 32 # 127 # 26 # 169 # 0 23 # 10 # 48 # 27 # 52 # 52 # 39 # 87 # 50 # 128 # 49 # 170 # 23 24 # 11 # 18 # 28 # 32 # 53 # 40 # 89 # 9 # 130 # 13 # 171 # 46 25 # 11 # 48 # 29 # 12 # 54 # 41 # 90 # 28 # 131 # 37 # 173 # 8 26 # 12 # 18 # 29 # 53 # 55 # 43 # 91 # 48 # 133 # 1 # 174 # 31 27 # 12 # 49 # 30 # 35 # 56 # 46 # 93 # 8 # 134 # 24 # 175 # 53 28 # 13 # 20 # 31 # 18 # 57 # 50 # 94 # 28 # 135 # 48 # 177 # 16 29 # 13 # 51 # 32 # 1 # 58 # 54 # 95 # 48 # 137 # 11 # 178 # 38 30 # 14 # 22 # 32 # 45 # 59 # 59 # 97 # 9 # 138 # 34 # 180 # 0 </note> <pb o="375" file="411" n="412" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div793" type="section" level="1" n="302"> <head xml:id="echoid-head313" xml:space="preserve">AD LATITVDINEM <lb/>Graduum 49.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♎ # ## ♏ # ## ♐ # ## ♑ # ## ♒ # ## ♓ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 180 # 0 # 221 # 26 # 262 # 51 # 300 # 1 # 327 # 15 # 345 # 38 1 # 181 # 22 # 222 # 49 # 264 # 12 # 301 # 6 # 327 # 59 # 346 # 9 2 # 182 # 44 # 214 # 12 # 265 # 32 # 302 # 10 # 328 # 42 # 346 # 40 3 # 184 # 7 # 225 # 36 # 266 # 52 # 303 # 14 # 329 # 25 # 347 # 11 4 # 185 # 29 # 226 # 59 # 268 # 12 # 304 # 16 # 330 # 17 # 347 # 42 5 # 186 # 52 # 228 # 23 # 269 # 32 # 305 # 19 # 330 # 48 # 348 # 12 6 # 188 # 14 # 229 # 47 # 270 # 51 # 306 # 20 # 331 # 28 # 348 # 42 7 # 189 # 37 # 231 # 11 # 272 # 10 # 307 # 21 # 332 # 8 # 349 # 12 8 # 191 # 0 # 232 # 34 # 273 # 28 # 308 # 21 # 332 # 47 # 349 # 41 9 # 192 # 23 # 233 # 58 # 274 # 46 # 309 # 20 # 333 # 27 # 350 # 11 10 # 193 # 46 # 235 # 21 # 276 # 3 # 310 # 18 # 334 # 6 # 350 # 40 11 # 195 # 8 # 236 # 44 # 277 # 20 # 311 # 15 # 334 # 44 # 351 # 9 12 # 196 # 31 # 238 # 7 # 278 # 36 # 312 # 12 # 335 # 22 # 351 # 38 13 # 197 # 53 # 239 # 30 # 279 # 53 # 313 # 8 # 335 # 59 # 352 # 6 14 # 199 # 16 # 240 # 53 # 281 # 9 # 314 # 4 # 336 # 37 # 352 # 35 15 # 200 # 39 # 242 # 16 # 282 # 25 # 314 # 59 # 337 # 14 # 353 # 3 16 # 202 # 2 # 243 # 40 # 283 # 40 # 315 # 53 # 337 # 50 # 353 # 32 17 # 203 # 25 # 245 # 3 # 284 # 54 # 316 # 46 # 338 # 25 # 354 # 0 18 # 204 # 48 # 246 # 26 # 286 # 7 # 317 # 38 # 339 # 0 # 354 # 28 19 # 206 # 11 # 247 # 49 # 287 # 20 # 318 # 30 # 339 # 36 # 354 # 56 20 # 207 # 34 # 249 # 12 # 288 # 32 # 319 # 21 # 340 # 11 # 355 # 24 21 # 208 # 57 # 250 # 35 # 289 # 44 # 320 # 11 # 340 # 45 # 355 # 52 22 # 210 # 20 # 251 # 57 # 290 # 55 # 321 # 1 # 341 # 19 # 356 # 20 23 # 211 # 43 # 253 # 20 # 292 # 6 # 321 # 50 # 341 # 52 # 356 # 47 24 # 213 # 6 # 254 # 42 # 293 # 16 # 322 # 38 # 342 # 26 # 357 # 15 25 # 214 # 30 # 256 # 4 # 294 # 25 # 323 # 26 # 342 # 59 # 357 # 42 26 # 215 # 53 # 257 # 26 # 295 # 34 # 324 # 13 # 343 # 31 # 358 # 10 27 # 217 # 16 # 258 # 47 # 296 # 42 # 324 # 59 # 344 # 3 # 358 # 38 28 # 218 # 39 # 260 # 9 # 297 # 49 # 325 # 45 # 344 # 35 # 359 # 5 29 # 220 # 2 # 261 # 30 # 298 # 55 # 326 # 30 # 345 # 7 # 359 # 33 30 # 221 # 26 # 262 # 51 # 300 # 1 # 327 # 15 # 345 # 38 # 360 # 0 </note> <pb o="376" file="412" n="413" rhead="Comment in III. Cap. Sphæræ."/> </div> <div xml:id="echoid-div794" type="section" level="1" n="303"> <head xml:id="echoid-head314" xml:space="preserve">TABVLA ASCENSIONVM <lb/>Obliquarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♈ # ## ♉ # ## ♊ # ## ♋ # ## ♌ # ## ♍ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 0 # 0 # 13 # 52 # 31 # 47 # 58 # 47 # 96 # 11 # 138 # 4 1 # 0 # 26 # 14 # 22 # 32 # 31 # 59 # 53 # 97 # 33 # 139 # 29 2 # 0 # 53 # 14 # 53 # 33 # 15 # 61 # 0 # 99 # 55 # 140 # 53 3 # 1 # 19 # 15 # 24 # 34 # 0 # 62 # 7 # 100 # 18 # 143 # 18 4 # 1 # 46 # 15 # 55 # 34 # 46 # 63 # 15 # 101 # 40 # 143 # 42 5 # 2 # 13 # 16 # 26 # 35 # 32 # 64 # 24 # 103 # 3 # 145 # 6 6 # 2 # 39 # 16 # 58 # 36 # 19 # 65 # 40 # 104 # 26 # 146 # 30 7 # 3 # 6 # 17 # 31 # 37 # 7 # 69 # 48 # 105 # 49 # 147 # 54 8 # 3 # 32 # 18 # 3 # 37 # 55 # 67 # 59 # 107 # 12 # 149 # 18 9 # 3 # 59 # 18 # 36 # 38 # 44 # 69 # 6 # 108 # 35 # 150 # 42 10 # 4 # 26 # 19 # 9 # 39 # 33 # 70 # 18 # 109 # 58 # 152 # 6 11 # 4 # 53 # 19 # 43 # 40 # 23 # 71 # 31 # 111 # 22 # 153 # 30 12 # 5 # 20 # 20 # 17 # 41 # 14 # 72 # 44 # 112 # 46 # 154 # 54 13 # 5 # 47 # 20 # 52 # 42 # 6 # 73 # 58 # 114 # 10 # 156 # 18 14 # 6 # 14 # 21 # 26 # 42 # 59 # 75 # 12 # 115 # 34 # 157 # 42 15 # 6 # 42 # 22 # 1 # 43 # 53 # 76 # 27 # 116 # 59 # 159 # 6 16 # 7 # 9 # 22 # 36 # 44 # 47 # 77 # 43 # 118 # 23 # 160 # 30 17 # 7 # 37 # 23 # 12 # 45 # 42 # 78 # 59 # 119 # 47 # 161 # 54 18 # 8 # 4 # 23 # 49 # 46 # 38 # 80 # 16 # 121 # 11 # 163 # 17 19 # 8 # 32 # 24 # 26 # 47 # 35 # 81 # 33 # 122 # 35 # 164 # 41 20 # 9 # 0 # 25 # 4 # 48 # 32 # 82 # 51 # 123 # 59 # 166 # 4 21 # 9 # 28 # 25 # 42 # 49 # 30 # 84 # 9 # 125 # 23 # 167 # 28 22 # 9 # 57 # 26 # 21 # 50 # 29 # 85 # 27 # 126 # 48 # 168 # 52 23 # 10 # 26 # 27 # 0 # 51 # 29 # 89 # 46 # 128 # 12 # 170 # 16 24 # 10 # 55 # 27 # 39 # 52 # 29 # 88 # 6 # 129 # 37 # 171 # 40 25 # 11 # 24 # 28 # 19 # 53 # 30 # 89 # 26 # 131 # 2 # 173 # 3 26 # 11 # 53 # 28 # 59 # 54 # 32 # 90 # 47 # 132 # 27 # 174 # 27 27 # 12 # 23 # 29 # 40 # 55 # 35 # 92 # 8 # 133 # 51 # 175 # 50 28 # 12 # 52 # 30 # 22 # 56 # 38 # 93 # 29 # 135 # 16 # 177 # 14 29 # 13 # 22 # 31 # 4 # 57 # 42 # 94 # 50 # 136 # 40 # 178 # 37 30 # 13 # 52 # 31 # 47 # 58 # 47 # 96 # 11 # 138 # 4 # 180 # 0 </note> <pb o="377" file="413" n="414" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div795" type="section" level="1" n="304"> <head xml:id="echoid-head315" xml:space="preserve">AD LATITVDINEM <lb/>Graduum 50.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♎ # ## ♏ # ## ♐ # ## ♑ # ## ♒ # ## ♓ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 180 # 0 # 121 # 56 # 263 # 49 # 301 # 13 # 328 # 13 # 346 # 8 1 # 181 # 23 # 223 # 20 # 265 # 10 # 302 # 18 # 328 # 56 # 346 # 38 2 # 182 # 46 # 224 # 44 # 266 # 31 # 303 # 22 # 329 # 38 # 347 # 8 3 # 184 # 10 # 226 # 9 # 267 # 52 # 304 # 25 # 330 # 20 # 347 # 37 4 # 185 # 33 # 227 # 33 # 269 # 13 # 305 # 28 # 331 # 1 # 348 # 7 5 # 186 # 57 # 228 # 58 # 270 # 34 # 306 # 30 # 332 # 41 # 348 # 36 6 # 188 # 20 # 230 # 23 # 271 # 54 # 307 # 31 # 332 # 21 # 349 # 5 7 # 189 # 44 # 231 # 48 # 273 # 14 # 308 # 31 # 333 # 0 # 349 # 34 8 # 191 # 8 # 233 # 12 # 274 # 33 # 307 # 31 # 333 # 39 # 350 # 3 9 # 192 # 32 # 234 # 37 # 275 # 51 # 310 # 30 # 334 # 18 # 350 # 32 10 # 193 # 56 # 236 # 1 # 277 # 9 # 311 # 28 # 334 # 56 # 351 # 0 11 # 195 # 19 # 237 # 25 # 278 # 27 # 312 # 25 # 335 # 34 # 351 # 28 12 # 196 # 43 # 238 # 49 # 279 # 44 # 313 # 22 # 336 # 11 # 351 # 56 13 # 198 # 6 # 240 # 13 # 281 # 1 # 314 # 18 # 336 # 48 # 352 # 27 14 # 199 # 30 # 241 # 37 # 282 # 17 # 315 # 13 # 337 # 24 # 352 # 51 15 # 200 # 54 # 243 # 1 # 283 # 33 # 316 # 7 # 337 # 59 # 353 # 18 16 # 202 # 18 # 244 # 26 # 284 # 48 # 317 # 1 # 338 # 34 # 353 # 46 17 # 203 # 42 # 245 # 50 # 286 # 2 # 317 # 54 # 339 # 8 # 354 # 13 18 # 205 # 6 # 247 # 14 # 287 # 16 # 318 # 46 # 339 # 43 # 354 # 40 19 # 206 # 30 # 248 # 38 # 288 # 29 # 319 # 37 # 340 # 17 # 355 # 7 20 # 207 # 54 # 250 # 2 # 289 # 42 # 320 # 27 # 340 # 51 # 355 # 34 21 # 209 # 18 # 251 # 25 # 290 # 54 # 321 # 16 # 341 # 24 # 356 # 1 22 # 210 # 42 # 252 # 48 # 292 # 1 # 322 # 5 # 341 # 57 # 356 # 28 23 # 212 # 6 # 254 # 11 # 293 # 12 # 322 # 53 # 342 # 30 # 356 # 54 24 # 213 # 30 # 255 # 34 # 294 # 20 # 323 # 41 # 343 # 2 # 357 # 21 25 # 214 # 54 # 256 # 57 # 295 # 36 # 324 # 28 # 343 # 34 # 357 # 47 26 # 216 # 38 # 258 # 20 # 296 # 45 # 325 # 14 # 344 # 5 # 358 # 14 27 # 217 # 42 # 259 # 42 # 297 # 53 # 326 # 0 # 344 # 36 # 358 # 41 28 # 219 # 7 # 261 # 5 # 299 # 0 # 326 # 45 # 345 # 7 # 359 # 7 29 # 220 # 31 # 262 # 27 # 300 # 7 # 327 # 29 # 345 # 32 # 359 # 34 30 # 221 # 56 # 263 # 49 # 301 # 13 # 328 # 13 # 346 # 8 # 360 # 0 </note> <pb o="378" file="414" n="415" rhead="Comment. in III. Cap. Sphæræ"/> </div> <div xml:id="echoid-div796" type="section" level="1" n="305"> <head xml:id="echoid-head316" xml:space="preserve">TABVLA ASCENSIONVM <lb/>Obliquarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♈ # ## ♉ # ## ♊ # ## ♋ # ## ♌ # ## ♍ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 0 # 0 # 13 # 21 # 30 # 46 # 57 # 31 # 95 # 10 # 137 # 33 1 # 0 # 25 # 13 # 50 # 31 # 29 # 58 # 37 # 96 # 33 # 138 # 59 2 # 0 # 50 # 14 # 20 # 32 # 13 # 59 # 44 # 97 # 56 # 140 # 24 3 # 1 # 16 # 14 # 50 # 32 # 57 # 60 # 51 # 99 # 19 # 141 # 50 4 # 1 # 41 # 15 # 20 # 33 # 42 # 61 # 59 # 100 # 42 # 143 # 15 5 # 2 # 7 # 15 # 50 # 34 # 27 # 63 # 8 # 102 # 6 # 144 # 40 6 # 2 # 32 # 16 # 21 # 35 # 13 # 64 # 18 # 103 # 30 # 146 # 6 7 # 2 # 58 # 16 # 53 # 36 # 0 # 65 # 29 # 104 # 54 # 147 # 31 8 # 3 # 24 # 17 # 24 # 36 # 48 # 66 # 40 # 106 # 18 # 148 # 56 9 # 3 # 50 # 17 # 56 # 37 # 36 # 67 # 52 # 107 # 42 # 150 # 21 10 # 4 # 16 # 18 # 28 # 38 # 25 # 69 # 4 # 109 # 7 # 151 # 46 11 # 4 # 42 # 19 # 1 # 39 # 15 # 70 # 17 # 110 # 32 # 152 # 11 12 # 5 # 8 # 19 # 34 # 40 # 5 # 71 # 30 # 111 # 57 # 154 # 36 13 # 5 # 34 # 20 # 7 # 40 # 56 # 72 # 44 # 113 # 22 # 156 # 1 14 # 6 # 0 # 20 # 40 # 41 # 48 # 73 # 59 # 114 # 47 # 157 # 26 15 # 6 # 26 # 21 # 14 # 42 # 41 # 75 # 5 # 116 # 12 # 158 # 50 16 # 6 # 52 # 21 # 49 # 43 # 35 # 76 # 32 # 117 # 37 # 160 # 15 17 # 7 # 19 # 22 # 25 # 44 # 30 # 77 # 50 # 119 # 2 # 161 # 40 18 # 7 # 46 # 23 # 1 # 45 # 25 # 79 # 8 # 120 # 27 # 163 # 5 19 # 8 # 13 # 23 # 37 # 46 # 21 # 80 # 25 # 221 # 52 # 164 # 30 20 # 8 # 40 # 24 # 13 # 47 # 18 # 81 # 43 # 123 # 18 # 165 # 54 21 # 9 # 7 # 24 # 50 # 48 # 16 # 83 # 2 # 124 # 43 # 167 # 19 22 # 9 # 35 # 25 # 28 # 49 # 14 # 84 # 21 # 126 # 9 # 168 # 44 23 # 10 # 2 # 26 # 6 # 50 # 13 # 85 # 41 # 127 # 35 # 170 # 8 24 # 10 # 30 # 26 # 44 # 51 # 13 # 87 # 1 # 129 # 1 # 171 # 33 25 # 10 # 58 # 27 # 22 # 52 # 14 # 88 # 21 # 130 # 26 # 172 # 57 26 # 11 # 26 # 28 # 1 # 53 # 16 # 89 # 42 # 131 # 52 # 174 # 22 27 # 11 # 55 # 28 # 41 # 54 # 19 # 91 # 4 # 133 # 17 # 175 # 46 28 # 12 # 23 # 29 # 22 # 55 # 22 # 92 # 26 # 134 # 43 # 177 # 11 29 # 12 # 52 # 30 # 4 # 56 # 26 # 93 # 48 # 136 # 8 # 178 # 36 30 # 13 # 21 # 30 # 46 # 57 # 31 # 95 # 10 # 137 # 33 # 180 # 0 </note> <pb o="379" file="415" n="416" rhead="Ioan. de Sacro Boſco"/> </div> <div xml:id="echoid-div797" type="section" level="1" n="306"> <head xml:id="echoid-head317" xml:space="preserve">AD LATITVDINEM <lb/>Graduum 51.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♎ # ## ♏ # ## ♐ # ## ♑ # ## ♒ # ## ♓ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 180 # 0 # 222 # 27 # 264 # 50 # 302 # 29 # 329 # 14 # 346 # 39 1 # 181 # 24 # 223 # 52 # 266 # 12 # 303 # 34 # 329 # 56 # 347 # 8 2 # 182 # 49 # 225 # 17 # 267 # 34 # 304 # 38 # 330 # 38 # 347 # 34 3 # 184 # 13 # 226 # 43 # 268 # 56 # 305 # 41 # 331 # 19 # 348 # 5 4 # 185 # 38 # 228 # 8 # 270 # 18 # 306 # 44 # 331 # 59 # 348 # 34 5 # 187 # 3 # 229 # 34 # 271 # 39 # 307 # 46 # 332 # 38 # 349 # 2 6 # 188 # 27 # 230 # 59 # 272 # 59 # 308 # 47 # 333 # 16 # 349 # 30 7 # 189 # 5@ # 232 # 25 # 274 # 19 # 309 # 47 # 333 # 54 # 349 # 58 8 # 191 # 16 # 233 # 51 # 275 # 39 # 310 # 46 # 334 # 32 # 350 # 25 9 # 192 # 41 # 235 # 17 # 276 # 58 # 311 # 44 # 335 # 10 # 350 # 53 10 # 194 # 6 # 236 # 42 # 278 # 17 # 312 # 42 # 335 # 47 # 351 # 20 11 # 195 # 30 # 238 # 8 # 279 # 35 # 313 # 39 # 336 # 23 # 351 # 47 12 # 196 # 55 # 239 # 33 # 280 # 52 # 314 # 35 # 336 # 59 # 352 # 14 13 # 198 # 20 # 240 # 58 # 282 # 10 # 315 # 30 # 337 # 35 # 352 # 41 14 # 199 # 45 # 242 # 23 # 283 # 28 # 316 # 2@ # 338 # 11 # 253 # 8 15 # 201 # 10 # 243 # 48 # 284 # 45 # 317 # 19 # 338 # 46 # 353 # 34 16 # 202 # 34 # 245 # 13 # 286 # 1 # 318 # 12 # 339 # 20 # 354 # 0 17 # 203 # 59 # 246 # 38 # 287 # 16 # 319 # 4 # 339 # 53 # 354 # 26 18 # 205 # 34 # 248 # 3 # 288 # 30 # 319 # 55 # 340 # 26 # 354 # 52 19 # 206 # 49 # 249 # 28 # 289 # 43 # 320 # 45 # 340 # 59 # 355 # 18 20 # 208 # 14 # 250 # 53 # 290 # 56 # 321 # 35 # 341 # 32 # 355 # 44 21 # 209 # 39 # 252 # 18 # 292 # 8 # 322 # 24 # 342 # 4 # 356 # 10 22 # 211 # 4 # 253 # 42 # 293 # 20 # 323 # 12 # 342 # 36 # 356 # 36 23 # 212 # 29 # 255 # 6 # 294 # 31 # 324 # 0 # 343 # 7 # 357 # 2 24 # 213 # 54 # 256 # 30 # 295 # 42 # 324 # 47 # 343 # 39 # 357 # 28 25 # 215 # 20 # 257 # 54 # 296 # 52 # 325 # 33 # 344 # 10 # 357 # 53 26 # 216 # 44 # 259 # 18 # 298 # 1 # 326 # 18 # 344 # 40 # 358 # 19 27 # 218 # 10 # 260 # 41 # 299 # 9 # 327 # 3 # 345 # 10 # 358 # 44 28 # 219 # 36 # 262 # 4 # 300 # 16 # 327 # 47 # 345 # 40 # 359 # 10 29 # 221 # 1 # 263 # 27 # 301 # 23 # 328 # 31 # 346 # 10 # 359 # 35 30 # 222 # 27 # 264 # 50 # 302 # 29 # 329 # 14 # 346 # 39 # 360 # 0 </note> <pb o="380" file="416" n="417" rhead="Comment. in III. Cap. Sphæræ"/> </div> <div xml:id="echoid-div798" type="section" level="1" n="307"> <head xml:id="echoid-head318" xml:space="preserve">TABVLA ASCENSIONVM <lb/>Obliquarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♈ # ## ♉ # ## ♊ # ## ♋ # ## ♌ # ## ♍ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 0 # 0 # 12 # 48 # 29 # 42 # 56 # 11 # 94 # 6 # 137 # @0 1 # 0 # 24 # 13 # 16 # 30 # 24 # 57 # 17 # 95 # 30 # 138 # 37 2 # 0 # 48 # 13 # 45 # 31 # 7 # 58 # 24 # 96 # 54 # 139 # 54 3 # 1 # 13 # 14 # 14 # 31 # 50 # 59 # 31 # 98 # 18 # 141 # 20 4 # 1 # 37 # 14 # 43 # 32 # 34 # 60 # 39 # 99 # 42 # 142 # 47 5 # 2 # 2 # 15 # 12 # 33 # 18 # 61 # 48 # 101 # 7 # 144 # 13 6 # 2 # 26 # 15 # 42 # 34 # 3 # 62 # 58 # 102 # 32 # 145 # 40 7 # 2 # 51 # 16 # 13 # 34 # 49 # 64 # 9 # 103 # 57 # 147 # 6 8 # 3 # 15 # 16 # 43 # 35 # 36 # 65 # 20 # 105 # 22 # 148 # 32 9 # 3 # 40 # 17 # 14 # 36 # 14 # 66 # 32 # 106 # 47 # 149 # 58 10 # 4 # 5 # 17 # 45 # 37 # 12 # 67 # 45 # 108 # 12 # 151 # 24 11 # 4 # 30 # 18 # 16 # 38 # 1 # 68 # 59 # 109 # 38 # 152 # 50 12 # 4 # 55 # 18 # 48 # 38 # 51 # 70 # 13 # 111 # 4 # 154 # 16 13 # 5 # 20 # 19 # 20 # 39 # 42 # 71 # 28 # 112 # 30 # 155 # 42 14 # 5 # 45 # 19 # 52 # 40 # 34 # 72 # 44 # 113 # 56 # 157 # 8 15 # 6 # 10 # 20 # 25 # 41 # 26 # 74 # 0 # 115 # 23 # 158 # 39 16 # 6 # 35 # 20 # 59 # 42 # 19 # 75 # 17 # 116 # 49 # 160 # 0 17 # 7 # 1 # 21 # 34 # 43 # 13 # 76 # 34 # 118 # 15 # 161 # 26 18 # 7 # 26 # 22 # 8 # 44 # 8 # 77 # 52 # 119 # 42 # 162 # 52 19 # 7 # 52 # 22 # 43 # 45 # 3 # 79 # 11 # 121 # 8 # 164 # 18 20 # 8 # 18 # 23 # 18 # 45 # 59 # 80 # 30 # 122 # 35 # 165 # 43 21 # 8 # 44 # 23 # 54 # 46 # 56 # 81 # 50 # 124 # 2 # 167 # 9 22 # 9 # 11 # 24 # 31 # 47 # 54 # 83 # 10 # 125 # 28 # 168 # 35 23 # 9 # 37 # 25 # 8 # 48 # 53 # 84 # 31 # 126 # 55 # 170 # 1 24 # 10 # 4 # 25 # 45 # 49 # 53 # 85 # 51 # 128 # 22 # 171 # 27 25 # 10 # 31 # 26 # 23 # 50 # 54 # 87 # 12 # 129 # 48 # 172 # 52 26 # 10 # 58 # 27 # 2 # 51 # 56 # 88 # 34 # 131 # 15 # 174 # 18 27 # 11 # 25 # 27 # 41 # 52 # 59 # 89 # 57 # 132 # 41 # 175 # 44 28 # 11 # 53 # 28 # 21 # 54 # 2 # 91 # 20 # 134 # 8 # 177 # 9 29 # 12 # 20 # 29 # 1 # 55 # 6 # 92 # 43 # 135 # 34 # 178 # 35 30 # 12 # 48 # 29 # 42 # 56 # 11 # 94 # 6 # 137 # 0 # 180 # 0 </note> <pb o="381" file="417" n="418" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div799" type="section" level="1" n="308"> <head xml:id="echoid-head319" xml:space="preserve">AD LATITVDINEM <lb/>Graduum 52.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♎ # ## ♏ # ## ♐ # ## ♑ # ## ♒ # ## ♓ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 180 # 0 # 223 # 1 # 265 # 54 # 303 # 49 # 330 # 18 # 347 # 12 1 # 181 # 25 # 224 # 26 # 267 # 17 # 304 # 54 # 330 # 59 # 347 # 40 2 # 182 # 51 # 225 # 52 # 268 # 40 # 305 # 50 # 331 # 39 # 348 # 7 3 # 184 # 16 # 227 # 19 # 270 # 3 # 307 # 1 # 332 # 19 # 348 # 35 4 # 185 # 42 # 228 # 45 # 271 # 26 # 308 # 4 # 332 # 58 # 349 # 2 5 # 187 # 8 # 230 # 12 # 272 # 48 # 309 # 6 # 333 # 37 # 349 # 29 6 # 188 # 33 # 231 # 38 # 474 # 9 # 310 # 7 # 334 # 15 # 349 # 56 7 # 189 # 59 # 233 # 5 # 275 # 29 # 311 # 7 # 334 # 52 # 350 # 23 8 # 191 # 25 # 234 # 32 # 276 # 50 # 312 # 6 # 335 # 29 # 350 # 49 9 # 192 # 51 # 235 # 58 # 278 # 10 # 313 # 4 # 336 # 6 # 351 # 16 10 # 194 # 17 # 237 # 25 # 279 # 30 # 314 # 1 # 336 # 42 # 351 # 42 11 # 195 # 42 # 238 # 52 # 280 # 49 # 314 # 57 # 337 # 17 # 352 # 8 12 # 197 # 8 # 240 # 18 # 282 # 8 # 315 # 52 # 337 # 52 # 352 # 34 13 # 198 # 34 # 241 # 45 # 283 # 26 # 316 # 47 # 338 # 26 # 352 # 59 14 # 200 # 0 # 243 # 11 # 284 # 43 # 317 # 41 # 33@ # 1 # 353 # 25 15 # 201 # 26 # 244 # 37 # 286 # 9 # 318 # 34 # 339 # 35 # 353 # 50 16 # 202 # 52 # 246 # 4 # 287 # 16 # 319 # 26 # 340 # 8 # 354 # 15 17 # 204 # 18 # 247 # 30 # 288 # 32 # 320 # 18 # 340 # 40 # 354 # 40 18 # 205 # 44 # 248 # 56 # 289 # 47 # 321 # 9 # 341 # 12 # 355 # 5 19 # 207 # 10 # 250 # 22 # 291 # 1 # 321 # 59 # 341 # 44 # 355 # 30 20 # 208 # 36 # 251 # 48 # 292 # 15 # 322 # 48 # 342 # 15 # 355 # 55 21 # 210 # 2 # 253 # 13 # 293 # 28 # 323 # 36 # 342 # 46 # 356 # 20 22 # 211 # 28 # 254 # 38 # 294 # 40 # 324 # 24 # 343 # 17 # 356 # 45 23 # 212 # 54 # 256 # 3 # 295 # 51 # 325 # 11 # 343 # 47 # 357 # 9 24 # 214 # 20 # 257 # 28 # 297 # 2 # 325 # 57 # 344 # 18 # 357 # 34 25 # 215 # 47 # 258 # 53 # 298 # 12 # 326 # 42 # 344 # 48 # 357 # 58 26 # 217 # 13 # 260 # 18 # 299 # 21 # 327 # 26 # 345 # 17 # 358 # 23 27 # 218 # 40 # 261 # 42 # 300 # 29 # 328 # 10 # 345 # 46 # 358 # 47 28 # 220 # 6 # 263 # 6 # 301 # 36 # 328 # 53 # 346 # 15 # 359 # 12 29 # 221 # 33 # 264 # 30 # 302 # 43 # 329 # 36 # 346 # 44 # 359 # 36 30 # 223 # 0 # 265 # 54 # 303 # 49 # 330 # 18 # 347 # 12 # 360 # 0 </note> <pb o="382" file="418" n="419" rhead="Comment. in III. Cap. Sphæræ"/> </div> <div xml:id="echoid-div800" type="section" level="1" n="309"> <head xml:id="echoid-head320" xml:space="preserve">TABVLA ASCENSIONVM <lb/>Obliquarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♈ # ## ♉ # ## ♊ # ## ♋ # ## ♌ # ## ♍ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 0 # 0 # 12 # 14 # 28 # 34 # 54 # 46 # 92 # 58 # 136 # 26 1 # 0 # 23 # 12 # 41 # 28 # 15 # 55 # 52 # 94 # 23 # 137 # 54 2 # 0 # 46 # 13 # 8 # 29 # 57 # 56 # 59 # 95 # 48 # 139 # 22 3 # 1 # 9 # 13 # 36 # 30 # 39 # 58 # 6 # 97 # 13 # 140 # 49 4 # 1 # 32 # 14 # 4 # 31 # 22 # 59 # 14 # 98 # 38 # 142 # 7 5 # 1 # 56 # 14 # 32 # 32 # 6 # 60 # 23 # 100 # 4 # 143 # 44 6 # 2 # 19 # 15 # 1 # 32 # 51 # 61 # 33 # 101 # 30 # 145 # 12 7 # 2 # 43 # 15 # 30 # 33 # 36 # 62 # 44 # 102 # 56 # 146 # 39 8 # 3 # 6 # 15 # 59 # 34 # 22 # 63 # 56 # 104 # 22 # 148 # 7 9 # 3 # 30 # 16 # 29 # 35 # 8 # 65 # 9 # 105 # 48 # 149 # 34 10 # 3 # 54 # 16 # 59 # 35 # 55 # 66 # 22 # 107 # 15 # 151 # 1 11 # 4 # 17 # 17 # 29 # 36 # 43 # 67 # 3 # 108 # 42 # 152 # 29 12 # 4 # 41 # 18 # 0 # 37 # 32 # 68 # 51 # 110 # 9 # 153 # 56 13 # 5 # 5 # 18 # 31 # 38 # 22 # 70 # 6 # 111 # 36 # 155 # 23 14 # 5 # 29 # 19 # 32 # 39 # 13 # 71 # 22 # 113 # 4 # 156 # 50 15 # 5 # 53 # 19 # 34 # 40 # 5 # 72 # 39 # 114 # 32 # 158 # 17 16 # 6 # 17 # 20 # 7 # 40 # 57 # 73 # 57 # 115 # 59 # 159 # 44 17 # 6 # 41 # 20 # 40 # 41 # 50 # 75 # 15 # 117 # 26 # 161 # 11 18 # 7 # 5 # 21 # 13 # 42 # 44 # 76 # 34 # 118 # 54 # 162 # 38 19 # 7 # 30 # 21 # 47 # 43 # 39 # 77 # 53 # 120 # 21 # 164 # 5 20 # 7 # 55 # 22 # 20 # 44 # 36 # 79 # 13 # 121 # 49 # 165 # 32 21 # 8 # 20 # 22 # 50 # 45 # 33 # 80 # 34 # 123 # 17 # 166 # 59 22 # 8 # 45 # 23 # 31 # 46 # 31 # 81 # 55 # 124 # 45 # 168 # 26 23 # 9 # 10 # 24 # 7 # 47 # 30 # 83 # 16 # 126 # 13 # 169 # 53 24 # 19 # 36 # 24 # 43 # 48 # 29 # 84 # 38 # 127 # 41 # 171 # 20 25 # 10 # 2 # 25 # 20 # 49 # 29 # 86 # 0 # 129 # 8 # 172 # 46 26 # 10 # 28 # 25 # 58 # 50 # 30 # 87 # 22 # 13 # 36 # 174 # 13 27 # 10 # 54 # 26 # 36 # 51 # 32 # 88 # 45 # 132 # 4 # 175 # 40 28 # 11 # 20 # 27 # 15 # 52 # 35 # 90 # 9 # 133 # 31 # 177 # 7 29 # 11 # 47 # 27 # 54 # 53 # 40 # 91 # 33 # 134 # 59 # 178 # 34 30 # 12 # 14 # 28 # 34 # 54 # 46 # 92 # 58 # 136 # 26 # 180 # 0 </note> <pb o="383" file="419" n="420" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div801" type="section" level="1" n="310"> <head xml:id="echoid-head321" xml:space="preserve">AD LATITVDINEM <lb/>Graduum 53.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♎ # ## ♏ # ## ♐ # ## ♑ # ## ♒ # ## ♓ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 180 # 0 # 223 # 34 # 267 # 2 # 305 # 14 # 331 # 26 # 347 # 46 1 # 181 # 26 # 225 # 1 # 268 # 27 # 306 # 20 # 332 # 6 # 348 # 13 2 # 182 # 53 # 226 # 29 # 269 # 51 # 307 # 25 # 332 # 45 # 348 # 40 3 # 184 # 20 # 227 # 56 # 271 # 15 # 308 # 28 # 333 # 24 # 349 # 6 4 # 185 # 47 # 229 # 24 # 272 # 38 # 309 # 30 # 334 # 2 # 349 # 32 5 # 187 # 14 # 230 # 52 # 274 # 0 # 310 # 31 # 334 # 40 # 349 # 58 6 # 188 # 40 # 232 # 19 # 275 # 22 # 311 # 31 # 335 # 17 # 350 # 24 7 # 190 # 7 # 233 # 47 # 276 # 44 # 312 # 30 # 335 # 53 # 350 # 50 8 # 191 # 34 # 235 # 15 # 278 # 5 # 313 # 21 # 336 # 29 # 351 # 15 9 # 193 # 1 # 236 # 43 # 279 # 26 # 314 # 27 # 337 # 4 # 351 # 40 10 # 194 # 28 # 238 # 11 # 280 # 47 # 315 # 24 # 337 # 39 # 352 # 5 11 # 196 # 55 # 239 # 39 # 282 # 7 # 316 # 21 # 338 # 13 # 352 # 30 12 # 197 # 22 # 241 # 6 # 283 # 26 # 317 # 16 # 338 # 47 # 352 # 55 13 # 198 # 49 # 242 # 24 # 284 # 45 # 318 # 10 # 339 # 20 # 353 # 19 14 # 200 # 16 # 244 # 1 # 286 # 3 # 319 # 3 # 339 # 53 # 353 # 42 15 # 201 # 43 # 245 # 28 # 287 # 21 # 319 # 55 # 340 # 26 # 354 # 7 16 # 203 # 10 # 246 # 56 # 288 # 38 # 320 # 47 # 340 # 58 # 354 # 31 17 # 204 # 37 # 248 # 2@ # 289 # 54 # 321 # 38 # 341 # 29 # 354 # 55 18 # 206 # 4 # 249 # 51 # 291 # 9 # 322 # 28 # 342 # 0 # 355 # 19 19 # 207 # 31 # 251 # 18 # 292 # 24 # 323 # 17 # 342 # 31 # 355 # 43 20 # 208 # 59 # 252 # 45 # 293 # 38 # 324 # 5 # 343 # 1 # 356 # 6 21 # 210 # 26 # 254 # 12 # 294 # 51 # 324 # 52 # 343 # 31 # 356 # 30 22 # 211 # 53 # 255 # 38 # 296 # 4 # 325 # 38 # 344 # 1 # 356 # 54 23 # 213 # 21 # 257 # 4 # 297 # 16 # 326 # 24 # 344 # 30 # 357 # 17 24 # 214 # 48 # 258 # 30 # 298 # 27 # 327 # 9 # 344 # 59 # 357 # 41 25 # 216 # 16 # 259 # 56 # 299 # 37 # 327 # 54 # 345 # 28 # 358 # 4 26 # 217 # 43 # 261 # 22 # 300 # 46 # 328 # 38 # 345 # 56 # 358 # 28 27 # 219 # 11 # 262 # 47 # 301 # 54 # 329 # 21 # 346 # 24 # 358 # 51 28 # 220 # 38 # 264 # 12 # 303 # 1 # 330 # 3 # 346 # 52 # 359 # 14 29 # 222 # 6 # 265 # 37 # 304 # 8 # 330 # 45 # 347 # 19 # 359 # 37 30 # 223 # 34 # 267 # 2 # 305 # 14 # 331 # 26 # 547 # 46 # 360 # 0 </note> <pb o="384" file="420" n="421" rhead="Comment. in III. Cap. Sphæræ"/> </div> <div xml:id="echoid-div802" type="section" level="1" n="311"> <head xml:id="echoid-head322" xml:space="preserve">TABVLA ASCENSIONVM <lb/>Obliquarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♈ # ## ♉ # ## ♊ # ## ♋ # ## ♌ # ## ♍ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 0 # 0 # 11 # 38 # 27 # 22 # 53 # 14 # 91 # 46 # 135 # 50 1 # 0 # 22 # 12 # 4 # 28 # 2 # 54 # 21 # 93 # 12 # 137 # 19 2 # 0 # 44 # 12 # 30 # 28 # 43 # 55 # 28 # 94 # 38 # 138 # 48 3 # 1 # 6 # 12 # 56 # 29 # 24 # 56 # 56 # 96 # 4 # 140 # 17 4 # 1 # 28 # 13 # 23 # 30 # 6 # 57 # 44 # 97 # 31 # 141 # 46 5 # 1 # 50 # 13 # 50 # 30 # 49 # 58 # 53 # 98 # 58 # 143 # 14 6 # 2 # 12 # 14 # 18 # 31 # 32 # 60 # 3 # 100 # 25 # 144 # 43 7 # 2 # 34 # 14 # 46 # 32 # 16 # 61 # 14 # 101 # 52 # 146 # 12 8 # 2 # 57 # 1@ # 14 # 33 # 1 # 62 # 26 # 103 # 19 # 147 # 41 9 # 3 # 19 # 15 # 42 # 33 # 47 # 63 # 39 # 104 # 47 # 149 # 10 10 # 3 # 42 # 16 # 11 # 34 # 33 # 64 # 53 # 106 # 15 # 150 # 38 11 # 4 # 4 # 16 # 40 # 35 # 20 # 66 # 8 # 107 # 43 # 152 # 7 12 # 4 # 27 # 17 # 9 # 36 # 8 # 67 # 23 # 109 # 11 # 153 # 35 13 # 4 # 49 # 17 # 38 # 36 # 57 # 68 # 39 # 110 # 40 # 155 # 3 14 # 5 # 12 # 18 # @8 # 37 # 48 # 69 # 56 # 112 # 8 # 156 # 31 15 # 5 # 35 # 18 # 39 # 38 # 39 # 71 # 13 # 113 # 37 # 157 # 59 16 # 5 # 58 # 19 # 11 # 39 # 31 # 72 # 31 # 115 # 5 # 159 # 28 17 # 6 # 21 # 19 # 43 # 40 # 24 # 73 # 50 # 116 # 34 # 160 # 56 18 # 6 # 44 # 20 # 15 # 41 # 18 # 75 # 10 # 118 # 3 # 162 # 24 19 # 7 # 8 # 20 # 46 # 42 # 12 # 76 # 30 # 119 # 32 # 163 # 52 20 # 7 # 32 # 21 # 21 # 43 # 7 # 77 # 51 # 121 # 1 # 165 # 20 21 # 7 # 56 # 21 # 54 # 44 # 3 # 79 # 13 # 122 # 30 # 166 # 48 22 # 8 # 20 # 22 # 28 # 45 # 0 # 80 # 35 # 123 # 59 # 168 # 16 23 # 8 # 44 # 23 # 3 # 45 # 58 # 81 # 57 # 125 # 28 # 169 # 44 24 # 9 # 8 # 23 # 38 # 46 # 58 # 83 # 20 # 126 # 57 # 171 # 12 25 # 9 # 32 # 24 # 14 # 47 # 59 # 84 # 43 # 128 # 26 # 172 # 40 26 # 9 # 57 # 24 # 50 # 49 # 0 # 86 # 6 # 129 # 55 # 174 # 8 27 # 10 # 22 # 25 # 27 # 50 # 2 # 87 # 30 # 131 # 24 # 175 # 36 28 # 10 # 47 # 26 # 5 # 51 # 5 # 88 # 55 # 132 # 53 # 177 # 4 29 # 11 # 12 # 26 # 43 # 52 # 9 # 90 # 20 # 134 # 22 # 178 # 32 30 # 11 # 48 # 27 # 22 # 53 # 14 # 91 # 46 # 135 # 50 # 180 # 0 </note> <pb o="385" file="421" n="422" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div803" type="section" level="1" n="312"> <head xml:id="echoid-head323" xml:space="preserve">AD LATITVDINEM <lb/>Graduum 54.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♎ # ## ♏ # ## ♐ # ## ♑ # ## ♒ # ## ♓ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 180 # 0 # 224 # 10 # 268 # 14 # 306 # 46 # 332 # 38 # 348 # 22 1 # 181 # 28 # 225 # 38 # 269 # 40 # 307 # 51 # 333 # 17 # 348 # 48 2 # 182 # 56 # 227 # 7 # 271 # 5 # 308 # 55 # 333 # 55 # 349 # 13 3 # 184 # 24 # 228 # 36 # 272 # 30 # 309 # 58 # 334 # 33 # 349 # 38 4 # 185 # 52 # 230 # 5 # 273 # 54 # 311 # 0 # 335 # 10 # 350 # 3 5 # 187 # 20 # 231 # 34 # 275 # 17 # 312 # 1 # 335 # 46 # 350 # 28 6 # 188 # 48 # 233 # 3 # 276 # 40 # 313 # 2 # 336 # 22 # 350 # 52 7 # 190 # 16 # 234 # 32 # 278 # 3 # 314 # 2 # 336 # 57 # 351 # 16 8 # 191 # 44 # 236 # 1 # 279 # 25 # 315 # 0 # 337 # 32 # 351 # 40 9 # 193 # 12 # 237 # 30 # 280 # 47 # 315 # 57 # 338 # 6 # 352 # 4 10 # 194 # 40 # 238 # 59 # 282 # 9 # 316 # 53 # 338 # 39 # 352 # 28 11 # 196 # 8 # 240 # 28 # 283 # 30 # 417 # 48 # 339 # 12 # 352 # 52 12 # 197 # 36 # 241 # 57 # 284 # 50 # 318 # 42 # 339 # 45 # 353 # 16 13 # 199 # 4 # 243 # 26 # 286 # 10 # 319 # 36 # 340 # 17 # 353 # 39 14 # 200 # 32 # 244 # 55 # 287 # 29 # 320 # 29 # 340 # 49 # 354 # 2 15 # 202 # 1 # 246 # 23 # 288 # 47 # 321 # 21 # 341 # 21 # 254 # 25 16 # 203 # 29 # 257 # 52 # 290 # 4 # 322 # 12 # 341 # 52 # 354 # 48 17 # 204 # 53 # 249 # 20 # 291 # 21 # 323 # 3 # 342 # 22 # 355 # 11 18 # 206 # 25 # 250 # 49 # 292 # 37 # 323 # 52 # 342 # 51 # 355 # 33 19 # 207 # 53 # 252 # 17 # 293 # 52 # 324 # 40 # 343 # 20 # 355 # 56 20 # 209 # 22 # 253 # 45 # 295 # 7 # 325 # 27 # 343 # 49 # 356 # 18 21 # 210 # 50 # 255 # 13 # 296 # 21 # 326 # 13 # 344 # 18 # 356 # 41 22 # 212 # 19 # 256 # 41 # 297 # 34 # 526 # 59 # 344 # 46 # 357 # 3 23 # 213 # 48 # 258 # 8 # 298 # 46 # 327 # 44 # 345 # 14 # 357 # 26 24 # 215 # 17 # 259 # 35 # 399 # 57 # 328 # 28 # 345 # 42 # 357 # 48 25 # 216 # 46 # 261 # 2 # 301 # 7 # 329 # 11 # 346 # 10 # 358 # 10 26 # 218 # 14 # 262 # 29 # 302 # 16 # 329 # 54 # 346 # 37 # 358 # 32 27 # 219 # 43 # 263 # 56 # 303 # 24 # 330 # 36 # 347 # 4 # 358 # 54 28 # 221 # 12 # 265 # 22 # 304 # 32 # 331 # 17 # 347 # 30 # 359 # 16 29 # 222 # 41 # 266 # 48 # 305 # 39 # 331 # 58 # 347 # 56 # 359 # 38 30 # 224 # 10 # 268 # 14 # 306 # 46 # 332 # 38 # 348 # 22 # 360 # 0 </note> <pb o="386" file="422" n="423" rhead="Comment. in III. Cap. Sphæræ"/> </div> <div xml:id="echoid-div804" type="section" level="1" n="313"> <head xml:id="echoid-head324" xml:space="preserve">TABVLA ASCENSIONVM <lb/>Obliquarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♈ # ## ♉ # ## ♊ # ## ♋ # ## ♌ # ## ♍ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 0 # 0 # 11 # 1 # 26 # 6 # 51 # 37 # 90 # 30 # 135 # 13 1 # 0 # 20 # 11 # 25 # 26 # 44 # 52 # 42 # 91 # 57 # 136 # 43 2 # 0 # 41 # 11 # 50 # 27 # 23 # 53 # 49 # 93 # 24 # 138 # 13 3 # 1 # 2 # 12 # 15 # 28 # 3 # 54 # 57 # 94 # 52 # 139 # 43 4 # 1 # 23 # 12 # 40 # 28 # 44 # 56 # 6 # 96 # 20 # 141 # 13 5 # 1 # 44 # 13 # 6 # 29 # 26 # 57 # 16 # 97 # 48 # 142 # 43 6 # 2 # 5 # 13 # 32 # 30 # 8 # 58 # 27 # 99 # 16 # 144 # 13 7 # 2 # 26 # 13 # 59 # 30 # 51 # 59 # 39 # 100 # 44 # 145 # 43 8 # 2 # 47 # 14 # 26 # 31 # 35 # 60 # 52 # 102 # 13 # 147 # 13 9 # 3 # 8 # 14 # 53 # 32 # 20 # 62 # 5 # 103 # 42 # 148 # 43 10 # 3 # 30 # 15 # 20 # 33 # 6 # 63 # 19 # 105 # 11 # 150 # 12 11 # 3 # 51 # 15 # 48 # 33 # 53 # 64 # 34 # 106 # 40 # 151 # 42 12 # 4 # 12 # 16 # 16 # 34 # 41 # 65 # 50 # 108 # 10 # 153 # 12 13 # 4 # 34 # 16 # 44 # 35 # 29 # 67 # 7 # 109 # 40 # 154 # 41 14 # 4 # 55 # 17 # 13 # 36 # 18 # 68 # 24 # 111 # 10 # 156 # 11 15 # 5 # 17 # 17 # 42 # 37 # 8 # 69 # 42 # 112 # 40 # 157 # 40 16 # 5 # 39 # 18 # 12 # 37 # 59 # 71 # 1 # 114 # 10 # 159 # 10 17 # 6 # 1 # 18 # 34 # 38 # 51 # 72 # 21 # 115 # 40 # 160 # 39 18 # 6 # 23 # 19 # 14 # 39 # 44 # 73 # 31 # 117 # 10 # 162 # 8 19 # 6 # 45 # 19 # 45 # 40 # 38 # 75 # 2 # 118 # 40 # 163 # 38 20 # 7 # 7 # 20 # 17 # 41 # 33 # 76 # 24 # 120 # 10 # 165 # 8 21 # 7 # 29 # 20 # 49 # 42 # 29 # 77 # 4@ # 121 # 40 # 166 # 38 22 # 7 # 52 # 21 # 22 # 43 # 26 # 79 # 8 # 123 # 11 # 168 # 7 23 # 8 # 15 # 21 # 55 # 44 # 24 # 80 # 31 # 124 # 42 # 69 # 36 24 # 8 # 38 # 22 # 26 # 45 # 23 # 81 # 55 # 126 # 12 # 171 # 5 25 # 9 # 1 # 23 # 4 # 46 # 22 # 83 # 20 # 127 # 42 # 172 # 36 26 # 9 # 35 # 23 # 39 # 47 # 23 # 84 # 45 # 129 # 13 # 174 # 4 27 # 9 # 49 # 24 # 15 # 48 # 25 # 86 # 11 # 130 # 43 # 175 # 33 28 # 10 # 13 # 24 # 51 # 49 # 28 # 87 # 37 # 332 # 13 # 177 # 2 29 # 10 # 37 # 25 # 28 # 50 # 32 # 89 # 3 # 133 # 43 # 178 # 31 30 # 11 # 1 # 26 # 6 # 51 # 37 # 90 # 30 # 135 # 13 # 180 # 0 </note> <pb o="387" file="423" n="424" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div805" type="section" level="1" n="314"> <head xml:id="echoid-head325" xml:space="preserve">AD LATITVDINEM <lb/>Graduum 55.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♎ # ## ♏ # ## ♐ # ## ♑ # ## ♒ # ## ♓ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 180 # 0 # 224 # 47 # 269 # 30 # 308 # 23 # 333 # 54 # 348 # 59 1 # 181 # 29 # 226 # 17 # 270 # 56 # 309 # 28 # 334 # 32 # 349 # 23 2 # 182 # 58 # 227 # 47 # 272 # 23 # 310 # 32 # 335 # @9 # 349 # 47 3 # 184 # 27 # 229 # 17 # 273 # 49 # 311 # 35 # 335 # 45 # 350 # 11 4 # 185 # 56 # 230 # 47 # 275 # 15 # 312 # 37 # 336 # 21 # 350 # 35 5 # 187 # 26 # 232 # 18 # 276 # 40 # 313 # 38 # 336 # 56 # 350 # 59 6 # 188 # 55 # 233 # 48 # 278 # 5 # 314 # 37 # 337 # 31 # 351 # 22 7 # 190 # 24 # 235 # 18 # 279 # 29 # 315 # 36 # 338 # 5 # 351 # 45 8 # 191 # 53 # 236 # 49 # 280 # 52 # 316 # 34 # 338 # 38 # 352 # 8 9 # 193 # 22 # 238 # 20 # 282 # 14 # 317 # 31 # 339 # 11 # 352 # 31 10 # 194 # 52 # 239 # 50 # 283 # 36 # 318 # 27 # 339 # 43 # 352 # 53 11 # 196 # 21 # 141 # 20 # 284 # 58 # 319 # 22 # 340 # 15 # 353 # 15 12 # 197 # 50 # 242 # 50 # 286 # 19 # 320 # 16 # 340 # 46 # 353 # 37 13 # 199 # 20 # 244 # 20 # 287 # 39 # 321 # 9 # 341 # 17 # 353 # 59 14 # 200 # 4@ # 245 # 50 # 288 # 59 # 322 # 1 # 341 # 48 # 354 # 21 15 # 202 # 19 # 247 # 20 # 290 # 18 # 322 # 52 # 342 # 18 # 354 # 43 16 # 203 # 48 # 248 # 50 # 291 # 36 # 323 # 42 # 342 # 47 # 355 # 5 17 # 205 # 18 # 250 # 20 # 292 # 53 # 324 # 31 # 343 # 16 # 355 # 26 18 # 206 # 47 # 251 # 50 # 294 # 10 # 325 # 19 # 343 # 44 # 355 # 48 19 # 208 # 17 # 253 # 20 # 295 # 26 # 326 # 7 # 344 # 12 # 356 # 9 20 # 209 # 47 # 254 # 49 # 296 # 41 # 326 # 54 # 344 # 40 # 356 # 30 21 # 211 # 17 # 256 # 18 # 297 # 55 # 327 # 40 # 345 # 7 # 356 # 52 22 # 212 # 47 # 357 # 47 # 299 # 8 # 328 # 25 # 345 # 34 # 357 # 13 23 # 214 # 17 # 259 # 16 # 300 # 31 # 329 # 9 # 346 # 1 # 357 # 34 24 # 215 # 47 # 260 # 44 # 301 # 33 # 329 # 52 # 346 # 29 # 357 # 55 25 # 217 # 17 # 262 # 12 # 302 # 44 # 330 # 34 # 346 # 54 # 358 # 16 26 # 218 # 47 # 263 # 40 # 303 # 54 # 331 # 16 # 347 # 20 # 358 # 37 27 # 220 # 17 # 265 # 8 # 305 # 3 # 331 # 57 # 347 # 45 # 358 # 58 28 # 221 # 47 # 266 # 36 # 306 # 11 # 332 # 37 # 348 # 10 # 359 # 19 29 # 223 # 17 # 268 # 3 # 307 # 8 # 333 # 16 # 348 # 35 # 359 # 40 30 # 224 # 47 # 269 # 30 # 308 # 23 # 333 # 54 # 348 # 59 # 360 # 0 </note> <pb o="388" file="424" n="425" rhead="Comment. in III. Cap. Sphæræ."/> </div> <div xml:id="echoid-div806" type="section" level="1" n="315"> <head xml:id="echoid-head326" xml:space="preserve">TABVLA ASCENSIONVM <lb/>Obliquarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♈ # ## ♉ # ## ♊ # ## ♋ # ## ♌ # ## ♍ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 0 # 0 # 10 # 21 # 24 # 44 # 49 # 52 # 89 # 8 # 134 # 33 1 # 0 # 19 # 10 # 44 # 25 # 21 # 50 # 58 # 90 # 37 # 136 # 5 2 # 0 # 39 # 11 # 7 # 25 # 59 # 52 # 5 # 92 # 6 # 137 # 39 3 # 0 # 58 # 11 # 31 # 26 # 38 # 53 # 13 # 93 # 35 # 139 # 8 4 # 1 # 18 # 11 # 55 # 27 # 18 # 54 # 22 # 95 # 4 # 140 # 39 5 # 1 # 38 # 12 # 19 # 27 # 59 # 55 # 32 # 96 # 33 # 142 # 10 6 # 1 # 57 # 12 # 44 # 28 # 40 # 56 # 43 # 98 # 3 # 143 # 42 7 # 2 # 17 # 13 # 9 # 29 # 21 # 57 # 55 # 99 # 33 # 145 # 13 8 # 2 # 37 # 13 # 34 # 30 # 5 # 59 # 8 # 101 # 3 # 146 # 45 9 # 2 # 57 # 14 # 0 # 30 # 48 # 60 # 22 # 102 # 33 # 148 # 16 10 # 3 # 17 # 14 # 26 # 31 # 37 # 61 # 37 # 104 # 3 # 149 # 47 11 # 3 # 37 # 14 # 52 # 32 # 17 # 62 # 53 # 105 # 34 # 151 # 18 12 # 3 # 57 # 15 # 19 # 33 # 3 # 64 # 9 # 107 # 5 # 152 # 49 13 # 4 # 17 # 15 # 46 # 33 # 50 # 65 # 26 # 108 # 36 # 154 # 20 14 # 4 # 37 # 16 # 13 # 34 # 39 # 66 # 44 # 110 # 7 # 155 # 51 15 # 4 # 57 # 16 # 41 # 35 # 29 # 68 # 3 # 111 # 39 # 157 # 21 16 # 5 # 17 # 17 # 10 # 36 # 20 # 69 # 23 # 113 # 10 # 158 # 52 17 # 5 # 38 # 17 # 39 # 37 # 12 # 70 # 44 # 114 # 41 # 160 # 23 18 # 5 # 59 # 18 # 9 # 38 # 4 # 72 # 5 # 116 # 12 # 161 # 54 19 # 6 # 20 # 18 # 39 # 38 # 57 # 73 # 27 # 117 # 44 # 163 # 25 20 # 6 # 41 # 19 # 9 # 39 # 51 # 74 # 50 # 119 # 16 # 164 # 55 21 # 7 # 2 # 19 # 40 # 40 # 46 # 76 # 13 # 120 # 48 # 166 # 26 22 # 7 # 23 # 20 # 12 # 41 # 42 # 77 # 37 # 122 # 20 # 167 # 57 23 # 7 # 45 # 20 # 44 # 42 # 39 # 79 # 2 # 123 # 52 # 169 # 27 24 # 8 # 6 # 21 # 16 # 43 # 38 # 80 # 27 # 125 # 24 # 170 # 58 25 # 8 # 26 # 21 # 49 # 44 # 38 # 81 # 53 # 126 # 55 # 172 # 28 26 # 8 # 50 # 22 # 22 # 45 # 39 # 83 # 19 # 128 # 37 # 173 # 59 27 # 9 # 13 # 22 # 56 # 46 # 41 # 84 # 46 # 129 # 59 # 175 # 29 28 # 9 # 35 # 23 # 31 # 47 # 44 # 86 # 13 # 131 # 30 # 177 # 0 29 # 9 # 58 # 24 # 7 # 48 # 48 # 87 # 40 # 133 # 2 # 178 # 30 30 # 10 # 51 # 24 # 44 # 49 # 52 # 89 # 8 # 134 # 33 # 180 # 0 </note> <pb o="389" file="425" n="426" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div807" type="section" level="1" n="316"> <head xml:id="echoid-head327" xml:space="preserve">AD LATITVDINEM <lb/>Graduum 56.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♎ # ## ♏ # ## ♐ # ## ♑ # ## ♒ # ## ♓ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 180 # 0 # 225 # 27 # 270 # 52 # 310 # 8 # 335 # 16 # 349 # 39 1 # 181 # 30 # 226 # 38 # 272 # 20 # 311 # 12 # 335 # 53 # 350 # 2 2 # 183 # 0 # 228 # 30 # 273 # 47 # 312 # 16 # 336 # 29 # 350 # 25 3 # 184 # 31 # 230 # 1 # 275 # 14 # 313 # 19 # 337 # 4 # 350 # 47 4 # 186 # 1 # 231 # 33 # 276 # 41 # 314 # 21 # 337 # 38 # 351 # 10 5 # 187 # 32 # 233 # 5 # 278 # 7 # 315 # 22 # 338 # 11 # 351 # 32 6 # 189 # 2 # 234 # 36 # 279 # 33 # 316 # 22 # 338 # 44 # 351 # 54 7 # 190 # 33 # 236 # 8 # 280 # 58 # 317 # 21 # 339 # 16 # 352 # 15 8 # 192 # 3 # 237 # 40 # 282 # 23 # 318 # 18 # 339 # 48 # 352 # 37 9 # 193 # 34 # 239 # 12 # 283 # 47 # 319 # 14 # 340 # 20 # 352 # 58 10 # 195 # 5 # 240 # 44 # 285 # 10 # 320 # 9 # 340 # 51 # 353 # 19 11 # 196 # 35 # 242 # 16 # 286 # 33 # 321 # 3 # 341 # 21 # 353 # 40 12 # 198 # 6 # 243 # 48 # 287 # 55 # 321 # 56 # 441 # 51 # 354 # 1 13 # 199 # 37 # 245 # 19 # 289 # 16 # 322 # 48 # 342 # 21 # 354 # 22 14 # 201 # 8 # 246 # 50 # 290 # 37 # 323 # 40 # 342 # 50 # 354 # 43 15 # 202 # 39 # 248 # 21 # 291 # 57 # 324 # 31 # 343 # 19 # 355 # 3 16 # 204 # 9 # 249 # 53 # 293 # 16 # 325 # 21 # 343 # 47 # 355 # 33 17 # 205 # 40 # 251 # 24 # 294 # 34 # 326 # 10 # 344 # 14 # 355 # 43 18 # 207 # 11 # 252 # 55 # 295 # 51 # 326 # 57 # 344 # 41 # 356 # 3 19 # 208 # 42 # 254 # 26 # 297 # 7 # 327 # 43 # 345 # 8 # 356 # 23 20 # 210 # 13 # 255 # 57 # 298 # 23 # 328 # 28 # 345 # 34 # 356 # 43 21 # 211 # 44 # 257 # 27 # 299 # 38 # 329 # 12 # 346 # 0 # 357 # 3 22 # 213 # 15 # 258 # 57 # 300 # 52 # 329 # 55 # 346 # 26 # 357 # 23 23 # 214 # 47 # 260 # 27 # 302 # 5 # 330 # 38 # 346 # 51 # 357 # 43 24 # 216 # 18 # 261 # 57 # 303 # 17 # 331 # 20 # 347 # 16 # 358 # 3 25 # 217 # 50 # 263 # 27 # 304 # 28 # 332 # 1 # 347 # 41 # 358 # 22 26 # 219 # 21 # 264 # 56 # 305 # 38 # 332 # 42 # 348 # 5 # 358 # 42 27 # 220 # 52 # 266 # 25 # 306 # 47 # 333 # 22 # 348 # 29 # 359 # 2 28 # 222 # 24 # 267 # 54 # 307 # 55 # 334 # 1 # 348 # 53 # 359 # 21 29 # 223 # 55 # 269 # 23 # 309 # 2 # 334 # 39 # 349 # 16 # 359 # 42 30 # 225 # 27 # 270 # 52 # 310 # 8 # 335 # 16 # 349 # 39 # 360 # 0 </note> <pb o="390" file="426" n="427" rhead="Comment. in III. Cap Sphæræ"/> </div> <div xml:id="echoid-div808" type="section" level="1" n="317"> <head xml:id="echoid-head328" xml:space="preserve">TABVLA ASCENSIONVM <lb/>Obliquarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♈ # ## ♉ # ## ♊ # ## ♋ # ## ♌ # ## ♍ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 0 # 0 # 9 # 39 # 23 # 17 # 47 # 58 # 87 # 41 # 133 # 51 1 # 0 # 18 # 10 # 0 # 23 # 53 # 49 # 5 # 89 # 11 # 135 # 24 2 # 0 # 36 # 10 # 22 # 24 # 30 # 50 # 12 # 90 # 41 # 136 # 57 3 # 0 # 54 # 10 # 44 # 25 # 7 # 51 # 20 # 92 # 11 # 138 # 30 4 # 1 # 12 # 11 # 6 # 25 # 45 # 52 # 29 # 93 # 42 # 140 # 3 5 # 1 # 31 # 11 # 29 # 26 # 24 # 53 # 39 # 95 # 13 # 141 # 35 6 # 1 # 49 # 11 # 52 # 27 # 4 # 54 # 50 # 96 # 44 # 143 # 8 7 # 2 # 7 # 12 # 16 # 27 # 45 # 56 # 2 # 98 # 15 # 144 # 41 8 # 2 # 26 # 12 # 40 # 28 # 27 # 57 # 15 # 99 # 47 # 146 # 14 9 # 2 # 44 # 13 # 4 # 29 # 9 # 58 # 30 # 101 # 19 # 147 # 47 10 # 3 # 3 # 13 # 29 # 29 # 52 # 59 # 46 # 102 # 51 # 149 # 19 11 # 3 # 21 # 13 # 54 # 30 # 36 # 61 # 3 # 103 # 23 # 150 # 52 12 # 3 # 40 # 14 # 19 # 31 # 21 # 62 # 20 # 105 # 56 # 152 # 24 13 # 3 # 59 # 14 # 45 # 32 # 7 # 63 # 38 # 107 # 29 # 153 # 57 14 # 4 # 18 # 15 # 11 # 32 # 54 # 64 # 57 # 109 # 2 # 155 # 29 15 # 4 # 37 # 15 # 37 # 33 # 43 # 66 # 18 # 110 # 35 # 157 # 1 16 # 4 # 56 # 16 # 4 # 34 # 33 # 67 # 38 # 112 # 7 # 158 # 33 17 # 5 # 15 # 16 # 32 # 35 # 24 # 69 # 0 # 113 # 40 # 160 # 5 18 # 5 # 34 # 17 # 0 # 36 # 17 # 70 # 23 # 115 # 13 # 161 # 47 19 # 5 # 53 # 17 # 28 # 37 # 7 # 71 # 46 # 116 # 46 # 163 # 9 20 # 6 # 13 # 17 # 57 # 38 # 0 # 73 # 10 # 118 # 19 # 164 # 41 21 # 6 # 33 # 18 # 26 # 38 # 55 # 74 # 34 # 119 # 42 # 166 # 13 22 # 6 # 53 # 18 # 56 # 39 # 51 # 75 # 59 # 121 # 25 # 167 # 45 23 # 7 # 15 # 19 # 26 # 40 # 48 # 77 # 25 # 122 # 38 # 169 # 17 24 # 7 # 33 # 19 # 57 # 41 # 46 # 78 # 51 # 124 # 31 # 170 # 49 25 # 7 # 53 # 20 # 29 # 42 # 45 # 80 # 18 # 126 # 5 # 172 # 11 26 # 8 # 14 # 21 # 1 # 43 # 46 # 81 # 46 # 127 # 39 # 173 # 53 27 # 8 # 35 # 21 # 34 # 44 # 48 # 83 # 14 # 129 # 12 # 175 # 25 28 # 8 # 56 # 22 # 8 # 45 # 51 # 84 # 43 # 130 # 45 # 176 # 37 29 # 9 # 17 # 22 # 42 # 46 # 54 # 86 # 12 # 132 # 18 # 178 # 29 30 # 9 # 39 # 23 # 17 # 47 # 58 # 87 # 41 # 133 # 51 # 180 # 0 </note> <pb o="391" file="427" n="428" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div809" type="section" level="1" n="318"> <head xml:id="echoid-head329" xml:space="preserve">AD LATITVDINEM <lb/>Graduum 57.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♎ # ## ♏ # ## ♐ # ## ♑ # ## ♒ # ## ♓ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 180 # 0 # 226 # 9 # 272 # 19 # 312 # 2 # 336 # 43 # 350 # 21 1 # 181 # 31 # 227 # 42 # 273 # 48 # 313 # 6 # 337 # 18 # 350 # 43 2 # 183 # 3 # 229 # 15 # 275 # 17 # 314 # 9 # 337 # 52 # 351 # 4 3 # 184 # 35 # 230 # 48 # 276 # 46 # 315 # 12 # 338 # 26 # 351 # 25 4 # 186 # 7 # 232 # 21 # 278 # 14 # 316 # 14 # 338 # 59 # 351 # 46 5 # 187 # 39 # 233 # 55 # 279 # 42 # 317 # 15 # 339 # 31 # 352 # 7 6 # 189 # 11 # 235 # 29 # 281 # 9 # 318 # 14 # 340 # 3 # 352 # 27 7 # 190 # 43 # 237 # 2 # 282 # 35 # 319 # 12 # 340 # 34 # 352 # 47 8 # 192 # 15 # 238 # 35 # 284 # 1 # 320 # 9 # 341 # 4 # 353 # 7 9 # 193 # 47 # 240 # 7 # 285 # 26 # 321 # 5 # 341 # 34 # 353 # 27 10 # 195 # 19 # 241 # 41 # 286 # 50 # 322 # 0 # 342 # 3 # 353 # 47 11 # 196 # 51 # 243 # 14 # 288 # 14 # 322 # 53 # 342 # 32 # 354 # 7 12 # 198 # 23 # 244 # 47 # 289 # 37 # 323 # 45 # 343 # 0 # 354 # 16 13 # 299 # 55 # 246 # 20 # 191 # 0 # 324 # 36 # 343 # 28 # 354 # 45 14 # 201 # 27 # 247 # 53 # 292 # 22 # 325 # 27 # 343 # 56 # 355 # 4 15 # 202 # 59 # 249 # 25 # 293 # 43 # 326 # 17 # 344 # 23 # 355 # 23 16 # 204 # 31 # 250 # 58 # 295 # 3 # 327 # 6 # 344 # 49 # 355 # 42 17 # 206 # 3 # 252 # 31 # 296 # 22 # 327 # 53 # 345 # 15 # 356 # 1 18 # 207 # 36 # 354 # 4 # 297 # 40 # 328 # 39 # 345 # 41 # 356 # 20 19 # 209 # 8 # 255 # 37 # 298 # 57 # 329 # 24 # 346 # 6 # 356 # 39 20 # 210 # 41 # 257 # 9 # 300 # 14 # 330 # 8 # 346 # 31 # 356 # 57 21 # 212 # 13 # 258 # 41 # 301 # 30 # 330 # 51 # 346 # 56 # 357 # 16 22 # 213 # 46 # 260 # 13 # 302 # 45 # 331 # 33 # 347 # 20 # 357 # 34 23 # 215 # 19 # 261 # 45 # 303 # 58 # 332 # 15 # 347 # 44 # 357 # 53 24 # 216 # 52 # 263 # 16 # 305 # 10 # 332 # 56 # 348 # 8 # 358 # 11 25 # 218 # 25 # 264 # 47 # 306 # 21 # 333 # 36 # 348 # 31 # 358 # 29 26 # 219 # 57 # 266 # 18 # 307 # 31 # 334 # 15 # 348 # 54 # 358 # 48 27 # 221 # 30 # 267 # 49 # 308 # 40 # 334 # 53 # 349 # 16 # 359 # 6 28 # 223 # 3 # 269 # 19 # 309 # 48 # 335 # 30 # 349 # 38 # 359 # 24 29 # 224 # 36 # 270 # 49 # 310 # 55 # 336 # 7 # 350 # 0 # 359 # 42 30 # 226 # 9 # 272 # 19 # 312 # 2 # 336 # 43 # 350 # 21 # 360 # 0 </note> <pb o="392" file="428" n="429" rhead="Comment. in III. Cap. Sphæræ."/> </div> <div xml:id="echoid-div810" type="section" level="1" n="319"> <head xml:id="echoid-head330" xml:space="preserve">TABVLA ASCENSIONVM <lb/>Obliquarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♈ # ## ♉ # ## ♊ # ## ♋ # ## ♌ # ## ♍ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 0 # 0 # 8 # 54 # 21 # 43 # 45 # 54 # 86 # 7 # 133 # 6 1 # 0 # 16 # 9 # 14 # 22 # 17 # 47 # 0 # 87 # 38 # 134 # 41 2 # 0 # 33 # 9 # 34 # 22 # 52 # 48 # 7 # 89 # 10 # 136 # 15 3 # 0 # 50 # 9 # 55 # 23 # 28 # 49 # 15 # 90 # 42 # 137 # 50 4 # 1 # 7 # 10 # 16 # 24 # 5 # 50 # 25 # 92 # 14 # 139 # 24 5 # 1 # 24 # 10 # 37 # 24 # 43 # 51 # 36 # 93 # 47 # 140 # 58 6 # 1 # 48 # 10 # 59 # 25 # 21 # 52 # 48 # 95 # 20 # 142 # 33 7 # 1 # 57 # 11 # 21 # 26 # 0 # 54 # 1 # 96 # 53 # 144 # 7 8 # 2 # 14 # 11 # 43 # 26 # 40 # 55 # 16 # 98 # 26 # 145 # 41 9 # 2 # 31 # 12 # 5 # 27 # 21 # 56 # 31 # 99 # 59 # 147 # 15 10 # 2 # 48 # 12 # 28 # 28 # 3 # 57 # 47 # 101 # 33 # 148 # 49 11 # 3 # 5 # 12 # 51 # 28 # 46 # 59 # 4 # 103 # 7 # 150 # 23 12 # 3 # 22 # 13 # 15 # 29 # 20 # 60 # 22 # 104 # 42 # 151 # 57 13 # 3 # 40 # 13 # 39 # 30 # 15 # 61 # 41 # 106 # 16 # 153 # 31 14 # 3 # 57 # 14 # 3 # 31 # 1 # 63 # 1 # 107 # 51 # 155 # 5 15 # 4 # 15 # 14 # 28 # 31 # 48 # 64 # 22 # 109 # 26 # 156 # 39 16 # 4 # 32 # 14 # 53 # 32 # 36 # 65 # 44 # 111 # 0 # 158 # 13 17 # 4 # 50 # 15 # 19 # 33 # 25 # 67 # 7 # 112 # 34 # 159 # 46 18 # 5 # 7 # 15 # 45 # 34 # 16 # 68 # 31 # 114 # 9 # 161 # 20 19 # 5 # 25 # 16 # 12 # 35 # 8 # 69 # 56 # 115 # 43 # 162 # 53 20 # 5 # 43 # 16 # 39 # 36 # 1 # 71 # 21 # 117 # 18 # 164 # 26 21 # 6 # 1 # 17 # 7 # 36 # 55 # 72 # 47 # 118 # 53 # 166 # 0 22 # 6 # 20 # 17 # 35 # 37 # 50 # 74 # 14 # 120 # 28 # 167 # 34 23 # 6 # 38 # 18 # 4 # 38 # 46 # 75 # 41 # 122 # 3 # 169 # 7 24 # 6 # 57 # 18 # 33 # 39 # 43 # 77 # 9 # 123 # 38 # 170 # 41 25 # 7 # 16 # 19 # 3 # 40 # 42 # 78 # 37 # 125 # 31 # 172 # 14 26 # 7 # 35 # 19 # 33 # 41 # 42 # 80 # 6 # 126 # 48 # 173 # 48 27 # 7 # 54 # 20 # 4 # 42 # 43 # 81 # 36 # 128 # 23 # 175 # 21 28 # 8 # 14 # 20 # 36 # 43 # 45 # 83 # 6 # 129 # 57 # 176 # 54 29 # 8 # 34 # 21 # 9 # 44 # 49 # 84 # 36 # 131 # 32 # 178 # 27 30 # 8 # 54 # 21 # 43 # 45 # 54 # 86 # 7 # 133 # 6 # 180 # 0 </note> <pb o="393" file="429" n="430" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div811" type="section" level="1" n="320"> <head xml:id="echoid-head331" xml:space="preserve">AD LATITVDINEM <lb/>Graduum 58.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♎ # ## ♏ # ## ♐ # ## ♑ # ## ♒ # ## ♓ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 180 # 0 # 226 # 54 # 273 # 53 # 314 # 6 # 338 # 17 # 351 # 6 1 # 181 # 33 # 228 # 28 # 275 # 24 # 315 # 11 # 338 # 51 # 351 # 26 2 # 183 # 6 # 230 # 3 # 276 # 54 # 316 # 15 # 339 # 24 # 351 # 46 3 # 184 # 39 # 231 # 37 # 278 # 24 # 317 # 17 # 339 # 56 # 352 # 6 4 # 186 # 12 # 233 # 12 # 279 # 54 # 318 # 18 # 340 # 27 # 352 # 25 5 # 187 # 46 # 234 # 47 # 281 # 23 # 319 # 18 # 340 # 57 # 352 # 44 6 # 189 # 19 # 236 # 22 # 282 # 51 # 320 # 17 # 341 # 27 # 353 # 3 7 # 190 # 53 # 237 # 57 # 284 # 16 # 321 # 14 # 341 # 56 # 353 # 22 8 # 192 # 26 # 239 # 32 # 285 # 46 # 322 # 10 # 342 # 25 # 353 # 40 9 # 194 # 0 # 241 # 7 # 287 # 13 # 323 # 5 # 342 # 53 # 353 # 59 10 # 195 # 34 # 242 # 42 # 288 # 39 # 323 # 59 # 343 # 21 # 354 # 17 11 # 197 # 7 # 244 # 17 # 290 # 4 # 324 # 52 # 343 # 48 # 354 # 35 12 # 198 # 40 # 245 # 51 # 291 # 29 # 325 # 45 # 344 # 15 # 354 # 53 13 # 200 # 14 # 247 # 26 # 292 # 53 # 326 # 35 # 344 # 41 # 355 # 10 14 # 201 # 47 # 249 # 0 # 294 # 16 # 327 # 24 # 345 # 7 # 355 # 28 15 # 203 # 21 # 250 # 34 # 295 # 38 # 328 # 12 # 345 # 32 # 355 # 45 16 # 204 # 55 # 252 # 9 # 296 # 59 # 328 # 59 # 345 # 57 # 356 # 3 17 # 206 # 29 # 353 # 44 # 298 # 19 # 329 # 45 # 346 # 21 # 356 # 20 18 # 208 # 3 # 255 # 18 # 299 # 38 # 330 # 30 # 346 # 45 # 356 # 38 19 # 209 # 37 # 256 # 53 # 300 # 56 # 331 # 14 # 347 # 9 # 356 # 55 20 # 211 # 11 # 258 # 27 # 302 # 13 # 331 # 57 # 347 # 32 # 357 # 12 21 # 212 # 45 # 260 # 1 # 303 # 29 # 332 # 39 # 347 # 55 # 357 # 29 22 # 214 # 19 # 261 # 34 # 304 # 44 # 333 # 20 # 348 # 17 # 357 # 46 23 # 215 # 53 # 263 # 7 # 305 # 59 # 334 # 0 # 348 # 39 # 358 # 13 24 # 217 # 27 # 264 # 40 # 307 # 12 # 334 # 39 # 349 # 1 # 358 # 20 25 # 219 # 2 # 266 # 13 # 308 # 24 # 335 # 17 # 349 # 23 # 358 # 36 26 # 220 # 36 # 267 # 46 # 309 # 35 # 335 # 55 # 349 # 44 # 358 # 53 27 # 222 # 10 # 269 # 18 # 310 # 45 # 336 # 32 # 350 # 5 # 359 # 10 28 # 223 # 45 # 270 # 50 # 311 # 53 # 337 # 8 # 350 # 26 # 359 # 27 29 # 225 # 19 # 272 # 22 # 313 # 0 # 337 # 43 # 350 # 46 # 359 # 44 30 # 226 # 54 # 273 # 53 # 314 # 6 # 338 # 17 # 351 # 6 # 360 # 0 </note> <pb o="394" file="430" n="431" rhead="Comment. in III. Cap. Sphæræ."/> </div> <div xml:id="echoid-div812" type="section" level="1" n="321"> <head xml:id="echoid-head332" xml:space="preserve">TABVLA ASCENSIONVM <lb/>Obliquarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♈ # ## ♉ # ## ♊ # ## ♋ # ## ♌ # ## ♍ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 0 # 0 # 8 # 6 # 20 # 2 # 43 # 39 # 84 # 26 # 132 # 18 1 # 0 # 15 # 8 # 25 # 20 # 34 # 44 # 45 # 85 # 59 # 133 # 55 2 # 0 # 30 # 8 # 44 # 21 # 7 # 45 # 52 # 87 # 33 # 135 # 31 3 # 0 # 45 # 9 # 3 # 21 # 14 # 47 # 1 # 88 # 7 # 137 # 7 4 # 1 # 0 # 9 # 22 # 22 # 16 # 48 # 11 # 90 # 41 # 138 # 43 5 # 1 # 6 # 9 # 41 # 22 # 53 # 49 # 22 # 92 # 15 # 140 # 19 6 # 1 # 31 # 10 # 1 # 23 # 30 # 50 # 34 # 93 # 50 # 141 # 55 7 # 1 # 46 # 10 # 21 # 24 # 8 # 51 # 48 # 95 # 25 # 143 # 31 8 # 2 # 2 # 10 # 42 # 24 # 46 # 53 # 3 # 97 # 0 # 145 # 7 9 # 2 # 17 # 11 # 3 # 25 # 25 # 54 # 19 # 98 # 35 # 146 # 43 10 # 2 # 33 # 11 # 24 # 26 # 5 # 55 # 36 # 100 # 11 # 148 # 18 11 # 2 # 48 # 11 # 45 # 26 # 46 # 56 # 54 # 101 # 49 # 149 # 54 12 # 3 # 4 # 12 # 7 # 27 # 28 # 58 # 13 # 103 # 23 # 151 # 29 13 # 3 # 19 # 12 # 29 # 28 # 12 # 59 # 33 # 104 # 59 # 153 # 5 14 # 3 # 55 # 12 # 51 # 28 # 57 # 60 # 54 # 106 # 35 # 154 # 40 15 # 3 # 51 # 13 # 14 # 29 # 43 # 62 # 17 # 108 # 12 # 156 # 15 16 # 4 # 7 # 13 # 38 # 30 # 30 # 63 # 41 # 109 # 48 # 157 # 51 17 # 4 # 23 # 14 # 2 # 31 # 18 # 65 # 5 # 111 # 24 # 159 # 26 18 # 4 # 39 # 14 # 27 # 32 # 7 # 66 # 30 # 113 # 1 # 161 # 1 19 # 4 # 55 # 15 # 52 # 32 # 58 # 67 # 56 # 114 # 37 # 162 # 36 20 # 5 # 12 # 15 # 17 # 33 # 50 # 69 # 23 # 116 # 14 # 164 # 11 21 # 5 # 29 # 15 # 43 # 34 # 43 # 79 # 51 # 117 # 50 # 165 # 46 22 # 5 # 46 # 16 # 9 # 35 # 37 # 72 # 18 # 119 # 27 # 167 # 21 23 # 6 # 3 # 16 # 36 # 36 # 33 # 73 # 48 # 121 # 4 # 168 # 56 24 # 6 # 20 # 17 # 3 # 37 # 30 # 75 # 17 # 122 # 41 # 170 # 31 25 # 6 # 37 # 17 # 31 # 38 # 28 # 76 # 47 # 124 # 17 # 172 # 6 26 # 6 # 54 # 18 # 0 # 39 # 28 # 78 # 18 # 125 # 54 # 173 # 41 27 # 7 # 12 # 18 # 30 # 40 # 29 # 79 # 49 # 127 # 30 # 175 # 16 28 # 7 # 38 # 19 # 0 # 41 # 31 # 81 # 23 # 129 # 6 # 176 # 51 29 # 7 # 48 # 19 # 31 # 42 # 34 # 82 # 53 # 130 # 42 # 178 # 26 30 # 8 # 6 # 20 # 2 # 43 # 39 # 84 # 26 # 132 # 18 # 180 # 0 </note> <pb o="395" file="431" n="432" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div813" type="section" level="1" n="322"> <head xml:id="echoid-head333" xml:space="preserve">AD LATITVDINEM <lb/>Graduum 59.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♎ # ## ♏ # ## ♐ # ## ♑ # ## ♒ # ## ♓ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M 0 # 180 # 0 # 227 # 42 # 275 # 34 # 316 # 21 # 339 # 58 # 351 # 54 1 # 181 # 34 # 229 # 18 # 277 # 7 # 317 # 26 # 340 # 29 # 352 # 12 2 # 183 # 9 # 230 # 54 # 278 # 39 # 318 # 29 # 341 # 0 # 352 # 30 3 # 184 # 44 # 232 # 30 # 280 # 11 # 319 # 31 # 341 # 30 # 352 # 48 4 # 186 # 19 # 234 # 6 # 281 # 42 # 320 # 32 # 342 # 0 # 353 # 6 5 # 187 # 54 # 235 # 43 # 283 # 13 # 321 # 32 # 342 # 29 # 353 # 23 6 # 189 # 29 # 237 # 19 # 284 # 43 # 322 # 30 # 342 # 57 # 353 # 40 7 # 191 # 4 # 238 # 56 # 286 # 12 # 323 # 27 # 343 # 24 # 353 # 57 8 # 192 # 39 # 240 # 33 # 287 # 41 # 324 # 23 # 343 # 51 # 354 # 14 9 # 194 # 14 # 242 # 10 # 289 # 9 # 325 # 17 # 344 # 17 # 354 # 31 10 # 195 # 49 # 243 # 46 # 290 # 37 # 326 # 10 # 344 # 43 # 354 # 48 11 # 197 # 24 # 245 # 23 # 292 # 4 # 327 # 2 # 345 # 8 # 355 # 5 12 # 198 # 59 # 246 # 59 # 293 # 30 # 327 # 53 # 345 # 33 # 355 # 21 13 # 200 # 34 # 248 # 36 # 294 # 55 # 328 # 42 # 345 # 58 # 355 # 37 14 # 202 # 9 # 250 # 12 # 296 # 19 # 329 # 30 # 346 # 22 # 355 # 53 15 # 203 # 45 # 251 # 48 # 297 # 43 # 330 # 17 # 346 # 49 # 356 # 9 16 # 205 # 20 # 253 # 25 # 299 # 6 # 331 # 3 # 347 # 9 # 356 # 25 17 # 206 # 55 # 255 # 1 # 300 # 27 # 331 # 48 # 347 # 31 # 356 # 41 18 # 208 # 31 # 256 # 37 # 301 # 47 # 332 # 32 # 347 # 53 # 356 # 56 19 # 210 # 6 # 358 # 13 # 303 # 6 # 333 # 14 # 348 # 15 # 357 # 12 20 # 211 # 42 # 259 # 49 # 304 # 24 # 333 # 55 # 348 # 36 # 357 # 27 21 # 213 # 17 # 261 # 25 # 305 # 41 # 334 # 32 # 348 # 57 # 357 # 43 22 # 214 # 53 # 263 # 0 # 306 # 57 # 335 # 14 # 349 # 18 # 357 # 58 23 # 215 # 29 # 264 # 35 # 308 # 12 # 335 # 52 # 349 # 39 # 358 # 14 24 # 218 # 5 # 266 # 10 # 309 # 26 # 336 # 30 # 349 # 59 # 358 # 29 25 # 219 # 41 # 267 # 45 # 310 # 38 # 337 # 7 # 350 # 19 # 358 # 44 26 # 221 # 17 # 269 # 19 # 311 # 49 # 337 # 44 # 350 # 38 # 359 # 0 27 # 222 # 53 # 270 # 53 # 312 # 59 # 338 # 19 # 350 # 57 # 359 # 15 28 # 224 # 29 # 272 # 27 # 314 # 8 # 338 # 53 # 351 # 16 # 359 # 30 29 # 226 # 5 # 274 # 1 # 315 # 15 # 339 # 26 # 351 # 35 # 359 # 45 30 # 227 # 42 # 275 # 34 # 316 # 21 # 339 # 58 # 351 # 54 # 360 # 0 </note> <pb o="396" file="432" n="433" rhead="Comment. in III. Cap. Sphæræ."/> </div> <div xml:id="echoid-div814" type="section" level="1" n="323"> <head xml:id="echoid-head334" xml:space="preserve">TABVLA ASCENSIONVM <lb/>Obliquarum.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♈ # ## ♉ # ## ♊ # ## ♋ # ## ♌ # ## ♍ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 0 # 0 # 7 # 16 # 18 # 12 # 41 # 8 # 82 # 36 # 131 # 28 1 # 0 # 13 # 7 # 33 # 18 # 42 # 42 # 14 # 84 # 11 # 133 # 6 2 # 0 # 27 # 7 # 50 # 19 # 13 # 43 # 22 # 85 # 47 # 134 # 44 3 # 0 # 40 # 8 # 7 # 19 # 45 # 44 # 31 # 87 # 23 # 136 # 22 4 # 0 # 54 # 8 # 24 # 20 # 18 # 45 # 41 # 88 # 59 # 138 # 0 5 # 1 # 8 # 8 # 41 # 20 # 53 # 46 # 53 # 90 # 36 # 139 # 37 6 # 1 # 21 # 8 # 59 # 21 # 28 # 48 # 6 # 92 # 13 # 141 # 15 7 # 1 # 35 # 9 # 17 # 22 # 4 # 49 # 20 # 93 # 50 # 142 # 53 8 # 1 # 49 # 9 # 36 # 22 # 40 # 50 # 36 # 95 # 27 # 144 # 30 9 # 2 # 3 # 9 # 55 # 23 # 17 # 51 # 53 # 97 # 4 # 146 # 8 10 # 2 # 17 # 10 # 15 # 23 # 55 # 53 # 11 # 98 # 42 # 147 # 45 11 # 2 # 31 # 10 # 35 # 24 # 35 # 54 # 30 # 100 # 20 # 149 # 23 12 # 2 # 45 # 10 # 55 # 25 # 16 # 55 # 50 # 101 # 58 # 151 # 0 13 # 2 # 59 # 11 # 15 # 25 # 58 # 57 # 12 # 103 # 36 # 152 # 37 14 # 3 # 13 # 11 # 35 # 26 # 41 # 58 # 35 # 105 # 14 # 154 # 14 15 # 3 # 27 # 11 # 55 # 27 # 25 # 59 # 59 # 106 # 53 # 155 # 51 16 # 3 # 41 # 12 # 16 # 28 # 10 # 61 # 24 # 108 # 31 # 157 # 28 17 # 3 # 55 # 12 # 38 # 28 # 57 # 62 # 50 # 110 # 9 # 159 # 5 18 # 4 # 10 # 13 # 1 # 29 # 45 # 64 # 17 # 111 # 47 # 160 # 42 19 # 4 # 24 # 13 # 24 # 30 # 34 # 65 # 45 # 113 # 26 # 162 # 19 20 # 4 # 39 # 13 # 48 # 31 # 25 # 67 # 13 # 115 # 5 # 163 # 55 21 # 4 # 54 # 14 # 12 # 32 # 17 # 68 # 42 # 116 # 44 # 165 # 32 22 # 5 # 9 # 14 # 36 # 33 # 10 # 70 # 12 # 118 # 23 # 167 # 9 23 # 5 # 24 # 15 # 1 # 34 # 5 # 71 # 43 # 120 # 1 # 168 # 45 24 # 5 # 39 # 15 # 26 # 35 # 1 # 73 # 15 # 121 # 39 # 170 # 22 25 # 5 # 55 # 15 # 52 # 35 # 59 # 74 # 47 # 123 # 17 # 171 # 58 26 # 6 # 11 # 16 # 19 # 36 # 58 # 76 # 20 # 124 # 56 # 173 # 35 27 # 6 # 27 # 16 # 47 # 37 # 58 # 77 # 53 # 126 # 34 # 175 # 11 28 # 6 # 43 # 17 # 15 # 39 # 0 # 79 # 27 # 128 # 12 # 176 # 48 29 # 6 # 59 # 17 # 43 # 40 # 3 # 81 # 1 # 129 # 50 # 178 # 24 30 # 7 # 16 # 18 # 12 # 41 # 8 # 82 # 36 # 131 # 28 # 180 # 0 </note> <pb o="397" file="433" n="434" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div815" type="section" level="1" n="324"> <head xml:id="echoid-head335" xml:space="preserve">AD LATITVDINEM <lb/>Graduum 60.</head> <note position="right" xml:space="preserve"> <lb/> # ## ♎ # ## ♏ # ## ♐ # ## ♑ # ## ♒ # ## ♓ G. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. 0 # 180 # 0 # 228 # 32 # 277 # 24 # 318 # 52 # 341 # 48 # 352 # 44 1 # 181 # 36 # 230 # 10 # 278 # 59 # 319 # 57 # 342 # 17 # 353 # 1 2 # 183 # 12 # 231 # 48 # 280 # 33 # 321 # 0 # 342 # 45 # 353 # 17 3 # 184 # 49 # 233 # 26 # 282 # 7 # 322 # 2 # 343 # 13 # 353 # 33 4 # 186 # 25 # 235 # 4 # 283 # 40 # 323 # 2 # 343 # 41 # 353 # 49 5 # 188 # 2 # 236 # 43 # 285 # 13 # 324 # 1 # 344 # 8 # 354 # 5 6 # 189 # 38 # 238 # 21 # 286 # 45 # 324 # 59 # 344 # 34 # 354 # 21 7 # 191 # 15 # 239 # 59 # 288 # 17 # 325 # 55 # 344 # 59 # 354 # 36 8 # 192 # 51 # 241 # 37 # 289 # 48 # 326 # 50 # 345 # 24 # 354 # 51 9 # 194 # 28 # 243 # 16 # 291 # 18 # 327 # 43 # 345 # 48 # 355 # 6 10 # 196 # 5 # 244 # 55 # 292 # 47 # 328 # 35 # 346 # 12 # 355 # 21 11 # 197 # 41 # 246 # 34 # 294 # 15 # 329 # 26 # 346 # 36 # 355 # 36 12 # 199 # 18 # 248 # 13 # 295 # 43 # 330 # 15 # 346 # 59 # 355 # 50 13 # 200 # 55 # 249 # 51 # 297 # 10 # 331 # 3 # 347 # 22 # 356 # 5 14 # 202 # 32 # 251 # 29 # 298 # 36 # 331 # 50 # 347 # 44 # 356 # 19 15 # 204 # 9 # 353 # 7 # 300 # 1 # 332 # 35 # 348 # 5 # 356 # 33 16 # 205 # 46 # 254 # 46 # 301 # 25 # 333 # 19 # 348 # 25 # 356 # 47 17 # 207 # 23 # 256 # 24 # 302 # 48 # 334 # 2 # 348 # 45 # 357 # 1 18 # 209 # 0 # 258 # 2 # 304 # 10 # 334 # 44 # 349 # 5 # 357 # 15 19 # 210 # 37 # 259 # 40 # 305 # 30 # 335 # 25 # 349 # 25 # 357 # 29 20 # 212 # 15 # 261 # 18 # 306 # 49 # 336 # 5 # 349 # 45 # 357 # 43 21 # 213 # 52 # 262 # 56 # 408 # 7 # 336 # 43 # 350 # 5 # 357 # 57 22 # 215 # 30 # 264 # 31 # 309 # 24 # 337 # 20 # 350 # 24 # 358 # 11 23 # 217 # 7 # 266 # 10 # 310 # 40 # 337 # 56 # 350 # 43 # 358 # 25 24 # 218 # 45 # 267 # 47 # 311 # 54 # 338 # 32 # 351 # 1 # 358 # 39 25 # 220 # 23 # 269 # 24 # 313 # 7 # 339 # 7 # 351 # 19 # 358 # 52 26 # 222 # 0 # 271 # 1 # 314 # 19 # 339 # 42 # 351 # 36 # 359 # 6 27 # 223 # 38 # 272 # 37 # 315 # 29 # 340 # 15 # 351 # 53 # 359 # 20 28 # 225 # 16 # 274 # 13 # 316 # 38 # 340 # 47 # 352 # 10 # 359 # 33 29 # 226 # 54 # 275 # 49 # 317 # 46 # 341 # 18 # 352 # 27 # 359 # 47 30 # 228 # 32 # 277 # 24 # 318 # 52 # 341 # 48 # 352 # 44 # 360 # 0 </note> <pb o="398" file="434" n="435" rhead="Comment. in III. Cap. Sphæræ"/> <p> <s xml:id="echoid-s14845" xml:space="preserve">Ex tabulis quoque aſcenſionum obliquarum facile colliges aſcenſionem <lb/>cuiuslibet ſigni Zodiaci per ſe ſumpti, uel etiam arcus cuiuſuis non à princi-<lb/>pio ♈, inchoati, veluti in ſubſequenti formula conſpicis.</s> <s xml:id="echoid-s14846" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>### Aſcenſiones obliquæ ſignorum Romæ. # G. # M. <lb/>♈ Aries # ♓ Piſces # # 17 # 21 <lb/>♉ Taurus # ♒ Aquarius # # 21 # 6 <lb/>♊ Cemini # ♑ Capricornus # # 28 # 30 <lb/>♋ Cancer # ♐ Sagittarius # # 35 # 54 <lb/>♌ Leo # ♏ Scorpius # # 38 # 42 <lb/>♍ Virgo # ♎ Libra # # 38 # 27 <lb/></note> <p> <s xml:id="echoid-s14847" xml:space="preserve"><emph style="sc">Seqvitvr</emph> ex his, ſegmenta ſignorum eo rectius oriri@, quo viciniora <lb/> <anchor type="note" xlink:label="note-434-02a" xlink:href="note-434-02"/> ſunt puncto æquinoctij Autumnalis, obliquius autem, quo propinquiores <lb/>puncto æquinoctij Verni exiſtunt, quia videlicet rectiores ibi angulos cum Ho <lb/>rizonte conſtituunt, hic autem obliquiores, ut conſtat ex materiali ſphæra, & </s> <s xml:id="echoid-s14848" xml:space="preserve"><lb/>formula præcedenti.</s> <s xml:id="echoid-s14849" xml:space="preserve"/> </p> <div xml:id="echoid-div815" type="float" level="2" n="1"> <note position="left" xlink:label="note-434-02" xlink:href="note-434-02a" xml:space="preserve">Quæ figna <lb/>in ſphæra <lb/>obliqua re-<lb/>ctius, & quę <lb/>obliquius <lb/>@riantur.</note> </div> <p> <s xml:id="echoid-s14850" xml:space="preserve"><emph style="sc">Prraeterea</emph> ex tabulis aſcenſionũ obliquarum perſpicuum eſt, quo <lb/> <anchor type="note" xlink:label="note-434-03a" xlink:href="note-434-03"/> obliquior fuerit aliqua ſphæra, eo magis differre aſcenſiones arcuum Eclipti-<lb/>cæ ab aſcenſionibus rectis, quę nimirũ fiunt in ſphęra recta: </s> <s xml:id="echoid-s14851" xml:space="preserve">idemq́; </s> <s xml:id="echoid-s14852" xml:space="preserve">intellige <lb/>de deſcenſionibus. </s> <s xml:id="echoid-s14853" xml:space="preserve">Hoc ipſum demonſtratur clariſsime ex ſphęricis triangulis.</s> <s xml:id="echoid-s14854" xml:space="preserve"/> </p> <div xml:id="echoid-div816" type="float" level="2" n="2"> <note position="left" xlink:label="note-434-03" xlink:href="note-434-03a" xml:space="preserve">Quo obli-<lb/>quior eſt <lb/>ſphæra, eo <lb/>magis aſcẽ-<lb/>ſione@, de-<lb/>ſcẽſionesq; <lb/>ſignorum <lb/>differũt ab <lb/>aſcenſioni-<lb/>bus deſcen. <lb/>ſionibuſq; <lb/>in ſphæra <lb/>recta.</note> </div> <p> <s xml:id="echoid-s14855" xml:space="preserve"><emph style="sc">Deniqve</emph> in formula præcedẽti vides, in ſphęra obliqua ſex ſigna in <lb/>ſemicirculo Zodiaci deſcendente contenta, nimirum ♋, ♌, ♍, ♎, ♏, ♐, ori-<lb/>ri recte, & </s> <s xml:id="echoid-s14856" xml:space="preserve">conſequenter occidere oblique: </s> <s xml:id="echoid-s14857" xml:space="preserve">ſex aũt ſigna in ſemicirculo Zodia-<lb/>ci aſcẽdente cõprehenſa, vt ♑, ♒,♓,♈,♉,♊, oriri oblique, & </s> <s xml:id="echoid-s14858" xml:space="preserve">occidere recte. <lb/></s> <s xml:id="echoid-s14859" xml:space="preserve">Quod intellige in maiori parte ſphæræ obliquæ verſus Septentrionẽ. </s> <s xml:id="echoid-s14860" xml:space="preserve">Nam ijs, <lb/>quorũ vertex capitis eſt intra circulũ arcticũ, & </s> <s xml:id="echoid-s14861" xml:space="preserve">polum, ſemper aliqua pars Zo-<lb/>diaci extat ſupra Horizontẽ, & </s> <s xml:id="echoid-s14862" xml:space="preserve">aliqua infra eundẽ uel maior, uel minor, pro-<lb/> <anchor type="note" xlink:label="note-434-04a" xlink:href="note-434-04"/> ut magis, aut minus ad polũ accedit eorũ uertex. </s> <s xml:id="echoid-s14863" xml:space="preserve">Vnde quædam ſigna ibi nec <lb/>recte, nec oblique oriẽtur, occidentve; </s> <s xml:id="echoid-s14864" xml:space="preserve">Ijs præterea, qui minorẽ habent latitu-<lb/>dinem, ſeu diſtantiam ab Aequatore, quam gr. </s> <s xml:id="echoid-s14865" xml:space="preserve">10. </s> <s xml:id="echoid-s14866" xml:space="preserve">oriuntur oblique ♍, ♎, & </s> <s xml:id="echoid-s14867" xml:space="preserve"><lb/>tamen continentur in ſemicirculo Zodiaci deſcendente; </s> <s xml:id="echoid-s14868" xml:space="preserve">Econtrario uero <lb/>♊, & </s> <s xml:id="echoid-s14869" xml:space="preserve">♑, oriuntur recte, & </s> <s xml:id="echoid-s14870" xml:space="preserve">tamen compreh enduntur in ſemicirculo <lb/>Zodiaci aſcendente. </s> <s xml:id="echoid-s14871" xml:space="preserve">Quoniam cũ priora illa duo ſigna orian-<lb/>tur oblique in ſphæra recta, ut dictum eſt, poſteriora ve-<lb/>ro duo recte, non poterunt eorum aſcenſiones in <lb/>tam modica ſphæræ obliquitate tantum va-<lb/>riari, ut illa oriantur iam recte, hęc ve-<lb/>ro oblique, ut conſtat ex do-<lb/>ctrina ſphæricorum <lb/>triangulo-<lb/>rum.</s> <s xml:id="echoid-s14872" xml:space="preserve"/> </p> <div xml:id="echoid-div817" type="float" level="2" n="3"> <note position="left" xlink:label="note-434-04" xlink:href="note-434-04a" xml:space="preserve">Quæ ſigna <lb/>in ſphæra <lb/>obliqua o-<lb/>@iantur re-<lb/>cte, & quæ <lb/>obliquæ, & <lb/>vbi hæc ve-<lb/>@a nõ ſint.</note> </div> <pb o="399" file="435" n="436" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div819" type="section" level="1" n="325"> <head xml:id="echoid-head336" style="it" xml:space="preserve">DE DIEBVS NATVRALIBVS. <lb/>& artificialibus.</head> <p style="it"> <s xml:id="echoid-s14873" xml:space="preserve">EX prędict is etiam patet, quòd dies naturales ſunt inęquales. <lb/></s> <s xml:id="echoid-s14874" xml:space="preserve"> <anchor type="note" xlink:label="note-435-01a" xlink:href="note-435-01"/> Eſt enim dies natur alis reuolutio Aequinoctialis circa ter-<lb/>ram ſemel, cum tanta parte, quantam interim Solpertranſit <lb/>motu proprio contra Firmamentum. </s> <s xml:id="echoid-s14875" xml:space="preserve">Sed cum aſcenſiones <lb/>illorum arcuum ſint inæquales, ut p atet per prædicta, tam in ſphærare-<lb/> <anchor type="note" xlink:label="note-435-02a" xlink:href="note-435-02"/> cta, quam in obliqua, & </s> <s xml:id="echoid-s14876" xml:space="preserve">penes additamenta illarum aſcenſionum conſide-<lb/>rentur dies naturales, illi de neceſſitate erunt inæquales; </s> <s xml:id="echoid-s14877" xml:space="preserve">In ſphæra quidem <lb/>recta, propter unicam cauſam ſcilicet propter obliquitatem Zodiaci: </s> <s xml:id="echoid-s14878" xml:space="preserve">In ſpæ <lb/>rauero obliqua, propter duas cauſas, ſcilicet propter obliquitatem Zodiaci, <lb/>& </s> <s xml:id="echoid-s14879" xml:space="preserve">obliquitatem Horizontis obliqui. </s> <s xml:id="echoid-s14880" xml:space="preserve">Tertia ſolet aſſignari cauſa, eccentri-<lb/>@itas circuli Solis.</s> <s xml:id="echoid-s14881" xml:space="preserve"/> </p> <div xml:id="echoid-div819" type="float" level="2" n="1"> <note position="right" xlink:label="note-435-01" xlink:href="note-435-01a" xml:space="preserve">Dies natu-<lb/>ralis <lb/>quid.</note> <note position="right" xlink:label="note-435-02" xlink:href="note-435-02a" xml:space="preserve">Dies natu-<lb/>rales cur <lb/>ſint inæ-<lb/>quales.</note> </div> </div> <div xml:id="echoid-div821" type="section" level="1" n="326"> <head xml:id="echoid-head337" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s14882" xml:space="preserve"><emph style="sc">AGgreditvr</emph> iam 2. </s> <s xml:id="echoid-s14883" xml:space="preserve">partem huius cap. </s> <s xml:id="echoid-s14884" xml:space="preserve">in qua de diebus natu-<lb/>ralibus, artificialibusq; </s> <s xml:id="echoid-s14885" xml:space="preserve">diſſeritur. </s> <s xml:id="echoid-s14886" xml:space="preserve">Quod igitur attinet ad dies Na-<lb/>turales, ait, ex ijs, quæ de ortu & </s> <s xml:id="echoid-s14887" xml:space="preserve">occaſu ſignorum ſunt dicta, con <lb/>ſequi, dies naturales inter ſe eſſe inęquales. </s> <s xml:id="echoid-s14888" xml:space="preserve">Quod ut declaret, <lb/>deſinit diem naturalem dicens, Eum eſſe reuolutionem Aequino <lb/>ctialis circa terrã ſemel cum tanta parte, quãta reſpondet illi parti Zodiaci, <lb/>quã interim Sol pertranſit proprio motu ab occidente in orientẽ contra mo-<lb/>tum primi mobilis, donec ad idẽ punctum à quo receſſit, reuertatur. </s> <s xml:id="echoid-s14889" xml:space="preserve">Dicitur. </s> <s xml:id="echoid-s14890" xml:space="preserve">n. <lb/></s> <s xml:id="echoid-s14891" xml:space="preserve">dies naturalis reuolutio Solis ab uno puncto fixo ad idem punctũ Quod nul-<lb/>la ratione ſieri poteſt, quin totus Aequator ſemel circumuolutus ſic cum ali-<lb/>qua adhuc parte, quæ cooritur cum 59. </s> <s xml:id="echoid-s14892" xml:space="preserve">min. </s> <s xml:id="echoid-s14893" xml:space="preserve">& </s> <s xml:id="echoid-s14894" xml:space="preserve">8. </s> <s xml:id="echoid-s14895" xml:space="preserve">ſec. </s> <s xml:id="echoid-s14896" xml:space="preserve">fere. </s> <s xml:id="echoid-s14897" xml:space="preserve">Nam tantũ fere ſpa-<lb/>cium conficit Sol in Zodiaco fingulis die bus proprio motu. </s> <s xml:id="echoid-s14898" xml:space="preserve">Qm̃ uero dictũ eſt <lb/>arcus æquales Zodiaci habere inęquales aſcenſiones tã in ſphæra recta, quàm <lb/>in obliqua, manifeſtũ eſt, inæquales partes Aequatoris adiici ad totum Aequa <lb/>torem uariis diebus, ut dies naturales conficiantur. </s> <s xml:id="echoid-s14899" xml:space="preserve">Quare neceſſe eſt, in quali <lb/>bet ſphæra ſiue recta, ſiue obliqua, inęquales eſſe dies naturales inter ſe: </s> <s xml:id="echoid-s14900" xml:space="preserve">in <lb/>ſphæra quidem recta, propter obliquitatem Zodiaci. </s> <s xml:id="echoid-s14901" xml:space="preserve">Hinc enim efficitur, ęqua <lb/>les arcus Zodiaci habere aſcenſiones inæquales, ut ex dictis conſtat. </s> <s xml:id="echoid-s14902" xml:space="preserve">Poteſt ad-<lb/>di altera cauſa, nempe eccentricitas Solis Propter enim orbem deferentẽ cor-<lb/>pus ſolare, qui eccentricus eſt, irregulariter mouetur Sol in ecliptica, ut ex <lb/>Theoricis planetarũ conſtat: </s> <s xml:id="echoid-s14903" xml:space="preserve">Vnde maiorẽ arcuũ percurret proprio motu uno <lb/>die, quàm alio, & </s> <s xml:id="echoid-s14904" xml:space="preserve">ideo inæquales arcus Aequatoris correſpondebunt proprio <lb/>motui Solis. </s> <s xml:id="echoid-s14905" xml:space="preserve">In ſphæra autem obliqua ſunt dies naturales inæquales, ut ait, <lb/>ob tres cauſas, quarum duæ ſunt, quas iam recitauimus, tertia uero obliqui-<lb/>tas Horizõtis. </s> <s xml:id="echoid-s14906" xml:space="preserve">Quo enim obliquior eſt Horizon, eo uel obliquius, uel rectius <lb/>oriuntur partes Zodiaci, ut dictum eſt. </s> <s xml:id="echoid-s14907" xml:space="preserve">Vnde ſi dies naturales initium ſu- <pb o="400" file="436" n="437" rhead="Comment. in III. Cap. Sphæræ."/> mant ab Horizonte, hoc eſt, ab ortu Solis, uel ab occaſu, neceſſe eſt, dies Na-<lb/>turales fieri inęquales propter Horizontis obliquitatem. </s> <s xml:id="echoid-s14908" xml:space="preserve">Veruntamen, quia <lb/>Aſtronomi dies non inchoãt ab Horizonte, ſed à Meridiano, qui inſtar eſt Ho <lb/>rizontis recti in qua cunq; </s> <s xml:id="echoid-s14909" xml:space="preserve">ſphæræ obliquit ate, reijcitur communiter hæc ter-<lb/>tia cauſa, & </s> <s xml:id="echoid-s14910" xml:space="preserve">ſolum duæ reliquæ afferri conſueuerunt.</s> <s xml:id="echoid-s14911" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14912" xml:space="preserve"><emph style="sc">Astronomi</emph> porro, quoniam in ſupputatione motuum requirunt dies <lb/> <anchor type="note" xlink:label="note-436-01a" xlink:href="note-436-01"/> Naturales æquales, hac arte redigunt hanc inæqualitatem ad ęqualitatem. <lb/></s> <s xml:id="echoid-s14913" xml:space="preserve">Componunt omnia illa additamenta Aequatoris ſimul, quæ efficiunt unam in <lb/>tegram reuolutionem Aequatoris, cum in anno Sol totum Zodiacum percur-<lb/>rat: </s> <s xml:id="echoid-s14914" xml:space="preserve">Deinde totum Aequatorem, hoc eſt, aggregatum ex illis additamentis, <lb/>diuidunt in tot partes æquales, quot dies in anno cõtinentur, quarum quæli-<lb/>bet continet fere min. </s> <s xml:id="echoid-s14915" xml:space="preserve">59. </s> <s xml:id="echoid-s14916" xml:space="preserve">ſec. </s> <s xml:id="echoid-s14917" xml:space="preserve">8. </s> <s xml:id="echoid-s14918" xml:space="preserve">& </s> <s xml:id="echoid-s14919" xml:space="preserve">ſingulas ſingulis reuolutionibus Aequatori <lb/> <anchor type="note" xlink:label="note-436-02a" xlink:href="note-436-02"/> adijciunt, atque ita redduntur dies Naturales inter ſe æquales, qui Mediocres <lb/>vel Aſtronomici appellari ſolent, quod hi medium teneant inter exceſſus, & </s> <s xml:id="echoid-s14920" xml:space="preserve"><lb/>defectus dierũ Naturalium inæqualium, & </s> <s xml:id="echoid-s14921" xml:space="preserve">his ſoli Aſtronomi utãtur in ſuis <lb/>computationtbus, Alij autem dicuntur Differentes. </s> <s xml:id="echoid-s14922" xml:space="preserve">Et quamuis vnus dies Na-<lb/>turalis Differens parum ab uno die Naturali mediocri differat, & </s> <s xml:id="echoid-s14923" xml:space="preserve">inſenſibili-<lb/>ter, in pluribus tamen diebus ſenſibilis colligitur omnino diuerſitas, ut patet. <lb/></s> <s xml:id="echoid-s14924" xml:space="preserve">Vt autem facilius inæqualitas iſta dierum Naturalium ad ęqualitatem reuo-<lb/>cetur, compoſuerunt Aſtronomi tabulam æquationis dierum, ut uidere eſt in <lb/>tabulis Aſtronomicis Alphonſi regis, uel aliorum Aſtronomorum. </s> <s xml:id="echoid-s14925" xml:space="preserve">Qua de re <lb/>plura ſcribemus in Theorica Solis.</s> <s xml:id="echoid-s14926" xml:space="preserve"/> </p> <div xml:id="echoid-div821" type="float" level="2" n="1"> <note position="left" xlink:label="note-436-01" xlink:href="note-436-01a" xml:space="preserve">Dies Natu-<lb/>rales qua <lb/>arte ad æ-<lb/>qualitatem <lb/>redigantur <lb/>ab Aſtrono <lb/>mis.</note> <note position="left" xlink:label="note-436-02" xlink:href="note-436-02a" xml:space="preserve">Dies Me-<lb/>diocres, qui <lb/>& æqualis <lb/>& Aſtrono <lb/>mici dicun-<lb/>tur, qui.</note> </div> <p> <s xml:id="echoid-s14927" xml:space="preserve"><emph style="sc">De</emph> varijs initijs dierum Naturalium apud uarias gentes ſatis ſuperq. </s> <s xml:id="echoid-s14928" xml:space="preserve">egi <lb/>mus in 5. </s> <s xml:id="echoid-s14929" xml:space="preserve">officio Meridiani circuli, & </s> <s xml:id="echoid-s14930" xml:space="preserve">in Prolegomenis noſtræ Gnomonices.</s> <s xml:id="echoid-s14931" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">Quot paral <lb/>le@os Sol de <lb/>ſcribat ab <lb/>@no ſol@ti-<lb/>@io ad alte <lb/>rum, motu <lb/>primi mobi <lb/>lis.</note> <p style="it"> <s xml:id="echoid-s14932" xml:space="preserve">NOT ANDVM etiam, quod Sol tendens à primo puncto Capri-<lb/>corni per Arietem uſque ad primum punctum Cancri, raptu Firmamenti <lb/>deſcribit. </s> <s xml:id="echoid-s14933" xml:space="preserve">182. </s> <s xml:id="echoid-s14934" xml:space="preserve">parallelos; </s> <s xml:id="echoid-s14935" xml:space="preserve">Qui quidem paralleli, etſi non omnino ſint circu-<lb/>li, ſed ſpiræ, cum tamen non ſit in hoc error ſenſibilis, in hoc uis non conſti-<lb/>tuatur, ſi circuli appellentur: </s> <s xml:id="echoid-s14936" xml:space="preserve">De numero quorum circulorum ſunt duo <lb/>Tropici, & </s> <s xml:id="echoid-s14937" xml:space="preserve">unus Aequinoctialis.</s> <s xml:id="echoid-s14938" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s14939" xml:space="preserve">ITEM iam dictos circulos deſcribit Sol raptu Firmamenti deſcendens <lb/>à primo puncto Cancri per Libram, uſq; </s> <s xml:id="echoid-s14940" xml:space="preserve">ad primum punctum Capricorni.</s> <s xml:id="echoid-s14941" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s14942" xml:space="preserve">ET iſti circuli, dierum Natur alium circuli appellantur. </s> <s xml:id="echoid-s14943" xml:space="preserve">Arcus autẽ, <lb/> <anchor type="note" xlink:label="note-436-04a" xlink:href="note-436-04"/> qui ſunt ſupra Horizontem, ſunt arcus dierum artificialium. </s> <s xml:id="echoid-s14944" xml:space="preserve">Arcus uero, <lb/>qui ſunt ſub Horizonte, ſunt arcus noctium artificialium.</s> <s xml:id="echoid-s14945" xml:space="preserve"/> </p> <div xml:id="echoid-div822" type="float" level="2" n="2"> <note position="left" xlink:label="note-436-04" xlink:href="note-436-04a" xml:space="preserve">Circuli die <lb/>rum Natu-<lb/>ralium, & <lb/>arcus dierũ <lb/>noctiumq; <lb/>artificialiũ <lb/>qui.</note> </div> </div> <div xml:id="echoid-div824" type="section" level="1" n="327"> <head xml:id="echoid-head338" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s14946" xml:space="preserve"><emph style="sc">Volens</emph> iam auctor agere de diebus, & </s> <s xml:id="echoid-s14947" xml:space="preserve">noctibus artificialibus, docet <lb/>Solem, dum mouetur à principio ♑, per ♈, uſque ad principium ♋, deſcribe <lb/>re ad motum diurnum primi mobilis 182. </s> <s xml:id="echoid-s14948" xml:space="preserve">parallelos, ſingulos uidelicet die-<lb/>bus ſingulis; </s> <s xml:id="echoid-s14949" xml:space="preserve">Totidemque, & </s> <s xml:id="echoid-s14950" xml:space="preserve">eoſdem à principio ♋, per ♎, uſque ad princi-<lb/>pium ♑. </s> <s xml:id="echoid-s14951" xml:space="preserve">Qui circuli quamuis non ſint perfecti, ſed potius ſpiræ, propter con-<lb/>tinuum motum Solis ſub E@liptica uerſus orientẽ, tamen quia inſenſibilis eſt <lb/>error, in numernm circulorum referuntur. </s> <s xml:id="echoid-s14952" xml:space="preserve">Atque hi circuli uocantur circuli <pb o="401" file="437" n="438" rhead="Ioan. de Sacro Boſco."/> dierum Naturalium, quoniam finguli ſingulis diebus Naturalibus deſcribun-<lb/>tur: </s> <s xml:id="echoid-s14953" xml:space="preserve">At uero arcus eorum, qui ſupra Horizontem extant conſpicui, dicuntur <lb/>arcus dierum artificialium; </s> <s xml:id="echoid-s14954" xml:space="preserve">Qui uero ſub Horizonte exiſtunt, arcus noctium <lb/>artificialium, quia nimirum illos Sol deſcribit temporibus diurnis, hos uero <lb/>nocturnis. </s> <s xml:id="echoid-s14955" xml:space="preserve">Vnde nil aliud erit dies artificialis, quàm mora Solis ſupra Horizon <lb/>rem: </s> <s xml:id="echoid-s14956" xml:space="preserve">Nox autem mora eiuſdem infra Horizontem.</s> <s xml:id="echoid-s14957" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14958" xml:space="preserve"><emph style="sc">Hinc</emph> ſequitur, cum Sol motu diurno uniformiter moueatur, ſi arcus ſupra <lb/> <anchor type="note" xlink:label="note-437-01a" xlink:href="note-437-01"/> Horizontem exiſtentes æquales fuerint arcubus ſub Horizonte, dies æquales <lb/>eſſe noctibus: </s> <s xml:id="echoid-s14959" xml:space="preserve">Si uero arcus ſupra Horizontem maiores extiterunt, uel mino-<lb/>res, dies etim maiores eſſe noctibus, uel minores.</s> <s xml:id="echoid-s14960" xml:space="preserve"/> </p> <div xml:id="echoid-div824" type="float" level="2" n="1"> <note position="right" xlink:label="note-437-01" xlink:href="note-437-01a" xml:space="preserve">Dies, & n@r <lb/>artificial@@ <lb/>quid.</note> </div> <p> <s xml:id="echoid-s14961" xml:space="preserve"><emph style="sc">Qvamqvam</emph> autem Sol deſcendens, uel aſcendens ab uno ſolſtitio <lb/>ad aliud, hoc eſt, percurrens ſemicirculũ Zodiaci deſcendentem, aut aſcenden <lb/>tem, deſcribat 182. </s> <s xml:id="echoid-s14962" xml:space="preserve">parallelos, & </s> <s xml:id="echoid-s14963" xml:space="preserve">ſemis fere: </s> <s xml:id="echoid-s14964" xml:space="preserve">Tamen eo decurrẽte ab uno æqui <lb/> <anchor type="note" xlink:label="note-437-02a" xlink:href="note-437-02"/> noctio ad aliud, ideſt, perambulante eo ſemicirculum Zodiaci Borealem, uel <lb/>Auſtralem, longe, aliter res ſeſe habet. </s> <s xml:id="echoid-s14965" xml:space="preserve">Nam percurrens ſemicirculum Boreal@ <lb/>deſcribit fere 187. </s> <s xml:id="echoid-s14966" xml:space="preserve">parallelos, perambulans uero ſemicirculum Auſtralem, del@ <lb/>neat tantum 178. </s> <s xml:id="echoid-s14967" xml:space="preserve">parallelos fere. </s> <s xml:id="echoid-s14968" xml:space="preserve">Quod facile colliges ſupputando dies, qui in <lb/>tercedunt inter diem 21. </s> <s xml:id="echoid-s14969" xml:space="preserve">Martij, circa quem hoc tempore fit ęquinoct ũ Ver-<lb/>num, & </s> <s xml:id="echoid-s14970" xml:space="preserve">diem 24. </s> <s xml:id="echoid-s14971" xml:space="preserve">Septembris, in quem fere nunc incidit ęquinoct ũ autumna-<lb/>le. </s> <s xml:id="echoid-s14972" xml:space="preserve">Sunt enim à 21. </s> <s xml:id="echoid-s14973" xml:space="preserve">die Martii uſque ad 24. </s> <s xml:id="echoid-s14974" xml:space="preserve">Septembris, dies 187. </s> <s xml:id="echoid-s14975" xml:space="preserve">At à 24. </s> <s xml:id="echoid-s14976" xml:space="preserve">die <lb/>Septembris ad 21. </s> <s xml:id="echoid-s14977" xml:space="preserve">Martij, dies duntaxat 178. </s> <s xml:id="echoid-s14978" xml:space="preserve">Ratio uero huius eſt, quia Sol exi <lb/>ſtens in ſemicirculo Boreali, ideſt, decurrens ab ♈, per ♋, uſq; </s> <s xml:id="echoid-s14979" xml:space="preserve">ad ♎, quo ui-<lb/>cinior exiſtit principio ♋, eo magts hoc tempore accedit ad augem ſui Eccen <lb/>trici, hoc eſt, ad pũctum, quod longiſſime abeſt à terris; </s> <s xml:id="echoid-s14980" xml:space="preserve">quo uero propinquior <lb/>fit principio ♑, eo magis accedit ad oppoſitum augis Eccentrici, hoc eſt, ad <lb/>punctum, quod maxime uicinium centro terræ exiſtit: </s> <s xml:id="echoid-s14981" xml:space="preserve">Vnde maiorem partem <lb/>Eccentriciibi percurrit, quàm hic, & </s> <s xml:id="echoid-s14982" xml:space="preserve">ob id plus temporis requirit, ut illam par <lb/>tem percurrat, quam ut iſtam perambulet, cum in Eccentrico vniformiter fera <lb/>tur. </s> <s xml:id="echoid-s14983" xml:space="preserve">Verum hoc planius fiet in Theoricis planetarum.</s> <s xml:id="echoid-s14984" xml:space="preserve"/> </p> <div xml:id="echoid-div825" type="float" level="2" n="2"> <note position="right" xlink:label="note-437-02" xlink:href="note-437-02a" xml:space="preserve">Sol mot@ <lb/>primi mobi <lb/>lis ab Arie <lb/>@e ad Lib@@ <lb/>plurespa al <lb/>lelos deſcri <lb/>bit, quàm à <lb/>Lib a ad <lb/>Arietem, & <lb/>quam ob <lb/>cauſam hęc <lb/>inęqualit@@ <lb/>fiat.</note> </div> <note position="right" xml:space="preserve">In ſphær@ <lb/>recta ſem@ <lb/>fiet aquino <lb/>ctium, & <lb/>q@are hoc <lb/>fiat.</note> <p style="it"> <s xml:id="echoid-s14985" xml:space="preserve">IN Sphæra igitur recta, cum Horizon ſphæræ rectæ tranſeat per po-<lb/>los mundi, diuidit omnes circulos iſtos in partes æquales. </s> <s xml:id="echoid-s14986" xml:space="preserve">Vnde tanti ſunt ar <lb/>cus dierum, quanti ſunt arcus noctium apud ex ſtentes ſub Aequinoctiali. <lb/></s> <s xml:id="echoid-s14987" xml:space="preserve">Vnde patet, quod exiſtentibus ſub Aequinoctiali, in quacunque parte Fir-<lb/>mamenti ſit Sol, eſt ſemper æquinoctium.</s> <s xml:id="echoid-s14988" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div827" type="section" level="1" n="328"> <head xml:id="echoid-head339" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s14989" xml:space="preserve"><emph style="sc">Dictvm</emph> eſt, arcus illos parallelorum à Solis motu diurno deſcripto-<lb/>rum, qui ſupra Horizontem extant, eſſe arcus dierum artificialium; </s> <s xml:id="echoid-s14990" xml:space="preserve">eos au-<lb/>rem, qui ſub Horizonte latent, arcus noctium. </s> <s xml:id="echoid-s14991" xml:space="preserve">Quoniam igitur in ſphęra re-<lb/>cta arcus cuiuslibet paralleli ſupra Horizontem æqualis eſt arcui eiuſdẽ ſub <lb/>Horizonte, propterea quòd per propoſ. </s> <s xml:id="echoid-s14992" xml:space="preserve">15. </s> <s xml:id="echoid-s14993" xml:space="preserve">lib. </s> <s xml:id="echoid-s14994" xml:space="preserve">1. </s> <s xml:id="echoid-s14995" xml:space="preserve">Theod. </s> <s xml:id="echoid-s14996" xml:space="preserve">Horizon rectus, cum <lb/>per eorum polos, qui ijdem ſunt, qui poli mundi, incedat, omnes bifariam <lb/>diuidit; </s> <s xml:id="echoid-s14997" xml:space="preserve">man@feſtum eſt, ſemper diem eſſe æqualem nocti, in quocunque gra-<lb/>du, & </s> <s xml:id="echoid-s14998" xml:space="preserve">ſigno Zodiaci Sol exiſtat, quia ſemper deſcribit parallelum, cuius una <lb/>medietas eſt ſupra Horizo@tem, altera uero infra, & </s> <s xml:id="echoid-s14999" xml:space="preserve">ex conſequenti tantum <pb o="402" file="438" n="439" rhead="Comment. in II. Cap. Sphæræ."/> temporis ſpatium conſumit in hemiſ phærio, ſupero quantum in infero. </s> <s xml:id="echoid-s15000" xml:space="preserve">Quod <lb/>quidem perſpicue ſatis int ueri poteſt quiuis in ſphæra materiali.</s> <s xml:id="echoid-s15001" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15002" xml:space="preserve"><emph style="sc">Alia</emph> cauſa afferri poteſt, cur uidelicet perpetuo dies ſint ęquales nocti-<lb/> <anchor type="note" xlink:label="note-438-01a" xlink:href="note-438-01"/> bus in ſphæra recta; </s> <s xml:id="echoid-s15003" xml:space="preserve">quia nimirum c um ſingulis medietatibus Zodiaci, quę ſin-<lb/>gulis diebus oriuntur, cooriuntur etiam ſingulæ medietates Aequatoris, ut <lb/>conſtat ex tabula aſcenſionum rectarum, & </s> <s xml:id="echoid-s15004" xml:space="preserve">manifeſtum eſt ex doctrina ſphæri-<lb/>corum triangulorum. </s> <s xml:id="echoid-s15005" xml:space="preserve">Vnde cum gra. </s> <s xml:id="echoid-s15006" xml:space="preserve">15. </s> <s xml:id="echoid-s15007" xml:space="preserve">Aequatoris efficiant unam horam, <lb/>erunt quolibet die 12. </s> <s xml:id="echoid-s15008" xml:space="preserve">horę, totidemque qualibet nocte, & </s> <s xml:id="echoid-s15009" xml:space="preserve">idcirco ſemper erit <lb/>æquinoctium in ſphæra recta.</s> <s xml:id="echoid-s15010" xml:space="preserve"/> </p> <div xml:id="echoid-div827" type="float" level="2" n="1"> <note position="left" xlink:label="note-438-01" xlink:href="note-438-01a" xml:space="preserve">Alia cauſa <lb/>perpetui æ-<lb/>quinocti in <lb/>ſphæra re-<lb/>cta.</note> </div> <p style="it"> <s xml:id="echoid-s15011" xml:space="preserve">IN Sphæra autem decliui Horizon obliquus diuidit ſolum Aequino-<lb/> <anchor type="note" xlink:label="note-438-02a" xlink:href="note-438-02"/> ctialem in duas partes æquales. </s> <s xml:id="echoid-s15012" xml:space="preserve">Vnde quando Sol eſt in alterutro puncto-<lb/>rum æquinoctialium, tunc arcus diei æquatur arcui noctis, & </s> <s xml:id="echoid-s15013" xml:space="preserve">fit æquino-<lb/>ctium in uniuerſa terra.</s> <s xml:id="echoid-s15014" xml:space="preserve"/> </p> <div xml:id="echoid-div828" type="float" level="2" n="2"> <note position="left" xlink:label="note-438-02" xlink:href="note-438-02a" xml:space="preserve">In ſphæra <lb/>obliqua di <lb/>es inęqua-<lb/>les ſunt no <lb/>ctibus, & <lb/>quare, exce <lb/>ptisduobus <lb/>ęquinoctij.</note> </div> <p style="it"> <s xml:id="echoid-s15015" xml:space="preserve">OMNES uero alios circulos diuidit Horizon obliquus in partes <lb/>inæquales, ita quòd in omnibus circulis, qui ſunt ab Aequinoctiali uſque ad <lb/>tropicum ♋, & </s> <s xml:id="echoid-s15016" xml:space="preserve">in ipſo Tropico ♋, maior eſt ar cus diei, quàm noct@s, ideſt, <lb/>arc{us} ſupra Horizontem, quam ſub Horizonte. </s> <s xml:id="echoid-s15017" xml:space="preserve">Vnde in toto tempore, quo <lb/>Sol mouetur à principio ♈, per ♋, uſque in finem ♍, maior antur dies ſupra <lb/>noctes, & </s> <s xml:id="echoid-s15018" xml:space="preserve">tanto plus, quanto magis accedit Sol ad ♋, & </s> <s xml:id="echoid-s15019" xml:space="preserve">tanto min{us}, quã <lb/>to magis recedit. </s> <s xml:id="echoid-s15020" xml:space="preserve">Econuerſo autem ſe habet de dieb{us}, & </s> <s xml:id="echoid-s15021" xml:space="preserve">noctib{us}, dum Sol <lb/>eſt inſignis <emph style="sc">A</emph>uſtralibus. </s> <s xml:id="echoid-s15022" xml:space="preserve">In omnibus enim circulis, quos Sol deſcribit inter <lb/><emph style="sc">A</emph>equinoctialem, & </s> <s xml:id="echoid-s15023" xml:space="preserve">Tropicum Capricorni, maior eſt arc{us} ſub Horizon-<lb/>te, & </s> <s xml:id="echoid-s15024" xml:space="preserve">minor ſupra. </s> <s xml:id="echoid-s15025" xml:space="preserve">Vnde arc{us} diei minor eſt, quàm arcus noctis, & </s> <s xml:id="echoid-s15026" xml:space="preserve">ſecun-<lb/>dum proportionem arcuum minor antur dies ſupra noctes; </s> <s xml:id="echoid-s15027" xml:space="preserve">& </s> <s xml:id="echoid-s15028" xml:space="preserve">quanto circu <lb/>li ſunt propinquiores Tropico hyemali, tanto magis minorantur dies.</s> <s xml:id="echoid-s15029" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div830" type="section" level="1" n="329"> <head xml:id="echoid-head340" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s15030" xml:space="preserve"><emph style="sc">Qvoniam</emph> Horizon obliquus, cum non tranſeat per polos mundi, nul-<lb/>lum circulum parallelum à Sole deſcriptũ motu primi mobilis diuidit bifariã, <lb/>præterquam Aequatorem, qui eſt circulus maximus, ut ex Theodoſij elemen <lb/>tis ſphæricis conſtat; </s> <s xml:id="echoid-s15031" xml:space="preserve">fit, ut Sole exiſtente in alterutro punctorum æquinoctia <lb/>lium, in quacunq; </s> <s xml:id="echoid-s15032" xml:space="preserve">ſphæra decliui, in qua Horizon, & </s> <s xml:id="echoid-s15033" xml:space="preserve">Aequator ſeſe mutuo ſe <lb/>cant, dies nocti æqualis exiſtat, (quod bis contingit in anno) quia tantus arcus <lb/>Aequatoris eſt ſupra Horizontẽ, quantus infra. </s> <s xml:id="echoid-s15034" xml:space="preserve">At uero Sole exiſtente in aliis <lb/>punctis Zodiaci quibuſcunque, dies noctibus inæquales reddantur, ita ut, ubi <lb/>polus Septentrionalis attollitur ſupra Horizontem, ma@ores fiant dies, quàm <lb/> <anchor type="note" xlink:label="note-438-03a" xlink:href="note-438-03"/> noctes, dum Sol in ſignis Borealibus moratur: </s> <s xml:id="echoid-s15035" xml:space="preserve">cõtra vero dies minores, quàm <lb/>noctes, dum Sol in Auſtralibus ſignis exiſtit, eoq; </s> <s xml:id="echoid-s15036" xml:space="preserve">maior inęqualitas dierum, <lb/>& </s> <s xml:id="echoid-s15037" xml:space="preserve">noctium conſpiciatur, quo magis ad Tropicos Sol accedit, quia tunc in par-<lb/>tes magis inęquales paralleli Solis diuiduntur ab Horizõte, ut ex Theodoſio <lb/>de monſtrari poteſt, maxime ex propoſ. </s> <s xml:id="echoid-s15038" xml:space="preserve">19. </s> <s xml:id="echoid-s15039" xml:space="preserve">& </s> <s xml:id="echoid-s15040" xml:space="preserve">20. </s> <s xml:id="echoid-s15041" xml:space="preserve">lib. </s> <s xml:id="echoid-s15042" xml:space="preserve">2. </s> <s xml:id="echoid-s15043" xml:space="preserve">Vnde Sole deſcribente <lb/>Tro picum ♋, dies maxima cxiſtet, minima uero nox: </s> <s xml:id="echoid-s15044" xml:space="preserve">At Sole ten ente princi-<lb/>diẽ ♑, minima exiſtet dies, maxima uero nox, & </s> <s xml:id="echoid-s15045" xml:space="preserve">c. </s> <s xml:id="echoid-s15046" xml:space="preserve">Itaque dum Sol mouetur <lb/>à ♑. </s> <s xml:id="echoid-s15047" xml:space="preserve">per ♈, uſqpe ad ♋, creſcent dies, & </s> <s xml:id="echoid-s15048" xml:space="preserve">noctes minuentur. </s> <s xml:id="echoid-s15049" xml:space="preserve">Dum uero à ♋, <pb o="403" file="439" n="440" rhead="Ioan. de Sacro Boſco."/> per ♎, ad ♑, Sol progreditur, decreſcent iterum dies eadem proportione, qua <lb/>antea creu erant, & </s> <s xml:id="echoid-s15050" xml:space="preserve">noctes augebuntur.</s> <s xml:id="echoid-s15051" xml:space="preserve"/> </p> <div xml:id="echoid-div830" type="float" level="2" n="1"> <note position="left" xlink:label="note-438-03" xlink:href="note-438-03a" xml:space="preserve">Maxima <lb/>dies, & mi’ <lb/>nima ubi <lb/>ſiat inſ phæ <lb/>ra obliqua <lb/>& ubi dies <lb/>maio@es <lb/>ſint nocti-<lb/>bus, aut cõ <lb/>tra.</note> </div> <note position="right" xml:space="preserve">Qui dies <lb/>artificiales <lb/>quibus no-<lb/>ctibus ſint <lb/>æquales in <lb/>ſphæra obli <lb/>qua.</note> <p style="it"> <s xml:id="echoid-s15052" xml:space="preserve">VNDE uidetur, quòd ſi ſumantur duo circuli æquidiſtantes ab Ae-<lb/>quinoctiali ex diuerſis partibus, quantus eſt arcus diei in uno, tantus eſt ar-<lb/>cus noctis in reliquo. </s> <s xml:id="echoid-s15053" xml:space="preserve">Ex hoc ſequi uidetur, quòd ſi duo dies Naturales ſu-<lb/>mantur in anno æqualiter remoti ab alterutro æquinoctiorum in oppoſitis <lb/>partibus, quanta eſt dies artificialis unius, tanta eſt nox alterius, et e conuer <lb/>ſo. </s> <s xml:id="echoid-s15054" xml:space="preserve">Sed hoc eſt, quantum eſt uulgi ſenſibilitatem in Horizontis fixione. </s> <s xml:id="echoid-s15055" xml:space="preserve">Ra-<lb/>tio enim per ademptionem Solis contra Firmamentum in obliquitate Zodia-<lb/>ci uerius dijudicat.</s> <s xml:id="echoid-s15056" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div832" type="section" level="1" n="330"> <head xml:id="echoid-head341" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s15057" xml:space="preserve"><emph style="sc">Qvod</emph> hic dicit, ſi duo paralleli circuli æquales, æqualiterq; </s> <s xml:id="echoid-s15058" xml:space="preserve">ab Aequa-<lb/>tore diſtantes ſumantur, alter quidem Boream uerſus, alter uero Auſtrum uer <lb/>ſus, arcum diurnum unius æqualem eſſe arcui nocturno alterius, & </s> <s xml:id="echoid-s15059" xml:space="preserve">cõtra, cla-<lb/>riſſime demonſtrant Theodoſius lib. </s> <s xml:id="echoid-s15060" xml:space="preserve">2. </s> <s xml:id="echoid-s15061" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s15062" xml:space="preserve">19. </s> <s xml:id="echoid-s15063" xml:space="preserve">Vnde ſi ſumantur duo dies <lb/>Naturales ęqualiter hinc inde remoti à die ęquinoctiali, (vt v.</s> <s xml:id="echoid-s15064" xml:space="preserve">g. </s> <s xml:id="echoid-s15065" xml:space="preserve">dies triceſima <lb/>Martij, & </s> <s xml:id="echoid-s15066" xml:space="preserve">duodecima Martij; </s> <s xml:id="echoid-s15067" xml:space="preserve">Nam utraq; </s> <s xml:id="echoid-s15068" xml:space="preserve">nouem diebus diſtat à viceſimaprima <lb/> <anchor type="note" xlink:label="note-439-02a" xlink:href="note-439-02"/> die Martij, in qua fit æquinoctium Vernum noſtra ætate) erit tanta dies artifi-<lb/>cialis vnius, quanta nox alterius, & </s> <s xml:id="echoid-s15069" xml:space="preserve">contra. </s> <s xml:id="echoid-s15070" xml:space="preserve">Hoc uero intelligendum, inquit, eſt <lb/>ſecundum iudicium ſenſus, quoniam præciſe loquẽdo erit aliqua inęqualitas <lb/>propter inęqualem Solis motum ſub Zodiaco, uel etiam propter aſcenſiones <lb/>deſcenſionesq; </s> <s xml:id="echoid-s15071" xml:space="preserve">inæquales arcuum Zodiaci, quos Sol proprio motu percurrit <lb/>ab occaſu in ortum; </s> <s xml:id="echoid-s15072" xml:space="preserve">ſed hæc inæqualitas ſub ſenſum cadere non poteſt.</s> <s xml:id="echoid-s15073" xml:space="preserve"/> </p> <div xml:id="echoid-div832" type="float" level="2" n="1"> <note position="right" xlink:label="note-439-02" xlink:href="note-439-02a" xml:space="preserve">In ſphæra <lb/>obliqua æ-<lb/>quales ſunt <lb/>duo dies ar <lb/>tificiales <lb/>quicunque <lb/>abalterutro <lb/>ſolſtitiorũ <lb/>æqualiter <lb/>diſtantes.</note> </div> <p> <s xml:id="echoid-s15074" xml:space="preserve"><emph style="sc">Eadem</emph> ratione erunt duo dies artificiales æqualiter diſtantes ab alte-<lb/>rutro ſolſtitio inter ſe æquales. </s> <s xml:id="echoid-s15075" xml:space="preserve">Idemque dices de noctibus: </s> <s xml:id="echoid-s15076" xml:space="preserve">quia in his vnum <lb/>& </s> <s xml:id="echoid-s15077" xml:space="preserve">eundem parallelum Sol ad motum primi mobilis deſcribit.</s> <s xml:id="echoid-s15078" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s15079" xml:space="preserve">QVANTO quidem polus mundi magis eleuatur ſupra Horizontem, <lb/> <anchor type="note" xlink:label="note-439-03a" xlink:href="note-439-03"/> tanto maiores ſunt dies æſtatis, quando Sol eſt in ſignis Septentrionalibus: <lb/></s> <s xml:id="echoid-s15080" xml:space="preserve">Et e conuerſo, quando eſt in ſignis Auſtralibus. </s> <s xml:id="echoid-s15081" xml:space="preserve">Tanto enim magis mino-<lb/>rantur dies ſupranoctes.</s> <s xml:id="echoid-s15082" xml:space="preserve"/> </p> <div xml:id="echoid-div833" type="float" level="2" n="2"> <note position="right" xlink:label="note-439-03" xlink:href="note-439-03a" xml:space="preserve">Quo maior <lb/>eſt poli alti <lb/>tudo, eo ma <lb/>ior fit inæ-<lb/>qualitasdie <lb/>rum & no-<lb/>ctum artifi-<lb/>cialium.</note> </div> </div> <div xml:id="echoid-div835" type="section" level="1" n="331"> <head xml:id="echoid-head342" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s15083" xml:space="preserve"><emph style="sc">Qvo</emph> magis polus ſupra Horizontem extollitur, eo maiores fiunt arcus <lb/>diurni uerſus polum conſpicuum, & </s> <s xml:id="echoid-s15084" xml:space="preserve">nocturni minores: </s> <s xml:id="echoid-s15085" xml:space="preserve">Arcus uero diurni ver <lb/>ſus alterum polum minores, & </s> <s xml:id="echoid-s15086" xml:space="preserve">nocturni maiores, ut uidere eſt in ſphæra ma-<lb/>teriali. </s> <s xml:id="echoid-s15087" xml:space="preserve">Vnde maiores erunt die<unsure/>s æſtiui in regione magis Septentrionali, quàm <lb/> <anchor type="note" xlink:label="note-439-04a" xlink:href="note-439-04"/> in minus Septentrionali, & </s> <s xml:id="echoid-s15088" xml:space="preserve">noctes æſtatis minores. </s> <s xml:id="echoid-s15089" xml:space="preserve">Contra uero minores erũt <lb/>dies hyemales in magis Septentrionali regione, quàm in minus Septentriona-<lb/>li, & </s> <s xml:id="echoid-s15090" xml:space="preserve">noctes maiores.</s> <s xml:id="echoid-s15091" xml:space="preserve"/> </p> <div xml:id="echoid-div835" type="float" level="2" n="1"> <note position="right" xlink:label="note-439-04" xlink:href="note-439-04a" xml:space="preserve">In ciuitate <lb/>borealiori <lb/>minoressũt <lb/>dies in hye <lb/>me, quàm <lb/>in ciu@tate <lb/>minus bo-<lb/>reali, ſed <lb/>maiores in <lb/>æſtate.</note> </div> <p> <s xml:id="echoid-s15092" xml:space="preserve"><emph style="sc">Hinc</emph> efficitur, ſi ſumantur duę ciuitates, quarum latitudines ſint Borea@ <lb/>les, maiores eſſe dies hyemales à ♑, uſque ad ♈, in minus Boreali, quàm in <lb/>Septentrionaliori, donec in æquinoctio Verno dies reddantur ęquales in utra <lb/>que; </s> <s xml:id="echoid-s15093" xml:space="preserve">At poſt æquinoctium Vernum, dies æſtiuos ſtatim maiores effi ci in ciui-<lb/>tate, quæ ad Boream magis uergit, cum tamen à Solſtitio hyberno ad æſtiuum <lb/>vſque in utraque dies continue accreſcant.</s> <s xml:id="echoid-s15094" xml:space="preserve"/> </p> <pb o="404" file="440" n="441" rhead="Comment. in III. Cap. Sphæræ."/> <p style="it"> <s xml:id="echoid-s15095" xml:space="preserve">NOT ANDV M etiam, quod ſex ſigna, quæ ſunt à principio Can-<lb/> <anchor type="note" xlink:label="note-440-01a" xlink:href="note-440-01"/> eri per Libram, uſque in finem Sagittarij, hahent aſcenſiones ſuas in ſphæ-<lb/>ra obliqua ſimul iunctas, maiores aſcenſionibus ſex ſignorum, quę ſunt à <lb/>principio Capricorniper Arietem, uſque ad finem Geminorũ. </s> <s xml:id="echoid-s15096" xml:space="preserve">Vnde illa ſex <lb/>ſigna prius dicta, dicuntur recte oriri, iſta uero ſex, obliquę<unsure/>. </s> <s xml:id="echoid-s15097" xml:space="preserve">Vnde uerſus.</s> <s xml:id="echoid-s15098" xml:space="preserve"/> </p> <div xml:id="echoid-div836" type="float" level="2" n="2"> <note position="left" xlink:label="note-440-01" xlink:href="note-440-01a" xml:space="preserve">Slgna in <lb/>ſphęra obli <lb/>qua recte <lb/>orientia, & <lb/>obliq; quæ <lb/>ſunt.</note> </div> <p> <s xml:id="echoid-s15099" xml:space="preserve">Recta meant, obliqua cadunt à ſidere Cancri, <lb/>Donec finitur chiron, ſed cętera ſigna <lb/>Naſcuntur prono, deſcendunt tramite recto.</s> <s xml:id="echoid-s15100" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">Alia caù<unsure/>ſa <lb/>inæqualita <lb/>tis dierum, <lb/>& noctium <lb/>in ſphæra <lb/>obliqua.</note> <p style="it"> <s xml:id="echoid-s15101" xml:space="preserve">ET quando eſt nobis maxima dies in æſtate, ſcilicet Sole exiſtente in <lb/>principio Cancri, tunc oriuntur de die ſex ſigna directe orientia, de nocte au <lb/>tem ſex oblique. </s> <s xml:id="echoid-s15102" xml:space="preserve">E conuerſo quando nobis eſt minimus dies in anno, ſcilicet <lb/>Sole exiſtente in prineipio Capricorni, tunc oriuntur de die ſex ſigna obli-<lb/>que orientia, de nocte uero ſex directe. </s> <s xml:id="echoid-s15103" xml:space="preserve">Quando autem Sol eſt in alterutro <lb/>punctorum æquinoctialium, tunc de die oriuntur tria ſigna directe orientia, <lb/>& </s> <s xml:id="echoid-s15104" xml:space="preserve">tria oblique, & </s> <s xml:id="echoid-s15105" xml:space="preserve">de nocte ſimiliter. </s> <s xml:id="echoid-s15106" xml:space="preserve">Eſt enim regula; </s> <s xml:id="echoid-s15107" xml:space="preserve">Quantuncunque bre-<lb/>uis uel prolixa ſit dies uel nox, ſex ſigna oriuntur de die, & </s> <s xml:id="echoid-s15108" xml:space="preserve">ſex de nocte. <lb/></s> <s xml:id="echoid-s15109" xml:space="preserve">Nec propter prolixitatem, uel breuitatem diei uel noctis, plura, uel paucio-<lb/>ra ſigna oriuntur.</s> <s xml:id="echoid-s15110" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s15111" xml:space="preserve">IN omnibus autem alijs circulis, qui ſunt à latere Aequinoctialis, uel <lb/>ex parte Auſtrali, uel Septentrionali, maiorantur, uel minorantur dies uel <lb/>noctes, ſecundum quod plura, uel pauciora de ſignis directe orientibus, uel <lb/>oblique, de die uel nocte oriuntur.</s> <s xml:id="echoid-s15112" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div838" type="section" level="1" n="332"> <head xml:id="echoid-head343" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s15113" xml:space="preserve"><emph style="sc">Reddit</emph> aliam cauſam, cur nobis in hemiſphærio Septentrionali degen <lb/>tibus maxima dies contingat, & </s> <s xml:id="echoid-s15114" xml:space="preserve">minima nox, Sole tenente principium ♋: </s> <s xml:id="echoid-s15115" xml:space="preserve">Eo <lb/>dem deinde exiſtente in principio ♑, minima dies, & </s> <s xml:id="echoid-s15116" xml:space="preserve">nox maxima: </s> <s xml:id="echoid-s15117" xml:space="preserve">Illo autem <lb/>ingrediente principium ♈, vel ♎, dies nocti æquali efficiatur. </s> <s xml:id="echoid-s15118" xml:space="preserve">Quoniã enim <lb/>figna contenta in ſemicirculo Zodiaci deſcendente oriuntur recte in ſphæra <lb/>obliqua, & </s> <s xml:id="echoid-s15119" xml:space="preserve">recta ſex oblique, vt ſupra diximus; </s> <s xml:id="echoid-s15120" xml:space="preserve">omni aũt die ſex præciſe ſigna <lb/>oriuntur, ut & </s> <s xml:id="echoid-s15121" xml:space="preserve">ante oſtendimus; </s> <s xml:id="echoid-s15122" xml:space="preserve">efficitur, ut Sole exiſtente in primo pũcto ♋, <lb/>priora illa ſigna recte orientia ſupra Horizontẽ in die aſcẽdant; </s> <s xml:id="echoid-s15123" xml:space="preserve">poſteriora ue-<lb/>ro ſex oblique orientia in nocte: </s> <s xml:id="echoid-s15124" xml:space="preserve">Vnde maxima erit dies, & </s> <s xml:id="echoid-s15125" xml:space="preserve">minima nox. </s> <s xml:id="echoid-s15126" xml:space="preserve">Con-<lb/>tra uero, Sole exiſtente in principio ♑. </s> <s xml:id="echoid-s15127" xml:space="preserve">Nam tunc poſteriora ſigna ſex, quæ <lb/>oblique oriuntur, ſupra Horizontem in die emergunt, & </s> <s xml:id="echoid-s15128" xml:space="preserve">priora ſex, quę recte <lb/>oriuntur, in nocte. </s> <s xml:id="echoid-s15129" xml:space="preserve">Quare minima efficietur dies, maxima uero nox. </s> <s xml:id="echoid-s15130" xml:space="preserve">At Sole <lb/>poſſidente alterutrum punctorum æquinoctialium, oriuntur in die tria ſigna <lb/>recte, & </s> <s xml:id="echoid-s15131" xml:space="preserve">tria oblique, ſimiliterque in nocte; </s> <s xml:id="echoid-s15132" xml:space="preserve">Idcirco æquinoctium contingit.</s> <s xml:id="echoid-s15133" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15134" xml:space="preserve"><emph style="sc">Hinc</emph> perſpicua etiam eſt ratio, cur in æſtate dies longiores ſint noctibus, <lb/>& </s> <s xml:id="echoid-s15135" xml:space="preserve">in hyeme noctes maiores diebus, quia ſcilicet in æſtate plura ſigna recte <lb/>oriuntur tempore diurno, quàm nocturno: </s> <s xml:id="echoid-s15136" xml:space="preserve">In hyeme uero plura recte aſcen-<lb/>dunt tempore nocturno, quàm diurno, ut conſtat ex dictis.</s> <s xml:id="echoid-s15137" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15138" xml:space="preserve"><emph style="sc">Cvm</emph> autem in ſphæra obliqua ſex hæc ſigna, ♋, ♌, ♍, ♎, ♏, ♐, recte <pb o="405" file="441" n="442" rhead="Ioan. de Sacro Boſco."/> oriri dicuntur, & </s> <s xml:id="echoid-s15139" xml:space="preserve">occidere oblique@ſex vero hæc, ♑, ♒, ♓, ♈, ♉, ♊, obliqu<emph style="sub">e</emph> <lb/>oriri, & </s> <s xml:id="echoid-s15140" xml:space="preserve">occidere recte, excipienda eſt ſphæra obliqua, in qua altitudo poli <lb/>comp@ehendit plures gradus quam 66 {1/2}. </s> <s xml:id="echoid-s15141" xml:space="preserve">Nam ibi quædam ſigna nullo modo <lb/>oriuntur: </s> <s xml:id="echoid-s15142" xml:space="preserve">Excipienda eſt quoque ſphæra obliqua, in qua poli eleuatio minor <lb/> <anchor type="note" xlink:label="note-441-01a" xlink:href="note-441-01"/> eſt, quàm grad. </s> <s xml:id="echoid-s15143" xml:space="preserve">10. </s> <s xml:id="echoid-s15144" xml:space="preserve">vt ſupra diximus. </s> <s xml:id="echoid-s15145" xml:space="preserve">Ibi enim hæcregula vera non eſt, niſi in-<lb/>telligamus omnes arcus, qui initium ſumunt à principio ♋, vſque ad finem <lb/>♐, oriri recte, arcus vero, qui incipiunt à primo puncto ♑, vſque ad finem ♊, <lb/>oriri oblique: </s> <s xml:id="echoid-s15146" xml:space="preserve">quod quidem eſt veriſſimum.</s> <s xml:id="echoid-s15147" xml:space="preserve"/> </p> <div xml:id="echoid-div838" type="float" level="2" n="1"> <note position="right" xlink:label="note-441-01" xlink:href="note-441-01a" xml:space="preserve">Quom odo <lb/>verum eſſe <lb/>poſsit, in <lb/>omni ſphæ-<lb/>ra obliqua <lb/>ſex ſigna o-<lb/>riri recte, & <lb/>ſex obliquę.</note> </div> <p style="it"> <s xml:id="echoid-s15148" xml:space="preserve">EX his colligitur, quòd, cum hora Naturalis ſit ſpatium temporis, in <lb/>quo medietas ſigni peroritur, in qualibet die artificiali, ſimiliter & </s> <s xml:id="echoid-s15149" xml:space="preserve">in no-<lb/>cte ſunt duodecim horæ Naturales.</s> <s xml:id="echoid-s15150" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div840" type="section" level="1" n="333"> <head xml:id="echoid-head344" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s15151" xml:space="preserve">Ex eo, quòd quolibet die anni ſiue breui, ſiue longo, ſex ſigna oriuntur, <lb/> <anchor type="note" xlink:label="note-441-02a" xlink:href="note-441-02"/> & </s> <s xml:id="echoid-s15152" xml:space="preserve">ſex occidunt, colligit, tam in die, quàm in nocte quacunque reperiri 12. </s> <s xml:id="echoid-s15153" xml:space="preserve">ho-<lb/>ras Naturales. </s> <s xml:id="echoid-s15154" xml:space="preserve">Eſt enim hora Naturalis, vt inquit, ſpatium tẽporis, quo medie-<lb/>tas cuiuſlibet ſigni exoritur. </s> <s xml:id="echoid-s15155" xml:space="preserve">Quod vt planius fiat, dicenda erunt pauca de ho-<lb/> <anchor type="note" xlink:label="note-441-03a" xlink:href="note-441-03"/> ris. </s> <s xml:id="echoid-s15156" xml:space="preserve">Sunt igitur duo genera horarum. </s> <s xml:id="echoid-s15157" xml:space="preserve">Quædam dicuntur æquales, ſiue æqui-<lb/>noctiales: </s> <s xml:id="echoid-s15158" xml:space="preserve">quædam vero appellantur inæquales, temporariæ, naturales, vel Pla-<lb/>netariæ. </s> <s xml:id="echoid-s15159" xml:space="preserve">Hora æqualis eſt vigeſima quarta pars diei naturalis. </s> <s xml:id="echoid-s15160" xml:space="preserve">Vnde ſicut to-<lb/> <anchor type="note" xlink:label="note-441-04a" xlink:href="note-441-04"/> ta dies naturalis continet 360. </s> <s xml:id="echoid-s15161" xml:space="preserve">grad. </s> <s xml:id="echoid-s15162" xml:space="preserve">Aequatoris, ita quoque vna hora æqualis <lb/>complectitur grad. </s> <s xml:id="echoid-s15163" xml:space="preserve">15. </s> <s xml:id="echoid-s15164" xml:space="preserve">Aèquatoris. </s> <s xml:id="echoid-s15165" xml:space="preserve">Nam ex integra Aequatoris reuolutione <lb/>efficitur dies Naturalis, vt dictum eſt, & </s> <s xml:id="echoid-s15166" xml:space="preserve">ex aſcenſione grad. </s> <s xml:id="echoid-s15167" xml:space="preserve">15. </s> <s xml:id="echoid-s15168" xml:space="preserve">Aequatoris <lb/>hora conſtituitur. </s> <s xml:id="echoid-s15169" xml:space="preserve">Omittimus enim nunc modicum illum exceſſum, qui addi <lb/>deberet, propter motũ Solis, quoniam inſenſibilis eſt. </s> <s xml:id="echoid-s15170" xml:space="preserve">Dicuntur huiuſmodi ho-<lb/>ræ æquales, quia ſemper eiuſdẽ ſunt magnitudinis toto anni ſpatio, eo qu òd <lb/>ſint vigeſimæ quartę partes diei Naturalis, qui ſemper idẽ eſt ſenſibiliter. </s> <s xml:id="echoid-s15171" xml:space="preserve">Di-<lb/>cuntur quoque ęquino ctiales, eo quòd ad vniformen motum Aequinoctialis <lb/>circuli referantur. </s> <s xml:id="echoid-s15172" xml:space="preserve">Hora vero inęqualis duplex eſt. </s> <s xml:id="echoid-s15173" xml:space="preserve">Quędam enim eſt ſpatium <lb/> <anchor type="note" xlink:label="note-441-05a" xlink:href="note-441-05"/> temporis, quo medietas ſigni peroritur, de qua auctor noſter eſt locutus, quo <lb/>pacto tam in die artificiali, quàm in nocte conſtituuntur 12. </s> <s xml:id="echoid-s15174" xml:space="preserve">horę & </s> <s xml:id="echoid-s15175" xml:space="preserve">inter ſe <lb/>inęquales, & </s> <s xml:id="echoid-s15176" xml:space="preserve">horis alterius diei, noctiſve, quia non omnes medietates ſigno-<lb/>rum ęqualiter aſcendunt, vt ex dictis conſtat: </s> <s xml:id="echoid-s15177" xml:space="preserve">Quędam vero eſt duodecima <lb/>pars cuiuſlibet diei artificialis, vel noctis: </s> <s xml:id="echoid-s15178" xml:space="preserve">Qua ratione horę vnius diei erunt <lb/>inter ſe ęquales, inęquales tamen horis alterius diei, niſi hęc dies illi ſit ęqua-<lb/>lis. </s> <s xml:id="echoid-s15179" xml:space="preserve">Idem dices de horis 12. </s> <s xml:id="echoid-s15180" xml:space="preserve">nocturnis. </s> <s xml:id="echoid-s15181" xml:space="preserve">Solum in ęquinoctijs congruunt hę ho-<lb/> <anchor type="note" xlink:label="note-441-06a" xlink:href="note-441-06"/> rę ęquino ctialibus horis tam in die, quàm in nocte, quia tunc etiam dies arti-<lb/>ficialis continet 12. </s> <s xml:id="echoid-s15182" xml:space="preserve">horas ęquinoctiales, totidemque nox. </s> <s xml:id="echoid-s15183" xml:space="preserve">Ex his perſpicuum <lb/>eſt, cur iſtę horę dicantur inęquales. </s> <s xml:id="echoid-s15184" xml:space="preserve">Vocantur quoque temporales, quia ſecun <lb/>dum variationem temporum, nempe dierum, & </s> <s xml:id="echoid-s15185" xml:space="preserve">noctium, ipſę quoque varian-<lb/>tur. </s> <s xml:id="echoid-s15186" xml:space="preserve">Dicuntur denique Naturales, quia Natura magiſtra homines didicerunt, <lb/>per tales horas diſtingui dominia Planetarum, pręſertim ſi de horis inęquali-<lb/>bus primi generis loquamur. </s> <s xml:id="echoid-s15187" xml:space="preserve">Quamobrem ſunt etiam Planetarię dictę: </s> <s xml:id="echoid-s15188" xml:space="preserve">per has <lb/>etenim 24. </s> <s xml:id="echoid-s15189" xml:space="preserve">horas diei, & </s> <s xml:id="echoid-s15190" xml:space="preserve">noctis dominantur Planetę ſuo ordine, vt ſupra dixi-<lb/> <anchor type="note" xlink:label="note-441-07a" xlink:href="note-441-07"/> mus, cum de ordine Pla netarum ageremus.</s> <s xml:id="echoid-s15191" xml:space="preserve"/> </p> <div xml:id="echoid-div840" type="float" level="2" n="1"> <note position="right" xlink:label="note-441-02" xlink:href="note-441-02a" xml:space="preserve">Hora Nàtu <lb/>ralis quid.</note> <note position="right" xlink:label="note-441-03" xlink:href="note-441-03a" xml:space="preserve">Horarum <lb/>diuiſio.</note> <note position="right" xlink:label="note-441-04" xlink:href="note-441-04a" xml:space="preserve">Horæ ęqua-<lb/>les, vel ęqu@ <lb/>noctiales <lb/>quæ, & cur <lb/>ſic dicãtur.</note> <note position="right" xlink:label="note-441-05" xlink:href="note-441-05a" xml:space="preserve">Horarũ in. <lb/>ęqualium <lb/>duo gene-<lb/>ra.</note> <note position="right" xlink:label="note-441-06" xlink:href="note-441-06a" xml:space="preserve">Horæ inæ-<lb/>quales cur <lb/>dicãtur tẽ-<lb/>porales Na <lb/>turales, & <lb/>Planetariæ.</note> <note position="right" xlink:label="note-441-07" xlink:href="note-441-07a" xml:space="preserve">Qua arte <lb/>quantitas <lb/>horarũ inæ <lb/>qualiũ co-<lb/>gnoſcatur.</note> </div> <p> <s xml:id="echoid-s15192" xml:space="preserve"><emph style="sc">Cognoscetvr</emph> quantitas cuiuslibet horę inęqualis prioris generis, <lb/>ſi aſcenſiones inueniantur medietatum omnium ſignorum, eęque ad horas <pb o="406" file="442" n="443" rhead="Comment. in III. Cap. Sphæræ"/> reducantur: </s> <s xml:id="echoid-s15193" xml:space="preserve">Poſterioris vero generis horæ inæquales notæ erunt, ſi quælibet <lb/>dies art@ficialis, vel nox in 12. </s> <s xml:id="echoid-s15194" xml:space="preserve">partes æquales diſtribuatur. </s> <s xml:id="echoid-s15195" xml:space="preserve">Vt quia dies artifi-<lb/>rialis Romæ, Sole exiſtẽte in principio ♋, cõpl@ ctitur gr. </s> <s xml:id="echoid-s15196" xml:space="preserve">226. </s> <s xml:id="echoid-s15197" xml:space="preserve">min. </s> <s xml:id="echoid-s15198" xml:space="preserve">6. </s> <s xml:id="echoid-s15199" xml:space="preserve">erit duo-<lb/>decima pars nẽpe hora inæqualis, grad. </s> <s xml:id="echoid-s15200" xml:space="preserve">18. </s> <s xml:id="echoid-s15201" xml:space="preserve">min. </s> <s xml:id="echoid-s15202" xml:space="preserve">50. </s> <s xml:id="echoid-s15203" xml:space="preserve">fere, qui gradus, & </s> <s xml:id="echoid-s15204" xml:space="preserve">minuta <lb/>conſtituunt horam æqualem 1. </s> <s xml:id="echoid-s15205" xml:space="preserve">& </s> <s xml:id="echoid-s15206" xml:space="preserve">min. </s> <s xml:id="echoid-s15207" xml:space="preserve">15. </s> <s xml:id="echoid-s15208" xml:space="preserve">& </s> <s xml:id="echoid-s15209" xml:space="preserve">ſic de cæteris. </s> <s xml:id="echoid-s15210" xml:space="preserve">Vel quia tota dies <lb/>prædicta cõtinet horas 15. </s> <s xml:id="echoid-s15211" xml:space="preserve">mi. </s> <s xml:id="echoid-s15212" xml:space="preserve">4. </s> <s xml:id="echoid-s15213" xml:space="preserve">erit duodecima pars rurſus hora 1. </s> <s xml:id="echoid-s15214" xml:space="preserve">mi. </s> <s xml:id="echoid-s15215" xml:space="preserve">15. </s> <s xml:id="echoid-s15216" xml:space="preserve">fere.</s> <s xml:id="echoid-s15217" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div842" type="section" level="1" n="334"> <head xml:id="echoid-head345" xml:space="preserve">QVA ARTE INVENIATVR QVANTITAS <lb/>cuiuslibet diei artificialis & noctis, in quacunque regione, in <lb/>qua altitudo poli non excedit grad. 66. min. 30.</head> <p> <s xml:id="echoid-s15218" xml:space="preserve"><emph style="sc">Qvamvis</emph> in 7. </s> <s xml:id="echoid-s15219" xml:space="preserve">officio Aequatoris docuerimus, quonam modo inda-<lb/> <anchor type="note" xlink:label="note-442-01a" xlink:href="note-442-01"/> ganda ſit quantitas cuiuſuis diei artificialis, at q; </s> <s xml:id="echoid-s15220" xml:space="preserve">noctis, beneficio Aequatoris, <lb/>tamẽ id ipſum exequemur multo certius ex doctrina Sinuum. </s> <s xml:id="echoid-s15221" xml:space="preserve">Cumenim Me <lb/>ridianus diuidat ſingulos arcus & </s> <s xml:id="echoid-s15222" xml:space="preserve">diurnos, & </s> <s xml:id="echoid-s15223" xml:space="preserve">nocturnos bifariam, ſi inueniatur <lb/>differentia arcus ſemidiurni in ſphęra obliqua, qua differt ab arcu ſemidiurno <lb/>in ſphæra recta, ignorari non poterit arcus ſemidiurnus in propoſita ſphæra <lb/>obliqua Nã quia Sole decurrente per ſigna Borealia, arcus quilibet ſemidiur-<lb/>nus ſphęræ obliquæ ſuperat arcum ſemidiurnum ſphæræ rectæ, qui ſemper eſt <lb/>Quadrans, hoc eſt, grad. </s> <s xml:id="echoid-s15224" xml:space="preserve">90. </s> <s xml:id="echoid-s15225" xml:space="preserve">ſiue horarum 6. </s> <s xml:id="echoid-s15226" xml:space="preserve">per totum circulũ anni, ad dita hu <lb/>iuſmodi differentia arcui ſemidinrno ſphæræ rectæ, aut eadẽ detracta ex arcu <lb/>ſemidiurno ſphęræ rectæ, Sole nimitum exiſtẽte in ſignis Meridionalibus, quo <lb/>niam tunc ſuperatur quiuis arcus ſemidiurnus ab arcu ſemidiurno ſphæræ re-<lb/>ctæ, vt ex propoſ. </s> <s xml:id="echoid-s15227" xml:space="preserve">16. </s> <s xml:id="echoid-s15228" xml:space="preserve">lib. </s> <s xml:id="echoid-s15229" xml:space="preserve">2. </s> <s xml:id="echoid-s15230" xml:space="preserve">Theodoſij conſtat, dabit arcum ſemidiurnum, quo <lb/>duplicato habebitur integer arcus diurnus. </s> <s xml:id="echoid-s15231" xml:space="preserve">Hoc rurſus ſublato ex circulo in-<lb/>tegro, ſiue ex horis 24. </s> <s xml:id="echoid-s15232" xml:space="preserve">relinquetur arcus nocturnus. </s> <s xml:id="echoid-s15233" xml:space="preserve">Item arcus ſemidiurnus <lb/>ablatus ex ſemicirculo, ſiue ex horis 12. </s> <s xml:id="echoid-s15234" xml:space="preserve">relinquet arcum ſeminocturnum.</s> <s xml:id="echoid-s15235" xml:space="preserve"/> </p> <div xml:id="echoid-div842" type="float" level="2" n="1"> <note position="left" xlink:label="note-442-01" xlink:href="note-442-01a" xml:space="preserve">Quo pacto <lb/>reperiatur <lb/>arcus ſemi-<lb/>diurnus ex <lb/>differentia <lb/>inter arcũ <lb/>ſemidiur <lb/>nũ in ſphæ <lb/>ra recta, & <lb/>arcũ ſemi-<lb/>diurnum in <lb/>ſphęra obli <lb/>qua.</note> </div> <p> <s xml:id="echoid-s15236" xml:space="preserve"><emph style="sc">Haec</emph> autem differentia cuiuslibet arcus ſemidiurni non aliter inuenie-<lb/> <anchor type="note" xlink:label="note-442-02a" xlink:href="note-442-02"/> tur, quàm aſcenſionalis differentia cuiuſuis puncti Eclipticæ. </s> <s xml:id="echoid-s15237" xml:space="preserve">Nam vt demon-<lb/>ſtrat Nicolaus Copernicus lib. </s> <s xml:id="echoid-s15238" xml:space="preserve">2. </s> <s xml:id="echoid-s15239" xml:space="preserve">cap. </s> <s xml:id="echoid-s15240" xml:space="preserve">7. </s> <s xml:id="echoid-s15241" xml:space="preserve">& </s> <s xml:id="echoid-s15242" xml:space="preserve">nos alibi quoque demonſtrauimus, <lb/>eadem eſt differentia aſcenſionalis, quæ eſt inter ſemidiurnum arcum ſphæræ <lb/>obliquæ & </s> <s xml:id="echoid-s15243" xml:space="preserve">ſemidiuruum arcum ſphæræ rectæ. </s> <s xml:id="echoid-s15244" xml:space="preserve">Quare, ſi differentia aſcenſiona <lb/>lis cuiuſuis puncti Eclipticæ addatut uel ſubtrahatur, prout Sol in ſignis Bo-<lb/>realibus, vel Auſtralibus verſabitur, ab arcu ſemidiurno ſphæræ rectæ, hoc eſt, <lb/>à Quadrante, notus erit arcus ſemidiurnus quæſitus. </s> <s xml:id="echoid-s15245" xml:space="preserve"><emph style="sc">Exemplvm</emph>. </s> <s xml:id="echoid-s15246" xml:space="preserve">Romæ, Sole <lb/>exiſtente in principio ♋, differentia aſcenſionalis eſt grad. </s> <s xml:id="echoid-s15247" xml:space="preserve">23. </s> <s xml:id="echoid-s15248" xml:space="preserve">min. </s> <s xml:id="echoid-s15249" xml:space="preserve">3. </s> <s xml:id="echoid-s15250" xml:space="preserve">hoc eſt, <lb/>tanto maior eſt arcus ſemidiurnus eo tempore Romæ, quàm in ſphæra recta, <lb/>quia Cancer eſt ſignum Septentrionale. </s> <s xml:id="echoid-s15251" xml:space="preserve">Igitur ſi ad Quadrantem, ideſt, ad gra. <lb/></s> <s xml:id="echoid-s15252" xml:space="preserve">90. </s> <s xml:id="echoid-s15253" xml:space="preserve">apponantur grad. </s> <s xml:id="echoid-s15254" xml:space="preserve">23. </s> <s xml:id="echoid-s15255" xml:space="preserve">min. </s> <s xml:id="echoid-s15256" xml:space="preserve">3. </s> <s xml:id="echoid-s15257" xml:space="preserve">habebitur arcus ſemidiurnus Romæ, Sole exi-<lb/>ſtente in primo puncto ♋, quod noſtra ętate fit 22. </s> <s xml:id="echoid-s15258" xml:space="preserve">die Iunij, grad. </s> <s xml:id="echoid-s15259" xml:space="preserve">113. </s> <s xml:id="echoid-s15260" xml:space="preserve">min. </s> <s xml:id="echoid-s15261" xml:space="preserve">3. </s> <s xml:id="echoid-s15262" xml:space="preserve"><lb/>hoc eſt, horarum 7. </s> <s xml:id="echoid-s15263" xml:space="preserve">min. </s> <s xml:id="echoid-s15264" xml:space="preserve">32. </s> <s xml:id="echoid-s15265" xml:space="preserve">Arcus autem diurnus continebit gra. </s> <s xml:id="echoid-s15266" xml:space="preserve">226. </s> <s xml:id="echoid-s15267" xml:space="preserve">min. </s> <s xml:id="echoid-s15268" xml:space="preserve">6. </s> <s xml:id="echoid-s15269" xml:space="preserve">id <lb/>eſt, horas 15. </s> <s xml:id="echoid-s15270" xml:space="preserve">min. </s> <s xml:id="echoid-s15271" xml:space="preserve">4. </s> <s xml:id="echoid-s15272" xml:space="preserve">Pari ratione, ſi eadem differentia à Quadrante detrahatur, <lb/>relinquetur arcus, ſemidiurnus, Sole tenente primum gradum ♑, grad. </s> <s xml:id="echoid-s15273" xml:space="preserve">66. </s> <s xml:id="echoid-s15274" xml:space="preserve">mi. </s> <s xml:id="echoid-s15275" xml:space="preserve"><lb/>57. </s> <s xml:id="echoid-s15276" xml:space="preserve">hoc eſt, horarum 4. </s> <s xml:id="echoid-s15277" xml:space="preserve">min. </s> <s xml:id="echoid-s15278" xml:space="preserve">28. </s> <s xml:id="echoid-s15279" xml:space="preserve">fere, &</s> <s xml:id="echoid-s15280" xml:space="preserve">c. </s> <s xml:id="echoid-s15281" xml:space="preserve">Differentiam quoque inter arcum ſe-<lb/>midiurnum ſphæræ rectæ, & </s> <s xml:id="echoid-s15282" xml:space="preserve">arcum ſemidiurnum ſphæræ obliquæ ſupputare <lb/>docuimus propoſ. </s> <s xml:id="echoid-s15283" xml:space="preserve">34. </s> <s xml:id="echoid-s15284" xml:space="preserve">lib. </s> <s xml:id="echoid-s15285" xml:space="preserve">1. </s> <s xml:id="echoid-s15286" xml:space="preserve">noſtræ Gnomonices.</s> <s xml:id="echoid-s15287" xml:space="preserve"/> </p> <div xml:id="echoid-div843" type="float" level="2" n="2"> <note position="left" xlink:label="note-442-02" xlink:href="note-442-02a" xml:space="preserve">Differentia <lb/>inter arcũ <lb/>ſemidiutur-<lb/>num ſphæ-<lb/>rærectæ, & <lb/>arcũ ſemi-<lb/>diurnum <lb/>ſphæræ ob-<lb/>liquæ quo <lb/>pacto repe-<lb/>riatur.</note> </div> <p> <s xml:id="echoid-s15288" xml:space="preserve"><emph style="sc">Reperiatvr</emph> quoque alia ratione quantitas cuiuslibet diei. </s> <s xml:id="echoid-s15289" xml:space="preserve">Si namq. <lb/></s> <s xml:id="echoid-s15290" xml:space="preserve">ſubducatur aſcenſio obliqua cuiuſque puncti Eclipticæ ab aſcenſione obliqua <pb o="407" file="443" n="444" rhead="Ioan. de Sacro Boſco."/> puncti oppoſiti, adiecto prius integro circulo, ſi ſubtractio fieri nequeat, relin <lb/>quetur arcus diur nus. </s> <s xml:id="echoid-s15291" xml:space="preserve">EXEMPLVM. </s> <s xml:id="echoid-s15292" xml:space="preserve">Romæ Sole exiſtente in principio ♋, ſi <lb/> <anchor type="note" xlink:label="note-443-01a" xlink:href="note-443-01"/> ſubtrahatur aſcenſio obliqua primi puncti ♋, nempe gr. </s> <s xml:id="echoid-s15293" xml:space="preserve">66. </s> <s xml:id="echoid-s15294" xml:space="preserve">min. </s> <s xml:id="echoid-s15295" xml:space="preserve">57. </s> <s xml:id="echoid-s15296" xml:space="preserve">ex aſcẽſio <lb/>ne obliqua principij ♑, puncti oppoſiti, nimirum ex gr. </s> <s xml:id="echoid-s15297" xml:space="preserve">293. </s> <s xml:id="echoid-s15298" xml:space="preserve">min. </s> <s xml:id="echoid-s15299" xml:space="preserve">3. </s> <s xml:id="echoid-s15300" xml:space="preserve">remanebit <lb/>arcus diurnus, gr. </s> <s xml:id="echoid-s15301" xml:space="preserve">226. </s> <s xml:id="echoid-s15302" xml:space="preserve">min. </s> <s xml:id="echoid-s15303" xml:space="preserve">6. </s> <s xml:id="echoid-s15304" xml:space="preserve">hoc eſt, horarum 15. </s> <s xml:id="echoid-s15305" xml:space="preserve">min. </s> <s xml:id="echoid-s15306" xml:space="preserve">4. </s> <s xml:id="echoid-s15307" xml:space="preserve">ut prius. </s> <s xml:id="echoid-s15308" xml:space="preserve">Sic quoque, <lb/>ſi poſterior aſcenſio dematur à priori, additis prius 360. </s> <s xml:id="echoid-s15309" xml:space="preserve">gr. </s> <s xml:id="echoid-s15310" xml:space="preserve">hoceſt, ex gr. </s> <s xml:id="echoid-s15311" xml:space="preserve">426. <lb/></s> <s xml:id="echoid-s15312" xml:space="preserve">min. </s> <s xml:id="echoid-s15313" xml:space="preserve">57. </s> <s xml:id="echoid-s15314" xml:space="preserve">habebitur arcus diurnus, Sole exiſtente in principio ♑, gr. </s> <s xml:id="echoid-s15315" xml:space="preserve">133. </s> <s xml:id="echoid-s15316" xml:space="preserve">min. </s> <s xml:id="echoid-s15317" xml:space="preserve">54. </s> <s xml:id="echoid-s15318" xml:space="preserve"><lb/>hoc eſt, horarum 8. </s> <s xml:id="echoid-s15319" xml:space="preserve">min. </s> <s xml:id="echoid-s15320" xml:space="preserve">56. </s> <s xml:id="echoid-s15321" xml:space="preserve">Ratio autem huius operationis manifeſta eſt. </s> <s xml:id="echoid-s15322" xml:space="preserve">Quo <lb/>niam enim illa medietas Zodiaci, quæ incipit à gradu Solis, terminaturque in <lb/>oppoſito gradu, aſcendit die propoſita ſupra Horizontem præciſe; </s> <s xml:id="echoid-s15323" xml:space="preserve">unde eius <lb/>aſcenſio dabit arcum diurnum, &</s> <s xml:id="echoid-s15324" xml:space="preserve">c.</s> <s xml:id="echoid-s15325" xml:space="preserve"/> </p> <div xml:id="echoid-div844" type="float" level="2" n="3"> <note position="right" xlink:label="note-443-01" xlink:href="note-443-01a" xml:space="preserve">Quantitas <lb/>diei in ſphę <lb/>ra obliqua <lb/>quo pacto <lb/>ex aſcẽſio-<lb/>ne obliqua <lb/>inueniatur</note> </div> <p> <s xml:id="echoid-s15326" xml:space="preserve"><emph style="sc">Est</emph> adhuc alius modus inueniendi arcus diurni. </s> <s xml:id="echoid-s15327" xml:space="preserve">Nam vt demonſtrat Ge-<lb/> <anchor type="note" xlink:label="note-443-02a" xlink:href="note-443-02"/> ber in opere Aſtronomico, & </s> <s xml:id="echoid-s15328" xml:space="preserve">nos demonſtrauimus propoſ. </s> <s xml:id="echoid-s15329" xml:space="preserve">34. </s> <s xml:id="echoid-s15330" xml:space="preserve">li. </s> <s xml:id="echoid-s15331" xml:space="preserve">1. </s> <s xml:id="echoid-s15332" xml:space="preserve">noſtræ Gno <lb/>monices. </s> <s xml:id="echoid-s15333" xml:space="preserve">Vt eſt ſinus complementi declinationis puncti Eclipticæ, quod Sol <lb/>occupat, ad ſinum totum, ita quoque eſt ſinus complementi latitudinis ortiuæ <lb/>eiuſdem puncti ad ſinum arcus ſemidiurni, Sole obtinente ſigna Auſtralia, uel <lb/>ad ſinũ arcus ſemino cturni, Sole in ſignis Borealibus exiſtente. </s> <s xml:id="echoid-s15334" xml:space="preserve">Vnde ſi iuxta <lb/>præceptũ regulæ proportionum, multiplicetur ſinus totus in ſinum cõplemen <lb/>ti latitudinis ortiuæ, & </s> <s xml:id="echoid-s15335" xml:space="preserve">productus numerus diuidatur per ſinum cõplementi <lb/>declinationis, habebitur ſinus arcus ſemidiurni, ſi Sol poſſidet ſigna Auſtralia, <lb/>uel ſinus arcus ſeminocturni, ſi idẽ in ſignis Borealibus commoratur. </s> <s xml:id="echoid-s15336" xml:space="preserve">EXEM-<lb/>PLVM. </s> <s xml:id="echoid-s15337" xml:space="preserve">Romæ, Sole exiſtente in principio ♑. </s> <s xml:id="echoid-s15338" xml:space="preserve">Declinatio Solis eſt gr. </s> <s xml:id="echoid-s15339" xml:space="preserve">23. </s> <s xml:id="echoid-s15340" xml:space="preserve">min. <lb/></s> <s xml:id="echoid-s15341" xml:space="preserve">30. </s> <s xml:id="echoid-s15342" xml:space="preserve">Latitudo ortiua grad. </s> <s xml:id="echoid-s15343" xml:space="preserve">32. </s> <s xml:id="echoid-s15344" xml:space="preserve">min. </s> <s xml:id="echoid-s15345" xml:space="preserve">27. </s> <s xml:id="echoid-s15346" xml:space="preserve">Multiplico ſinum totum, 100000. </s> <s xml:id="echoid-s15347" xml:space="preserve">in ſinũ <lb/>complementi latitudinis ortiuæ, nempe in 84386. </s> <s xml:id="echoid-s15348" xml:space="preserve">& </s> <s xml:id="echoid-s15349" xml:space="preserve">productum 8438600000. </s> <s xml:id="echoid-s15350" xml:space="preserve"><lb/>diuido per ſinum complemẽti declinationis, hoc eſt, per 91706. </s> <s xml:id="echoid-s15351" xml:space="preserve">& </s> <s xml:id="echoid-s15352" xml:space="preserve">exibit ſinus <lb/>arcus ſemidiurni 92018. </s> <s xml:id="echoid-s15353" xml:space="preserve">cui reſpondent gr. </s> <s xml:id="echoid-s15354" xml:space="preserve">66. </s> <s xml:id="echoid-s15355" xml:space="preserve">min. </s> <s xml:id="echoid-s15356" xml:space="preserve">57. </s> <s xml:id="echoid-s15357" xml:space="preserve">Eadem arte inuenietur <lb/>ſinus arcus ſeminocturni, Sole tenente principium ♋, 92018. </s> <s xml:id="echoid-s15358" xml:space="preserve">&</s> <s xml:id="echoid-s15359" xml:space="preserve">c.</s> <s xml:id="echoid-s15360" xml:space="preserve"/> </p> <div xml:id="echoid-div845" type="float" level="2" n="4"> <note position="right" xlink:label="note-443-02" xlink:href="note-443-02a" xml:space="preserve">Arcus ſemi <lb/>diurn’ quo <lb/>pacto ex ſi-<lb/>nubus ſup-<lb/>putetur.</note> </div> <p> <s xml:id="echoid-s15361" xml:space="preserve"><emph style="sc">Hinc</emph> perſpicuum eſt, qua ratione conſtruatur tabula continens arcus ſe-<lb/> <anchor type="note" xlink:label="note-443-03a" xlink:href="note-443-03"/> midiurnos. </s> <s xml:id="echoid-s15362" xml:space="preserve">Satis enim erit, ſi inueſtigentur arcus ſemidiurni unius Quadran-<lb/>tis Eclipticæ. </s> <s xml:id="echoid-s15363" xml:space="preserve">Hi enim ſubtracti ex ſemicirculo relin quunt arcus ſemidiurnos <lb/>Quadrantis oppoſiti: </s> <s xml:id="echoid-s15364" xml:space="preserve">At arcus hi ſemidiurni æquales ſunt collateralium Qua <lb/>drantum arcubus ſemidiurnis, ut ex ſuperioribus conſtat.</s> <s xml:id="echoid-s15365" xml:space="preserve"/> </p> <div xml:id="echoid-div846" type="float" level="2" n="5"> <note position="right" xlink:label="note-443-03" xlink:href="note-443-03a" xml:space="preserve">Qua arte ta <lb/>bula arcuũ <lb/>ſemidiurno <lb/>rum conſti-<lb/>tuatur.</note> </div> <p> <s xml:id="echoid-s15366" xml:space="preserve"><emph style="sc">Hoc</emph> ingenio compoſita eſt ſubſequens tabula continens arcus ſemidiur-<lb/>nos in horis, & </s> <s xml:id="echoid-s15367" xml:space="preserve">minutis per ternos gradus omnium ſignorũ, ad quamcunq; </s> <s xml:id="echoid-s15368" xml:space="preserve">ele <lb/>uationem poli, dummodo maior non fuerit quàm 56. </s> <s xml:id="echoid-s15369" xml:space="preserve">gr. </s> <s xml:id="echoid-s15370" xml:space="preserve">neque minor, quã 36. <lb/></s> <s xml:id="echoid-s15371" xml:space="preserve">grad. </s> <s xml:id="echoid-s15372" xml:space="preserve">Vnde cognito per aliquod inſtrumẽtum, in quo nam figno, & </s> <s xml:id="echoid-s15373" xml:space="preserve">gradu Sol <lb/>exiſtat quolibet die, facile cognoſcetur quantitas diei. </s> <s xml:id="echoid-s15374" xml:space="preserve">Quod ſi gradus Solis <lb/>præciſe non inuentus fuerit in ſequentis tabulæ ſiniſtro, uel dextro latere, eli-<lb/>cienda erit pars proportionalis, eo modo, ut iam ſæpe dictum eſt. </s> <s xml:id="echoid-s15375" xml:space="preserve">Ita cernis <lb/>Romæ, quando Sol eſt in gra. </s> <s xml:id="echoid-s15376" xml:space="preserve">27. </s> <s xml:id="echoid-s15377" xml:space="preserve">fere ♈, quod hoc tempore contingit die 18. </s> <s xml:id="echoid-s15378" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-443-04a" xlink:href="note-443-04"/> Aprilis, arcum ſemidiurnum continere horas 6. </s> <s xml:id="echoid-s15379" xml:space="preserve">min. </s> <s xml:id="echoid-s15380" xml:space="preserve">38.</s> <s xml:id="echoid-s15381" xml:space="preserve"/> </p> <div xml:id="echoid-div847" type="float" level="2" n="6"> <note position="right" xlink:label="note-443-04" xlink:href="note-443-04a" xml:space="preserve">Quomodo <lb/>ex arcu ſe-<lb/>midiurno <lb/>inueniatur <lb/>arcus ſemi-<lb/>nocturnus <lb/>& tempus <lb/>meridici <lb/>more Italo-<lb/>rum.</note> </div> <p> <s xml:id="echoid-s15382" xml:space="preserve">SI arcus ſemidiurnus in ſequenti tabula repertus ſubtrahatur ex 12. </s> <s xml:id="echoid-s15383" xml:space="preserve">horis, <lb/>relinquitur arcus ſeminocturnus: </s> <s xml:id="echoid-s15384" xml:space="preserve">Si uero ex 24. </s> <s xml:id="echoid-s15385" xml:space="preserve">horis, reliquæ horæ oſtendẽt <lb/>horam meridiei more Italorum, qui horas ab occaſu ſupputant. </s> <s xml:id="echoid-s15386" xml:space="preserve">Quod ſi arcus <lb/>diurnus integer ex 24. </s> <s xml:id="echoid-s15387" xml:space="preserve">dematur, remanebit hora ortus Solis more Italorum, <lb/>& </s> <s xml:id="echoid-s15388" xml:space="preserve">tota nox artificialis, à qua ſi iterum detrahatur arcus ſeminocturnus, relin-<lb/>querur tempus mediæ noctis. </s> <s xml:id="echoid-s15389" xml:space="preserve">Exempla in promptu quilibet habere poteſt.</s> <s xml:id="echoid-s15390" xml:space="preserve"/> </p> <pb o="408" file="444" n="445" rhead="Comment. in II. Cap. Sphæræ"/> </div> <div xml:id="echoid-div849" type="section" level="1" n="335"> <head xml:id="echoid-head346" xml:space="preserve">TABVLA TEMPORIS SE-<lb/>midiurni in ſignis borealibus.</head> <note position="right" xml:space="preserve"> <lb/> ## Poli # ## 36 # ## 37 # ## 38 # ## 39 # ## 40 # ## 41 # ## 42 # ## Altitudo ## G. # ## H.M. # ## H.M. # ## H.M. # ## H.M. # ## H.M. # ## H.M. # ## H.M. ♈ # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 30 # 3 # 6 # 3 # 6 # 4 # 6 # 4 # 6 # 4 # 6 # 4 # 6 # 4 # 6 # 4 # 27 # 6 # 6 # 7 # 6 # 7 # 6 # 8 # 6 # 8 # 6 # 8 # 6 # 8 # 6 # 9 # 24 # 9 # 6 # 10 # 6 # 11 # 6 # 12 # 6 # 12 # 6 # 12 # 6 # 12 # 6 # 13 # 21 # 12 # 6 # 14 # 6 # 14 # 6 # 15 # 6 # 15 # 6 # 16 # 6 # 17 # 6 # 17 # 18 # 15 # 6 # 17 # 6 # 18 # 6 # 18 # 6 # 19 # 6 # 20 # 6 # 21 # 6 # 21 # 15 # 18 # 6 # 21 # 6 # 22 # 6 # 22 # 9 # 23 # 6 # 24 # 6 # 23 # 6 # 26 # 12 # 21 # 6 # 24 # 6 # 25 # 6 # 26 # 6 # 27 # 6 # 28 # 6 # 29 # 6 # 30 # 9 # 24 # 6 # 27 # 6 # 28 # 6 # 30 # 9 # 31 # 6 # 32 # 6 # 33 # 6 # 34 # 6 # 27 # 6 # 31 # 6 # 32 # 6 # 33 # 6 # 34 # 6 # 36 # 6 # 37 # 6 # 38 # 3 ♉ # 0 # 6 # 34 # 6 # 35 # 6 # 37 # 6 # 38 # 6 # 39 # 6 # 41 # 6 # 42 # 0 # ♍ # 3 # 6 # 37 # 6 # 39 # 6 # 40 # 6 # 41 # 6 # 43 # 6 # 45 # 6 # 46 # 29 # 6 # 6 # 40 # 6 # 42 # 6 # 43 # 6 # 45 # 6 # 47 # 6 # 48 # 6 # 50 # 24 # 9 # 6 # 43 # 6 # 45 # 6 # 47 # 6 # 48 # 6 # 51 # 6 # 52 # 6 # 54 # 21 # 12 # 6 # 46 # 6 # 48 # 6 # 50 # 6 # 52 # 6 # 54 # 6 # 56 # 6 # 58 # 18 # 15 # 6 # 49 # 6 # 51 # 6 # 53 # 6 # 55 # 6 # 58 # 6 # 59 # 7 # 1 # 15 # 18 # 6 # 52 # 6 # 54 # 6 # 56 # 6 # 58 # 7 # 0 # 7 # 3 # 7 # 5 # 12 # 21 # 6 # 55 # 6 # 57 # 6 # 59 # 7 # 1 # 7 # 3 # 7 # 6 # 7 # 8 # 9 # 24 # 6 # 57 # 7 # 0 # 7 # 2 # 7 # 4 # 7 # 6 # 7 # 9 # 7 # 11 # 6 # 27 # 7 # 0 # 7 # 2 # 7 # 4 # 7 # 7 # 7 # 9 # 7 # 12 # 7 # 15 # 3 ♊ # 0 # 7 # 2 # 7 # 4 # 7 # 7 # 7 # 9 # 7 # 12 # 7 # 15 # 7 # 17 # 0 # ♌ # 3 # 7 # 4 # 7 # 7 # 7 # 9 # 7 # 12 # 7 # 14 # 7 # 17 # 7 # 20 # 27 # 6 # 7 # 6 # 7 # 9 # 7 # 12 # 7 # 14 # 7 # 17 # 7 # 19 # 7 # 23 # 24 # 9 # 7 # 8 # 7 # 10 # 7 # 13 # 7 # 16 # 7 # 19 # 7 # 22 # 7 # 25 # 21 # 12 # 7 # 9 # 7 # 12 # 7 # 15 # 7 # 17 # 7 # 20 # 7 # 23 # 7 # 27 # 18 # 15 # 7 # 11 # 7 # 13 # 7 # 16 # 7 # 19 # 7 # 22 # 7 # 25 # 7 # 28 # 15 # 18 # 7 # 12 # 7 # 14 # 7 # 17 # 7 # 20 # 7 # 24 # 7 # 26 # 7 # 30 # 12 # 21 # 7 # 13 # 7 # 15 # 7 # 18 # 7 # 21 # 7 # 25 # 7 # 27 # 7 # 31 # 9 # 24 # 7 # 13 # 7 # 26 # 7 # 19 # 7 # 22 # 7 # 25 # 7 # 28 # 7 # 32 # 6 # 27 # 7 # 14 # 7 # 16 # 7 # 19 # 7 # 22 # 7 # 25 # 7 # 29 # 7 # 32 # 3 # 30 # 7 # 15 # 7 # 17 # 7 # 19 # 7 # 22 # 7 # 26 # 7 # 30 # 7 # 32 # 0 # ♋ </note> <pb o="409" file="445" n="446" rhead="Iovn. de Sacro Boſco."/> </div> <div xml:id="echoid-div850" type="section" level="1" n="336"> <head xml:id="echoid-head347" xml:space="preserve">TABVLA TEMPORIS SE-<lb/>midiurni in ſignis Borealibus.</head> <note position="right" xml:space="preserve"> <lb/> ## Poli # ## 43 # ## 44 # ## 45 # ## 46 # ## 47 # ## 48 # ## 49 # ## Altitudo ## G. # ## H.M. # ## H.M. # ## H.M. # ## H.M. # ## H.M. # ## H.M. # ## H.M. ♈ # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 30 # 3 # 6 # 4 # 6 # 5 # 6 # 5 # 6 # 5 # 6 # 5 # 6 # 7 # 6 # 6 # 27 # 6 # 6 # 9 # 6 # 9 # 6 # 10 # 6 # 10 # 6 # 10 # 6 # 11 # 6 # 11 # 24 # 9 # 6 # 13 # 6 # 14 # 6 # 14 # 6 # 15 # 9 # 15 # 6 # 16 # 6 # 16 # 21 # 12 # 6 # 18 # 6 # 18 # 6 # 19 # 6 # 20 # 6 # 20 # 6 # 21 # 6 # 22 # 18 # 15 # 6 # 22 # 6 # 23 # 6 # 24 # 6 # 25 # 6 # 26 # 6 # 26 # 6 # 27 # 15 # 18 # 6 # 27 # 6 # 27 # 6 # 29 # 6 # 30 # 6 # 31 # 6 # 32 # 6 # 33 # 12 # 21 # 6 # 31 # 6 # 32 # 6 # 33 # 6 # 34 # 6 # 36 # 6 # 37 # 6 # 38 # 9 # 24 # 6 # 35 # 6 # 36 # 6 # 38 # 6 # 39 # 6 # 41 # 6 # 42 # 6 # 44 # 6 # 27 # 6 # 40 # 6 # 41 # 6 # 43 # 6 # 44 # 6 # 46 # 6 # 47 # 6 # 49 # 3 ♉ # 0 # 6 # 44 # 6 # 45 # 6 # 47 # 6 # 49 # 6 # 50 # 6 # 52 # 6 # 54 # 0 # ♓ # 3 # 6 # 48 # 6 # 50 # 6 # 51 # 6 # 53 # 6 # 55 # 6 # 57 # 6 # 58 # 27 # 6 # 6 # 52 # 6 # 54 # 6 # 56 # 6 # 57 # 7 # 0 # 7 # 2 # 7 # 4 # 24 # 9 # 6 # 56 # 6 # 58 # 7 # 0 # 7 # 2 # 7 # 5 # 7 # 7 # 7 # 9 # 21 # 12 # 7 # 0 # 7 # 2 # 7 # 4 # 7 # 7 # 7 # 9 # 7 # 12 # 7 # 15 # 18 # 15 # 7 # 4 # 7 # 6 # 7 # 8 # 7 # 11 # 7 # 13 # 7 # 17 # 7 # 19 # 15 # 18 # 7 # 7 # 7 # 10 # 7 # 12 # 7 # 15 # 7 # 18 # 7 # 21 # 7 # 24 # 12 # 21 # 7 # 11 # 7 # 13 # 7 # 16 # 7 # 19 # 7 # 22 # 7 # 25 # 7 # 28 # 9 # 24 # 7 # 14 # 7 # 17 # 7 # 20 # 7 # 23 # 7 # 26 # 7 # 29 # 7 # 32 # 6 # 27 # 7 # 17 # 7 # 20 # 7 # 23 # 7 # 26 # 7 # 29 # 7 # 33 # 7 # 36 # 3 ♊ # 0 # 7 # 20 # 7 # 23 # 7 # 26 # 7 # 30 # 7 # 33 # 7 # 36 # 7 # 40 # 0 # ♌ # 3 # 7 # 23 # 7 # 26 # 7 # 29 # 7 # 33 # 7 # 36 # 7 # 40 # 7 # 44 # 27 # 6 # 7 # 26 # 7 # 29 # 7 # 32 # 7 # 36 # 7 # 39 # 7 # 43 # 7 # 47 # 24 # 9 # 7 # 28 # 7 # 31 # 7 # 35 # 7 # 38 # 7 # 42 # 7 # 46 # 7 # 50 # 21 # 12 # 7 # 30 # 7 # 33 # 7 # 37 # 7 # 40 # 7 # 44 # 7 # 48 # 7 # 53 # 18 # 15 # 7 # 32 # 7 # 35 # 7 # 39 # 7 # 42 # 7 # 46 # 7 # 50 # 7 # 55 # 15 # 18 # 7 # 33 # 7 # 37 # 7 # 40 # 7 # 44 # 7 # 48 # 7 # 52 # 7 # 57 # 12 # 21 # 7 # 34 # 7 # 38 # 7 # 41 # 7 # 45 # 7 # 49 # 7 # 54 # 7 # 58 # 9 # 24 # 7 # 35 # 7 # 39 # 7 # 42 # 7 # 46 # 7 # 50 # 7 # 55 # 7 # 59 # 6 # 27 # 7 # 35 # 7 # 39 # 7 # 43 # 7 # 47 # 7 # 51 # 7 # 56 # 7 # 0 # 3 # 30 # 7 # 36 # 7 # 39 # 7 # 43 # 7 # 47 # 7 # 51 # 7 # 56 # 7 # 0 # 0 # ♋ </note> <pb o="410" file="446" n="447" rhead="Comment. in III. Cap. Sphæræ"/> </div> <div xml:id="echoid-div851" type="section" level="1" n="337"> <head xml:id="echoid-head348" xml:space="preserve">TABVLA TEMPORIS SE-<lb/>midiurni in ſignis Borealibus.</head> <note position="right" xml:space="preserve"> <lb/> ## Poli # ## 50 # ## 51 # ## 52 # ## 53 # ## 54 # ## 55 # ## 56 # ## Altitudo # G. # ## H.M. # ## H.M. # ## H.M. # ## H.M. # ## H.M. # ## H.M. # ## H.M. ♈ # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 30 # 3 # 6 # 6 # 6 # 6 # 6 # 6 # 6 # 6 # 6 # 7 # 6 # 7 # 6 # 7 # 27 # 6 # 6 # 11 # 6 # 12 # 6 # 12 # 6 # 13 # 6 # 13 # 6 # 14 # 6 # 14 # 24 # 9 # 6 # 17 # 6 # 18 # 6 # 18 # 6 # 19 # 6 # 20 # 6 # 20 # 6 # 21 # 21 # 12 # 6 # 23 # 6 # 24 # 6 # 24 # 6 # 25 # 6 # 26 # 6 # 27 # 6 # 28 # 18 # 15 # 6 # 28 # 6 # 29 # 6 # 31 # 6 # 32 # 6 # 33 # 6 # 34 # 6 # 35 # 15 # 18 # 6 # 34 # 6 # 35 # 6 # 37 # 6 # 38 # 6 # 39 # 6 # 41 # 6 # 42 # 12 # 21 # 6 # 40 # 6 # 41 # 6 # 43 # 6 # 44 # 6 # 46 # 6 # 48 # 6 # 49 # 9 # 24 # 6 # 45 # 6 # 47 # 6 # 49 # 6 # 50 # 6 # 52 # 6 # 54 # 6 # 56 # 6 # 27 # 6 # 51 # 6 # 53 # 6 # 55 # 6 # 57 # 6 # 59 # 7 # 1 # 7 # 3 # 3 ♉ # 0 # 6 # 56 # 6 # 58 # 7 # 0 # 7 # 3 # 7 # 5 # 7 # 8 # 7 # 10 # 0 # ♍ # 3 # 7 # 1 # 7 # 4 # 7 # 6 # 7 # 9 # 7 # 11 # 7 # 14 # 7 # 17 # 27 # 6 # 7 # 7 # 7 # 9 # 7 # 12 # 7 # 15 # 7 # 17 # 7 # 21 # 7 # 24 # 24 # 9 # 7 # 12 # 7 # 15 # 7 # 17 # 7 # 20 # 7 # 24 # 7 # 27 # 7 # 30 # 21 # 12 # 7 # 17 # 7 # 20 # 7 # 23 # 7 # 26 # 7 # 30 # 7 # 33 # 7 # 37 # 18 # 15 # 7 # 22 # 7 # 25 # 7 # 28 # 7 # 32 # 7 # 35 # 7 # 39 # 7 # 43 # 15 # 18 # 7 # 27 # 7 # 30 # 7 # 34 # 7 # 37 # 7 # 41 # 7 # 45 # 7 # 49 # 12 # 21 # 7 # 31 # 7 # 35 # 7 # 39 # 7 # 42 # 7 # 47 # 7 # 51 # 7 # 55 # 9 # 24 # 7 # 36 # 7 # 39 # 7 # 41 # 7 # 48 # 7 # 52 # 7 # 56 # 8 # 1 # 6 # 27 # 7 # 40 # 7 # 44 # 7 # 48 # 7 # 52 # 7 # 57 # 8 # 2 # 8 # 7 # 3 ♊ # 0 # 7 # 44 # 7 # 48 # 7 # 52 # 7 # 57 # 8 # 2 # 8 # 7 # 8 # 12 # 0 # ♌ # 3 # 7 # 48 # 7 # 52 # 7 # 56 # 8 # 1 # 8 # 6 # 8 # 12 # 8 # 17 # 27 # 6 # 7 # 51 # 7 # 56 # 8 # 0 # 8 # 5 # 8 # 10 # 8 # 16 # 8 # 22 # 24 # 9 # 7 # 54 # 7 # 59 # 8 # 4 # 8 # 9 # 8 # 14 # 8 # 20 # 8 # 26 # 21 # 12 # 7 # 57 # 8 # 2 # 8 # 7 # 8 # 12 # 8 # 17 # 8 # 23 # 8 # 30 # 18 # 15 # 7 # 59 # 8 # 4 # 8 # 9 # 8 # 15 # 8 # 20 # 8 # 26 # 8 # 33 # 15 # 18 # 8 # 1 # 8 # 6 # 8 # 11 # 8 # 17 # 8 # 23 # 8 # 29 # 8 # 36 # 12 # 21 # 8 # 3 # 8 # 8 # 8 # 13 # 8 # 19 # 8 # 25 # 8 # 31 # 8 # 38 # 9 # 24 # 8 # 4 # 8 # 9 # 8 # 14 # 8 # 20 # 8 # 26 # 8 # 32 # 8 # 39 # 6 # 27 # 8 # 4 # 8 # 10 # 8 # 15 # 8 # 21 # 8 # 27 # 8 # 33 # 8 # 40 # 3 # 30 # 8 # 5 # 8 # 10 # 8 # 15 # 8 # 22 # 8 # 27 # 8 # 34 # 8 # 40 # 0 # ♋ </note> <pb o="411" file="447" n="448" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div852" type="section" level="1" n="338"> <head xml:id="echoid-head349" xml:space="preserve">TABVLA TEMPORIS SE-<lb/>midiurni in ſignis Auſtrallbus.</head> <note position="right" xml:space="preserve"> <lb/> ## Poli # ## 36 # ## 37 # ## 38 # ## 39 # ## 40 # ## 41 # ## 42 # ## Altitudo # G. # ## H.M. # ## H.M. # ## H.M. # ## H.M. # ## H.M. # ## H.M. # ## H.M. ♎ # O # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 30 # 3 # 5 # 57 # 5 # 56 # 5 # 56 # 5 # 56 # 5 # 56 # 5 # 56 # 5 # 56 # 27 # 6 # 5 # 53 # 5 # 53 # 5 # 52 # 5 # 52 # 5 # 52 # 5 # 52 # 5 # 51 # 24 # 9 # 5 # 50 # 5 # 49 # 5 # 49 # 5 # 48 # 5 # 48 # 5 # 48 # 5 # 47 # 21 # 12 # 5 # 46 # 5 # 46 # 5 # 45 # 5 # 45 # 5 # 44 # 5 # 43 # 5 # 43 # 18 # 15 # 5 # 43 # 5 # 42 # 5 # 41 # 5 # 52 # 5 # 40 # 5 # 39 # 5 # 39 # 15 # 18 # 5 # 39 # 5 # 38 # 5 # 3 # 5 # 37 # 5 # 36 # 5 # 35 # 5 # 34 # 12 # 21 # 5 # 36 # 5 # 35 # 5 # 35 # 5 # 33 # 5 # 33 # 5 # 31 # 5 # 30 # 9 # 24 # 5 # 33 # 5 # 32 # 5 # 34 # 5 # 29 # 5 # 28 # 5 # 27 # 5 # 26 # 6 # 27 # 5 # 29 # 5 # 28 # 5 # 27 # 5 # 26 # 5 # 24 # 5 # 23 # 5 # 22 # 3 ♏ # 0 # 5 # 26 # 2 # 25 # 5 # 23 # 5 # 22 # 5 # 21 # 5 # 19 # 5 # 18 # 0 # 3 # 5 # 23 # 5 # 21 # 5 # 20 # 5 # 19 # 5 # 17 # 5 # 15 # 5 # 14 # 27 # 6 # 5 # 20 # 5 # 18 # 5 # 17 # 5 # 15 # 5 # 13 # 5 # 12 # 5 # 10 # 24 # 9 # 5 # 17 # 5 # 15 # 5 # 15 # 5 # 12 # 5 # 9 # 5 # 8 # 5 # 6 # 21 # 12 # 5 # 14 # 5 # 12 # 5 # 10 # 5 # 8 # 5 # 6 # 5 # 4 # 4 # 2 # 18 # 15 # 5 # 11 # 5 # 9 # 5 # 7 # 5 # 5 # 5 # 2 # 4 # 1 # 4 # 59 # 15 # 18 # 5 # 8 # 5 # 6 # 5 # 4 # 5 # 2 # 5 # 0 # 4 # 57 # 4 # 55 # 12 # 21 # 5 # 5 # 5 # 3 # 5 # 1 # 4 # 59 # 4 # 57 # 4 # 54 # 4 # 52 # 9 # 24 # 5 # 3 # 5 # 0 # 4 # 58 # 4 # 56 # 4 # 54 # 4 # 51 # 4 # 49 # 6 # 27 # 5 # 0 # 4 # 58 # 4 # 56 # 4 # 53 # 4 # 51 # 4 # 48 # 4 # 45 # 3 ♐ # O # 4 # 58 # 4 # 56 # 4 # 53 # 4 # 51 # 4 # 48 # 4 # 45 # 4 # 43 # 0 # ♒ # 3 # 4 # 56 # 4 # 53 # 4 # 51 # 4 # 48 # 4 # 46 # 4 # 43 # 4 # 40 # 27 # 6 # 4 # 54 # 4 # 52 # 4 # 49 # 4 # 46 # 4 # 43 # 4 # 41 # 4 # 37 # 24 # 9 # 4 # 52 # 4 # 50 # 4 # 47 # 4 # 44 # 4 # 41 # 4 # 38 # 4 # 35 # 21 # 12 # 4 # 51 # 4 # 48 # 4 # 45 # 4 # 43 # 4 # 40 # 4 # 37 # 4 # 33 # 18 # 15 # 4 # 49 # 4 # 47 # 4 # 44 # 4 # 41 # 4 # 38 # 4 # 35 # 4 # 32 # 15 # 18 # 4 # 48 # 4 # 46 # 4 # 43 # 4 # 40 # 4 # 37 # 4 # 34 # 4 # 30 # 12 # 21 # 4 # 47 # 4 # 45 # 4 # 42 # 4 # 39 # 4 # 36 # 4 # 33 # 4 # 29 # 9 # 24 # 4 # 47 # 4 # 44 # 4 # 41 # 4 # 38 # 4 # 35 # 4 # 32 # 4 # 28 # 6 # 27 # 4 # 46 # 4 # 44 # 4 # 41 # 4 # 38 # 4 # 35 # 4 # 31 # 4 # 28 # 3 # 30 # 4 # 46 # 6 # 43 # 4 # 41 # 4 # 38 # 4 # 34 # 4 # 30 # 4 # 28 # 0 </note> <pb o="412" file="448" n="449" rhead="Comment. in III. Cap. Sphæræ"/> </div> <div xml:id="echoid-div853" type="section" level="1" n="339"> <head xml:id="echoid-head350" xml:space="preserve">TABVLA TEMPORIS SE-<lb/>mdiurni in ſignis Auſtralibus.</head> <note position="right" xml:space="preserve"> <lb/> ## Poli # ## 43 # ## 44 # ## 45 # ## 46 # ## 47 # ## 48 # ## 49 # ## Altitudo # G. # ## H.M. # ## H.M. # ## H.M. # ## H.M. # ## H.M. # ## H.M. # ## H.M. ♎ # O # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 30 # 3 # 5 # 56 # 5 # 55 # 5 # 55 # 5 # 55 # 5 # 55 # 5 # 55 # 5 # 54 # 27 # 6 # 5 # 51 # 5 # 41 # 5 # 51 # 5 # 50 # 5 # 50 # 5 # 49 # 5 # 49 # 24 # 9 # 5 # 47 # 5 # 46 # 5 # 46 # 5 # 45 # 5 # 45 # 5 # 44 # 5 # 44 # 21 # 12 # 5 # 42 # 5 # 42 # 5 # 46 # 5 # 40 # 5 # 40 # 5 # 39 # 5 # 38 # 18 # 15 # 5 # 38 # 5 # 30 # 5 # 35 # 5 # 34 # 5 # 34 # 5 # 34 # 5 # 33 # 15 # 18 # 5 # 33 # 5 # 32 # 5 # 31 # 5 # 30 # 5 # 29 # 5 # 28 # 5 # 27 # 12 # 21 # 5 # 29 # 5 # 28 # 5 # 27 # 5 # 26 # 5 # 24 # 5 # 23 # 5 # 22 # 9 # 24 # 5 # 25 # 5 # 24 # 5 # 22 # 5 # 21 # 5 # 19 # 5 # 18 # 5 # 16 # 6 # 27 # 5 # 20 # 5 # 19 # 5 # 17 # 5 # 16 # 5 # 14 # 5 # 13 # 5 # 11 # 3 ♏ # 0 # 5 # 16 # 5 # 15 # 5 # 13 # 5 # 11 # 5 # 10 # 5 # 8 # 5 # 6 # 0 # 3 # 5 # 12 # 5 # 10 # 5 # 9 # 5 # 7 # 5 # 5 # 5 # 3 # 5 # 1 # 27 # 6 # 5 # 8 # 5 # 6 # 5 # 4 # 5 # 3 # 5 # 0 # 4 # 58 # 4 # 55 # 24 # 9 # 5 # 4 # 5 # 2 # 5 # 0 # 4 # 58 # 4 # 55 # 4 # 53 # 4 # 51 # 21 # 12 # 5 # 0 # 4 # 58 # 4 # 56 # 4 # 53 # 4 # 51 # 4 # 48 # 4 # 45 # 18 # 15 # 4 # 56 # 4 # 54 # 4 # 52 # 4 # 49 # 4 # 47 # 4 # 43 # 4 # 41 # 15 # 18 # 4 # 53 # 4 # 50 # 4 # 48 # 4 # 45 # 4 # 42 # 4 # 39 # 4 # 36 # 12 # 21 # 4 # 49 # 4 # 47 # 4 # 44 # 4 # 41 # 4 # 38 # 4 # 35 # 4 # 32 # 9 # 24 # 4 # 46 # 4 # 43 # 4 # 40 # 4 # 37 # 4 # 34 # 4 # 32 # 4 # 28 # 6 # 27 # 4 # 43 # 4 # 4P # 4 # 37 # 4 # 34 # 4 # 31 # 4 # 27 # 4 # 24 # 3 ♐ # 0 # 4 # 40 # 4 # 37 # 4 # 34 # 4 # 30 # 4 # 27 # 4 # 24 # 4 # 20 # 0 # ♒ # 3 # 4 # 37 # 4 # 34 # 4 # 31 # 4 # 27 # 4 # 24 # 4 # 21 # 4 # 16 # 27 # 6 # 4 # 34 # 4 # 31 # 3 # 28 # 4 # 24 # 4 # 21 # 4 # 17 # 4 # 13 # 24 # 9 # 4 # 32 # 4 # 29 # 4 # 25 # 4 # 22 # 4 # 18 # 4 # 14 # 4 # 10 # 21 # 12 # 4 # 30 # 4 # 37 # 4 # 23 # 4 # 20 # 4 # 16 # 4 # 12 # 4 # 7 # 18 # 15 # 4 # 28 # 4 # 25 # 4 # 21 # 4 # 18 # 4 # 14 # 4 # 10 # 4 # 5 # 15 # 18 # 4 # 27 # 4 # 23 # 4 # 20 # 4 # 16 # 4 # 12 # 4 # 8 # 4 # 3 # 12 # 21 # 4 # 26 # 4 # 22 # 4 # 18 # 4 # 15 # 4 # 11 # 4 # 6 # 4 # 2 # 9 # 24 # 4 # 24 # 4 # 21 # 4 # 18 # 4 # 14 # 4 # 10 # 4 # 1 # 4 # 1 # 6 # 27 # 4 # 25 # 4 # 21 # 4 # 17 # 4 # 13 # 4 # 9 # 4 # 0 # 4 # 0 # 3 # 30 # 4 # 25 # 4 # 21 # 4 # 17 # 4 # 13 # 4 # 9 # 4 # 0 # 4 # 0 # 0 # ♑ </note> <pb o="413" file="449" n="450" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div854" type="section" level="1" n="340"> <head xml:id="echoid-head351" xml:space="preserve">TABVLA TEMPORIS SE-<lb/>midiurni in ſignis Auſtralibus.</head> <note position="right" xml:space="preserve"> <lb/> ## Poli # ## 50 # ## 51 # ## 52 # ## 53 # ## 54 # ## 55 # ## 56 # ## Altitudo # G. # ## H.M. # ## H.M. # ## H.M. # ## H.M. # ## H.M. # ## H.M. # ## H.M. ♎ # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 30 # 3 # 5 # 54 # 5 # 54 # 5 # 54 # 5 # 54 # 5 # 53 # 5 # 53 # 5 # 53 # 27 # 6 # 5 # 49 # 5 # 48 # 5 # 48 # 5 # 47 # 5 # 47 # 5 # 46 # 5 # 46 # 24 # 9 # 5 # 43 # 5 # 42 # 5 # 42 # 5 # 41 # 5 # 40 # 5 # 40 # 5 # 39 # 21 # 12 # 5 # 37 # 5 # 36 # 5 # 36 # 5 # 35 # 5 # 34 # 5 # 33 # 5 # 32 # 18 # 15 # 5 # 32 # 5 # 31 # 5 # 29 # 5 # 28 # 5 # 27 # 5 # 26 # 5 # 25 # 15 # 18 # 5 # 26 # 5 # 25 # 5 # 23 # 5 # 22 # 5 # 21 # 5 # 19 # 5 # 18 # 12 # 21 # 5 # 20 # 5 # 19 # 5 # 17 # 5 # 16 # 5 # 14 # 5 # 12 # 5 # 11 # 9 # 24 # 5 # 15 # 5 # 13 # 5 # 11 # 5 # 10 # 5 # 8 # 5 # 6 # 5 # 4 # 6 # 27 # 5 # 9 # 5 # 7 # 5 # 5 # 5 # 3 # 5 # 1 # 4 # 59 # 4 # 57 # 3 ♏ # 0 # 5 # 4 # 5 # 2 # 5 # 0 # 4 # 57 # 4 # 55 # 4 # 52 # 4 # 50 # 0 # ♓ # 3 # 4 # 59 # 4 # 56 # 4 # 54 # 4 # 51 # 4 # 49 # 4 # 49 # 4 # 43 # 27 # 6 # 4 # 53 # 4 # 51 # 4 # 48 # 4 # 45 # 4 # 43 # 4 # 39 # 4 # 36 # 24 # 9 # 4 # 48 # 4 # 45 # 4 # 43 # 4 # 40 # 4 # 36 # 4 # 33 # 4 # 30 # 21 # 12 # 4 # 43 # 4 # 40 # 4 # 37 # 4 # 34 # 4 # 30 # 4 # 27 # 4 # 23 # 18 # 15 # 4 # 38 # 4 # 35 # 4 # 32 # 4 # 28 # 4 # 25 # 4 # 21 # 4 # 17 # 15 # 18 # 4 # 33 # 4 # 30 # 4 # 26 # 4 # 23 # 4 # 19 # 4 # 15 # 4 # 11 # 12 # 21 # 4 # 29 # 4 # 25 # 4 # 21 # 4 # 18 # 4 # 13 # 4 # 9 # 4 # 5 # 9 # 24 # 4 # 24 # 4 # 21 # 4 # 17 # 4 # 12 # 4 # 8 # 4 # 4 # 3 # 59 # 6 # 27 # 4 # 20 # 4 # 16 # 4 # 12 # 4 # 8 # 4 # 3 # 3 # 5 # 3 # 53 # 3 ♐ # 0 # 4 # 16 # 4 # 12 # 4 # 8 # 4 # 3 # 3 # 58 # 3 # 5 # 3 # 48 # 0 # ♒ # 3 # 4 # 12 # 4 # 8 # 4 # 4 # 3 # 59 # 3 # 54 # 3 # 48 # 3 # 43 # 27 # 6 # 4 # 9 # 4 # 4 # 4 # 0 # 3 # 50 # 3 # 50 # 3 # 44 # 3 # 38 # 24 # 9 # 4 # 6 # 4 # 1 # 3 # 56 # 3 # 46 # 3 # 46 # 3 # 40 # 3 # 34 # 21 # 12 # 4 # 3 # 3 # 58 # 3 # 53 # 3 # 43 # 3 # 43 # 3 # 37 # 3 # 30 # 18 # 15 # 4 # 1 # 3 # 56 # 3 # 51 # 3 # 40 # 3 # 40 # 3 # 34 # 3 # 27 # 15 # 18 # 3 # 59 # 3 # 54 # 3 # 49 # 3 # 37 # 3 # 37 # 3 # 31 # 3 # 24 # 12 # 21 # 3 # 57 # 3 # 52 # 3 # 47 # 3 # 35 # 3 # 35 # 3 # 29 # 3 # 22 # 9 # 24 # 3 # 56 # 3 # 51 # 3 # 46 # 3 # 40 # 3 # 34 # 3 # 28 # 3 # 21 # 6 # 27 # 3 # 56 # 3 # 50 # 3 # 45 # 3 # 39 # 3 # 33 # 3 # 27 # 3 # 20 # 3 # 30 # 3 # 55 # 3 # 50 # 3 # 45 # 3 # 38 # 3 # 33 # 3 # 26 # 3 # 20 # 0 # ♑ </note> <pb o="414" file="450" n="451" rhead="Comment. in I. Cap. Sphæræ"/> </div> <div xml:id="echoid-div855" type="section" level="1" n="341"> <head xml:id="echoid-head352" style="it" xml:space="preserve">DE DIVERSITATE DIERVM ET NOCTIVM <lb/>artificialium per omnia terræ lo@a.</head> <p style="it"> <s xml:id="echoid-s15391" xml:space="preserve">NOTANTVR autem, quod illis, quorum Zenith eſt <lb/> <anchor type="note" xlink:label="note-450-01a" xlink:href="note-450-01"/> in Aequinoctiali circulo, Sol bis in anno tranſit per Ze <lb/>nith capitis eorum, ſcilicet, quando eſt in principio A-<lb/>rietis, & </s> <s xml:id="echoid-s15392" xml:space="preserve">in principio Libræ. </s> <s xml:id="echoid-s15393" xml:space="preserve">Et tunc ſunt illis duo al-<lb/>ta ſolſtitia, quoniam Sol directe tranſit ſupra capita <lb/>eorum. </s> <s xml:id="echoid-s15394" xml:space="preserve">Sunt iterum illis duo ima ſolſtitia, quando eſt <lb/>in primis punctis Cancri, & </s> <s xml:id="echoid-s15395" xml:space="preserve">Capricorni, & </s> <s xml:id="echoid-s15396" xml:space="preserve">dicuntur <lb/>ima, quia tunc Sol maxime remouetur à Zenith capitis eorum. </s> <s xml:id="echoid-s15397" xml:space="preserve">Vnde ex <lb/>prædictis patet, cum ſemper habeant Aequinoctium, in anno quatuor habe <lb/>bunt ſolſtitia, duo alta, & </s> <s xml:id="echoid-s15398" xml:space="preserve">duo ima. </s> <s xml:id="echoid-s15399" xml:space="preserve">Patet etiam, quod duas habent æſtates, <lb/>Sole ſcilicet exiſtente in alterutro punctorum Aequinoctialium, uel prope. <lb/></s> <s xml:id="echoid-s15400" xml:space="preserve">Duas etiam habent hyemes, ſcilicet Sole exiſtente in primis punctis Cãcri, <lb/>& </s> <s xml:id="echoid-s15401" xml:space="preserve">Capricorni, uel prope. </s> <s xml:id="echoid-s15402" xml:space="preserve">Et hoc eſt, quod dicit Alphraganus, quod æſtas, et <lb/>hyems, ſcilicet noſtræ, ſunt illis unius, & </s> <s xml:id="echoid-s15403" xml:space="preserve">eiuſdem complexionis. </s> <s xml:id="echoid-s15404" xml:space="preserve">quoniam <lb/>duo tempora, quæ ſunt nobis æſtas, & </s> <s xml:id="echoid-s15405" xml:space="preserve">hyems, ſunt illis duę hyemes, unde <lb/>ex illis uerſuum Lucani patet expoſitio.</s> <s xml:id="echoid-s15406" xml:space="preserve"/> </p> <div xml:id="echoid-div855" type="float" level="2" n="1"> <note position="left" xlink:label="note-450-01" xlink:href="note-450-01a" xml:space="preserve">Proprieta-<lb/>tes eorum, <lb/>quorum Ze <lb/>nith in æꝗ-<lb/>noctiali cir <lb/>culo eſt.</note> </div> <p> <s xml:id="echoid-s15407" xml:space="preserve">Deprenſum eſt hunc eſſe locum, qua circulus alti</s> </p> <p> <s xml:id="echoid-s15408" xml:space="preserve">Solſtitij medium ſignorum percutit orbem.</s> <s xml:id="echoid-s15409" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s15410" xml:space="preserve">Ibi enim appellat Lucanus circulum alti Solſtitij Aequinoctialem, in <lb/>quo contingunt dua alta ſolſtitia in Aequiuoctiali exiſtentibus. </s> <s xml:id="echoid-s15411" xml:space="preserve">Orbem <lb/>ſignorum appellat Zodiacum, quem medium, ideſt, mediatum, hoc eſt, di-<lb/>uiſum in duo media, Aequinoctialis percutit, ideſt, diuidit. </s> <s xml:id="echoid-s15412" xml:space="preserve">Illis etiam in an <lb/>no contingit habere quatuor umbras. </s> <s xml:id="echoid-s15413" xml:space="preserve">Cum enim Sol eſt in alterutro pun-<lb/>ctorum Aequinoctialium, tunc mane iacitur umbra eorum uerſus Occiden <lb/>tem, ueſpere uero è conuerſo: </s> <s xml:id="echoid-s15414" xml:space="preserve">In meridie uero eſt illis umbra perpendicula-<lb/>ris, cum Sol ſit ſupra caput eorum. </s> <s xml:id="echoid-s15415" xml:space="preserve">Cum autem Sol eſt in ſignis Septentrio <lb/>nalibus, tunc iacitur umbra eorum uerſus Auſtrum: </s> <s xml:id="echoid-s15416" xml:space="preserve">Quando eſt in Au-<lb/>ſtralibus, tunc iacitur uerſus Septentrionem. </s> <s xml:id="echoid-s15417" xml:space="preserve">Illis autem oriuntur, & </s> <s xml:id="echoid-s15418" xml:space="preserve">oc-<lb/>cidunt ſtellæ, quę ſunt iuxta polos, ſicut & </s> <s xml:id="echoid-s15419" xml:space="preserve">quibuſdam alijs habitantibus <lb/>circa Aequinoctialem. </s> <s xml:id="echoid-s15420" xml:space="preserve">Vnde Lucanus ſic inquit.</s> <s xml:id="echoid-s15421" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15422" xml:space="preserve">Tunc furor extremos mouit Romanus Horeſtas.</s> <s xml:id="echoid-s15423" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15424" xml:space="preserve">Carmanosq́ue duces, quorum iam flexus in Auſtrum</s> </p> <p> <s xml:id="echoid-s15425" xml:space="preserve">Aether non totam, mergi tamen aſpicit Arcton</s> </p> <p> <s xml:id="echoid-s15426" xml:space="preserve">Lucet & </s> <s xml:id="echoid-s15427" xml:space="preserve">exigua uelox ubi nocte Bootes.</s> <s xml:id="echoid-s15428" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s15429" xml:space="preserve">Ergo mergitur, & </s> <s xml:id="echoid-s15430" xml:space="preserve">parum lucet. </s> <s xml:id="echoid-s15431" xml:space="preserve">Item Ouidius de eadem ſtella.</s> <s xml:id="echoid-s15432" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15433" xml:space="preserve">Tingitur Oceano cuſtos Erimanthidos vrſæ,</s> </p> <p> <s xml:id="echoid-s15434" xml:space="preserve">Aequoreaſq́ue ſuo ſidere turbat aquas.</s> <s xml:id="echoid-s15435" xml:space="preserve"/> </p> <pb o="415" file="451" n="452" rhead="Ioan. de Sacro Boſco."/> <p style="it"> <s xml:id="echoid-s15436" xml:space="preserve">In ſitu autem noſtro nunquam occidunt illœ ſtellę. </s> <s xml:id="echoid-s15437" xml:space="preserve">Vnde Virgilius.</s> <s xml:id="echoid-s15438" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15439" xml:space="preserve">Hic vertex nobis ſemper ſublimis, at illum <lb/>Sub pedibus ſtyx atra videt, maneſq́; </s> <s xml:id="echoid-s15440" xml:space="preserve">profundi.</s> <s xml:id="echoid-s15441" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s15442" xml:space="preserve">Et Lucanus</s> </p> <p> <s xml:id="echoid-s15443" xml:space="preserve">Axis inocciduus gemina clariſsimus Arcto.</s> <s xml:id="echoid-s15444" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s15445" xml:space="preserve">Item Virgilius in Georg. </s> <s xml:id="echoid-s15446" xml:space="preserve">ſic inquit.</s> <s xml:id="echoid-s15447" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15448" xml:space="preserve">Arctos O ceani metuentes æquore tingi.</s> <s xml:id="echoid-s15449" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div857" type="section" level="1" n="342"> <head xml:id="echoid-head353" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s15450" xml:space="preserve"><emph style="sc">AGit</emph> in tertia hac capitis parte de quibuſdam ptoprietatibus eo-<lb/> <anchor type="note" xlink:label="note-451-01a" xlink:href="note-451-01"/> rum, qui in uariis terræ locis habitant, nec non de quibuſdam di-<lb/>uerſitatibus dierum, ac noctium artificialium. </s> <s xml:id="echoid-s15451" xml:space="preserve">Sunt autem ſeptem <lb/>loca terræ, quorum proprietates explicat, quoniam ſeptem modis <lb/>uariari poteſt uertex capitis, procedendo ab Aequatore uerſus al-<lb/>terutrum polorum. </s> <s xml:id="echoid-s15452" xml:space="preserve">Primus locus eſt eorum, quorum Zenith in Aequinoctia-<lb/>li circulo conſtituitur. </s> <s xml:id="echoid-s15453" xml:space="preserve">Atque his ſex proprietatibus aſsignar.</s> <s xml:id="echoid-s15454" xml:space="preserve"/> </p> <div xml:id="echoid-div857" type="float" level="2" n="1"> <note position="right" xlink:label="note-451-01" xlink:href="note-451-01a" xml:space="preserve">Septem mo <lb/>dis variari <lb/>põt Zenith <lb/>ab Aequato <lb/>re verſus al <lb/>terutrũ po-<lb/>lorum.</note> </div> <p> <s xml:id="echoid-s15455" xml:space="preserve">I. </s> <s xml:id="echoid-s15456" xml:space="preserve">Bis in anno tranſit Sol per eorum Zenith, ſemel in principio ♈, exiſtens, <lb/>& </s> <s xml:id="echoid-s15457" xml:space="preserve">iterum in principio ♎.</s> <s xml:id="echoid-s15458" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15459" xml:space="preserve">II. </s> <s xml:id="echoid-s15460" xml:space="preserve">Habent quatuor Solſtitia in anno, duo alta, quando uidelicet Sol eſt <lb/>in Aequino ctiali circulo, quia tunc maxime ad eorum Zenith accedit Sol, ſi-<lb/>cut & </s> <s xml:id="echoid-s15461" xml:space="preserve">nobis Solſtitium altum appellari ſolet Solſtitium æſtiuum, quod al-<lb/>tiſſimus tunc Sol ſit in meridie ſupra Horizontem: </s> <s xml:id="echoid-s15462" xml:space="preserve">Habent quoque duo Sol-<lb/>ſtitiàima, quando uidelicet Sol eſt in Tropicis, quoniam tunc maxime re-<lb/>mouetur Sol ab eorum uertice capitis, ſicut & </s> <s xml:id="echoid-s15463" xml:space="preserve">nos ſolemus Solſtitium bru-<lb/>male appellare imum, quia longiſſime tunc à nobis Sol recedit. </s> <s xml:id="echoid-s15464" xml:space="preserve">Quod ſi <lb/>proprie ſumamus Solſtitiu@, nempe pro conuerſione Solis, cum Sol non <lb/>uidetur mutare declinationem ſuam ab Aequatore, habebunt tantum duo <lb/>Solſtitia ima, Sole exiſtente in Tropicis, quorum unum nobis altum eſt, & </s> <s xml:id="echoid-s15465" xml:space="preserve"><lb/>alterum imum. </s> <s xml:id="echoid-s15466" xml:space="preserve">Carmina autem Lucani adducta ad comprobandum duo alta <lb/>Solſtitia non ſunt ad rem, cum circulus alti Solſtitiiu ocetur à Lucano Tro-<lb/>picus ♋, ut ſupra diximus, cum de ortu & </s> <s xml:id="echoid-s15467" xml:space="preserve">occaſu ſignorum in ſphæra recta <lb/>agerem us.</s> <s xml:id="echoid-s15468" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15469" xml:space="preserve">III. </s> <s xml:id="echoid-s15470" xml:space="preserve">Habent perpetuo Aequin octium.</s> <s xml:id="echoid-s15471" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15472" xml:space="preserve">IIII. </s> <s xml:id="echoid-s15473" xml:space="preserve">Habent duas ęſtates in anno, totidemq́. </s> <s xml:id="echoid-s15474" xml:space="preserve">hyemes, ſi uidelicet ęſtas <lb/>dicat exceſſum caloris, hyems uero caloris remiſsienem; </s> <s xml:id="echoid-s15475" xml:space="preserve">Aeſtates quidem, So-<lb/>le exiſtente in Aequatore, hyemes uero, eodem tenente puncta Tropica. </s> <s xml:id="echoid-s15476" xml:space="preserve">Vn-<lb/>de inquit Alphraganus diff. </s> <s xml:id="echoid-s15477" xml:space="preserve">6. </s> <s xml:id="echoid-s15478" xml:space="preserve">quod noſtra æſtas, & </s> <s xml:id="echoid-s15479" xml:space="preserve">hyems ſunt illius unius eiuſ <lb/>demq. </s> <s xml:id="echoid-s15480" xml:space="preserve">complexionis, quia noſtra æſtas eſt illis quoque hyems. </s> <s xml:id="echoid-s15481" xml:space="preserve">Eadem ratione <lb/>poſſemus dicere, quod habent duplex Ver, & </s> <s xml:id="echoid-s15482" xml:space="preserve">duplicem Autumnum, in tempo <lb/>ribus nimirum mediis inter ęſtates, at que hyemes.</s> <s xml:id="echoid-s15483" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15484" xml:space="preserve">V. </s> <s xml:id="echoid-s15485" xml:space="preserve">habent quatuor differentias umbrarum, unam occidentẽ uerſus, quan-<lb/>do Sol exoritur; </s> <s xml:id="echoid-s15486" xml:space="preserve">alteram orientem uerſus occidente Sole; </s> <s xml:id="echoid-s15487" xml:space="preserve">tertiam in meridie <lb/>uerſus Auſtrum, dum Sol eſt in ſignis Septentrionalibus; </s> <s xml:id="echoid-s15488" xml:space="preserve">quartam in meridie <lb/>Septentrionem uerſus, Sole tenente ſigna Auſtralis: </s> <s xml:id="echoid-s15489" xml:space="preserve">Sole uero exiſtente in <lb/>Æquatore, nullam efficiunt umbram in meridie.</s> <s xml:id="echoid-s15490" xml:space="preserve"/> </p> <pb o="416" file="452" n="453" rhead="Comment. in III. Cap. Sphæræ"/> <p> <s xml:id="echoid-s15491" xml:space="preserve">VI. </s> <s xml:id="echoid-s15492" xml:space="preserve">Omnes ſtellæ, & </s> <s xml:id="echoid-s15493" xml:space="preserve">omnia puncta cœli, polis exceptis, oriuntur ipfis, at-<lb/>que occidunt, quia videlicet eorum Horizon ſecat omnes parallelos deſcri-<lb/>ptos ad primum motum, cum per polos ipſorum incedat. </s> <s xml:id="echoid-s15494" xml:space="preserve">Hæc omnia perſpi-<lb/>ſpicua ſunt in ſphæra materiali. </s> <s xml:id="echoid-s15495" xml:space="preserve">Carmina autem, quæ ex Poetis ad hanc re@ <lb/>adducit, quantam vim habeant, & </s> <s xml:id="echoid-s15496" xml:space="preserve">quàm apte, & </s> <s xml:id="echoid-s15497" xml:space="preserve">congruenter huc afferantur, <lb/>aliorum ſit iudicium.</s> <s xml:id="echoid-s15498" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s15499" xml:space="preserve"><emph style="sc">ILLIS</emph> autem, quorum Zenith eſt inter Aequinoctialem, & </s> <s xml:id="echoid-s15500" xml:space="preserve">Tropi-<lb/> <anchor type="note" xlink:label="note-452-01a" xlink:href="note-452-01"/> cum Cancri, contingit bis in anno, quod Sol tranſit per Zenith capitis eo-<lb/>rum: </s> <s xml:id="echoid-s15501" xml:space="preserve">Quod ſic patet. </s> <s xml:id="echoid-s15502" xml:space="preserve">Intelligatur circulus parallelus Aequinoctiali tran-<lb/>ſiens per Zenith capitis eorum; </s> <s xml:id="echoid-s15503" xml:space="preserve">Ille circulus interſecabit Zodiacum in <lb/>duobus locis æquidiſtantibus à principio Cancri. </s> <s xml:id="echoid-s15504" xml:space="preserve">Sol igitur exiſtens in il-<lb/>lis duobus punctis tranſit per Zenith capitis eorum. </s> <s xml:id="echoid-s15505" xml:space="preserve">Vnde duas habent <lb/>æſtates, & </s> <s xml:id="echoid-s15506" xml:space="preserve">duas hyemes; </s> <s xml:id="echoid-s15507" xml:space="preserve">quatuor ſolſtitia, & </s> <s xml:id="echoid-s15508" xml:space="preserve">quatuor umbras, ſicut exi-<lb/>ſtentes ſub Aequinoctiali. </s> <s xml:id="echoid-s15509" xml:space="preserve">Et in tali ſitu dicunt quidam Arabiam eſſe. <lb/></s> <s xml:id="echoid-s15510" xml:space="preserve">Vnde Lucanus loquens de Arabibus uenientibus Romam in auxilium <lb/>Pompeio, inquit.</s> <s xml:id="echoid-s15511" xml:space="preserve"/> </p> <div xml:id="echoid-div858" type="float" level="2" n="2"> <note position="left" xlink:label="note-452-01" xlink:href="note-452-01a" xml:space="preserve">Proprieta-<lb/>tes eorũ, ꝗ <lb/>Zenith ha-<lb/>benr inter <lb/>Aequatorẽ <lb/>& @ropicũ <lb/>Cancri.</note> </div> <p> <s xml:id="echoid-s15512" xml:space="preserve">Ignotum vobis Arabes veniſtis in orbem,</s> </p> <p> <s xml:id="echoid-s15513" xml:space="preserve">Vmbras mirati nemorum non ire ſiniſtras.</s> <s xml:id="echoid-s15514" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s15515" xml:space="preserve">Quoniam in partibus ſuis quandoque erant illis umbræ dextræ, quandoque <lb/>finiſtr æ, quandoque perpendiculares, quandoque orientales, quandoque oc-<lb/>eidentalis: </s> <s xml:id="echoid-s15516" xml:space="preserve">Sed quando uenerunt Romam citra Tropicum Cancri, tunc ſem-<lb/>per habebant umbras ſeptentrionales.</s> <s xml:id="echoid-s15517" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div860" type="section" level="1" n="343"> <head xml:id="echoid-head354" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s15518" xml:space="preserve"><emph style="sc">Secvndvs</emph> locus eſt eorum, quorum Zenith eſt inter Aequinoctialem <lb/>circulum, & </s> <s xml:id="echoid-s15519" xml:space="preserve">Tropicum Cancri. </s> <s xml:id="echoid-s15520" xml:space="preserve">His igitur quatuor proprietates tribuit.</s> <s xml:id="echoid-s15521" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15522" xml:space="preserve">I. </s> <s xml:id="echoid-s15523" xml:space="preserve">Bis in anno habent Solem ſupra Zenith capitis.</s> <s xml:id="echoid-s15524" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15525" xml:space="preserve">II. </s> <s xml:id="echoid-s15526" xml:space="preserve">Duas habent æſtates, & </s> <s xml:id="echoid-s15527" xml:space="preserve">duas hyemes, ſed vna hyems frigidior exiſtit, <lb/>quam altera, ea nimirum, in qua magis à vertice illorũ Sol remouetur, quod <lb/>ſit, Sole exiſtente in ♑.</s> <s xml:id="echoid-s15528" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15529" xml:space="preserve">III. </s> <s xml:id="echoid-s15530" xml:space="preserve">Quatuor etiam ſolſtitia habent, duo nimirum alta, & </s> <s xml:id="echoid-s15531" xml:space="preserve">duo ima.</s> <s xml:id="echoid-s15532" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15533" xml:space="preserve">IIII. </s> <s xml:id="echoid-s15534" xml:space="preserve">Habent quoque quadruplicem vmbram, ſicutij, qui ſub Aequatore <lb/>degunt. </s> <s xml:id="echoid-s15535" xml:space="preserve">His adde, quod habent inæqualitatem dierum, ac noctium per to-<lb/>tum annum, exceptis diebus æquinoctij tempore. </s> <s xml:id="echoid-s15536" xml:space="preserve">Item quòd non omnia aſtra, <lb/>ſeu puncta cœli ipſis oriuntur, & </s> <s xml:id="echoid-s15537" xml:space="preserve">occidunt. </s> <s xml:id="echoid-s15538" xml:space="preserve">Vtclare cernitur in ſphæra ma-<lb/>teriali. </s> <s xml:id="echoid-s15539" xml:space="preserve">Quod autem dicit, Arabiam ſecundum quoſdam in hoc ſitu colloca-<lb/>ri, intelligendum eſt de Arabia Felici. </s> <s xml:id="echoid-s15540" xml:space="preserve">Hæc enim ſecundum maiorem par-<lb/>tem inter Aequatorem, & </s> <s xml:id="echoid-s15541" xml:space="preserve">Tropicum ♋, ſita eſt.</s> <s xml:id="echoid-s15542" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s15543" xml:space="preserve"><emph style="sc">ILLIS</emph> ſiquidem, quorũ Zenith eſt in Tropico Cancri, cõtingit, quòd ſe-<lb/> <anchor type="note" xlink:label="note-452-02a" xlink:href="note-452-02"/> mel in anno tranſit Sol per Zenith capitis eorum, ſcilicet, quando eſt in pri-<lb/>mo puncto Cancri, & </s> <s xml:id="echoid-s15544" xml:space="preserve">tunc in una hora diei unius totius anni eſt illis umbra <lb/>perpendicularis. </s> <s xml:id="echoid-s15545" xml:space="preserve">In tali ſitu dicitur eſſe Syene ciuitas. </s> <s xml:id="echoid-s15546" xml:space="preserve">Vnde Lucanus.</s> <s xml:id="echoid-s15547" xml:space="preserve"/> </p> <div xml:id="echoid-div860" type="float" level="2" n="1"> <note position="left" xlink:label="note-452-02" xlink:href="note-452-02a" xml:space="preserve">Proprieta-<lb/>tes eorũ, ꝗ <lb/>Zenith ha-<lb/>bẽt in Tro-<lb/>pico Cãcri.</note> </div> <pb o="417" file="453" n="454" rhead="Ioan. de Sacro Boſco."/> <p> <s xml:id="echoid-s15548" xml:space="preserve">.</s> <s xml:id="echoid-s15549" xml:space="preserve">. .</s> <s xml:id="echoid-s15550" xml:space="preserve">. .</s> <s xml:id="echoid-s15551" xml:space="preserve">. Vmbras nuſquam flectente Syene.</s> <s xml:id="echoid-s15552" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s15553" xml:space="preserve"><emph style="sc">Hoc</emph> intellige in meridie ſcilicet unius diei, cuius umbra mane por-<lb/>recta Occidentalis, ſero Orientalis, & </s> <s xml:id="echoid-s15554" xml:space="preserve">per reſiduum totius anni iacitur il-<lb/>lis umbra Septentrionalis.</s> <s xml:id="echoid-s15555" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div862" type="section" level="1" n="344"> <head xml:id="echoid-head355" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s15556" xml:space="preserve"><emph style="sc">Tertivs</emph> locus eorum eſt, quorum Zenith eſt directe in Tropico ♋. <lb/></s> <s xml:id="echoid-s15557" xml:space="preserve">Quibus duas proprietates adſcribit.</s> <s xml:id="echoid-s15558" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15559" xml:space="preserve">I. </s> <s xml:id="echoid-s15560" xml:space="preserve">Semel in anno incedit illis Sol per uerticem capitis, quando ſcilicet eſt <lb/>in principio ♋.</s> <s xml:id="echoid-s15561" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15562" xml:space="preserve">II. </s> <s xml:id="echoid-s15563" xml:space="preserve">Tres differentias umbrarum poſſident, Orientalem veſperi, occidenta-<lb/>lem mane, & </s> <s xml:id="echoid-s15564" xml:space="preserve">Septentrionalẽ in meridie. </s> <s xml:id="echoid-s15565" xml:space="preserve">Sole tamẽ exiſtente in principio ♋, <lb/>nullam habent umbram in meridie. </s> <s xml:id="echoid-s15566" xml:space="preserve">In tali ſitu dicitur eſſe vrbs Aegypti Sye <lb/>ne, ubi, auctore Plinio, Aſtronomi puteum altiſſimum conſtruxerunt, in quo, <lb/>Sole exiſtente in principio ♋, nulla perſpicitur umbra, ſed totus à Sole illu <lb/>ſtratur. </s> <s xml:id="echoid-s15567" xml:space="preserve">His addere poſſumus, quòd habeãt inæqualitatẽ dierũ, æquinoctijs ex <lb/>ceptis: </s> <s xml:id="echoid-s15568" xml:space="preserve">quod duo tantum habeãt Solſtitia, unum altum, alterum imum; </s> <s xml:id="echoid-s15569" xml:space="preserve">quòd <lb/>ſ@nam habeãt æſtatem, & </s> <s xml:id="echoid-s15570" xml:space="preserve">vnam hyemem; </s> <s xml:id="echoid-s15571" xml:space="preserve">quod denique non omnnia puncta cę <lb/>li illis oriantue, & </s> <s xml:id="echoid-s15572" xml:space="preserve">occidant. </s> <s xml:id="echoid-s15573" xml:space="preserve">Quæ omnia perſpicua ſunt in ſphæra materiali.</s> <s xml:id="echoid-s15574" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s15575" xml:space="preserve"><emph style="sc">Illis</emph> uero, quorum Zenith eſt inter Tropicum ♋, & </s> <s xml:id="echoid-s15576" xml:space="preserve">circulum Ar <lb/> <anchor type="note" xlink:label="note-453-01a" xlink:href="note-453-01"/> cticum, contingit, quòd Sol in ſempiternum non tranſit per zenith capitis <lb/>eorum, & </s> <s xml:id="echoid-s15577" xml:space="preserve">illis ſemper iacitur umbra uerſus Septentrionem. </s> <s xml:id="echoid-s15578" xml:space="preserve">Talis eſt <lb/>ſitus noſter. </s> <s xml:id="echoid-s15579" xml:space="preserve">Notandum etiam, quod Aethiopia, uel aliqua pars eius eſt <lb/>citra Tropicum Cancri ſecundum aliquos. </s> <s xml:id="echoid-s15580" xml:space="preserve">Vnde Lucanus.</s> <s xml:id="echoid-s15581" xml:space="preserve"/> </p> <div xml:id="echoid-div862" type="float" level="2" n="1"> <note position="right" xlink:label="note-453-01" xlink:href="note-453-01a" xml:space="preserve">Proprieta-<lb/>tes eorum. <lb/>qui zenith <lb/>habent in-<lb/>ter tropicũ <lb/>cãcri, & ci@ <lb/>culum Ar-<lb/>cticum.</note> </div> <p> <s xml:id="echoid-s15582" xml:space="preserve">Aethiopumq́ue ſolum, quod non premeretur ab ulla</s> </p> <p> <s xml:id="echoid-s15583" xml:space="preserve">Signiferi regione poli, ni poplite lapſo</s> </p> <p> <s xml:id="echoid-s15584" xml:space="preserve">Vltima curuati procederet vngula Tauri.</s> <s xml:id="echoid-s15585" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s15586" xml:space="preserve"><emph style="sc">Dicvnt</emph> enim quidam, quod ibi ſumitur ſignum ęquiuoce, pro <lb/>duodecima parte Zodiaci, & </s> <s xml:id="echoid-s15587" xml:space="preserve">pro forma animalis, quod ſecundum maio-<lb/>rem partem ſui eſt in ſigno, quod denominat. </s> <s xml:id="echoid-s15588" xml:space="preserve">Vnde Taurus, cum ſit in Zo-<lb/>diaco ſecundum maiorem ſuipartem, tamen extendit pedem ſuum ultra <lb/>Tropicum Cancri, & </s> <s xml:id="echoid-s15589" xml:space="preserve">ita premit Aethiopiam, licet nulla pars Zodiaci pre <lb/>mat eam. </s> <s xml:id="echoid-s15590" xml:space="preserve">Si enim pes Tauri, de quo loquitur Poeta, extenderetur uerſus <lb/>Aequinoctialem, ut eßet in directo Arietis, uel alterius ſigni, tunc preme-<lb/>retur ab Ariete, uel Virgine, & </s> <s xml:id="echoid-s15591" xml:space="preserve">alijs ſignis: </s> <s xml:id="echoid-s15592" xml:space="preserve">quod patet per circulum <lb/>Aequinoctiali parallelum circumductum per Zenith capitis ipſorum Ae-<lb/>thiopum, & </s> <s xml:id="echoid-s15593" xml:space="preserve">per Arietem, & </s> <s xml:id="echoid-s15594" xml:space="preserve">Virginem, uel alia ſigna. </s> <s xml:id="echoid-s15595" xml:space="preserve">Sed cum ratio <lb/>Phyſica huic contrarietur (non enim ita eßent denigrati, ſi in temperata <lb/>naſcerentur regione habitabili) dicendum, quòd illa pars Aethiopię, de <lb/>qua loquitur Lucanus, eſt ſub Aequinoctiali circulo, & </s> <s xml:id="echoid-s15596" xml:space="preserve">quod per Tauri, <pb o="418" file="454" n="455" rhead="Comment. in III. Cap. Sphæræ"/> pes Tauri, de quo loquitur, extenditur uerſus Aequinoctialem. </s> <s xml:id="echoid-s15597" xml:space="preserve">Sed diſtin-<lb/>guitur tunc inter ſigna Cardinalia, & </s> <s xml:id="echoid-s15598" xml:space="preserve">regiones. </s> <s xml:id="echoid-s15599" xml:space="preserve">Nam ſigna Cardinalia di-<lb/>cuntur duo ſigna, in quibus contingunt Solſtitia, & </s> <s xml:id="echoid-s15600" xml:space="preserve">duo, in quibus contin-<lb/>gunt æquinoctia. </s> <s xml:id="echoid-s15601" xml:space="preserve">Regiones autem appellantur ſigna intermedia. </s> <s xml:id="echoid-s15602" xml:space="preserve">Et ſecun-<lb/>dum hoc patet, quòd cum Aethiopia ſit ſub Aequinoctiali, non premitur <lb/>ab aliqua regione, ſed à duobus ſignis tantum Cardinalibus, ſcilicet A-<lb/>riete, & </s> <s xml:id="echoid-s15603" xml:space="preserve">Libra.</s> <s xml:id="echoid-s15604" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div864" type="section" level="1" n="345"> <head xml:id="echoid-head356" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s15605" xml:space="preserve"><emph style="sc">Qvartvs</emph> locus eſt eorum, quorum vertex collocatur inter Tropicum <lb/>♋, & </s> <s xml:id="echoid-s15606" xml:space="preserve">circulum Arcticum. </s> <s xml:id="echoid-s15607" xml:space="preserve">His duas quoque attribuit proprietates.</s> <s xml:id="echoid-s15608" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15609" xml:space="preserve">I. </s> <s xml:id="echoid-s15610" xml:space="preserve">Nunquam Sol tranſit per eorum uerticem capitis.</s> <s xml:id="echoid-s15611" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15612" xml:space="preserve">II. </s> <s xml:id="echoid-s15613" xml:space="preserve">Tres differentias umbrarum habent, ſicut ij, qui in præcedenti ſitu habi <lb/>tant; </s> <s xml:id="echoid-s15614" xml:space="preserve">hoc uno dempto, quòd nunquam habent umbram perpendicularem. </s> <s xml:id="echoid-s15615" xml:space="preserve">In <lb/>hoc ſitu, ait, putarunt nonnulli, collocatam eſſe Aethiopiam, quod ex Luca-<lb/>no probabant. </s> <s xml:id="echoid-s15616" xml:space="preserve">Quod tamen ipſe refutat, explicans aliter Lucanum, ut ex lite-<lb/>ra patet. </s> <s xml:id="echoid-s15617" xml:space="preserve">Sed quicquid ſit de Lucano, certum eſt Aethiopiæ magnam partem <lb/>ſitã eſſe ſub Aequinoctiali circulo. </s> <s xml:id="echoid-s15618" xml:space="preserve">Quã uero conuenines ſit expoſi tio noſtri <lb/>auctoris, alij iudicent. </s> <s xml:id="echoid-s15619" xml:space="preserve">A multis enim, præcipue a Scaligero in Poetica, repre-<lb/>henditur Lucanus. </s> <s xml:id="echoid-s15620" xml:space="preserve">Verum tamen eſt, quod auctor dicit, ungulam Tauri porri<unsure/> <lb/>gi verſus Aequatorem. </s> <s xml:id="echoid-s15621" xml:space="preserve">Hiſce duabus proprietatibus addere licet, quod habi-<lb/>tantes in hoc ſitu terræ duo habent ſolſtitia, altum vnum, & </s> <s xml:id="echoid-s15622" xml:space="preserve">imum alterum. <lb/></s> <s xml:id="echoid-s15623" xml:space="preserve">Item quod illis ſemel eſt æſtas, & </s> <s xml:id="echoid-s15624" xml:space="preserve">ſemel hyems, habentq́; </s> <s xml:id="echoid-s15625" xml:space="preserve">inæqualitatem die-<lb/>rũ & </s> <s xml:id="echoid-s15626" xml:space="preserve">noctium; </s> <s xml:id="echoid-s15627" xml:space="preserve">& </s> <s xml:id="echoid-s15628" xml:space="preserve">quod non omnia ſrdera illis oriuntur, atque occidunt.</s> <s xml:id="echoid-s15629" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s15630" xml:space="preserve"><emph style="sc">Illis</emph> autem, quorum Zenith eſt in circulo Arctico, contingit in <lb/> <anchor type="note" xlink:label="note-454-01a" xlink:href="note-454-01"/> quolibet die, & </s> <s xml:id="echoid-s15631" xml:space="preserve">tempore anni, quod Zenith capitis eorum eſt idem cum <lb/>polo Zodiaci, & </s> <s xml:id="echoid-s15632" xml:space="preserve">tunc habent Zodiacum, ſiue Eclipticam pro Horizonte. <lb/></s> <s xml:id="echoid-s15633" xml:space="preserve">Et hoc eſt, quod dicit Aphraganus, quod ibi circulus Zodiaci flectitur ſu-<lb/>pra circulum hemiſphęrij. </s> <s xml:id="echoid-s15634" xml:space="preserve">Sed cum Firmamentum continue moueatur, <lb/>circulus Horizontis interſecabunt ſe in partes ęquales. </s> <s xml:id="echoid-s15635" xml:space="preserve">Vnde ſtatim me-<lb/>dietas una Zodiaci emergit ſupra Horizontem, & </s> <s xml:id="echoid-s15636" xml:space="preserve">reliqua deprimitur <lb/>ſub Horizonte ſubito. </s> <s xml:id="echoid-s15637" xml:space="preserve">Et hoc eſt, quod dicit <emph style="sc">A</emph>lphraganus, quod ibi oc-<lb/>cidunt repente ſex ſigna, & </s> <s xml:id="echoid-s15638" xml:space="preserve">reliqua ſex oriuntur. </s> <s xml:id="echoid-s15639" xml:space="preserve">Cum etiam Eclipti-<lb/>ca ſit Horizon illorum, erit Tropicus Cancri totus ſupra Horizontem, <lb/>& </s> <s xml:id="echoid-s15640" xml:space="preserve">totus tropicus Capricorni ſub Horizonte; </s> <s xml:id="echoid-s15641" xml:space="preserve">& </s> <s xml:id="echoid-s15642" xml:space="preserve">ſic, Sol exiſtente in <lb/>primo puncto Cancri, erit illis una dies 24. </s> <s xml:id="echoid-s15643" xml:space="preserve">horarum, & </s> <s xml:id="echoid-s15644" xml:space="preserve">quaſi inſtans <lb/>pro nocte, quia in inſtanti Sol tranſit Horizontem, & </s> <s xml:id="echoid-s15645" xml:space="preserve">ſtatim emergit, & </s> <s xml:id="echoid-s15646" xml:space="preserve"><lb/>ille contactus eſt illis pro nocte. </s> <s xml:id="echoid-s15647" xml:space="preserve">E conuerſo contingit illis, Sole exiſten- <pb o="419" file="455" n="456" rhead="Ioan. de Sacro Boſco."/> te in primo puncto Capricorni. </s> <s xml:id="echoid-s15648" xml:space="preserve">Eſt enim tunc illis una nox 24. </s> <s xml:id="echoid-s15649" xml:space="preserve">horarum, <lb/>& </s> <s xml:id="echoid-s15650" xml:space="preserve">quaſi inſtans pro die.</s> <s xml:id="echoid-s15651" xml:space="preserve"/> </p> <div xml:id="echoid-div864" type="float" level="2" n="1"> <note position="left" xlink:label="note-454-01" xlink:href="note-454-01a" xml:space="preserve">Proprieta-<lb/>ſes eorũ, ꝗ <lb/>Zenith ha-<lb/>bent in cir <lb/>gulo Arcti-<lb/>@@.</note> </div> </div> <div xml:id="echoid-div866" type="section" level="1" n="346"> <head xml:id="echoid-head357" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s15652" xml:space="preserve"><emph style="sc">Qvintvs</emph> locus eorum eſt, qui habent verticem capitis præcife in cir-<lb/>culo Arctico, quibus vnicã proprietatẽ aſſignat, quod uidelicet in quolibet <lb/>die anni vertex capitis eorum idem efficitur cũ polo Zodiaci. </s> <s xml:id="echoid-s15653" xml:space="preserve">Ex quo conſe-<lb/>quitur, Zodiacum tunc vicem gerere Horizõtis, & </s> <s xml:id="echoid-s15654" xml:space="preserve">idcirco quaſi in ictu oculi, <lb/>quàm primũ polus Zodiaci ad motum primi mobilis a uertice capitis receſſe-<lb/>rit, ſeſe mutuo bifariam interſecabunt Zodiacus atque Horizon, cum ſint cir <lb/>culi maximi, ita vt repente, ſicut ait Alphraganus Differ. </s> <s xml:id="echoid-s15655" xml:space="preserve">7. </s> <s xml:id="echoid-s15656" xml:space="preserve">oriatur una medie-<lb/>tas Eclipticę, hoc eſt, ſex ſigna appareant ſupra Horizontem, alia vero medie-<lb/>tas repente occidat, id eſt, reliqua ſex ſigna ſubito occultentur, deſcendantq́. <lb/></s> <s xml:id="echoid-s15657" xml:space="preserve">ſub Horizontẽ. </s> <s xml:id="echoid-s15658" xml:space="preserve">Hinc etiam ſit, ut totus Tropicus ♋, exiſtat ſupra Horizon-<lb/>tem, & </s> <s xml:id="echoid-s15659" xml:space="preserve">totus Tropicus ♑, infra eundem, ita ut principium ♋, & </s> <s xml:id="echoid-s15660" xml:space="preserve">principiũ ♑ <lb/>tangant & </s> <s xml:id="echoid-s15661" xml:space="preserve">radant quodam modo Horizontẽ. </s> <s xml:id="echoid-s15662" xml:space="preserve">Quare Sole exiſtente in princi-<lb/>pio ♋, habebunt diem 24. </s> <s xml:id="echoid-s15663" xml:space="preserve">horarũ, & </s> <s xml:id="echoid-s15664" xml:space="preserve">quaſi inſtans pro nocte, quia in inſtanti <lb/>quaſi Sol pertranſit Horizontem, & </s> <s xml:id="echoid-s15665" xml:space="preserve">ſtatim iterum emergit, immo nunquam <lb/>perfecte tunc occidet, ſed continget Horizontem: </s> <s xml:id="echoid-s15666" xml:space="preserve">Exiſtẽte uero Sole in prin-<lb/>cipio ♑, ob eandem rationem habebunt noctem 24. </s> <s xml:id="echoid-s15667" xml:space="preserve">horarum, & </s> <s xml:id="echoid-s15668" xml:space="preserve">quafi inſtans <lb/>pro die: </s> <s xml:id="echoid-s15669" xml:space="preserve">Quæ omnia clariſſime perſpiciũtur in ſphæra materiali. </s> <s xml:id="echoid-s15670" xml:space="preserve">Adde, quod <lb/>non omnia ſidera illis oriuntur, atque occidunt.</s> <s xml:id="echoid-s15671" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s15672" xml:space="preserve"><emph style="sc">ILLIS</emph> autem, quorum Zenith eſt inter circulum Arcticum, & </s> <s xml:id="echoid-s15673" xml:space="preserve">po-<lb/> <anchor type="note" xlink:label="note-455-01a" xlink:href="note-455-01"/> lum mundi Arcticum, contingit, quod Horizon illorum interſecat Zodia-<lb/>cum in duobus punctis æquidiſtantibus à principio ♋, & </s> <s xml:id="echoid-s15674" xml:space="preserve">in reuolutione <lb/>Firmamenti contingit, quod illa portio Zodiaci intercepta ſemper relinqua <lb/>tur ſupra Horizontem. </s> <s xml:id="echoid-s15675" xml:space="preserve">Vnde patet, quòd quàmdiu Sol eſt in illa portione <lb/>intercepta, erit unus dies continuus ſine nocte. </s> <s xml:id="echoid-s15676" xml:space="preserve">Ergo ſi illa portio fuerit <lb/>ad quantitatem ſigni unius, erit ibi dies continuus unius menſis ſine no-<lb/>cte: </s> <s xml:id="echoid-s15677" xml:space="preserve">Si ad quantitatem duorum ſignorum, erit dies continuus duorum men-<lb/>ſium ſine nocte, & </s> <s xml:id="echoid-s15678" xml:space="preserve">ita deinceps. </s> <s xml:id="echoid-s15679" xml:space="preserve">Similiter contingit eiſdem, quòd portio <lb/>Zodiaci intercepta ab alijs duobus punctis æquidiſtantibus a principio Ca-<lb/>pricorni, ſemper relinquatur ſub Horizonte. </s> <s xml:id="echoid-s15680" xml:space="preserve">Vnde cum Sol eſt in illa por <lb/>tione intercepta, erit una nox continua ſine die, breuis uel magna ſecun-<lb/>dum quantitatem interceptæ portionis. </s> <s xml:id="echoid-s15681" xml:space="preserve">Signa autem reliqua, quæ eis <lb/>oriuntur, & </s> <s xml:id="echoid-s15682" xml:space="preserve">occidunt, præpoſtere oriuntur, & </s> <s xml:id="echoid-s15683" xml:space="preserve">occidunt. </s> <s xml:id="echoid-s15684" xml:space="preserve">Oriuntur præpo-<lb/>ſtere, ſicut ♉, ante ♈; </s> <s xml:id="echoid-s15685" xml:space="preserve">♈, ante ♓; </s> <s xml:id="echoid-s15686" xml:space="preserve">♓, ante ♒; </s> <s xml:id="echoid-s15687" xml:space="preserve">& </s> <s xml:id="echoid-s15688" xml:space="preserve">tamen ſigna his oppoſi-<lb/>ta oriuntur recto ordine, & </s> <s xml:id="echoid-s15689" xml:space="preserve">occidunt præpoſtere; </s> <s xml:id="echoid-s15690" xml:space="preserve">ut ♏, ante ♎; </s> <s xml:id="echoid-s15691" xml:space="preserve">♎, an-<lb/>te ♍, & </s> <s xml:id="echoid-s15692" xml:space="preserve">tamen ſigna his oppoſita occidunt directe, illa ſcilicet, quæ orieba@ <lb/>tur præpoſterè, ut Taurus, &</s> <s xml:id="echoid-s15693" xml:space="preserve">c.</s> <s xml:id="echoid-s15694" xml:space="preserve"/> </p> <div xml:id="echoid-div866" type="float" level="2" n="1"> <note position="right" xlink:label="note-455-01" xlink:href="note-455-01a" xml:space="preserve">Propriet@-<lb/>tes eorum. <lb/>quorum Ze <lb/>nith eſt in <lb/>ter circulũ <lb/>arcticum, & <lb/>polum ar-<lb/>cticum.</note> </div> <pb o="420" file="456" n="457" rhead="Comment. in III. Cap. Sphæræ"/> </div> <div xml:id="echoid-div868" type="section" level="1" n="347"> <head xml:id="echoid-head358" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s15695" xml:space="preserve"><emph style="sc">Sextvs</emph> locus eſt eorum, qui inter circulum Arcticum, & </s> <s xml:id="echoid-s15696" xml:space="preserve">polum mun-<lb/>di Arcticum habitant, quibus duas tribuit proprietates.</s> <s xml:id="echoid-s15697" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15698" xml:space="preserve">I. </s> <s xml:id="echoid-s15699" xml:space="preserve">Horizon ſecat ſingulis diebus Zodiacũ in duobus punctis æqualiter re-<lb/>motis à principio ♋; </s> <s xml:id="echoid-s15700" xml:space="preserve">& </s> <s xml:id="echoid-s15701" xml:space="preserve">pars illa intercepta inter duo illa puncta nunquam ad <lb/>motum primi mobilis ſub Horizontem deſcendit, ſed ſemper apparet. </s> <s xml:id="echoid-s15702" xml:space="preserve">Ex quo <lb/>efficitur, Sole illam portionem percurrente, cõtinuum eſſe diem abſq; </s> <s xml:id="echoid-s15703" xml:space="preserve">nocte, <lb/>ita ut ſi fuerit portio illa 30. </s> <s xml:id="echoid-s15704" xml:space="preserve">grad. </s> <s xml:id="echoid-s15705" xml:space="preserve">ſit dies illa artificialis ferme 30. </s> <s xml:id="echoid-s15706" xml:space="preserve">dierũ natu-<lb/>ralium, &</s> <s xml:id="echoid-s15707" xml:space="preserve">c. </s> <s xml:id="echoid-s15708" xml:space="preserve">Eadem ratione ſecabitur Zodiacus ab Horizõte alijs duobus pun-<lb/>ctis æqualiter diſtantibus a principio ♑, & </s> <s xml:id="echoid-s15709" xml:space="preserve">ſegmentum Zodiaci inter duo illa <lb/>puncta comprehenſum nunquã ori@ur ad motũ primi mobilis ſupra Horizon-<lb/>tem, ſed perpetuo deliteſcit, eſtq́. </s> <s xml:id="echoid-s15710" xml:space="preserve">æqualis priori ſegmento ſemper conſpicuo. <lb/></s> <s xml:id="echoid-s15711" xml:space="preserve">Vnde Sole percurrente dictum ſegmentum, habebunt noctẽ continuam abſq; </s> <s xml:id="echoid-s15712" xml:space="preserve"><lb/>die, ita ut ſi fuerit ſegmentum illud 30. </s> <s xml:id="echoid-s15713" xml:space="preserve">grad. </s> <s xml:id="echoid-s15714" xml:space="preserve">ſit nox illa compoſita quaſi ex <lb/>30. </s> <s xml:id="echoid-s15715" xml:space="preserve">diebus Naturalibus, &</s> <s xml:id="echoid-s15716" xml:space="preserve">c. </s> <s xml:id="echoid-s15717" xml:space="preserve">Hoc autem manifeſtum eſt in ſphæra materiali, ſi <lb/>ita ſtatuatur, ut Colurus ſolſtitiorum idem ſit, qui Meridianus, ponaturq́ue <lb/>Cancer ad partes poli Arctici, hoc eſt, Septentrionem uerſus ſupra Horizon-<lb/>tem, & </s> <s xml:id="echoid-s15718" xml:space="preserve">Capricornus ad partes poli Antarctici, ſiue uerſus Meridiem infra <lb/>Horizontem. </s> <s xml:id="echoid-s15719" xml:space="preserve">Si enim tunc concipiatur deſcribi parallelus tangens Horizon-<lb/>tem, ſecabitur Ecliptica duobus in punctis, quæ intercipiunt arcum non occi-<lb/>dentem, ut manifeſtum eſt, ſi poſitio ſphæræ recte concipiatur: </s> <s xml:id="echoid-s15720" xml:space="preserve">eritque dictus <lb/>arcus maior, aut minor, prout principium ♋, magis, aut minus ſupra <lb/>Horizontem attollitur, cum in Meridiano ex parte Septentrionis colloca-<lb/>tum fuerit.</s> <s xml:id="echoid-s15721" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15722" xml:space="preserve">II. </s> <s xml:id="echoid-s15723" xml:space="preserve">Reliqua ſigna, quæ illis oriuntur, atque occidunt, præpoſtero ordine <lb/> <anchor type="note" xlink:label="note-456-01a" xlink:href="note-456-01"/> oriuntur, occiduntque, hoc eſt ‘non eo ordine oriuntur, & </s> <s xml:id="echoid-s15724" xml:space="preserve">occidũt, quo in alijs <lb/>partibus mundi oriuntur, atque occidunt, ita ut v.</s> <s xml:id="echoid-s15725" xml:space="preserve">g. </s> <s xml:id="echoid-s15726" xml:space="preserve">ſemper ♈, ante ♉, oria-<lb/>tur, & </s> <s xml:id="echoid-s15727" xml:space="preserve">occidat; </s> <s xml:id="echoid-s15728" xml:space="preserve">Sed ſigna iuxta æquinoctium Vernum exiſtentia oriuntur prę-<lb/>poſtere, id eſt, ♉, oritur ante ♈: </s> <s xml:id="echoid-s15729" xml:space="preserve">& </s> <s xml:id="echoid-s15730" xml:space="preserve">♈, ante ♓, &</s> <s xml:id="echoid-s15731" xml:space="preserve">c. </s> <s xml:id="echoid-s15732" xml:space="preserve">Occidunt autem recto ordi-<lb/>ne, nempe ♓, ante ♈: </s> <s xml:id="echoid-s15733" xml:space="preserve">& </s> <s xml:id="echoid-s15734" xml:space="preserve">♈, ante ♉, &</s> <s xml:id="echoid-s15735" xml:space="preserve">c. </s> <s xml:id="echoid-s15736" xml:space="preserve">utin alijs poſitionibus ſphærę: </s> <s xml:id="echoid-s15737" xml:space="preserve">At uero <lb/>ſigna exiſtentia prope æquinoctium Autumnale occidunt præpoſtere, id eſt, ♐ <lb/>occidit ante ♏, & </s> <s xml:id="echoid-s15738" xml:space="preserve">♏, ante ♎, &</s> <s xml:id="echoid-s15739" xml:space="preserve">c. </s> <s xml:id="echoid-s15740" xml:space="preserve">Oriuntur autem ordine recto, vt in alijs <lb/>ſphæræ poſitionibus, hoc eſt, ♎, ante ♏, & </s> <s xml:id="echoid-s15741" xml:space="preserve">♏, ante ♐, &</s> <s xml:id="echoid-s15742" xml:space="preserve">c. </s> <s xml:id="echoid-s15743" xml:space="preserve">Quæ omnia perſpi-<lb/>cua ſunt in inſtrumento materiali. </s> <s xml:id="echoid-s15744" xml:space="preserve">His quoque adde, quòd non omnia aſtra <lb/>illius oriuntur, & </s> <s xml:id="echoid-s15745" xml:space="preserve">occidunt.</s> <s xml:id="echoid-s15746" xml:space="preserve"/> </p> <div xml:id="echoid-div868" type="float" level="2" n="1"> <note position="left" xlink:label="note-456-01" xlink:href="note-456-01a" xml:space="preserve">@gna præpo <lb/>ſtere orien-<lb/>@ia, & occi-<lb/>@e<unsure/>n@ia quę.</note> </div> <note position="left" xml:space="preserve">Quanta ſit <lb/>@ic<unsure/>s conti-<lb/>nua inter <lb/>polum, & <lb/>circulum ar <lb/>@@icum, quo <lb/>@acto inqui <lb/>@atur.</note> <p> <s xml:id="echoid-s15747" xml:space="preserve"><emph style="sc">Qvod</emph> ſi ſcire lubeat, quanta ſit dies continua, item que nox in prædicto <lb/>loco, ubi uertex capitis conſtituitur inter circulum Arcticum, & </s> <s xml:id="echoid-s15748" xml:space="preserve">polum Arcti <lb/>cum, id hac arte aſſequeris. </s> <s xml:id="echoid-s15749" xml:space="preserve">Detrahe altitudinem poli (quæ maior neceſſario <lb/>erit, quàm grad. </s> <s xml:id="echoid-s15750" xml:space="preserve">66. </s> <s xml:id="echoid-s15751" xml:space="preserve">min. </s> <s xml:id="echoid-s15752" xml:space="preserve">30.) </s> <s xml:id="echoid-s15753" xml:space="preserve">ex Quadrante, nempe ex grad. </s> <s xml:id="echoid-s15754" xml:space="preserve">90. </s> <s xml:id="echoid-s15755" xml:space="preserve">& </s> <s xml:id="echoid-s15756" xml:space="preserve">remaneb@t <lb/>declinatio principij arcus ſemper apparentis: </s> <s xml:id="echoid-s15757" xml:space="preserve">Vnde ex tabula declinationũ fa-<lb/>cile reperies initium illius arcus, cuius medietas eſt inter initiũ illud, & </s> <s xml:id="echoid-s15758" xml:space="preserve">prin-<lb/>cipium ♋, quare duplicatus dabit integrum arcum ſemper conſpicuũ: </s> <s xml:id="echoid-s15759" xml:space="preserve">oppoſi <lb/>tus uero huic perpetuo occultatur. </s> <s xml:id="echoid-s15760" xml:space="preserve">Habito autem arcu, ex uero motu Solis <lb/>facile cognoſces, quot diebus Naturalibus eum percurrat, & </s> <s xml:id="echoid-s15761" xml:space="preserve">ex conſequen-<lb/>ti habebis quantitatem diei continuæ, nec non noctis continuæ. </s> <s xml:id="echoid-s15762" xml:space="preserve">EXEM-<lb/>PLVM. </s> <s xml:id="echoid-s15763" xml:space="preserve">Vbi eleuatur polus Arcticus grad. </s> <s xml:id="echoid-s15764" xml:space="preserve">69. </s> <s xml:id="echoid-s15765" xml:space="preserve">min. </s> <s xml:id="echoid-s15766" xml:space="preserve">48. </s> <s xml:id="echoid-s15767" xml:space="preserve">detraho hanc poli al- <pb o="421" file="457" n="458" rhead="Ioan. de Sacro Boſco."/> titudinem ex 90. </s> <s xml:id="echoid-s15768" xml:space="preserve">grad. </s> <s xml:id="echoid-s15769" xml:space="preserve">relinquiturq́. </s> <s xml:id="echoid-s15770" xml:space="preserve">declinatio principij arcus ſemper appa-<lb/>rentis grad. </s> <s xml:id="echoid-s15771" xml:space="preserve">20. </s> <s xml:id="echoid-s15772" xml:space="preserve">min. </s> <s xml:id="echoid-s15773" xml:space="preserve">11. </s> <s xml:id="echoid-s15774" xml:space="preserve">cui ex tabula declinationum reſpõdet principium ♊, <lb/>aut finis ♋. </s> <s xml:id="echoid-s15775" xml:space="preserve">Quare arcus à principio ♊, vſq; </s> <s xml:id="echoid-s15776" xml:space="preserve">ad finem ♋, ſemper apparebit, <lb/>& </s> <s xml:id="echoid-s15777" xml:space="preserve">arcus à principio ♐, vſque ad finem ♑, perpetuo deliteſcet, &</s> <s xml:id="echoid-s15778" xml:space="preserve">c. </s> <s xml:id="echoid-s15779" xml:space="preserve">Ob maio-<lb/>rem tamen commoditatem appoſui ſequentem tabellam ex Orontio, in qua <lb/>habes arcus ſemper apparentes, & </s> <s xml:id="echoid-s15780" xml:space="preserve">continuos dies pro ſingulis gradibus alti-<lb/>tudinis poli, incipiendo à grad. </s> <s xml:id="echoid-s15781" xml:space="preserve">67. </s> <s xml:id="echoid-s15782" xml:space="preserve">uſque ad 90.</s> <s xml:id="echoid-s15783" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15784" xml:space="preserve"><emph style="sc">Æqvales</emph> ſunt arcus ſemper occulti arcubus ſemper apparentibus, at no-<lb/> <anchor type="note" xlink:label="note-457-01a" xlink:href="note-457-01"/> ctes continuæ diebus continuis æquales non ſunt: </s> <s xml:id="echoid-s15785" xml:space="preserve">quia Sol uelocius pertran-<lb/>ſit arcus prope ♑, quàm prope ♋; </s> <s xml:id="echoid-s15786" xml:space="preserve">cum ibi ſit oppoſitum augis hac tempe-<lb/>ſtate, hic uero aux ipſa, ut in Theoricis explicabitur. </s> <s xml:id="echoid-s15787" xml:space="preserve">Quocirca minores ali-<lb/>quanto erunt noctes continuæ diebus continuis. </s> <s xml:id="echoid-s15788" xml:space="preserve">Quod intellige, vbi polus <lb/>Arcticus ſupra Horizo ntem eleuatur. </s> <s xml:id="echoid-s15789" xml:space="preserve">Nam ubi polus Antarcticus ſupra Ho-<lb/>rizontem conſpicitur, erunt ob rationem iam dictam dies continui minores <lb/>noctibus continuis, ut conſtat.</s> <s xml:id="echoid-s15790" xml:space="preserve"/> </p> <div xml:id="echoid-div869" type="float" level="2" n="2"> <note position="right" xlink:label="note-457-01" xlink:href="note-457-01a" xml:space="preserve">Noctes con <lb/>tinuæ die-<lb/>bus conti-<lb/>nuis æqua-<lb/>les nõ ſunt <lb/>& quar<unsure/>e.</note> </div> </div> <div xml:id="echoid-div871" type="section" level="1" n="348"> <head xml:id="echoid-head359" xml:space="preserve">TABVLA MAXIMORVM <lb/>DIERVM, VBI POLVS ELEVATVR <lb/>pluribus gradibus, quam 66 {1/2}.</head> <note position="right" xml:space="preserve"> <lb/>Eleua- \\ tio poli # ## Arcus ſem- \\ per apparẽs # ### Dies con- \\ tinuus. <lb/>G. # G. # M. # D. # H. # M. <lb/>67 # 22 # 52 # 22 # 1 # 40 <lb/>68 # 40 # 0 # 42 # 1 # 16 <lb/>69 # 52 # 0 # 54 # 16 # 25 <lb/>70 # 61 # 26 # 64 # 13 # 46 <lb/>71 # 70 # 26 # 74 # 0 # 0 <lb/>72 # 78 # 22 # 82 # 6 # 39 <lb/>73 # 84 # 56 # 89 # 4 # 58 <lb/>74 # 92 # 12 # 96 # 17 # 0 <lb/>75 # 96 # 10 # 104 # 1 # 4 <lb/>76 # 105 # 16 # 110 # 7 # 27 <lb/>77 # 111 # 20 # 116 # 14 # 22 <lb/>78 # 117 # 6 # 122 # 17 # 6 <lb/></note> <note position="right" xml:space="preserve"> <lb/>Eleua-- \\ tio poli # ## Arcus ſem- \\ per apparẽs # ### Dies con \\ tinuus. <lb/>G. # G. # M. # D. # H. # M. <lb/>79 # 122 # 46 # 127 # 9 # 55 <lb/>80 # 128 # 22 # 134 # 4 # 58 <lb/>81 # 133 # 50 # 139 # 31 # 36 <lb/>82 # 139 # 6 # 145 # 6 # 43 <lb/>83 # 144 # 22 # 151 # 2 # 6 <lb/>84 # 149 # 36 # 156 # 3 # 3 <lb/>85 # 154 # 42 # 161 # 5 # 23 <lb/>86 # 159 # 50 # 166 # 11 # 23 <lb/>87 # 164 # 52 # 171 # 21 # 47 <lb/>88 # 169 # 58 # 176 # 5 # 29 <lb/>89 # 174 # 58 # 181 # 21 # 58 <lb/>90 # 180 # 10 # 187 # 6 # 39 <lb/></note> <pb o="422" file="458" n="459" rhead="Comment. in III. Cap. Sphæræ"/> <p style="it"> <s xml:id="echoid-s15791" xml:space="preserve">ILLIS autem, quorum zenith eſt in polo Arctico, contingit, quod <lb/> <anchor type="note" xlink:label="note-458-01a" xlink:href="note-458-01"/> illorum Horizon eſt idem, quod Aequinoctialis. </s> <s xml:id="echoid-s15792" xml:space="preserve">Vnde cum Aequinoctia-<lb/>lis interſecet Zodiacum in duas partes æquales, ſic & </s> <s xml:id="echoid-s15793" xml:space="preserve">illorum Horizon re <lb/>linquit medietatem Zodiaci ſupra ſe, & </s> <s xml:id="echoid-s15794" xml:space="preserve">reliquam infra. </s> <s xml:id="echoid-s15795" xml:space="preserve">Vnde cum Sol <lb/>decurrit per illam medietatem, quæ eſt à principio Arietis, uſque ad fi-<lb/>nem Virginis, unus erit dies continuus ſine nocte, & </s> <s xml:id="echoid-s15796" xml:space="preserve">cum Sol decurrit in <lb/>reliqua medietate, quæ eſt à principio Libræ, uſque ad finem Piſcium, erit <lb/>nox una continua ſine die. </s> <s xml:id="echoid-s15797" xml:space="preserve">Quare & </s> <s xml:id="echoid-s15798" xml:space="preserve">una medietas totius anni eſt una <lb/>dies artificialis, & </s> <s xml:id="echoid-s15799" xml:space="preserve">alia medietas eſt unanox. </s> <s xml:id="echoid-s15800" xml:space="preserve">Vnde totus annus eſt ibi <lb/>unus dies naturalis. </s> <s xml:id="echoid-s15801" xml:space="preserve">Sed cum ibi nunquam magis 23. </s> <s xml:id="echoid-s15802" xml:space="preserve">gradibus Sol ſub <lb/>Horizonte deprimatur, uidetur, quòd illis ſit dies continuus ſine nocte. </s> <s xml:id="echoid-s15803" xml:space="preserve">Nã <lb/>& </s> <s xml:id="echoid-s15804" xml:space="preserve">nobis dies dicitur ante Solis ortum ſupra Horizontem. </s> <s xml:id="echoid-s15805" xml:space="preserve">Hoc autem <lb/>eſt quantum ad uulgarem ſenſibilitatem. </s> <s xml:id="echoid-s15806" xml:space="preserve">Non enim eſt dies artificialis, <lb/>quãtum ad Phyſicam rationem, niſi ab ortu Solis uſque ad occaſum eius <lb/>ſub Horizonte. </s> <s xml:id="echoid-s15807" xml:space="preserve">Ad hoc igitur, quòd lux uidetur ibi eße perpetua, (quo-<lb/>niam dies eſt, antequam Sol leuetur ſuper terram, per 18. </s> <s xml:id="echoid-s15808" xml:space="preserve">gradus, ut di-<lb/>cit Ptolemæus, alij uero magiſtri dicunt 30. </s> <s xml:id="echoid-s15809" xml:space="preserve">ſcilicet per quantitatẽ unius <lb/>ſigni) dicendum, quod aer eſt ibi nubiloſus, & </s> <s xml:id="echoid-s15810" xml:space="preserve">ſpiſſus. </s> <s xml:id="echoid-s15811" xml:space="preserve">Radius enim Sola-<lb/>ris ibi exiſtens debilis uirtutis magis de uaporibus eleuat, quàm poſſit con-<lb/>ſumere: </s> <s xml:id="echoid-s15812" xml:space="preserve">Vnde aerem non ſerenat, & </s> <s xml:id="echoid-s15813" xml:space="preserve">non eſt dies.</s> <s xml:id="echoid-s15814" xml:space="preserve"/> </p> <div xml:id="echoid-div871" type="float" level="2" n="1"> <note position="left" xlink:label="note-458-01" xlink:href="note-458-01a" xml:space="preserve">Proprieta-<lb/>tes eorũ, ꝗ <lb/>Zenith ha-<lb/>b<unsure/>ent<unsure/> in po <lb/>lo arctico.</note> </div> </div> <div xml:id="echoid-div873" type="section" level="1" n="349"> <head xml:id="echoid-head360" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s15815" xml:space="preserve"><emph style="sc">Septimvs</emph>, ac vltimus locus eſt eorum, qui ſub polo Arctico degunt, qui-<lb/>bus unam aſſignat proprietatem, quod uidelicet unicam habent diem natu-<lb/>ralem in toto anno, & </s> <s xml:id="echoid-s15816" xml:space="preserve">per dimidium an@um diem vnum artificialem, & </s> <s xml:id="echoid-s15817" xml:space="preserve">pe@ <lb/>dimidiũ reliquum annum noctem unam artificialem. </s> <s xml:id="echoid-s15818" xml:space="preserve">Quod intelligendũ eſt <lb/>ſi Sol regulariter in Zodiaco moueretur. </s> <s xml:id="echoid-s15819" xml:space="preserve">Nam cum uelocius ferat̃ per ſemi, <lb/>circulum Zodiac<unsure/>i Auſtralem, quàm per ſemicirculũ Borealẽ, ut ex Theoricis <lb/>Planetarum conſtat, erit dies artificialis paulo maior 6. </s> <s xml:id="echoid-s15820" xml:space="preserve">menſibus, & </s> <s xml:id="echoid-s15821" xml:space="preserve">nox ali-<lb/>quanto minor 6. </s> <s xml:id="echoid-s15822" xml:space="preserve">menſibus. </s> <s xml:id="echoid-s15823" xml:space="preserve">Soluit deinde tacitam quandam obiectionẽ. </s> <s xml:id="echoid-s15824" xml:space="preserve">Cum-<lb/>e<unsure/>nim iuxta Ptolemæum, & </s> <s xml:id="echoid-s15825" xml:space="preserve">cõiorem ſententiã incipiat dies, (includendo etiã <lb/>crepuſculum) exiſtente Sole 18. </s> <s xml:id="echoid-s15826" xml:space="preserve">grad. </s> <s xml:id="echoid-s15827" xml:space="preserve">infra Horizontem, & </s> <s xml:id="echoid-s15828" xml:space="preserve">Sol nunquam ma-<lb/>gis infra Horizontem deprimatur, quàm per grad. </s> <s xml:id="echoid-s15829" xml:space="preserve">23. </s> <s xml:id="echoid-s15830" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s15831" xml:space="preserve">quanta nimirum eſt <lb/>maxima Solis declinatio, uidetur, quod maior ibi exiſtat dies, quàm nox in to <lb/>to anno. </s> <s xml:id="echoid-s15832" xml:space="preserve">Vulgus enim appellat diem, moram Solis ſupra Horizontem unà <lb/>cum crepuſculo matutino, & </s> <s xml:id="echoid-s15833" xml:space="preserve">ueſpertino. </s> <s xml:id="echoid-s15834" xml:space="preserve">Reſpondet auctor ad hanc dubita-<lb/>tionem, ob nubiloſum aerem ibi exiſtentem, propter debilitatem radiorum <lb/>ſolariũ, qui fere ſunt æquidiſtantes Horizonti, crepuſcula non poſſe eſſe tam <lb/>clara, ut aerem reddere poſſint ſerenum, diemq; </s> <s xml:id="echoid-s15835" xml:space="preserve">efficere. </s> <s xml:id="echoid-s15836" xml:space="preserve">Poſſet quoque re-<lb/>ſponderi, quicquid ſit de crepuſculis, Aſtronomus loqui de die & </s> <s xml:id="echoid-s15837" xml:space="preserve">nocte arti-<lb/>ficiali proprie, prout videlicet Dies artificialis eſt mora Solis ſupra Horizon <lb/>@em. </s> <s xml:id="echoid-s15838" xml:space="preserve">Nam hac ratione uerum erit, ſub polo eſſe diem quaſi per dimidium an- <pb o="423" file="459" n="460" rhead="Ioan. de Sacro Boſco."/> num, ſimiliterq́; </s> <s xml:id="echoid-s15839" xml:space="preserve">noctem, ut ex ſphæra materiali conſtat. </s> <s xml:id="echoid-s15840" xml:space="preserve">His adde, quòd non <lb/>omnia puncta cæli illis oriuntur, & </s> <s xml:id="echoid-s15841" xml:space="preserve">occidunt, ſed perpetuo media pars eorum <lb/>conſpicua exiſtit, & </s> <s xml:id="echoid-s15842" xml:space="preserve">altera medietas ſub Horizonte latet.</s> <s xml:id="echoid-s15843" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15844" xml:space="preserve"><emph style="sc">Eadem</emph> hæc 7. </s> <s xml:id="echoid-s15845" xml:space="preserve">loca concipienda, atque intelligenda ſunt in altera me-<unsure/> <lb/> <anchor type="note" xlink:label="note-459-01a" xlink:href="note-459-01"/> dietate cæli ab Aequatore uerſus Meridionalem polum. </s> <s xml:id="echoid-s15846" xml:space="preserve">Verum omnia, quæ <lb/>in his dicta ſunt de ſignis Borealibus, in illis intelligenda ſunt de ſignis Au-<unsure/> <lb/>ſtralibus, & </s> <s xml:id="echoid-s15847" xml:space="preserve">contra.</s> <s xml:id="echoid-s15848" xml:space="preserve"/> </p> <div xml:id="echoid-div873" type="float" level="2" n="1"> <note position="right" xlink:label="note-459-01" xlink:href="note-459-01a" xml:space="preserve">Quo pact@ <lb/>eædem pro-<lb/>prietates in <lb/>telligendæ <lb/>ſint inſphæ <lb/>ra auſtrali.</note> </div> </div> <div xml:id="echoid-div875" type="section" level="1" n="350"> <head xml:id="echoid-head361" xml:space="preserve">DE DIVISIONE CLIMATVM.</head> <note position="right" xml:space="preserve">Quanta ſit <lb/>por<unsure/>tio ter-<lb/>ræ habita-<lb/>bilis ſecun <lb/>dũ auctorẽ <lb/>& quo mo-<lb/>do ſeptem <lb/>climaia ab <lb/>eo deſcribã <lb/>tur.</note> <p style="it"> <s xml:id="echoid-s15849" xml:space="preserve"><emph style="sc">INteligatvr</emph> autem quidam circulus in ſuperficie ter-<lb/>rę directe ſuppoſitus Aeq<unsure/>uinoctiali. </s> <s xml:id="echoid-s15850" xml:space="preserve">Intelligatur etiam alius <lb/>circulus in ſuperficie terrę tranſiens per orientem & </s> <s xml:id="echoid-s15851" xml:space="preserve">occiden <lb/>tem, & </s> <s xml:id="echoid-s15852" xml:space="preserve">per polos mundi. </s> <s xml:id="echoid-s15853" xml:space="preserve">I ſti duo circuli interſecant ſeſe in duo <lb/>buslocis ad angullos rectos ſphærales; </s> <s xml:id="echoid-s15854" xml:space="preserve">etdiuidũt totã terrã in quatuor quar <lb/>tas; </s> <s xml:id="echoid-s15855" xml:space="preserve">Quarum una eſt noſtra habitabilis, illa ſcilicet, quæ intercipitur inter <lb/>ſemicirculum d@ctum ab oriente in occidentem in ſuperficie Aequinoctia <lb/>lis, & </s> <s xml:id="echoid-s15856" xml:space="preserve">ſemicirculum ductum ab oriente in occidentem per polum Arcti-<lb/>cum. </s> <s xml:id="echoid-s15857" xml:space="preserve">Nec tamen illa quarta tota eſt habitabilis, quoniam partes illius pro-<lb/>p<unsure/> nquę. </s> <s xml:id="echoid-s15858" xml:space="preserve">Aequinoctiali inhabitabiles ſunt propter nimium calorem. </s> <s xml:id="echoid-s15859" xml:space="preserve">Simili-<lb/>ter partes eius propinquæ polo Arctico inhabitabiles ſunt propter nimiã <lb/>frigiditatem. </s> <s xml:id="echoid-s15860" xml:space="preserve">Intelligatur igitur una linea æquidiſtans ab Aequinoctia-<lb/>li, diuidens partes inhabitabiles propter e<unsure/>alorem, à partibus iahabitabili-<lb/>bus, quæ ſunt uerſus Septentrionem. </s> <s xml:id="echoid-s15861" xml:space="preserve">Intelligatur etiam alia linea æqui-<lb/>dictans à polo Arctico, diuidens partes quartę, quæ ſunt uerſus Septen-<lb/>trionem, inhabitabiles propter frigus, à partibus habitabilibus, quæ <lb/>ſunt uerſus Aequinoctialem: </s> <s xml:id="echoid-s15862" xml:space="preserve">Inter iſtas etiam duas lineas extremas intel <lb/>ligantur ſex lineæ par allelæ Aequinoctiali, quæcum duabus prioribus di-<lb/>uidunt partem totalem quartæ habitabilem in ſeptem portiones, quę dicũ <lb/>tur ſeptem Climata.</s> <s xml:id="echoid-s15863" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div876" type="section" level="1" n="351"> <head xml:id="echoid-head362" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s15864" xml:space="preserve"><emph style="sc">Haec</emph> eſt quarta huius cap. </s> <s xml:id="echoid-s15865" xml:space="preserve">pars, in qua auctor climata mundi deſcribit, <lb/>eo quod variato climate, varietur quoq; </s> <s xml:id="echoid-s15866" xml:space="preserve">neceſſario ortus, & </s> <s xml:id="echoid-s15867" xml:space="preserve">occaſus ſignorũ, <lb/>nec non quautitas dierum artificialium, & </s> <s xml:id="echoid-s15868" xml:space="preserve">noctium. </s> <s xml:id="echoid-s15869" xml:space="preserve">Vt igitur declaret, quid-<lb/>nam ipſe per clima intelligat, ait concipiendũ eſſe circulum in ſuperficie terrę <lb/>directe ſuppoſitũ Aequinoctiali; </s> <s xml:id="echoid-s15870" xml:space="preserve">Item alium tranſeuntẽ per polos mundi, & </s> <s xml:id="echoid-s15871" xml:space="preserve"><lb/>per puncta orientis, & </s> <s xml:id="echoid-s15872" xml:space="preserve">occidẽtis, intellige abſoluti, ideſt, per inſulas Canarias <lb/>quæ r<unsure/>erminant occidentem, & </s> <s xml:id="echoid-s15873" xml:space="preserve">per punctum, quod ab ipſis orientem uerſus in <lb/>eodem parallelo grad. </s> <s xml:id="echoid-s15874" xml:space="preserve">180. </s> <s xml:id="echoid-s15875" xml:space="preserve">diſtat, hoc enim terminat orientem. </s> <s xml:id="echoid-s15876" xml:space="preserve">Tanta enim <lb/>viſa fuit antiquis longitudo terræ habitabilis, ut uidere eſt apud Ptolomæũ.</s> <s xml:id="echoid-s15877" xml:space="preserve"> <pb o="424" file="460" n="461" rhead="Comment. in III Cap. Sphæræ"/> His duobus circulis diuidetur tota ſuperficies terræ in quatuor Quadrãtes, <lb/>quorum unus eſt hic noſter habitabilis, ille ſcilicet, qui continetur ſemicir-<lb/>culo Aequatoris, & </s> <s xml:id="echoid-s15878" xml:space="preserve">alio ſemicirculo Septentrionali, qui deſcriptus fuit per <lb/>Orientem, Occidentemq́ue, & </s> <s xml:id="echoid-s15879" xml:space="preserve">polum Arcticum. </s> <s xml:id="echoid-s15880" xml:space="preserve">Non quòd, ut<unsure/> auctor inquit, <lb/>totus iſte Quadrans terræ habitetur, quia dicit hoc falſum eſſe, cum tam pars <lb/>prope Aequatorem ob nimium caloris exceſſum, quàm pars iuxta polum Ar-<lb/>cticũ propter nimiũ frigus habitari nequeat. </s> <s xml:id="echoid-s15881" xml:space="preserve">Vnde ſubiungit, intelligendã eſ-<lb/>ſe lineã æquidiſtantem Aequatori, quæ dirimat partem in habitabilẽ propter <lb/>calorem à parte habitabili uerſus Septentrionem. </s> <s xml:id="echoid-s15882" xml:space="preserve">Pari ratione concipiendã <lb/>eſſe aliam lineam Aequatori æquidiſtantẽ, ſeu ęqualiter à polo Arctico remo <lb/>tam, quæ ſeparet partẽ inhabitabilẽ propter frigus à parte habitabili uerſus <lb/>Meridiem. </s> <s xml:id="echoid-s15883" xml:space="preserve">Nam pars Quadrantis terræ inter dictas duas lineas comprehenſa <lb/>habitatur duntaxat. </s> <s xml:id="echoid-s15884" xml:space="preserve">Quod ſi inter has duas lineas parallelas aliæ ſex paralle-<lb/>læ deſcribantur, diuiſa erit tota pars terræ habitabilis in ſeptem partes, quæ <lb/>ſeptem climata mundi nuncupantur. </s> <s xml:id="echoid-s15885" xml:space="preserve">Quãtum autem una linea ab altera di-<lb/>ſtare debeat, ut climata conſtituantur, ex ſequentibus manifeſtum erit.</s> <s xml:id="echoid-s15886" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">Clima quid.<unsure/> <lb/>ſit.</note> <p style="it"> <s xml:id="echoid-s15887" xml:space="preserve">DICITVR autem Clima, tantum ſpatium terræ, per quantum ſen <lb/>ſibiliter uariatur horologium. </s> <s xml:id="echoid-s15888" xml:space="preserve">Idem namque dies ęſtiuus aliquantus, qui <lb/>eſt in una regione, ſenſibiliter eſt minor in regione propinquiori Auſtro. <lb/></s> <s xml:id="echoid-s15889" xml:space="preserve">Spatium igitur tantum, quantum incipit dies idem ſenſibiliter uariari, di-<lb/>tur Clima; </s> <s xml:id="echoid-s15890" xml:space="preserve">Nec eſt idem horologium cũ principio, & </s> <s xml:id="echoid-s15891" xml:space="preserve">fine huius ſpatij ob <lb/>ſeruatum. </s> <s xml:id="echoid-s15892" xml:space="preserve">Horæ enim diei ſenſibiliter uariantur, quare & </s> <s xml:id="echoid-s15893" xml:space="preserve">horologium.</s> <s xml:id="echoid-s15894" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div877" type="section" level="1" n="352"> <head xml:id="echoid-head363" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s15895" xml:space="preserve"><emph style="sc">Docet</emph> iam clarius, quantum debeat eſſe ſpatium inter duas lineas pa-<lb/>rallelas interiectum, ut Clima conſtituatur, dicẽs Clima eſſe tantum ſpatium <lb/>in ſuperficie terræ, in quanto notabiliter dies æſtiua, nempe maxima, uaria-<lb/>tur, ſcilicet per ſemihoram. </s> <s xml:id="echoid-s15896" xml:space="preserve">Ita ut Clima non ſit aliud, quam certum ſpa-<lb/>tium Zonæ temperatæ, & </s> <s xml:id="echoid-s15897" xml:space="preserve">habitabilis, inter cuius principium, & </s> <s xml:id="echoid-s15898" xml:space="preserve">finem, (proce <lb/>dendo à polo ad Aequatorem, & </s> <s xml:id="echoid-s15899" xml:space="preserve">contra) maximæ diei æſtiuæ, uel noctis hy-<lb/>bernæ quantitas per ſemihoram augetur, uel diminuitur; </s> <s xml:id="echoid-s15900" xml:space="preserve">adeo ut ſi v.</s> <s xml:id="echoid-s15901" xml:space="preserve">g. </s> <s xml:id="echoid-s15902" xml:space="preserve">dies <lb/>maxima in principio alicuius climatis uerſus Auſtrum continet hora 15. </s> <s xml:id="echoid-s15903" xml:space="preserve">In <lb/>fine uerſus polum compre hendat hora 15 {1/2}. </s> <s xml:id="echoid-s15904" xml:space="preserve">Quod ſi non uelimus rationem <lb/>habere temperatæ Zonæ, poterit in uniuerſum dici Clima eſſe ſpatium terræ <lb/>inter duos parallelos comprehenſum, in quo longiſſima dies nel creſcit, uel <lb/>decreſcit per dimidiam horam. </s> <s xml:id="echoid-s15905" xml:space="preserve">Qua ratione plura erunt Climata conſtituen <lb/>da, quàm ſeptem, ut mox dicemus.</s> <s xml:id="echoid-s15906" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s15907" xml:space="preserve">MEDIVM igitur primi Climatis eſt, ubi maioris diei prolixitas <lb/> <anchor type="note" xlink:label="note-460-02a" xlink:href="note-460-02"/> eſt 13. </s> <s xml:id="echoid-s15908" xml:space="preserve">horarũ, & </s> <s xml:id="echoid-s15909" xml:space="preserve">eleuatur polus mundi ſupra circulum hemiſphęrij 16. <lb/></s> <s xml:id="echoid-s15910" xml:space="preserve">gradibus, & </s> <s xml:id="echoid-s15911" xml:space="preserve">duabus tertijs unius, & </s> <s xml:id="echoid-s15912" xml:space="preserve">dicitur Clima dia Meroes. </s> <s xml:id="echoid-s15913" xml:space="preserve">Initium <lb/>uero eius eſt, ubi diei maioris prolixitas eſt 12. </s> <s xml:id="echoid-s15914" xml:space="preserve">horarum, & </s> <s xml:id="echoid-s15915" xml:space="preserve">dimidię, & </s> <s xml:id="echoid-s15916" xml:space="preserve"><lb/>quartę unius horę, & </s> <s xml:id="echoid-s15917" xml:space="preserve">eleuatur polus ſupra Horizontem gradibus 12. </s> <s xml:id="echoid-s15918" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s15919" xml:space="preserve">dimidio, & </s> <s xml:id="echoid-s15920" xml:space="preserve">quarta unius gradus. </s> <s xml:id="echoid-s15921" xml:space="preserve">Et extenditur eius latitudo uſque <pb o="425" file="461" n="462" rhead="Ioan. de Sacro Boſco."/> ad locum, ubi longitudo prolixioris diei eſt 13. </s> <s xml:id="echoid-s15922" xml:space="preserve">horarum, & </s> <s xml:id="echoid-s15923" xml:space="preserve">quartæ unius, <lb/>& </s> <s xml:id="echoid-s15924" xml:space="preserve">eleuatur polus ſupra Horizontem 20. </s> <s xml:id="echoid-s15925" xml:space="preserve">gradibus, & </s> <s xml:id="echoid-s15926" xml:space="preserve">dimidio: </s> <s xml:id="echoid-s15927" xml:space="preserve">Quod ſpa-<lb/>cium terræ eſt 440. </s> <s xml:id="echoid-s15928" xml:space="preserve">milliariorum. <lb/></s> <s xml:id="echoid-s15929" xml:space="preserve"> <anchor type="note" xlink:label="note-461-01a" xlink:href="note-461-01"/> </s> </p> <div xml:id="echoid-div877" type="float" level="2" n="1"> <note position="left" xlink:label="note-460-02" xlink:href="note-460-02a" xml:space="preserve">Clima pri-<lb/>@um.</note> <note position="right" xlink:label="note-461-01" xlink:href="note-461-01a" xml:space="preserve">Clima ſ@-<lb/>cundum.</note> </div> <p style="it"> <s xml:id="echoid-s15930" xml:space="preserve">MEDIVM autem ſecundi Climatis eſt, ubi maior dies eſt 13. </s> <s xml:id="echoid-s15931" xml:space="preserve">ho-<lb/>rarum, & </s> <s xml:id="echoid-s15932" xml:space="preserve">dimidiæ, & </s> <s xml:id="echoid-s15933" xml:space="preserve">eleuatio poli ſupra Horizontem 24. </s> <s xml:id="echoid-s15934" xml:space="preserve">graduum, & </s> <s xml:id="echoid-s15935" xml:space="preserve"><lb/>quartæ partis unius gradus. </s> <s xml:id="echoid-s15936" xml:space="preserve">Et dicitur Clima dia Syenes. </s> <s xml:id="echoid-s15937" xml:space="preserve">Latitudo ue-<lb/>ro eius eſt ex termino primi Climatis uſque ad locum, ubi fit dies proli-<lb/>xior 13. </s> <s xml:id="echoid-s15938" xml:space="preserve">horarum, & </s> <s xml:id="echoid-s15939" xml:space="preserve">dimidiæ, & </s> <s xml:id="echoid-s15940" xml:space="preserve">quartæ partis unius horæ, et eleuatur po <lb/>lus 27. </s> <s xml:id="echoid-s15941" xml:space="preserve">gradibus, & </s> <s xml:id="echoid-s15942" xml:space="preserve">dimidio. </s> <s xml:id="echoid-s15943" xml:space="preserve">Et ſpatium terræ eſt 400. </s> <s xml:id="echoid-s15944" xml:space="preserve">milliariorum. <lb/></s> <s xml:id="echoid-s15945" xml:space="preserve"> <anchor type="note" xlink:label="note-461-02a" xlink:href="note-461-02"/> </s> </p> <div xml:id="echoid-div878" type="float" level="2" n="2"> <note position="right" xlink:label="note-461-02" xlink:href="note-461-02a" xml:space="preserve">Clima ter-<lb/>tium.</note> </div> <p style="it"> <s xml:id="echoid-s15946" xml:space="preserve">MEDIVM tertij Climatis eſt, ubifit longitudo prolixioris diei 14. <lb/></s> <s xml:id="echoid-s15947" xml:space="preserve">horarum, & </s> <s xml:id="echoid-s15948" xml:space="preserve">eleuatio poli ſupra Horizontem 30. </s> <s xml:id="echoid-s15949" xml:space="preserve">graduum, & </s> <s xml:id="echoid-s15950" xml:space="preserve">dimidij, <lb/>& </s> <s xml:id="echoid-s15951" xml:space="preserve">quartæ unius partis, & </s> <s xml:id="echoid-s15952" xml:space="preserve">dicitur clima dia Alexandrias. </s> <s xml:id="echoid-s15953" xml:space="preserve">Latitudo eius <lb/>eſt ex termino ſecundi Climatis uſque ad e@m locum, ubi prolixior dies eſt <lb/>14. </s> <s xml:id="echoid-s15954" xml:space="preserve">hor arum, & </s> <s xml:id="echoid-s15955" xml:space="preserve">quartæ unius, altitudo poli 33. </s> <s xml:id="echoid-s15956" xml:space="preserve">graduum, & </s> <s xml:id="echoid-s15957" xml:space="preserve">duarum ter-<lb/>tiarum: </s> <s xml:id="echoid-s15958" xml:space="preserve">Quod ſpatium terræ eſt 350. </s> <s xml:id="echoid-s15959" xml:space="preserve">milliariorum.</s> <s xml:id="echoid-s15960" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s15961" xml:space="preserve">MEDIVM quarti Climatis eſt, ubi maioris diei prolixitas eſt 14. <lb/></s> <s xml:id="echoid-s15962" xml:space="preserve"> <anchor type="note" xlink:label="note-461-03a" xlink:href="note-461-03"/> horarum, & </s> <s xml:id="echoid-s15963" xml:space="preserve">dimidiæ: </s> <s xml:id="echoid-s15964" xml:space="preserve">& </s> <s xml:id="echoid-s15965" xml:space="preserve">axis altitudo 36. </s> <s xml:id="echoid-s15966" xml:space="preserve">graduum, & </s> <s xml:id="echoid-s15967" xml:space="preserve">duarum quinta-<lb/>rum, & </s> <s xml:id="echoid-s15968" xml:space="preserve">dicitur dia Rhodon. </s> <s xml:id="echoid-s15969" xml:space="preserve">Latitudo uero eius eſt ex termino tertij Clima <lb/>tis, uſque ad eum locum, ubi prolixitas maioris diei eſt 14. </s> <s xml:id="echoid-s15970" xml:space="preserve">horarum, & </s> <s xml:id="echoid-s15971" xml:space="preserve">di-<lb/>midiæ, & </s> <s xml:id="echoid-s15972" xml:space="preserve">quartæ partis unius; </s> <s xml:id="echoid-s15973" xml:space="preserve">eleuatio autem poli 39. </s> <s xml:id="echoid-s15974" xml:space="preserve">graduum: </s> <s xml:id="echoid-s15975" xml:space="preserve">Quod ſpa <lb/>tium terræ eſt 300. </s> <s xml:id="echoid-s15976" xml:space="preserve">milliarium. <lb/></s> <s xml:id="echoid-s15977" xml:space="preserve"> <anchor type="note" xlink:label="note-461-04a" xlink:href="note-461-04"/> </s> </p> <div xml:id="echoid-div879" type="float" level="2" n="3"> <note position="right" xlink:label="note-461-03" xlink:href="note-461-03a" xml:space="preserve">Clima <lb/>quartum.</note> <note position="right" xlink:label="note-461-04" xlink:href="note-461-04a" xml:space="preserve">Clima <lb/>quintum.</note> </div> <p style="it"> <s xml:id="echoid-s15978" xml:space="preserve">MEDIVM quinti Climatis eſt, ubi maior dies eſt 15. </s> <s xml:id="echoid-s15979" xml:space="preserve">horarum, & </s> <s xml:id="echoid-s15980" xml:space="preserve"><lb/>eleuatio poli 41. </s> <s xml:id="echoid-s15981" xml:space="preserve">gradus, & </s> <s xml:id="echoid-s15982" xml:space="preserve">tertiæ unius; </s> <s xml:id="echoid-s15983" xml:space="preserve">& </s> <s xml:id="echoid-s15984" xml:space="preserve">dicitur Clima dia Romes. </s> <s xml:id="echoid-s15985" xml:space="preserve">La-<lb/>titudo uero eius eſt ex termino quarti Climatis, uſque ad eum locum, <lb/>ubi prolixitas maximi diei fit 15. </s> <s xml:id="echoid-s15986" xml:space="preserve">horarum, & </s> <s xml:id="echoid-s15987" xml:space="preserve">quartæ unius, & </s> <s xml:id="echoid-s15988" xml:space="preserve">eleua-<lb/>tio axis 43. </s> <s xml:id="echoid-s15989" xml:space="preserve">gradum, & </s> <s xml:id="echoid-s15990" xml:space="preserve">dimidij: </s> <s xml:id="echoid-s15991" xml:space="preserve">Quod ſpacium terræ eſt 255. </s> <s xml:id="echoid-s15992" xml:space="preserve">millia-<lb/>riorum.</s> <s xml:id="echoid-s15993" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s15994" xml:space="preserve">MEDIVM ſexti Climatis eſt, ubi prolixior dies eſt 15. </s> <s xml:id="echoid-s15995" xml:space="preserve">horarum <lb/> <anchor type="note" xlink:label="note-461-05a" xlink:href="note-461-05"/> & </s> <s xml:id="echoid-s15996" xml:space="preserve">dimidię; </s> <s xml:id="echoid-s15997" xml:space="preserve">& </s> <s xml:id="echoid-s15998" xml:space="preserve">eleuatur polus ſupra Horizontem 45. </s> <s xml:id="echoid-s15999" xml:space="preserve">gradibus, & </s> <s xml:id="echoid-s16000" xml:space="preserve">dua-<lb/>bus quintis unius: </s> <s xml:id="echoid-s16001" xml:space="preserve">Et dicitur Clima dia Boriſtheneos. </s> <s xml:id="echoid-s16002" xml:space="preserve">Latitudo uero eius <lb/>eſt ex termino quinti Climatis, uſque ad eum locum, ubi longitudo diei <lb/>prolixioris eſt 15. </s> <s xml:id="echoid-s16003" xml:space="preserve">horarum, & </s> <s xml:id="echoid-s16004" xml:space="preserve">dimidiæ, & </s> <s xml:id="echoid-s16005" xml:space="preserve">quartæ unius: </s> <s xml:id="echoid-s16006" xml:space="preserve">& </s> <s xml:id="echoid-s16007" xml:space="preserve">axis ele-<lb/>uatio 47. </s> <s xml:id="echoid-s16008" xml:space="preserve">graduum, & </s> <s xml:id="echoid-s16009" xml:space="preserve">quartæ unius: </s> <s xml:id="echoid-s16010" xml:space="preserve">Quæ diſtantia terræ eſt 212. </s> <s xml:id="echoid-s16011" xml:space="preserve">mil-<lb/>liariorum.</s> <s xml:id="echoid-s16012" xml:space="preserve"/> </p> <div xml:id="echoid-div880" type="float" level="2" n="4"> <note position="right" xlink:label="note-461-05" xlink:href="note-461-05a" xml:space="preserve">Clima ſex-<lb/>tum.</note> </div> <p style="it"> <s xml:id="echoid-s16013" xml:space="preserve">MEDIVM autem ſeptimi Climatis eſt, ubi maior prolixitas diei <lb/> <anchor type="note" xlink:label="note-461-06a" xlink:href="note-461-06"/> eſt 16. </s> <s xml:id="echoid-s16014" xml:space="preserve">horarum; </s> <s xml:id="echoid-s16015" xml:space="preserve">& </s> <s xml:id="echoid-s16016" xml:space="preserve">eleuatio poli ſupra Horizontem 48. </s> <s xml:id="echoid-s16017" xml:space="preserve">graduum, & </s> <s xml:id="echoid-s16018" xml:space="preserve"><lb/>duarum tertiarum. </s> <s xml:id="echoid-s16019" xml:space="preserve">Et dicitur Clima dia Riphæon. </s> <s xml:id="echoid-s16020" xml:space="preserve">Latitudo uero eius <lb/>eſt ex termino ſexti Climatis, uſque ad eu@ locum, ubi maxima dies eſt <pb o="426" file="462" n="463" rhead="Comment. in III. Cap. Sphæræ"/> 16. </s> <s xml:id="echoid-s16021" xml:space="preserve">horarum, & </s> <s xml:id="echoid-s16022" xml:space="preserve">quartæ unius, & </s> <s xml:id="echoid-s16023" xml:space="preserve">eleuatur polus mundi ſupra Horizon-<lb/>tem 50. </s> <s xml:id="echoid-s16024" xml:space="preserve">gradibus & </s> <s xml:id="echoid-s16025" xml:space="preserve">dimidio: </s> <s xml:id="echoid-s16026" xml:space="preserve">Quod ſpatium terræ eſt 185. </s> <s xml:id="echoid-s16027" xml:space="preserve">milliario-<lb/>rum. <lb/></s> <s xml:id="echoid-s16028" xml:space="preserve"> <anchor type="note" xlink:label="note-462-01a" xlink:href="note-462-01"/> </s> </p> <div xml:id="echoid-div881" type="float" level="2" n="5"> <note position="right" xlink:label="note-461-06" xlink:href="note-461-06a" xml:space="preserve">Clima ſept@ <lb/>mum.</note> <note position="left" xlink:label="note-462-01" xlink:href="note-462-01a" xml:space="preserve">Cur non <lb/>ſint plura <lb/>climata, <lb/>quã ſeptẽ.</note> </div> <p style="it"> <s xml:id="echoid-s16029" xml:space="preserve">VLTRA autem huius ſeptimi Climatis terminum, licet plurès <lb/>ſint inſulæ, & </s> <s xml:id="echoid-s16030" xml:space="preserve">hominum habitationes, quidquid tamen ſit, quoniam pra-<lb/>uæ eſt habitationis, ſub Climate non computatur.</s> <s xml:id="echoid-s16031" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div883" type="section" level="1" n="353"> <head xml:id="echoid-head364" xml:space="preserve">COMMENTARIVS.</head> <note position="left" xml:space="preserve">Quid au-<lb/>ctor in ſin-<lb/>gulis clima <lb/>tibus expli <lb/>cet.</note> <p> <s xml:id="echoid-s16032" xml:space="preserve"><emph style="sc">Percvrrit</emph> hocloco omnia ſeptem Climata docens, quanta ſit dies <lb/>maxima in medio cuiuslibet Climatis, quanta item ſit eleuatio poli, & </s> <s xml:id="echoid-s16033" xml:space="preserve">quo-<lb/>nam pacto appelletur quoduis Clima; </s> <s xml:id="echoid-s16034" xml:space="preserve">Nan@ medium cuiuſque Climatis de-<lb/>nominatur uel à ciuitate aliqua inſigni, vel inſula, vel fluuio, vel monte, per <lb/>quem nim irum tranſit parallelus, qui per medium Climatis deſcribitur. </s> <s xml:id="echoid-s16035" xml:space="preserve">Tan-<lb/>dem, quot milliaria complectatur latitudo cuiuslibet Climatis, tribuens <lb/>cuilibet gradui terreno milliaria 56 {2/3}. </s> <s xml:id="echoid-s16036" xml:space="preserve">quot nimirum Alphraganus conce-<lb/>debat, ut ſupra diximus. </s> <s xml:id="echoid-s16037" xml:space="preserve">Deinde determinat quoque quantito<unsure/>tem maximæ <lb/>diei, & </s> <s xml:id="echoid-s16038" xml:space="preserve">eleuationem poli tam in principio, quàm in fine cuiuſque Climatis: <lb/></s> <s xml:id="echoid-s16039" xml:space="preserve">Verum hæc omnia perſpicua ſunt in litera, conſpiciunturq; </s> <s xml:id="echoid-s16040" xml:space="preserve">manifeſte in ſe-<lb/>quenti tabula.</s> <s xml:id="echoid-s16041" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16042" xml:space="preserve"><emph style="sc">Svbivngit</emph> tamen, etiamſi ſint aliæ habitationes extra hæc ſeptem <lb/>Climata, eas non computari ab auctoribus inter Climata, quia non ſunt ad-<lb/>modum commodæ, ſed uel calidæ nimis, uel frigidæ.</s> <s xml:id="echoid-s16043" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>## Clima- \\ ta. # ## Maxima \\ dies. # ## Altitudo \\ Poli. # Millia- \\ ria. # <emph style="sc">D</emph>enominationes \\ Climatum. <lb/># # H. # M. # G. # M. <lb/># Initium # 12 # 45 # 12 # 45 <lb/>I. # Medium # 13 # 0 # 16 # 40 # 440 # Per Meroen ci- \\ uitatẽ <emph style="sc">A</emph> ethiopię <lb/># Finis. # 13 # 15 # 20 # 30 <lb/># Initium # 13 # 15 # 30 # 30 <lb/>II. # Medium # 13 # 30 # 24 # 15 # 400 # Per Syenen vrbẽ \\ Aegypti. <lb/># Finis. # 13 # 45 # 27 # 30 <lb/># Initium # 13 # 45 # 27 # 30 <lb/>III. # Medium # 14 # 0 # 30 # 45 # 350 # Per Alexãdriam \\ Aegypti Metro- \\ polim. <lb/># Finis. # 14 # 15 # 33 # 40 <lb/># Initium # 14 # 15 # 33 # 40 <lb/>IIII. # Medium # 14 # 30 # 36 # 24 # 300 # Per Rhodum In \\ ſulam. <lb/># Finis. # 14 # 45 # 39 # 0 <lb/># Initium # 14 # 45 # 39 # 0 <lb/>V. # Medium # 15 # 0 # 41 # 20 # 255 # Per Romam ca- \\ put mundi. <lb/># Finis. # 15 # 15 # 43 # 30 <lb/></note> <pb o="427" file="463" n="464" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve"> <lb/>## Clima- \\ ta. # ## Maxima \\ dies. # ## Altitudo \\ Poli. # Millia- \\ ria. # Denominationes \\ Climatum. <lb/># # H. # M. # G. # M. <lb/># Initium # 15 # 15 # 43 # 30 <lb/>VI. # Medium # 15 # 30 # 45 # 24 # 212 # Per Boriſthenẽ flu \\ men Sarmatiæ. <lb/># Finis # 15 # 45 # 47 # 15 <lb/># Initium # 15 # 45 # 47 # 15 <lb/>VII. # Medium # 16 # 0 # 48 # 40 # 185 # Per Alphæos mõ- \\ tes Sermatiæ. <lb/># Finis # 16 # 15 # 50 # 30 <lb/></note> <p style="it"> <s xml:id="echoid-s16044" xml:space="preserve"><emph style="sc">Omnis</emph> itaque inter terminum initialem Climatum, & </s> <s xml:id="echoid-s16045" xml:space="preserve">finalem <lb/> <anchor type="note" xlink:label="note-463-02a" xlink:href="note-463-02"/> eorundem diuerſitas eſt trium horarum, & </s> <s xml:id="echoid-s16046" xml:space="preserve">dimidiæ; </s> <s xml:id="echoid-s16047" xml:space="preserve">Et ex eleuatione po-<lb/>li ſupra Horizontem 37. </s> <s xml:id="echoid-s16048" xml:space="preserve">gr. </s> <s xml:id="echoid-s16049" xml:space="preserve">& </s> <s xml:id="echoid-s16050" xml:space="preserve">45. </s> <s xml:id="echoid-s16051" xml:space="preserve">min. </s> <s xml:id="echoid-s16052" xml:space="preserve">Sic igitur patet uniuſcuiuſque <lb/>climatis latitudo à principio ipſius uerſus Aequinoctialem uſque in finem <lb/>eiuſdem uerſus polum Arcticum; </s> <s xml:id="echoid-s16053" xml:space="preserve">Et quod primi Climatis latitudo eſt ma <lb/>ior latitudine ſecundi, & </s> <s xml:id="echoid-s16054" xml:space="preserve">ſic deinceps. </s> <s xml:id="echoid-s16055" xml:space="preserve">Longitudo autem climatis poteſt <lb/>appellari linea ducta ab oriente in occidentem, æquiſtans Aequinoctiali. <lb/></s> <s xml:id="echoid-s16056" xml:space="preserve">Vnde longitudo primi Climatis eſt maior longitudine ſecundi, & </s> <s xml:id="echoid-s16057" xml:space="preserve">ſic dein-<lb/>ceps, quod cõtingit propter anguſtiam ſphæræ. </s> <s xml:id="echoid-s16058" xml:space="preserve">Spatium quoque inter prin-<lb/>cipium primi Climatis, & </s> <s xml:id="echoid-s16059" xml:space="preserve">finem ſeptimi eſt 2142. </s> <s xml:id="echoid-s16060" xml:space="preserve">milliariorum.</s> <s xml:id="echoid-s16061" xml:space="preserve"/> </p> <div xml:id="echoid-div883" type="float" level="2" n="1"> <note position="right" xlink:label="note-463-02" xlink:href="note-463-02a" xml:space="preserve">Diuerſitas <lb/>quoad ho-<lb/>ras, & alti-<lb/>tudinẽ poli <lb/>in ſeptem <lb/>climatibus <lb/>& alię nõ-<lb/>nullæ com-<lb/>parationes <lb/>inter illa.</note> </div> </div> <div xml:id="echoid-div885" type="section" level="1" n="354"> <head xml:id="echoid-head365" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s16062" xml:space="preserve"><emph style="sc">Colligit</emph> quinque ex ijs, quæ dicta ſunt.</s> <s xml:id="echoid-s16063" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16064" xml:space="preserve">I. </s> <s xml:id="echoid-s16065" xml:space="preserve">Differentiam inter maximum diem primi climatis in principio, & </s> <s xml:id="echoid-s16066" xml:space="preserve">maxi <lb/>mum diem ſeptimi climatis in fine eſſe Hor. </s> <s xml:id="echoid-s16067" xml:space="preserve">3. </s> <s xml:id="echoid-s16068" xml:space="preserve">min. </s> <s xml:id="echoid-s16069" xml:space="preserve">30.</s> <s xml:id="echoid-s16070" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16071" xml:space="preserve">II. </s> <s xml:id="echoid-s16072" xml:space="preserve">Exceſſum altitudiuis poli in extremo ſeptimi climatis ſupra altitudinẽ <lb/>poli initio primi climatis comprehendere grad. </s> <s xml:id="echoid-s16073" xml:space="preserve">37. </s> <s xml:id="echoid-s16074" xml:space="preserve">min. </s> <s xml:id="echoid-s16075" xml:space="preserve">45. </s> <s xml:id="echoid-s16076" xml:space="preserve">Quæ perſpicua <lb/>ſunt ex dictis, & </s> <s xml:id="echoid-s16077" xml:space="preserve">tabula præmiſſa.</s> <s xml:id="echoid-s16078" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16079" xml:space="preserve">III. </s> <s xml:id="echoid-s16080" xml:space="preserve">Latitudinem primi climatis eſſe maiorem latitudine ſecundi, & </s> <s xml:id="echoid-s16081" xml:space="preserve">ſecũ <lb/>di latitudinẽ maiorem, quam tertij, &</s> <s xml:id="echoid-s16082" xml:space="preserve">c. </s> <s xml:id="echoid-s16083" xml:space="preserve">ut cernitur in prædicta tabula. </s> <s xml:id="echoid-s16084" xml:space="preserve">Quod <lb/>autem mutatio unius ſemihoræ in quãtitate maximæ diei minus ſpatium re <lb/>quirat in regione magis ſeptentrionali, quàm in magis Auſtrali, non eſt huius <lb/>loci demonſtrare: </s> <s xml:id="echoid-s16085" xml:space="preserve">Demonſtratur aut id elegantiſſime à Petro Nonio Luſita <lb/>no in quadam appendice huius ſphæræ, quam nos in ijs, quæ ad primum Mo <lb/>bile ſpectant, clariorem reddemus; </s> <s xml:id="echoid-s16086" xml:space="preserve">ubi oſtendit, maius incrementum ſuſcipe-<lb/>re dies, ſi tribus v.</s> <s xml:id="echoid-s16087" xml:space="preserve">g. </s> <s xml:id="echoid-s16088" xml:space="preserve">gradibus ad polum accedatur, quàm decrementum, ſi toti <lb/>dem gradibus ad Aequatorem accedatur.</s> <s xml:id="echoid-s16089" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16090" xml:space="preserve">IIII. </s> <s xml:id="echoid-s16091" xml:space="preserve">Longitudinem primi climatis ab ortu in occaſum eſſe maiorem lon-<lb/>gitudine ſec@ndi, & </s> <s xml:id="echoid-s16092" xml:space="preserve">ſecundi longitudinem maiorem, quàm tertij, &</s> <s xml:id="echoid-s16093" xml:space="preserve">c. </s> <s xml:id="echoid-s16094" xml:space="preserve">quod <lb/>quidem accidit, vt ait, quia iuxta polum conſtringitur quodammodo ſphæ-<lb/>ra, ut con@at in parallelis circulis, qui minores ſunt prope polos, quàm iuxta <lb/>Aequatorem.</s> <s xml:id="echoid-s16095" xml:space="preserve"/> </p> <pb o="428" file="464" n="465" rhead="Comment. in III. Cap. Sphæræ"/> <p> <s xml:id="echoid-s16096" xml:space="preserve">V. </s> <s xml:id="echoid-s16097" xml:space="preserve">Spatium terreſtre a principio primi climatis ad ſinem uſq; </s> <s xml:id="echoid-s16098" xml:space="preserve">ſeptimi, pro-<lb/>cedendo ſemper directe ab Aequatore uerſus polũ, continere mill aria 2142. <lb/></s> <s xml:id="echoid-s16099" xml:space="preserve">vt conſtat ex dictis.</s> <s xml:id="echoid-s16100" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16101" xml:space="preserve"><emph style="sc">Qvamvis</emph> vero apud antiquos conſtituta ſint duntaxat ſeptem prædicta <lb/> <anchor type="note" xlink:label="note-464-01a" xlink:href="note-464-01"/> climata, tamen à recentioribus nunc multo plura conſtituuntur. </s> <s xml:id="echoid-s16102" xml:space="preserve">Non enim <lb/>verum eſt, quod auctor hoc loco, ait ſolum partem quandam vnius Quadrã-<lb/>tis terræ eſſe habitabilem, quoniam cõpertum eſt iam, totum mare eſſe per-<lb/>miſtum cum terra, ita ut vbique reperiantur vel continentes, vel inſulæ, ver-<lb/>ſus quamcunque partem in Oceano nauigatio inſtituatur, neque vllã regio-<lb/>nem eſſe tam calidam, frigidamve, in qua degere homines non poſſint: </s> <s xml:id="echoid-s16103" xml:space="preserve">immo <lb/>vbiuis locorum reperiuntur & </s> <s xml:id="echoid-s16104" xml:space="preserve">homines, & </s> <s xml:id="echoid-s16105" xml:space="preserve">alia animalia habitare. </s> <s xml:id="echoid-s16106" xml:space="preserve">Adde quòd <lb/>non eſt neceſſarium ad conſtitutionem Climatum, omnes terræ partes habita <lb/>biles eſſe, ſed ſatis eſt, certam quandam obſeruare rationem in augmento ma-<lb/> <anchor type="note" xlink:label="note-464-02a" xlink:href="note-464-02"/> ximorum dierum in varijs eleuationibus poli. </s> <s xml:id="echoid-s16107" xml:space="preserve">Itaque Aſtronomi ſecuti Pto-<lb/>lemæum in Diſt. </s> <s xml:id="echoid-s16108" xml:space="preserve">2. </s> <s xml:id="echoid-s16109" xml:space="preserve">cap. </s> <s xml:id="echoid-s16110" xml:space="preserve">6. </s> <s xml:id="echoid-s16111" xml:space="preserve">deſcribunt in ſuperficiæ terræ circulos parallelos, <lb/>ab Aequatore verſus polum Arcticũ procedendo, tanto ſpatio inter ſe diftan-<lb/>tes, quantum requiritur, ut maxima dies unius differat quadrante vnius ho-<lb/>ræ à maxima die alterius paralleli proxime ſequentis. </s> <s xml:id="echoid-s16112" xml:space="preserve">Ex quo ſequitur, tres <lb/>huiuſmodi parallelos ſpatium terræ continere, quod Clima dicitur. </s> <s xml:id="echoid-s16113" xml:space="preserve">Nam ſi <lb/>ab vno parallelo ad tertium procedas, inuenies diem maximum uariatum fuiſ <lb/>ſe per ſemihoram. </s> <s xml:id="echoid-s16114" xml:space="preserve">Parallelus autem medius triũ dicitur parallelus per me-<lb/>dium climatis, non quòd clima ab ipſo bifariam diuidatur; </s> <s xml:id="echoid-s16115" xml:space="preserve">hoc enim falſum <lb/>eſt, cum maiorem partem climatis auferat uerſus Aequatorem, & </s> <s xml:id="echoid-s16116" xml:space="preserve">minorem <lb/>uerſus polum, ut dictum eſt; </s> <s xml:id="echoid-s16117" xml:space="preserve">ſed quod ſpatium temporis, quo maxima dies in <lb/>initio climatis differt à maxima die in fine eiuſdem, nempe ſemihoram, diui-<lb/>dat in duos quadrantes vnius horæ æquales.</s> <s xml:id="echoid-s16118" xml:space="preserve"/> </p> <div xml:id="echoid-div885" type="float" level="2" n="1"> <note position="left" xlink:label="note-464-01" xlink:href="note-464-01a" xml:space="preserve">Maiorem <lb/>eſſe partem <lb/>terræ habi-<lb/>tabilis, quã <lb/>ab auctore <lb/>ponitur.</note> <note position="left" xlink:label="note-464-02" xlink:href="note-464-02a" xml:space="preserve">Paralleli in <lb/>terra quan-<lb/>to ſpatio à <lb/>Ptolemæo, <lb/>& alijs A-<lb/>ſtronomis <lb/>deſcribãtur</note> </div> <p> <s xml:id="echoid-s16119" xml:space="preserve"><emph style="sc">Hac</emph> ratione recentiores conſtituunt climata 23. </s> <s xml:id="echoid-s16120" xml:space="preserve">incipiendo à primo cli-<lb/> <anchor type="note" xlink:label="note-464-03a" xlink:href="note-464-03"/> mate antiquorum, & </s> <s xml:id="echoid-s16121" xml:space="preserve">verſus polum Arcticum procedendo, donec maximum <lb/>diem inueniant comprehendere 24. </s> <s xml:id="echoid-s16122" xml:space="preserve">horas, vt ex ſequenti tabula conſtabit, in <lb/>qua continentur etiam omnes paralleli, & </s> <s xml:id="echoid-s16123" xml:space="preserve">dies maximi omnium parallelorũ, <lb/>altitudinesq́. </s> <s xml:id="echoid-s16124" xml:space="preserve">poli, hoc eſt, quantum recedunt ab Aequatore. </s> <s xml:id="echoid-s16125" xml:space="preserve">Item quot gra-<lb/>dus Clima quodlibet conſtituant ab Aequatore verſus polum: </s> <s xml:id="echoid-s16126" xml:space="preserve">Vnde facile <lb/>inuenientur milliaria, quæ clima continet, tribuendo ſingulis gradibus mil-<lb/>liaria 62 {1/2}. </s> <s xml:id="echoid-s16127" xml:space="preserve">iuxta Ptolemæum.</s> <s xml:id="echoid-s16128" xml:space="preserve"/> </p> <div xml:id="echoid-div886" type="float" level="2" n="2"> <note position="left" xlink:label="note-464-03" xlink:href="note-464-03a" xml:space="preserve">Recentio-<lb/>res 23. clima <lb/>ta cõſtituũt</note> </div> <p> <s xml:id="echoid-s16129" xml:space="preserve"><emph style="sc">Porro</emph> ijdem hi paralleli, & </s> <s xml:id="echoid-s16130" xml:space="preserve">climata intelligẽda ſunt in altero hemiſphæ <lb/>rio ab Aequatore verſus polum Antarcticum, ita tamen, ut contraria nomina <lb/>ſortiantur. </s> <s xml:id="echoid-s16131" xml:space="preserve">Verbi gratia, Quintum clima Auſtrię dicatur Oppoſitum cli ma-<lb/>ti per Romam, &</s> <s xml:id="echoid-s16132" xml:space="preserve">c.</s> <s xml:id="echoid-s16133" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16134" xml:space="preserve"><emph style="sc">Ex</emph> dictis facile intelligitur, quid interſit inter clima, & </s> <s xml:id="echoid-s16135" xml:space="preserve">Zonam. </s> <s xml:id="echoid-s16136" xml:space="preserve">Nam Zo-<lb/> <anchor type="note" xlink:label="note-464-04a" xlink:href="note-464-04"/> na dicitur ſpatium terræ inter duos Tropicos, vel inter alterutrum Tropico-<lb/>rum, & </s> <s xml:id="echoid-s16137" xml:space="preserve">uicinum circulum polarem, uel inter alterutrum circulorum polariũ,-<lb/>& </s> <s xml:id="echoid-s16138" xml:space="preserve">proximum mundi polum interpoſitum: </s> <s xml:id="echoid-s16139" xml:space="preserve">Qua ratione quinque Zonæ repe-<lb/>riuntur, quarum duæ frigidæ dicuntur, & </s> <s xml:id="echoid-s16140" xml:space="preserve">vna torrida, & </s> <s xml:id="echoid-s16141" xml:space="preserve">duæ temperatæ inter <lb/>torridam, & </s> <s xml:id="echoid-s16142" xml:space="preserve">frigidas. </s> <s xml:id="echoid-s16143" xml:space="preserve">At vero Clima complectitur ſpatium terræ, in quo ac-<lb/>cidit uarietas maximę diei per ſemihoram; </s> <s xml:id="echoid-s16144" xml:space="preserve">Ex quo fit, in una Zona plura poſ-<lb/>ſe climata contineri.</s> <s xml:id="echoid-s16145" xml:space="preserve"/> </p> <div xml:id="echoid-div887" type="float" level="2" n="3"> <note position="left" xlink:label="note-464-04" xlink:href="note-464-04a" xml:space="preserve">Quomodo <lb/>difſerãt Zo-<lb/>na, & Cli-<lb/>ma.</note> </div> <p> <s xml:id="echoid-s16146" xml:space="preserve"><emph style="sc">Si</emph> quis uberius deſideret cognoſcere proprietate omnium parallelorum <lb/>legat cap. </s> <s xml:id="echoid-s16147" xml:space="preserve">6. </s> <s xml:id="echoid-s16148" xml:space="preserve">Dict. </s> <s xml:id="echoid-s16149" xml:space="preserve">2. </s> <s xml:id="echoid-s16150" xml:space="preserve">Ptolemæi.</s> <s xml:id="echoid-s16151" xml:space="preserve"/> </p> <pb o="429" file="465" n="466" rhead="Ioan. de Sacro Boſco."/> <note position="right" xml:space="preserve"> <lb/>########## TABVLA CLIMATVM SECVNDVM \\ Recentiores. <lb/>Paral \\ leli. # ## Climata. # ## Maxima \\ dies. # ## Altitudo \\ Poli. # ## Amplitudo \\ climatum. # Denominationes \\ Climatum. <lb/># # # H. # M. # G. # M. # G. # M. <lb/>1 # # # 12 # 0 # 0 # 0 <lb/>2 # # # 12 # 15 # 4 # 1<emph style="sub">8</emph> # 8 # 34 <lb/>3 # # # 12 # 30 # 8 # 34 <lb/>4 # # Princip. # 12 # 45 # 12 # 43 <lb/>5 # I. # Medium # 13 # 0 # 16 # 43 # 7 # 50 # Per Meroen. <lb/>6 # # Finis # 13 # 15 # 20 # 33 <lb/>6 # # Princip # 13 # 15 # 20 # 33 <lb/>7 # II. # Medium # 13 # 30 # 23 # 11 # 7 # 3 # Per Syenen ſub \\ Tropico 69. <lb/>8 # # Finis # 13 # 45 # 27 # 36 <lb/>8 # # Princip. # 13 # 45 # 27 # 36 <lb/>9 # III. # Medium # 14 # 0 # 30 # 47 # 6 # 9 # Per Alexandriam \\ Aegypti. <lb/>10 # # Finis # 14 # 15 # 33 # 45 <lb/>10 # # Princip. # 14 # 15 # 33 # 45 <lb/>11 # IIII. # Medium # 14 # 30 # 36 # 30 # 5 # 17 # Per Rhodum, & \\ Babilonum. <lb/>12 # # Finis # 14 # 45 # 39 # 1 <lb/>12 # # Princip. # 14 # 45 # 39 # 2 <lb/>13 # V. # Medium # 15 # 0 # 41 # 22 # 4 # 30 # Per Romam, Corſi \\ cã, & Helleſpontũ. <lb/>14 # # Finis # 15 # 15 # 43 # 32 <lb/>14 # # Princip. # 15 # 15 # 43 # 32 <lb/>15 # VI. # Medium # 15 # 30 # 44 # 29 # 3 # 48 # Per Venetias, & \\ Mediolanum. <lb/>16 # # Finis # 15 # 45 # 4720 <lb/>16 # # Princip. # 15 # 45 # 47 # 20 <lb/>17 # VII. # Medium # 16 # 0 # 49 # 1 # 3 # 13 # Per Podoliam, & \\ Tartariã minorem <lb/>18 # # Finis # 16 # 15 # 50 # 33 <lb/>18 # # Princip. # 16 # 15 # 50 # 33 <lb/>19 # VIII. # Medium # 16 # 30 # 51 # 58 # 2 # 44 # Per Vvitebergam. <lb/>20 # # Finis # 16 # 45 # 53 # 57 <lb/>20 # # Princip. # 16 # 45 # 53 # 17 <lb/>21 # IX. # Medium # 17 # 0 # 54 # 29 # 2 # 17 # Per Roſtochium. <lb/>22 # # Finis # 17 # 15 # 55 # 34 <lb/>22 # # Princip. # 17 # 15 # 55 # 34 <lb/>23 # X. # Medium # 17 # 30 # 56 # 37 # 2 # 0 # Per Hyberniam, \\ & Moſcouiam. <lb/>24 # # Finis # 17 # 45 # 57 # 34 <lb/>24 # # Princip. # 17 # 45 # 57 # 34 <lb/>25 # XI. # Medium # 18 # 0 # 58 # 26 # 1 # 40 # Per Bohus caſtrum \\ Noruegiæ. <lb/>26 # # Finis # 18 # 15 # 56 # 14 <lb/></note> <pb o="430" file="466" n="467" rhead="Comment in III. Cap. Sphæræ"/> <note position="right" xml:space="preserve"> <lb/>########## TABVLA CLIMATVM SECVNDVM \\ Recentiores. <lb/>Paral \\ leli. # Climata. # ## Maxima \\ dies. # ## Altitudo \\ Poli. # ## Amplitudo \\ climatum. # Denominationes \\ Climatum. <lb/># # H. # M. # G. # M. # G. # M. <lb/>26 # Princip. # 18 # 15 # 59 # 14 <lb/>27 # XII. Medium # 18 # 30 # 59 # 59 # 1 # 26 # Per Gothiam. <lb/>28 # Finis # 18 # 45 # 60 # 40 <lb/>28 # Princip. # 18 # 45 # 60 # 40 <lb/>29 # XIII. Medium # 19 # 0 # 61 # 18 # 1 # 13 # Per Bergis Norue- \\ giæ. <lb/>30 # Finis # 19 # 15 # 61 # 53 <lb/>30 # Princip. # 19 # 15 # 61 # 53 <lb/>31 # XIIII. Medium # 19 # 30 # 62 # 25 # 1 # 1 # Per Viburgum \\ Filandiæ. <lb/>32 # Finis # 19 # 45 # 62 # 54 <lb/>32 # Princip. # 19 # 45 # 62 # 54 <lb/>33 # XV. Medium # 20 # 0 # 63 # 22 # 0 # 52 # Per Arotiam Sue- \\ tiæ. <lb/>34 # Finis # 20 # 15 # 63 # 46 <lb/>34 # Princip. # 20 # 15 # 63 # 46 <lb/>35 # XVI. Medium # 20 # 30 # 64 # 6 # 0 # 44 # Per DalenKanlij \\ fluuij oſtia. <lb/>36 # Finis. # 20 # 45 # 64 # 30 <lb/>36 # Princip. # 20 # 45 # 64 # 30 <lb/>37 # XVII. Medium # 21 # 0 # 64 # 49 # 0 # 36 # Per reli-<lb/>38 # Finis # 21 # 15 # 65 # 9 <lb/>38 # Princip. # 21 # 15 # 65 # 9 <lb/>39 # XVIII. Medium # 21 # 30 # 65 # 21 # 0 # 29 # qua loca <lb/>40 # Finis # 21 # 45 # 65 # 35 <lb/>40 # Princip. # 21 # 45 # 65 # 35 <lb/>41 # XIX. Medium # 22 # 0 # 65 # 47 # 0 # 22 # Noruegiæ, <lb/>42 # Finis # 22 # 15 # 65 # 57 <lb/>42 # Princip. # 22 # 15 # 65 # 57 <lb/>43 # XX. Medium # 22 # 30 # 66 # 6 # 0 # 17 # Suetiæ, <lb/>44 # Finis # 22 # 45 # 66 # 14 <lb/>44 # Princip. # 22 # 45 # 66 # 14 <lb/>45 # XXI. Medium # 23 # 0 # 66 # 20 # 0 # 11 # Albæ Ruſſiæ, <lb/>46 # Finis # 23 # 15 # 66 # 25 <lb/>46 # Princip. # 23 # 15 # 66 # 25 <lb/>47 # XXII. Medium # 23 # 30 # 66 # 28 # 0 # 5 # & vicinarum <lb/>48 # Finis # 23 # 45 # 66 # 28 <lb/>49 # XXIII. # 24 # 40 # 66 # 31 # 0 # 0 # Inſularum. <lb/></note> </div> <div xml:id="echoid-div889" type="section" level="1" n="355"> <head xml:id="echoid-head366" xml:space="preserve">FINIS TERTII CAPITIS.</head> <pb o="431" file="467" n="468"/> </div> <div xml:id="echoid-div890" type="section" level="1" n="356"> <head xml:id="echoid-head367" xml:space="preserve">CAPVT QVARTVM <lb/>DE CIRCVLIS, ETMOTIBVS <lb/>Planetarum, & de cauſis eclipſium <lb/>Solis, & Lunæ.</head> <figure> <image file="467-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/467-01"/> </figure> <p style="it"> <s xml:id="echoid-s16152" xml:space="preserve">NOTANDVM, quod Sol habet unicum cir-<lb/>culum, per quem mouetur in ſuperficie lineæ <lb/>eclipticæ, & </s> <s xml:id="echoid-s16153" xml:space="preserve">eſt eccentricus. </s> <s xml:id="echoid-s16154" xml:space="preserve">Eccentricus qui-<lb/>dem circulus dicitur non omnis circulus, ſed <lb/>ſolum talis, qui diuidens terram in duas par-<lb/>tes æquales, non habet centrum fuum cum cen-<lb/>tro terræ, ſed extra. </s> <s xml:id="echoid-s16155" xml:space="preserve">Punctus autem in eceen-<lb/>trico, qui maxime accedit ad firmamentum, <lb/>appellatur Aux, quod interpretatur eleuatio. </s> <s xml:id="echoid-s16156" xml:space="preserve">Punctus uero oppoſitus, <lb/>qui maximæ remotionis eſt à Firmamento, dicitur oppoſitum Augis. <lb/></s> <s xml:id="echoid-s16157" xml:space="preserve">Solis autem ab occidente in orientem duo ſunt motus, quorum unus eſt <lb/>@i proprius in circulo ſuo eccentrico, quo mouetur in omni die, ac nocte <lb/>60. </s> <s xml:id="echoid-s16158" xml:space="preserve">minutis fere. </s> <s xml:id="echoid-s16159" xml:space="preserve">Alius uero tardior eſt motus ſphæræipſius ſupra po-<lb/>los axis circuli ſignorum, & </s> <s xml:id="echoid-s16160" xml:space="preserve">eſt æqualis motui ſphæræ ſtellarum fixarum, <lb/>ſcilicet in 100. </s> <s xml:id="echoid-s16161" xml:space="preserve">annis gradu uno. </s> <s xml:id="echoid-s16162" xml:space="preserve">Ex his itaque duobus motibus colligi-<lb/>tur curſus eius incirculo ſignorum ab occidente in Orientem, per quam <lb/>abſcindit circulum ſignorum in 365. </s> <s xml:id="echoid-s16163" xml:space="preserve">diebus, & </s> <s xml:id="echoid-s16164" xml:space="preserve">quartaunius diei, præter <lb/>rem modicam, quę nullius eſt ſenſibilitatis.</s> <s xml:id="echoid-s16165" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div891" type="section" level="1" n="357"> <head xml:id="echoid-head368" xml:space="preserve">COMMENTARIVS.</head> <note position="right" xml:space="preserve">Argume@-<unsure/> <lb/>tũ 4. cap.</note> <p> <s xml:id="echoid-s16166" xml:space="preserve"><emph style="sc">POstqvam</emph> in præcedentibus auctor egit de motu primi mo-<lb/>bilis, qui fit ab ortu in occaſum, & </s> <s xml:id="echoid-s16167" xml:space="preserve">de ijs, quæ illum motum <lb/>ſequuntur, nempe de ortu, & </s> <s xml:id="echoid-s16168" xml:space="preserve">occaſu ſignorum, de diebus, & </s> <s xml:id="echoid-s16169" xml:space="preserve"><lb/>noctibus, &</s> <s xml:id="echoid-s16170" xml:space="preserve">c. </s> <s xml:id="echoid-s16171" xml:space="preserve">Difputat nunc in ultimo huius operis capite de <lb/>motu aliorum cœlorum, qui fit ab occaſu in ortum: </s> <s xml:id="echoid-s16172" xml:space="preserve">ac præci-<lb/>pue de motu Solis ac Lunæ, vt nobis aperiat rationes eclipſium Lunarium, <lb/>& </s> <s xml:id="echoid-s16173" xml:space="preserve">Solarium. </s> <s xml:id="echoid-s16174" xml:space="preserve">At quoniam hæc omnia breuiſſime ab auctore perſtringuntur, <lb/>propterea & </s> <s xml:id="echoid-s16175" xml:space="preserve">nos breuiſſimi hac in parte erimus, præſertim quia tractatio <lb/>hæc, ſi pro dignitate tractari debet, longiorem expoſtulat ſermonem, per-<lb/>@inetq́. </s> <s xml:id="echoid-s16176" xml:space="preserve">ad Theoricas planetarum, quas, ſauente Deo, breui in lucem edemus.</s> <s xml:id="echoid-s16177" xml:space="preserve"/> </p> <pb o="432" file="468" n="469" rhead="Comment. in III. Cap. Sphæræ"/> </div> <div xml:id="echoid-div892" type="section" level="1" n="358"> <head xml:id="echoid-head369" xml:space="preserve">ECCENTRICI, ET EPICYCLI QVIBVS <lb/>φαινομένοις ab Aſtronomis inuenti ſint in cœlo.</head> <p> <s xml:id="echoid-s16178" xml:space="preserve">QVIA vero auctor hoc loco docet ex recepto Aſtronomorũ de-<lb/>creto, Planetas moueri in orbibus eccentricis, & </s> <s xml:id="echoid-s16179" xml:space="preserve">epicyclis, quos <lb/>nonnulli philoſophorum cum Auerroeè medio prorſus tollere <lb/>conantur, tanquam repugnantes Ariſtoteli, & </s> <s xml:id="echoid-s16180" xml:space="preserve">philoſophiæ natu-<lb/>rali: </s> <s xml:id="echoid-s16181" xml:space="preserve">idcirco antequam contextũ auctoris interpreter, operæ pre-<lb/>tium me facturum arbitror, ſi breuiter hoc loco (ut illis, qui enixe id à me fla <lb/>gitarunt, ſatisfaciam) adducã experientias varias, quibus Ptolemæus, Alphra-<lb/>ganus, Thebit, & </s> <s xml:id="echoid-s16182" xml:space="preserve">alij fere Aſtronomi omnes maxime permoti fuerunt, vt in <lb/>cœlis orbes eccentricos, & </s> <s xml:id="echoid-s16183" xml:space="preserve">epicyclos eſſe crederent: </s> <s xml:id="echoid-s16184" xml:space="preserve">Deinde vero proponam <lb/>potiſſimas rationes Auerrois, ſectatorumq; </s> <s xml:id="echoid-s16185" xml:space="preserve">ipſius, quibus huiuſmodi orbes <lb/>impetunt, & </s> <s xml:id="echoid-s16186" xml:space="preserve">omnino deſtruere conantur: </s> <s xml:id="echoid-s16187" xml:space="preserve">Tertio denique eaſdẽ diſſoluam, & </s> <s xml:id="echoid-s16188" xml:space="preserve"><lb/>ſriuolas eſſe oſtendam; </s> <s xml:id="echoid-s16189" xml:space="preserve">vt quilibet intelligat, Aſtronomos nõ ſine ratione, ſed <lb/>magna induſtria, & </s> <s xml:id="echoid-s16190" xml:space="preserve">incredibili felicitate hoſce orbes in cœli inueniſſe@ philo-<lb/>ſophos autem, qui Auerroem ſequuntur, temere tanto impetu in eoſdem in-<lb/>ſultare. </s> <s xml:id="echoid-s16191" xml:space="preserve">Sed ante omnia paucis explicandum eſt, quo pacto orbes eccentrici, <lb/>& </s> <s xml:id="echoid-s16192" xml:space="preserve">epicycli in cœlo ſint concipiendi, vt facilius poſtea intelligatur, phænome <lb/>na ab Aſtronomis ubiuis locorum obſeruata, poſitis illis orbibus in cœlo, <lb/>defendi facili negotio poſſe, ijſdem uero orbibus ſublatis, phænomena locum <lb/>non habere, ſed omnia prorſus corruere.</s> <s xml:id="echoid-s16193" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16194" xml:space="preserve"><emph style="sc">Orbis</emph> igitur eccentricus in cœlo cuiuſuis planetæ, qui Eccentricus ſim-<lb/> <anchor type="note" xlink:label="note-468-01a" xlink:href="note-468-01"/> pliciter dicitur, eſt ille, cuius tam concauum, quàm conuexum habet centrũ à <lb/>cẽtro Vniuerſi, ſeu totius cœli diuerſum, ita ut uniformis ſit, quoad craſſitiẽ <lb/>inſtar cuiuſlibet ſphæræ cęleſtis, ſitq; </s> <s xml:id="echoid-s16195" xml:space="preserve">immerſus intra craſſitiẽ totius cęli, & </s> <s xml:id="echoid-s16196" xml:space="preserve"><lb/>terram ipſam ambiat. </s> <s xml:id="echoid-s16197" xml:space="preserve">Ex quo fit, ut (cum cęlum totũ cuiuſcunq; </s> <s xml:id="echoid-s16198" xml:space="preserve">planetæ ſit <lb/>quaqua uerſus uniformis craſſitiei, habeatq; </s> <s xml:id="echoid-s16199" xml:space="preserve">centrũ cum toto mundo commu <lb/>ne) circa orbem eccentricũ conſiſtant alij duo orbes difformis craſſitiei, vnus <lb/>ſupra ipſum, & </s> <s xml:id="echoid-s16200" xml:space="preserve">alter infra; </s> <s xml:id="echoid-s16201" xml:space="preserve">ita ut ſuperior tenuiſſimus ſit ea parte, qua eccẽtri-<lb/>cus orbis maxime à centro mundi recedit, craſſiſſimus uero in parte oppoſita <lb/>ubi idem eccẽtricus proximus terræ eſt; </s> <s xml:id="echoid-s16202" xml:space="preserve">contra uero in inferiori pars craſſiſſi-<lb/>ma tenuiſſimæ ſuperioris ſubſit, craſſiſſimæ uero tenuiſſima. </s> <s xml:id="echoid-s16203" xml:space="preserve">Ita enim tã con-<lb/>uexa ſuperficies ſuperioris orbis, quã concaua inferioris idem centrũ habebit <lb/>quod totum cœlum planetæ, nempe centrum mundi, ut res poſtulat: </s> <s xml:id="echoid-s16204" xml:space="preserve">concaua <lb/>autem ſuperficies ſuperioris, & </s> <s xml:id="echoid-s16205" xml:space="preserve">cõuexa inferioris idem habebit centrũ, quod <lb/>orbis eccentricus; </s> <s xml:id="echoid-s16206" xml:space="preserve">atq; </s> <s xml:id="echoid-s16207" xml:space="preserve">adeo totum cęlum tam ſecũdum concauum, quam ſe-<lb/>cundum conuexum æqualiter à centro mundi diſtabit: </s> <s xml:id="echoid-s16208" xml:space="preserve">qu od non contingeret <lb/>ſi circa eccentricũ orbem non ponerentur duo hi poſteriores inæqualem ha-<lb/>bentes craſſitiem; </s> <s xml:id="echoid-s16209" xml:space="preserve">qui ab auctoribus dici ſolent Eccentrici ſecundũ quid, pro-<lb/> <anchor type="note" xlink:label="note-468-02a" xlink:href="note-468-02"/> pterea quòd ſecundum unam ſuperficiem extremam idem habent centrũ cũ <lb/>toto Vniuerſo, ſecundum uero alteram aliud: </s> <s xml:id="echoid-s16210" xml:space="preserve">quemadmodũ & </s> <s xml:id="echoid-s16211" xml:space="preserve">prior appella-<lb/>tur Eccentricus ſimpliciter, quòd ſecundum utramq; </s> <s xml:id="echoid-s16212" xml:space="preserve">ſuperficiẽ diuerſum ha-<lb/>beat centrum à centro totius Vniuerſi. </s> <s xml:id="echoid-s16213" xml:space="preserve">Itaq; </s> <s xml:id="echoid-s16214" xml:space="preserve">ſi cęlum planetæ cuiuſuis pla-<lb/>no ſecetur per duo puncta Eccentrici ſimpliciter, quorũ unũ à terra ſit remo <lb/>tiſſimum, alterum uero propinquiſſimum terræ, efficietur ſectio, qualẽ appo-<lb/>ſita figura refert, in qua Eccẽtricus ſimpliciter exprimitur per orbem album, <lb/>cuius centrum tam ſecundũ conuexum, quàm ſecundum concauũ eſt F. </s> <s xml:id="echoid-s16215" xml:space="preserve">Duo <pb o="433" file="469" n="470" rhead="Ioan. de Sacro Boſco."/> autem orbes circunſtantes nig ri repreſentant eccentricos ſecundũ quid, quo-<lb/>rum ſuperiores conuexa ſuper ficies A B C D, & </s> <s xml:id="echoid-s16216" xml:space="preserve">cõcaua inferioris centrũ habct <lb/>E, quod ẽt mundi totius cen <lb/> <anchor type="figure" xlink:label="fig-469-01a" xlink:href="fig-469-01"/> trũ eſt, ita vt totũ cælũ mũdo <lb/>ſit concentricũ ſimpliciter, id <lb/>eſt, tã ſecundũ ſuperficiẽ con-<lb/>uexã, quã ſecundũ cõcauam. <lb/></s> <s xml:id="echoid-s16217" xml:space="preserve">Superficies uero tã concaua <lb/>ſuperioris orbis, quàm cõue-<lb/>xa inſerioris ex F, cẽtro eccen <lb/>trici ſimpliciter deſcribitur. </s> <s xml:id="echoid-s16218" xml:space="preserve"><lb/>Quæ cũ ita ſint, cõponetur cę <lb/>lũ totũ cuiuſq; </s> <s xml:id="echoid-s16219" xml:space="preserve">planetæ ex tri <lb/>bus orbib. </s> <s xml:id="echoid-s16220" xml:space="preserve">partialibus, eccen <lb/>trico ſimpliciter, & </s> <s xml:id="echoid-s16221" xml:space="preserve">duob. </s> <s xml:id="echoid-s16222" xml:space="preserve">ec-<lb/>centricis ſecundũ quid; </s> <s xml:id="echoid-s16223" xml:space="preserve">exce-<lb/> <anchor type="note" xlink:label="note-469-01a" xlink:href="note-469-01"/> pto cælo Mercurij, & </s> <s xml:id="echoid-s16224" xml:space="preserve">cęlo Lu <lb/>næ. </s> <s xml:id="echoid-s16225" xml:space="preserve">Vtrũq; </s> <s xml:id="echoid-s16226" xml:space="preserve">enim horũ ex plu <lb/>rib. </s> <s xml:id="echoid-s16227" xml:space="preserve">orbibus conſtituitur, vt in <lb/>Theoricis exponetur.</s> <s xml:id="echoid-s16228" xml:space="preserve"/> </p> <div xml:id="echoid-div892" type="float" level="2" n="1"> <note position="left" xlink:label="note-468-01" xlink:href="note-468-01a" xml:space="preserve">Orbis@ eccẽ-<lb/>tricus ſim-<lb/>pliciter @d.</note> <note position="left" xlink:label="note-468-02" xlink:href="note-468-02a" xml:space="preserve">Eccentrici <lb/>ſecũ dũ @d. <lb/>qui ſint.</note> <figure xlink:label="fig-469-01" xlink:href="fig-469-01a"> <image file="469-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/469-01"/> </figure> <note position="right" xlink:label="note-469-01" xlink:href="note-469-01a" xml:space="preserve">Cælum cu-<lb/>iuſq; plane <lb/>tæ ex pluri <lb/>bus orbibus <lb/>cõponitur.</note> </div> <p> <s xml:id="echoid-s16229" xml:space="preserve"><emph style="sc">Epicyclvs</emph> aũt eſt ſphæ-<lb/> <anchor type="note" xlink:label="note-469-02a" xlink:href="note-469-02"/> rula ſolida intra craſſitiẽ ec-<lb/>centrici ſimpliciter immerſa, <lb/>ita ut circa ſuũ propriũ cen-<lb/>trũ circũuolui poſſit. </s> <s xml:id="echoid-s16230" xml:space="preserve">Huiuſ-<lb/>modi ſphærula in dicta figu-<lb/>ra repræſentatur per c@culũ <lb/>ex cẽtro G, deſcriptũ. </s> <s xml:id="echoid-s16231" xml:space="preserve">In epi-<lb/>cyclo affixus eſt Planeta, & </s> <s xml:id="echoid-s16232" xml:space="preserve"><lb/>ad eius motũ circa centrũ G, <lb/>defertur, ideoq́ à Ptolemæo <lb/>appellatus eſt orbis reuoluẽs ſtellã, ſeu planetã; </s> <s xml:id="echoid-s16233" xml:space="preserve">Epicyclus aũt ad motũ eccen <lb/>trici ſimpliciter circa terrã circũuehitur, Sole excepto, ꝗ nõ habet epicyclum, <lb/>ſed in ipſo eccẽtrico ſimpliciter fixus ad eius motũ circũducitur. </s> <s xml:id="echoid-s16234" xml:space="preserve">Vñ orbis ec-<lb/> <anchor type="note" xlink:label="note-469-03a" xlink:href="note-469-03"/> cẽtricus ſimpliciter ab artificib. </s> <s xml:id="echoid-s16235" xml:space="preserve">deferẽs epicyclũ, ſeu planetã nominatur. </s> <s xml:id="echoid-s16236" xml:space="preserve">Cir-<lb/>cumferẽtia porro G H, in orbe eccentrico ad motũ centri epicycli G, vel cẽtri <lb/>Solis deſcripta dici ſolet circulus eccentricus: </s> <s xml:id="echoid-s16237" xml:space="preserve">Cuius punctũ a terra remotiſſi <lb/>mũ, quale eſt illud, quod ſub A, collocatur, & </s> <s xml:id="echoid-s16238" xml:space="preserve">in quo centrũ Solis exiſtit, quod-<lb/>que à recta ducta ꝑ centra E, F, indicatur, Aux dicitur: </s> <s xml:id="echoid-s16239" xml:space="preserve">oppoſitum uero punctũ <lb/>H, terræ propinquiſſimũ appellatur Augis oppoſitũ: </s> <s xml:id="echoid-s16240" xml:space="preserve">Linea deniq. </s> <s xml:id="echoid-s16241" xml:space="preserve">recta A C, <lb/>per cẽtra E F, ducta nominari cõſueuit linea augis, quia in hac reperitur Aux,, <lb/>eiuſq. </s> <s xml:id="echoid-s16242" xml:space="preserve">oppoſitum, hoc eſt, punctum circuli eccentrici a terra maxime remotũ, <lb/>& </s> <s xml:id="echoid-s16243" xml:space="preserve">punctum, quod ad terram maxime accedit, ut in Theoricis demonſtratur. <lb/></s> <s xml:id="echoid-s16244" xml:space="preserve">Sed iã ad phænomena explicanda accedamus, quibus maxime Aſtronomi ſunt <lb/>impulſi, ut eccentricos orbes, atq. </s> <s xml:id="echoid-s16245" xml:space="preserve">epicyclos in ſphæris cęleſtibus inuenerint.</s> <s xml:id="echoid-s16246" xml:space="preserve"/> </p> <div xml:id="echoid-div893" type="float" level="2" n="2"> <note position="right" xlink:label="note-469-02" xlink:href="note-469-02a" xml:space="preserve">Epicyclus <lb/>quid.</note> <note position="right" xlink:label="note-469-03" xlink:href="note-469-03a" xml:space="preserve">Circulus <lb/>eccẽtricus @ <lb/>aux, oppo-<lb/>ſitum au-<lb/>gis, & lineæ <lb/>augis quid.</note> </div> <note position="right" xml:space="preserve">Antiqui <lb/>cur puta-<lb/>rint aſtra <lb/>caſu ferr@.</note> <p> <s xml:id="echoid-s16247" xml:space="preserve"><emph style="sc">Igitvr</emph>, aut paulo altius rem exordiar, cũ antiqui ſeculi homines ani-<lb/>maduerterent ſtellas, maxime erraticas, quæ Planetæ dicũtur, uarijs motibus <lb/>ferri, ita ut uunc curſum quaſi incitare, nunc uero eundẽ inhibere uiderẽtur:</s> <s xml:id="echoid-s16248" xml:space="preserve"> <pb o="434" file="470" n="471" rhead="Comment. in IIII. Cap. Sphæræ"/> nunc eas omni quaſi carere motu cernerent, ita vt illas in eodẽ loco cæli hæ-<lb/>rere putares; </s> <s xml:id="echoid-s16249" xml:space="preserve">nunc eaſdem retrocedere in Zodiaco: </s> <s xml:id="echoid-s16250" xml:space="preserve">modo eas proxime ad ter-<lb/>rã accedere, & </s> <s xml:id="echoid-s16251" xml:space="preserve">modo eaſdem longiſſime ab ea remoueri; </s> <s xml:id="echoid-s16252" xml:space="preserve">& </s> <s xml:id="echoid-s16253" xml:space="preserve">denique ſexcentas <lb/>alias huius generis varietates, & </s> <s xml:id="echoid-s16254" xml:space="preserve">quaſi irregularitates in planetis deprehende <lb/>rent: </s> <s xml:id="echoid-s16255" xml:space="preserve">in maximos, & </s> <s xml:id="echoid-s16256" xml:space="preserve">minime tolerãdos errores de motibus aſtrorũ lapſi ſunt, <lb/>ita ut opinarentur, ea in motibus ſuis carere certis, ſtatisq́. </s> <s xml:id="echoid-s16257" xml:space="preserve">legibus, & </s> <s xml:id="echoid-s16258" xml:space="preserve">eiuſcemo <lb/>di uarietates motuũ caſu potius aliquo ipſis accidere, quàm firma, certaq́. </s> <s xml:id="echoid-s16259" xml:space="preserve">ra-<lb/>tione. </s> <s xml:id="echoid-s16260" xml:space="preserve">Verum poſteriores, & </s> <s xml:id="echoid-s16261" xml:space="preserve">ſanioris mentis homines, cum cœpiſſent res cęle-<lb/>ftes rectius, ſubtilius, ſcrupuloſiusq́; </s> <s xml:id="echoid-s16262" xml:space="preserve">intueri, in eam ſententiam uenerunt, ut <lb/>pronuncia@ent, @ummæ eſſe dementiæ, putare, in corporum cæleſtium motibus <lb/> <anchor type="note" xlink:label="note-470-01a" xlink:href="note-470-01"/> aliquam reperiri irregularitatem, difformitatem, inæqualitatemve: </s> <s xml:id="echoid-s16263" xml:space="preserve">ſed e cõtra <lb/>rio in ipſis ſummam æqualitatem, vniformitatẽ, ac regularitatẽ poni debere. <lb/></s> <s xml:id="echoid-s16264" xml:space="preserve">Cum enim plurima in hiſce inferioribus, & </s> <s xml:id="echoid-s16265" xml:space="preserve">caducis rebus ordinatim, & </s> <s xml:id="echoid-s16266" xml:space="preserve">certa <lb/>ſeruata lege moueri uideamus, cur idipsũ corporibus cæleſtibus, quę ſunt om-<lb/>nium nobiliſſima, negari debet? </s> <s xml:id="echoid-s16267" xml:space="preserve">Immo uero & </s> <s xml:id="echoid-s16268" xml:space="preserve">rationes naturales perſuadere <lb/>uidentur, nullam eſſe poſſe in motibus cæleſtibus irregularitatem. </s> <s xml:id="echoid-s16269" xml:space="preserve">Nam ſi cæli <lb/>irregulariter, & </s> <s xml:id="echoid-s16270" xml:space="preserve">inæqualiter mouerentur, hoc fieret aut in principio motus, ut <lb/>in proiectis accidit, quæ in principio uelocius mouẽtur: </s> <s xml:id="echoid-s16271" xml:space="preserve">aut in medio, ut in ani <lb/>malibus uidemus: </s> <s xml:id="echoid-s16272" xml:space="preserve">aut deniq; </s> <s xml:id="echoid-s16273" xml:space="preserve">in fine, ut contingit in Naturalibus. </s> <s xml:id="echoid-s16274" xml:space="preserve">Cum igitur <lb/>motus corporum cæleſtium careant hiſce terminis, fieri non poteſt, ut in ipſis <lb/>reperiatur aliqua inæqualitas, aut irregularitas. </s> <s xml:id="echoid-s16275" xml:space="preserve">Deinde ſi irregulariter moue-<lb/>rentur cæli, ita ut modo tardius, & </s> <s xml:id="echoid-s16276" xml:space="preserve">modo uelocius cierentur, id fieri nõ poſſet, <lb/>niſi eorũ uirtutes motrices nunc debiliores, nũc uero firmiores redderentur, <lb/>aut certe eorum potentiæ reſiſtentes nunc augerentur, nunc uero diminueren-<lb/>tur. </s> <s xml:id="echoid-s16277" xml:space="preserve">Motus enim tardior efficitur, quando, manente eadem potentia reſiſtente <lb/>in mobili, uel medio, potentia mouens debilitatur, aut manente eadẽ potẽtia <lb/>mouẽte, reſiſtẽtia augetur in mobili, vel medio: </s> <s xml:id="echoid-s16278" xml:space="preserve">Velocior aũt motus redditur, <lb/>cũ, manẽte eadẽ reſiſtẽtia in mobili uel medio, uirtus motrix augetur, aut ma-<lb/>nẽte eadẽ uirtute morrice, reſiſtẽtia in mobili, uel medio diminuitur. </s> <s xml:id="echoid-s16279" xml:space="preserve">Sed neu-<lb/>trũ horũ in cœleſtibus motibus reperiri poteſt. </s> <s xml:id="echoid-s16280" xml:space="preserve">Intelligentiæ enim, quæ ſecun <lb/>dũ doctrinã communẽ philoſophorũ, cælos mouent, immutabiles ſunt omni-<lb/>no: </s> <s xml:id="echoid-s16281" xml:space="preserve">corpora itẽ cæleſtia, ſi Ariſtoteli, eiusq́. </s> <s xml:id="echoid-s16282" xml:space="preserve">ſectatoribus credimus, omnis corru <lb/>ptionis, augmentationis, & </s> <s xml:id="echoid-s16283" xml:space="preserve">diminutionis expertia ſunt, & </s> <s xml:id="echoid-s16284" xml:space="preserve">infatigabilia. </s> <s xml:id="echoid-s16285" xml:space="preserve">Non et <lb/>go cæleſtia corpora motu irregulari cientur, ſed certis, perpetuis, ac conſtanti-<lb/>bus legibus circumferuntur. </s> <s xml:id="echoid-s16286" xml:space="preserve">Id quod maxime experiẽtiæ, & </s> <s xml:id="echoid-s16287" xml:space="preserve">Phænomena Aſtro <lb/>nomorũ declarant. </s> <s xml:id="echoid-s16288" xml:space="preserve">Deprehenſum enim eſt, Solem periodum ſuam abſoluere <lb/>ſemper ſpatio 365. </s> <s xml:id="echoid-s16289" xml:space="preserve">dierum, cum quadrante unius diei fere: </s> <s xml:id="echoid-s16290" xml:space="preserve">Martem quoq. </s> <s xml:id="echoid-s16291" xml:space="preserve">ſpa-<lb/>tio duorũ ferme annorũ Zodiacũ totũ circuire: </s> <s xml:id="echoid-s16292" xml:space="preserve">Iouẽ 12. </s> <s xml:id="echoid-s16293" xml:space="preserve">& </s> <s xml:id="echoid-s16294" xml:space="preserve">ſic de reliquis pla-<lb/>netis. </s> <s xml:id="echoid-s16295" xml:space="preserve">Argumento igitur eſt, Planetas habere certas, & </s> <s xml:id="echoid-s16296" xml:space="preserve">ſtatas ſuorũ motuum le <lb/>ges: </s> <s xml:id="echoid-s16297" xml:space="preserve">Alias fieri nõ poſſet, ut tã conſtantes periodos in ſuis motibus ſeruarent.</s> <s xml:id="echoid-s16298" xml:space="preserve"/> </p> <div xml:id="echoid-div894" type="float" level="2" n="3"> <note position="left" xlink:label="note-470-01" xlink:href="note-470-01a" xml:space="preserve">In motibus <lb/>cælorũ non <lb/>eſſe irregu-<lb/>latitatem.</note> </div> <p> <s xml:id="echoid-s16299" xml:space="preserve"><emph style="sc">Haec</emph> cum ita eſſe ratio perſuaderet, quotidie tamen a peritis Aſtronomis <lb/> <anchor type="note" xlink:label="note-470-02a" xlink:href="note-470-02"/> multæ irregularitates, ut diximus, in motu cælorum obſeruarẽtur, cogitandũ <lb/>fuit, vndenam irregularitates huiuſcemodi proficiſcerentur. </s> <s xml:id="echoid-s16300" xml:space="preserve">Ac primum qui-<lb/>dem uenit illis in mentem, quemlibet planetam non uno motu, ſed plurib. </s> <s xml:id="echoid-s16301" xml:space="preserve">cir <lb/>cumuehi. </s> <s xml:id="echoid-s16302" xml:space="preserve">Si enim unum tantummodo haberet motum: </s> <s xml:id="echoid-s16303" xml:space="preserve">nulla ratione ſupradi-<lb/>ctæ apparentiæ, & </s> <s xml:id="echoid-s16304" xml:space="preserve">aliæ, quas infra explanabimus, locum haberent, cum unus ac <lb/>idem motus regularis ſimul, atque irregularis eſſe nequeat. </s> <s xml:id="echoid-s16305" xml:space="preserve">Concludendũ igi-<lb/>tur fuit, ſingulis planetis uarios eſſe motus attribuendos, quorum unuſquiſq.</s> <s xml:id="echoid-s16306" xml:space="preserve"> <pb o="435" file="471" n="472" rhead="Ioan. de Sacro Boſco."/> per ſe conſideratus regularis ſit, & </s> <s xml:id="echoid-s16307" xml:space="preserve">æqualis, vt ratio dictat, omnes tñ ſimul ap-<lb/>parentem illam irregularitatem efficiant, ut paulo poſt perſpicuũ fiet. </s> <s xml:id="echoid-s16308" xml:space="preserve">Quo-<lb/>niam uero impoſſibile eſt, ſecundum decreta Ariſtorelis, & </s> <s xml:id="echoid-s16309" xml:space="preserve">philoſophorũ, uni <lb/>& </s> <s xml:id="echoid-s16310" xml:space="preserve">eidem orbi cęleſti, cũ ſit corpus ſimplex, plures ineſſe motus; </s> <s xml:id="echoid-s16311" xml:space="preserve">coacti ſunt ſin-<lb/>gulis planetarũ ſphæris plures aſſignare orbes partiales, ex quibus tota ſphæ-<lb/>ra cõponantur, ut ex multitudine motuũ horum orbium cauſas apparentis il-<lb/>lius irregularitatis poſſent explicare. </s> <s xml:id="echoid-s16312" xml:space="preserve">Vnde quo motus alicuius planetæ magis <lb/>uarius apparebat, eo etiam plures illi motus, atque orbes tribuendi erant.</s> <s xml:id="echoid-s16313" xml:space="preserve"/> </p> <div xml:id="echoid-div895" type="float" level="2" n="4"> <note position="left" xlink:label="note-470-02" xlink:href="note-470-02a" xml:space="preserve">Planetas <lb/>Pluribuscie <lb/>@i motibus.</note> </div> <p> <s xml:id="echoid-s16314" xml:space="preserve">Hos autem orbes partiales non eodem modo omnes Aſtronomi conſti-<lb/> <anchor type="note" xlink:label="note-471-01a" xlink:href="note-471-01"/> tuerunt. </s> <s xml:id="echoid-s16315" xml:space="preserve">Eudoxus enim, & </s> <s xml:id="echoid-s16316" xml:space="preserve">Calippus, quorum opinio tempore Ariſtotelis, vt <lb/>conſtat ex lib. </s> <s xml:id="echoid-s16317" xml:space="preserve">12. </s> <s xml:id="echoid-s16318" xml:space="preserve">Metaph. </s> <s xml:id="echoid-s16319" xml:space="preserve">celebris fuit, & </s> <s xml:id="echoid-s16320" xml:space="preserve">quam etiam Auerroes multis in lo-<lb/>cis, cum ſuis ſectatoribus, defendere nititur, diuidebant ſingulos orbes totales <lb/>planetarum in plures orbes partiales concentricos, hoc eſt, idem centrũ cum <lb/>toto cęlo, & </s> <s xml:id="echoid-s16321" xml:space="preserve">mundo habentes commune: </s> <s xml:id="echoid-s16322" xml:space="preserve">quos quidem aiebant moueri ſuper <lb/>diuerſos polos in partes diuerſas. </s> <s xml:id="echoid-s16323" xml:space="preserve">Ex qua poſitione efficitur, ut etiãſi quilibet <lb/>orbis partialis per ſe conſideratus regulariter incedat, tamen, quia unus retar-<lb/>dat quodammodo alterũ, uel impellit, planeta ipſe irregulariter uideatur mo <lb/>ueri. </s> <s xml:id="echoid-s16324" xml:space="preserve">Quæ quidẽ opinio (quã totis uiribus inter recentiores Hieronymus Fra-<lb/>caſtorius in libe@o, quẽ de Homocẽtricis inſcripſit, defendere conatur, & </s> <s xml:id="echoid-s16325" xml:space="preserve">quã <lb/>probare uidetur Lucillus Philalætus in libris de cęlo, quibuſdã mutatis) licet <lb/>aliquas apparentias, quæ ad tarditatem, uelocitatemq́; </s> <s xml:id="echoid-s16326" xml:space="preserve">motus pertinent, tueri <lb/>poſſit, nullo tamen pacto oĩ<unsure/>um apparentiarum, quæ quotidiana experientia <lb/>in planetis deprehenduntur, rationẽ reddere poteſt, ut mox manifeſtabimus.</s> <s xml:id="echoid-s16327" xml:space="preserve"/> </p> <div xml:id="echoid-div896" type="float" level="2" n="5"> <note position="right" xlink:label="note-471-01" xlink:href="note-471-01a" xml:space="preserve">Sphæræ pla <lb/>netarum in <lb/>orbes cõce@ <lb/>tricos diui <lb/>debãtur ab <lb/>Eudoxo, & <lb/>Calippo.</note> </div> <p> <s xml:id="echoid-s16328" xml:space="preserve"><emph style="sc">Idcirco</emph> Ptolemæus Aſtronomorum facile princeps, (quãuis non deſint <lb/> <anchor type="note" xlink:label="note-471-02a" xlink:href="note-471-02"/> qui dicant, idẽ prius feciſſe Pythagoricos, licet minus dilucide, & </s> <s xml:id="echoid-s16329" xml:space="preserve">accurate, <lb/>quos imitatus deinde eſt Hipparcus) cũ Albategnio, Thebith, & </s> <s xml:id="echoid-s16330" xml:space="preserve">alijs Aſtrono <lb/>mis quàm plurimis, cõſiderans defectũ horum orbiũ homocentricorũ, ſiue idẽ <lb/>centrũ cum toto cęlo habentiũ, ad defendenda omnia φ{αι}νόμενα in planetis <lb/>obſeruata, aliam uiã coactus eſt excogitare, qua omnia, quæ in planetarũ mo-<lb/>tibus apparent, defendi poſſent. </s> <s xml:id="echoid-s16331" xml:space="preserve">Cũ vero diu cogitaſſet, uidit, (ut erat ingenio <lb/>perſpicaciſſimo) nulla id poſſe ratione facilius, & </s> <s xml:id="echoid-s16332" xml:space="preserve">cõmodius fieri, quàm per or <lb/>bes Eccentricos, & </s> <s xml:id="echoid-s16333" xml:space="preserve">Epicyclos, qui diuerſum habẽt centrum à centro totius cę-<lb/>li, ut ſupra expoſuimus. </s> <s xml:id="echoid-s16334" xml:space="preserve">Itaq; </s> <s xml:id="echoid-s16335" xml:space="preserve">ſingulos orbes planetarũ diuiſit in Eccentricos <lb/>orbes partiales, additis in ſingulis planetis, uno Sole excepto, ſingulis Epicy-<lb/>clis, quia per ſolos Eccentricos omnium apparentiarũ ratio dari non poterat. <lb/></s> <s xml:id="echoid-s16336" xml:space="preserve">Auerroes quoq; </s> <s xml:id="echoid-s16337" xml:space="preserve">in commentarijs in Almageſtum Ptolemæi aſſerit, dari Ec-<lb/>centricos orbes, & </s> <s xml:id="echoid-s16338" xml:space="preserve">Epicyclos in ſphæris cęleſtibus. </s> <s xml:id="echoid-s16339" xml:space="preserve">Apparentiæ autem, quæ <lb/>Ptolemæũ, & </s> <s xml:id="echoid-s16340" xml:space="preserve">alios Aſtronomos impulerunt, ut in cęlis huiuſmo di orbes ec-<lb/>centricos, & </s> <s xml:id="echoid-s16341" xml:space="preserve">epicyclos eſſe crederent, fuerunt non paucæ, eæque inſignes ad-<lb/>modum, & </s> <s xml:id="echoid-s16342" xml:space="preserve">illuſtres, e quibus nunc nonnullas in medium proferemus.</s> <s xml:id="echoid-s16343" xml:space="preserve"/> </p> <div xml:id="echoid-div897" type="float" level="2" n="6"> <note position="right" xlink:label="note-471-02" xlink:href="note-471-02a" xml:space="preserve">Ptolemæus-<lb/>cũ alijs A-<lb/>ſtronomis <lb/>diuiſit ſphę <lb/>tas planeta <lb/>rum in or-<lb/>bes eccẽtri <lb/>cos & epicy <lb/>clos.</note> </div> <p> <s xml:id="echoid-s16344" xml:space="preserve">I. </s> <s xml:id="echoid-s16345" xml:space="preserve"><emph style="sc">Sol</emph>, Luna, & </s> <s xml:id="echoid-s16346" xml:space="preserve">quæuis alia ſtellarum errantium, ut ab Aſtronomis pe-<lb/> <anchor type="note" xlink:label="note-471-03a" xlink:href="note-471-03"/> ritioribus diligentiſſime eſt obſeruatũ, modo remotior à terra, modo propin-<lb/>quior apparet: </s> <s xml:id="echoid-s16347" xml:space="preserve">Item (quod ex priori ſequitur) diameter eius modo maior, mo-<lb/>do minor, atque adeo & </s> <s xml:id="echoid-s16348" xml:space="preserve">ipſa ſtella nunc maior, nunc minor uidetur: </s> <s xml:id="echoid-s16349" xml:space="preserve">Sol enim <lb/>(ut cæteros nunc planetas omittam) exiſtens in ♑, aut in alijs ſignis auſtrali-<lb/>bus, maior apparet, quàm cum in ♋, uel in alijs ſignis borealibus moratur; </s> <s xml:id="echoid-s16350" xml:space="preserve">ita <lb/>ut hac tempeſtate in ♑, maximus appareat, in ♋, uero minimus, diameterque <lb/>eius ibi maxima, hic uero minima: </s> <s xml:id="echoid-s16351" xml:space="preserve">hæc autẽ inæqualitas paulatim tollatur, &</s> <s xml:id="echoid-s16352" xml:space="preserve"> <pb o="436" file="472" n="473" rhead="Comment. in IIII. Cap. Sphæræ"/> variæ magnitudinis Sol cernatur, prout à ♑, & </s> <s xml:id="echoid-s16353" xml:space="preserve">uel ♋, recedit; </s> <s xml:id="echoid-s16354" xml:space="preserve">ac proinde eius <lb/>diameter uiſa uarios arcus ex Zodiaco abscindat. </s> <s xml:id="echoid-s16355" xml:space="preserve">Cum ergo, ut a Perſpecti-<lb/>uis demonſtratur, res eadem, quo propinquior eſt, eo maior ui deatur, eo uero <lb/>minor, quo longius a uiſu noſtro ſe ſubducit, dubium non eſt, Solem, Lunam, <lb/>& </s> <s xml:id="echoid-s16356" xml:space="preserve">reliquos planetas in orbibus, qui diuerſum centrum habent a cen tro terræ <lb/>circumferri, ut nunc pro pius ad terram accedere poſſint, nunc autem ab ea <lb/>longius digredi. </s> <s xml:id="echoid-s16357" xml:space="preserve">Si namque in orbibus idèm cum terra centrum habentibus <lb/>veherentur, æquali@er ſemper a terra diſtarent, atque adeo ſemper eiuſdem <lb/>magnitudinis ſeſe obtutui oculorũ obiicerent, quod experientiæ omnino ad-<lb/> <anchor type="figure" xlink:label="fig-472-01a" xlink:href="fig-472-01"/> uerſatur. </s> <s xml:id="echoid-s16358" xml:space="preserve">Hoc planius <lb/>ut fiat, ſit Zodiacus <lb/>A B C D, cuius cen-<lb/>trum E, idem quod <lb/>mundi, & </s> <s xml:id="echoid-s16359" xml:space="preserve">ex centro <lb/>alio F, deſcribatur Ec-<lb/>centricus circulus G <lb/>H I, cum tribus cor-<lb/>poribus Solaribus, quo <lb/>rum G, in Auge ſit <lb/>remotiſſimum a cen-<lb/>tro mundi; </s> <s xml:id="echoid-s16360" xml:space="preserve">I, propin-<lb/>quiſſimum; </s> <s xml:id="echoid-s16361" xml:space="preserve">H, uero <lb/>in mediocri diſtantia. <lb/></s> <s xml:id="echoid-s16362" xml:space="preserve">Poſito igitur, cen-<unsure/> <lb/>trum Solis in circulo <lb/>eccentrico G H I mo-<lb/>ueri r perſpicuum eſt, <lb/>corpus Solis, licet ex <lb/>ſe ſit ſemper eiuſdem <lb/>magnitudinis, tamen <lb/>propter uarias, & </s> <s xml:id="echoid-s16363" xml:space="preserve">inæ-<lb/>quales a terra diſtantias, cuius inæqualitatis cauſa eſt Eccentricus, in quo de <lb/>fertur, nunc minus, nunc maius noſtro apparere uiſui, prout maiorem, mino-<lb/>remve diſtantiã a nobis obtinet; </s> <s xml:id="echoid-s16364" xml:space="preserve">Ita ut, cum fuerit in G, nempe in ♋, diame-<lb/>ter eius uiſa per lineas EK, EL, corpus Solare tangentes auferat ex Zodiaco <lb/>arcũ KL, qui cõtinet quatuor partes ex ijs, quarũ fere octo cõtinentur in arcu <lb/>O P, quem lineæ tangentes EO, EP, ex Zodiaco aſcindũt, cũ Sol eſt in I, hoc <lb/>eſt, in ♑, & </s> <s xml:id="echoid-s16365" xml:space="preserve">quarũ ferme ſex in arcu MN, includuntur, qui Zodiaco intercipi-<lb/>tur inter lineas contingentes EM, EN, Sole poſito in H, ideſt, in ♈, uel ♎. </s> <s xml:id="echoid-s16366" xml:space="preserve"><lb/>Quod ſi circulus G H I, deferens Solẽ ſub Zodiaco ab occaſu in ortũ circa E, <lb/>centrũ mundi, ſeu Zodiaci eſſet deſciptus, hæc apparentia locum nõ haberet: </s> <s xml:id="echoid-s16367" xml:space="preserve"><lb/>quia Sol ſemper ęqualiter a nobis diſtaret. </s> <s xml:id="echoid-s16368" xml:space="preserve">Idemque dicendum eſt de alijs pla <lb/>netis. </s> <s xml:id="echoid-s16369" xml:space="preserve">Hanc apparentiam concedit Auerroes) vt mi@ũ ſit, quàm inconſtans hac <lb/>in parte fuerit) lib. </s> <s xml:id="echoid-s16370" xml:space="preserve">1. </s> <s xml:id="echoid-s16371" xml:space="preserve">Meteo 1. </s> <s xml:id="echoid-s16372" xml:space="preserve">ubi ait. </s> <s xml:id="echoid-s16373" xml:space="preserve">Videtur, quòd Natura æqualizauit in hoc. </s> <s xml:id="echoid-s16374" xml:space="preserve"><lb/>Nam cum remittitur calor, qui eſt per reflexionem, vt Sole exiſtente, in ♑, accidit <lb/>æqualitas in calefactione ex propinquitate: </s> <s xml:id="echoid-s16375" xml:space="preserve">& </s> <s xml:id="echoid-s16376" xml:space="preserve">e contrario, quando accidit intenſa <lb/>caliditas propter reflexionem ad angulos rectos, uel prope, ut dum Sol eſt in ♋, <lb/>diſtat tunc magis Sol à centro terræ, ut remittatur calor.</s> <s xml:id="echoid-s16377" xml:space="preserve">] Idem lib. </s> <s xml:id="echoid-s16378" xml:space="preserve">12. </s> <s xml:id="echoid-s16379" xml:space="preserve">Me@aph.</s> <s xml:id="echoid-s16380" xml:space="preserve">@ <pb o="437" file="473" n="474" rhead="Ioan. de Sacro Boſco."/> comm. </s> <s xml:id="echoid-s16381" xml:space="preserve">45. </s> <s xml:id="echoid-s16382" xml:space="preserve">fatetur, Lunam aliquando eſſe remotiorem, aliquando vero propin-<lb/>quiorem.</s> <s xml:id="echoid-s16383" xml:space="preserve"/> </p> <div xml:id="echoid-div898" type="float" level="2" n="7"> <note position="right" xlink:label="note-471-03" xlink:href="note-471-03a" xml:space="preserve">I <lb/>Apparẽtia <lb/>probans da <lb/>ti Eccentri-<lb/>cos.</note> <figure xlink:label="fig-472-01" xlink:href="fig-472-01a"> <image file="472-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/472-01"/> </figure> </div> <p> <s xml:id="echoid-s16384" xml:space="preserve"><emph style="sc">Vervm</emph> ad hãc apparentiam reſpondent Aduerſarij, concedentes, uerum <lb/>eſſe, Solem aliquando maiorẽ, aliquando minorem cerni, non propter minorẽ, <lb/>maioremve diſtantiã eius à terra; </s> <s xml:id="echoid-s16385" xml:space="preserve">quia ſemper æqualiter à terra diſtat, cum <lb/>(ut ipſi aiunt) in concentrico orbe feratur, ſed propter vapores, qui inter So-<lb/>lem, & </s> <s xml:id="echoid-s16386" xml:space="preserve">noſtrum uiſum interponuntur, diſgregantq; </s> <s xml:id="echoid-s16387" xml:space="preserve">radios viſuales, ita ut So-<lb/>lem nunc maiorem, nunc minorem intueamur, etiamſi ſemper in orbe con-<lb/>centrico, & </s> <s xml:id="echoid-s16388" xml:space="preserve">æquali diſtantia à terra ferratur. </s> <s xml:id="echoid-s16389" xml:space="preserve">Idemq́ue de alijs planetis dicen-<lb/>dum eſt.</s> <s xml:id="echoid-s16390" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16391" xml:space="preserve"><emph style="sc">Caetervm</emph> hæc reſponſio nullius eſt momenti. </s> <s xml:id="echoid-s16392" xml:space="preserve">Non enim ſolum Sol. <lb/></s> <s xml:id="echoid-s16393" xml:space="preserve">& </s> <s xml:id="echoid-s16394" xml:space="preserve">alij planetæ maiores uiſi ſunt, quando uaporibus aer abundabat, ſed etiam <lb/>quando cœlum erat ſereniſſimum, & </s> <s xml:id="echoid-s16395" xml:space="preserve">planeta idem eandem ſupra Horizontem <lb/>habebat altitudinem. </s> <s xml:id="echoid-s16396" xml:space="preserve">Verbi gratia, Sol exiſtens in ♋, ubi hodie Aux Solis re-<lb/>peritur, habensq́; </s> <s xml:id="echoid-s16397" xml:space="preserve">altitudinem ſupra Horizontem grad. </s> <s xml:id="echoid-s16398" xml:space="preserve">20. </s> <s xml:id="echoid-s16399" xml:space="preserve">ita vt a Zenith di-<lb/>ſtantiam haberet grad. </s> <s xml:id="echoid-s16400" xml:space="preserve">70. </s> <s xml:id="echoid-s16401" xml:space="preserve">multo minor ſemper apparuit Aſtronomis doctiſſi-<lb/>mis, quàm in ♑, vbi nunc eſt oppoſitũ Augis, licet eadem eſſet aeris ſerenitas, <lb/>altitudoq; </s> <s xml:id="echoid-s16402" xml:space="preserve">eius ſupra Horizontem cõplecteretur grad. </s> <s xml:id="echoid-s16403" xml:space="preserve">20. </s> <s xml:id="echoid-s16404" xml:space="preserve">diſtaretq́; </s> <s xml:id="echoid-s16405" xml:space="preserve">à Zenith <lb/>grad. </s> <s xml:id="echoid-s16406" xml:space="preserve">70. </s> <s xml:id="echoid-s16407" xml:space="preserve">ut prius. </s> <s xml:id="echoid-s16408" xml:space="preserve">Neque etiam valet, quod dicunt: </s> <s xml:id="echoid-s16409" xml:space="preserve">Licet eandem Sol obtineat <lb/>altitudinem, ſitq́ue ſemper cœlum ſerenum; </s> <s xml:id="echoid-s16410" xml:space="preserve">tamen quia, Sole exiſtente in ♑, <lb/>ubi oppoſitum Augis ponimus, hyems eſt, ac proinde aer craſſior, eodem uero <lb/>exiſtente in ♋, ubi Aux à nobis ſtatuitur, æſtas eſt, atque adeo aer rarior, & </s> <s xml:id="echoid-s16411" xml:space="preserve"><lb/>ſubtilior, fit, ut Sol in ♑, appareat maior, in ♋, autem minor. </s> <s xml:id="echoid-s16412" xml:space="preserve">Non ualet inquã, <lb/>quia aliquando tempore æſtatis mult@ caliginoſius eſt cœlũ, quàm in hyeme, <lb/>& </s> <s xml:id="echoid-s16413" xml:space="preserve">tamen ibi Sol uiſus eſt minor, hic autem maior. </s> <s xml:id="echoid-s16414" xml:space="preserve">Deinde, quia exiſtente cœlo <lb/>ſereno, craſſities acris non poteſt eſſe tanta, ut tantam inæqualitatem in Solis <lb/>magnitudine efficiat, pręſertim cum in duobus proximis diebus, quorum alter <lb/>fuit ſerenus, alter caliginoſus, nunquam tanta ſit deprehenſa diuerſitas. </s> <s xml:id="echoid-s16415" xml:space="preserve">Præ-<lb/>terea dicant, quic quid uelint, de Sole, in Luna certe conuincantur, nec eſſe eſt. </s> <s xml:id="echoid-s16416" xml:space="preserve"><lb/>Luna enim, ut in eius Theorica explicatur, ſingulis menſibus mutat Augem, <lb/>ita ut in ſpatio cuiuslibet menſis Aux ipſius, & </s> <s xml:id="echoid-s16417" xml:space="preserve">oppoſitum Augis exiſtat ſub ſin <lb/>gulis ſignis Zodiaci; </s> <s xml:id="echoid-s16418" xml:space="preserve">Ipſaſque tam in æſtate, quàm in hyeme ſingulis menſibus <lb/>bis in Auge reperitur, & </s> <s xml:id="echoid-s16419" xml:space="preserve">bis in Augis oppoſito: </s> <s xml:id="echoid-s16420" xml:space="preserve">nihilominus tamen nunc mi-<lb/>nor, nunc maior apparet. </s> <s xml:id="echoid-s16421" xml:space="preserve">Non ergo locum habet ſolutio in Luna. </s> <s xml:id="echoid-s16422" xml:space="preserve">Accedit etiã, <lb/>quòd Sol non ſemper in eodem ſigno ſuam Augem habet fixam, ſed mutabi-<lb/>lem ſemper & </s> <s xml:id="echoid-s16423" xml:space="preserve">continue ad anteriores partes Zodiaci, ut in eius Theorica de-<lb/>monſtratur; </s> <s xml:id="echoid-s16424" xml:space="preserve">futurumque@ aliquando eſt, ut eius Aux in ♑, & </s> <s xml:id="echoid-s16425" xml:space="preserve">oppoſitum Augis <lb/>in ♋, exiſtat: </s> <s xml:id="echoid-s16426" xml:space="preserve">& </s> <s xml:id="echoid-s16427" xml:space="preserve">tamen Sol hactenus, ſicut & </s> <s xml:id="echoid-s16428" xml:space="preserve">Luna, ſemper minor apparuit, & </s> <s xml:id="echoid-s16429" xml:space="preserve"><lb/>propinquior terræ in Auge, quamuis locum mutauerit, quàm in oppoſito Au-<lb/>gis. </s> <s xml:id="echoid-s16430" xml:space="preserve">Et profecto mirabile uidetur, planetis exiſtentibus in oppoſito Augis, ſem-<lb/>per tantam eſſe caliginem, in Auge uero tantam ſerenitatem, ut ibi ſemper eo <lb/>dem modo maiores, hic vero minores appareant.</s> <s xml:id="echoid-s16431" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16432" xml:space="preserve"><emph style="sc">Videns</emph> Hieronymus Fracaſtorius, ſolutionem hanc non poſſe omnino <lb/>ſatisfacere adductæ apparentiæ, & </s> <s xml:id="echoid-s16433" xml:space="preserve">rem ſubtilius introſpiciens, aliud commen-<lb/>tum præter uapores interiectos excogitauit. </s> <s xml:id="echoid-s16434" xml:space="preserve">Dicit enim, non ſolum ob craſſio <lb/>rem aerem interpoſitum Planetas maiores apparere, dum ſunt in eo loco cæli, <lb/>ubi oppoſitum Augis ſtatuimus, ſed etiam, ac præcipue, quia partes illę cœli, in <lb/>quibus Augis oppoſitum ponitur, ſunt denſiores, ita ut refrangantur ibi radij <pb o="438" file="474" n="475" rhead="Comment. in IIII. Cap. Sphæræ"/> uiſuales, atque ob id maiores, propinquioresq; </s> <s xml:id="echoid-s16435" xml:space="preserve">nobis appareant. </s> <s xml:id="echoid-s16436" xml:space="preserve">Subtile ſane, <lb/>ſed omnino futile figmentum. </s> <s xml:id="echoid-s16437" xml:space="preserve">Si enim propter denſitatem illarum partium cę <lb/>li planetæ maiores cernerentur, non apparerent eiuſdem ſplendoris, ac clarita <lb/>tis per illas partes denſiores, & </s> <s xml:id="echoid-s16438" xml:space="preserve">per alias partes minus denfas, ſed ibi minorem <lb/>haberent ſplendorem, hic vero maiorem: </s> <s xml:id="echoid-s16439" xml:space="preserve">quando quidem denſitas illa tãta eſt, <lb/>vt ſenſibiliter maiores appareant. </s> <s xml:id="echoid-s16440" xml:space="preserve">Quod eſt abſu@dũ. </s> <s xml:id="echoid-s16441" xml:space="preserve">Idem namq́; </s> <s xml:id="echoid-s16442" xml:space="preserve">planeta tam <lb/>clarus, & </s> <s xml:id="echoid-s16443" xml:space="preserve">ſplendidus videtur, cæteris paribus, cum maior apparet, quàm cum <lb/>minor. </s> <s xml:id="echoid-s16444" xml:space="preserve">Adde quod, ſi eſſet illa denſitas, eædem ſtellę fixæ in Zodiaco exiſtentes <lb/>vno tempore maiores nobis apparerent, quando nimirum illis ſupponuntur <lb/>partes illæ denſiores, quàm alio tempore, quod cum experientia pugnat. </s> <s xml:id="echoid-s16445" xml:space="preserve">Im-<lb/>mo vero, cum Luna bis in Auge, & </s> <s xml:id="echoid-s16446" xml:space="preserve">bis in oppoſito Augis exiſtat ſingulis men-<lb/>ſibus, non poterit apparentia hæc in denſitatem illam referri, niſi quis dicat, to <lb/>tum cælum Lunæ ſub Zodiaco denſitatibus illis eſſe reſperſum. </s> <s xml:id="echoid-s16447" xml:space="preserve">Quod abſurdũ <lb/>eſt. </s> <s xml:id="echoid-s16448" xml:space="preserve">Sequeretur enim, Lunam ſemper eiuſdem debere magnitudinis apparere. <lb/></s> <s xml:id="echoid-s16449" xml:space="preserve">Non ergo denſiores illæ partes in cęlo Lunæ poni poſſunt.</s> <s xml:id="echoid-s16450" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16451" xml:space="preserve">II. </s> <s xml:id="echoid-s16452" xml:space="preserve"><emph style="sc">Sol</emph> in Zodiaco circa centrũ terræ, ſeu mundi, irregulariter, & </s> <s xml:id="echoid-s16453" xml:space="preserve">inæqua-<lb/> <anchor type="note" xlink:label="note-474-01a" xlink:href="note-474-01"/> liter mouetur, ut Solis luce clarius apparet in ſemicirculo eclipticæ boreali, <lb/>& </s> <s xml:id="echoid-s16454" xml:space="preserve">ſemicirculo auſtrali. </s> <s xml:id="echoid-s16455" xml:space="preserve">Quotannis. </s> <s xml:id="echoid-s16456" xml:space="preserve">n. </s> <s xml:id="echoid-s16457" xml:space="preserve">experimur, Solem plures dies inſumere, <lb/>dum ſex ſigna borealia in priori ſemicirculo contenta percurrit, quàm dum in <lb/>ſex alijs auſtralibus moratur, quæ in ſemicirculo auſtrali continentur. </s> <s xml:id="echoid-s16458" xml:space="preserve">Nam vt <lb/>ab æquinoctio Verno, id eſt, à principio ♈, per ♉, ♊, & </s> <s xml:id="echoid-s16459" xml:space="preserve">alia ſigna borealia vſq; <lb/></s> <s xml:id="echoid-s16460" xml:space="preserve">ad æquinoctium autumnale, id eſt, ad principiũ ♎, moueatur, requiruntur dies <lb/>187. </s> <s xml:id="echoid-s16461" xml:space="preserve">Vt autem feratur ab æquinoctio autumnali, hoc eſt, à principio ♎, per <lb/>♏, ♐, & </s> <s xml:id="echoid-s16462" xml:space="preserve">reliqua ſigna auſtralia uſq; </s> <s xml:id="echoid-s16463" xml:space="preserve">ad æquinoctiũ vernum, ſiue ad principiũ <lb/>♈, dies tantũmodo 178. </s> <s xml:id="echoid-s16464" xml:space="preserve">neceſſarij ſunt. </s> <s xml:id="echoid-s16465" xml:space="preserve">Id quod quilibet uel facile deprehen-<lb/>det, ſi in Calẽdario numeret dies à die 21. </s> <s xml:id="echoid-s16466" xml:space="preserve">Martij incluſiue, in quo æquinoctiũ <lb/>Vernũ noſtra tempeſtate contingit, uſq; </s> <s xml:id="echoid-s16467" xml:space="preserve">ad diem 24. </s> <s xml:id="echoid-s16468" xml:space="preserve">Septembris excluſiue, in <lb/>quem autumnale æquinoctiũ hoc tempore incidit. </s> <s xml:id="echoid-s16469" xml:space="preserve">Deprehendentur enim ibi <lb/>dies 187. </s> <s xml:id="echoid-s16470" xml:space="preserve">hic autem tantum dies 178. </s> <s xml:id="echoid-s16471" xml:space="preserve">Ex quo liquido conſtat, Solem inæquali-<lb/>ter ſub Zodiaco moueri, cum arcus eius æquales, @empe duos ſemicirculos, <lb/>temporibus inæqualibus percurrat. </s> <s xml:id="echoid-s16472" xml:space="preserve">Quoniã vero Sol, vt & </s> <s xml:id="echoid-s16473" xml:space="preserve">alia aſtra, quemad-<lb/>modum ſupra diximus, regulariter proprio motu ferri debet in ſuo orbe, per-<lb/>ſpicuum eſt, eum proprio motu non vehi circa centrum Zodiaci, ſeu mundi, <lb/>cum circa hoc centrum moueatur inæqualiter, ut dictũ eſt. </s> <s xml:id="echoid-s16474" xml:space="preserve">Quare regulariter <lb/>feratur, neceſſe eſt, circa aliud centrum à centro mundi diuerſum, atq; </s> <s xml:id="echoid-s16475" xml:space="preserve">adeo in <lb/>orbe eccentrico, qui uidelicet ex illo centro deſcribitur: </s> <s xml:id="echoid-s16476" xml:space="preserve">quia hinc neceſſario <lb/>ſequitur, Solẽ ſub Zodiaco, & </s> <s xml:id="echoid-s16477" xml:space="preserve">circa centrum mundi irregulariter moueri, ut <lb/>experientia docet. </s> <s xml:id="echoid-s16478" xml:space="preserve">Neceſſe eſt enim, ſidus quodcunque, ſi circa centrum eccen-<lb/>trici à centro mundi diuerſum regulariter mouetur, irregulariter ferri circa <lb/>centrũ mundi: </s> <s xml:id="echoid-s16479" xml:space="preserve">Et ſi circa centrũ mundi circũducitur irregulariter, regulariter <lb/>circa eccentrici centrum, hoc eſt, circa aliud centrum, moueri. </s> <s xml:id="echoid-s16480" xml:space="preserve">Sit enim Zodia-<lb/>cus A B C D, cuius centrum E, idem quod mundi; </s> <s xml:id="echoid-s16481" xml:space="preserve">Eccentricus G H I K, cu-<lb/>ius centrum F, à centro E, diuerſum. </s> <s xml:id="echoid-s16482" xml:space="preserve">Ducta autem per centra E, F, Augis li-<lb/>nea A C, ſecet eam in centro E, ad angulos rectos recta B D, quæ neceſſa-<lb/>rio Zodiacum quidem in duos ſemicirculos æquales BAD, BCD, partietur, <lb/>cum per eius centrum ducatur, eccentricum uero in duos arcus inæquales, cũ <lb/>per eius centrum non tranſeat, quarum maior erit HGK, in qua centrum eccen <lb/>trici, & </s> <s xml:id="echoid-s16483" xml:space="preserve">Aux reperitur, minor autem H I K, in qua Augis oppoſitum exiſtit.</s> <s xml:id="echoid-s16484" xml:space="preserve"> <pb o="439" file="475" n="476" rhead="Ioan. de Sacro Boſco."/> Itaque ſi Sol in Eccẽtrico circa centrum F, ponatur regulariter moueri, per-<lb/>curret maiorem portionem H G K, in maiori tempore, quàm minorẽ I H K. <lb/></s> <s xml:id="echoid-s16485" xml:space="preserve"> <anchor type="figure" xlink:label="fig-475-01a" xlink:href="fig-475-01"/> Eodem autem tẽ<unsure/>-<lb/>pore reſpectu cen <lb/>tri terræ E, abſol-<lb/>uit Sol ſemicircu <lb/>lũ Zodiaci B A D, <lb/>quo portionẽ Ec-<lb/>cẽtrici H G K, per-<lb/>currit. </s> <s xml:id="echoid-s16486" xml:space="preserve">Et quo tem <lb/>pore portionẽ Ec-<lb/>cẽtrici K I H, per-<lb/>ambulat, eodem al <lb/>terum ſemicirculũ <lb/>Zodiaci D C B, per <lb/>meat reſpectu ce@ <lb/>tri terrę. </s> <s xml:id="echoid-s16487" xml:space="preserve">Nam cum <lb/>Sol eſt in puncto <lb/>Eccentrici H, exi-<lb/>ſtit reſpectu centri <lb/>terræ E, in puncto <lb/>Zodiaci B; </s> <s xml:id="echoid-s16488" xml:space="preserve">Et dum <lb/>eſt in pũcto Eccen <lb/>trici G, apparet in <lb/>puncto Zodiaci A; <lb/></s> <s xml:id="echoid-s16489" xml:space="preserve">Dum deniq; </s> <s xml:id="echoid-s16490" xml:space="preserve">eſt in <lb/>puncto eccentrici K, conſpicitur è terra in puncto Zodiaci D: </s> <s xml:id="echoid-s16491" xml:space="preserve">adeo vt Sol, cũ <lb/>portionem eccentrici H G K, percurrit, uideatur è centro terræ abſoluere ſe-<lb/>micirculum Zodiaci BAD: </s> <s xml:id="echoid-s16492" xml:space="preserve">ac proinde reliquum ſemicirculum Zodiaci DCB, <lb/>videatur peragere, dum alteram portionem Eccentrici K I H, conficit. </s> <s xml:id="echoid-s16493" xml:space="preserve">Igitur <lb/>maiori etiam tempore percurret Sol ſemicirculum Zodiaci BAD, quàm ſemi <lb/>circulum DCB: </s> <s xml:id="echoid-s16494" xml:space="preserve">ac propterea inæqualiter ſub Zodiaco mouebitur, nempe tar <lb/>dius ſub ſemicirculo B A D, & </s> <s xml:id="echoid-s16495" xml:space="preserve">uelocius ſub ſemicirculo DCB. </s> <s xml:id="echoid-s16496" xml:space="preserve">Rurſus ſi Sol <lb/>ponatur ſub Zodiaco circa centrum mundi E, inæqualiter moueri, ita ut uelo <lb/>cius v.</s> <s xml:id="echoid-s16497" xml:space="preserve">g. </s> <s xml:id="echoid-s16498" xml:space="preserve">feratur circa punctum C, quàm circa punctũ A, fiet, ut neceſſario cir-<lb/>ca aliud centrum, & </s> <s xml:id="echoid-s16499" xml:space="preserve">in orbe ãliquo eccentrico regulariter cieatur. </s> <s xml:id="echoid-s16500" xml:space="preserve">Quoniam <lb/>enim uelocius ferri ponitur in ſemicirculo circa punctũ C, quàm in ſemicir-<lb/>culo circa punctum A, conficiet illum minori tẽpore, quam hunc: </s> <s xml:id="echoid-s16501" xml:space="preserve">Igitur tẽpo-<lb/>ribus æqualibus percurret portionibus Zodiaci inæquales, maiorem nimirum <lb/>circa C, quàm circa A. </s> <s xml:id="echoid-s16502" xml:space="preserve">Sit ergo LCM, portio maior, quàm Sol eodẽ tempore <lb/>percurrat, quo minorem portionem M A L. </s> <s xml:id="echoid-s16503" xml:space="preserve">Ductis aũt ex E, centro mundi, <lb/>ſeu Zodiaci, rectis E L, E M, abſcindantur inter ſe æquales E N, E O, quãtę-<lb/>cun que, & </s> <s xml:id="echoid-s16504" xml:space="preserve">iungatur recta N O, ad quam ex E, perpendicularis excitetur E F, <lb/>& </s> <s xml:id="echoid-s16505" xml:space="preserve">in vtramque partem eijciatur uſque ad puncta A, C, in Zodiaco, Et quoniã <lb/>in triangulo E N O, latera EN, EO, æqualia ſunt, æquales erũt anguli N, O. </s> <s xml:id="echoid-s16506" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-475-01a" xlink:href="note-475-01"/> Sunt aũt & </s> <s xml:id="echoid-s16507" xml:space="preserve">anguli recti ad E, æquales & </s> <s xml:id="echoid-s16508" xml:space="preserve">latera E N, E O, in triangulis E F N, <lb/> <anchor type="note" xlink:label="note-475-02a" xlink:href="note-475-02"/> EFO, quæ rectis angulis opponuntur, æqualia. </s> <s xml:id="echoid-s16509" xml:space="preserve">Igitur & </s> <s xml:id="echoid-s16510" xml:space="preserve">latera F N, FO, æqua-<lb/>lia erunt, Facto ergo F, centro, tranſibit circulus GNIO, ex F, ad interuallum <pb o="440" file="476" n="477" rhead="Comment. in IIII. Cap. Sphæræ"/> FN, deſcriptus per punctum O. </s> <s xml:id="echoid-s16511" xml:space="preserve">In hoc igitur circulo eccentrico circa centrũ <lb/>F, diuerſum à centro mundi dico Solem regulariter moueri. </s> <s xml:id="echoid-s16512" xml:space="preserve">Quoniã enim ſe-<lb/>micirculi N I O, O G N, æquales ſunt, eosq́. </s> <s xml:id="echoid-s16513" xml:space="preserve">temporibus æqualibus Sol per-<lb/>currit, ijſdem nimirum, quibus arcus Zodiaci inæquales L C M, M A L, pertran-<lb/>ſit, quæ tempora poſita ſunt æqualia; </s> <s xml:id="echoid-s16514" xml:space="preserve">(cum enim Sol eſt in puncto N, apparet <lb/>in Zodiaco ex E, centro mundi ſub puncto L: </s> <s xml:id="echoid-s16515" xml:space="preserve">& </s> <s xml:id="echoid-s16516" xml:space="preserve">dum eſt in puncto O, cernitur <lb/>ſub puncto M@ac proinde Sol portionem NIO, in circulo GNIO, eodem tem-<lb/>pore perambulat, in quo arcũ Zodiaci LCM, peragrare conſpicitur, & </s> <s xml:id="echoid-s16517" xml:space="preserve">reliquã <lb/>propterea portionem O G N, eodem tempore, quo arcũ Zodiaci M A L) li-<lb/>quido conſtat, Solem in circulo eccentrico G N I O, vniformiter, ac regulari-<lb/>ter moueri, quando quidem æquales ſemicirculos æqualibus temporibus ab-<lb/>ſoluit. </s> <s xml:id="echoid-s16518" xml:space="preserve">Vides igitur, non mirum eſſe, ꝙ Sol pluribus diebus ab æquinoctio Ver <lb/>no ad æquinoctium autumnale moueatur, quàm ab autumnali ad Vernum, ſi <lb/>in orbe eccentrico ferri ponatur: </s> <s xml:id="echoid-s16519" xml:space="preserve">quia neceſſario hinc ſequitur, eum irregula <lb/>riter moueti circa centrum mundi, & </s> <s xml:id="echoid-s16520" xml:space="preserve">ſub Zodiaco, ut oſtendimus. </s> <s xml:id="echoid-s16521" xml:space="preserve">Idem in alijs <lb/>etiam planetis demonſtrabitur, ut patet.</s> <s xml:id="echoid-s16522" xml:space="preserve"/> </p> <div xml:id="echoid-div899" type="float" level="2" n="8"> <note position="left" xlink:label="note-474-01" xlink:href="note-474-01a" xml:space="preserve">II <lb/>Apparentia <lb/>probans da <lb/>ri eccentri-<lb/>cos.</note> <figure xlink:label="fig-475-01" xlink:href="fig-475-01a"> <image file="475-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/475-01"/> </figure> <note position="right" xlink:label="note-475-01" xlink:href="note-475-01a" xml:space="preserve">5. Primi.</note> <note position="right" xlink:label="note-475-02" xlink:href="note-475-02a" xml:space="preserve">26. Primi.</note> </div> <p> <s xml:id="echoid-s16523" xml:space="preserve"><emph style="sc">Est</emph> autem hæc apparentia de irregula@itate motus planetarum tam inſi <lb/>gnis, & </s> <s xml:id="echoid-s16524" xml:space="preserve">perſpicua, ut Ptolemæus ex ipſa colligat rationibus Geometricis eccẽ <lb/>tricitatem Solis, id eſt, diſtantiam centri orbis eccentrici Solis à centro mun-<lb/>di, & </s> <s xml:id="echoid-s16525" xml:space="preserve">locum Augis in Zodiaco@in alijs autẽ planetis magnitudines diametro-<lb/>rum Epicyclorum, & </s> <s xml:id="echoid-s16526" xml:space="preserve">multa alia, ut, Deo fauente, in Theoricis manifeſtabi-<lb/>mus. </s> <s xml:id="echoid-s16527" xml:space="preserve">Eadem hæc apparentia tantum habuit robur apud Auerroem, ut coege-<lb/>rit illum fateri lib. </s> <s xml:id="echoid-s16528" xml:space="preserve">1. </s> <s xml:id="echoid-s16529" xml:space="preserve">Meteor. </s> <s xml:id="echoid-s16530" xml:space="preserve">neceſſe eſſe, vt Sol moueatur regulariter in orbe <lb/>eccentrico, quando quidem circa centrum terræ ita itregulariter mouetur. </s> <s xml:id="echoid-s16531" xml:space="preserve">Vt <lb/>etiam ex hoc loco eius inconſtantia appareat, quia alibi eccentricos omnino <lb/>è medio ſuſtulit.</s> <s xml:id="echoid-s16532" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16533" xml:space="preserve">III. </s> <s xml:id="echoid-s16534" xml:space="preserve"><emph style="sc">Observatvm</emph> eſt ſæpenumero, eclipſes Solis fuiſſe inæquales, li-<lb/> <anchor type="note" xlink:label="note-476-01a" xlink:href="note-476-01"/> cet in ſingulis Sol, & </s> <s xml:id="echoid-s16535" xml:space="preserve">Luna eundem ſitum habuerint: </s> <s xml:id="echoid-s16536" xml:space="preserve">quæ inæqualitas aliun-<lb/>de prouenire non potuit, quàm ab eccentrico. </s> <s xml:id="echoid-s16537" xml:space="preserve">Quod vt planius fiat, accipien-<lb/>dum erita Perſpectiuis: </s> <s xml:id="echoid-s16538" xml:space="preserve">Quandocũque corpus aliquod luminoſum illuminat <lb/>aliud minus, quo propinquiora inter ſe fuerint hæc duo corpora, eo maiorẽ <lb/>partẽ minoris illuminari, & </s> <s xml:id="echoid-s16539" xml:space="preserve">uehementius, at minorem umbrã effici, quã quan <lb/>do maiorem inter ſe habuerint diſtãtiam. </s> <s xml:id="echoid-s16540" xml:space="preserve">Tunc enim minor pars minoris illu <lb/>ſtrabitur, at maior efficietur umbra. </s> <s xml:id="echoid-s16541" xml:space="preserve">E contrario uero: </s> <s xml:id="echoid-s16542" xml:space="preserve">quãdo corpus aliquod <lb/>luminoſum illuminat aliud maius, quo minorem inter ſe diſtantiã habuerint, <lb/> <anchor type="figure" xlink:label="fig-476-01a" xlink:href="fig-476-01"/> co minorem partem maioris illuminari, at ampliorem proijci umbram, quàm <lb/>quando longius unum ab altero abfuerit. </s> <s xml:id="echoid-s16543" xml:space="preserve">Tunc enim maior pars maioris illu <pb o="441" file="477" n="478" rhead="Ioan. de Sacro Boſco."/> ſtrabitur, at minor vmbra efficietur. </s> <s xml:id="echoid-s16544" xml:space="preserve">Quę omnia in propoſita figura ob oculos <lb/>ponuntur, in qua corpus luminoſum, & </s> <s xml:id="echoid-s16545" xml:space="preserve">maius eſt A; </s> <s xml:id="echoid-s16546" xml:space="preserve">opacũ uero, ac minus R, <lb/>modo propius ad A, accedẽs, modo magis ab eo diſtãs. </s> <s xml:id="echoid-s16547" xml:space="preserve">Vides igitur, in propin <lb/>quiori diſtantia corpus luminoſum A, maiorem partem minoris corporis B, il <lb/>luſtrare, & </s> <s xml:id="echoid-s16548" xml:space="preserve">minorem efficere umbram, quàm in maiori diſtantia, ubi idem cor <lb/>pus luminoſum A, minorem partem minotis corporis B, illuminat, & </s> <s xml:id="echoid-s16549" xml:space="preserve">maiorẽ <lb/>umbram proijcit. </s> <s xml:id="echoid-s16550" xml:space="preserve">Rurſus uides, ſi A, corpus maius ſit opacum: </s> <s xml:id="echoid-s16551" xml:space="preserve">& </s> <s xml:id="echoid-s16552" xml:space="preserve">B, minus lu-<lb/>minoſum, minorem partem corporis opaci A, illuminari à corpore luminoſo <lb/>B, propinquiori, & </s> <s xml:id="echoid-s16553" xml:space="preserve">mai orem proijci umbrã, quàm a corpore B, remotiori. </s> <s xml:id="echoid-s16554" xml:space="preserve">Ma-<lb/>ior enim tũc pars corporis A, illuminatur, & </s> <s xml:id="echoid-s16555" xml:space="preserve">minor umbra proijcitur, ut per-<lb/>ſpicuum eſt in lineis tangentibus tam Solem, quàm Lunam.</s> <s xml:id="echoid-s16556" xml:space="preserve"/> </p> <div xml:id="echoid-div900" type="float" level="2" n="9"> <note position="left" xlink:label="note-476-01" xlink:href="note-476-01a" xml:space="preserve">III. <lb/>Apparẽtia <lb/>probans da <lb/>ri eccentri-<lb/>@os.</note> <figure xlink:label="fig-476-01" xlink:href="fig-476-01a"> <image file="476-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/476-01"/> </figure> </div> <p> <s xml:id="echoid-s16557" xml:space="preserve">Hoc poſito, deprehenſum eſt à ſolertiſſimis Aſtronomis non ſemel, Lu-<lb/>minaribus, Sole ſcilicet ac Luna, in eodem ſitu manentibus, v.</s> <s xml:id="echoid-s16558" xml:space="preserve">g. </s> <s xml:id="echoid-s16559" xml:space="preserve">in capite, uel <lb/>cauda Draconis, (vbi neceſſe eſt exiſtere vtrumq; </s> <s xml:id="echoid-s16560" xml:space="preserve">planetam, ut eclipſis contin-<lb/>gat, ut infra docebimus) ſeruataq́; </s> <s xml:id="echoid-s16561" xml:space="preserve">eadem diuerſitate aſpectus, Eclipſes Solis <lb/>(quæ fiunt ex interpoſitione Lunæ inter noſtrum aſpectum, & </s> <s xml:id="echoid-s16562" xml:space="preserve">Solẽ.) </s> <s xml:id="echoid-s16563" xml:space="preserve">vno tem <lb/>pore maiores fuiſſe, longioriq́; </s> <s xml:id="echoid-s16564" xml:space="preserve">tẽpore duraſſe, & </s> <s xml:id="echoid-s16565" xml:space="preserve">in maiori portione terræ ap <lb/>paruiſſe, maioremq́; </s> <s xml:id="echoid-s16566" xml:space="preserve">partem Solis obſcuraram fuiſſe, quàm alio tempore. </s> <s xml:id="echoid-s16567" xml:space="preserve">Hoc <lb/>autẽ fieri nullo pacto potuiſſet, niſi dicamus, duos illos planetas aliquando mi <lb/>norem habuiſſe diſtantiã à terra, aut inter ſe, aliquando uero maiorem. </s> <s xml:id="echoid-s16568" xml:space="preserve">Nam <lb/>quando Sollongius à<unsure/> Luna abeſt, tunc, ut dictũ eſt, maior proiicietur umbra <lb/>in terra a Luna, quæ Sole minor eſt, & </s> <s xml:id="echoid-s16569" xml:space="preserve">maior pars Lunę a Sole illuminabitur. <lb/></s> <s xml:id="echoid-s16570" xml:space="preserve">Ex quo fit, tempore Eclipſis Solaris maiorẽ tractũ terræ obſcurari, & </s> <s xml:id="echoid-s16571" xml:space="preserve">longio-<lb/>re tempore Eclipſim durare. </s> <s xml:id="echoid-s16572" xml:space="preserve">Contrarium uero continget, ſi Sol minorem à <lb/>Luna habuerit diſtãtiam. </s> <s xml:id="echoid-s16573" xml:space="preserve">Tunc enim minor umbra a Luna in terra efficietur, <lb/>& </s> <s xml:id="echoid-s16574" xml:space="preserve">maior ipſius pars a Sole illuſtrabitur: </s> <s xml:id="echoid-s16575" xml:space="preserve">ac proinde tempore Eclipſis Solaris <lb/>minor terræ ſuperficies obſcurabitur, minoriq́ue tempore Eclipſis durabit. </s> <s xml:id="echoid-s16576" xml:space="preserve">Vt <lb/>in proxima figura apparere poteſt, in qua corpus Solare ſit A, terra L, Luna <lb/>autẽ ſit B, modo remotior a Sole, & </s> <s xml:id="echoid-s16577" xml:space="preserve">propinquior terræ, modo ꝓpinquior So <lb/>li, & </s> <s xml:id="echoid-s16578" xml:space="preserve">longius a terra diſtans. </s> <s xml:id="echoid-s16579" xml:space="preserve">Dum igitur duo hęc luminaria non poſſint mino <lb/>rem, aut maiorem diſtantiam habere inter ſe, vel a terra, niſi in Eccentricis <lb/>moueri ponantur (Si namque in cõcentricis ueherẽtur, eandem ſemper diſtã <lb/>tiam haberent tum inter ſe, tum etiam a terra, ut patet.) </s> <s xml:id="echoid-s16580" xml:space="preserve">rationi ualde con-<lb/>ſentaneũ eſt, dari in cælis orbes eccẽtricos, in quibus planetæ moueantur, ut <lb/>poſſint aliquando magis, & </s> <s xml:id="echoid-s16581" xml:space="preserve">alſquando minus diſtare inter ſe, uel a terra, ac <lb/>proinde ratio poſſit reddi illius inæqualitatis in Eclipſi Solari.</s> <s xml:id="echoid-s16582" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16583" xml:space="preserve"><emph style="sc">Et</emph> ut, quod ipſi quoq; </s> <s xml:id="echoid-s16584" xml:space="preserve">aliquando obſeruauimus hac in parte, in medium <lb/>proferamus, recitabo duas inſignes Eclipſes Solis, quæ meo tempore cõtige-<lb/>runt non ita pridem, quarum unam anno 1559. </s> <s xml:id="echoid-s16585" xml:space="preserve">Conimbricæ in Luſitania cir-<lb/>ca meridiẽ obſeruani, in qua interponebatur Luna dire<unsure/>cte inter uiſum, ac So-<lb/>lem, ita ut totum Solem nõ modico temporis interuallo contegeret, eſſentq́; <lb/></s> <s xml:id="echoid-s16586" xml:space="preserve">tenebrę quodammodo maiores, quàm nocturnę. </s> <s xml:id="echoid-s16587" xml:space="preserve">Neq; </s> <s xml:id="echoid-s16588" xml:space="preserve">enim, ubi pedẽ quis po <lb/>neret, videre poterat, clariſſimeq́; </s> <s xml:id="echoid-s16589" xml:space="preserve">ſtellæ in cælo apparebãt, & </s> <s xml:id="echoid-s16590" xml:space="preserve">(quod mirabile <lb/>erat) aues ex aere in terram, præ horrore tam tetræ obſcuritatis, decidebant. </s> <s xml:id="echoid-s16591" xml:space="preserve"><lb/>Alteram Romæ anno 1567. </s> <s xml:id="echoid-s16592" xml:space="preserve">circa etiam meridiem conſpexi, in qua rurſus Lu <lb/>na etſi inter uiſum, ac Solem interijciebatur, non totum tamen Solem obſcu <lb/>rabat, ut in priori, ſed (quod nunquam fortaſſis alias euenit) relinquebatur <lb/>in Sole circulus quidam exilis undiq́ue totam Lunam ambiens. </s> <s xml:id="echoid-s16593" xml:space="preserve">Ex quibus <pb o="442" file="478" n="479" rhead="Comment. in IIII. Cap. Sphæræ"/> duabus elipſibus perſpicue admodum colligitur, Solem, & </s> <s xml:id="echoid-s16594" xml:space="preserve">Lunam in vtraque <lb/>eclipſi non habuiſſe eandem diſtantiam à terra, vel inter ſe. </s> <s xml:id="echoid-s16595" xml:space="preserve">Si enim eandem <lb/>diſtantiã & </s> <s xml:id="echoid-s16596" xml:space="preserve">inter ſe, & </s> <s xml:id="echoid-s16597" xml:space="preserve">à terra habuiſſent, quis non uidet, eodem modo Solem <lb/>debuiſſe in utraque eclipſi obſcurari? </s> <s xml:id="echoid-s16598" xml:space="preserve">Id quod à Perſpectiuis facile demonſtra <lb/>bitur, & </s> <s xml:id="echoid-s16599" xml:space="preserve">res perſpicua eſt in manu. </s> <s xml:id="echoid-s16600" xml:space="preserve">Si namque manus eandem ſemper diſtan-<lb/>tiam habet à muro aliquo, & </s> <s xml:id="echoid-s16601" xml:space="preserve">ab oculo, ita ut inter murum, & </s> <s xml:id="echoid-s16602" xml:space="preserve">oculum colloce-<lb/>tur, perpetuo eandem partem muri è conſpectu auferet, non autem nunc ma-<lb/>iorem, & </s> <s xml:id="echoid-s16603" xml:space="preserve">nunc minorem. </s> <s xml:id="echoid-s16604" xml:space="preserve">Igitur nulla ratione dici poteſt, duo hæc luminaria <lb/>in concentricis orbibus moueri, quia hac ratione ſemper æqua liter inter ſe, <lb/>& </s> <s xml:id="echoid-s16605" xml:space="preserve">à terra diſtarent; </s> <s xml:id="echoid-s16606" xml:space="preserve">atque adeo apparentia hęc eclipſium Sola rium locum nul <lb/>lo modo poſſet habere.</s> <s xml:id="echoid-s16607" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16608" xml:space="preserve"><emph style="sc">Rvrsvs</emph> non raro animaduerſum eſt, luminaribus eiſdem in eodem ſitu <lb/>exiſtentibus, vtpote uno in capite Draconis, & </s> <s xml:id="echoid-s16609" xml:space="preserve">in cauda altero, & </s> <s xml:id="echoid-s16610" xml:space="preserve">Luna ean-<lb/>dem latitudinem habente, eclipſes Lunares (quæ fiunt ex interpoſitione ter-<lb/>ræ inter Solem, ac Lunam, quia tunc Luna terræ umbram ingreditur, ita ut à <lb/>radijs Solaribus amplius non illuſtretur, ut poſtea dicemus.) </s> <s xml:id="echoid-s16611" xml:space="preserve">uno tempore ci-<lb/>tius incepiſſe, & </s> <s xml:id="echoid-s16612" xml:space="preserve">maiores fuiſſe, longiorique tẽpore duraſſe, quàm alio tempo <lb/>re. </s> <s xml:id="echoid-s16613" xml:space="preserve">Quod fieri nulla ratione potuiſſet, niſi Luna in una eclipſi maiorem umbrã <lb/>terræ fuiſſet ingreſſa, quàm in alia. </s> <s xml:id="echoid-s16614" xml:space="preserve">Ita enim fit, ut in illa indiguerit longiori <lb/>tẽpore, ut ſeſe ab umbra expediret, quam in hac, atq; </s> <s xml:id="echoid-s16615" xml:space="preserve">adeo maior ibi, quã hic <lb/>eclipſis Lunæ cõtigerit. </s> <s xml:id="echoid-s16616" xml:space="preserve">Atqui terra maiorem umbram efficere nõ poteſt uno <lb/>tempore, quàm alio, niſi Sol@ad eam nunc magis, nũc minus accedat, ut ad ini-<lb/>tium huius tertiæ apparentiæ docuimus: </s> <s xml:id="echoid-s16617" xml:space="preserve">Neque etiam Luna, ſi umbra terræ <lb/>ſemper eſſet eadem, nunc maiorem umbram pertranſiret, nunc minorem, niſi <lb/>magis uno tempore ad terram accedat, quàm alio. </s> <s xml:id="echoid-s16618" xml:space="preserve">Cum ergo neq; </s> <s xml:id="echoid-s16619" xml:space="preserve">Sol, neque <lb/>Luna terræ magis poſſit appropinquare uno tempore, quàm alio, niſi eccẽtri <lb/>cum utrique planetæ tribuamus, in quo circũferatur, ut patet, non erit alienũ <lb/>à ueritate exiſtimare, eccentricos orbes in ſphæris cæleſtibus exiſtere. </s> <s xml:id="echoid-s16620" xml:space="preserve">Exem-<lb/>plum huius rei habes in hac appoſita figura, ubi A, ſignificat Solem modo ter-<lb/> <anchor type="figure" xlink:label="fig-478-01a" xlink:href="fig-478-01"/> ræ B, propinquiorem, modo ab eadem magis remotum. </s> <s xml:id="echoid-s16621" xml:space="preserve">Ex quo ſit, ut aliquan-<lb/>do minor ſit umbra terræ, aliquando maior, quàm quidẽ Luna expreſſa per li-<lb/>teram C, in eclipſi pertranſit. </s> <s xml:id="echoid-s16622" xml:space="preserve">Atque hæc apparentia tantã etiam apud Auer- <pb o="443" file="479" n="480" rhead="Ioan. de Sacro Boſco."/> roem vim habuit, ut ingenue aſſeruerit lib. </s> <s xml:id="echoid-s16623" xml:space="preserve">2. </s> <s xml:id="echoid-s16624" xml:space="preserve">de cælo, comm. </s> <s xml:id="echoid-s16625" xml:space="preserve">32. </s> <s xml:id="echoid-s16626" xml:space="preserve">Fortaſſe non <lb/>alia via defendi poſſe hanc apparentiam de Eclipſi Lunari, quàm per orbẽ Ec-<lb/>centricum, quod tamen alibi negauit. </s> <s xml:id="echoid-s16627" xml:space="preserve">Ecce aliam inconſtantiam Auerrois.</s> <s xml:id="echoid-s16628" xml:space="preserve"/> </p> <div xml:id="echoid-div901" type="float" level="2" n="10"> <figure xlink:label="fig-478-01" xlink:href="fig-478-01a"> <image file="478-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/478-01"/> </figure> </div> <note position="right" xml:space="preserve">IIII. <lb/>Apparentia <lb/>probans. eſ <lb/>ſe Eccentr@ <lb/>cos.</note> <p> <s xml:id="echoid-s16629" xml:space="preserve">IIII. </s> <s xml:id="echoid-s16630" xml:space="preserve">In Luna, Mercurio, & </s> <s xml:id="echoid-s16631" xml:space="preserve">Venere non ſemper ab Aſtronomis inuenta eft <lb/>eadem diuerſitas a ſpectus, ſed modo maior, modo minor, etiamſi planeta eun-<lb/>dem ſitum habuerit: </s> <s xml:id="echoid-s16632" xml:space="preserve">ita vt in Luna v.</s> <s xml:id="echoid-s16633" xml:space="preserve">g. </s> <s xml:id="echoid-s16634" xml:space="preserve">aliquando diuerſitas aſpectus compre-<lb/>henderit grad. </s> <s xml:id="echoid-s16635" xml:space="preserve">1. </s> <s xml:id="echoid-s16636" xml:space="preserve">min. </s> <s xml:id="echoid-s16637" xml:space="preserve">6. </s> <s xml:id="echoid-s16638" xml:space="preserve">aliquando vero tantummodo grad. </s> <s xml:id="echoid-s16639" xml:space="preserve">0. </s> <s xml:id="echoid-s16640" xml:space="preserve">min. </s> <s xml:id="echoid-s16641" xml:space="preserve">50. </s> <s xml:id="echoid-s16642" xml:space="preserve">ut ait Gẽ <lb/>ma Friſius non ignobilis ſcriptor inter recentiores, & </s> <s xml:id="echoid-s16643" xml:space="preserve">hoc, Luna habente ean-<lb/>dem altitudinem ſupra Horizontem. </s> <s xml:id="echoid-s16644" xml:space="preserve">Neceſſe igitur eſt, planetam modo altio-<lb/>rem fieri reſpectu centri terræ, modo humiliorem. </s> <s xml:id="echoid-s16645" xml:space="preserve">Quando enim planeta eſt <lb/>humilior, hoc eſt, terræ propinquior, maiorẽ admittit aſpectus diuerſitatẽ, quan <lb/>do vero ſublimior à terra fertur, minorem: </s> <s xml:id="echoid-s16646" xml:space="preserve">dummodo tam ibi, quàm hic eandẽ <lb/>habeat ſupra Horizontem altitudinem, vt ſupra demonſtrauimus cap. </s> <s xml:id="echoid-s16647" xml:space="preserve">1. </s> <s xml:id="echoid-s16648" xml:space="preserve">cum <lb/>de ordine ſphærarum cæleſtium diſputaremus, & </s> <s xml:id="echoid-s16649" xml:space="preserve">perſpicuè etiam apparet in <lb/>hac præſenti figura, in qua ad ſiniſtram aſtrum <lb/>modo remotius à terra, modo propinquius ter-<lb/>ræ, eandem habet altitudinem reſpectu lineæ re <lb/>ctæ ductæ ex centro mundi per centrum aſtri, <lb/> <anchor type="figure" xlink:label="fig-479-01a" xlink:href="fig-479-01"/> hoc eſt, eandem altitudinem veram, ſiue eun-<lb/>dem locum verum: </s> <s xml:id="echoid-s16650" xml:space="preserve">Ad dextram uero aſtrum <lb/>nunc minus à terra diſtans, nunc magis, eandem <lb/>habet altitudinem reſpectu lineæ rectę eductæ <lb/>ab oculo, ſeu ſuperficie terrę per aſtri centrum. <lb/></s> <s xml:id="echoid-s16651" xml:space="preserve">Non poteſt autem unum, idemque aſtrum mo <lb/>do terrę propinquius fieri, modo ab eadem ab-<lb/>eſſe longius, ſi in orbe concentrico feratur, ſed <lb/>ſolum, ſi in Eccentrico, ut ex dictis perſpicuum eſt. </s> <s xml:id="echoid-s16652" xml:space="preserve">Non ergo ſine ratione A-<lb/>ſtronomi planetas in Eccentricis orbibus circumduci affirmarunt. </s> <s xml:id="echoid-s16653" xml:space="preserve">Hę ſunt <lb/>quatuor apparentiæ, (relictis multis alijs) quibus merito Aſtronomi conten <lb/>dunt perſuadere, planetarum ſphęras componi ex orbibus eccentricis, in qui-<lb/>bus proprijs motibus deferantur ab occaſu in ortum. </s> <s xml:id="echoid-s16654" xml:space="preserve">Quæ quidem eodem or-<lb/>dine probant, & </s> <s xml:id="echoid-s16655" xml:space="preserve">conuincunt, in omnibus Planetis, uno excepto Sole, dari etiã <lb/>Epicyclos, in quibus ipſi planetæ reuoluantur, ut ex ijs, quæ iam ſequuntur, <lb/>perſpicuum fiet.</s> <s xml:id="echoid-s16656" xml:space="preserve"/> </p> <div xml:id="echoid-div902" type="float" level="2" n="11"> <figure xlink:label="fig-479-01" xlink:href="fig-479-01a"> <image file="479-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/479-01"/> </figure> </div> <p> <s xml:id="echoid-s16657" xml:space="preserve">I. </s> <s xml:id="echoid-s16658" xml:space="preserve"><emph style="sc">Planetae</emph>, Sole excepto, exiſtentes in Auge Eccentrici, id eſt, <lb/> <anchor type="note" xlink:label="note-479-02a" xlink:href="note-479-02"/> in puncto Eccentrici à terra remotiſſimo, non eodem ſemper modo ſe habet <lb/>ad terram. </s> <s xml:id="echoid-s16659" xml:space="preserve">Nunc enim ſublimiores, nunc humiliores feruntur: </s> <s xml:id="echoid-s16660" xml:space="preserve">Nunc) quod ex <lb/>primo ſequitur.) </s> <s xml:id="echoid-s16661" xml:space="preserve">diametri eorum minores, nunc maiores; </s> <s xml:id="echoid-s16662" xml:space="preserve">Planetæ denique ipſi <lb/>propterea modo minores, modo maiores apparent, minoremq; </s> <s xml:id="echoid-s16663" xml:space="preserve">nunc ſuis dia-<lb/>metris portionem Zodiaci abſcindunt, nunc maiorem: </s> <s xml:id="echoid-s16664" xml:space="preserve">Idemq; </s> <s xml:id="echoid-s16665" xml:space="preserve">prorſus contin-<lb/>git, planetis in oppoſito Augis Eccentrici exiſtentibus. </s> <s xml:id="echoid-s16666" xml:space="preserve">Hæc autem diuerſitas <lb/>ratione ſolius Eccentrici fieri non poteſt. </s> <s xml:id="echoid-s16667" xml:space="preserve">Cum enim Aux Eccentrici ſemper <lb/>ſit in eadem diſtantia à terra planeta in Auge exiſtens ſemper eodem modo ap <lb/>pareret, quoad propinquitatem, & </s> <s xml:id="echoid-s16668" xml:space="preserve">diſtantiam, magnitudinem, & </s> <s xml:id="echoid-s16669" xml:space="preserve">paruitatem. <lb/></s> <s xml:id="echoid-s16670" xml:space="preserve">Idemq́; </s> <s xml:id="echoid-s16671" xml:space="preserve">accideret, planeta in oppoſito Angis exiſtente. </s> <s xml:id="echoid-s16672" xml:space="preserve">Deberet namq; </s> <s xml:id="echoid-s16673" xml:space="preserve">ſemper <lb/>planeta in Auge eſſe remotiſſimus à terra, & </s> <s xml:id="echoid-s16674" xml:space="preserve">in Augis oppoſito propinquiſ-<lb/>ſimus, (ut in Sole experimur, qui ſolum in eccentrico orbe circum fertur.) </s> <s xml:id="echoid-s16675" xml:space="preserve">cum <lb/>tamen ali quando remotior, ali quando propinquior appareat tam in Auge Ec- <pb o="444" file="480" n="481" rhead="Comment. in IIII. Cap. Sphæræ"/> centrici, quàm in oppoſito Augis. </s> <s xml:id="echoid-s16676" xml:space="preserve">Immerſus igitur erit intra craſſitiem Eccen <lb/>trici Epicyclus, ad cuius motũ planeta reuoluatur. </s> <s xml:id="echoid-s16677" xml:space="preserve">Ita enim nullo labore præ-<lb/>dictæ diuerſitatis cauſam reddemus. </s> <s xml:id="echoid-s16678" xml:space="preserve">Sit enim Zodiacus, cui cẽtrum idem cum <lb/>centro mundi ſit A; </s> <s xml:id="echoid-s16679" xml:space="preserve">Eccentricus uero deferens planetam ſit BCDE, cuius cen-<lb/>trum F, à mundi centro diuerſum; </s> <s xml:id="echoid-s16680" xml:space="preserve">Aux Eccentrici ſit B, & </s> <s xml:id="echoid-s16681" xml:space="preserve">oppoſitum Augis D. <lb/></s> <s xml:id="echoid-s16682" xml:space="preserve"> <anchor type="figure" xlink:label="fig-480-01a" xlink:href="fig-480-01"/> Quod ſi Luna v.</s> <s xml:id="echoid-s16683" xml:space="preserve">g. </s> <s xml:id="echoid-s16684" xml:space="preserve">ſolum in hoc Eccen-<lb/>trico moueretur, proculdubio in Au-<lb/>ge B, remotiſſima ſemper à nobis cer-<lb/>neretur, & </s> <s xml:id="echoid-s16685" xml:space="preserve">minima: </s> <s xml:id="echoid-s16686" xml:space="preserve">In oppoſito ue-<lb/>ro Augis D, propinquiſſima nobis, & </s> <s xml:id="echoid-s16687" xml:space="preserve"><lb/>maxima perpetuo appareret. </s> <s xml:id="echoid-s16688" xml:space="preserve">Cuius <lb/>contrarium accidere deprehenſum eſt <lb/>ab Aſtronomis. </s> <s xml:id="echoid-s16689" xml:space="preserve">At poſito Epicyclo <lb/>G H I, in quo planeta affigatur in <lb/>pancto G, uel I, liquido conſtat, Lu-<lb/>nam, (quod de alijs etiam planetis in <lb/>telligas.) </s> <s xml:id="echoid-s16690" xml:space="preserve">quamuis in Auge Eccen-<lb/>trici, vel oppoſito Augis extiterit, ta-<lb/>men quia tunc reperitur v.</s> <s xml:id="echoid-s16691" xml:space="preserve">g. </s> <s xml:id="echoid-s16692" xml:space="preserve">in Epicy-<lb/>clo ad punctum G, remotiorem à no-<lb/>bis apparere, quàm cum in Epicyclo <lb/>ad punctum I, extiterit. </s> <s xml:id="echoid-s16693" xml:space="preserve">Sed dicet for-<lb/>taſſe aliquis, fruſtra conceſſos eſſe Ec-<lb/>centricos, ſi per Epicyclum tueri poſſumus, planetas modoà terra eſſe remo-<lb/>tiores, modo minus diſtantes. </s> <s xml:id="echoid-s16694" xml:space="preserve">Cui reſpondendum eſt, quemadmodum per ſo-<lb/>lum Eccentricum hęc apparentia defendi non poteſt, ut diximus, ita quoque <lb/>eandem per ſolum Epicyclum defendi non poſſe. </s> <s xml:id="echoid-s16695" xml:space="preserve">Compertum namque eſt <lb/>à Mathematicis, Lunam v.</s> <s xml:id="echoid-s16696" xml:space="preserve">g. </s> <s xml:id="echoid-s16697" xml:space="preserve">exiſtentem in puncto Epicycli G, à terra remotiſ-<lb/>ſimo, non ſemper eandem à terra habuiſſe diſtantiam, neque eiuſdem ſemper <lb/>apparuiſſe magnitudinis. </s> <s xml:id="echoid-s16698" xml:space="preserve">Quod idem accidere cognouerunt, dum Luna in <lb/>puncto Epicycli I, terræ proximo exiſtebat. </s> <s xml:id="echoid-s16699" xml:space="preserve">Idemque in alijs planetis obſer-<lb/>uarunt. </s> <s xml:id="echoid-s16700" xml:space="preserve">Neceſſe igitur eſt, Epicyclum deferri in orbe Eccentrico, non autem <lb/>in concentrico, ut tanta diuerſitas locum inueniat. </s> <s xml:id="echoid-s16701" xml:space="preserve">Quare non fruſtra in pla-<lb/>netis, præter Epicyclum, Eccentricus conſtituitur, cum vterque orbis neceſſa-<lb/>rius ſit, ut præd@ctam apparentiam tueamur. </s> <s xml:id="echoid-s16702" xml:space="preserve">Vidi ego certe paucis annis ela-<lb/>pſis Martem tanta magnitudine, ut duplo tunc maior cœlo ſereniſſimo appa-<lb/>reret, quàm alio tempore, & </s> <s xml:id="echoid-s16703" xml:space="preserve">multi mirarentur exiſtimantes, nouum in cœlo ſy <lb/>dus effulſiſſe. </s> <s xml:id="echoid-s16704" xml:space="preserve">Quod idcirco dixerim, ut ſtudioſus lector videat, tam illuſtrem <lb/>eſſe hanc apparentiam de magnitudine planetarum, quæ ſine Eccentricis & </s> <s xml:id="echoid-s16705" xml:space="preserve"><lb/>Epicyclis defendi non poteſt, ut ſponte ſeſe oculis noſtris interdum obijciat ſi-<lb/>ne miniſterio inſtrumentorum.</s> <s xml:id="echoid-s16706" xml:space="preserve"/> </p> <div xml:id="echoid-div903" type="float" level="2" n="12"> <note position="right" xlink:label="note-479-02" xlink:href="note-479-02a" xml:space="preserve">I <lb/>Apparentia <lb/>probans da <lb/>ri Epicy-<lb/>elos.</note> <figure xlink:label="fig-480-01" xlink:href="fig-480-01a"> <image file="480-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/480-01"/> </figure> </div> <p> <s xml:id="echoid-s16707" xml:space="preserve">II. </s> <s xml:id="echoid-s16708" xml:space="preserve"><emph style="sc">Omnes</emph> planetæ, præter Solem, exiſtentes in Auge Eccentrici, quã-<lb/> <anchor type="note" xlink:label="note-480-01a" xlink:href="note-480-01"/> uis ex ſe ibi tardius moueantur reſpectu centri terrę, ut ſupra de Sole eſt di-<lb/>ctum, tamen aliam adhuc ibi deprehenſi ſunt habere irregularitatem. </s> <s xml:id="echoid-s16709" xml:space="preserve">Nam Lu-<lb/>na v.</s> <s xml:id="echoid-s16710" xml:space="preserve">g. </s> <s xml:id="echoid-s16711" xml:space="preserve">aliquando uelocius in Auge, aliquando tardius uiſa eſt moueri. </s> <s xml:id="echoid-s16712" xml:space="preserve">Idem-<lb/>que in Augis oppoſito compertum eſt: </s> <s xml:id="echoid-s16713" xml:space="preserve">ita ut Luna aliquando in Zodiaco per-<lb/>currat uno die ferme grad. </s> <s xml:id="echoid-s16714" xml:space="preserve">15. </s> <s xml:id="echoid-s16715" xml:space="preserve">alio uero die tantum grad. </s> <s xml:id="echoid-s16716" xml:space="preserve">11. </s> <s xml:id="echoid-s16717" xml:space="preserve">Quod quidem <lb/>ficut per ſolum Eccentricum defendi nequit, (alias namque eadem apparentia <pb o="445" file="481" n="482" rhead="Ioan. de Sacro Boſco."/> in Sole reperiri deberet quod falſum eſt. </s> <s xml:id="echoid-s16718" xml:space="preserve">Mouetur enim ſemper eadẽ tardita-<lb/>te, dũ eſt in Auge, dũ uero in Augis oppoſito eſt, eadem celeritate.) </s> <s xml:id="echoid-s16719" xml:space="preserve">ita facilli-<lb/>mo negotio eã tuobimur, ſi in Epicyclo Lunã moueri ponamus, & </s> <s xml:id="echoid-s16720" xml:space="preserve">in E@centri <lb/>co, ut ex ſuperiori ſigura cõſtat. </s> <s xml:id="echoid-s16721" xml:space="preserve">Si. </s> <s xml:id="echoid-s16722" xml:space="preserve">n. </s> <s xml:id="echoid-s16723" xml:space="preserve">Eccentricus Lunæ ſecundũ ſignorũ ſuc-<lb/>ceſſ@on@ moueatur, (vt re uera mouetur) hoc eſt, ab ♈, in ♉, & </s> <s xml:id="echoid-s16724" xml:space="preserve">à ♉, in ♊, &</s> <s xml:id="echoid-s16725" xml:space="preserve">c. <lb/></s> <s xml:id="echoid-s16726" xml:space="preserve">nempe in dicta figura ex C, in B, & </s> <s xml:id="echoid-s16727" xml:space="preserve">ex B, in E, &</s> <s xml:id="echoid-s16728" xml:space="preserve">c. </s> <s xml:id="echoid-s16729" xml:space="preserve">Epicyclus autem eiuſdem fe <lb/>ratur in ſuperiori quidẽ parte (ut in eius Theorica oſteneitur) contra ſucceſ <lb/>ſionem ſignorum, motu videlicet motui Eccentrici cõtrario, puta, ex G, in H, <lb/>ſumendo Epicyclũ ſuperiorem in ſigura, uel ex H, in G, ſumẽdo inferiorẽ, In <lb/>parte autem inferiori Epicycli ſecundum ſignorũ ſucceſſionẽ, quemadmodũ <lb/>& </s> <s xml:id="echoid-s16730" xml:space="preserve">Eccentricus, nempe in Epicyclo ſuperiori nominatæ figuræ ex H, in I, at in <lb/>inferiori ex I, in H; </s> <s xml:id="echoid-s16731" xml:space="preserve">perſpicue intelligitur, Lunam, dũ reuoluitur in ſuperiori <lb/>parte Epicyclir ferri tardius, cũ contramotũ Eccentrici vehatur: </s> <s xml:id="echoid-s16732" xml:space="preserve">in parte vero <lb/>inferiori incitatius, cum geminetur quodãmodo eius motus uerſus eandẽ pa@ <lb/>tem. </s> <s xml:id="echoid-s16733" xml:space="preserve">Accedit etiã, quòd Luna in ſuo Eccentrico regulariter mouetur circa cẽ <lb/>trum terrę, (vt in eius Theorica cũ Ptolomęo demonſtrabimus) vnde ſine Epi <lb/>cyclo rationẽ huiuſce tarditatis, velocitatisq́; </s> <s xml:id="echoid-s16734" xml:space="preserve">reddere non poſſumus. </s> <s xml:id="echoid-s16735" xml:space="preserve">Hæc va-<lb/>rietas in alijs etiam planetis, præter Solẽ, notata eſt ſuo modo. </s> <s xml:id="echoid-s16736" xml:space="preserve">Vnde & </s> <s xml:id="echoid-s16737" xml:space="preserve">ipſi in <lb/>Epicyclis reuoluentur. </s> <s xml:id="echoid-s16738" xml:space="preserve">Cęterũ multo euidentius in ſuperioribus tribus pla-<lb/>netis, Marte, Ioue, & </s> <s xml:id="echoid-s16739" xml:space="preserve">Saturno, nec nõ in Mercurio, ac Venere, Epicyclus inuẽ-<lb/>tus eſt. </s> <s xml:id="echoid-s16740" xml:space="preserve">Hi enim planetæ nunc progredi in Zodiaco à<unsure/> partibus occidentalibus <lb/>verſus orientales cernuntur, nunc uero retrocedere a partibus orientalibus <lb/>uerſus occidentales. </s> <s xml:id="echoid-s16741" xml:space="preserve">Dũ em̃ ſunt in ſuperiori parte Epicycli, voluuntur ſecun <lb/>dũ ſucceſſionẽ ſignorũ, quemadmodũ & </s> <s xml:id="echoid-s16742" xml:space="preserve">in Eccentrico: </s> <s xml:id="echoid-s16743" xml:space="preserve">Vnde incitatur eorũ <lb/>motus ab occaſu in ortũ, & </s> <s xml:id="echoid-s16744" xml:space="preserve">ſic progredi uidẽtur; </s> <s xml:id="echoid-s16745" xml:space="preserve">ita ut ſi v. </s> <s xml:id="echoid-s16746" xml:space="preserve">g. </s> <s xml:id="echoid-s16747" xml:space="preserve">aliquis illorũ eſt <lb/>in gr. </s> <s xml:id="echoid-s16748" xml:space="preserve">1. </s> <s xml:id="echoid-s16749" xml:space="preserve">♌, mox futurus ſit in gr. </s> <s xml:id="echoid-s16750" xml:space="preserve">2. </s> <s xml:id="echoid-s16751" xml:space="preserve">deinde in 3. </s> <s xml:id="echoid-s16752" xml:space="preserve">&</s> <s xml:id="echoid-s16753" xml:space="preserve">c. </s> <s xml:id="echoid-s16754" xml:space="preserve">Dum uero in parte Epicy-<lb/>cli inferiori uerſantur, cientur cõtra ſignorũ ſucceſſionẽ, hoc eſt, cõtra motũ <lb/>quẽ Epicyclus habet in Eccentrico: </s> <s xml:id="echoid-s16755" xml:space="preserve">atque ita retrogredi uidentur, ita ut, ſi v. </s> <s xml:id="echoid-s16756" xml:space="preserve">g. </s> <s xml:id="echoid-s16757" xml:space="preserve"><lb/>illorum quiſpiã in grad. </s> <s xml:id="echoid-s16758" xml:space="preserve">4. </s> <s xml:id="echoid-s16759" xml:space="preserve">♌, uerſatur, mox futurus ſit in grad. </s> <s xml:id="echoid-s16760" xml:space="preserve">3. </s> <s xml:id="echoid-s16761" xml:space="preserve">deinde in 2. </s> <s xml:id="echoid-s16762" xml:space="preserve"><lb/>&</s> <s xml:id="echoid-s16763" xml:space="preserve">c. </s> <s xml:id="echoid-s16764" xml:space="preserve">quę omnia clarius explicabũtur in Theoricis Cur uero retrogradatio hęc <lb/>in Luna non appareat, cum tamen in <gap/> Epicyclo in diuerſas cieatur partes, <lb/>& </s> <s xml:id="echoid-s16765" xml:space="preserve">diſſimiles, in eius Eheorica oſtendemus. </s> <s xml:id="echoid-s16766" xml:space="preserve">Itaq; </s> <s xml:id="echoid-s16767" xml:space="preserve">cũ hæc apparentia nullo mo-<lb/>do ſine Epicyclo, facillime autem, illo poſito, defendi poſſit, ut ex dictis con-<lb/>ſtat, veriſimile erit, quemlibet planetam, Sole excepto, in Epicyclo moueri.</s> <s xml:id="echoid-s16768" xml:space="preserve"/> </p> <div xml:id="echoid-div904" type="float" level="2" n="13"> <note position="left" xlink:label="note-480-01" xlink:href="note-480-01a" xml:space="preserve">II. <lb/>Apparentia <lb/>probant da <lb/>@i Epicyclos</note> </div> <note position="right" xml:space="preserve">III <lb/>Apparentia <lb/>probans da-<lb/>ri Epicyclos@</note> <p> <s xml:id="echoid-s16769" xml:space="preserve">III. </s> <s xml:id="echoid-s16770" xml:space="preserve"><emph style="sc">Veteres</emph> ac dilihentes aſtrorum obſeruatores conſiderarunt <lb/>aliquando duas eclipſes Lunares, Sole & </s> <s xml:id="echoid-s16771" xml:space="preserve">Luna in eodem ſitu in utraque ma-<lb/>nentibus, puta Sole in capite Draconis, & </s> <s xml:id="echoid-s16772" xml:space="preserve">Luna in cauda, exiſtenteq́; </s> <s xml:id="echoid-s16773" xml:space="preserve">Sole in <lb/>vtraque in eodem loco Eccentrici, ita ut in utraq; </s> <s xml:id="echoid-s16774" xml:space="preserve">eandem à terra diſtantiam <lb/>habuerit, atque adeo eandem utrobique umbram terra proiecerit; </s> <s xml:id="echoid-s16775" xml:space="preserve">inuene-<lb/>runtq; </s> <s xml:id="echoid-s16776" xml:space="preserve">alteram eclipſiũ longiori tempore duraſſe, quàm alteram. </s> <s xml:id="echoid-s16777" xml:space="preserve">Cuius qui-<lb/>dem inæqualitatis cauſa Eccentrico ſoli tribui non poteſt. </s> <s xml:id="echoid-s16778" xml:space="preserve">Maior enim, uel <lb/>minor duratio eclipſis accidit ob ingreſſum Lunæ in maiorem, uel minorem <lb/>umbram terræ: </s> <s xml:id="echoid-s16779" xml:space="preserve">At tunc in vtraque eclipſi eadem ſemper fuit umbra terræ, cũ <lb/>Sol ponatu@ æqualiter a terra in utraque remotus. </s> <s xml:id="echoid-s16780" xml:space="preserve">Oportet igitur Lunam <lb/>ipſam in altera eclipſium minus remotam fuiſſe à terra, in alt@@@ uero ma-<lb/>gis. </s> <s xml:id="echoid-s16781" xml:space="preserve">Nam cum terræ umbra porrigatur in conum, quod terra minor ſit, <lb/>quàm Sol, fit, ut quo propinquior terræ fuerit vmbra, eo latior ſit, quo ne-<lb/>ro remotior à terra, eo anguſtior, & </s> <s xml:id="echoid-s16782" xml:space="preserve">minus lata. </s> <s xml:id="echoid-s16783" xml:space="preserve">Ex quo fit, Lunam, quo <pb o="446" file="482" n="483" rhead="Comment. in IIII. Cap. Sphæræ"/> propinquior fuerit terræ, eo maiorem pertranſire umbram, eo autem minorẽ, <lb/>quo longius à terra receſſerit; </s> <s xml:id="echoid-s16784" xml:space="preserve">atq; </s> <s xml:id="echoid-s16785" xml:space="preserve">adeo eclipſes fieri inæquales, quoad magni <lb/>tudinem, ac durationem. </s> <s xml:id="echoid-s16786" xml:space="preserve">Verum hæc minor, maiorve diſtantia Lunæ à terra <lb/>in eclipſi Lunari tribui nullo modo poteſt eius Eccentrico. </s> <s xml:id="echoid-s16787" xml:space="preserve">Ratione enim Ec-<lb/>centrici Luna in omni eclipſi tam Solari, quàm Lunari eandem habet à terra <lb/>diſtantiã; </s> <s xml:id="echoid-s16788" xml:space="preserve">propterea quò<unsure/>d Luna (ut in eius Theorica declarabitur) tam in con-<lb/>iunctionibus eius cum Sole, quàm in oppoſitionibus (Fit autẽ omnis eclipſis <lb/>Solis in aliqua coniunctione, & </s> <s xml:id="echoid-s16789" xml:space="preserve">eclipſis Lunæ in oppoſitione aliqua) ſemper <lb/>in Auge ſui Eccentrici exiſtit. </s> <s xml:id="echoid-s16790" xml:space="preserve">Confugiendum igitur eſt ad Epicyclũ. </s> <s xml:id="echoid-s16791" xml:space="preserve">Sic enim <lb/>ſine magno labore tuebimur hanc inæqualitatem eclipſiũ Lunariũ, licet lumi <lb/>naria ambo eundẽ ſitũ habeant, quoad caput, & </s> <s xml:id="echoid-s16792" xml:space="preserve">caudã Draconis, æqualiterq́@ <lb/>ſemper Solà terra diſtet, & </s> <s xml:id="echoid-s16793" xml:space="preserve">Luna in Auge ſui Eccentrici exiſtat. </s> <s xml:id="echoid-s16794" xml:space="preserve">Nam in una <lb/>eclipſium poteſt Luna eſſe in puncto Epicycli terræ proximo, in alia uero in <lb/>puncto remotiſſimo à terra. </s> <s xml:id="echoid-s16795" xml:space="preserve">Vnde maior erit prior eclipſis, longioriq; </s> <s xml:id="echoid-s16796" xml:space="preserve">tẽpore <lb/>durabit, quàm poſterior: </s> <s xml:id="echoid-s16797" xml:space="preserve">quia in illa pertrãſit Luna maiorẽ umbram terræ, in <lb/>hac autem minorem. </s> <s xml:id="echoid-s16798" xml:space="preserve">Exemplum habes in propoſita hac figura, in qua ABCD@ <lb/> <anchor type="figure" xlink:label="fig-482-01a" xlink:href="fig-482-01"/> refert Eccentricum Solis; </s> <s xml:id="echoid-s16799" xml:space="preserve">FIGL, Eccentricum, qui centrum Epicycli Lunæ de <lb/>fert: </s> <s xml:id="echoid-s16800" xml:space="preserve">FHGK, Eclipticam, quæ Eccentricũ Lunæ ſecat in punctis F, & </s> <s xml:id="echoid-s16801" xml:space="preserve">G, quorũ <lb/>F. </s> <s xml:id="echoid-s16802" xml:space="preserve">v. </s> <s xml:id="echoid-s16803" xml:space="preserve">g. </s> <s xml:id="echoid-s16804" xml:space="preserve">caput Draconis, at G, cauda Draconis nominatur: </s> <s xml:id="echoid-s16805" xml:space="preserve">A, eſt Sol in capite <lb/>Draconis exiſtẽs; </s> <s xml:id="echoid-s16806" xml:space="preserve">E, terra, & </s> <s xml:id="echoid-s16807" xml:space="preserve">G, centrum Epicycli in cauda Draconis exiſtens, <lb/>&</s> <s xml:id="echoid-s16808" xml:space="preserve">c. </s> <s xml:id="echoid-s16809" xml:space="preserve">Quod ſi quis dicat, hinc ſequi, nõ recte nos ſupra ex Eclipſibus collegiſſe, <lb/>dari Eccentricum Solis, quandoquidẽ, vt hic diximus, maior & </s> <s xml:id="echoid-s16810" xml:space="preserve">minor eclipſis <lb/>per Epicyclum fieri pot@ſt: </s> <s xml:id="echoid-s16811" xml:space="preserve">occurrendum eſt, Epicyclum Lunæ ſatis non eſſe.</s> <s xml:id="echoid-s16812" xml:space="preserve"> <pb o="447" file="483" n="484" rhead="Ioan. de Sacro Boſco."/> Nam deprehenſæ ſuntduę eclipſes Lunares inter ſe inæquales, exiſtentious lu <lb/>minaribus in eodem, ut diximus, ſitu, quoad caput, & </s> <s xml:id="echoid-s16813" xml:space="preserve">caudam Draconis, & </s> <s xml:id="echoid-s16814" xml:space="preserve">ma-<lb/>nente Luna in eadẽ parte Epicycli, puta uel in ſuperiori, uel inſeriori. </s> <s xml:id="echoid-s16815" xml:space="preserve">Non po <lb/>teſt autem huius inęqualitatis cauſa aſſrgnari, niſi dicamus, luminaria in una <lb/>eclipſi minorem inter ſe habuiſſe diſtantiam, uel certe alterum planetarum ma <lb/>gis ad terram acceſſiſſe, uel magis ab ea receſſiſſe, quàm in altera. </s> <s xml:id="echoid-s16816" xml:space="preserve">Cum ergo <lb/>minor hæc, aut maior diſtantia in Epicyclum Lunę non poſſit referri, quod Lu <lb/>na in eadem ſemper parte Epicycli ponatur extitiſſe in utraque eclipſi, neceſſa <lb/>rio dandus erit etiam Eccentricus.</s> <s xml:id="echoid-s16817" xml:space="preserve"/> </p> <div xml:id="echoid-div905" type="float" level="2" n="14"> <figure xlink:label="fig-482-01" xlink:href="fig-482-01a"> <image file="482-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/482-01"/> </figure> </div> <p> <s xml:id="echoid-s16818" xml:space="preserve">IIII. </s> <s xml:id="echoid-s16819" xml:space="preserve"><emph style="sc">Observatvm</emph> eſt, Lunam in eodem puncto ſui Eccentrici exi-<lb/>ſtentem, in Auge v.</s> <s xml:id="echoid-s16820" xml:space="preserve">g. </s> <s xml:id="echoid-s16821" xml:space="preserve">vel oppoſito Augis, non ſemper eandem aſpectus diuer-<lb/> <anchor type="note" xlink:label="note-483-01a" xlink:href="note-483-01"/> ſitatem habere, ſed modo maiorem, modo minorem. </s> <s xml:id="echoid-s16822" xml:space="preserve">Quod nulla ratione fieri <lb/>poteſt, niſi in eodem puncto Eccentrici modo magis accedat ad terram, & </s> <s xml:id="echoid-s16823" xml:space="preserve">mo-<lb/>do magis ab eadem diſtet. </s> <s xml:id="echoid-s16824" xml:space="preserve">Quocirca in Luna concedendus etiam eſt Epicy-<lb/>clus. </s> <s xml:id="echoid-s16825" xml:space="preserve">Hoc enim poſito, dicta apparentia nullam prorſus habebit difficultatem. <lb/></s> <s xml:id="echoid-s16826" xml:space="preserve"> <anchor type="figure" xlink:label="fig-483-01a" xlink:href="fig-483-01"/> Vt in propoſita figura manifeſtum <lb/>eſſe poteſt, in qua ad ſiniſtram ſum-<lb/>pta ſunt duo puncta oppoſita in Epi <lb/>cyclo uiſa, nimirum per rectam li-<lb/>neam ab oculo per centrum Epicy-<lb/>cli eductam: </s> <s xml:id="echoid-s16827" xml:space="preserve">ad dextram uero acce-<lb/>pta ſunt duo puncta oppoſita in Epi <lb/>cyclo uera, hoc eſt, per lineam rectã <lb/>è<unsure/> centro terræ per centrum Epicy-<lb/>cli porrectam. </s> <s xml:id="echoid-s16828" xml:space="preserve">In quibus quidem <lb/>punctis ſidus Lunare collocatur. </s> <s xml:id="echoid-s16829" xml:space="preserve">Cæ <lb/>tera ex ipſa figura ſunt perſpicua.</s> <s xml:id="echoid-s16830" xml:space="preserve"/> </p> <div xml:id="echoid-div906" type="float" level="2" n="15"> <note position="right" xlink:label="note-483-01" xlink:href="note-483-01a" xml:space="preserve">IIII. <lb/>Apparentia <lb/>probãs darĩ<unsure/> <lb/>Epicyclos.</note> <figure xlink:label="fig-483-01" xlink:href="fig-483-01a"> <image file="483-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/483-01"/> </figure> </div> <p> <s xml:id="echoid-s16831" xml:space="preserve"><emph style="sc">His</emph>, & </s> <s xml:id="echoid-s16832" xml:space="preserve">multis alijs apparentijs, quas dedita opera hic omittimus, accedunt <lb/> <anchor type="note" xlink:label="note-483-02a" xlink:href="note-483-02"/> tres rationes, quæ cõfirmare uidentur, dari in ſphæris cæleſtibus orbes Eccen-<lb/>tricos, & </s> <s xml:id="echoid-s16833" xml:space="preserve">Epicyclos: </s> <s xml:id="echoid-s16834" xml:space="preserve">quarum prima hæc ſit. </s> <s xml:id="echoid-s16835" xml:space="preserve">Ab omnibus Aſtronomis, ac philo-<lb/>ſophis tanquam euidens, & </s> <s xml:id="echoid-s16836" xml:space="preserve">per ſe notum recipitur, quemlibet orbem cęleſtem <lb/>ſuperiorem ſuo motu ſecum trahere inferiorem orbem ſibi contiguum, & </s> <s xml:id="echoid-s16837" xml:space="preserve">con <lb/>centricum. </s> <s xml:id="echoid-s16838" xml:space="preserve">Id quod experientia ipſa magiſtra ueriſſimum eſſe dedicimus. </s> <s xml:id="echoid-s16839" xml:space="preserve">Vi-<lb/> <anchor type="note" xlink:label="note-483-03a" xlink:href="note-483-03"/> demus enim ſphæras omnium planetarum, ſimul cũ Firmamento, & </s> <s xml:id="echoid-s16840" xml:space="preserve">nono cœ <lb/>lo, ſpatio @4. </s> <s xml:id="echoid-s16841" xml:space="preserve">horarum ad motum diurnum primi mobilis rapi ab ortu in occa-<lb/>ſum. </s> <s xml:id="echoid-s16842" xml:space="preserve">Rurſus experimur, eaſdem ſphæras planetarum, unà cum Firmamento ad <lb/>motum nonę ſphæræ trahi ab occaſu in ortũ, licet tardiſſime, nempe in ſpatio <lb/>49000. </s> <s xml:id="echoid-s16843" xml:space="preserve">annorum ſecundum Alphonſum, uel ſecundum Ptolemæum in ſpatio <lb/>36000. </s> <s xml:id="echoid-s16844" xml:space="preserve">annorum. </s> <s xml:id="echoid-s16845" xml:space="preserve">Denique animaduerſum eſt, omnes cœlos planetarum paula <lb/>tim etiam moueri ad motũ trepidationis, ſeu acceſſus, & </s> <s xml:id="echoid-s16846" xml:space="preserve">receſſus octauæ ſphæ-<lb/>ræ. </s> <s xml:id="echoid-s16847" xml:space="preserve">Cuius rei ſignum eſt, quod maximæ Solis declinationes, & </s> <s xml:id="echoid-s16848" xml:space="preserve">aliorum plane-<lb/>tarum mutatæ ſunt. </s> <s xml:id="echoid-s16849" xml:space="preserve">Cum igitur maxima ſingularitas motuũ in planetis repe-<lb/>riatur, ita ut nullius motus proprius inferiori planetæ cõmunicetur, ut cuiuis <lb/>uel parum experto Aſtronomo, etiam aduerſarijs, notum eſſe poteſt, & </s> <s xml:id="echoid-s16850" xml:space="preserve">à nemi-<lb/>ne negatur, (Iuppiter enim nihil prorſus habet ex motu. </s> <s xml:id="echoid-s16851" xml:space="preserve">30. </s> <s xml:id="echoid-s16852" xml:space="preserve">annorum Saturni; <lb/></s> <s xml:id="echoid-s16853" xml:space="preserve">Itemq. </s> <s xml:id="echoid-s16854" xml:space="preserve">Marti nihil communicatur ex motu 12. </s> <s xml:id="echoid-s16855" xml:space="preserve">annorum Iouis, & </s> <s xml:id="echoid-s16856" xml:space="preserve">ſic de cęte-<lb/>ris, ut omnes aſſirmant.) </s> <s xml:id="echoid-s16857" xml:space="preserve">perſpicuum eſſe uidetur, orbes planetarum uectores <lb/>non eſſe concentricos. </s> <s xml:id="echoid-s16858" xml:space="preserve">Alioquin motus cuiuslibet ſuperioris omnibus inferio- <pb o="448" file="484" n="485" rhead="Comment. in IIII. Cap. Sphæræ"/> ribus planetis communicaretur, quemadmodũ id contingere videmus in ſphę <lb/>ris totalibus, ut diximus. </s> <s xml:id="echoid-s16859" xml:space="preserve">Quod cum fieri non uideamus, ut & </s> <s xml:id="echoid-s16860" xml:space="preserve">aduerſarij te-<lb/>ſtantur, dici non poterit, planetas ferri in orbibus concentricis, ſed in eccen-<lb/>tricis. </s> <s xml:id="echoid-s16861" xml:space="preserve">Ita enim experien@ia illa adducta de ſingularitate motuum in planetis <lb/>facillime locũ inueniet. </s> <s xml:id="echoid-s16862" xml:space="preserve">Diuerſitas enim centorum impedimento eſt, quo mi <lb/>nus eccen tricus orbis cuiuſuis planetæ proxime inferiorem orbem ſibi conti <lb/>guũ, cuius concaua ſuperficies concentrica eſt toti<unsure/> mundo, ſecum rapiat, niſi <lb/>cælorũ penetratio, aut ſciſſio daretur, ut ex inſtrumento materia li facile per-<lb/>cipi poteſt: </s> <s xml:id="echoid-s16863" xml:space="preserve">Et utcunque etiam intelligitur ex figura prima huius quæſtionis <lb/>Qui enim fieri poteſt, ſi attentius res conſideretur, ut orbis ſimpliter eccentri <lb/>cus G H, circa ſuum centrum F, trahat proxime inferiorem orbem eccentri-<lb/>cum ſecundum quid, cuius ſuperficies concaua, unà cum toto cælo, æqualiter <lb/>à centro mundi E, diſtat, niſi hic inferior orbis penetret, aut ſcindat cælũ in-<lb/>ferioris planetæ, quod intra concauum dicti orbis eccentrici ſecundum quid <lb/>continetur? </s> <s xml:id="echoid-s16864" xml:space="preserve">Scio auctores orbiũ contricorũ confingere infra ſingulorum pla-<lb/>netarum orbes, ſingulos orbes reſtituentes, quos Fracaſtorius Circitores ap-<lb/>pellat, quorum oſſiciũ ſit, vt quantum ſuperiòres planetæ inferiores trahun-<lb/>ſuis motibus, tantũ ipſi inferiores planetas in contrariam partem reſtituantt <lb/>Verum hoc figmẽto ſimile eſſe uidetur. </s> <s xml:id="echoid-s16865" xml:space="preserve">Præterquam enim, quod hac ratione. <lb/></s> <s xml:id="echoid-s16866" xml:space="preserve">maxima confuſio in motibus introducitur, non uideo, quo pacto primum mo-<lb/>bile omnibus inferioribus ſphæris motum diurnum poſſit communicare, cũ <lb/>in medio poſiti ſint circitores illi, qui inferiores ſphæras omnino prohibent, <lb/>ne à ſuperioribus rapiantur, niſi quis dicat, ſingulas ſphæras planetarũ pro-<lb/>prios habere mocus diurnos ab ortu in occaſum, qui in ſpatio 24. </s> <s xml:id="echoid-s16867" xml:space="preserve">horarum ab <lb/>ſoluantur, quòd nouum eſt, atque inauditum, & </s> <s xml:id="echoid-s16868" xml:space="preserve">a nemine hactenus cõceſſum.</s> <s xml:id="echoid-s16869" xml:space="preserve"/> </p> <div xml:id="echoid-div907" type="float" level="2" n="16"> <note position="right" xlink:label="note-483-02" xlink:href="note-483-02a" xml:space="preserve">Aliæ ratio-<lb/>nes confir-<lb/>mantes da <lb/>ri Eccentri-<lb/>cos & Epi-<lb/>cyclos.</note> <note position="right" xlink:label="note-483-03" xlink:href="note-483-03a" xml:space="preserve">@. Ratio.</note> </div> <p> <s xml:id="echoid-s16870" xml:space="preserve"><emph style="sc">Secvnda</emph> ratio hæc eſt. </s> <s xml:id="echoid-s16871" xml:space="preserve">Si planetę in orbibus eccentricis non defe-<lb/> <anchor type="note" xlink:label="note-484-01a" xlink:href="note-484-01"/> runtur ab occaſu in ortum, deuehentur utiq; </s> <s xml:id="echoid-s16872" xml:space="preserve">aut per orbes concentricos, aut <lb/>certe per ſeſe mouebuntur in cælis, ut piſces in mari, uel aues in aere: </s> <s xml:id="echoid-s16873" xml:space="preserve">Sed hi-<lb/>ſce duobus modis nõ mouentur. </s> <s xml:id="echoid-s16874" xml:space="preserve">Igitur in ecceniricis feruntur. </s> <s xml:id="echoid-s16875" xml:space="preserve">Cõſecutio ma <lb/>nifeſta eſt: </s> <s xml:id="echoid-s16876" xml:space="preserve">Maior quoq; </s> <s xml:id="echoid-s16877" xml:space="preserve">propoſitio patet ex ſufficienti partium enumeratione. <lb/></s> <s xml:id="echoid-s16878" xml:space="preserve">Minor uero probatur, quoad utramq; </s> <s xml:id="echoid-s16879" xml:space="preserve">partem. </s> <s xml:id="echoid-s16880" xml:space="preserve">Quòd enim plaue@æ non mo-<lb/>ueantur per ſeſe, (ut a poſteriori parte incipiamus.) </s> <s xml:id="echoid-s16881" xml:space="preserve">veluti piſces in mari, uel <lb/>aues in aere, multis rationibus probare nititur Ariſtoteles iu lib. </s> <s xml:id="echoid-s16882" xml:space="preserve">de cęlo, & </s> <s xml:id="echoid-s16883" xml:space="preserve">a <lb/>nobis euidenti argumento confirmatum eſt ſupra, quando cap. </s> <s xml:id="echoid-s16884" xml:space="preserve">1. </s> <s xml:id="echoid-s16885" xml:space="preserve">oſtẽdimus cũ <lb/>auctore, cælum ab oriente uolui in occidentem; </s> <s xml:id="echoid-s16886" xml:space="preserve">& </s> <s xml:id="echoid-s16887" xml:space="preserve">eſt communis omniũ phi-<lb/>loſophorum, & </s> <s xml:id="echoid-s16888" xml:space="preserve">Aſtronomorum doctrina. </s> <s xml:id="echoid-s16889" xml:space="preserve">Immo ſi ita mouerentur, & </s> <s xml:id="echoid-s16890" xml:space="preserve">non po-<lb/>tius ad motũ orbium, in quibus ſunt, nullam certam ſcientiam de illorum mo <lb/>tibus habere poſſemus. </s> <s xml:id="echoid-s16891" xml:space="preserve">Cum enim, ut in ſuperioribus apparentijs dictum eſt, <lb/>planetæ aliquando magis, aliquando minus a terra abſint: </s> <s xml:id="echoid-s16892" xml:space="preserve">interdum velocius <lb/>moueantur, @terdum qua ſi curſum inhibeant; </s> <s xml:id="echoid-s16893" xml:space="preserve">nunc ſtare uideantur, nũc pro-<lb/>gredi ſub Zodiaco ab occaſu in ortum, nunc retrogredi; </s> <s xml:id="echoid-s16894" xml:space="preserve">quis eſt, qui non ui-<lb/>deat, planetas, ſi mouentur ut piſces, ſeu aues, aliquando ſuos circulos, quos <lb/>ab occaſu in ortum deſcribunt debere relinquere, ut magis poſſint a terra re <lb/>cedere, & </s> <s xml:id="echoid-s16895" xml:space="preserve">ad eandem accedere; </s> <s xml:id="echoid-s16896" xml:space="preserve">aliquando autem proprium curſum negligere, <lb/>rurſusq́; </s> <s xml:id="echoid-s16897" xml:space="preserve">in oppoſitam partem retrocedendo niti; </s> <s xml:id="echoid-s16898" xml:space="preserve">aliquando denique curſum <lb/>omnino fiſtere in cęlo, ut penitus non moueantur? </s> <s xml:id="echoid-s16899" xml:space="preserve">Quæ ſi fierent, quo nã mo-<lb/>do, obſecro, eorum periodi ſtefiniri poterunt; </s> <s xml:id="echoid-s16900" xml:space="preserve">qua item ratione cognoſci, qua-<lb/>nam in parte cæli altius a terra digreſſuri ſint planetæ, & </s> <s xml:id="echoid-s16901" xml:space="preserve">iterum ad terrã re- <pb o="449" file="485" n="486" rhead="Ioan. de Sacro Boſco."/> uerſuri, &</s> <s xml:id="echoid-s16902" xml:space="preserve">c. </s> <s xml:id="echoid-s16903" xml:space="preserve">Quòd etiã planetæ non circumducantur ab occaſu in ortum in <lb/>orbibus concentricis, ita perſpicuum fiet. </s> <s xml:id="echoid-s16904" xml:space="preserve">Primum, quia hac ratione non poſ-<lb/>ſunt ſupra adducta phænomena defẽdi, maxime illa, quæ de maiori, minoriq́@ <lb/>diſtãtia a terra, ac de maiore, minoreq; </s> <s xml:id="echoid-s16905" xml:space="preserve">planetarũ magnitudine ſunt obſerua <lb/>ta. </s> <s xml:id="echoid-s16906" xml:space="preserve">Quòd ſi alias apparẽtias, nẽpe tarditatẽ motus, ac uelocitatẽ; </s> <s xml:id="echoid-s16907" xml:space="preserve">directionem, <lb/>retrogradationẽ, ac ſtationẽ planetarũ tueri contendũt per orbes concentri <lb/>cos, id ſolũ in genere, & </s> <s xml:id="echoid-s16908" xml:space="preserve">ualde cõſuſe efficere vidẽtur. </s> <s xml:id="echoid-s16909" xml:space="preserve">Dicũt enim, omnia hęc <lb/>prouenire, eo quòd unus orbis cõcẽtricus modo alterũ retardet, modo magis <lb/>promoueat, modo retroducat, &</s> <s xml:id="echoid-s16910" xml:space="preserve">c. </s> <s xml:id="echoid-s16911" xml:space="preserve">ſed quo pacto, quando, & </s> <s xml:id="echoid-s16912" xml:space="preserve">in qua cæli parte <lb/>hæc fieri debeant, non docent. </s> <s xml:id="echoid-s16913" xml:space="preserve">Deinde, quia multa abſurda, & </s> <s xml:id="echoid-s16914" xml:space="preserve">incommoda ex <lb/>poſitione orbium concentricorum conſequũtur. </s> <s xml:id="echoid-s16915" xml:space="preserve">Primum quidem, quoniã, ut <lb/>paulo ante dictũ eſt, inferioribus planetis cõmunicarentur motus ſuperiorũ, <lb/>quod cũ experientia pugnat. </s> <s xml:id="echoid-s16916" xml:space="preserve">Deinde vero, quia uolentes oĩa per cõcentricos <lb/>orbes tueri, fingunt orbes quoſdã in ſphæris planetarũ, quieos deferant à ſe-<lb/>ptẽtrione in auſtrũ, & </s> <s xml:id="echoid-s16917" xml:space="preserve">cõtra. </s> <s xml:id="echoid-s16918" xml:space="preserve">Quo poſito, quis tã hebes eſt, & </s> <s xml:id="echoid-s16919" xml:space="preserve">iners, qui non ui-<lb/>deat, Solem non poſſe ſemper ſubecliptica incedere, maxime ſub ecliptica pri <lb/>mi mobilis, quòd illo motu nõ ſertur; </s> <s xml:id="echoid-s16920" xml:space="preserve">cum per ſe ab ortu cieatur in occaſum, <lb/>vnũ autẽ corpus ſimplex unũ tantũ poſſit habere motũ? </s> <s xml:id="echoid-s16921" xml:space="preserve">Immo ſi moueretur <lb/>à ſeptentrione in auſtrũ, uel contra, mutaretur in eadẽ ciuitate perpetuo alti-<lb/>tudo poli. </s> <s xml:id="echoid-s16922" xml:space="preserve">quod eſt contra maniſeſtiſſimas experientias. </s> <s xml:id="echoid-s16923" xml:space="preserve">Quis itẽ tam rudis, & </s> <s xml:id="echoid-s16924" xml:space="preserve"><lb/>ignarus eſt, qui hoc poſito, non perſpiciat, Solẽ aliquãdo futurũ in polo arcti <lb/>co, aliquando antarctico; </s> <s xml:id="echoid-s16925" xml:space="preserve">aliquando oriturũ in ea parte, ubi nũc occidit, & </s> <s xml:id="echoid-s16926" xml:space="preserve">ali <lb/>qñ occaſurum ibi, ubi nunc eundem cernimus oriri? </s> <s xml:id="echoid-s16927" xml:space="preserve">Quod quidem ingenue <lb/>fatetur Hieronymus Fracaſtorius princeps orbiũ concentricorum: </s> <s xml:id="echoid-s16928" xml:space="preserve">& </s> <s xml:id="echoid-s16929" xml:space="preserve">in ſphæ-<lb/>ra materiali facile apparet@ hoc aliqñ debere ſequi ex huiuſmodi motu cęlorũ <lb/>à ſeptentrione in auſtrũ, & </s> <s xml:id="echoid-s16930" xml:space="preserve">cõtra. </s> <s xml:id="echoid-s16931" xml:space="preserve">Immo idem affirmat, bis iam ab orbe condi-<lb/>to hoc accidiſſe, ſecundum quoſdã Aegyptios. </s> <s xml:id="echoid-s16932" xml:space="preserve">Hoc autem quàm falſum ſit, & </s> <s xml:id="echoid-s16933" xml:space="preserve"><lb/>ri duculum, quis non uidet? </s> <s xml:id="echoid-s16934" xml:space="preserve">Per hiſtorias ſiquidem, & </s> <s xml:id="echoid-s16935" xml:space="preserve">traditiones Mathematĩ <lb/>corũ & </s> <s xml:id="echoid-s16936" xml:space="preserve">philoſophorum cognouimus à tẽpore 2000. </s> <s xml:id="echoid-s16937" xml:space="preserve">annorũ, & </s> <s xml:id="echoid-s16938" xml:space="preserve">eo amplius hu <lb/>cuſque (ut retroacta tempora omittamus) Solẽ, & </s> <s xml:id="echoid-s16939" xml:space="preserve">alias erraticas ſtellas ſtatis <lb/>anni diebus in eadẽ ciuitate prope idem punctũ Horizõtis oriri, & </s> <s xml:id="echoid-s16940" xml:space="preserve">occidere, <lb/>eandemq́; </s> <s xml:id="echoid-s16941" xml:space="preserve">habere altitudinem meridianã, & </s> <s xml:id="echoid-s16942" xml:space="preserve">eandem magnitudinẽ diei, ac no <lb/>ctis. </s> <s xml:id="echoid-s16943" xml:space="preserve">Quæ tamẽ omnia mutari debuiſſent in tanto annorũ interuallo, ſi motus <lb/>ille in rerũ natura exiſteret. </s> <s xml:id="echoid-s16944" xml:space="preserve">Si igitur ab exordio mundi, ex cõmuni ſententia, <lb/>noudũ eff<unsure/>luxerunt anni 7000. </s> <s xml:id="echoid-s16945" xml:space="preserve">quo modo non erit fabulæ anili perſimile, bis <lb/>iã factã eſſe tãtam mutationẽ in Sole Omitto plurima alia abſurda, quæ inde <lb/>conſequuntur: </s> <s xml:id="echoid-s16946" xml:space="preserve">Neque uero quiſquam nobis obiiciat motũ trepidationis, quo <lb/>omnes ſtellæ, ac planetæ cientur: </s> <s xml:id="echoid-s16947" xml:space="preserve">quia cũ hic motus ſit tam imperceptibilis, ut <lb/>vix à peritiſſimis Aſtronomis deprehendatur, non poterit notabilis mutatio <lb/>fieri in ſtellis, & </s> <s xml:id="echoid-s16948" xml:space="preserve">planetis, ut patet in maxima declinatione, quæ à tẽpore Pto <lb/>lemæi ad noſtram uſq; </s> <s xml:id="echoid-s16949" xml:space="preserve">ætatem nondum ad dimidiatũ gradum decreuit. </s> <s xml:id="echoid-s16950" xml:space="preserve">Ad-<lb/>de, hunc motũ non circũducere aſtra circulariter a ſeptentrione in auſtrũ, ſed <lb/>ſolum planetas eo motu trepidare quaſi, & </s> <s xml:id="echoid-s16951" xml:space="preserve">nunc paulatim a ſeptẽtrione in au <lb/>ſtrũ, nunc iterũ ab auſtro in ſeptentrionẽ uehi inſenſibili mutatione. </s> <s xml:id="echoid-s16952" xml:space="preserve">Poſtre-<lb/>mo ex orbibus concentricis maxima oritur confuſio, ob ingentẽ corũ multi-<lb/>tudinẽ, quã eorũ defenſores introducũt. </s> <s xml:id="echoid-s16953" xml:space="preserve">Ex quo etiã ſequatur, neceſſe eſt, mi-<lb/> <anchor type="note" xlink:label="note-485-01a" xlink:href="note-485-01"/> ra perturb atio motuũ. </s> <s xml:id="echoid-s16954" xml:space="preserve">Ponunt enim, ut apud Fracaſtoriũ eſt manifeſtũ, orbes, <lb/>ſeu ſpheras mobiles 77. </s> <s xml:id="echoid-s16955" xml:space="preserve">vel 79. </s> <s xml:id="echoid-s16956" xml:space="preserve">octo quidẽ ſtellatas, reliquas uero oẽs ſtellis <pb o="450" file="486" n="487" rhead="Comment. in IIII. Cap. Sphæræ"/> priuatas, quarum ſex ſupra Firmamentum collocant. </s> <s xml:id="echoid-s16957" xml:space="preserve">quod non ſolum maiori <lb/>parti Aſtronomorum aduerſatur, qui hactenus duas tantũ ſphæras cęleſtes nõ <lb/>ſtellatas ſupra Firmamentũ inuenerũt; </s> <s xml:id="echoid-s16958" xml:space="preserve">verũ etiã pugnat cum omnibus Peri-<lb/>pateticis, qui, ex Ariſtotelis ſententia, ne unum quidem orbem ſupra Firma-<lb/> <anchor type="note" xlink:label="note-486-01a" xlink:href="note-486-01"/> mentum admittere uolunt. </s> <s xml:id="echoid-s16959" xml:space="preserve">Tantam confuſionẽ vitant ij, qui eccentricos or-<lb/>bes ponunt in cælis; </s> <s xml:id="echoid-s16960" xml:space="preserve">quia in uuiuerſum orbes duntaxat 33. </s> <s xml:id="echoid-s16961" xml:space="preserve">concedũt, ambien <lb/>tes quidem terram 28. </s> <s xml:id="echoid-s16962" xml:space="preserve">ſex vero Epicyclos, qui totiextra terram extant. </s> <s xml:id="echoid-s16963" xml:space="preserve">Vn-<lb/>de non erit tanta motuũ multitudo, præſertim cum ſemper duo orbes eccen-<lb/>trici ſecundũ quid ſimul proportionaliter progrediantur, ut in Theoricis ex-<lb/>plicatur, ita ut octo orbibus motus proprius denegetur, ſintq; </s> <s xml:id="echoid-s16964" xml:space="preserve">quilibet duo <lb/>orbes eccentrici ſecundũ quid inſtar vnius orbis, cum eodẽ ſemper motu am-<lb/>bo ferantur. </s> <s xml:id="echoid-s16965" xml:space="preserve">Itaq; </s> <s xml:id="echoid-s16966" xml:space="preserve">cum, ſecundũ celeberrimũ philoſophorum axioma, fruſtra <lb/>fiat per plura, quod fieri poteſt æquè bene per pauciora; </s> <s xml:id="echoid-s16967" xml:space="preserve">ponantur autẽ à no-<lb/>bis triplo fere pauciores Eccentrici, quàm ab aduerſarijs concentrici, & </s> <s xml:id="echoid-s16968" xml:space="preserve">non <lb/>ſolũ ęque bene, ſed multo melius omnia φαινόμενα pereccẽtricos defendãtur <lb/>quàm per concentricos, cũ ſexcentarũ apparrentiarũ ratio per concẽtricos dari <lb/>nequeat, ut ex dictis perſpicuum eſt; </s> <s xml:id="echoid-s16969" xml:space="preserve">quis dubitabit, potius in cælis eſſe orbes <lb/>eccentricos, & </s> <s xml:id="echoid-s16970" xml:space="preserve">Epicyclos conſtituendos, quàm cõcentricos, præſertim cũ natu <lb/>rali philoſophiæ eccentrici nihil omnino repugnent, ut ex ſolutionibus ar-<lb/>gumentorum Auerrois, eiusq́ue ſectatorum conſtabit?</s> <s xml:id="echoid-s16971" xml:space="preserve"/> </p> <div xml:id="echoid-div908" type="float" level="2" n="17"> <note position="left" xlink:label="note-484-01" xlink:href="note-484-01a" xml:space="preserve">2. Ratio.</note> <note position="right" xlink:label="note-485-01" xlink:href="note-485-01a" xml:space="preserve">Quot orbes <lb/>concentricã <lb/>ponantur à <lb/>Fracaſlori@</note> <note position="left" xlink:label="note-486-01" xlink:href="note-486-01a" xml:space="preserve">Quot orbes@ <lb/>pona@tur <lb/>ab ij, qui Ec <lb/>centricos cõ <lb/>cedunt.</note> </div> <p> <s xml:id="echoid-s16972" xml:space="preserve"><emph style="sc">Postremo</emph> ita licebit propoſitum cocludere Sicut in philoſophia na <lb/> <anchor type="note" xlink:label="note-486-02a" xlink:href="note-486-02"/> turali per effectus deueni<unsure/>mus in cognitione cauſarum, ita etiam in Aſtrono-<lb/>mia, quæ de corporibus cęleſtibus à nobis remotiſſimis agit, neceſſe eſt, ut in <lb/>cognitionem ipſorum, coordinationẽ, conſtitutionemq́; </s> <s xml:id="echoid-s16973" xml:space="preserve">perueniamus ex effe <lb/>ctibus, hoc eſt, ex motibus ſtellarũ per ſenſus noſtros perceptis. </s> <s xml:id="echoid-s16974" xml:space="preserve">Quemadmo-<lb/>dum enim ex generatione, & </s> <s xml:id="echoid-s16975" xml:space="preserve">corruptione mutua rerũ naturaliũ phil oſophi <lb/>naturales cũ Ariſtoteles Materiam primam cum alijs duobus principijs tranſ <lb/>mutationis naturalis, & </s> <s xml:id="echoid-s16976" xml:space="preserve">multa alia collegerũt: </s> <s xml:id="echoid-s16977" xml:space="preserve">ſic etiã Aſtronomi per motus <lb/>cęlorum in genere uarios ab ortu in occaſum, & </s> <s xml:id="echoid-s16978" xml:space="preserve">ab occaſu in ortũ inueſtiga-<lb/>runt certum numerum ſphærarum cęleſtium; </s> <s xml:id="echoid-s16979" xml:space="preserve">alij quidẽ octo, quod octo tãtũ <lb/>diuerſos motus in genere cognouerint, alij autem decẽ ex decem motibus di-<lb/>uerſis in genere notatis: </s> <s xml:id="echoid-s16980" xml:space="preserve">Item eadem ratione per alia φαινόμενα ordinẽ inter <lb/>cęleſtes ſphęras conſtituerunt, ut cap. </s> <s xml:id="echoid-s16981" xml:space="preserve">1. </s> <s xml:id="echoid-s16982" xml:space="preserve">copioſe à nobis eſt expoſitum. </s> <s xml:id="echoid-s16983" xml:space="preserve">Quam <lb/>obrem conueniẽs eſt, & </s> <s xml:id="echoid-s16984" xml:space="preserve">rationi maxime conſentaneum, ut ex motibus plane <lb/>tarũ particularibus, & </s> <s xml:id="echoid-s16985" xml:space="preserve">uariis apparentijs Aſtronomi inquirant numerum par-<lb/>tialium orbiũ, qui planetas tã uarijs motibus circumducunt, eorumq́; </s> <s xml:id="echoid-s16986" xml:space="preserve">cõffitu <lb/>tionẽ, ac figurã: </s> <s xml:id="echoid-s16987" xml:space="preserve">ea tamen lege, ac conditione, ut omnium motuum, apparen-<lb/>tiarumq́ue cauſæ poſſint cõmode aſſignari, nullumq́ue inde abſurdum, quod <lb/>philoſophiæ naturali repugnet, inferri poſſit. </s> <s xml:id="echoid-s16988" xml:space="preserve">Quocirca cũ Eccentrici orbes, <lb/>& </s> <s xml:id="echoid-s16989" xml:space="preserve">Epicycli ſint eiuſ@odi, ut per illos Aſtronomi nullo labore omnia φαινόμε <lb/>να teneãtur, ut partim ex dictis liquet, partim ex Theoricis planius intellige <lb/>tur, nullũq́; </s> <s xml:id="echoid-s16990" xml:space="preserve">ex ipſis abſurdum, aut incõmodum ſequatur in naturali philoſo-<lb/>phia, ut mox ex ſolutione argumentorum, quęcõ@@a huiuſmodi orbes ab ad-<lb/>uerſarijs afferri ſolent, conſtabit: </s> <s xml:id="echoid-s16991" xml:space="preserve">merito decreuerunt Aſtronomi, planetas in <lb/> <anchor type="note" xlink:label="note-486-03a" xlink:href="note-486-03"/> orbibus eccentricis, atq; </s> <s xml:id="echoid-s16992" xml:space="preserve">Epicyclis ueh@, non autem in cõcentricis, cum ꝑ hos <lb/>tueri non poſſimus tam multiplicem uarietatem in motibus planetarum.</s> <s xml:id="echoid-s16993" xml:space="preserve"/> </p> <div xml:id="echoid-div909" type="float" level="2" n="18"> <note position="left" xlink:label="note-486-02" xlink:href="note-486-02a" xml:space="preserve">@ ratio pro-<lb/>bans da@i <lb/>Eccentricos <lb/>& Epicy-<lb/>clos.</note> <note position="left" xlink:label="note-486-03" xlink:href="note-486-03a" xml:space="preserve">@eſponſio <lb/>aduerſario-<lb/>@umad ter-<lb/>tiam ratio-<lb/>@e@.</note> </div> <p> <s xml:id="echoid-s16994" xml:space="preserve"><emph style="sc">Vervm</emph> hanc rationem eneruare conantur aduerſarij dicentes: </s> <s xml:id="echoid-s16995" xml:space="preserve">ſe con-<lb/>cedere, poſitis orbib, eccẽtricis, & </s> <s xml:id="echoid-s16996" xml:space="preserve">Epicyclis, omnia φαινόμενα poſſe defendi <pb o="451" file="487" n="488" rhead="Ioan. de Sacro Boſco."/> non tamen ex hoc ſequi, dictos orbes in rerum Natura reperiri, ſed eſſe omni <lb/>no fictitios: </s> <s xml:id="echoid-s16997" xml:space="preserve">tum quia fortaſſis omnes apparentiæ poſſunt cõmodiore uia de-<lb/>fendi, licetea nobis ad huc ſit ignota, tum etiam, quia fieri poteſt, ut per di-<lb/>ctos orbes uere apparentiæ defendantur, quamuis ipſi omnino fictitij ſint, & </s> <s xml:id="echoid-s16998" xml:space="preserve"><lb/>nullo modo uera cauſa illarum apparentiarum:</s> <s xml:id="echoid-s16999" xml:space="preserve"><unsure/> quemadmodum etiam ex fal-<lb/>ſo uerum colligere licet, ut ex Dialectica Ariſtotelis conſtat.</s> <s xml:id="echoid-s17000" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17001" xml:space="preserve"><emph style="sc">His</emph> poſſumus addere confirmationem hoc modo. </s> <s xml:id="echoid-s17002" xml:space="preserve">Nicolaus Copernicus <lb/>in opere de reuolutionibus orbium cęleſtiũ tuetur omnia φ{αι}νόμενα alia via, <lb/>ponendo ſcilicet Firmamentum immobile, & </s> <s xml:id="echoid-s17003" xml:space="preserve">fixum, Solem quoque fixum in <lb/>centro Vniuerſi, tribuendoq; </s> <s xml:id="echoid-s17004" xml:space="preserve">terræ exiſtenti in tertio cęlo triplicẽ motũ, &</s> <s xml:id="echoid-s17005" xml:space="preserve">c. <lb/></s> <s xml:id="echoid-s17006" xml:space="preserve">Quate neceſſarij nõ ſunt Eccẽtrici, & </s> <s xml:id="echoid-s17007" xml:space="preserve">Epicycli ad φ{αι}νόμενα tuenda in plane-<lb/>tis. </s> <s xml:id="echoid-s17008" xml:space="preserve">Rurſus Ptolemæus per Epicyclum reddit omniũ apparentiarũ cauſam in <lb/>Sole, quas per Eccentricũ defendit: </s> <s xml:id="echoid-s17009" xml:space="preserve">Non ergo colligi poteſt ex tertio noſtro <lb/>argumento, Solem in Eccentrico moueri, cum fortaſſis in Epicyclo uehatur.</s> <s xml:id="echoid-s17010" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17011" xml:space="preserve"><emph style="sc">Dicendvm</emph> n@h@lominus eſt, tertium noſtrum argumentum ſuum robur <lb/> <anchor type="note" xlink:label="note-487-01a" xlink:href="note-487-01"/> retinere, reſponſionemque aduerſariorũ nihil concludere. </s> <s xml:id="echoid-s17012" xml:space="preserve">Primum enim, ſi <lb/>commodiorẽ uiam habent, exhibeant illam nobis, contentique erimus, & </s> <s xml:id="echoid-s17013" xml:space="preserve">il-<lb/>lis maximas agemus gratias. </s> <s xml:id="echoid-s17014" xml:space="preserve">Nihil enim aliud contendunt Aſtronomi, quàm <lb/>ut omnia φ{αι}νόμενα in cęlo quàm cõmodiſſime tueantur, ſiue hoc fiat per ec-<lb/>centricos o@bes, & </s> <s xml:id="echoid-s17015" xml:space="preserve">Epicyclos, ſiue alio modo. </s> <s xml:id="echoid-s17016" xml:space="preserve">Et quia nulla uia hactenus com <lb/>modior inuenta eſt, quàm ea, quæ per Eccẽtricos, & </s> <s xml:id="echoid-s17017" xml:space="preserve">Epicyclos omnia defen-<lb/>dit, credibile ualde eſt, ſphæras cæleſtes ex orbibus eiuſmodi conſtare. </s> <s xml:id="echoid-s17018" xml:space="preserve">Quod <lb/>ſi commodiorẽ uiam nobis non poſſunt exhibere, certe acquieſcere deberẽt <lb/>huic uiæ ex tam uarijs φ{αι}νόμενοις collectæ: </s> <s xml:id="echoid-s17019" xml:space="preserve">ſi prorſus deſtruere nolunt non <lb/>tantũ philoſophiam naturalẽ, quę in ſcholis pręlegitur, ſed etiã intercludere <lb/>aditũ ad omnes alias artes, quæ per effectus cauſas inueſtigant. </s> <s xml:id="echoid-s17020" xml:space="preserve">Quotieſcunq; <lb/></s> <s xml:id="echoid-s17021" xml:space="preserve">enim quiſpiam per effectus manifeſtos cauſam aliquam collegerit, dicã idem <lb/>prorſue, quod ipſi, nimirũ aliam fortaſſe cauſam nobis ignotam dari poſſe illo-<lb/>rum effectuum. </s> <s xml:id="echoid-s17022" xml:space="preserve">Aut certeſi quieſcendum eſt in hac cauſa inuenta, ꝙ conne-<lb/>xio nem quandam habeat cũ effectibus, ex quibus collecta eſt, concedendi etiã <lb/>erunt Eccentrici, & </s> <s xml:id="echoid-s17023" xml:space="preserve">Epicycli: </s> <s xml:id="echoid-s17024" xml:space="preserve">qui tantam connexionem cum apparentijs ha-<lb/>bent, ut omnes per illorum motus facili negotio poſſint defendi. </s> <s xml:id="echoid-s17025" xml:space="preserve">Deinde, ſi <lb/>propterea non recte colligitur ex apparentijs, Eccentricos, & </s> <s xml:id="echoid-s17026" xml:space="preserve">Epicyclos in cę-<lb/>lis reperiri, quia ex falſo colligi poteſt verũ, ruet uniuerſa philoſophia natu-<lb/>ralis. </s> <s xml:id="echoid-s17027" xml:space="preserve">Nam eodẽ pacto, quando aliquis ex effectu noto concludet, hanc uel il-<lb/>lã eſſe illius cauſam, dicã ego, verũ id non eſſe, quia ex falſo licet colligere ue <lb/>rum: </s> <s xml:id="echoid-s17028" xml:space="preserve">atque ita omnia principia naturalia à philoſophis inuenta deſtruentur. </s> <s xml:id="echoid-s17029" xml:space="preserve"><lb/>Quod cum ſit abſurdũ, non recte eneruari uidetur noſtri argumẽti uis, ac ro-<lb/>bur ad a duerſarijs. </s> <s xml:id="echoid-s17030" xml:space="preserve">Dici etiam poteſt, regulam illam Dialecticorum [Ex falſo <lb/>ſequitur verum.</s> <s xml:id="echoid-s17031" xml:space="preserve">] non eſſe ad rem: </s> <s xml:id="echoid-s17032" xml:space="preserve">quia aliter ex falſo infertur uerũ, & </s> <s xml:id="echoid-s17033" xml:space="preserve">alter per <lb/>Eccentricos, & </s> <s xml:id="echoid-s17034" xml:space="preserve">Epicyclos defenduntur φ{αι}νόμενα. </s> <s xml:id="echoid-s17035" xml:space="preserve">Ibi enim ex uiformæ ſyllo <lb/>giſticæ uerum ex falſo colligitur. </s> <s xml:id="echoid-s17036" xml:space="preserve">Vnde cognita ueritate alicuius propoſitio-<lb/>nis, poſſunt diſponi præmiſſæ falſę in tali forma, ut neceſſario ex ui ſyllogiſmi <lb/>propoſitio illa uera concludatur. </s> <s xml:id="echoid-s17037" xml:space="preserve">Vt quia ego ſcio, animal eſſe ſenſitiuũ, poſ-<lb/>ſum conficere talem ſyllogiſmũ. </s> <s xml:id="echoid-s17038" xml:space="preserve">Omnis planta eſt ſenſitiua: </s> <s xml:id="echoid-s17039" xml:space="preserve">Omne animal eſt <lb/>planta. </s> <s xml:id="echoid-s17040" xml:space="preserve">Igitur omne animal eſt ſenſitiuũ. </s> <s xml:id="echoid-s17041" xml:space="preserve">Quod ſi de concluſione aliqua dubi <lb/>tem, nunquam ex falſis pręmiſſis acquirã certitudinẽ illius, etiamſi ex ui ſyl-<lb/>logiſmi recte colligatur. </s> <s xml:id="echoid-s17042" xml:space="preserve">quia alioquin omnia facile hoc modo cõcluderẽ. </s> <s xml:id="echoid-s17043" xml:space="preserve">Vt <pb o="452" file="488" n="489" rhead="Comment. in IIII. Cap. Sphæræ"/> fi ambigam, num omnis ſtella ſit rotunda, licet ex ui huius ſyllogiſmi [Omnis <lb/>lapis eſt rotundus: </s> <s xml:id="echoid-s17044" xml:space="preserve">Omnis ſtella eſt lapis. </s> <s xml:id="echoid-s17045" xml:space="preserve">Igitur omnis ſtella eſt rotunda.</s> <s xml:id="echoid-s17046" xml:space="preserve">] recte il-<lb/>lud inferam ex falſis præmiſſis, nunquã tamen certus reddar de prædicta con-<lb/>cluſione@ mihi dubia. </s> <s xml:id="echoid-s17047" xml:space="preserve">At ex orbibus eccentricis, & </s> <s xml:id="echoid-s17048" xml:space="preserve">epicyclis, non ſolum appa-<lb/>rentiæ iam olim cognitæ deſenduntur, ſed etiam ſuturæ prædicũtur, quarum <lb/>tẽpus omnino ignoratur: </s> <s xml:id="echoid-s17049" xml:space="preserve">ita, ut ſi ego dubitem, an v. </s> <s xml:id="echoid-s17050" xml:space="preserve">g. </s> <s xml:id="echoid-s17051" xml:space="preserve">in plenilunio Septẽbris <lb/>anni 1587. </s> <s xml:id="echoid-s17052" xml:space="preserve">futura ſit eclipſis Lunæ, certus omnino reddar ex mõtibus orbium <lb/>eccentricorum, & </s> <s xml:id="echoid-s17053" xml:space="preserve">epicyclorum, futuram eſſe eclipſim, ita ut amplius non du-<lb/>bitem. </s> <s xml:id="echoid-s17054" xml:space="preserve">Immo ex eiſdem motibus cognoſco, qua hora illa eclipſis inceptura <lb/>ſit, & </s> <s xml:id="echoid-s17055" xml:space="preserve">quanta pars Lunæ ſit obſcuranda. </s> <s xml:id="echoid-s17056" xml:space="preserve">Eodemq́. </s> <s xml:id="echoid-s17057" xml:space="preserve">modo omnes eclipſes tam <lb/>Solares, quàm Lunares prædici poſſunt, earumq́. </s> <s xml:id="echoid-s17058" xml:space="preserve">tempus, & </s> <s xml:id="echoid-s17059" xml:space="preserve">magnitudines, <lb/>cum tamen nullum certum inter ſe ordinem ſeruent, ita ut determinatũ tem <lb/>poris interuallum inter duas proximas interijciatur; </s> <s xml:id="echoid-s17060" xml:space="preserve">ſed aliquando in uno an <lb/>no duæ contingant, aliquando una, & </s> <s xml:id="echoid-s17061" xml:space="preserve">aliquando nulla. </s> <s xml:id="echoid-s17062" xml:space="preserve">Non eſt autem credi-<lb/>bile, quòd nos cogamus cęlos (cogere autem uidemur, ſi eccentrici, & </s> <s xml:id="echoid-s17063" xml:space="preserve">epicycli <lb/>fint figmenta, ut aduerſarij uolunt) ut noſtris obediant figmentis, mouean<unsure/>-<lb/>turque uti nos uolumus, uel uti noſtris principijs congruit.</s> <s xml:id="echoid-s17064" xml:space="preserve"/> </p> <div xml:id="echoid-div910" type="float" level="2" n="19"> <note position="right" xlink:label="note-487-01" xlink:href="note-487-01a" xml:space="preserve">Confutatio <lb/>reſpõſionis <lb/>aduerſario-<lb/>rum.</note> </div> <p> <s xml:id="echoid-s17065" xml:space="preserve"><emph style="sc">Qvod</emph> uero attinet ad Nicolaum Copernicum, dicimus, eũ non reſpue-<lb/>re eccentricos, & </s> <s xml:id="echoid-s17066" xml:space="preserve">epicyclos tanquam fictitios, & </s> <s xml:id="echoid-s17067" xml:space="preserve">philoſophiæ repu gnantes. <lb/></s> <s xml:id="echoid-s17068" xml:space="preserve">Ponit enim ipſe idem terram, tanquam epicyclum; </s> <s xml:id="echoid-s17069" xml:space="preserve">& </s> <s xml:id="echoid-s17070" xml:space="preserve">in Luna ſtatuit epicycli <lb/>epicyclum: </s> <s xml:id="echoid-s17071" xml:space="preserve">Sed hoc ſolum conati, ut periodos motuum planetarum emendet, <lb/>quas iam claudicare inuenerat. </s> <s xml:id="echoid-s17072" xml:space="preserve">Difficile enim admodum eſt, periodos motuũ <lb/>ita definire, ut multis annerum ſeculis à vero nõ deueniet, cũ nullus vnquam <lb/>mortalium unius planetę potuerit periodum ita determinare, ut nõ ſuperſint <lb/>aut deſint aliquæ minutiæ, quæ in magno annorũ interuallo, notabilẽ erro-<lb/>rem inducant. </s> <s xml:id="echoid-s17073" xml:space="preserve">Vt mirum ſane ſit, Deum Opt. </s> <s xml:id="echoid-s17074" xml:space="preserve">Max. </s> <s xml:id="echoid-s17075" xml:space="preserve">planetarum motus tantis <lb/>difficultatibus obſtruere uoluiſſe, ut nemo hominũ eos pſecte poſſit aſſequi, <lb/>ſed ſemper inueniat, quod in tanto artificio tam nobilium corporũ, & </s> <s xml:id="echoid-s17076" xml:space="preserve">in tan <lb/>@a eorũ motuũ harmonia, & </s> <s xml:id="echoid-s17077" xml:space="preserve">concordia admiretur, perpetuis laudibus eorum <lb/>conditorem, & </s> <s xml:id="echoid-s17078" xml:space="preserve">motorem celebrando. </s> <s xml:id="echoid-s17079" xml:space="preserve">Vt potiſſimum propter conſtit utionem <lb/>cęlorum, eorumq; </s> <s xml:id="echoid-s17080" xml:space="preserve">motus, in quibus ſemper ſupereſſe uidetur, quod ſumma di <lb/>ligentia inquiratur à ſolertiſſimis rerũ cæleſtium perſcrutatoribus, ſcriptum <lb/>@ſſe uideatur ab Eccleſiaſte cap. </s> <s xml:id="echoid-s17081" xml:space="preserve">3. </s> <s xml:id="echoid-s17082" xml:space="preserve">[Et mundũ tradidit diſputationi eorum] ne vi-<lb/>delicet aliquando, ſi perfecte cęlorũ numerũ, ordinem, conſtitutionem, & </s> <s xml:id="echoid-s17083" xml:space="preserve">mo <lb/>tum intellexiſſent homines, deſinerent opera Dei in quirere, & </s> <s xml:id="echoid-s17084" xml:space="preserve">admirari, & </s> <s xml:id="echoid-s17085" xml:space="preserve"><lb/>ingenia, ſublata exercendi cauſa, ceſſatione torperent. </s> <s xml:id="echoid-s17086" xml:space="preserve">Itaq; </s> <s xml:id="echoid-s17087" xml:space="preserve">quod alia via Co <lb/>pernicus φαινόμενα tueatur, mirũ non eſt. </s> <s xml:id="echoid-s17088" xml:space="preserve">Qu<unsure/>a enim ex motibus eccẽtrico-<lb/>@um, & </s> <s xml:id="echoid-s17089" xml:space="preserve">epicyclorũ cognouit tempus, quantitatem & </s> <s xml:id="echoid-s17090" xml:space="preserve">qualita@em apparentia-<lb/>@um tam futurarũ, quà<unsure/>m præteritorũ, potuit, ut erat ingenioſiſſimus, nouam <lb/>viam excogitare, qua illæ apparentiæ cõmodius (ut ipſe putabat) defendi poſ-<lb/>ſent, & </s> <s xml:id="echoid-s17091" xml:space="preserve">periodi motuum aliqua ex parte emendari, quas iam animaduerterat <lb/>claudicare, quod præcipuũ uidetur fuiſſe ſtudiũ Copernici, ut diximus. </s> <s xml:id="echoid-s17092" xml:space="preserve">quẽ-<lb/>admodũ etiam cognitam aliquam concluſionem poſſumus pluribus ſyllogiſ-<lb/>mis, etiam ex falſis præmiſſis, inferre. </s> <s xml:id="echoid-s17093" xml:space="preserve">Tantum autem abeſt, ut propter do-<lb/>ctrinam Copernici tollantur eccentrici, & </s> <s xml:id="echoid-s17094" xml:space="preserve">epicycli, vt multo magis propte-<lb/>rea ponendi ſint. </s> <s xml:id="echoid-s17095" xml:space="preserve">Idcirco enim Aſtronomi hos orbes excogitarunt, quia cer-<lb/>to certius ex varijs phænomenis deprehenderunt, planetas non ferri ſem-<lb/>per æquali diſtantia à terra. </s> <s xml:id="echoid-s17096" xml:space="preserve">Quod quidem libenter copernicus admittit, cum <pb o="453" file="489" n="490" rhead="Ioan. de Sacro Boſco."/> ſecũdum eius doctrinam planetæ ſemper inæqualem à terra habeãt diſtantia, <lb/>ut pater ex poſitione terræ extra centrum mundi in tertio cælo. </s> <s xml:id="echoid-s17097" xml:space="preserve">Solũ hoc ex <lb/>eius poſitione colligitur, non eſſe certum omnino, talem eſſe conſtitutionẽ Ec <lb/>centricorum & </s> <s xml:id="echoid-s17098" xml:space="preserve">Epicyclorum, qualem Ptolemæus facit: </s> <s xml:id="echoid-s17099" xml:space="preserve">quan doquidem multa <lb/> <anchor type="note" xlink:label="note-489-01a" xlink:href="note-489-01"/> φοινόμενα poſſunt alia uia defendi. </s> <s xml:id="echoid-s17100" xml:space="preserve">Neque uero nos in hac qu ęſtione aliud cõ <lb/>tendimus lectori perſuadere, quàm planetas non ferri æquali ſemper diſtãtia <lb/>a terra: </s> <s xml:id="echoid-s17101" xml:space="preserve">atq; </s> <s xml:id="echoid-s17102" xml:space="preserve">adeo uel eſſe in cælis orbes Eccentricos, & </s> <s xml:id="echoid-s17103" xml:space="preserve">Epicyclos eo ordine, <lb/>quo eos poſuit Ptolemæus, uel certe aliquam horũ effectuũ ponendã eſſe cau-<lb/>ſam æquiualẽtẽ Eccẽtricis, & </s> <s xml:id="echoid-s17104" xml:space="preserve">Epicyclis. </s> <s xml:id="echoid-s17105" xml:space="preserve">Quod ſi poſitio Copernici nihil falſi, <lb/>& </s> <s xml:id="echoid-s17106" xml:space="preserve">abſurdi inuolueret, dubiũ ſane eſſet, utri opinioni, Ptolemæine, an Coper-<lb/>nici potius, (quod attinet ad huiuſmodi φοινόμενα tuenda) adhęrendum eſ-<lb/>ſet. </s> <s xml:id="echoid-s17107" xml:space="preserve">Sed quoniam multa abſurda, & </s> <s xml:id="echoid-s17108" xml:space="preserve">erronea in Copernici poſitione continen-<lb/>tur, ut quod terra nõ ſit in medio Firmamẽti, moueaturq́; </s> <s xml:id="echoid-s17109" xml:space="preserve">triplici motu, quod <lb/> <anchor type="note" xlink:label="note-489-02a" xlink:href="note-489-02"/> qua ratione fieri poſſit, uix in@elligo, cum ſecũdum philoſophos uni corpori <lb/>ſimplici unus debeatur motus;</s> <s xml:id="echoid-s17110" xml:space="preserve"><unsure/> & </s> <s xml:id="echoid-s17111" xml:space="preserve">quod Sol in cẽtro mundi ſtatuatur, ſitq; </s> <s xml:id="echoid-s17112" xml:space="preserve">om-<lb/>nis motus expers. </s> <s xml:id="echoid-s17113" xml:space="preserve">quæ omnia cum communi doctrina philoſophorũ, & </s> <s xml:id="echoid-s17114" xml:space="preserve">Aſtro-<lb/>nomorum pugnant, & </s> <s xml:id="echoid-s17115" xml:space="preserve">uidenturijs, quæ ſacræ literæ pleriſque locis docent, cõ <lb/>tradicere, ut copioſius cap. </s> <s xml:id="echoid-s17116" xml:space="preserve">1. </s> <s xml:id="echoid-s17117" xml:space="preserve">pertractauimus: </s> <s xml:id="echoid-s17118" xml:space="preserve">Idcirco anteponẽda uidetur opi <lb/>nio Ptolemæi huic Copernici inuentioni. </s> <s xml:id="echoid-s17119" xml:space="preserve">Ex quibus omnibus liquet, tam eſſe <lb/>probabile, dari eccentricos orbes, & </s> <s xml:id="echoid-s17120" xml:space="preserve">Epicyclos, quàm probabile eſt, dari octo, <lb/>aut decem cælos mobiles, cum tam cælorum numerus, quàm dicti orbes ex <lb/>φοινόμενοις, & </s> <s xml:id="echoid-s17121" xml:space="preserve">motibus inuenti ſint ab Aſtronomis.</s> <s xml:id="echoid-s17122" xml:space="preserve"/> </p> <div xml:id="echoid-div911" type="float" level="2" n="20"> <note position="right" xlink:label="note-489-01" xlink:href="note-489-01a" xml:space="preserve">@ræcipuu@ <lb/>in hac quæ <lb/>ftione pro-<lb/>poſitum <lb/>quod ſit.</note> <note position="right" xlink:label="note-489-02" xlink:href="note-489-02a" xml:space="preserve">Abſur@a. <lb/>quæ ſequun <lb/>tur poſitio-<lb/>nem Cope@ <lb/>nici.</note> </div> <p> <s xml:id="echoid-s17123" xml:space="preserve"><emph style="sc">Iam</emph> uero ex eo, quod Ptolemæus tam per Epicyclum, quam per Eccen-<lb/>tricum φοινόμενα Solis tuetur, ſolum colligitur, incertum eſſe, an in Eccentri <lb/>co, an in Epicyclo Sol feratur: </s> <s xml:id="echoid-s17124" xml:space="preserve">Sed utrumuis dicatur, perſpicuum eſt, Solem in-<lb/>ęqualiter a terra diſtare, & </s> <s xml:id="echoid-s17125" xml:space="preserve">minime in orbe cõcentrico ferri, quod ſatis nobis <lb/> <anchor type="note" xlink:label="note-489-03a" xlink:href="note-489-03"/> eſt, ut diximus. </s> <s xml:id="echoid-s17126" xml:space="preserve">Potius tamen Ptolemæus elegit Eccentricum orbem in Sole, <lb/>propterea quod centrum terræ ambit, & </s> <s xml:id="echoid-s17127" xml:space="preserve">circundat. </s> <s xml:id="echoid-s17128" xml:space="preserve">Sed proponamus iam argu <lb/>menta Auerrois, eiusq́; </s> <s xml:id="echoid-s17129" xml:space="preserve">ſectatorum, eaq́. </s> <s xml:id="echoid-s17130" xml:space="preserve">refellamus, ut hinc quoque appareat, <lb/>Eccentricos, & </s> <s xml:id="echoid-s17131" xml:space="preserve">Epicyclos non eſſe monſtra, aut portenta, nihilq́; </s> <s xml:id="echoid-s17132" xml:space="preserve">omnino phi-<lb/>loſophiæ naturali repugnare, ut falſo aduerſarij putant.</s> <s xml:id="echoid-s17133" xml:space="preserve"/> </p> <div xml:id="echoid-div912" type="float" level="2" n="21"> <note position="right" xlink:label="note-489-03" xlink:href="note-489-03a" xml:space="preserve">Argumenta <lb/>aduerſus Ec <lb/>centricos, <lb/>& Epicyclos</note> </div> <note position="right" xml:space="preserve">1. obiectio.</note> <p> <s xml:id="echoid-s17134" xml:space="preserve"><emph style="sc">Primvm</emph> igitur aduerſarij cum Auerroe ita argumentatur. </s> <s xml:id="echoid-s17135" xml:space="preserve">Ex Ariſtote <lb/>lis ſententia in lib. </s> <s xml:id="echoid-s17136" xml:space="preserve">de cælo, motus ſimplex eſt triplex, a medio, ad medium, & </s> <s xml:id="echoid-s17137" xml:space="preserve"><lb/>circa medium: </s> <s xml:id="echoid-s17138" xml:space="preserve">quorum priores duo elementis congruunt, poſterior autem cor <lb/>poribus cæleſtibus. </s> <s xml:id="echoid-s17139" xml:space="preserve">Sed ſi darentur Eccentrici, & </s> <s xml:id="echoid-s17140" xml:space="preserve">Epicycli, moueretur aliquod <lb/>corpus cæleſte ad medium, & </s> <s xml:id="echoid-s17141" xml:space="preserve">a medio, cum eorum una pars magis ad terram <lb/>accedat, & </s> <s xml:id="echoid-s17142" xml:space="preserve">altera minus. </s> <s xml:id="echoid-s17143" xml:space="preserve">Cum ergo hoc ſit abſurdum, quòd corpora cæle-<lb/>ſtia neque grauia ſint, neque leuia, ut naturalem propenſionem habere poſ-<lb/>ſint ad motum ad medium, & </s> <s xml:id="echoid-s17144" xml:space="preserve">a medio: </s> <s xml:id="echoid-s17145" xml:space="preserve">non dabuntur orbes Eccentrici, & </s> <s xml:id="echoid-s17146" xml:space="preserve"><lb/>Epicycli.</s> <s xml:id="echoid-s17147" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17148" xml:space="preserve">2. </s> <s xml:id="echoid-s17149" xml:space="preserve"><emph style="sc">Corpvs</emph> cæleſte, auctore Ariſtotele, eſt perfecte ſphæricum. </s> <s xml:id="echoid-s17150" xml:space="preserve">Sed or-<lb/>bes Eccenttici ſecundum quid circunſtantes Eccentricum ſimpliciter, perfecte <lb/>ſphærici non ſunt, cum ex una parte craſſiores ſint, & </s> <s xml:id="echoid-s17151" xml:space="preserve">ex altera tenuiores. </s> <s xml:id="echoid-s17152" xml:space="preserve">Er-<lb/> <anchor type="note" xlink:label="note-489-05a" xlink:href="note-489-05"/> go non ſunt concedendi.</s> <s xml:id="echoid-s17153" xml:space="preserve"/> </p> <div xml:id="echoid-div913" type="float" level="2" n="22"> <note position="right" xlink:label="note-489-05" xlink:href="note-489-05a" xml:space="preserve">2. obiectio.</note> </div> <p> <s xml:id="echoid-s17154" xml:space="preserve">3. </s> <s xml:id="echoid-s17155" xml:space="preserve">SI darentur orbes Eccentrici ſecundum quid, non poſſent moueri ſine <lb/>penetratione, aut ſciſſione cælorum, cum craſſior pars unius ingredi debeat <lb/> <anchor type="note" xlink:label="note-489-06a" xlink:href="note-489-06"/> partem eiuſdem tenuiorem. </s> <s xml:id="echoid-s17156" xml:space="preserve">Pari ratione, ſubintrante ſubtiliori parte locum <lb/>craſſioris, dabitur aut uacuum, cum pars tenuior explere nequeat locum craſ- <pb o="454" file="490" n="491" rhead="Comment. in IIII. Cap. Sphæræ"/> ſioris, aut certe rarefactio cęli. </s> <s xml:id="echoid-s17157" xml:space="preserve">Quæ cum abſurda ſint, abſurdum etiam erit <lb/>ponere orbes Eccentricos.</s> <s xml:id="echoid-s17158" xml:space="preserve"/> </p> <div xml:id="echoid-div914" type="float" level="2" n="23"> <note position="right" xlink:label="note-489-06" xlink:href="note-489-06a" xml:space="preserve">3. obiectio.</note> </div> <p> <s xml:id="echoid-s17159" xml:space="preserve">4. </s> <s xml:id="echoid-s17160" xml:space="preserve"><emph style="sc">Arristoteles</emph> lib. </s> <s xml:id="echoid-s17161" xml:space="preserve">2. </s> <s xml:id="echoid-s17162" xml:space="preserve">de cælo affirmat, omnia φαινόμον α plane <lb/> <anchor type="note" xlink:label="note-490-01a" xlink:href="note-490-01"/> tarum defendi poſſe per plitralitatem motuum. </s> <s xml:id="echoid-s17163" xml:space="preserve">Fruſtra ergo ponuntur Ec-<lb/>centrici, & </s> <s xml:id="echoid-s17164" xml:space="preserve">Epicycli, repugnantq; </s> <s xml:id="echoid-s17165" xml:space="preserve">ſaltem Ariſtoteli.</s> <s xml:id="echoid-s17166" xml:space="preserve"/> </p> <div xml:id="echoid-div915" type="float" level="2" n="24"> <note position="left" xlink:label="note-490-01" xlink:href="note-490-01a" xml:space="preserve">4 Obiectio.</note> </div> <p> <s xml:id="echoid-s17167" xml:space="preserve">5. </s> <s xml:id="echoid-s17168" xml:space="preserve"><emph style="sc">Idem</emph> eſt locus totius, & </s> <s xml:id="echoid-s17169" xml:space="preserve">partis: </s> <s xml:id="echoid-s17170" xml:space="preserve">Locus autem cœli, ut vult Auerroes, <lb/> <anchor type="note" xlink:label="note-490-02a" xlink:href="note-490-02"/> eſt centrum mundi. </s> <s xml:id="echoid-s17171" xml:space="preserve">Idem ergo erit centrum totalium ſphærarũ, & </s> <s xml:id="echoid-s17172" xml:space="preserve">partialiũ. <lb/></s> <s xml:id="echoid-s17173" xml:space="preserve">Omnes ergo orbes concentrici ſunt, nullus autem eccentricus.</s> <s xml:id="echoid-s17174" xml:space="preserve"/> </p> <div xml:id="echoid-div916" type="float" level="2" n="25"> <note position="left" xlink:label="note-490-02" xlink:href="note-490-02a" xml:space="preserve">5. Obiectio.</note> </div> <p> <s xml:id="echoid-s17175" xml:space="preserve">6. </s> <s xml:id="echoid-s17176" xml:space="preserve"><emph style="sc">Qvanto</emph> magis diſtat ſphæra aliqua à primo principio, tanto plu <lb/> <anchor type="note" xlink:label="note-490-03a" xlink:href="note-490-03"/> ribus motibus indiget, vt ſuam perfectionem adipiſcatur, uel cõſeruet, ut vult <lb/>Ariſtoteles. </s> <s xml:id="echoid-s17177" xml:space="preserve">Non ergo concedendi ſunt Eccẽtrici, & </s> <s xml:id="echoid-s17178" xml:space="preserve">Epicycli, cum ijs poſitis, <lb/>pauciores motus habeat Sol, quàm Saturnus, Iuppiter, & </s> <s xml:id="echoid-s17179" xml:space="preserve">Mars, qui primo En <lb/>ti ſunt propinquiores.</s> <s xml:id="echoid-s17180" xml:space="preserve"/> </p> <div xml:id="echoid-div917" type="float" level="2" n="26"> <note position="left" xlink:label="note-490-03" xlink:href="note-490-03a" xml:space="preserve">6. Obiectio.</note> </div> <note position="left" xml:space="preserve">7. Obiectio.</note> <p> <s xml:id="echoid-s17181" xml:space="preserve">7. </s> <s xml:id="echoid-s17182" xml:space="preserve"><emph style="sc">Si</emph> in rerum natura exiſtunt Eccentrici, mouebuntur utique circa pro-<lb/>pria centra; </s> <s xml:id="echoid-s17183" xml:space="preserve">Sed in omni centro, circa quod fit motus cœli, eſt terra quie-<lb/>ſcens, cum omne id, quod mouetur, indigeat quieſcente, ut uult Ariſtote-<lb/>les. </s> <s xml:id="echoid-s17184" xml:space="preserve">Quotergo ſunt Eccentrici, & </s> <s xml:id="echoid-s17185" xml:space="preserve">Epicycli, tot erunt terræ quieſcentes, quod <lb/>abſurdum eſt.</s> <s xml:id="echoid-s17186" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17187" xml:space="preserve">8. </s> <s xml:id="echoid-s17188" xml:space="preserve">SI dantur Eccentrici, erit in rerum natura (vt ait Auguſtinus Niphus) <lb/> <anchor type="note" xlink:label="note-490-05a" xlink:href="note-490-05"/> aliquid ſuperuacaneum, & </s> <s xml:id="echoid-s17189" xml:space="preserve">otioſum, puta unus ex duobus orbibus eccentricis <lb/>ſecundum quid, qui deferũt augem planetæ. </s> <s xml:id="echoid-s17190" xml:space="preserve">Vterlibet enim ipſcrum ſatis eſt <lb/>ad deferendam augem, eiuſq; </s> <s xml:id="echoid-s17191" xml:space="preserve">oppoſitum, ut patet. </s> <s xml:id="echoid-s17192" xml:space="preserve">Quare alter ſuper fluus <lb/>cum nullum habeat uſum. </s> <s xml:id="echoid-s17193" xml:space="preserve">Hæ ſunt rationes, quibus aduerſarij probare nitũ <lb/>tur, orbes Eccentricos, & </s> <s xml:id="echoid-s17194" xml:space="preserve"><emph style="sc">E</emph>picyclos è medio eſſe tollendos: </s> <s xml:id="echoid-s17195" xml:space="preserve">quibus addemus <lb/>aliàs tres, quas Hieronymus Fracaſtorius ad finem libelli Homocentricorum <lb/>adducit tanquam demonſtrationes, quæ refelli non poſſint: </s> <s xml:id="echoid-s17196" xml:space="preserve">ha@ũ prima oſtẽ-<lb/>dens, in Sole nullo pacto dari Eccentricum, hæc eſt.</s> <s xml:id="echoid-s17197" xml:space="preserve"/> </p> <div xml:id="echoid-div918" type="float" level="2" n="27"> <note position="left" xlink:label="note-490-05" xlink:href="note-490-05a" xml:space="preserve">@. Obiectio.</note> </div> <p> <s xml:id="echoid-s17198" xml:space="preserve"><emph style="sc">Si</emph> daretur Eccentricus orbis in Sole, cuius nimirum unum punctum maxi <lb/> <anchor type="note" xlink:label="note-490-06a" xlink:href="note-490-06"/> me a terra recedat, ſiue a centro mundi, & </s> <s xml:id="echoid-s17199" xml:space="preserve">quod & </s> <s xml:id="echoid-s17200" xml:space="preserve">Aequatoris centrum eſt, <lb/>& </s> <s xml:id="echoid-s17201" xml:space="preserve">unum maxime accedat, deſcribet punctum illud maximæ remotum, atque <lb/>adeo, & </s> <s xml:id="echoid-s17202" xml:space="preserve">Sol in illo exlſtẽs, motu diurno parallelum magis ab Aequatore di-<lb/>ſtantem, quàm pũctum aliud terræ proximum. </s> <s xml:id="echoid-s17203" xml:space="preserve">Quare maximæ declinatione@ <lb/>Solis inter ſe æquales non erunt, ſed ſeptentrionalis, ubi hodie aux, ſeu pun-<lb/>ctũ remotiſſimum exiſtit, maior erit, quàm auſtralis, ubi nunc oppoſitũ augis, <lb/>ſeu punctum terris proximum, reperitur; </s> <s xml:id="echoid-s17204" xml:space="preserve">cum tamen Aſtronomi omnes ob-<lb/>ſeruarint, maximã Solis declinationem borealem auſtrali eſſe æqualẽ. </s> <s xml:id="echoid-s17205" xml:space="preserve">Rurſus <lb/>in ſphæra obliqua, Sole exiſtente in auge, nẽpe in ♋, eſſet arcus diurnus ma <lb/>ior arcu nocturno, eodem exiſtente in oppoſito augis, hoc eſt, in ♑, quod cõ <lb/>muni experientiæ aduerſatur. </s> <s xml:id="echoid-s17206" xml:space="preserve">Sole enim exiſtente in gradibus Eclipticæ op <lb/>poſitis, deſcribuntur duo paralleli, quorum unius arcus diurnus æqualis eſt <lb/>arcui nocturno alterius. </s> <s xml:id="echoid-s17207" xml:space="preserve">Poſteriorum deinde rationum, quæ Epicyclos Vene-<lb/>ris, & </s> <s xml:id="echoid-s17208" xml:space="preserve">Lunæ è medio tollunt, prima eſt eiuſmodi.</s> <s xml:id="echoid-s17209" xml:space="preserve"/> </p> <div xml:id="echoid-div919" type="float" level="2" n="28"> <note position="left" xlink:label="note-490-06" xlink:href="note-490-06a" xml:space="preserve">@. Obiectio. <lb/>Fracaſtorij.</note> </div> <p> <s xml:id="echoid-s17210" xml:space="preserve"><emph style="sc">Si</emph> Epicyclus Veneris tantæ eſſet magnitudinis, ut eius ſemidiameter cõ-<lb/> <anchor type="note" xlink:label="note-490-07a" xlink:href="note-490-07"/> prehẽdat gr. </s> <s xml:id="echoid-s17211" xml:space="preserve">43. </s> <s xml:id="echoid-s17212" xml:space="preserve">& </s> <s xml:id="echoid-s17213" xml:space="preserve">tota diameter gra. </s> <s xml:id="echoid-s17214" xml:space="preserve">86. </s> <s xml:id="echoid-s17215" xml:space="preserve">pertingeret fere uſq; </s> <s xml:id="echoid-s17216" xml:space="preserve">ad c@ntrũ terrę. <lb/></s> <s xml:id="echoid-s17217" xml:space="preserve">Nã ſi ſemidiameter præciſe cõtineret gr. </s> <s xml:id="echoid-s17218" xml:space="preserve">45. </s> <s xml:id="echoid-s17219" xml:space="preserve">tranſiret Epicyclus per centrum <lb/>terræ præciſe. </s> <s xml:id="echoid-s17220" xml:space="preserve">quod ipſe Geometrice conatur probare. </s> <s xml:id="echoid-s17221" xml:space="preserve">Cũ ergo hoc abſurdũ <lb/>ſit, & </s> <s xml:id="echoid-s17222" xml:space="preserve">contra experientiam, non erit in rerum natura Epicyclus Veneris.</s> <s xml:id="echoid-s17223" xml:space="preserve"/> </p> <div xml:id="echoid-div920" type="float" level="2" n="29"> <note position="left" xlink:label="note-490-07" xlink:href="note-490-07a" xml:space="preserve">2. Obiectio. <lb/>Fracaſtorij.</note> </div> <note position="left" xml:space="preserve">3. Obiectio. <lb/>Fracaſtorij.</note> <p> <s xml:id="echoid-s17224" xml:space="preserve"><emph style="sc">Postremo</emph> ſi Luna circumuolueretur in Epicyclo, non ſemper @i- <pb o="455" file="491" n="492" rhead="Ioan. de Sacro Boſco."/> deremus eandem Lunæ medietatem, <lb/> <anchor type="figure" xlink:label="fig-491-01a" xlink:href="fig-491-01"/> ſed quando eſt in parte Epicycli infe-<lb/>riori, vna nobis appareret, & </s> <s xml:id="echoid-s17225" xml:space="preserve">quan-<lb/>do eſt in ſuperiori parte, altera, vt <lb/>in hac appoſita figuta manifeſtum eſt. <lb/></s> <s xml:id="echoid-s17226" xml:space="preserve">Nam dum Luna eſt in parte inferiori <lb/>Epicycli, apparebit nobis eius me-<lb/>dietas, in qua litera A; </s> <s xml:id="echoid-s17227" xml:space="preserve">Dum vero <lb/>verſatur in parte ſuperiori, obijcietur <lb/>nobis altera medietas, in qua litera <lb/>B. </s> <s xml:id="echoid-s17228" xml:space="preserve">Sed hoc eſt contra quotidianam <lb/>experientiam. </s> <s xml:id="echoid-s17229" xml:space="preserve">Videmus enim per-<lb/>petuo maculas Lunæ ad nos vergere. </s> <s xml:id="echoid-s17230" xml:space="preserve"><lb/>Ex quo ſequitur, eandem nos ſem-<lb/>per medietatem intueri. </s> <s xml:id="echoid-s17231" xml:space="preserve">Apparet igi-<lb/>tur vanitas Epicycli in Luna. </s> <s xml:id="echoid-s17232" xml:space="preserve">Affert <lb/>quidem Fracaſtorius loco citato alias rationes, quas, quia nullius ſunt mo-<lb/>menti, conſulto prætermittimus.</s> <s xml:id="echoid-s17233" xml:space="preserve"/> </p> <div xml:id="echoid-div921" type="float" level="2" n="30"> <figure xlink:label="fig-491-01" xlink:href="fig-491-01a"> <image file="491-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/491-01"/> </figure> </div> <p> <s xml:id="echoid-s17234" xml:space="preserve"><emph style="sc">His</emph> autem omnibus argumentis facile ſatisfaciemus. </s> <s xml:id="echoid-s17235" xml:space="preserve">Ad primũ enim re-<lb/> <anchor type="note" xlink:label="note-491-01a" xlink:href="note-491-01"/> ſpondemus, Eccentricos, & </s> <s xml:id="echoid-s17236" xml:space="preserve">Epicyclos moueri circa medium propriũ, hoc eſt <lb/>circa propria centra. </s> <s xml:id="echoid-s17237" xml:space="preserve">Quod autem hoc motu nunc ad terram magis accedãt, <lb/>nunc longius ab ea dimoueantur, hoc non eſt abſurdũ; </s> <s xml:id="echoid-s17238" xml:space="preserve">quia hic acceſſus, & </s> <s xml:id="echoid-s17239" xml:space="preserve"><lb/>receſſus non fit per lineam rectam, quem ſolum à corporibus cęleſtibus Ari-<lb/>ſtoteles ex cluſit, cũ ſolis elemẽtis conueniat, quæ grauia ſunt, ac leuia. </s> <s xml:id="echoid-s17240" xml:space="preserve">Quòd <lb/>ſi quis contendat, Ariſtotelem contrarium putaſſe, condonãdum ei hoc erit. <lb/></s> <s xml:id="echoid-s17241" xml:space="preserve">Locutus eſt enim de illis duntaxat motibus, qui ſuo tempore cogniti erant, <lb/>quales ſunt à medio, & </s> <s xml:id="echoid-s17242" xml:space="preserve">ad medium per lineam rectam, & </s> <s xml:id="echoid-s17243" xml:space="preserve">circa mediũ mun-<lb/>di. </s> <s xml:id="echoid-s17244" xml:space="preserve">Quod ſi motus Eccentricorum, & </s> <s xml:id="echoid-s17245" xml:space="preserve">Epicyclorum ſuo tempore noti fuiſſent, <lb/>non dubito, quin aliter de motu circa medium locutus fuiſſet. </s> <s xml:id="echoid-s17246" xml:space="preserve">Si vero aduer-<lb/>ſarijs ſolutio hæc non ſatisfacit, probandum illis non erit, omnem motũ cæ-<lb/>leſtem fieri debere circa centrum mundi, quod nunquam aſſequentur. </s> <s xml:id="echoid-s17247" xml:space="preserve">Non <lb/>enim ad ipſos ſpectat, leges præſcribere motibus cæleſtibus, ſed ad Deũ Opt. </s> <s xml:id="echoid-s17248" xml:space="preserve"><lb/>Max. </s> <s xml:id="echoid-s17249" xml:space="preserve">qui infinita ſua bonitate, ac prouidentia iudicauit expedire, ut planetæ <lb/>non in concentricis orbibus ferrentur circa terram.</s> <s xml:id="echoid-s17250" xml:space="preserve"/> </p> <div xml:id="echoid-div922" type="float" level="2" n="31"> <note position="right" xlink:label="note-491-01" xlink:href="note-491-01a" xml:space="preserve">Solutio @ <lb/>obiectionis</note> </div> <p> <s xml:id="echoid-s17251" xml:space="preserve"><emph style="sc">Secvndam</emph> obiectionem ſoluemus, ſi dicamus, omnes orbes Eccentricos, <lb/> <anchor type="note" xlink:label="note-491-02a" xlink:href="note-491-02"/> etiam illos ſecundũ quid, atq; </s> <s xml:id="echoid-s17252" xml:space="preserve">Epicyclos, perfectiſſime eſſe ſphæricos, quoad <lb/>propria cẽtra. </s> <s xml:id="echoid-s17253" xml:space="preserve">Superficies enim extimæ oĩum horum orbiũ ſecundum oẽs par-<lb/>tes æqualiter à ſuis centris abſunt. </s> <s xml:id="echoid-s17254" xml:space="preserve">Neq; </s> <s xml:id="echoid-s17255" xml:space="preserve">uero obſtat, quòd orbes Eccẽtrici ſe <lb/>cundum quid, craſſiores ſunt una parte, quàm alia: </s> <s xml:id="echoid-s17256" xml:space="preserve">quia nulla ratio naturalis <lb/>perſuadere poteſt, omnes orbes cæleſtes debere eſſe uniformis, & </s> <s xml:id="echoid-s17257" xml:space="preserve">æqualis craſ <lb/>ſitiei. </s> <s xml:id="echoid-s17258" xml:space="preserve">Si uero Ariſtoteles contrariũ docuit, nos ei hac in parte nõ credimus.</s> <s xml:id="echoid-s17259" xml:space="preserve"/> </p> <div xml:id="echoid-div923" type="float" level="2" n="32"> <note position="right" xlink:label="note-491-02" xlink:href="note-491-02a" xml:space="preserve">Solutio 2. <lb/>obiectionis</note> </div> <p> <s xml:id="echoid-s17260" xml:space="preserve"><emph style="sc">Qvod</emph> ad tertium argumentum attinet, uehementer miror, Auerroem, <lb/> <anchor type="note" xlink:label="note-491-03a" xlink:href="note-491-03"/> & </s> <s xml:id="echoid-s17261" xml:space="preserve">Auerroiſtas, quos uerius hac in parte Erroiſtas dixeris, tam infenſo animo <lb/>in Eccentricos, & </s> <s xml:id="echoid-s17262" xml:space="preserve">Epicyclos ferri.</s> <s xml:id="echoid-s17263" xml:space="preserve">, ut intelligere noluerint, qua ratione mo-<lb/>ueantur. </s> <s xml:id="echoid-s17264" xml:space="preserve">Non enim duo illi Eccentrici ſecundũ quid ita mouentur, ut pars te <lb/>nuuior unius ſuccedat in locum craſſioris, & </s> <s xml:id="echoid-s17265" xml:space="preserve">contra, ut ipſi falſo imaginãtur; <lb/></s> <s xml:id="echoid-s17266" xml:space="preserve">ſed proportionaliter ita ſimul feruntur, ut perpetuo pars craſſior inferioris <lb/>ſubſit tenuiori parti ſuperioris, & </s> <s xml:id="echoid-s17267" xml:space="preserve">contra, ſecumq; </s> <s xml:id="echoid-s17268" xml:space="preserve">circumducant Eccentricũ <pb o="456" file="492" n="493" rhead="Comment. in IIII. Cap. Sphæræ"/> ſimpliciter, ita ut alium motum non habeant, quàm totum cælũ planetæ. </s> <s xml:id="echoid-s17269" xml:space="preserve">Ha-<lb/>beret autem uim argumentum, ſi Eccentricus ſimpliciter quieſceret, & </s> <s xml:id="echoid-s17270" xml:space="preserve">Eccen <lb/>trici ſecundum quid circunſtantes mouerentur, quod uerum non eſt.</s> <s xml:id="echoid-s17271" xml:space="preserve"/> </p> <div xml:id="echoid-div924" type="float" level="2" n="33"> <note position="right" xlink:label="note-491-03" xlink:href="note-491-03a" xml:space="preserve">Solutio 3. <lb/>obiectionis</note> </div> <note position="left" xml:space="preserve">Solutio 4. <lb/>obiectionis</note> <p> <s xml:id="echoid-s17272" xml:space="preserve"><emph style="sc">Ad</emph> quartam obiectionem reſpondendum eſt, Ariſtotelẽ ſemper eius fuiſ-<lb/>ſe ſententiæ, ut in rebus Aſtronomicis conſulendos eſſe Aſtronomos cenſe-<lb/>ret. </s> <s xml:id="echoid-s17273" xml:space="preserve">Vnde tunc ſecutus eſt Aſtronomos ſui temporis, nempe Eudoxum, & </s> <s xml:id="echoid-s17274" xml:space="preserve">Ca-<lb/>lippum, qui nitebantur omnia φαινόμενα tueri per circulos concentricos. </s> <s xml:id="echoid-s17275" xml:space="preserve">Nõ <lb/>dubito autem, quin, ſi tempore Ptolemęi extitiſſet, amplexus fuiſſet Eccentri-<lb/>cos, & </s> <s xml:id="echoid-s17276" xml:space="preserve">Epicyclos, quandoquidem omnia commodiſſime ea ratione defendun <lb/>tur. </s> <s xml:id="echoid-s17277" xml:space="preserve">Semper enim affirmat; </s> <s xml:id="echoid-s17278" xml:space="preserve">in rebus Aſtronomicis Aſtronomis fidem eſſe ha-<lb/>bendam.</s> <s xml:id="echoid-s17279" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17280" xml:space="preserve"><emph style="sc">Ad</emph> quintam rationem dicimus, illam opinionem, quòd cælum in loco ſit <lb/> <anchor type="note" xlink:label="note-492-02a" xlink:href="note-492-02"/> per centrum, propriam eſſe Auuerrois. </s> <s xml:id="echoid-s17281" xml:space="preserve">Vnde ſi illam uelimus acceptare, nihil <lb/>contra nos concludit argumentum. </s> <s xml:id="echoid-s17282" xml:space="preserve">Si quis tamen eam opinionem defendere <lb/>uoluerit, poterit dicere, Eccentricos etiam orbes, atque Epicyclos eſſe in loco <lb/>per ſua centra. </s> <s xml:id="echoid-s17283" xml:space="preserve">Centrum autem mundi eſſe locum totalium cælorum, non au <lb/>tem orbium partialium. </s> <s xml:id="echoid-s17284" xml:space="preserve">Si uero urgeat quis, eundem eſſe locum totius, & </s> <s xml:id="echoid-s17285" xml:space="preserve">par <lb/>tium, illud intelligendum eſt de loco communi, non autem de proprio. </s> <s xml:id="echoid-s17286" xml:space="preserve">Pars <lb/>enim quęlibet lapidis eundem locum habet cum lapide communem, non aũt <lb/>eundem locum proprium, cum locus debeat eſſe locato æqualis. </s> <s xml:id="echoid-s17287" xml:space="preserve">Sic igitur ſi <lb/>tueri quis uelit ſententiam Auerrois, dicere poterit, locum communem om <lb/>niũ ſphærarum tam partialium, quàm totalium, non eſſe centrum mundi: </s> <s xml:id="echoid-s17288" xml:space="preserve">ſed <lb/>centrum abſolute, quodcuuque illud ſit, uel certe aggregatũ ex omnibus cen <lb/>tris: </s> <s xml:id="echoid-s17289" xml:space="preserve">atque ita eas ha bere eundem locũ communem, nimirum, centrum, quem <lb/>libet tamen orbem habere proprium locum, nempe centrum proprium.</s> <s xml:id="echoid-s17290" xml:space="preserve"/> </p> <div xml:id="echoid-div925" type="float" level="2" n="34"> <note position="left" xlink:label="note-492-02" xlink:href="note-492-02a" xml:space="preserve">Solutio 5. <lb/>obiectionis</note> </div> <p> <s xml:id="echoid-s17291" xml:space="preserve"><emph style="sc">Ad</emph> ſextum argumentum reſpondemus, non ſolum ſecundum orbes Eccẽ <lb/> <anchor type="note" xlink:label="note-492-03a" xlink:href="note-492-03"/> tricos, & </s> <s xml:id="echoid-s17292" xml:space="preserve">Epicyclos Solẽ pauciores motus habere, quàm ſuperiores planetas, <lb/>ſed etiam ſecundum concentricos, ut conſtat ex Fracaſtorio cap. </s> <s xml:id="echoid-s17293" xml:space="preserve">24. </s> <s xml:id="echoid-s17294" xml:space="preserve">ubi nume <lb/>rum orbium percenſet. </s> <s xml:id="echoid-s17295" xml:space="preserve">Vnde negamus, orbes cæleſtes, quo inferiores ſunt eo <lb/>pluribus debere motibus cieri, & </s> <s xml:id="echoid-s17296" xml:space="preserve">eo paucioribus, quo ſuperiores, cũ experien-<lb/>tia contrarium docuerit, ut & </s> <s xml:id="echoid-s17297" xml:space="preserve">aduerſarij fatentur.</s> <s xml:id="echoid-s17298" xml:space="preserve"/> </p> <div xml:id="echoid-div926" type="float" level="2" n="35"> <note position="left" xlink:label="note-492-03" xlink:href="note-492-03a" xml:space="preserve">Solutio 6. <lb/>obìectionis</note> </div> <p> <s xml:id="echoid-s17299" xml:space="preserve"><emph style="sc">Ad</emph> obiectionem ſeptimam negandum eſt, terram quieſcentem neceſſariã <lb/> <anchor type="note" xlink:label="note-492-04a" xlink:href="note-492-04"/> eſſe in quolibet centro, ut circa illam orbes cæleſtes moueantur, Quamuis <lb/>Deus Opt. </s> <s xml:id="echoid-s17300" xml:space="preserve">Max. </s> <s xml:id="echoid-s17301" xml:space="preserve">terram hanc uel omnino auferret, uel aliò impelleret extra <lb/>centrum mundi, adhuc cęli motu diurno ueherentur circa medium mundi.</s> <s xml:id="echoid-s17302" xml:space="preserve"/> </p> <div xml:id="echoid-div927" type="float" level="2" n="36"> <note position="left" xlink:label="note-492-04" xlink:href="note-492-04a" xml:space="preserve">Solutio 7. <lb/>obiectionis</note> </div> <p> <s xml:id="echoid-s17303" xml:space="preserve"><emph style="sc">Ad</emph> octauum argumentum dicendum eſt, duos orbes eccentricos ſecun-<lb/> <anchor type="note" xlink:label="note-492-05a" xlink:href="note-492-05"/> dum quid neceſſarios eſſe, ut totum cælum planetæ mundo concentricum in-<lb/>tegrent, ac compleant Vnde neuter eorum ſuperuacaneus cenſeri debet. </s> <s xml:id="echoid-s17304" xml:space="preserve">To-<lb/>tum enim cælum, quod ex illis componitur, proprium motum habet. </s> <s xml:id="echoid-s17305" xml:space="preserve">Non au <lb/>tem ſolum hi orbes ponuntur, ut augem deferant, eiuſque oppoſitum, quod <lb/>falſo obiectio affumit.</s> <s xml:id="echoid-s17306" xml:space="preserve"/> </p> <div xml:id="echoid-div928" type="float" level="2" n="37"> <note position="left" xlink:label="note-492-05" xlink:href="note-492-05a" xml:space="preserve">Solutio 8. <lb/>obiectionis</note> </div> <p> <s xml:id="echoid-s17307" xml:space="preserve"><emph style="sc">Iam</emph> uero, quod ad tria argumenta Fracaſtorij attinet, dicimus, primũ ni <lb/> <anchor type="note" xlink:label="note-492-06a" xlink:href="note-492-06"/> hil concludere in Sole. </s> <s xml:id="echoid-s17308" xml:space="preserve">Quoniam enim Sol tantam diſtantiam habet à terra, <lb/>ut uel nullam aſpectus diuerſitatẽ, uel certe inſenſibilem admittat, fit ut cum <lb/>planũ Eccentrici ipſius ſemper in plano Eclipticæ iaceat, (ut in Theoricis ex <lb/>plicabitur.) </s> <s xml:id="echoid-s17309" xml:space="preserve">perpetuo appareat ſub Ecliptica, ſi è terra conſpiciatur. </s> <s xml:id="echoid-s17310" xml:space="preserve">Vnde quã <lb/>do eſt in principio ♋, uel ♑, uidebitur eoſdẽ parallelos motu diurno deſcri-<lb/>bere, quos eadem principia ♋, & </s> <s xml:id="echoid-s17311" xml:space="preserve">♑, in primo mobili deſcribunt, qui æquales <pb o="457" file="493" n="494" rhead="Ioan. de Sacro Boſco."/> ſunt. </s> <s xml:id="echoid-s17312" xml:space="preserve">Neque obſtat, quòd Sol ſit in auge, quando eſt in ♋, & </s> <s xml:id="echoid-s17313" xml:space="preserve">in oppoſito au-<lb/>gis, quando eſt in ♑. </s> <s xml:id="echoid-s17314" xml:space="preserve">Alias Saturnus, dum eſt ſub Ecliptica, & </s> <s xml:id="echoid-s17315" xml:space="preserve">in principio ♋, <lb/>deſeriberet parallelum remotiorem ab Aequatore, quàm Iuppiter, cum Satur <lb/>nus longius a terra, quàm Iuppiter, diſtet. </s> <s xml:id="echoid-s17316" xml:space="preserve">Quod falſum eſt. </s> <s xml:id="echoid-s17317" xml:space="preserve">Vterq; </s> <s xml:id="echoid-s17318" xml:space="preserve">enim plane <lb/>ta, dum eſt ſub Ecliptica, & </s> <s xml:id="echoid-s17319" xml:space="preserve">in principio ♋, deprehẽſus eſt habere declinatio-<lb/>nem grad. </s> <s xml:id="echoid-s17320" xml:space="preserve">23 {1/2}. </s> <s xml:id="echoid-s17321" xml:space="preserve">deſcribereq; </s> <s xml:id="echoid-s17322" xml:space="preserve">motu diurno tropicum ♋. </s> <s xml:id="echoid-s17323" xml:space="preserve">Non ergo ſequitur, <lb/>declinationem maxim am Solis borealem maiorem eſſe maxima declinatio-<lb/>ne auſtrali: </s> <s xml:id="echoid-s17324" xml:space="preserve">& </s> <s xml:id="echoid-s17325" xml:space="preserve">in ſphæra obliqua maximum diem in æſtate long orem eſſe ma <lb/>xima nocte in hyeme. </s> <s xml:id="echoid-s17326" xml:space="preserve">Sequerentur autẽ omuia hæc abſurda, ſi Sol haberet no <lb/>tabilem diuerſitatem aſpectus. </s> <s xml:id="echoid-s17327" xml:space="preserve">Verum nihilominus eſt, centrum Solis in auge <lb/>exiſtentis deſcribere motu diurno in ſuo orbe parallelum magis diſtantẽ ab <lb/>Aequatore, quàm dum in oppoſito augis exiſtit, quia hic minus diſtantẽ de-<lb/>ſcribit: </s> <s xml:id="echoid-s17328" xml:space="preserve">Sed quia uterque parallelus, propter nimiam Solis diſtantiam a terra, <lb/>videtur deſcribi a pũctis, quæ in primo mobili terminãt rectæ lineæ a centro <lb/>terræ per augem, & </s> <s xml:id="echoid-s17329" xml:space="preserve">oppoſitũ augis emiſſæ, ſit ut æqualiter iudicentur ab Ae-<lb/>quatore abeſſe, quoad ſenſum.</s> <s xml:id="echoid-s17330" xml:space="preserve"/> </p> <div xml:id="echoid-div929" type="float" level="2" n="38"> <note position="left" xlink:label="note-492-06" xlink:href="note-492-06a" xml:space="preserve">Solutio 1. <lb/>obiectionis <lb/>Fracaſtorij</note> </div> <p> <s xml:id="echoid-s17331" xml:space="preserve"><emph style="sc">Ad</emph> ſecundum argumentũ Fracaſtorij reſpondemus, Aſtronomos non ſta-<lb/> <anchor type="note" xlink:label="note-493-01a" xlink:href="note-493-01"/> tuere, Epicycli Veneris ſemidiametrum continere grad. </s> <s xml:id="echoid-s17332" xml:space="preserve">43. </s> <s xml:id="echoid-s17333" xml:space="preserve">ſed partes 43. </s> <s xml:id="echoid-s17334" xml:space="preserve">ex <lb/>ijs, quarum 60. </s> <s xml:id="echoid-s17335" xml:space="preserve">in ſemidiametro circuli Eccentrici continentur. </s> <s xml:id="echoid-s17336" xml:space="preserve">Ex quo fit, ut <lb/>lineæ ex centro terræ emiſſæ, tangentesq́. </s> <s xml:id="echoid-s17337" xml:space="preserve">Epicyclũ auferant ex primo mobi-<lb/>li ad utraſque partes lineæ augis gradus ferme 45. </s> <s xml:id="echoid-s17338" xml:space="preserve">quot nimirum ad ſummum <lb/>Venus recedere uidetur a Sole tã uerſus ortũ, quàm uerſus occaſum. </s> <s xml:id="echoid-s17339" xml:space="preserve">Sed hinc <lb/>non ſequitur, Epicyclum fere ad terram uſq; </s> <s xml:id="echoid-s17340" xml:space="preserve">pertingere. </s> <s xml:id="echoid-s17341" xml:space="preserve">Cum enim, ut Ferne <lb/>lius Ambianas in ſua Coſmotheoria refert, Eccẽtrici circuli ſemidiameter cõ <lb/>tineat ſemidiametros terræ ferme 689. </s> <s xml:id="echoid-s17342" xml:space="preserve">cõprehendet propemodũ ſemidiame <lb/>ter Epicycli terræ ſemidiametros 435 {2/3}. </s> <s xml:id="echoid-s17343" xml:space="preserve">quem numerũ ſi ſubtrahamus ex di <lb/>ſtantia terræ ab oppoſito augis, quæ cõplectitur ſemidiametros terræ 674 {2/3}. <lb/></s> <s xml:id="echoid-s17344" xml:space="preserve">fere, continebit interuallũ inter centrũ terræ, & </s> <s xml:id="echoid-s17345" xml:space="preserve">oppoſitũ augis Epicycli, dum <lb/>Epicyclus terræ proximus eſt, nẽpe in oppoſito augis Eccentrici, ſemidiame-<lb/>tros terræ quaſi 179. </s> <s xml:id="echoid-s17346" xml:space="preserve">quæ diſtantia plura milliaria cõtinet, quã 640641. </s> <s xml:id="echoid-s17347" xml:space="preserve">Nos <lb/>tamcn hanc diſtantiam concaui Veneris ex Maurolyco in 1. </s> <s xml:id="echoid-s17348" xml:space="preserve">cap. </s> <s xml:id="echoid-s17349" xml:space="preserve">aliquãto mi-<lb/>norẽ conſtituimus, nempe terræ ſemidiametrorum 167 {2/3}. </s> <s xml:id="echoid-s17350" xml:space="preserve">id eſt, milliariornm <lb/>600167 {14/33}. </s> <s xml:id="echoid-s17351" xml:space="preserve">Non ergo Epicyclus Veneris terrã attingit, ſed tanto interuallo <lb/>ab ea diſtat, ut commode in eo cęlum Mercurij & </s> <s xml:id="echoid-s17352" xml:space="preserve">cęlum Lunæ, unà cum om-<lb/>nibus elementis includi poſſit Figuram porro propriam cum proportionibus <lb/>diametrorum Eccẽtrici, & </s> <s xml:id="echoid-s17353" xml:space="preserve">Epicycli in Theorica Veneris idem Fernelius de-<lb/>pinxit: </s> <s xml:id="echoid-s17354" xml:space="preserve">ut ex ea quo que facile appareat, Epicyclum Veneris terram non poſ-<lb/>ſe attingere, ſed intra craſſitiem Eccentrici orbis immerſum eſſe.</s> <s xml:id="echoid-s17355" xml:space="preserve"/> </p> <div xml:id="echoid-div930" type="float" level="2" n="39"> <note position="right" xlink:label="note-493-01" xlink:href="note-493-01a" xml:space="preserve">Solutio 2. <lb/>obiectionis <lb/>Fracaſtorij.</note> </div> <p> <s xml:id="echoid-s17356" xml:space="preserve"><emph style="sc">Postbemo</emph> pro Epicyclo Lunæ reſpondet Fernelius Ambianas libro cita-<lb/> <anchor type="note" xlink:label="note-493-02a" xlink:href="note-493-02"/> to, Lunam in Epicyclo circa proprium centrum proprium habere motum, <lb/>Epicycli motui conformem, in contrariam tamen partem. </s> <s xml:id="echoid-s17357" xml:space="preserve">Ex quo motu con-<lb/>ſequitur, at Luna ſemper eandem maculatam faciem nobis obuertat. </s> <s xml:id="echoid-s17358" xml:space="preserve">Neque <lb/>hoc mirum uideri debet, & </s> <s xml:id="echoid-s17359" xml:space="preserve">abſurdũ, quamuis Ariſtoteles ſtellis proprios mo <lb/>tus negauerit. </s> <s xml:id="echoid-s17360" xml:space="preserve">Cum enim φαινόμενα oſtendant, Lunã ferri in Epicyclo, & </s> <s xml:id="echoid-s17361" xml:space="preserve">ſem <lb/>per eandem faciem ad nos conuertere, neceſſe eſt, illam proprio motu circa <lb/>propriũ centrũ circũuolui, ut ſemper in ſtabili quodã libramẽto permaneat.</s> <s xml:id="echoid-s17362" xml:space="preserve"/> </p> <div xml:id="echoid-div931" type="float" level="2" n="40"> <note position="right" xlink:label="note-493-02" xlink:href="note-493-02a" xml:space="preserve">Solutio 3. <lb/>obiectionis <lb/>Fracaſtorij.</note> </div> <p> <s xml:id="echoid-s17363" xml:space="preserve"><emph style="sc">Ex</emph> his ergo omnibus conſtare arbitror, Eccentricos, & </s> <s xml:id="echoid-s17364" xml:space="preserve">Epicyclos nõ eſſe <lb/>adeo monſtroſos, & </s> <s xml:id="echoid-s17365" xml:space="preserve">abſurdos, ut ab aduerſarijs finguntur, eoſque ab Aſtrono- <pb o="458" file="494" n="495" rhead="Comment. in IIII. Cap. Sphæræ"/> mis non ſine magna cauſa inductos eſſe. </s> <s xml:id="echoid-s17366" xml:space="preserve">Quòd ſi propterea abſurdi ſunt cen <lb/>ſendi, quòd diuerſa habeant centra, & </s> <s xml:id="echoid-s17367" xml:space="preserve">Eccentrici ſecundũ quid habe<unsure/>ant inæ-<lb/>qualem craſſitiẽ: </s> <s xml:id="echoid-s17368" xml:space="preserve">Cur non item abſurdũ eſſe dicamus, quod Luna non habeat <lb/>æqualem denſitatem, ſed partes habeat alias alibi denſiores, ut eius maculæ <lb/>indicant? </s> <s xml:id="echoid-s17369" xml:space="preserve">Quas aduerſarij, ſi proprijs oculis nõ conſpexiſſent, nõ dubito, quin <lb/>propoſitas ab Aſtronomis etiam exſibilaturi fuerint. </s> <s xml:id="echoid-s17370" xml:space="preserve">Ita illis religio eſt, quic-<lb/>quam in cęlo admittere, quod à perfectiſſima uniformitate uel tantillum de-<lb/>clinare uideatur. </s> <s xml:id="echoid-s17371" xml:space="preserve">Quid? </s> <s xml:id="echoid-s17372" xml:space="preserve">quod in Firmamento, quod eſſe quaſi regulam cæte-<lb/>rorum orbium Ariſtotelei coguntur aſſerere, ſumma tamen apparet eſſe dif-<lb/>formitas tum ex aſtris, tum, ſi veritatem ſequamur, ex Lactea uia? </s> <s xml:id="echoid-s17373" xml:space="preserve">Cum igitur <lb/>hæc tanta inæqualitas in tota cæli profunditate, ſecundum denſitatem, ac ra-<lb/>ritatem, ne ab aduerſarijs quidem negetur, cur Eccentrici, & </s> <s xml:id="echoid-s17374" xml:space="preserve">Epicycli abſurdi <lb/>& </s> <s xml:id="echoid-s17375" xml:space="preserve">monſtroſi, propter ſolam centrorum diuerſitatem, & </s> <s xml:id="echoid-s17376" xml:space="preserve">inæqualem craſſitiem <lb/>cenſeantur? </s> <s xml:id="echoid-s17377" xml:space="preserve">Sed de Eccentricis, & </s> <s xml:id="echoid-s17378" xml:space="preserve">Epicyclis pro loco, & </s> <s xml:id="echoid-s17379" xml:space="preserve">tempore ſatis diſputæ <lb/>tum ſit. </s> <s xml:id="echoid-s17380" xml:space="preserve">Nunc ad intermiſſam expoſitionem auctoris reuertamur.</s> <s xml:id="echoid-s17381" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div933" type="section" level="1" n="359"> <head xml:id="echoid-head370" style="it" xml:space="preserve">NOTANDVM, quòd Sol habet unicam circulum, & c.</head> <head xml:id="echoid-head371" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s17382" xml:space="preserve"><emph style="sc">Primvm</emph> igitur agit auctor de orbe, & </s> <s xml:id="echoid-s17383" xml:space="preserve">motu Solis dicens, Solem habere <lb/>vnum circulum eccentricum, in quo perpetuo ſub Ecliptica deſertur ab oc-<lb/> <anchor type="note" xlink:label="note-494-01a" xlink:href="note-494-01"/> cidente in orientem. </s> <s xml:id="echoid-s17384" xml:space="preserve">Quod ut intelligatur, reuocanda ſunt in memoriam ea, <lb/>quæ paulo anre diximus, totum uidelicet cęlum Solis, quod idem habet cen <lb/>trum cum centro mundi cõmune, diuidi à Ptolemæo, & </s> <s xml:id="echoid-s17385" xml:space="preserve">recẽtioribus in tres <lb/>orbes partiales inter ſe conti guos, quorum ſupremus ſecundum ſuperſiciem <lb/>conuexam concentrices eſt mundo, hoc eſt, eius centrum non differt à mundi <lb/>centro: </s> <s xml:id="echoid-s17386" xml:space="preserve">at ſecundum concauam ſuperficiem eccentricus eſt, hoc eſt, aliud cen-<lb/>trum à centro mundi obtinet: </s> <s xml:id="echoid-s17387" xml:space="preserve">Infimus uero orbis uerſa uice ſecundum con-<lb/>cauam ſuperficiem mundo eſt concentricus, & </s> <s xml:id="echoid-s17388" xml:space="preserve">ſecundum conuexam eccentri-<lb/>cus: </s> <s xml:id="echoid-s17389" xml:space="preserve">Tertius denique, qui in medio horum eſt collocatus, ſecundum utramq; <lb/></s> <s xml:id="echoid-s17390" xml:space="preserve">ſuperficiem tam conuexam, quàm concauam eccentricus eſt, eo quòd conti-<lb/>guus ſit cõcauæ ſuperficiei ſuperioris orbis, & </s> <s xml:id="echoid-s17391" xml:space="preserve">conuexæ ſuperficiei in ferioris. </s> <s xml:id="echoid-s17392" xml:space="preserve"><lb/>Vnde priores duo orbes dici ſolent eccentrici ſecundum quid, quia ſecundũ <lb/>vnam tantum ſuperficiem diuerſum habent centrum a centro mundi; </s> <s xml:id="echoid-s17393" xml:space="preserve">Tertius <lb/>vero intermedius eccentricus ſimpliciter uocatur, in eoque infixus Sol mo-<lb/>uetur circa centrum eius ab occaſu in ortum, ita ut centrum Solis deſcribat <lb/>in anno circulum quendam ſub Ecliptica, cuius centrum idem eſt, quod cen-<lb/>trum orbis eccentrici ſimpliciter. </s> <s xml:id="echoid-s17394" xml:space="preserve">Hunc igitur circulum appellat hoc loco au-<lb/>ctor eccentricum, in quo Sol proprio motu muuetur.</s> <s xml:id="echoid-s17395" xml:space="preserve"/> </p> <div xml:id="echoid-div933" type="float" level="2" n="1"> <note position="left" xlink:label="note-494-01" xlink:href="note-494-01a" xml:space="preserve">Cœlum So <lb/>lis ex qui-<lb/>bus compo <lb/>natur.</note> </div> <p> <s xml:id="echoid-s17396" xml:space="preserve"><emph style="sc">Qvoniam</emph> vero iſte circulus diſtinctum habet centrum à centro mundi, <lb/>ſeu Firmamenti, efficitur, ut unum eius punctum, quod nimirum oſtenditur <lb/>à linea recta, quæ à centro mundi per centrum ipſius ducitur, ſit remotiſſimũ <lb/>a terra, & </s> <s xml:id="echoid-s17397" xml:space="preserve">propinquiſſimum Firmamẽto; </s> <s xml:id="echoid-s17398" xml:space="preserve">alterum uero, quod huic opponitur, <lb/>terris uiciniſſimum, & </s> <s xml:id="echoid-s17399" xml:space="preserve">longiſſime à Firmamento abſit. </s> <s xml:id="echoid-s17400" xml:space="preserve">Illud punctum, ait, ap-<lb/> <anchor type="note" xlink:label="note-494-02a" xlink:href="note-494-02"/> pellatur Aux Solis apud Arabes: </s> <s xml:id="echoid-s17401" xml:space="preserve">Hoc uero oppoſitum Augis.</s> <s xml:id="echoid-s17402" xml:space="preserve"/> </p> <div xml:id="echoid-div934" type="float" level="2" n="2"> <note position="left" xlink:label="note-494-02" xlink:href="note-494-02a" xml:space="preserve">Aux Solis, <lb/>& oppoſitũ <lb/>Augis @ d.</note> </div> <p> <s xml:id="echoid-s17403" xml:space="preserve"><emph style="sc">Deinde</emph> docet, Solem ab occaſu in ortum duplicem habere motum, <pb o="459" file="495" n="496" rhead="Ioan. de Sacro Boſco."/> vnum propriũ in ſuo eccẽtrico, in quo ſingulis diebus cõficit min. </s> <s xml:id="echoid-s17404" xml:space="preserve">59. </s> <s xml:id="echoid-s17405" xml:space="preserve">& </s> <s xml:id="echoid-s17406" xml:space="preserve">ſec. </s> <s xml:id="echoid-s17407" xml:space="preserve">8. <lb/></s> <s xml:id="echoid-s17408" xml:space="preserve">ferme. </s> <s xml:id="echoid-s17409" xml:space="preserve">Vnde ille eccentricus orbis appellari folet Deferens Solem, quia ad mo <lb/> <anchor type="note" xlink:label="note-495-01a" xlink:href="note-495-01"/> tum illius Sol defertur ſub Ecliptica ab occaſu in ortum. </s> <s xml:id="echoid-s17410" xml:space="preserve">Alterum deinde mo <lb/>tum habet tardiſſimum, quo mouetur ad motũ totius cæli Solis ab occaſu in <lb/>ortum in 100. </s> <s xml:id="echoid-s17411" xml:space="preserve">annis grad. </s> <s xml:id="echoid-s17412" xml:space="preserve">1. </s> <s xml:id="echoid-s17413" xml:space="preserve">iuxta Ptolemæum; </s> <s xml:id="echoid-s17414" xml:space="preserve">At ſecundum Alphonſum in <lb/>200. </s> <s xml:id="echoid-s17415" xml:space="preserve">annis grad. </s> <s xml:id="echoid-s17416" xml:space="preserve">1. </s> <s xml:id="echoid-s17417" xml:space="preserve">min. </s> <s xml:id="echoid-s17418" xml:space="preserve">28. </s> <s xml:id="echoid-s17419" xml:space="preserve">Et quia hoc motu duo illi orbes eccentrici ſecun-<lb/> <anchor type="note" xlink:label="note-495-02a" xlink:href="note-495-02"/> dum quid deferunt augem Solis, & </s> <s xml:id="echoid-s17420" xml:space="preserve">oppoſitum augis ad alia, & </s> <s xml:id="echoid-s17421" xml:space="preserve">alia puncta Ecli <lb/>pticæ, licet tardiſſime, dicti ſunt ab Aſtronomis. </s> <s xml:id="echoid-s17422" xml:space="preserve">Deferentes augem Solis. </s> <s xml:id="echoid-s17423" xml:space="preserve">Eſt <lb/>autem hoc tempore Aux Solis in 2. </s> <s xml:id="echoid-s17424" xml:space="preserve">fere grad. </s> <s xml:id="echoid-s17425" xml:space="preserve">♋. </s> <s xml:id="echoid-s17426" xml:space="preserve">& </s> <s xml:id="echoid-s17427" xml:space="preserve">oppoſitum eius in 2. </s> <s xml:id="echoid-s17428" xml:space="preserve">grad. <lb/></s> <s xml:id="echoid-s17429" xml:space="preserve">♑. </s> <s xml:id="echoid-s17430" xml:space="preserve">Ex his igitur duobus motibus, inquit, colligitur annuus motus Solis. </s> <s xml:id="echoid-s17431" xml:space="preserve">Ve-<lb/>rum conſtitutio horum trium orbium Solis, & </s> <s xml:id="echoid-s17432" xml:space="preserve">eorum motus, plenius explica-<lb/>ri ſolent in Theoricis Planetarum.</s> <s xml:id="echoid-s17433" xml:space="preserve"/> </p> <div xml:id="echoid-div935" type="float" level="2" n="3"> <note position="right" xlink:label="note-495-01" xlink:href="note-495-01a" xml:space="preserve">Sol duplicẽ <lb/>motum ha-<lb/>bet ab occa <lb/>ſuin ortũ.</note> <note position="right" xlink:label="note-495-02" xlink:href="note-495-02a" xml:space="preserve">Orbes defe <lb/>ren@es Au-<lb/>gem Solis <lb/>qui.</note> </div> <note position="right" xml:space="preserve">Cæli alio-<lb/>rum plane <lb/>tarum, præ-<lb/>ter Solem, <lb/>ex quibus <lb/>orbibus cõ-<lb/>ponantur.</note> <p style="it"> <s xml:id="echoid-s17434" xml:space="preserve"><emph style="sc">Qvilibet</emph> autem Planeta, præter Solem, tres habet circulos, <lb/>ſcilicet Aequantem, Deferentem, & </s> <s xml:id="echoid-s17435" xml:space="preserve">Epicyclum. </s> <s xml:id="echoid-s17436" xml:space="preserve">Aequans quidem Lu-<lb/>næeſt circulus concentricus cum terra, & </s> <s xml:id="echoid-s17437" xml:space="preserve">eſt in ſuperficie Eclipticæ. </s> <s xml:id="echoid-s17438" xml:space="preserve">Eius <lb/>uero Deferens eſt circulus eccentricus, nec eſt in ſuperficie Eclipticæ, im-<lb/>mo una eius medietas declinat uerſus Septentrionem, altera uerſus Au-<lb/> <anchor type="note" xlink:label="note-495-04a" xlink:href="note-495-04"/> ſtrum. </s> <s xml:id="echoid-s17439" xml:space="preserve">Et Deferens Aequantem interſecat in duobus locis: </s> <s xml:id="echoid-s17440" xml:space="preserve">Et figura in-<lb/>terſectionis appellatur Draco, quoniam lata eſt in medio, & </s> <s xml:id="echoid-s17441" xml:space="preserve">anguſtior <lb/>uerſus finem. </s> <s xml:id="echoid-s17442" xml:space="preserve">Interſectio igitur illa, per quam Luna mouetur ab Auſtro <lb/> <anchor type="note" xlink:label="note-495-05a" xlink:href="note-495-05"/> uerſus Aquilonem, appellatur caput Draconis. </s> <s xml:id="echoid-s17443" xml:space="preserve">Reliqua uero interſe-<lb/>ctio, per quam mouetur à Septentrione in Auſtrum, dicitur Cauda <lb/>Draconis.</s> <s xml:id="echoid-s17444" xml:space="preserve"/> </p> <div xml:id="echoid-div936" type="float" level="2" n="4"> <note position="right" xlink:label="note-495-04" xlink:href="note-495-04a" xml:space="preserve">Caput, & <lb/>cauda Dra-<lb/>conis in Lu <lb/>na quid.</note> <note position="right" xlink:label="note-495-05" xlink:href="note-495-05a" xml:space="preserve">Deferẽs, & <lb/>Aequansin <lb/>quinq; pla-<lb/>netis ſunt <lb/>eccẽtrici. & <lb/>in eadem <lb/>ſuperficie, <lb/>quæ ab Eclã <lb/>ptica decli-<lb/>nat.</note> </div> <p style="it"> <s xml:id="echoid-s17445" xml:space="preserve"><emph style="sc">Deferens</emph> quidem, & </s> <s xml:id="echoid-s17446" xml:space="preserve">Aequans cuiuslibet planetæ ſunt æqua-<lb/>les. </s> <s xml:id="echoid-s17447" xml:space="preserve">Et eſt ſciendum, quod tam Deferens, quàm Aequans, Saturni, Iouis, <lb/>Martis, Veneris, & </s> <s xml:id="echoid-s17448" xml:space="preserve">Mercurij, ſunt eccentrici, & </s> <s xml:id="echoid-s17449" xml:space="preserve">extra ſuperficiem Ecli-<lb/>pticæ, & </s> <s xml:id="echoid-s17450" xml:space="preserve">tamen ipſi ſunt in eadem ſuperficie.</s> <s xml:id="echoid-s17451" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">Epicyclus <lb/>quid.</note> <p style="it"> <s xml:id="echoid-s17452" xml:space="preserve"><emph style="sc">Qvilibet</emph> etiam planeta, præter Solem, habet Epicyclum. <lb/></s> <s xml:id="echoid-s17453" xml:space="preserve">Eſt autem Epicyclus circulus paruus, per cuius circunferentiam defer-<lb/>tur corpus planetæ, & </s> <s xml:id="echoid-s17454" xml:space="preserve">centrum Epicycli ſemper defertur in circunferen-<lb/>tia Deferentis.</s> <s xml:id="echoid-s17455" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div938" type="section" level="1" n="360"> <head xml:id="echoid-head372" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s17456" xml:space="preserve"><emph style="sc">Secvndo</emph> agit de orbibus, & </s> <s xml:id="echoid-s17457" xml:space="preserve">motibus aliorum planetarum dicens, <lb/>quemlibet illorum habere tres circulos, Aequantem ſcilicet, Deferentem, & </s> <s xml:id="echoid-s17458" xml:space="preserve"><lb/>Epicyclum. </s> <s xml:id="echoid-s17459" xml:space="preserve">Aequans quidem Lunæ eſt circulus concentricus cum terra, eſtq; <lb/></s> <s xml:id="echoid-s17460" xml:space="preserve">in ſuperficie Eclipticæ. </s> <s xml:id="echoid-s17461" xml:space="preserve">Dicitur autem hic circulus Aequans Lunæ, quia, vt ex <lb/>Theoricis cõſtat, ex motu huius cognoſcitur adæquate ac præciſe verus mo-<lb/>tus Lunæ. </s> <s xml:id="echoid-s17462" xml:space="preserve">Deferens autem Lunæ eſt circulus ſimpliciter eccentricus, ſicut So-<lb/>lis, hoc uno dempto, quòd hic Eccentricus non eſt in ſuperficie Eclipticæ, ue <lb/>lut ille Solis, ſed una eius medietas ab Ecliptica uerſus Septentrionem, altera <lb/>uero uerſus Auſtrum declinat. </s> <s xml:id="echoid-s17463" xml:space="preserve">Vnde efficitur, vt Luna per hunc circulũ dela- <pb o="460" file="496" n="497" rhead="Comment. in IIH. Cap. Sphæræ"/> ta reperiatur, quandoque extra eclipticam uerſus Septentrionem, quand oque <lb/>uerſus Auſtrum, nunquam autem præciſe ſub ecliptica, niſi in illis duobus pũ <lb/>ctis, in quibus ſe interſecant ecliptica, ſiue Aequans, & </s> <s xml:id="echoid-s17464" xml:space="preserve">Deferens circulus Lu-<lb/>næ. </s> <s xml:id="echoid-s17465" xml:space="preserve">Hunc Deferentem, qui eſt eccentricus ſimpliciter, circumſtãt alij duo ec-<lb/>centrici ſecundum quid, ueluti de Sole eſt dictum. </s> <s xml:id="echoid-s17466" xml:space="preserve">Ex duobus uero pũctis, in <lb/>quibus ſe interſecant Aequans, & </s> <s xml:id="echoid-s17467" xml:space="preserve">Deferens Lunæ, illud, per quod in Deferen <lb/>te Luna ad Septẽtrionem uehitur, caput Draconis dicitur; </s> <s xml:id="echoid-s17468" xml:space="preserve">alterum uero, per <lb/>quod in Auſtrum tendit, cauda Draconis: </s> <s xml:id="echoid-s17469" xml:space="preserve">Atque hæc duo puncta deferuntur <lb/>ab ortu in occaſum ab Aequante Lunæ: </s> <s xml:id="echoid-s17470" xml:space="preserve">eſt enim hic orbis Aequans ſupremus <lb/>in ſphæra Lunæ. </s> <s xml:id="echoid-s17471" xml:space="preserve">Quo circa ab Aſtronomis dici ſolet Deferens caput, & </s> <s xml:id="echoid-s17472" xml:space="preserve">caudã <lb/>Draconis, eſtq́; </s> <s xml:id="echoid-s17473" xml:space="preserve">maior eccentrico deferente Lunam.</s> <s xml:id="echoid-s17474" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17475" xml:space="preserve"><emph style="sc">Deferens</emph> autem, & </s> <s xml:id="echoid-s17476" xml:space="preserve">Aequans cuiuslibet alterius planetæ ſunt inter <lb/> <anchor type="note" xlink:label="note-496-01a" xlink:href="note-496-01"/> ſe æquales, & </s> <s xml:id="echoid-s17477" xml:space="preserve">eccentrici ſimpliciter, & </s> <s xml:id="echoid-s17478" xml:space="preserve">uterque eſt extra ſuperficiem eclipti-<lb/>cæ, quamuis ambo in vna, eademq́. </s> <s xml:id="echoid-s17479" xml:space="preserve">ſuperficie exiſtant. </s> <s xml:id="echoid-s17480" xml:space="preserve">Excogitati ſunt autem <lb/>in iſtis planetis circuli Aequantes (non enim ſunt orbes reales, & </s> <s xml:id="echoid-s17481" xml:space="preserve">partes ſphe <lb/>rarum planetarum, quemadmodum Deferens, & </s> <s xml:id="echoid-s17482" xml:space="preserve">eccentrici ſecũdum quid: </s> <s xml:id="echoid-s17483" xml:space="preserve">fed <lb/>ſolum imaginarij.) </s> <s xml:id="echoid-s17484" xml:space="preserve">ut irregularitas Deferentis cuiuslibet planetæ ad æqualita <lb/>tem reuocetur beneficio proprij Aequantis, vt ex Theoricis liquido conſtabit. <lb/></s> <s xml:id="echoid-s17485" xml:space="preserve">Habet quoque quilibet Deferens planetæ duos alios eccentricos ſecundum <lb/>quid, unum ſupra ſe, alterum uero infra, ut de Sole diximus, qui appellantur <lb/>deferentes augẽ. </s> <s xml:id="echoid-s17486" xml:space="preserve">Solus Mercurius habet quatuor orbes eccentricos ſecundum <lb/>quid, quorum duo dicuntur Deferentes augem eccentrici, ſeu deferentis Mer <lb/>curium, alij duo deferentes augem Aequantis.</s> <s xml:id="echoid-s17487" xml:space="preserve"/> </p> <div xml:id="echoid-div938" type="float" level="2" n="1"> <note position="left" xlink:label="note-496-01" xlink:href="note-496-01a" xml:space="preserve">Cut æquan <lb/>tes orbes <lb/>ſint in pla-<lb/>netis exco-<lb/>gitati.</note> </div> <p> <s xml:id="echoid-s17488" xml:space="preserve"><emph style="sc">Qvilibet</emph> porro planeta, excepto Sole, habet pręter dictos circulos <lb/>adhuc epicyclum, hoc eſt, orbem paruulum in orbe deferente immerſum, in <lb/>quo defertur planeta. </s> <s xml:id="echoid-s17489" xml:space="preserve">Eſt enim corpus planetæ in epicyclo infixum: </s> <s xml:id="echoid-s17490" xml:space="preserve">Centrum <lb/>tamen epicycli perpetuo defertur ad motum eccentrici, ſeu deferentis. </s> <s xml:id="echoid-s17491" xml:space="preserve">cæte-<lb/>rum hæc vix, aut difficile intelligi poſſunt abſque inſtrumentis Theoricarum. <lb/></s> <s xml:id="echoid-s17492" xml:space="preserve">Vberius tamen omnia hæc exponemus in Theoricis planetarum.</s> <s xml:id="echoid-s17493" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div940" type="section" level="1" n="361"> <head xml:id="echoid-head373" style="it" xml:space="preserve">DE STATIONE, DIRECTIONE, ET <lb/>Retrogradatione Planetarum.</head> <p style="it"> <s xml:id="echoid-s17494" xml:space="preserve">SI igitur duæ lineæ ducantur acentro terræ, ita quod includant epi-<lb/> <anchor type="note" xlink:label="note-496-02a" xlink:href="note-496-02"/> cyclum alicuius planetæ, una ex parte orientis, reliqua ex parte occi-<lb/>dentis, punctus contactus ex parte orientis dicitur ſtatio prima; </s> <s xml:id="echoid-s17495" xml:space="preserve">punctus <lb/>uero contactus ex parte occidentis, dicitur ſtatio ſecunda. </s> <s xml:id="echoid-s17496" xml:space="preserve">Et quando <lb/>planeta eſt in alterutra illarum ſtationum, dicitur ſtationarius. </s> <s xml:id="echoid-s17497" xml:space="preserve">Arcus <lb/>uero epicycli ſuperior inter duas ſtationes interceptus, dicitur directio. <lb/></s> <s xml:id="echoid-s17498" xml:space="preserve">Et quando planeta eſt in illo, tunc dicitur directus. </s> <s xml:id="echoid-s17499" xml:space="preserve">Arcus uero epicy-<lb/>cli inferior inter duas ſtationes interceptus, dicitur retrogradatio. </s> <s xml:id="echoid-s17500" xml:space="preserve">Et <lb/>planeta ibiexiſtens dicitur retrogradus. </s> <s xml:id="echoid-s17501" xml:space="preserve">Lunę autem non asſignatur ſta <lb/>tio, directio, uel retrogradatio. </s> <s xml:id="echoid-s17502" xml:space="preserve">Vnde non dicitur Luna ſtationaria, di-<lb/>recta, uel retrograda, propter uelocitatem motus centri epicycli in ec-<lb/>centrico.</s> <s xml:id="echoid-s17503" xml:space="preserve"/> </p> <div xml:id="echoid-div940" type="float" level="2" n="1"> <note position="left" xlink:label="note-496-02" xlink:href="note-496-02a" xml:space="preserve">Pasſiones <lb/>planetarum <lb/>uariæ.</note> </div> <pb o="461" file="497" n="498" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div942" type="section" level="1" n="362"> <head xml:id="echoid-head374" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s17504" xml:space="preserve"><emph style="sc">Agit</emph> iam de paſſionibus quibuſdã planetarũ, videlicet de ſtatione plane-<lb/>tarum, directione, & </s> <s xml:id="echoid-s17505" xml:space="preserve">retrogradatione. </s> <s xml:id="echoid-s17506" xml:space="preserve">Dicit itaque, ſi ducantur duæ lineæ re-<lb/>ctæ à centro terræ con tingentes epicyclum, una ex parte orientis, altera vero <lb/>ex parte occidentis, puncta illa contactus dicuntur ſtationes, punctũ quidem <lb/>ex parte orientis, ſtatio prima: </s> <s xml:id="echoid-s17507" xml:space="preserve">ex parte autem occidentis, ſtatio ſecunda. </s> <s xml:id="echoid-s17508" xml:space="preserve">Pla-<lb/>neta igitur in alterutra illarũ ſtationum exiſtẽs dicitur ſtationarius, quia tũe <lb/>uidetur nobis planeta in ſuo epicyclo quodammodo ſtare, & </s> <s xml:id="echoid-s17509" xml:space="preserve">non mutare lo-<lb/>cum in Zodiaco ad motum eius in epicyclo, quoniam tunc uel aſcendit, uel <lb/>deſcendit. </s> <s xml:id="echoid-s17510" xml:space="preserve">Quod ſi ſtationem ſimpliciter intelligere uelimus, ita ut intelliga <lb/>mus punctũ epicycli, in quo cum planeta exiſtit, talẽ inter ſe proportionem <lb/>habent motus eccentrici, & </s> <s xml:id="echoid-s17511" xml:space="preserve">motus epicycli, ut omnino in eodem Zodiaci lo-<lb/>co planeta uideatur conſiſtere, fiet hoc paulo infra illa puncta contactus, vt <lb/>in Theoricis explicatur. </s> <s xml:id="echoid-s17512" xml:space="preserve">Arcus deinde epicycli, in quit, ſuperior inter duas ſta-<lb/>tiones interceptus, dicitur directio planetæ, planetaq́. </s> <s xml:id="echoid-s17513" xml:space="preserve">in eo exiſtens directus <lb/>uocatur, quia tunc mouetur ſecũdum ſncceſſionem, & </s> <s xml:id="echoid-s17514" xml:space="preserve">ordinem ſignorũ, hoc <lb/>eſt, ab occaſu in ortum, puta ab ♈, in ♉, ex ♉, in ♊, &</s> <s xml:id="echoid-s17515" xml:space="preserve">c. </s> <s xml:id="echoid-s17516" xml:space="preserve">Arcus uero inferior <lb/>dicitur retrogradatio, planetaq́. </s> <s xml:id="echoid-s17517" xml:space="preserve">ibi cõſtitutus, nuncupatur retrogradus, quia <lb/>incedit tunc contra ſignorum ſucceſſionem, ac ſeriem, id eſt, ab ortu in occa-<lb/>ſum, nempe ex ♈, in ♓, ex ♓ in ♒, & </s> <s xml:id="echoid-s17518" xml:space="preserve">c. </s> <s xml:id="echoid-s17519" xml:space="preserve">Quæ omnia intelligenda ſunt in pla-<lb/>netis habentibus epicyclũ, excepta Luna, ita ut in Sole, ac Luna hæc locũ nõ <lb/>habeant. </s> <s xml:id="echoid-s17520" xml:space="preserve">Nam planetarum epicycli, Luna dempta, mouentur in parte ſupe-<lb/>riori ſecundum ſucceſſionem ſignorum, in inferiori autem contra ſignorum <lb/>ſeriem. </s> <s xml:id="echoid-s17521" xml:space="preserve">Lunæ autem epicyclus è contrario mouetur contra ſucceſſionẽ ſigno-<lb/>rum in parte ſuperiori, ſecundũ vero ſeriem ſignorum in parte inferiori. </s> <s xml:id="echoid-s17522" xml:space="preserve">Vn-<lb/>de deberet Luna dici directa, quãdo eſt in inferiori parte epicycli, ꝗa ibi mo-<lb/>uetur ſecundum ſeriem ſignorum, retrograda uero in ſuperiori parte eiuſdẽ <lb/>collocata. </s> <s xml:id="echoid-s17523" xml:space="preserve">Verũtamen Luna neq; </s> <s xml:id="echoid-s17524" xml:space="preserve">dicitur directa, neq; </s> <s xml:id="echoid-s17525" xml:space="preserve">retrograda, ꝓpter uelo-<lb/> <anchor type="note" xlink:label="note-497-01a" xlink:href="note-497-01"/> cem motum ipſius in eccentrico. </s> <s xml:id="echoid-s17526" xml:space="preserve">Mouetur. </s> <s xml:id="echoid-s17527" xml:space="preserve">n. </s> <s xml:id="echoid-s17528" xml:space="preserve">Luna ad motum centri epicycli <lb/>in ſuo deferẽte uelociſſime ab occaſu in ortum. </s> <s xml:id="echoid-s17529" xml:space="preserve">Vnde dici non poterit ſtatio-<lb/>naria, neq; </s> <s xml:id="echoid-s17530" xml:space="preserve">directa, neque retrograda, quia motus cẽtri epicycli in deferente <lb/>vincit motũ propriũ epicycli: </s> <s xml:id="echoid-s17531" xml:space="preserve">Dicitur tamen in parte epicycli inferiori conſti-<lb/>tuta uelox, & </s> <s xml:id="echoid-s17532" xml:space="preserve">in ſuperiori, tarda, qm̃ ibi geminatur quaſi eius motus ab occaſu <lb/>in ortum, hic uero quodammodo retardatur, ut in Theoricis erit perſp@cuũ.</s> <s xml:id="echoid-s17533" xml:space="preserve"/> </p> <div xml:id="echoid-div942" type="float" level="2" n="1"> <note position="right" xlink:label="note-497-01" xlink:href="note-497-01a" xml:space="preserve">Cur Luna <lb/>nõ dicatur <lb/>ſtationaria <lb/>directa, vel <lb/>retrograda.</note> </div> </div> <div xml:id="echoid-div944" type="section" level="1" n="363"> <head xml:id="echoid-head375" style="it" xml:space="preserve">DE ECCLIPSI LVN AE</head> <p style="it"> <s xml:id="echoid-s17534" xml:space="preserve">CVM antem ſit Sol maior terra, neceße eſt, quod medietas ſphęrę <lb/> <anchor type="note" xlink:label="note-497-02a" xlink:href="note-497-02"/> terrę à Sole ſemper illuminentur, & </s> <s xml:id="echoid-s17535" xml:space="preserve">umbra terrę extenſain aere torna-<lb/>tilis minuatur in rotunditate, donec deficiat in ſuperficie circuli, ſignorum, <lb/>inſepar abilis à Nadir Solis. </s> <s xml:id="echoid-s17536" xml:space="preserve">Eſt autem Nadir Solis, punctus directe op-<lb/> <anchor type="note" xlink:label="note-497-03a" xlink:href="note-497-03"/> poſitus Soli in Firmamento. </s> <s xml:id="echoid-s17537" xml:space="preserve">Vnde cum in plenilunio Luna fuerit in capi-<lb/>te uel in cauda Draconis ſub Nadir Solis, tunc terra interponetur Soli, & </s> <s xml:id="echoid-s17538" xml:space="preserve"><lb/>Lunę: </s> <s xml:id="echoid-s17539" xml:space="preserve">Et conus umbrę terrę cadet ſuper corpus Lunę. </s> <s xml:id="echoid-s17540" xml:space="preserve">Vnde cum Luna <lb/>lumen non habeat niſi à Sole, in rei ueritate deficit à lumine. </s> <s xml:id="echoid-s17541" xml:space="preserve">Et eſt ecli-<lb/> <anchor type="note" xlink:label="note-497-04a" xlink:href="note-497-04"/> pſis generalis in omni terra, ſi ipſa fuerit in capite, uel cauda Draconis <lb/>directe: </s> <s xml:id="echoid-s17542" xml:space="preserve">Particularis uero, ſi fuerit prope intra metas determinatas ecli- <pb o="462" file="498" n="499" rhead="Comment in IIII. Cap. Sphæræ"/> pſi. </s> <s xml:id="echoid-s17543" xml:space="preserve">Et ſemper in plenilunio, uel circa contingit eclipſis. </s> <s xml:id="echoid-s17544" xml:space="preserve">Vnde cum non in <lb/> <anchor type="note" xlink:label="note-498-01a" xlink:href="note-498-01"/> qualibet oppoſitione, hoc eſt, plenilunio, ſit Luna in capite, uel cauda Dra-<lb/>conis, aut prope, nec ſuppoſita Nadir Solis, non eſt neceße, in quolibet ple <lb/>nilunio Lunam pati eclipſim.</s> <s xml:id="echoid-s17545" xml:space="preserve"/> </p> <div xml:id="echoid-div944" type="float" level="2" n="1"> <note position="right" xlink:label="note-497-02" xlink:href="note-497-02a" xml:space="preserve">Vmbra ter-<lb/>ræ conica.</note> <note position="right" xlink:label="note-497-03" xlink:href="note-497-03a" xml:space="preserve">Nadir So-<lb/>lis quid.</note> <note position="right" xlink:label="note-497-04" xlink:href="note-497-04a" xml:space="preserve">Eclipſis Lu <lb/>næ qñ fia@.</note> <note position="left" xlink:label="note-498-01" xlink:href="note-498-01a" xml:space="preserve">Cur non in <lb/>omni pleni <lb/>@unio fiat <lb/>@clipſis Lu-<lb/>@æ.</note> </div> </div> <div xml:id="echoid-div946" type="section" level="1" n="364"> <head xml:id="echoid-head376" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s17546" xml:space="preserve"><emph style="sc">Explicat</emph> hic, quonam pacto fiat eclipſis Lunæ, & </s> <s xml:id="echoid-s17547" xml:space="preserve">cur non patiatur <lb/>Luna eclipſim in omni plenilunio. </s> <s xml:id="echoid-s17548" xml:space="preserve">Cum enim Sol ſit multo maior quã terra, <lb/>vt in 1. </s> <s xml:id="echoid-s17549" xml:space="preserve">ca. </s> <s xml:id="echoid-s17550" xml:space="preserve">docuimus, neceſſe eſt, ut demõſtrat Vitellio lib. </s> <s xml:id="echoid-s17551" xml:space="preserve">2. </s> <s xml:id="echoid-s17552" xml:space="preserve">Peſpectiuæ, pro-<lb/>poſ. </s> <s xml:id="echoid-s17553" xml:space="preserve">27. </s> <s xml:id="echoid-s17554" xml:space="preserve">plus medietate terræ à Sole illuminari, & </s> <s xml:id="echoid-s17555" xml:space="preserve">propterea umbrã terræ ſimi <lb/>lem eſſe cono, ſeu turbini, cuius uertex a ſuperficie Eclipticæ nunquã recedit <lb/>eo quod neq; </s> <s xml:id="echoid-s17556" xml:space="preserve">centrum Solis ab eadẽ deflectat, ſemperq́ue eſt Soli oppoſitus, <lb/>cum terra ſit in centro Eclipticæ, nempe totius mundi. </s> <s xml:id="echoid-s17557" xml:space="preserve">Ex quo manifeſtũ eſt <lb/>cum fiat pleniluniũ, qñ Sol, ac Luna exiſtunt in gradibus per diametrum op-<lb/>poſitis; </s> <s xml:id="echoid-s17558" xml:space="preserve">Luna autẽ nõ ſit ſub Ecliptica, niſi quando fuerit in capite uel cauda <lb/>Draconis, ut paulo ante diximus; </s> <s xml:id="echoid-s17559" xml:space="preserve">in eo plenilunio dũtaxat Lunã pati eclipſim <lb/>in quo reperietur uel in capite, uel in cauda Draconis. </s> <s xml:id="echoid-s17560" xml:space="preserve">Ita enim fiet, ut Luna <lb/>ingrediatur umbrã terræ, impediaturq́; </s> <s xml:id="echoid-s17561" xml:space="preserve">quo minus a Sole illuſtretur. </s> <s xml:id="echoid-s17562" xml:space="preserve">Vnde cũ <lb/>ipſa lumen ſuũ a Sole mutuetur, neceſſe eſt, eam tunc deficere: </s> <s xml:id="echoid-s17563" xml:space="preserve">lumineq; </s> <s xml:id="echoid-s17564" xml:space="preserve">de-<lb/>ſtitui, eo quòd tunc terra interponitur præciſe inter Solẽ ac Lunã. </s> <s xml:id="echoid-s17565" xml:space="preserve">Tota qui-<lb/>dem Luna obſcurabitur in omni terra, ſi ipſa in plenilunio præciſe in capite, <lb/>uel cauda Draconis extiterit, quia tota intra umbrã mergetur: </s> <s xml:id="echoid-s17566" xml:space="preserve">Nõ tota uero, <lb/>ſi in pleniluino ꝓpe caput uel caudã Draconis reperta fuerit, ita tamẽ, ut um <lb/>bra terræ contegat partẽ aliquã Lunæ. </s> <s xml:id="echoid-s17567" xml:space="preserve">Ex his perſpicuũ eſt, cur philoſophi di-<lb/>cant, Eclipſim Lunæ eſſe interpoſitionẽ terræ inter Solẽ, atq; </s> <s xml:id="echoid-s17568" xml:space="preserve">Lunã; </s> <s xml:id="echoid-s17569" xml:space="preserve">quia ve-<lb/>re in eclipſi Lunæ exiſtit terra in eadẽ diametro, in qua dicti planetæ collocã <lb/>tur eo tẽpore, & </s> <s xml:id="echoid-s17570" xml:space="preserve">ſecundũ quã opponũtur. </s> <s xml:id="echoid-s17571" xml:space="preserve">Quoniã vero ut plurimum oppoſi-<lb/>tiones luminariũ fiunt, Luna non exiſtẽte in capite, uel cauda Draconis, neq; <lb/></s> <s xml:id="echoid-s17572" xml:space="preserve">ita prope, ut ab umbra poſſit cõtegi, idcirco nõ ſemper cõtingit eclipſis Lunæ <lb/>in omni Plenilunio. </s> <s xml:id="echoid-s17573" xml:space="preserve">Debet nãq; </s> <s xml:id="echoid-s17574" xml:space="preserve">Luna eſſe uel ĩ capite, uel in cauda Draconis, <lb/>vt eclipſis fiat. </s> <s xml:id="echoid-s17575" xml:space="preserve">Quæ quidem omnia clariora erunt in Theoricis planetarum.</s> <s xml:id="echoid-s17576" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div947" type="section" level="1" n="365"> <head xml:id="echoid-head377" xml:space="preserve">DE ECLIPSI SOLIS.</head> <note position="left" xml:space="preserve">Eclipſis So-<lb/>lis quando <lb/>fiat.</note> <p style="it"> <s xml:id="echoid-s17577" xml:space="preserve"><emph style="sc">Cvm</emph> autem Luna fuerit in capite, uel caude Draconis, uel prope, <lb/>uel intra metas ſupradictas, & </s> <s xml:id="echoid-s17578" xml:space="preserve">in coniunctione cum Sole, tunc corpus <lb/>Lunare interponetur inter aſpectum noſtrum, & </s> <s xml:id="echoid-s17579" xml:space="preserve">corpus Solare. </s> <s xml:id="echoid-s17580" xml:space="preserve">Vnde <lb/>obumbrabit nobis claritatem Solis, & </s> <s xml:id="echoid-s17581" xml:space="preserve">ita Sol patietur eclipſum, non quia <lb/>deficiat lumine, ſed deficit nobis, propter interpoſitum Lunę inter aſpe-<lb/>ctum noſtrum, & </s> <s xml:id="echoid-s17582" xml:space="preserve">Solare corpus. </s> <s xml:id="echoid-s17583" xml:space="preserve">Ex his patet, quod non ſempær eſt ecli-<lb/> <anchor type="note" xlink:label="note-498-03a" xlink:href="note-498-03"/> pſis Solis in coniunctione, ſiue in nouilunio. </s> <s xml:id="echoid-s17584" xml:space="preserve">Notandum etiam quod quan <lb/>do eſt eclipſis Lunę, eſt eclipſis in omni terra, ſed quando eſt eclipſis So-<lb/>lis, nequaquam: </s> <s xml:id="echoid-s17585" xml:space="preserve">Immo in uno climate eſt eclipſis, & </s> <s xml:id="echoid-s17586" xml:space="preserve">in alio non. </s> <s xml:id="echoid-s17587" xml:space="preserve">Quod con-<lb/>tingit propter diuerſitatem aſpectus in diuerſis climatibus. </s> <s xml:id="echoid-s17588" xml:space="preserve">Vnde Virgilius <lb/>elegantiſſime naturas utriuſque eclipſis ſub compendio tetigit, dicens.</s> <s xml:id="echoid-s17589" xml:space="preserve"/> </p> <div xml:id="echoid-div947" type="float" level="2" n="1"> <note position="left" xlink:label="note-498-03" xlink:href="note-498-03a" xml:space="preserve">Eclip ſis Lu <lb/>næ fit in re-<lb/>ta terra, ſed <lb/>Eclipſis So-<lb/>lis non.</note> </div> <p> <s xml:id="echoid-s17590" xml:space="preserve">Defectus Lunæ uarios, Solisq́; </s> <s xml:id="echoid-s17591" xml:space="preserve">labores.</s> <s xml:id="echoid-s17592" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s17593" xml:space="preserve">EX prædictis patet quod cum eclipſis Solis eſſet in paſſione domini <pb o="463" file="499" n="500" rhead="Ioan. de Sacro Boſco."/> & </s> <s xml:id="echoid-s17594" xml:space="preserve">eadẽ pasſio eſſet in plenilunio, illa eclipſis nõ fuit natur alis, immo mi-<lb/> <anchor type="note" xlink:label="note-499-01a" xlink:href="note-499-01"/> raculoſa, & </s> <s xml:id="echoid-s17595" xml:space="preserve">cõtraria naturæ, quia eclipſis Solis in nouilunio, uel circa de-<lb/>bet contingere. </s> <s xml:id="echoid-s17596" xml:space="preserve">Propter quod legitur, Dionyſiũ Areopagitã in eadem paſ-<lb/>ſione dixiſſe: </s> <s xml:id="echoid-s17597" xml:space="preserve">Aut Deus naturę<unsure/> patitur, aut mundi machina diſſoluetur.</s> <s xml:id="echoid-s17598" xml:space="preserve"/> </p> <div xml:id="echoid-div948" type="float" level="2" n="2"> <note position="right" xlink:label="note-499-01" xlink:href="note-499-01a" xml:space="preserve">Eclipſis So-<lb/>lis in paſ-<lb/>ſione Do-<lb/>mini fuit <lb/>miraculo-<lb/>ſa.</note> </div> </div> <div xml:id="echoid-div950" type="section" level="1" n="366"> <head xml:id="echoid-head378" xml:space="preserve">COMMENTARIVS.</head> <p> <s xml:id="echoid-s17599" xml:space="preserve"><emph style="sc">Postremo</emph> explicat, quonam modo fiat eclipſis Solis, dicens, Quan-<lb/>docunq. </s> <s xml:id="echoid-s17600" xml:space="preserve">Luna coniuncta cũ Sole, hoc eſt, in Nouilunio extiterit uel in capite, <lb/>vel in cauda Draconis, uel certe prope, intra tñ metas eclipſis, interponetur <lb/>inter aſpectum noſtrum, & </s> <s xml:id="echoid-s17601" xml:space="preserve">Solẽ: </s> <s xml:id="echoid-s17602" xml:space="preserve">Vnde occultabit nobis Solis claritatem, fietq́; <lb/></s> <s xml:id="echoid-s17603" xml:space="preserve">eclipſis Solis, nõ quod re ipſa Sol lumine deſtituatur, ſed reſpectu tantũmodo <lb/>noſtri, ob illam interpoſitionem Lunæ inter uiſum noſtrum, & </s> <s xml:id="echoid-s17604" xml:space="preserve">corpus Solare.</s> <s xml:id="echoid-s17605" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17606" xml:space="preserve"><emph style="sc">Neqve</emph> uero in omni coniunctione Lunæ cũ Sole, hoc eſt, nouilunio <lb/>eclipſis Solis continget, quia in omni coniũctione Luna ſeſe interponit inter <lb/>Solẽ, & </s> <s xml:id="echoid-s17607" xml:space="preserve">noſtrũ aſpectũ, ſed ſolummodo, quando ita Luna Soli coniungitur, id <lb/> <anchor type="note" xlink:label="note-499-02a" xlink:href="note-499-02"/> eſt, ita in eodẽ ſigno & </s> <s xml:id="echoid-s17608" xml:space="preserve">gradu exiſtit, in quo Sol, vt linea a noſtro oculo egre-<lb/>diens, & </s> <s xml:id="echoid-s17609" xml:space="preserve">per centrum Lunæ ducta ad Solẽ pertingat: </s> <s xml:id="echoid-s17610" xml:space="preserve">Quod fiet, quando Luna <lb/>in nouilunio reperta fuerit in capite Draconis, uel cauda, uel certe prope.</s> <s xml:id="echoid-s17611" xml:space="preserve"/> </p> <div xml:id="echoid-div950" type="float" level="2" n="1"> <note position="right" xlink:label="note-499-02" xlink:href="note-499-02a" xml:space="preserve">Cur non in <lb/>omni No-<lb/>uilunio ſit <lb/>eclip ſis So-<lb/>lis.</note> </div> <p> <s xml:id="echoid-s17612" xml:space="preserve"><emph style="sc">Docet</emph> deinde, id diſcriminis eſſe inter eclipſim Solis, ac Lunæ, quòd <lb/>eclipſis Lunæ uniuerſalis eſt in omni terra, ita ut in omnibus regionibus defi-<lb/>ciat lumẽ eius: </s> <s xml:id="echoid-s17613" xml:space="preserve">Solis uero eclipſis nequaquã un@uerſalis eſt, ſed poteſt eſſe ecli <lb/>pſis Solis in uno climate, & </s> <s xml:id="echoid-s17614" xml:space="preserve">in alio nõ; </s> <s xml:id="echoid-s17615" xml:space="preserve">lmmo in uno maior, & </s> <s xml:id="echoid-s17616" xml:space="preserve">in altero minor <lb/>eſſe poteſt: </s> <s xml:id="echoid-s17617" xml:space="preserve">Quia eclipſis Solis dependet ex aſpectu noſtro, qui diuerſus eſt in <lb/>diuerſis climatibus, ut in Theoticis explicatur: </s> <s xml:id="echoid-s17618" xml:space="preserve">Lunæ vero Eclipſis minime, <lb/>ſed tantum ex umbraterræ, quæ in omni climate ſemper eſt eadem.</s> <s xml:id="echoid-s17619" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17620" xml:space="preserve">Ex prædictis infert tandem auctor, quod cũ eclipſis Solis neceſſario fiat in <lb/>Nouilunio, ſeu in coniunctione Lunæ cũ Sole, illa eclipſis Solis, quæ contigit <lb/>in paſſione Domini, quando erat pleniluniũ, nõ fuit Naturalis, ſed miraculo-<lb/>ſa, & </s> <s xml:id="echoid-s17621" xml:space="preserve">contra Naturæ curſum, ac ordinem. </s> <s xml:id="echoid-s17622" xml:space="preserve">Potentia enim diuina Luna, relicto <lb/>ſuo proprio curſu, ad Solem acceſſit, ipſumq; </s> <s xml:id="echoid-s17623" xml:space="preserve">nobis occultauit. </s> <s xml:id="echoid-s17624" xml:space="preserve">Atq; </s> <s xml:id="echoid-s17625" xml:space="preserve">ob id, vt <lb/>teſtantur hiſtoriæ, Beatus Dionyſius Areopagita exclamauit eo tempore: </s> <s xml:id="echoid-s17626" xml:space="preserve">Aut <lb/>Deus Naturæ patitur, aut mundi machina diſſoluetur; </s> <s xml:id="echoid-s17627" xml:space="preserve">propter quòd erexerũt <lb/>altare conſecratum a Deo, quem illis paulo poſt B. </s> <s xml:id="echoid-s17628" xml:space="preserve">Paulus man@feſtauit, at-<lb/>que ita ad fidem, & </s> <s xml:id="echoid-s17629" xml:space="preserve">agnitionem ueri Dei perduxit, qui eſt Benedictus, & </s> <s xml:id="echoid-s17630" xml:space="preserve">glo-<lb/>rioſus in ſecula ſeculorum. </s> <s xml:id="echoid-s17631" xml:space="preserve">Amen.</s> <s xml:id="echoid-s17632" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17633" xml:space="preserve"><emph style="sc">Qvoniam</emph> uero quæ auctor in hoc cap. </s> <s xml:id="echoid-s17634" xml:space="preserve">de motibus planetarum, & </s> <s xml:id="echoid-s17635" xml:space="preserve">eclipſi <lb/>bus Solis ac Lunæ ſcripſit, adeo obſcura ſunt, ut paucis explicarinequeant; </s> <s xml:id="echoid-s17636" xml:space="preserve">Vi-<lb/>ſum hoc eſt loco (Id quod ſtudioſo Lectori pergratũ fore, cõplures mihi ſigni <lb/>ficarunt, atq; </s> <s xml:id="echoid-s17637" xml:space="preserve">adeo, ut hoc ipſum facerem, me impulerunt) tabulas quaſdam <lb/>ſubiũgere, quæ omnẽ doctrinã Theoricarũ planetarũ, quaſi in ſpeculo quodã, <lb/>ante oculos nobis proponant. </s> <s xml:id="echoid-s17638" xml:space="preserve">Quæ quidem tabulæ olim aberudito quodam <lb/>uiro compoſitæ ſunt, ſed eas nos incommodiorem formam redegimus, adie-<lb/>ctis, ex probatis ſcriptoribus, diſtantijs centrorum orbiũ eccentricorũ, & </s> <s xml:id="echoid-s17639" xml:space="preserve">Epi-<lb/>cyclorum à centro mundi, & </s> <s xml:id="echoid-s17640" xml:space="preserve">magnitudinibus ſemidiametrorũ eorundem or-<lb/>biũ in partibus, quarũ terræ ſemidiameter eſt una. </s> <s xml:id="echoid-s17641" xml:space="preserve">Rationes autem, quibus hæc <lb/>omnia inueſtigari poſſint, & </s> <s xml:id="echoid-s17642" xml:space="preserve">examinari, (Diſtantias enim cẽtrorum, & </s> <s xml:id="echoid-s17643" xml:space="preserve">magni-<lb/>tudines ſemid@ametrorũ examinare per tempus hic non licuit, ſed eas ex alijs, <lb/>auctoribus, ut ſcriptæ ſunt, accepimus) in noſtris theoricis explicabuntur.</s> <s xml:id="echoid-s17644" xml:space="preserve"/> </p> <pb o="464" file="500" n="501" rhead="Comment in IIII. Cap. Sphæræ"/> </div> <div xml:id="echoid-div952" type="section" level="1" n="367"> <head xml:id="echoid-head379" xml:space="preserve">THEORICA ORBIVM.</head> <note position="right" xml:space="preserve"> <lb/>ORBES PAR- \\ ticulare-, quibus \\ tota ſphæra *** \\ conſtat. # NOMINA AC \\ ſitus orbium pai \\ ticularium reſpe \\ ctu cẽtri mundi. # CENTRA \\ orbiũ, & cen- \\ trorum diſtã- \\ tiæ à centro \\ mundi. # AXES \\ orbium ſuper \\ quibus mouen \\ tur. <lb/>DVOAV- \\ gem eccentrici \\ deferentes. # CONCEN- \\ TRICI quo- \\ ad ſuperficies ex \\ tremas, ſphæris \\ ***, & ♀, conti \\ guas, ſecundũ re- \\ liquas, vero eccẽ \\ trici. Ideo vocati \\ eccentrici ſecun \\ dum quid. # MVNDI, \\ quoad extre- \\ mas ſuperſi- \\ cies. # ECLIPTI- \\ CAE octauæ \\ ſphæræ. <lb/>ECCEN- \\ TRICVS \\ deferens corpus \\ Solare. # ECCENTRI- \\ CVS ſimpliciter. # PROPRIVM \\ diſtãs à cẽtro \\ mundi uerſus \\ augem parti- \\ bus 44. min. 2 \\ quarũ terręſe \\ midiameter \\ habet unam. \\ Vel \\partibus 2. mi. \\ 16 {1/10}. qua- \\ rũ ſemidiame \\ ter eccentrici \\ habet 60. # AE QVI- \\ diſtans axi Ecli \\ pticæ octauæ \\ ſphæræ. <lb/></note> <pb o="465" file="501" n="502" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div953" type="section" level="1" n="368"> <head xml:id="echoid-head380" xml:space="preserve">ET MOTVVM *** SOLIS.</head> <note position="right" xml:space="preserve"> <lb/>POLI or- \\ bium, ſuper \\ quibus mouẽ \\ tur. # MOTVS propij, \\ fiue reuolutiones \\ orbium. # SEMIDIAME- \\ tri orbium in par- \\ tibus, quarũ ſemi- \\ diameter terræ eſt \\ vna. # SVPERFICIES \\ planæ orbiũ ad pla- \\ nũ Eclipticę inclina \\ tæ. # AVX Ec- \\ centrici, ad \\ annũ Chri \\ ſti 1554. <lb/>ECLIPTI \\ cæ octauę \\ ſphęræ. # AB occidente in \\ orientem, ideſt, ſe \\ cũdum ordinem \\ ſignorũin 49000. \\ annis. # PAR. MIN. \\ 1121. # 21. \\ quoad concauum: \\ at quoad conue- \\ xum. \\ 1216. # 5. # SVB Ecliptica \\ ſemper octauæ ſphę \\ ræ. # S. G. M. \\ 3. 1. 40. <lb/>ÆQVE re \\ motia polis \\ Eclipticæ o- \\ ctauæ ſphęrę # AB Occidente \\ in orientẽ in die- \\ bus 365. Hor. 5. \\ Min. 49. fere. # PAR. MIN. \\ 1165. # 23 # SVB Ecliptica \\ ſemper octauæ ſphę \\ ræ. <lb/></note> <pb o="466" file="502" n="503" rhead="Comment. in IIII. Cap. Sphæræ"/> </div> <div xml:id="echoid-div954" type="section" level="1" n="369"> <head xml:id="echoid-head381" xml:space="preserve">THEORICA ORBIVM,</head> <note position="right" xml:space="preserve"> <lb/>##### Sphę ☽, quinque orbes conſtituunt. <lb/># ORBES parti \\ culares, quibus \\ tota ſphæra ☽, \\ conſtat. # NOMINA, \\ ac ſitus orbium \\ particulariũ re- \\ ſpectu centrimũ \\ di. # CENTRA or- \\ bium, & centrorum \\ diſtantiæ à centro \\ mundi. # AXES or \\ bium, ſuper \\ quibus mo- \\ ucntur. <lb/># 2. AVGEM \\ Eccentrici defe \\ rentes. # CONCEN \\ trici partim, uti \\ deferentes Au- \\ gem ***. Inde Ec \\ cẽtrici ſecundũ \\ quid uocati. # MVNDI, quoad \\ ſuperficies extre. \\ mas. # AXEM \\ Eclipticæ ſu \\ per centro \\ mũdi inter- \\ ſecans. <lb/># ECCENTRI- \\ cusdeferẽs Epi- \\ cyclum. # ECCENTRI \\ cus ſimpliciter. # PROPRIVM \\ ad motum deferen \\ tium Augem mobi \\ le, diſtans à centro \\ mundi ſemidiame- \\ tris terrę 10. M. 9. \\ Vel Par. 12. Min. \\ 28 {1/2}. quarum ſemi \\ diameter Eccẽtrici \\ habet 60. # AEQVI- \\ diſtãs axi De \\ ferentiũ Au \\ gem. <lb/># DEFERENS \\ caput Draconis # CONCEN- \\ tricus mundo. # MVNDI. # ECLIPTI- \\ cæ. <lb/># EPICYCLVS. # TOTVS ex- \\ tra centrũ mun- \\ di circumfertur. # PROPRIVM \\ diſtans à centro mũ \\ di inęqualiter, à \\ centro tamen Ec- \\ centrici partib. 48. \\ M. 56. quarum ſemi \\ diameter terræ ha- \\ bet unam. # PERPEN- \\ dicularis ad \\ planum Ec- \\ centrici, & \\ Axi Eccen- \\ trici æquidi \\ ſtans. <lb/></note> <pb o="467" file="503" n="504" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div955" type="section" level="1" n="370"> <head xml:id="echoid-head382" xml:space="preserve">ET MOTVM ☽ LVNÆ.</head> <note position="right" xml:space="preserve"> <lb/>POLI or. \\ biũ, ſuper \\ quibus mo \\ uentur. # MOTVS pro \\ prij, ſiue reuolu- \\ tiones orbium. # SEMIDIAME \\ tri orbium in par- \\ tibus, quarũ ſemi- \\ diameter terræ eſt \\ vna. # SVPERFICIES \\ planæ orbium ad pla \\ nũ Eclipticæ inclina- \\ tæ. # AVX. Ec- \\ cẽtrici, ad \\ annũ Chri \\ ſti 1554. <lb/>DECLI- \\ nantes æ- \\ qualiter à \\ polis Zo- \\ diaci gr. 5. # AB Oriente in \\ occidentem in \\ diebus 32. H. 3. \\ Min. 5. # PAR. MIN. \\ 33. # 42. \\ quoad concauum. \\ Secundum@conue- \\ xum autem \\ 64. # 29. # DECLINANS \\ ab Ecliptica vtrinque \\ <lb/>declinatione fixa \\ gr. 5. # MOBIlis \\ ab ortuver \\ ſus occasũ \\ ad motum \\ deferẽtiũ \\ Augẽ Ec- \\ centrici \\ quotidie \\ gr. 11. M. 11. \\ Sec. 52. <lb/>ÆQVA- \\ liter diſtã \\ tes à polis \\ deferentiũ \\ Augem. # AB occaſu uerſus \\ ortum, id eſt, ſecũ \\ dum ſignorum \\ ſucceſſionem in \\ diebus 27. H. 7. \\ Min. 43. # PAR. MIN. \\ 48. # 56. # DECLINANS \\ ab Ecliptica vtrinque \\ gr. 5. & à plano defe \\ rentium Augem nũ \\ quam recedens. <lb/>ECLI- \\ pticæ. # AB ortu in oc- \\ caſum, i. contra ſi \\ gnorum ordinem \\ in annis 18. Mẽſ. \\ 7. diebus 12. # PAR. MIN. \\ 64. # 29. # SVB Ecliptica octa- \\ uæ ſphæræ. <lb/>ÆQVA- \\ liter remo \\ ti ab Axe, \\ ſeu polis \\ Eccẽtrici. # CONTRA ſi- \\ gnorũ ſequelã, i. \\ ab ortu in occasũ \\ i ſuperiori parte: \\ In inferiori autẽ \\ ſecundum ordinẽ \\ ſignorum, i. ab oc \\ caſu in ortum in \\ diebus 27. H. 13. \\ Min. 18. # PAR. MIN. \\ 5. # 5. \\ Vel in partibus, \\ quarum ſemidia- \\ meter Eccentrici. \\ habet 60. \\ 6. # 14. # DECLINANS \\ ab Ecliptica, & à ſu- \\ perficie plana Eccen \\ trici nunquam rece- \\ dens. <lb/></note> <pb o="468" file="504" n="505" rhead="Comment. in IIII. Cap. Sphæræ"/> </div> <div xml:id="echoid-div956" type="section" level="1" n="371"> <head xml:id="echoid-head383" xml:space="preserve">THEORICA ORBIVM.</head> <note position="right" xml:space="preserve"> <lb/>##### Sphæram 5. 4, ***, quaterni ſingulas orbes conſtiruunt: quin \\ etiam anintus concipiendus eſt, Æquans Ec- \\ centricus, qui ſolus circulus eſt. <lb/># ORBES par- \\ ticulares, ꝗ \\ bus totę ſphę \\ ræ variant. ♃. ***. \\ conſtant. # NOMINA ac \\ ſitus orbiũ par- \\ ticularium, re- \\ ſpectu centri \\ mundi. # CENTRA Orbium, & \\ centrorum diſtantiæ à cẽ \\ tro mundi. # AXES Or \\ bium, ſuper \\ quibus mouẽ \\ tur. <lb/># DVO Au- \\ gem Eccen- \\ trici deferen \\ tes. # CONCEN- \\ trici partim, & \\ Eccentrici ſecũ \\ dum quid, uti \\ deferentes au- \\ gem ***, & ☽. # MVNDI, quoad extre- \\ mas ſuperficies. Nam ſu- \\ perficies Eccentrico con- \\ tiguæ idem cẽtrum, quod \\ Eccentricus habent. # ECLIPTI- \\ cæ octauæ \\ ſphæræ. <lb/># ECCEN- \\ tricus defe- \\ rens Epicy- \\ clum. # ECCENTRI- \\ cus abſolute, \\ uel Deferens. # PROPRIVM, diſtans à \\ centro mundi ſemidia \\ metris terrę. # SECANS \\ axem Eclipti \\ cæ, ſed extra \\ centrum mũ \\ di. <lb/># # # variant. 980. # Min. 53. <lb/># # In # ♃. 532. # Min. 12. <lb/># # # ***. 503. # Min. 12. <lb/># # # Vel partibus. <lb/># # # variant. 3. # Min. 25. <lb/># # In # ♃. 2. # Min. 45. <lb/># # # ***. 6. # Min. 0. <lb/># # quarum ſemidiameter Ec \\ centrici habet 60. <lb/># AEQVANS \\ circulus. # AEQVANS \\ Eccentricus. # PROPRIVM, diſtans a \\ centro mundi duplo di- \\ ſtantiæ centri Eccentrici \\ à centro mundi. # AE QVIDI- \\ ſtans axi De- \\ ferentis uel \\ Eccentrici. <lb/># EPICY- \\ clus. # TOTVS ex- \\ tra centrum mũ \\ di. # PROPRIVM, inæqua- \\ liter à centro mundi re \\ motum. Iuxta quantitatẽ \\ uero ſemidiametri Eccen \\ trici, uel Deferentis à cen \\ tro Eccentrici. # MOBILIS \\ propter mo- \\ tum latitudi- \\ nis. <lb/></note> <pb o="469" file="505" n="506" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div957" type="section" level="1" n="372"> <head xml:id="echoid-head384" xml:space="preserve">ET MOTVVM @. ♃. ***.</head> <note position="right" xml:space="preserve"> <lb/>POLI or- \\ bium, ſuper \\ quibus moue \\ tur. # MOTVS ꝓprij, \\ ſiue reuolutiones \\ orbium. # SEMIDIAME \\ tri orbium in par- \\ tibus, quarũ ſemi- \\ diameter terrę eſt \\ vna. # SVPERFICIES \\ planæ orbium ad pla \\ nũ Eclipticæ inclina- \\ tæ. # AVX Ec \\ centrici, ad \\ annũ Chri- \\ ſti 1554. <lb/>ECLIPTI. \\ cæ octauæ \\ ſphæræ. # AB occaſu in or \\ tum, ideſt, ſecun- \\ dum ſignorum ſe \\ riem, in annis \\ 49000. # PAR. MIN. \\ quoad cõcauum. \\ variant. 14378. 19. \\ ♃. 8853. 47. \\ ***. 1216. 5. \\ quoad cõuexum. \\ variant. 22612. 30. \\ ♃. 14378. 19. \\ ***. 8853. 47. # SVB Ecliptica, \\ octauæ ſphęrę. # S. G. M. \\ variant \\ 8. 13. 28. \\ ♃ \\ 5. 23. 52. \\ *** \\ 4. 15. 27. <lb/>INÆQVA- \\ liter à polis \\ Eclipticæ de- \\ clinantes; po- \\ lus enim Se- \\ ptentrionalis \\ magis diſtat, \\ quàm auſtra- \\ lis. # AB occaſu in or- \\ tum, ideſt, ſecun- \\ dum ſignorũ ſuc- \\ ceſſionem, in an- \\ nis. \\ variant. 29. D. 155. H. 8. \\ ♃. 11. D. 313. \\ H. 17. \\ ***. 1. D. 321. \\ H. 22. # PAR. MIN. \\ variant. 17225. 16. \\ ♃. 11611. 31. \\ ***. 5032. 4. # DECLINANS \\ ab Ecliptica, declina \\ tione fixa, ita ut au- \\ ges ſemper in Boreã \\ uergant, & nunquam \\ Eclipticam pertran- \\ ſeant, deſeribantq́ue \\ Eclipticę octauę ſphę \\ rę circulos paralle- \\ los, uirtute motus \\ octauę ſphęrę. <lb/>ÆQVIDI- \\ ſtantes polis \\ Eccẽtrici, vel \\ Deferentis. # AB occaſu in or- \\ tum, ad motum \\ Eccẽtrici, ſeu De- \\ ferentis. # PAR. MIN. \\ variant. 17225. 16. \\ ♃. 11611. 31. \\ ***. 5032. 4. # DECLINANS \\ ab Ecliptica, & pla- \\ no Eccentrici nun- \\ quam recedens. <lb/>MOBILES, \\ propter mo- \\ tum latitudi- \\ nis. # SECVNDVM ſi- \\ gnorũ ordinẽ, id \\ eſt, ab occidẽt@ in \\ oriẽtem, in parte \\ ſuperiori: In infe- \\ riori autem con- \\ tra, ideſt, ab ortu \\ in occaſum, i Die \\ bus. \\ variant. 378. H. 2. \\ M. 23. \\ ♃. 398. H. 21. \\ M. 12. \\ ***. 779. H. 22. \\ M. 23. # PAR. MIN. \\ variant. 1866. 4. \\ ♃. 2225. 32. \\ ***. 3312. 47. \\ Vel in partibus, \\ quarum ſemidia- \\ meter Eccentrici \\ habet 60. \\ variant. 6. 30 \\ ♃. 11. 30 \\ ***. 39. 30 # DECLINANS \\ ab Ecliptica, In no- \\ dis tantum inclina- \\ tione carens. <lb/></note> <pb o="470" file="506" n="507" rhead="Comment. in IIII. Cap. Sphæræ"/> </div> <div xml:id="echoid-div958" type="section" level="1" n="373"> <head xml:id="echoid-head385" xml:space="preserve">THEORICA ORBIVM.</head> <note position="right" xml:space="preserve"> <lb/>##### Sphæram ♁<unsure/> quatuor prbes conſtituunt, quin & circulus alius \\ Æquans Eccentricus concipiendus eſt. <lb/># ORBES, qui- \\ bus tota ſphæra \\ ♀, conſtat. # NOMINA, \\ ac ſitus orbium \\ particularium re- \\ ſpectu centri mun \\ di. # CENTRA or \\ bium, & centrorum \\ diſtantiæ à centro \\ mundi. # AXES or- \\ bium, ſuper \\ quibus mo- \\ uentur. <lb/># 2. AVGEM \\ Eccentrici defe- \\ rentes. # CONCEN- \\ trici partim, & Ec- \\ centrici ſecundum \\ quid, ut in præce- \\ dentibus. # MVNDI, quoad \\ ſuperficies extre- \\ mas. Nam ſuperfi \\ cies Eccentrico cõ \\ tiguæ idem cẽtrum \\ <lb/>habent, quod <lb/>Eccẽ \\ tricus. # ECLIPTI- \\ cæ octauæ \\ ſphęrę. <lb/># ECCENTRI \\ cus deferens Epi- \\ cyclum. # ECCENTRI- \\ cus abſolute, uel \\ Deferens. # PROPRIVM di- \\ ſtans à cẽtro mũdi \\ <lb/>ſemidiametris ter- \\ ræ. 12. Min. 7. # A C C E- \\ dens, & rece- \\ dens ab Axe \\ Eclipticę pro \\ pter motũ Ec \\ <lb/>centrici in la \\ titudinẽ nũc \\ in Boream, \\ nunc in Au- \\ ſtrum. <lb/># # Vel partibus, qua- \\ rũ Eccentrici ſemi- \\ diameter eſt una. <lb/># # 1. Min. 8. <lb/># ÆQVANS \\ circulus. # AE QVANS \\ Eccentricus. # PROPRIVM \\ diſtans duplo plus \\ à centro mũdi, quã \\ centrum Eccentri- \\ ci, uel Deferentis. # AE Q V I- \\ diſtãs axi Ec- \\ centrici, uel \\ Deferentis. <lb/># EPICYCLVS. # TOTVS extra \\ mundi centrum \\ fertur. # PROPRIVM \\ à centro mundi dif \\ formiter diſtãs: iux \\ ta quantitatẽ uero \\ ſemidiametri Eccẽ \\ trici, uel Deferetis \\ à centro Eccentri- \\ ci. # MOBILIS \\ tam ad mo- \\ tum inclina- \\ tionis, quàm \\ reflexionis. <lb/></note> <pb o="471" file="507" n="508" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div959" type="section" level="1" n="374"> <head xml:id="echoid-head386" xml:space="preserve">ET MOTVVM ♀ VENERIS.</head> <note position="right" xml:space="preserve"> <lb/>POLI or \\ bium, ſuper \\ quibus mouẽ \\ tur. # MOTVS pro- \\ prij, ſiue reuolu- \\ tiones, orbium. # SEMIDIA \\ metri orbiũ in \\ pa@tibus, quarũ \\ ſemidiame@er \\ te@ræ eſt unà. # SVPERFICIES \\ <lb/>planæ orbium ad pla- \\ num Eclipticæ inclina \\ tæ. # AVX Ec- \\ centrici@ad \\ annũ Chri \\ ſti 1<unsure/>554. <lb/>ECLIPTI \\ cæ octauæ \\ ſpbæræ. # A B occaſu in or \\ tum, id eſt, ſecun \\ dum fignorũ ſuc \\ ceſſionem, in an- \\ nis 49000. # P A R. M I N \\ q@oad conca \\ uum. # S V B Ecliptica, octauæ \\ ſphæræ. # S. G. M. \\ 3. 2. 40. <lb/># # 67. 57. \\ at quoad con \\ uexum. <lb/># # 1. 21. 21. <lb/>MOBILES \\ ob iam dictũ \\ motum Eccẽ \\ trici in latitu \\ dinem. # A B occaſu in or \\ tum, id eſt, ſecun- \\ dum ſignorum or \\ <lb/>dinem, in diebus \\ 365. Hor. 5. \\ Min. 49. # PAR. MIN \\ 641. 45. # DECLINANS ab \\ Ecliptica, declinatione \\ mobili, quę Deuiatio <lb/>uo \\ catur; Epicyclum tamen \\ nunquam in meridiẽ, ſed \\ Septentrionẽ uerſus per \\ petuo retorquens ab Ecli \\ ptica, ut in Paſſionibus \\ planetarum explicatur. <lb/>AEQVIDI \\ ſtantes polis \\ Deferentis, \\ vel Eccentri- \\ ci. # A B occaſu in or- \\ tum ad motum Ec \\ centrici, ſeu Defe \\ <lb/>rentis. # P A R. M I N. # DECLINANS ab \\ Ecliptica, nunquã tamen \\ à plano Eccentrici rece- \\ dens, ſed eandem ſemper \\ <lb/>Deuiationem retinens. <lb/># # 641. 45. <lb/>MOBILES \\ cnm ad motũ \\ inclinationis \\ tum reflexio \\ nis. # SECVNDVM ſi \\ gnorũ ſequelã, id \\ eſt, ab occaſu in \\ ortum in parte ſu \\ periori: In inferio \\ ri aũt contra. i. ab \\ ortu in occaſum, \\ in diebus 583. # P A R. M I N. # A C C E D E N S \\ & recedens@ ab Ecl@ptica \\ propter motum deuiatio- \\ nis, inclinationis, & refle- \\ xionis, eam tamen nun- \\ quam tranſiens meri- \\ diem uerſus. <lb/># # 461. 41. <lb/># # Vel in partibus \\ quarum ſemi- \\ diameter Eccẽ \\ trici habet 60. <lb/># # 43. 10. <lb/># H. 22. M. 12. <lb/></note> <pb o="472" file="508" n="509" rhead="Comment. in IIII. Cap. Sphæræ"/> <note position="right" xml:space="preserve"> <lb/>##### Sphæram ☿,<unsure/> ſex orbes conſtitunnt; quin etiam duo circuli Eccen- \\ trici ſunt concipiendi, Aequans, & paruus. <lb/># ORBES \\ particula - \\ res, quibus \\ tota ſphęra \\ ☿. conſtat. # NOMINA ac \\ ſitus orbiũ par \\ ticularium, re- \\ ſpectu cẽtri mũ \\ di. # CENTRA Orbium, & \\ centrorum diſtantiæ à cen \\ tro mundi. # AXES Or- \\ bium, ſuper \\ <lb/>quibus mouẽ \\ tur. <lb/># 2. A V- \\ gem Aequã \\ tis deferen- \\ tes. # CONCEN- \\ trici partim, & \\ Eccentrici ſecũ \\ dum quid. # MVNDI, quoad ſuperfi- \\ cies extremas: quoad medias \\ autem proprium centrum \\ habẽt, idem nimirum, quod \\ <lb/>circulus paruus. # ECLIPTI- \\ cæ octauæ \\ ſphæræ. <lb/># 2. A V \\ gem Eccen \\ trici deferẽ \\ tes. # ECCENTRI- \\ ci omnino. # PROPRIVM, idem nem- \\ pe, quod circulus paruus, \\ quoad extremas ſuperficies: \\ quoad uero aliàs medias, \\ idem quod Eccentricus, ha \\ bentes. # ACcedens, & \\ recedẽs ab a- \\ xe Eclipticæ \\ octa. ſphæræ, \\ ob motũ Eccẽ \\ trici ĩ latitud. <lb/># E C C E N- \\ tricus defe- \\ rens Epicy- \\ clum. # ECCENTRI- \\ cus abſolute, \\ uel Deferens. # PROPRIVM mobile ad mo \\ tũ Deferẽtiũ augẽ Eccẽtrici \\ paruũ circulũ deſcribens, di- \\ ſtansq́; inæqualiter à centro \\ mũdi. Minima diſtantia con \\ tinet partes 3. Max.uero 9. \\ quarũ ſemidiameter Eccẽtri \\ ci hẽt 60. Vel Minima hẽt ſe \\ midiametros terræ 5. M. 48. \\ Maxima autem 17. Min. 24. # ÆQ V I D I- \\ ſtans axi Defe \\ rentium au- \\gem Eccentri \\ ci. <lb/># A E Q V A- \\ ns circulus. # A E Q V A N S \\ Eccentricus. # P R O P R I V M, diſtans à \\ centro mundi ſecundum mi \\ nimam diſtantiam centri Ec \\ centrici. # ÆQ V I D I- \\ ſtãs axi Defe- \\ rentium au- \\ gem Eccentri \\ ci. <lb/># C I R C V- \\ lus parnus. # T O T V S \\ extra centrum \\ mundi. # IDEM, quod Deferentium \\ augem Eccentrici. # I D E M, qui \\ Deferentium \\ augem Eccen \\ trici. <lb/># E P I C Y \\ clus. # T O T V S \\ extra centrum \\ mundi. # P R O P R I V M, diſtans à \\ centro Eccentrici iuxta ſe- \\ midiametri Eccentrici quan \\ titatem: à centro autem mũ- \\ di inæqualiter. # MOBILIS, tã \\ ad inclinatio- \\ nis, quàm re- \\ flexionis mo- \\ tum. <lb/></note> <pb o="473" file="509" n="510" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div960" type="section" level="1" n="375"> <head xml:id="echoid-head387" xml:space="preserve">ET MOTVM ☿ MERCVRII.</head> <note position="right" xml:space="preserve"> <lb/>POLI or. \\ biũ, ſuper \\ quibus mo \\ uentur. # M O T V S pro- \\ prij, ſiue reuolu- \\ tiones orbium. # S E M I D IAME- \\ tri orbium in par- \\ tibus, quarũ ſemi- \\ diameter terræ eſt \\ vna. # SVPERFICIES \\ planæ orbium ad pla \\ nũ Eclipticæ inclina- \\ tæ. # AVX Ec- \\ cẽtrici, ad \\ annũ Chri \\ ſti 1554. <lb/>E C L I- \\ pticæ octa \\ uæ ſphæ- \\ ræ. # AB occaſu in or \\ tum, id eſt, ſecun \\ dum ſigno<unsure/>rũ ſuc \\ ceſſionem, in an \\ nis 49000. # P A R. M I N. # S V B Ecliptica, \\ octauæ ſphæræ. # S. G. M. <lb/># # quoad concauum. # 7. 0. 54. <lb/># # 64. 59 <lb/># # quoad conuexum. <lb/># # 167 57 <lb/>M O B I \\ les, ppter \\ motũ Ec- \\ centrici in \\ latitudinẽ # A B ortu in oc- \\ caſum, id eſt, con \\ tra ſignorum or \\ dinem, in diebus \\ 365. H. 5. Min. # P A R. M I N. # DECLINANS \\ ab Ecliptica octauæ \\ ſphæræ, declinatione \\ mobili, Eccentrici \\ planum deuiare fa- \\ ciens. <lb/># # quoad concauum. <lb/># # 76. 5 <lb/># # quoad conuexum. <lb/># # 121. 51. <lb/>AEQVI- \\ diſtãtes po \\ lis Deferẽ \\ tium augẽ \\ Eccentri- \\ ci. # AB occaſu in or \\ tum, id eſt, ſecun \\ dum ſucceſſionẽ \\ ſignorum, in die \\ bus 365. H. 5. \\ Min. 49. # P A R. M I N. # DECLINANS \\ ab Ecliptica octauæ \\ ſphæræ, & nunquam \\ à plano Deferẽtium \\ augẽ Eccentrici rece \\ dẽs: Epicyclũ tñ ĩ me \\ ridiẽ ſemꝑ retorquẽs \\ ut in paſſionib. plane \\ tarum explicatur. <lb/># # 116. 3 <lb/>AEQVI- \\ liſtãtes po \\ @is Deferẽ \\ cium augẽ \\ Eccẽtrici. # AB occaſu in or \\ tum, ad motum \\ Eccentrici, ue@ \\ Deferentis. # P A R. M I N. # DECLINANS \\ ab Ecliptica octauæ \\ ſphærę, & à ſupe ficie \\ plana Eccentrici non \\ recedens. <lb/># # 116. 3. <lb/>I D E M, \\ qui Defe- \\ @ẽtium au \\ gem Eccẽ \\ trici. # A B ortu in oc \\ caſum, ad motum \\ Deferentiũ augẽ \\ Eccentrici. # P A R. M I N. # DECLINANS \\ ab Ecliptica, & à pla \\ no Deferentium au \\ gem non recedens. <lb/># # 5. 48 <lb/># # vel ĩ partib., quarũ \\ ſemidiameter Ec- \\ centrici habet 60. <lb/>M O B I- \\ les, ad mo \\ cum cũ in- \\ clinatiõis \\ tũ reflexio \\ nis. # A B occaſu in or \\ tum, id eſt, ſecun- \\ dum ſignorum ſe- \\ riẽ, in diebus 115. \\ Hor. 21. Min. 5. in \\ parte ſuperiori: in \\ inferiori autẽ cõ- \\ tra ſignorum ſe- \\ quelam. # P A R. M I N. # ACCEDENS, & \\ recedens ab Eclipti- \\ ca, propter motum \\ deuiationis, inclina- \\ tionis, & reflexionis; \\ eam tamen nunquam \\ uerſus Boream tran- \\ ſiens. <lb/># # 43. 31 <lb/># # Vel in partibus, \\ quarum ſemidia- \\ meter Eccentrici. \\ habet 60. <lb/># # 9. 0. <lb/></note> <pb o="474" file="510" n="511" rhead="Comment. in IIII. Cap. Sphæræ"/> </div> <div xml:id="echoid-div961" type="section" level="1" n="376"> <head xml:id="echoid-head388" xml:space="preserve">THEORICA ORBIVM, ETMOTVVM</head> <note position="right" xml:space="preserve"> <lb/># O R B E S, qui- \\ bus to@æ ſphæræ \\ conſtant. # NOMINA, ae \\ ſitus orbium reſpe \\ ctu centri mundi. # C E N T R A or- \\ bium. # A X E S \\ orbiũ, ſu- \\ per quib. \\ mouẽtur. <lb/>Primum Mobile \\ conſtituit orbis \\ vnicus. # O R B I S Vni- \\ cus, in quo decem \\ circuli, & alij com- \\ plures cõcipiũtur, \\ quorum præcipui \\ ſunt Aequinoctia- \\ lis, & Zodiacus. # C O N C E N- \\ tricus mundo. # M V N D I. # MVNDI. \\ in polum \\ vtrumque \\ deſinens. <lb/># # Primum mobile. <lb/>Sphæram nonam \\ conſtituit vnus \\ orbis. # VNVS orbis, in \\ quo præter Zodia- \\ cum, & duos circu \\ los paruos, nullus \\ alius intelligitur \\ circulus. # C O N C E N- \\ tricus. Nona ſphæ- \\ ra. # MVNDI. # ECLIP- \\ ticæ, uel \\ Zodiaci \\ primi mo \\ bilis. <lb/># # Secũdum mobile. <lb/>Sphæram octa- \\ uam unicus or- \\ bis conſtituit. # VNICVS or- \\ bis, in quo Zodia- \\ cus (Mobilis uo- \\ catus.) unà cum \\ ſtellis fixis exiſtit. \\ Diuiſus eſt autem \\ in 48. imagines cę \\ leſtes. # CONCENTRI- \\ cus. Octaua ſphæ- \\ ra. # MVNDI. # A C C E- \\ dens, & re \\ cedens ab \\ axe nonæ \\ ſphæræ. <lb/># # Firmamentum. <lb/></note> <pb o="475" file="511" n="512" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div962" type="section" level="1" n="377"> <head xml:id="echoid-head389" xml:space="preserve">PRIMI MOBILIS, NONAE SPHAERAE, ET OCTAVAE</head> <note position="right" xml:space="preserve"> <lb/>POLI or- \\ biũ, ſuper \\ quibus mo \\ uentur. # MOTVS proprij, \\ ſiue reuolutiones \\ orbium. # SEMIDIAME \\ tri orbium in par- \\ tibus, ex quibus ſe \\ midiameter terræ \\ habet unam. # SVPERFICIES \\ planæ Orbium. # AVX ad \\ annũ Chri \\ ſti. 1554. <lb/>MVNDI \\ Arcticus, \\ & Antar- \\ cticus. # AB Oriente in Oc \\ cidentem rediens \\ per mediam noctẽ \\ in Orientem in \\ hor. 24. & uocatur \\ Motus Raptus. # PAR. MIN. \\ 45225. 0. \\ & adhuc multo \\ maior. # PLANVM \\ Aequinoctialis cir \\ culi, a quo diſtat \\ planum eclipticæ \\ grad. 23. Min. 30. <lb/>ECLIP \\ ticę vel Zo \\ diaciprimi \\ mobilis. # AB Occidente \\ in Orientem re \\ currens in annis \\ 49000. & uocatur \\ Motus Augium. # PAR. MIN. \\ 45225. 0. \\ Et adhuc maior, \\ maior tamẽ quàm \\ ſemidiameter pri- \\ mi mobilis. # SVBEcliptica pri- \\ mi mobilis Eclipti \\ ca iſta perpetuo \\ manens. <lb/>ACCE \\ dentes, & \\ recedẽtes \\ ad motum \\ Axis. # ASEPTEN- \\ trione verſus ortũ, \\ recurrendo in ſe- \\ ptentrionem in an \\ nis 7000. ſuper \\ duobus circul@spar \\ uis, & uocatur mo \\ tus Trepidationis. # PAR. MIN. \\ 45225. 0. \\ quoad conuexum. \\ At quoad conca- \\ uum. \\ 32612. 30 # DECLINANS \\ frequẽter ab Ecli- \\ ptica tam nonæ \\ ſphærę, quàm Pri- \\ mi Mobilis. # AVX com \\ munis. \\ S. G. M. \\ 0. 20. 15. <lb/></note> <pb o="476" file="512" n="513" rhead="Comment. in IIII. Cap. Sphæræ"/> </div> <div xml:id="echoid-div963" type="section" level="1" n="378"> <head xml:id="echoid-head390" xml:space="preserve">DEFINITIONES TERMINORVM</head> <note position="right" xml:space="preserve"> <lb/># # *** # ☽ <lb/>HABITVDO PLA \\ netarum ad Solem. # SOL, TAN- \\ quam reliquorum \\ Planetarum prin- \\ ceps ad nullũ, ſed \\ omnes ad ipſum \\ quẽdam motus re \\ ſpectum habent. # DEFERENTESAV- \\ gem Eccentrici ita quotidie cõtra \\ ſignorum ordinẽ retrocedunt (Ec- \\ centrico tamen Epicyclũ interim \\ ſecundũ ſeriem ſignorum protru- \\ dente) ut linea medii motus ***, in \\ medio inter Augem Eccẽtrici ☽, \\ & Epicyclum ſemper reperiatur. \\ Quare in omni ☌, @ & oppoſitione \\ Epicyclus eſt in Auge: In quadra- \\ tura uero in Augis oppoſito. <lb/>AVX in 1. ſignificatione. # ## EST (in omnibus (punctum Ecccntrici a centro mundi re \\ Cuius oppoſitum eſt punctum eiuſdem Eccentrici terræ vi <lb/>AVX. in 2. ſignificatione. # ## EST (in omnibus) arcus Zodiaci à principio ♈, ſecundum <lb/>LONGITVDO media \\ Eccentrici. # ## EST punctum Eccentrici, quod eſtendit linea recta ad li- \\ neam Augis ad angulos rectos educta, in quo maxima ac- \\ cidit æquatio. <lb/>AVX Epicycli media. # # EST punctum Epicycli, quod \\ linea ex pũcto centro Eccentrici \\ oppoſito per cẽtrum Epicycli du \\ cta oſtendit. <lb/>AVX Epicycli vera. # # EST punctum circũferentię Epi-<lb/>LINEA medij motus \\ Planetæ. # EST quæ à cen- \\ tro mundi ad Zo- \\ diacum educitur \\ lineæ à centro, Ec- \\ centrici ad corpus \\ Solare exeunti æ- \\ quidiſtans. # EST, quæ a centro mundi per \\ centrum Epicycli uſq. ad Zodia- \\ cum protenditur. <lb/>LINEA ueri motus Pla- \\ netę. # ## EST quæ à centro mundi per corpus Planete educta, ad <lb/>Medius \\ Verus } Motus @ Planetę # ## EST arcus Zodiaci à principio ♈, ſecundum ſucceſſio-<lb/>Linea { Medij \\ Veri } Mot’ E \\ picycli. <lb/></note> <pb o="477" file="513" n="514" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div964" type="section" level="1" n="379"> <head xml:id="echoid-head391" xml:space="preserve">ASTRONOMICORVM.</head> <note position="right" xml:space="preserve"> <lb/>variant. # ♃. # ***. # ♀. # ☿. <lb/>### SINGVLI HORVM \\ planetarum tanto tempore re- \\ uoluuntur in ſuis Epicyclis, \\ quantum eſt à ☌, media cuiuſ \\ que eorum cum ***, vſque in ſe \\ quentem. Vnde in qualibet tali, \\ ☌, Planeta in Auge media ſui \\ Epicycli reperitur. # AVX ECCEN- \\ trici Augi ***, perpe \\ tuo cohæret. Sed & \\ medius ♀, motus sẽ \\ per idem eſt qui me \\ dius motus ***. \\ Hic media eorum \\ ☌, ſemper eſſe ſo- \\ let. # DEFERENTES AV- \\ gem Eccentrici vnà cum cen \\ tro Eccentrici contra ſigno- \\ rũ ſeriem in anno Solari re- \\ uoluuntur. Eccentricus ue- \\ ro in eodem tempore ſecun \\ dum eodem ſi gnorum mo- \\ uetur. Sed & cum ***, ſemper \\ ☌, mediam habet. vt Venus. <lb/>##### motiſſimũ, per lineã per utrũq; centrũ, mundi ſcilicet & Eccentrici, extenſam deſignatũ \\ ciniſſimum, in omnibus etiam, præterquam in ☿, ut in eius Theorica declaratur. <lb/>ſignorũ ſucceſſionẽ, uſq; ad lineã Augis computatus. In tabulis aux ſimpliciter uocatur. <lb/>##### # EST punctum Eccentrici, per lineam ex centro Eccentrici ad Augis lineam \\ ad angulos rectos eductam, oſtenſum. <lb/>##### # EST punctum circumſerentiæ Epicycli, per lineam à centro Aequantis per \\ centrum Epicycli eductam, terminatum. <lb/>##### cycli, quod indicat linea recta à centro mundi per centrum Epicycli protenſa. <lb/>##### # EST, quæ à centro mundi uſq; ad Zodiacum extenditur, lineæ ex centro \\ Aequantis per centrum Epicycli exeunti æquidiſtans. Vocaturq́ue linea me- \\ dij motus Planetæ, uel Epicycli in his 5. planetis. <lb/>##### Zodiacum uſque protenditur. <lb/>##### nem ſignorum uſque ad { Medij \\ Veri } Motus lineam numératus. <lb/>##### # EST, quę à cẽtro mũdi ad \\ Zodiacũ uſq; protenditur { Exeũti à cẽtro Aequãtis ad cẽtrũ Epicycli æquidiſtãs \\ Per centrum Epicycli tranſiens. <lb/></note> <pb o="478" file="514" n="515" rhead="Comment. in IIII. Cap. Sphæræ"/> </div> <div xml:id="echoid-div965" type="section" level="1" n="380"> <head xml:id="echoid-head392" xml:space="preserve">DEFINITIONES TERMINORVM.</head> <note position="right" xml:space="preserve"> <lb/># # *** # ☽ <lb/>Medius \\ Verus } Motus Epicycli <lb/>CENTRVM { Medium \\ Verum # # EST arcus Zodiaci inter li- \\ neam Augis Eccentrici, & li \\ neam medij motus ſecundũ \\ ſeriem ſignorum. Et dicitur \\ ſimpliciter centrum ☽. <lb/>Aequatio \\ centri { In Zodiaco \\ In Epicyclo # # EST arcus Epicycli inter \\ Augem eius mediam, & ue- \\ ram. Et dicitur ſimpliciter \\ Aequatio centri. <lb/>Argumentum { Medium \\ Verum # EST arcus Zodiaci inter \\ lineam augis, & lineam \\ medii motus comprehen \\ ſus. Et dicrtur ſimpliciter \\ Argumentum ***. # EST arcus Epicycli ab Auge eiuſ-<lb/>Aequatio Argumenti # EST arcus Zodiaci lineis \\ medij & ueri motus ***, \\ interiacẽs. Et dicitur ſim \\ pliciter Aequatio ***. # EST arcus Zodiaci inter li- \\ neas medij & ueri motus ☽, \\ cadens. <lb/>Compoſitio tabularum \\ Aequationum. # OMNIBVS Eccentrici \\ ſui locis cõmunis exiſtit # A D augem ſui Eccentrici. <lb/>DIVERSITAS \\ Diametri. # # EST exceſſus, quo Aequa \\ tiones Argumenti in oppoſi \\ to augis ſuperant Aequatio \\ nes in auge contingentes. <lb/>MINVTA Proportiona- \\ lia. # # SVNT particulæ exceſſus \\ lineæ augis ſuper lineam op \\ poſiti augis, diuiſi in 60. par- \\ tes æquales. <lb/>DIVERSITAS \\ Minutorum Proportiona \\ lium. # # SIMPLICIA, quia ad au- \\ gem Eccentrici omnia ſunt \\ intra Deferentem; ad oppo- \\ ſitum augis omnia extra. <lb/></note> <pb o="479" file="515" n="516" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div966" type="section" level="1" n="381"> <head xml:id="echoid-head393" xml:space="preserve">ASTRONOMICORVM.</head> <note position="right" xml:space="preserve"> <lb/>variant. # ♃. # ***. # ♀ # ☿ <lb/>#### EST arcus Zodiaci à principio ♈, ſecundum ſignorum \\ ſucceſsionem, uſque ad lineam # Medlj \\ Veri # Motus Epicycl <lb/>#### EST arcus Zodiaci à linea augis Eccentrici ſecundum \\ ſeriem ſignorum vſque ad lineam { Medij \\ Veri { Motus Epicycli <lb/>##### EST arcus { Zodiaci } \\ Epicycli # interceptus inter { lineas medij, & ueri motus Epicycli. \\ Augem mediam, & veram Epicycli. <lb/>##### dem { Media \\ Vera } ſecundum motũ Planetæ in Epicyclo, uſq. ad corpus ipſius ſupputatus <lb/>##### EST arcus Zodiaci lineis ueri motus Epicycli, & ueri motus Planetæ compre- \\ henſus. <lb/>### AD longitudines medias Eccentrici. # ## Ad ſitumi, ſiue diſtantiam S. 2. G. 4. \\ M. 30. ab Auge Aequantis. <lb/>### EST exceſſus Aequatio num argumentorũ in \\ oppoſito augis Eccẽtrici, ſuper lõgitudines me \\ dias, qui Propior uocatur. Et longitudinũ me- \\ diarũ ſuper Aequationes in Auge, qui Lõgior \\ dicitur. # ## EST differentia, qua Aequationes \\ argumentorum poſitę ad mediocrem \\ Epicycli à terra diſtantiam, differunt \\ ab Aequationibus in Auge, & mini- \\ ma diſtantia á terra. <lb/>### SVNT particulæ de exceſſu illo, quo linea au- \\ gis longior eſt latitudinum mediarum linea; & \\ hæc rurſus longior oppoſiti augis linea, utroq; \\ horum in 60. particulas ęqualees ſecto. # ## SVNT particulæ exceſſus lineæ augis \\ Aequantis, ſuper lineam mediocris \\ à terra diſtantię: Et rurſus huius ſuper \\ minimam diſtantiam, in 60. partes ę- \\ quales diſtributi. <lb/>### DVPLICIA, quia quædam ad augem Ec- \\ centrici omnia ſunt intra Deferentẽ; ſed ad lõ \\ gitudines medias omnia extra: Et dicuntur Mi- \\ nuta proportionalia longiora. Quędam autem \\ alia ad longitudines medias oĩa ſunt intra De \\ ferentim; ſed@ad oppoſitum augis omnia extra: \\ Et dicuntur Minuta Proportionalia. Propiora. # ## TRIPLICIA, Quædam enim ad au- \\ gẽ Aequatoris oĩa ſunt intra Deferen \\ tẽ, & ad medias longitudines oĩa ex \\ tra: Et dicũtur longiora. Quędam aũt \\ alia ad lõgitudines medias oĩa ſunt in \\ tra, & ad minimã à terra diſtantiã om \\ nia extra. Et dicuntur Propiora. Horũ \\ rurſum ad oppoſitũ augis Aequãtis \\ nõnulla ſunt intra, & nonnulla extra. \\ Tertia deniq; minuta proportionalia \\ ſunt particulæ exceſſus lineæ oppoſi- \\ ti augis ęquantis ſuper minimã à ter- \\ ra diſtantiã, &c. Qui exceſſus, qm̃ in- \\ ſenſibilis eſt, omittuntur propterea in \\ tabula hęc Minuta proportionalia. <lb/></note> <pb o="480" file="516" n="517" rhead="Comment. in IIII. Cap. Sphæræ"/> </div> <div xml:id="echoid-div967" type="section" level="1" n="382"> <head xml:id="echoid-head394" xml:space="preserve">PASSIONES</head> <note position="right" xml:space="preserve"> <lb/># *** # ☽ <lb/>PLANETÆ dicuntur { directi \\ Retrogradi \\ Stationarij # SOL ſemper eſt \\ Directus, cum nõ \\ habeat Epicyclũ. # LVNA ſemꝑ eſt Directa, \\ ꝗa cen trũ Epicycli maio- \\ rẽ arc ũ Zodiaci ad motum \\ Eccẽtrici ꝑcurrit ab occa \\ ſu in ortũ, quàm corpus ☽ \\ ad motũ Epicyli in ſupe- \\ riori parte contra ſignorũ \\ ordinem in quolibet die. <lb/>STATIO { Prima \\ Secunda <lb/>ARCVS { Directionis \\ Retrogradationis <lb/>CVRSV { Tardi, & minuti \\ Veloces, & aucti # ## QVANDO LINEA veri motus Planetę <lb/>Aucti \\ Minuti } Numero # ## QVANDO AE QVATIO argumenti <lb/>Aucti \\ Minuti { Lumine # # Quan- \\ do poſt { ☌ accedit à Sole. \\ oppoſitionẽ acce- \\ dit ad Solem. <lb/>ORIENTALES & Matutini \\ OCCIDENTALES & Veſpertini # # QVANDO { Mane ante So- \\ Veſperipoſt So <lb/>ORIENTES ortu { Matutino \\ Veſpertino # # HOC ortus genere caret, quia \\ propter uelocitatẽ eius Sol ab \\ ea recedere non poteſt. \\ DVM poſt ***, à Sole eo vſque \\ recedit, donec uideri incipiat. <lb/>OCCIDENTES occaſu { Matutino \\ Veſptino # # DVM poſt oppoſitionẽ ad So- \\ lem accedit, eius radijs tegi in- \\ cipiens. \\ HOC occaſu caret, cum ob ei’ \\ uelocitatem ab Solẽ accedere \\ non poſſit. <lb/>ASPECTVS Planetarũ { Trinus \\ Quadratus \\ Sextilis # EST, cum per # { Tertiam \\ Quartam \\ Sextam } Eclipticæ <lb/></note> <pb o="481" file="517" n="518" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div968" type="section" level="1" n="383"> <head xml:id="echoid-head395" xml:space="preserve">PLANETARVM.</head> <note position="right" xml:space="preserve"> <lb/>variant. # ♃. # ***. # ♀ # ☿. <lb/>##### QVANDO linea veri motus Planetæ { Progreditur ſecundũ \\ Regreditur contra \\ Sub vno Zodiaci loco ſtare videtur. # ſignorũ ſucceſſionẽ <lb/>### IN prima ſignificatione, eſt punctũ \\ Epicycli, in quo Planeta incipit # Regredi. \\ Dirigi. # In ſecunda aũt, eſt arcus ab auge Epi- \\ cycli, vſque ad iam dictum punctum. <lb/>EST arcus Epicycli, \\ à puncto ſtationis # Secundæ, per augem \\ Primæ per oppoſitũ augis # Epicycli, vſque \\ in punctum # Primæ \\ Secundæ # Statio- \\ nis. <lb/>Tardius \\ Velocius # #### quàm linea Medij motus, mouetur. <lb/>##### Additur Medio motui \\ Minuitur à Medio motu. <lb/>## QVANDO Sol # Recedit ab eis, \\ Accedit ad eos # Vel ipſi # à Sole. \\ ad Solem. <lb/>##### lem oriuntur. <lb/>##### lem occidunt. <lb/>##### QVANDO mane ante ***, ortum in plaga Orientali radios Solares exire, & nobis \\ apparere incipiunt, recedente ſcilicet Sole à variant, ♃, ***. Aut Venere, & Mercurio à Sole. <lb/>HI tres, quia propter tarditatem \\ eorum, à Sole recedere nequeũt, \\ tali ortus genere carent. # QVANDO à Sole tantum recedunt, ut in pla- \\ ga Occidentali, ueſperi apparere incipiunt. <lb/>### HI tres, propter eorum tardita- \\ tem, carent hoc occaſu. # ## DVM Soli tantum appropinquant, ut mane in pla \\ ga Orieutali apparere deſinant. <lb/>##### CVM ueſperi poſt Solis occaſum in plaga occidua radijs Solaribus tegi, ac nobis \\ ſenſim occultari incipiunt. <lb/>##### partem eorum uera loca diſtiterint. <lb/></note> <pb o="482" file="518" n="519" rhead="Comment. in IIII. Cap. Sphæræ."/> </div> <div xml:id="echoid-div969" type="section" level="1" n="384"> <head xml:id="echoid-head396" xml:space="preserve">PASSIONES</head> <note position="right" xml:space="preserve"> <lb/># # *** # ☾ <lb/>Coniunctio. { Media. \\ Vera. \\ Viſibilis. # FIT, quando lineæ # Mediorum \\ Verorum Ab oculo noſtro per corpora # Motuum ſecun-<lb/>Oppoſitio. { Media. \\ Vera. # FIT, quando lineæ # Mediorum \\ Verorum # Motuum ſecun-<lb/>Locus aſtri. { Verus. \\ Viſus. # ## EST punctum Firmamenti per lineam # A centro \\ Ab ocu-<lb/># Simpliciter, vel \\ in altitudine. # ### CIRCVLI magni ꝑ Zenith capitis, <lb/>Diuerſitas aſpectus. { In longitudine. \\ In latitudine. # EST arcus { ECLIPTICÆ terminatus duobus \\ CIRCVLI magni per locum uerum \\ alter per locũ verum, alter per locũ <lb/>Lunæ ad Solem. # QVO diuerſitas aſpectus Lunæ, tan-<lb/>Latitudo Lunæ viſa # EST arcus circuli magni, per polos Zodiaci, & locũ \\ tem per locum uiſum, interceptus. <lb/>Digiti Ecliptici # DICVNTVR duodecimæ partes. diametri cor-<lb/>Minuta # Caſus in eclipſi \\ Moræ in eclipſi Lunari. # Solari. \\ Lunari. # SVNT minuta Zodiaci, quæ Luna tan- \\ quã uelocior, Solem ſuperãdo percurrit # A princi \\ A princi \\ A princi <lb/></note> <note position="right" xml:space="preserve"> <lb/>Diameter viſualis # Solis. \\ Lunæ # IN auge \\ IN oppoſito augis # Eccentrici ſubtendit Mi-<lb/># IN auge Eccentrici # & auge Epicycli \\ & oppoſito augis Epicycli <lb/></note> <note position="right" xml:space="preserve"> <lb/>Stellæ # Declinatio. \\ Latitudo. # EST arcus circuli magni, per polos # Mundi \\ Zodiaci # tran-<lb/></note> <note position="right" xml:space="preserve"> <lb/>Latitudo Planetarum. # CARET latitudi- \\ ne. Nam Eccentri- \\ ci ſui plana ſuperfi- \\ cies à ſuperficio pla- \\ na Eclipticæ nuſ- \\ quam declinat. # SIMPLEX, propter declina- \\ tionem Eccentrici ab Eclipti \\ ca tantum recedentis, & Epi- \\ cycli planum ſemper ſecum \\ retinens. <lb/></note> <note position="right" xml:space="preserve"> <lb/>Argumentum latitudinis ☾ # Medium \\ Verum # EST arcus Zodiaci à linea veri motus capitis Drac@ <lb/></note> <pb o="483" file="519" n="520" rhead="Ioan. de Sacro Boſco."/> </div> <div xml:id="echoid-div970" type="section" level="1" n="385"> <head xml:id="echoid-head397" xml:space="preserve">PLANETARVM</head> <note position="right" xml:space="preserve"> <lb/>variant. # ♃. # ***. # ♀ # ☿ <lb/>##### dum Zodiaci longitudinem coniunguntur. \\ Planetarum ductæ coniunguntur in vnum. <lb/>##### dum Zodiaci longitudinem opponuntur. <lb/>##### mundi per ipſum aſtrum porrectam, determinatum. \\ lo noſtro per aſtrum extenſam demonſtratum. <lb/>##### & uerum locum aſtri tranſeuntis, uero loco, & apparenti eiuſdem interceptus. \\ circulis magnis à polis Zodiaci per locum uerum & uiſum productis. \\ aſtri, & polos Zodiaci tranſeuntis, interceptus duobus circulis Eclipticæ parallelis, quorũ \\ viſum incedit. \\ quam maior, diuerſitatem aſpectus Solis, tanquam minorem, ſuperat. <lb/>##### ☽, uerum, aut uiſum tranſeuntis, inter Eclipticam, & circulum ſibi æqu<unsure/>idiſtantẽ, inceden <lb/>##### poris Solaris, aut Lunaris, eclipſatæ. <lb/>##### pio Eclipſis Solaris, uſque ad eius medium. <lb/>##### pio Eclipſis Lunaris, vſq; ad { Mediũ eius, ſi fuerit particularis, aut vniuerſalis ſine mora. \\ Principiũ totalis obſcuratiõis, ſi vniuerſalis cũ mora fuerit <lb/>##### pio totalis obſcurationis, uſque ad medium Eclipſis Lunaris. <lb/>##### nuta # 31. \\ 34. <lb/>##### ſubtendit Minuta # 29. \\ 36. <lb/>##### ſeuntis, inter ſtellam & { Aequinoctialem \\ Eclipticam. { Interceptus. <lb/>### DVPLEX una propter \\ declinationẽ fixam Ec- \\ centrici ab Ecliptica: Al \\ tera propter Epicycli ſu \\ perficiem planã declinã \\ tẽ ab Eccentrico decli- \\ natione mobili, qua ac- \\ cedit & recedit à ſuꝑfi \\ cie plana Eccen <lb/>trici. \\ Hinc cõponitur latitu- \\ do trium Superiorum. # ## TRIPLEX, quarum prima uocatur Deuiatio. Et eſt de- \\ clinatio quædam mobilis Eccẽtrici ab Ecliptica, epicyclũ \\ tamen ♀, ſemper uerſus Boream, at ☿:<unsure/> ſemper uerſus auſtrũ \\ ab Ecliptica cõſeruantis. Secunda dicitur Declinatio, Vbi \\ ſcilicet diameter augis ueræ @picycli declinat à ſuperficie \\ plana Eccẽtrici, accedẽdo & recedendo ab eadem. Qui mo- \\ tus fit ſuper diametro longitudinum mediarum Epicycli. \\ Tertia uocatur Reflexio, Et eſt etiã auerſio quędã mobilis \\ diametri longitudinũ mediarũ Epicycli à ſuperficie plana \\ Eccentrici. Et fit ſuper diametro augis Epicycli, tanquam \\ axe. Ex quibus omnibus componitur latitudo ♀, & ☿ <lb/>nis, ad lineam { Medij Motu ☽, \\ Veri Motus ☽,} ſecundum ſignorum ſucceſſionem numeratus. <lb/></note> </div> <div xml:id="echoid-div971" type="section" level="1" n="386"> <head xml:id="echoid-head398" xml:space="preserve">FINIS QVARTI CAPITIS.</head> <pb file="520" n="521"/> </div> <div xml:id="echoid-div972" type="section" level="1" n="387"> <head xml:id="echoid-head399" xml:space="preserve">REGESTVM. <lb/>† † † ABCDEFGHIKLMNOPQRS <lb/>TVXYZ.</head> <p> <s xml:id="echoid-s17645" xml:space="preserve">Aa Bb Cc Dd Ee Ff Gg.</s> <s xml:id="echoid-s17646" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17647" xml:space="preserve">Omnes ſunt quaterniones præter G g, quę <lb/>quinternionem conſtituunt.</s> <s xml:id="echoid-s17648" xml:space="preserve"/> </p> <figure> <image file="520-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/520-01"/> </figure> </div> <div xml:id="echoid-div973" type="section" level="1" n="388"> <head xml:id="echoid-head400" xml:space="preserve">VENETIIIS. M D XCI.</head> <pb file="521" n="522"/> <pb file="522" n="523"/> <pb file="523" n="524"/> <handwritten/> <handwritten/> <handwritten/> <handwritten/> <pb file="524" n="525"/> </div></text> </echo>