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New Special Instructions
| author | Klaus Thoden <kthoden@mpiwg-berlin.mpg.de> |
|---|---|
| date | Wed, 30 Jul 2014 15:58:21 +0200 |
| parents | 22d6a63640c6 |
| children |
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<?xml version="1.0"?> <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd"> <archimedes xmlns:xlink="http://www.w3.org/1999/xlink"> <info> <author>Delfino, Federico</author> <title>De fluxu et refluxu aquae maris</title> <date>1559</date> <place>Venice</place> <translator/> <lang>la</lang> <cvs_file>delfi_fluxu_024_la_1559.xml</cvs_file> <cvs_version/> <locator>024.xml</locator> </info> <text> <front> </front> <body> <chap> <pb xlink:href="024/01/001.jpg"/><p type="main"> <s><emph type="center"/>FEDERICI DELPHINI, <lb/>MATHEMATICI PRAESTANTISSIMI, <lb/>DE FLVXV ET REFLVXV AQVAE MARIS, <lb/>SVBTILIS ET ERVDITA DISPVTATIOI<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> <s><emph type="center"/>Eiu&longs;dem<emph.end type="center"/><!-- REMOVE S--><emph type="center"/>DE MOTV OCTAVAE SPHAERAE.<emph.end type="center"/><!-- KEEP S--></s></p><figure id="id.024.01.001.1.jpg" xlink:href="024/01/001/1.jpg"/><p type="main"> <s><emph type="center"/>IN ACADEMIA VENETA, <lb/>M D LIX.<emph.end type="center"/><!-- KEEP S--></s></p><pb xlink:href="024/01/002.jpg"/><pb xlink:href="024/01/003.jpg"/><p type="main"> <s><emph type="center"/>ILLVSTRISSIMO ET REVERENDISS.<emph.end type="center"/><!-- REMOVE S--><emph type="center"/>CARDINALI TVRNONIO &c.<emph.end type="center"/></s></p><p type="main"> <s>VTINAM, uir præ&longs;tanti&longs;sime, cogitationes hominum uirtute præ­<lb/>&longs;tantium &longs;edem ac domicilium ita propinquum inuenirent in animis <lb/>Principum, & eorum, qui opibus abundant, ut ne diuturna peregri<lb/>natio, ante quàm ad agendum aggrederentur, uitam eorum termi­<lb/>naret. </s> <s>atque utinam potius, ut omni benignitate &longs;ubleuandi <expan abbr="&longs;u&longs;ten-tandi&qacute;">&longs;u&longs;ten­<lb/>tandique</expan>; &longs;unt, non contra multorum iniuriis uexarentur, <expan abbr="multa&qacute;">multaque</expan>;, ab <lb/>iniquis ad impediendum excogitata, reperirent, quibus in&longs;titutus <expan abbr="cũ">cum</expan> <lb/>laude cur&longs;us interrumpitur, & omnis ad præclare agendum uia plane <lb/>præcluditur. </s> <s>non enim earum modo uirtutum copia fioreret ætas no<lb/>&longs;tra, quæ antiquam exornarunt, atque illu&longs;trarunt; &longs;ed cum ueræ ac <lb/>diuinæ Chri&longs;tianæ religionis, diuino quodam munere, patefacta co­<lb/>gnitio &longs;it, qui fons uberrimus e&longs;t, ex quo bona omnia, ex quo ma­<lb/>nat ip&longs;a felicitas; fructus ferret ita præ&longs;tantes, ut antiquis &longs;æculis lon<lb/>ge omnibus antecelleret. </s> <s>propterea uidemus euenire ut, cum in ali<lb/>qua orbis terrarum parte tanquam ex nubibus huiu&longs;ce corruptæ æta­<lb/>tis lumen erumpit alicuius magnanimi <expan abbr="excel&longs;i&qacute;">excel&longs;ique</expan>; Principis; omnes <lb/>probitate ac uirtute præditi, non &longs;ecus atque uolucres, po&longs;t aliquod <lb/>dierum imbrem, lætæ &longs;olis radios excipientes, madefactas ac di&longs;si­<lb/>patas pennas exiccant, <expan abbr="apte&qacute;">apteque</expan>; conformant, recipiunt animos, <expan abbr="eos&qacute;">eosque</expan>; <lb/>ad illorum nomina per illu&longs;tres orbis terrarum partes ge&longs;tanda, & ad <lb/>eximias laudes longinquis nationibus &longs;ignificandas in&longs;tituunt. </s> <s>quæ <lb/>cum omnia, ut e&longs;t non minus prudentia <expan abbr="omni&qacute;">omnique</expan>; uirtute, quàm nobi<lb/>litate, excellens, Federicus Baduarius per&longs;picue uideret, <expan abbr="plane&qacute;">planeque</expan>; <lb/>intelligeret; mentem intendit in eam curam, ut tam multa <expan abbr="tam&qacute;">tamque</expan>; gra<lb/>uia, ingenuarum doctrinarum &longs;tudiis aduer&longs;a, nouis con&longs;iliis atque <lb/>in&longs;titutis, Deo duce, &longs;uperaret: & quemadmodum rapidis flumini­<lb/>bus, inu&longs;itato impetu extra ripas diffluentibus, ob&longs;i&longs;titur aggeribus <lb/>multiplici &longs;true lignorum compactis; ita multos in unum cœtum ui­<lb/>ros coegit, Chri&longs;tiana mente, <expan abbr="uitæ&qacute;">uitæque</expan> innocentia, & doctrinæ laude in <lb/>&longs;ignes: quo ex cœtu no&longs;tra exorta e&longs;t Academia: quæ tum in &longs;er­<lb/>monibus eruditis, ad litteras, aut ad præ&longs;entem rerum humana­<lb/>narum &longs;tatum &longs;pectantibus, horas collocans, <expan abbr="&longs;ua&qacute;">&longs;uaque</expan>;, aut aliorum <lb/>&longs;cripta, uel recentia, uel temporis uetu&longs;tate abdita, ingenio&longs;is cor­<lb/>rectionibus aut commentariis illu&longs;trans<gap/>, & ad communem &longs;tudio&longs;o­<lb/>rum utilitatem diuulgans, &longs;perat edituram &longs;e gentibus exempla ita <lb/>præclara, ut præ&longs;idiis ita firmis, ubi res po&longs;cere uidebitur, con&longs;titutis, <lb/>aut ita uitio&longs;is moribus extinctis atque &longs;ublatis, nouam imaginem, <lb/><expan abbr="nouam&qacute;">nouamque</expan> formam, &longs;i nos tanto munere Deus impertiuerit, orbis ter­<lb/>rarum accipiat. </s> <s>His no&longs;tris con&longs;iliis atque actionibus, minime dubi­<pb xlink:href="024/01/004.jpg"/>tamus, quin & omnes Principes bona mente præditi, & quicunque <lb/>&longs;ua uirtuti &longs;tudia dediderunt, magnopere faueant. </s> <s><expan abbr="iam&qacute;">iamque</expan>; &longs;atis mani­<lb/>fe&longs;ta elucere &longs;igna cernimus. </s> <s>ex quo uoluptatem capimus eiu&longs;modi, <lb/>ut, cum honor qua&longs;i pabulum &longs;it omnium artium, in hoc permanere <lb/>&longs;tatuamus excellenti in&longs;tituto, donec res ad optatum exitum tota <lb/>perducatur. </s> <s>Nam quis ita rudi, aut ita demi&longs;&longs;o e&longs;&longs;et animo, qui cum <lb/>honorificum &longs;ermonem à te, tam egregio Cardinali, tam graui ac &longs;a<lb/>piente uiro, no&longs;tra cum dignitate habitum, quem nobis rara uirtute <lb/>uir in&longs;ignis Bernardus Ta&longs;&longs;us narrauit, exaudiret, non &longs;e ip&longs;e acue­<lb/>ret, non qua&longs;i lima poliret, & ad &longs;ublimem ac nobilem rerum præ­<lb/>clari&longs;&longs;imarum cupiditatem erigeret? </s> <s>Hæc tua &longs;ingularis humanitas <lb/><expan abbr="eximia&qacute;">eximiaque</expan>; benignitas, uerbis amanti&longs;simis atque graui&longs;&longs;imis decla­<lb/>rata; tantum habet ponderis, <expan abbr="tantam&qacute;">tantamque</expan>; uim, ut po&longs;&longs;it nos, pro eo <lb/>quod ip&longs;i præ&longs;tare po&longs;&longs;umus, in iis actionibus confirmare, quæ ad <lb/>hanc u&longs;que diem cur&longs;um annorum tuorum, <expan abbr="animum&qacute;">animumque</expan>; tuum ita pro­<lb/>&longs;ecutæ &longs;unt, <expan abbr="ita&qacute;">itaque</expan>; muniuerunt, ut multo magis tibi mentes homi­<lb/>num deuinxerint, <expan abbr="clariorem&qacute;">clarioremque</expan>; tuo nomini gloriam pepererint, quàm <lb/>ullus unquam Princeps uel immen&longs;a exercituum, prouinciarum, re­<lb/>gnorum multitudine &longs;it adeptus. </s> <s>quæ quidem eo præ&longs;tantior e&longs;t, <expan abbr="eo&qacute;">eoque</expan>; <lb/>magis expetenda, quòd, cum à uera uirtute fluxerit, perpetuam fore <lb/>con&longs;tat: quæ uero pendet à terre&longs;tribus rebus, inanis pror&longs;us, cadu­<lb/>ca, mortalis e&longs;t. </s> <s>Neque tamen hæc tua tantum uerba præbere nobis <lb/>argumentum exi&longs;times &longs;ummæ tuæ uirtutis, <expan abbr="&longs;ummæ&qacute;">&longs;ummæque</expan>; probitatis. <lb/></s> <s>nam &longs;i pietas erga Deum infinita, non à te ad fictam &longs;peciem, &longs;ed ad <lb/>ueram fidem declarata; &longs;i erga inopes immen&longs;a tua benignitas, &longs;em­<lb/>per ex mi&longs;ericordia, non ex ambitione, deriuata; &longs;i prudentiæ &longs;in­<lb/>gularis in maximis maximorum Regum negociis, optimo ac laudabi<lb/>li mentis con&longs;ilio, non ob inanem aliquam laudis cupiditatem, exer<lb/>citata; &longs;i erga omnes, in quibus aliqua modo uirtus eniteat, eximia <lb/>liberalitas, ad uirtutem, non ad eam, quam aucupantur multi, famam <lb/>relata; &longs;i erga omnes homines immen&longs;a humanitas, ex benignitate <lb/>potius, quàm ex animi humilitate, exorta, non &longs;olum te apud ma­<lb/>ximum Regem tuum, <expan abbr="uniuer&longs;am&qacute;">uniuer&longs;amque</expan>; Galliam, &longs;umma tua fide, <expan abbr="&longs;in-gulari&qacute;">&longs;in­<lb/>gularique</expan>; con&longs;ilio iam per tot annos admini&longs;tratam, tanta in exi&longs;ti­<lb/>matione, atque auctoritate collocarunt, uerum etiam eos popu­<lb/>los, qui ob&longs;eruantiam ignorant, ad te tamen non mediocriter ob­<lb/>&longs;eruandum excitarunt, <expan abbr="fecerunt&qacute;">feceruntque</expan>; ut etiam inuidi, te admirentur, <lb/>omni procul amota & adulatione, & hominum intemperantium at­<lb/>que improborum iniquitate: quo nos animo decet e&longs;&longs;e, quibus u­<lb/>na propo&longs;ita uirtus e&longs;t, <expan abbr="qui&qacute;ue">quique</expan> in hac excel&longs;a urbe uiuentes, ocu­<lb/>lo quidem mentis Principes longe contemplamur, his autem cor­<lb/>poreis facile cernimus quanta in exi&longs;timatione, atque ob&longs;eruantia <lb/>&longs;is apud hanc &longs;ereni&longs;&longs;imam, ac &longs;apienti&longs;&longs;imam Rempublicam <expan abbr="apud&qacute;">apudque</expan>; <lb/>hos omnes populos, quibus & nunc & antehac tantarum, quæ in <pb xlink:href="024/01/005.jpg"/>te &longs;unt, uirtutum liberalitate, <expan abbr="&longs;imul&qacute;">&longs;imulque</expan>; tuæ Maie&longs;tatis illo frui contigit <lb/>a&longs;pectu, in quo, tanquam in lucidi&longs;&longs;imo cælo, &longs;plendent clari&longs;&longs;ima <lb/>&longs;idera, uel potius tuæ beatæ mentis puri&longs;&longs;imus <expan abbr="pulcherrimus&qacute;">pulcherrimusque</expan>; Sol. <lb/><!-- KEEP S--></s> <s>Nec tamen illud prætermittendum uidetur, quòd, cum tam illu&longs;tri <lb/>editus è &longs;tirpe &longs;is; cum honoribus cunctis, <expan abbr="animi&qacute;">animique</expan>; & corporis bo­<lb/>nis abundes; <expan abbr="cum&qacute;">cumque</expan>; tibi, tanta uirtute, tanta innocentia florenti, &longs;i­<lb/>ne ulla ueneni &longs;u&longs;picione liceat, tanquam monoceroti, ex omnibus <lb/>potare aquis actionum humanarum; tamen, cum illud e&longs;&longs;e uerum <lb/><expan abbr="unum&qacute;">unumque</expan>; bonum, quod ad Deum accedit, plane tibi per&longs;ua&longs;eris, ab­<lb/>ducis te, quantum potes, à cunctis negociis, atque à tot &longs;plendori<lb/>bus, qui te &longs;equuntur inuitum; <expan abbr="nos&qacute;">nosque</expan>; mones exemplo tuo, ut no­<lb/>&longs;trarum uoluntatum nauem con&longs;ilio regamus, ne illam fallaces ab&longs;or<lb/>beant fluctus, in quibus ip&longs;e tam &longs;æpe, tanta tranquillitate, tam fe­<lb/>lici cur&longs;u nauiga&longs;ti. </s> <s>Con&longs;tantiam ergo tuebimur; <expan abbr="ea&qacute;">eaque</expan>; duce, &longs;pera­<lb/>mus fore, ut aliquando te&longs;tatum apud omnes relinquamus, quem­<lb/>admodum nemo te omnium, qui uiuunt, uirtute anteit, & à fortu­<lb/>næ bonis egregie paratus es, ita neminem fore, qui aut iudicii te&longs;ti<lb/>monium illu&longs;trius, aut ueræ erga te præbeat ob&longs;eruantiæ. </s> <s>Quòd &longs;i <lb/>munus hoc, nunc à nobis ad te mi&longs;&longs;um, minime tibi fui&longs;&longs;e ingratum <lb/>cognouerimus: non modo iacta e&longs;&longs;e præclara operis à nobis in&longs;tituti <lb/>fundamenta, uerum aditum etiam aliquem ad &longs;peratam perfectio­<lb/>nem e&longs;&longs;e patefactum exi&longs;timabimus. </s> <s>Munus ip&longs;um in&longs;igne admodum <lb/>e&longs;t, tum quia nobili&longs;&longs;imum ac perdifficile continet argumentum, de <lb/>fluxu &longs;cilicet, & refluxu, <expan abbr="aliis&qacute;">aliisque</expan>; præterea marinæ aquæ motibus; <lb/>quæ quàm non aperta, quàm ardua cognitio &longs;it, Ari&longs;totelis, <expan abbr="alio-rum&qacute;">alio­<lb/>rumque</expan>; philo&longs;ophorum indu&longs;tria declarat; &longs;ed etiam quia rationes <lb/>non uulgares, nec à ueteribus perceptæ, in hoc libro exponuntur. <lb/></s> <s>Addidimus autem de motu octauæ &longs;phæræ &longs;ubtilem & eruditam di­<lb/>&longs;putationem, <expan abbr="id&qacute;">idque</expan>; merito. </s> <s>&longs;i quidem tanti, <expan abbr="tam&qacute;">tamque</expan>; uarii maris motus <lb/>non modo ad Solis <expan abbr="Lunæ&qacute;">Lunæque</expan>; cur&longs;um, &longs;ed ad primum etiam mobile re­<lb/>feruntur. </s> <s>Atque hæc eruditi&longs;&longs;ima, <expan abbr="ualde&qacute;">ualdeque</expan>; à multis optata &longs;cripta <lb/>cum in tenebris laterent, forta&longs;&longs;e, paulatim uetu&longs;tate corrupta, pe­<lb/>rii&longs;lent, ni&longs;i præ&longs;tantis uiri, & doctrina clari, Lucæ Hieronymi Con <lb/>tareni, patricii Veneti, cui præceptor fuit Delphinus ip&longs;e, horum <lb/>&longs;criptorum auctor, &longs;ingularis humanitas ea conce&longs;&longs;i&longs;&longs;et Academiæ <lb/>no&longs;træ: quæ &longs;tatim, cognito argumento, non minus iucundo, quàm <lb/>diflicili, munus ad te, &longs;uæ te&longs;timonium ob&longs;eruantiæ, mittendum <lb/>con&longs;tituit: cum ip&longs;am quidem rem, & pro tua excellenti doctrina, <lb/>& quia te in amœni&longs;&longs;imum Corneliani &longs;ece&longs;&longs;um, quietis, & ualetu­<lb/>dinis cau&longs;a, contuli&longs;ti, gratam fore opinaretur, animum tamen no­<lb/>&longs;trum tibi probari uehementius optaret, utpote qui ad tuam glo­<lb/>riam multo &longs;ublimiora cogitans, humilia tamen tuæ &longs;plendore di­<lb/>gnitatis putauit illu&longs;tranda. </s> <s>nec uero &longs;ibi unquam &longs;atisfaciet, donec <lb/>plane peripiciat, neminem po&longs;&longs;e ip&longs;o præ&longs;tantius ad tuum decus <pb xlink:href="024/01/006.jpg"/>amplificandum aut eloqui, aut agere, ni&longs;i qui te ip&longs;um uirtute, <expan abbr="ani-mo&qacute;">ani­<lb/>moque</expan>; adæquat. </s> <s>quod cum fieri uix po&longs;sit: ideo &longs;equitur, ut actiones <lb/>no&longs;træ nequaquam tibi uulgares uideri debeant. </s> <s>quo fit, ut amore <lb/>tuo ac fauore complectendi &longs;imus, <expan abbr="gratiam&qacute;">gratiamque</expan>; à te inire aliquam æ­<lb/>quum &longs;it, quòd Academia no&longs;tra, cum omnibus communem om­<lb/>nium parentem Chri&longs;tum pie colentibus, ab intimo corde preces <lb/>pie fundit, ut, ad no&longs;træ religionis utilitatem, ad ornamentum <lb/>omnium uirtutum, ad ætatis no&longs;træ gloriam, diuturnam tibi ui­<lb/>tam cum optima ualetudine con&longs;eruet. </s> <s>quandoquidem honores eos, <lb/>qui ab hominibus tribuuntur, iam nunc plero&longs;que po&longs;&longs;ides, & quia <lb/>Cardinalis; & quòd ex Principum familia ortus es: reliquos uero po&longs;<lb/>&longs;edi&longs;&longs;e iam primum propterea uideris, quia te iis maxime dignum <lb/>præ&longs;titi&longs;ti quam rem ne quis in dubium uocet, &longs;pectet animo ueram <lb/>tui &longs;anguinis nobilitatem, <expan abbr="tuas&qacute;">tuasque</expan>; actiones cæle&longs;ti fauore commen­<lb/>datas; quarum &longs;ublimitas dignitatem omnem, quæ conferri à mor­<lb/>talibus po&longs;&longs;it, maxime &longs;uperat. </s></p><p type="main"> <s>Illu&longs;tri&longs;&longs;imæ ac Reuerendi&longs;&longs;imæ <!-- REMOVE S-->D. tuæ dediti&longs;&longs;imi </s></p><p type="main"> <s>Mathematici Academiæ Venetæ. <!-- KEEP S--></s></p><pb xlink:href="024/01/007.jpg"/><p type="main"> <pb xlink:href="024/01/008.jpg"/> <s><emph type="center"/>ERRATA.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> <s>2. fal&longs;e, fal&longs;e. </s> <s>5. quarta, quartam. </s> <s>10. notum, motum. </s> <s>a tergo argumen­<lb/>tum, augmentum. </s> <s>12. aliquod fallunt, in aliquo uariant. </s> <s>13. die, diem. <lb/></s> <s>20. diferentis, deferentis. </s> <s>22. &longs;eptentrionale, &longs;eptentrionali. </s> <s>ibidem, &longs;e­<lb/>ptione, &longs;ectione. </s> <s>23. &longs;eptentrionale, &longs;eptentrionali. </s> <s>24. &longs;ectione, &longs;ectio­<lb/>nem. </s> <s>a tergo idem erratum emenda. </s> <s>ibidem, di&longs;tinguentem, di&longs;tinguenti. <lb/></s> <s>ibidem. </s> <s>accederat, acce&longs;&longs;erat. </s> <s>25. tam, tamen. </s> <s>ibidem. </s> <s>que, quam. </s> <s>ibidem, <lb/>octaue, octaua. </s> <s>26. tabolariis, tabulariis. </s> <s>a tergo, aere, are ubique. </s> <s>ultima, <lb/>qui, quod. </s></p><pb xlink:href="024/01/009.jpg" pagenum="1"/><p type="main"> <s><emph type="center"/>FEDERICI DELPHINI, <lb/>ARTIVM, ET MEDICINAE<emph.end type="center"/><!-- REMOVE S--><emph type="center"/>DOCTORIS, <lb/>mathematicarum di&longs;ciplinarum in celeberrimo gymna&longs;io <lb/>Patauino publici profe&longs;&longs;oris, <lb/>tractatus de FLVXV, & REFLVXV, &longs;eu cre­<lb/>mento, & decremento, aut acce&longs;&longs;u, & rece&longs;­<lb/>&longs;u, & quiete fal&longs;a, &longs;eu motu inordi­<lb/>nato aquæ maris.<emph.end type="center"/></s></p><p type="main"> <s>DE<gap/>O autem, quod &longs;uperius promi&longs;eram me dicturum <lb/><gap/>e huius mei tractatus de &longs;phæra, uidelicet de motu, & <lb/>quiete fal&longs;a aquæ maris ad motum primi mobilis; nunc re­<lb/>&longs;tat à me dicendum. </s> <s>& licet à præcedentibus magi&longs;tris facta <lb/>fuerit tractatio motus, & quietis fal&longs;æ aquæ maris, uidelicet <lb/>fluxus, & refluxus, &longs;eu crementi, & decrementi eius; & in <lb/>tractatibus eorum includantur omnes cau&longs;æ huiu&longs;modi mo<lb/>tus fluxus, & refluxus, &longs;eu crementi, & decrementi: quia <lb/>tamen non &longs;unt omnes ita manife&longs;te po&longs;itæ in tractatibus <lb/>eorum; nec po&longs;&longs;unt ab omnibus legentibus tractatus eorum <lb/>ita bene elici ex dictis eorum: ideo ego Federicus Delphi­<lb/>nus, artium, & medicinæ, & mathematicarum di&longs;ciplina­<lb/>rum doctor, decreui in i&longs;to meo tractatu eas diligenter & &longs;cri<lb/>bere, & bene, & clare exprimere: ut doctrina i&longs;ta fluxus, & <lb/>refluxus, &longs;eu crementi, & decrementi, & quietis fal&longs;æ, &longs;eu <lb/>motus inordinati aquæ maris, omnibus legentibus hunc <lb/>meum tractatum &longs;it manife&longs;tior. </s></p><p type="main"> <s>Pro facili autem intelligentia horum duorum modorum <lb/>motus aquæ maris, &longs;equentium motum &longs;olis, & lunæ ad mo­<lb/>tum primi mobilis, e&longs;t &longs;ciendum, primo, quòd, ubicunque <lb/>&longs;it homo in terra, orizon eius, &longs;icut dictum e&longs;t &longs;upra à me, <pb xlink:href="024/01/010.jpg"/>in tractatu meo de &longs;phera, &longs;emper &longs;ecat ei cælum in duo me­<lb/>dia, & medietas cæli &longs;emper e&longs;t &longs;upra orizontem eius, & <lb/>medietas infra. </s> <s>cum autem in omni medietate corporis &longs;phe<lb/>rici contineantur duæ quartæ: duæ quartæ cæli &longs;emper e­<lb/>runt &longs;upra orizontem eius, & duæ infra. </s> <s>quæ autem &longs;unt <lb/>&longs;upra orizontem, dicuntur quartæ diurnæ; & quæ &longs;unt &longs;ub <lb/>orizonte, dicuntur quartæ nocturnæ. </s> <s>harum autem qua­<lb/>tuor quartarum cæli duæ &longs;unt, in quibus fit fluxus, &longs;eu cre­<lb/>mentum aquæ maris; & duæ, in quibus fit refluxus, &longs;eu de­<lb/>crementum aquæ maris. </s> <s>quartæ, in quibus fit fluxus, &longs;eu <lb/>crementum, &longs;unt quarta, quæ e&longs;t ab ortu ad meridiem &longs;upra <lb/>orizontem; quæ e&longs;t quarta acce&longs;&longs;ionis diurnæ, &longs;eu crementi <lb/>diurni: & quarta ei oppo&longs;ita, quæ e&longs;t ab occa&longs;u ad medium <lb/>noctis &longs;ub orizonte: quæ e&longs;t quarta acce&longs;&longs;ionis nocturnæ. <lb/></s> <s>quartæ autem, in quibus fit refluxus, &longs;eu decrementum; <lb/>&longs;unt quarta, quæ e&longs;t à meridie ad occa&longs;um &longs;upra <expan abbr="orizont&etilde;">orizontem</expan>; <lb/>quæ e&longs;t quarta acce&longs;&longs;ionis diurnæ: & quarta ei oppo&longs;ita, <lb/>quæ e&longs;t à medio noctis ad ortum &longs;ub orizonte; quæ e&longs;t quar<lb/>ta rece&longs;&longs;ionis nocturnæ. </s></p><p type="main"> <s>Sciendum e&longs;t etiam &longs;ecundo, quòd octo &longs;unt puncta in cælo <lb/>pro fluxu, & refluxu, &longs;eu cremento, & decremento aquæ <lb/>maris: quorum quatuor &longs;unt fortia, & quatuor debilia. </s> <s>de­<lb/>bilium duo &longs;unt debilia pro fluxu, &longs;eu cremento, & duo pro <lb/>refluxu, &longs;eu decremento: debilia pro fluxu, &longs;eu cremento, <lb/>&longs;unt punctum orientis, & punctum occidentis, quæ &longs;unt <lb/>principia duarum quartarum fluxus. </s> <s>debilia pro refluxu, <lb/>&longs;eu decremento, &longs;unt punctum meridiei, & punctum me­<lb/>diæ noctis, quæ &longs;unt principia duarum quartarum refluxus. <lb/></s> <s>& i&longs;ta quatuor puncta di&longs;tant adinuicem per quartam cæli. <lb/></s> <s>fortium duo &longs;unt fortia pro fluxu, &longs;eu cremento, & duo pro <lb/>refluxu, &longs;eu decremento. </s> <s>fortia pro fluxu, &longs;eu cremento, <lb/>&longs;unt punctum medium inter orientem, & meridiem in quar<lb/>ta diurna fluxus, di&longs;tans ab oriente per 45 gradus (& à me­<lb/>ridie &longs;imiliter: & punctum medium inter occidentem, & <pb xlink:href="024/01/011.jpg" pagenum="2"/>medium noctis in quarta nocturna fluxus) di&longs;tans ab occa&longs;u <lb/>per 45 gradus, & à medio noctis &longs;imiliter. </s> <s>fortia pro refluxu <lb/>&longs;unt punctum medium inter meridiem, & occa&longs;um in quarta <lb/>diurna refluxus, di&longs;tans à meridie per 45 gradus, & ab occa <lb/>&longs;u &longs;imiliter: & punctum medium inter medium noctis, & or­<lb/>tum, in quarta nocturni refluxus, di&longs;tans à medio noctis per <lb/>45 gradus, & ab ortu &longs;imiliter: & &longs;icut puncta debilia di&longs;tant <lb/>adinuicem per quartam cæli; ita i&longs;ta fortia di&longs;tant adinuicem <lb/>per quartam cæli, habentibus orizontem rectum. </s></p><p type="main"> <s>Sciendum e&longs;t etiam tertio, quòd, præter i&longs;ta octo puncta di­<lb/>cta, habentibus orizontem rectum, &longs;unt multa alia puncta æ­<lb/>quipotentia, &longs;eu æqualis uirtutis: & talia puncta &longs;unt omnia <lb/>puncta cæli æqualiter di&longs;tantia, & quatuor punctis principali­<lb/>bus cæli, quæ puncta principalia cæli &longs;unt puncta orientis, pun<lb/>ctum occidentis, punctum meridiei, & punctum mediæ no­<lb/>ctis, uel à quatuor punctis fortibus cæli, quod e&longs;t idem: in <lb/>quartis tamen contrariæ operationis. </s> <s>&longs;unt enim omnia talia <lb/>puncta æqualis uirtutis, &longs;eu æquipotentia in mouendo aquam <lb/>maris: in orizonte autem obliquo aliter e&longs;t, ut infra uidebitur. </s></p><p type="main"> <s>Sciendum e&longs;t quarto, quòd &longs;ol, & luna omni men&longs;e &longs;unt &longs;i­<lb/>mul in eodem &longs;igno, gradu, & minuto; & i&longs;te &longs;itus appella­<lb/>tur coniunctio lunæ cum &longs;ole. </s> <s>inde ad octo dies, uel circa lu­<lb/>na e&longs;t elongata à &longs;ole per motum eius proprium per quartam <lb/>partem cæli: & hæc elongatio appellatur quadratura prima <lb/>lunæ cum &longs;ole. </s> <s>inde ad 14 dies, uel circa, e&longs;t elongata à &longs;ole, <lb/>per aliam quartam partem cæli, & &longs;ic per medietatem cæli. </s> <s>& <lb/>hæc di&longs;tantia appellatur oppo&longs;itio lunæ cum &longs;ole, &longs;eu plenilu <lb/>nium. </s> <s>inde ad 21 dies, uel circa, e&longs;t elongata ab oppo&longs;itione <lb/>eius cum &longs;ole, &longs;eu plenilunio, per aliam quartam partem cæ­<lb/>li, accedens ad ip&longs;am &longs;olem. </s> <s>& hæc di&longs;tantia appellatur qua­<lb/>dratura &longs;ecunda lunæ cum &longs;ole. </s> <s>& tunc luna di&longs;tat à &longs;ole per <lb/>quartam partem cæli, &longs;icut di&longs;tabat in quadratura prima. <lb/></s> <s>accedit ad coniunctionem eius cum &longs;ole. </s> <s>inde ad 20 dies, uel <lb/>circa luna e&longs;t iterum cum &longs;ole, & ei coniuncta, &longs;icut pri­<lb/>mo fuit. </s></p><pb xlink:href="024/01/012.jpg"/><p type="main"> <s>Sciendum quinto & ultimo, quòd &longs;ol, & luna ambo &longs;imul <lb/>omni die naturali, quæ e&longs;t tempus 24 horarum ad motum pri<lb/>mi mobilis &longs;unt cau&longs;æ fluxus, & refluxus, &longs;eu crementi, & <lb/>decrementi aquæ maris bis. </s> <s>i&longs;tis declarationibus præmi&longs;&longs;is, et <lb/>bene memoriæ retentis, declaremus quomodo &longs;ol, et luna am<lb/>bo &longs;imul omni die naturali ad motum primi mobilis &longs;unt cau­<lb/>&longs;æ fluxus, et refluxus, &longs;eu crementi, et decrementi aquæ ma <lb/>ris bis. </s> <s>&longs;i enim declarationes præmi&longs;&longs;æ bene memoriæ tenean<lb/>tur, et maxime i&longs;tæ, uidelicet quæ &longs;unt quartæ cæli; in qui­<lb/>bus fit fluxus, &longs;eu crementum aquæ maris; et quæ &longs;unt quar<lb/>tæ cæli; in quibus fit refluxus, &longs;eu decrementum aquæ maris; <lb/>et quæ &longs;unt puncta fortia pro fluxu; et quæ &longs;unt puncta for­<lb/>tia pro refluxu; et quæ &longs;unt debilia pro fluxu; et quæ &longs;unt <lb/>debilia pro refluxu, tota narratio motus, et quietis fal&longs;æ aquæ <lb/>maris clara erit. </s></p><p type="main"> <s>Sciendum e&longs;t primo (quantum ad fluxum, et refluxum, &longs;eu <lb/>crementum, et decrementum aquæ maris ad motum primi <lb/>mobilis) quòd quando &longs;ol, et luna &longs;unt coniuncti &longs;imul, quæ <lb/>coniunctio appellatur nouilunium, dum feruntur ad motum <lb/>primi mobilis ab ortu ad meridiem; quia ambæ uirtutes uide­<lb/>licet &longs;olis, et lunæ &longs;unt unitæ &longs;imul; et ambo luminaria, uide­<lb/>licet &longs;ol, et luna feruntur continue ad motum primi mobilis <lb/>per quartam fluxus, &longs;eu crementi diurni; quæ e&longs;t ab ortu ad <lb/>meridiem, fit continue fluxus, &longs;eu crementum diurnum a­<lb/>quæ maris: et dum feruntur à meridie ad occa&longs;um, quia fe­<lb/>runtur continue per quartam refluxus, &longs;eu decrementi diur­<lb/>ni, fit continue refluxus, &longs;eu decrementum diurnum: et dum <lb/>feruntur ab occa&longs;u ad medium noctis; quia feruntur per quar<lb/>tam fluxus nocturni, iterum fit continue fluxus, &longs;eu cremen <lb/>tum &longs;cilicet nocturnum: et dum feruntur à medio noctis ad <lb/>ortum; quia feruntur per quartam refluxus, &longs;eu decrementi <lb/>nocturni, iterum fit continue refluxus, &longs;eu decrementum &longs;ci­<lb/>licet nocturnum. </s> <s>& &longs;ic bis in die naturali fit fluxus, & bis re­<lb/>fluxus, &longs;eu bis crementum, & bis decrementum aquæ maris. <lb/></s> <s>Sciendum &longs;ecundo, quòd quando luna po&longs;t coniunctionem <pb xlink:href="024/01/013.jpg" pagenum="3"/>eius cum &longs;ole per motum eius proprium elongatur à &longs;ole uer­<lb/>&longs;us orientem &longs;ecundum ordinem &longs;ignorum eundo uer&longs;us qua­<lb/>draturam primam eius cum &longs;ole, quam appellant Nautæ, il <lb/>Quartirone: &longs;emper antequam luna per motum eius pro­<lb/>prium ueniat ad illam quartam primam, quæ e&longs;t di&longs;tantia lu­<lb/>næ à &longs;ole uer&longs;us orientem &longs;ecundum ordinem &longs;ignorum per <lb/>quartam partem cæli, quando &longs;ol e&longs;t tantum &longs;uper orizon­<lb/>tem ex parte orientis in quarta fluxus diurni, quantum luna <lb/>e&longs;t &longs;ub orizonte ex eadem parte orientis in quarta refluxus <lb/>nocturni; quia tunc &longs;ol tantum di&longs;tat à puncto forti fluxus &longs;u­<lb/>per orizontem, quantum luna à puncto forti refluxus &longs;ub ori<lb/>zonte ip&longs;i &longs;unt æquipotentes: & ideo tunc nec fit fluxus, ne­<lb/>que refluxus aquæ maris; &longs;ed aqua maris uidetur &longs;tare, & <lb/>tunc Veneti dicunt, L'acqua è &longs;tanca. </s> <s>cum autem &longs;ol per mo­<lb/>tum primi mobilis accedit ad punctum forte fluxus, qui e&longs;t &longs;u<lb/>pra orizontem in quarta diurna fluxus, luna per eundem mo­<lb/>tum primi mobilis recedit, & elongatur. </s> <s><expan abbr="tantund&etilde;">tantundem</expan> à puncto for<lb/>ti refluxus, qui e&longs;t &longs;ub orizonte in quarta nocturni refluxus <lb/>accedendo uer&longs;us punctum orientis debile fluxus: & tunc <lb/>quia &longs;ol e&longs;t magis propinquus puncto forte fluxus, qui e&longs;t &longs;u­<lb/>pra orizontem in quarta diurna fluxus, quàm luna puncto for <lb/>ti refluxus, qui e&longs;t &longs;ub orizonte in quarta nocturna refluxus: <lb/>debilitatur refluxus, & fortificatur fluxus, & aqua maris <lb/>tunc incipit fluere: & quanto magis &longs;ol appropinquat puncto <lb/>forti fluxus, qui e&longs;t &longs;upra orizontem in quarta diurna fluxus, <lb/>tanto magis luna elongatur à puncto forti refluxus, qui e&longs;t <lb/>&longs;ub orizonte in quarta nocturna refluxus appropinquando <lb/>puncto orientis debili fluxus; & ideo continuatur fluxus. <lb/></s> <s>cum autem &longs;ol per motum primi mobilis peruenit ad <expan abbr="punctũ">punctum</expan> <lb/>fortem fluxus, qui e&longs;t &longs;upra orizontem in quarta diurna flu<lb/>xus, luna e&longs;t elongata à puncto forti refluxus, qui e&longs;t &longs;upra <lb/>orizontem in quarta nocturna refluxus: & facta e&longs;t propin­<lb/>qua puncto orientis debili fluxus; & ideo adhuc continua­<lb/>tur fluxus. </s> <s>cum autem luna uenerit ad punctum orientis <lb/>debile fluxus, ip&longs;a tunc ad motum primi mobilis mouetur <pb xlink:href="024/01/014.jpg"/>per quartam diurnam fluxus accedendo &longs;cilicet ad punctum <lb/>forte fluxus, qui e&longs;t &longs;upra orizontem: & &longs;ol quia di&longs;tat à lu­<lb/>na, minus quarta &longs;imiliter mouetur per eandem quartam di­<lb/>urnam fluxus accedendo &longs;cilicet ad punctum meridiei debile <lb/>refluxus: et ideo quia ambo mouentur per quartam diurnam <lb/>fluxus, continuatur fluxus: & cum &longs;ol per motum primi mo<lb/>bilis peruenit ad punctum meridiei debile refluxus, quia luna <lb/>tunc e&longs;t magis propinqua puncto forti fluxus, qui e&longs;t &longs;upra, <lb/>quàm &longs;ol puncto forti refluxus; qui e&longs;t &longs;upra <expan abbr="orizont&etilde;">orizontem</expan> in quar<lb/>ta diurna refluxus, continuabitur adhuc fluxus: & cum luna <lb/>uenerit ad punctum forte fluxus in quarta diurna fluxus, &longs;ol <lb/>non erit adhuc in puncto forti refluxus in quarta diurna reflu<lb/>xus, eo quia &longs;ol di&longs;tat à luna minus quarta, &longs;ed accedet ad ip­<lb/>&longs;um, et luna tunc recedet à puncto forti fluxus, & minus di&longs;ta­<lb/>bit ab eo, quàm &longs;ol à puncto forti refluxus, et ideo adhuc <lb/>continuabitur fluxus, donec &longs;ol &longs;it tantum ultra meridiem uer<lb/>&longs;us occidentem in quarta diurna fluxus, quantum luna citra <lb/>meridiem uer&longs;us orientem in quarta diurna fluxus: & tunc <lb/>&longs;ol tantum di&longs;tabit à puncto forti refluxus, qui e&longs;t &longs;upra ori­<lb/>zontem ultra meridiem in quarta diurna refluxus, quantum <lb/>luna à puncto forti fluxus, qui e&longs;t &longs;upra orizontem ante meri­<lb/>diem in quarta diurna fluxus: et ex continenti &longs;ol, & luna e­<lb/>runt æquipotentes, & non fiet fluxus, neque refluxus, &longs;icut <lb/>prius dictum e&longs;t. </s> <s>cum autem &longs;ol per motum primi mobilis ac­<lb/>cedet ad punctum forte refluxus in quarta diurna refluxus, <lb/>luna per eundem motum primi mobilis elongabitur tantun­<lb/>dem à puncto forti fluxus in quarta diurna fluxus acceden­<lb/>do uer&longs;us punctum meridiei debile refluxus, et tunc luna plus <lb/>di&longs;tabit à puncto forti fluxus, quàm &longs;ol à puncto forti reflu­<lb/>xus; et &longs;ic &longs;ol erit potentior luna; et ideo tunc incipiet reflu­<lb/>xus aquæ maris, et continuabitur &longs;ecundum quod &longs;ol appro­<lb/>pinquabit puncto forti refluxus in quarta diurna refluxus; et <lb/>luna elongabitur à puncto forti fluxus in quarta diurna flu­<lb/>xus; et cum &longs;ol ueniet ad punctum forte refluxus, luna erit <lb/>elongata à puncto forti fluxus, et ideo adhuc continuabitur <pb xlink:href="024/01/015.jpg" pagenum="4"/>refluxus, et cum luna ueniet ad punctum meridiei debile re­<lb/>fluxus, &longs;ol erit elongatus à puncto forti refluxus in quarta di­<lb/>urna refluxus accedendo uer&longs;us punctum occidentis debile <lb/>fluxus; minus tamen di&longs;tabit &longs;ol à puncto forti refluxus, quàm <lb/>luna à puncto forti fluxus; & ideo adhuc continuabitur reflu<lb/>xus: & cum &longs;ol ueniet ad punctum occidentis debile, fluxus <lb/>luna facta erit propinqua puncto forti refluxus, qui e&longs;t &longs;upra <lb/>orizontem in quarta diurna refluxus, & minus di&longs;tabit ab eo, <lb/>quàm &longs;ol à puncto forti fluxus, qui e&longs;t &longs;ub orizonte in quar­<lb/>ta nocturna fluxus; eo quia ip&longs;a di&longs;tat à &longs;ole minus quarta par­<lb/>te cæli, & ideo adhuc continuabitur refluxus, donec &longs;ol fue­<lb/>rit tantum infra orizontem ex parte occidentis in quarta no­<lb/>cturna fluxus, quantum luna &longs;upra orizontem, ex parte occi <lb/>dentis in quarta nocturna fluxus, quantum luna &longs;upra orizon<lb/>tem ex eadem parte occidentis in quarta diurna refluxus: & <lb/>quia tunc &longs;ol tantum di&longs;tabit à puncto forti fluxus, qui e&longs;t &longs;ub <lb/>orizonte, ex parte occidentis in quarta nocturna fluxus, quar<lb/>tum luna à puncto forti refluxus, qui e&longs;t &longs;upra orizontem ex <lb/>eadem parte occidentis in quarta diurna refluxus: tunc &longs;ol, <lb/>& luna erunt æquipotentes, et non fiet fluxus, neque reflu­<lb/>xus. </s> <s>cum autem &longs;ol per motum primi mobilis accedet ad pun<lb/>ctum forte fluxus, qui e&longs;t &longs;ub orizonte in quarta nocturna flu<lb/>xus, luna per eundem motum primi mobilis elongabitur tan­<lb/>tundem à puncto forti refluxus, qui e&longs;t &longs;upra orizontem in <lb/>quarta diurna refluxus; & tunc &longs;ol minus di&longs;tabit à puncto <lb/>forti fluxus in quarta nocturna fluxus, quàm luna à puncto <lb/>forti refluxus in quarta diurna refluxus; & ideo &longs;ol erit poten<lb/>tior luna: & tunc iterum incipiet fluxus, & continuabitur, &longs;i­<lb/>cut dictum e&longs;t prius, donec &longs;ol &longs;it tantum ultra medium no­<lb/>ctis uer&longs;us orientem in quarta nocturna refluxus, quantum <lb/>luna citra medium noctis uer&longs;us occidentem in quarta noctur<lb/>na fluxus: & tunc tantum di&longs;tabit &longs;ol à puncto forti refluxus, <lb/>quantum luna à puncto forti fluxus, & ex continenti tunc &longs;ol, <lb/>& luna erunt æquipotentes, et non fiet fluxus, neque re­<lb/>fluxus. </s> <s>cum autem &longs;ol per motum primi mobilis accedit ad <pb xlink:href="024/01/016.jpg"/>punctum forte refluxus in quarta nocturna refluxus, luna <lb/>per eundem motum primi mobilis recedit, & elongatur tan­<lb/>tundem à puncto forti fluxus in quarta nocturna fluxus ac­<lb/>cedendo uer&longs;us punctum mediæ noctis debile refluxus: & <lb/>tunc &longs;ol minus di&longs;tabit à puncto forti refluxus in quarta no­<lb/>cturna refluxus, quàm luna à puncto forti fluxus in quarta <lb/>nocturna fluxus; & tunc debilitatur fluxus, & fortificatur re­<lb/>fluxus; & aqua maris tunc iterum incipit refluere, & conti­<lb/>nuabitur refluxus, &longs;icut dictum e&longs;t prius, donec &longs;ol &longs;it tantum <lb/>&longs;upra orizontem, ex parte orientis, quantum luna &longs;ub ori­<lb/>zonte, ex eadem parte orientis: & tunc &longs;ol tantum di&longs;tabit <lb/>à puncto forti fluxus, qui e&longs;t &longs;upra orizontem in quarta diur­<lb/>na fluxus, quantum luna à puncto forti refluxus; qui e&longs;t &longs;ub <lb/>orizonte in quarta nocturna refluxus: & tunc &longs;ol, & luna e­<lb/>runt æquipotentes, & non fiet fluxus, neque refluxus. </s> <s>dein­<lb/>de quotidie, ide&longs;t in qualibet die naturali &longs;imilis, ut iam dicta <lb/>e&longs;t mutatio, redibit, donec luna per motum eius proprium <lb/>ueniat ad quadraturam primam eius cum &longs;ole, quam appel­<lb/>lant nauræ, il Quartirone. <!-- KEEP S--></s> <s>Cum uero luna uenerit ad qua­<lb/>draturam primam eius cum &longs;ole, tunc cum &longs;ol erit in puncto <lb/>orientis debiti pro fluxu luna erit in puncto mediæ noctis de­<lb/>biti pro refluxu; & tunc &longs;ol tantum di&longs;tabit à puncto forti flu<lb/>xus, qui e&longs;t &longs;upra orizontem, ex parte orientis in quarta diur<lb/>na fluxus, quantum luna à puncto forti refluxus, qui e&longs;t &longs;ub <lb/>orizonte, ex eadem parte orientis in quarta nocturna reflu­<lb/>xus: & &longs;ic &longs;ol, & luna erunt æquipotentes, & non fiet flu­<lb/>xus, neque refluxus notabilis: &longs;cilicet &longs;ed fient minime cre­<lb/>menta, & minima decrementa. </s> <s>cum autem &longs;ol per motum pri<lb/>mi mobilis accedet ad punctum forte fluxus, qui e&longs;t &longs;upra o­<lb/>rizontem, ex parte orientis in quarta diurna fluxus, luna per <lb/>eundem motum primi mobilis accedet &longs;imiliter tantundem <lb/>ad punctum forte refluxus, qui e&longs;t &longs;ub orizonte, ex eadem <lb/>parte orientis in quarta nocturna refluxus, & continue ad mo<lb/>tum diurnum tantum di&longs;tabit &longs;ol à puncto forti fluxus, qui e&longs;t <lb/>&longs;upra orizontem in quarta diurna fluxus, quantum luna à <pb xlink:href="024/01/017.jpg" pagenum="5"/>puncto forti refluxus, qui e&longs;t &longs;ub orizonte in quarta noctur­<lb/>na refluxus, & ex continenti &longs;ol, & luna continue erunt æqui­<lb/>potentes, donec &longs;ol per motum primi mobilis ueniat ad pun­<lb/>ctum forte fluxus, qui e&longs;t &longs;upra orizontem: & tunc &longs;imiliter <lb/>luna ueniet ad punctum forte refluxus, qui e&longs;t &longs;ub orizon­<lb/>te, eo quia i&longs;ta puncta di&longs;tant adinuicem per quarta cæli, &longs;i­<lb/>cut &longs;ol, & luna di&longs;tant adinuicem per quartam cæli: & cum &longs;ol <lb/>per motum primi mobilis recedet à puncto forti fluxus, qui <lb/>e&longs;t &longs;upra orizontem in quarta diurna fluxus accedendo uer­<lb/>&longs;us punctum meridiei debile refluxus luna per eundem mo­<lb/>tum primi mobilis recedet &longs;imiliter tantundem à puncto forti <lb/>refluxus, qui e&longs;t &longs;ub orizonte accedendo uer&longs;us punctum o­<lb/>rientis debile fluxus, & continue tantum di&longs;tabit &longs;ol à puncto <lb/>forti fluxus, qui e&longs;t &longs;upra orizontem, quantum luna à pun­<lb/>cto forti refluxus, qui e&longs;t &longs;ub orizonte, donec &longs;ol ueniet ad <lb/>punctum meridiei debile refluxus, & tunc luna &longs;imiliter ue­<lb/>niet ad punctum orientis debile fluxus: & &longs;ol, & luna per to­<lb/>tum i&longs;tud tempus erunt æquipotentes continue, & ex conti­<lb/>nenti non fiet fluxus, neque refluxus notabilis, &longs;cilicet eo­<lb/>dem modo fiet, dum &longs;ol ad motum primi mobilis mouebitur <lb/>à meridie ad occa&longs;um, quia tunc luna per eundem motum pri<lb/>mi mobilis mouebitur ab ortu ad meridiem: & &longs;imiliter dum <lb/>&longs;ol mouebitur ab occa&longs;u ad medium noctis, quia tunc luna mo<lb/>uebitur à meridie ad occa&longs;um; & &longs;imiliter dum &longs;ol mouebitur <lb/>à medio noctis ad ortum, quia tunc luna mouebitur ab occa­<lb/>&longs;u ad medium noctis: & &longs;ic in toto tempore unius reuolutionis <lb/>cæli, quod e&longs;t una dies naturalis 24 horarum, aqua maris nec <lb/>fluet, nec refluet &longs;en&longs;ibiliter, &longs;ed uidebitur &longs;tare, quia &longs;ol, & <lb/>luna in toto tempore illius reuolutionis cæli erunt æquipo­<lb/>tentes &longs;emper &longs;ine notabili di&longs;paritate: & i&longs;tud accidit circa <lb/>octauam diem po&longs;t coniunctionem lunæ cum &longs;ole: & i&longs;tam <lb/>quietem fal&longs;am aquæ maris appellant Veneti, Acqua de fele. <lb/></s> <s>& utuntur i&longs;to dicto, Da gli otto a i noue l'acqua non &longs;i <lb/>moue. </s></p><p type="main"> <s>Cum autem luna elongatur à &longs;ole ultra quadraturam primam <pb xlink:href="024/01/018.jpg"/>tendendo uer&longs;us oppo&longs;itionem eius cum &longs;ole, tunc &longs;emper do <lb/>nec luna ueniet ad oppo&longs;itionem eius cum &longs;ole, cum &longs;ol erit <lb/>tantum &longs;upra orizontem ex parte orientis in quarta diurna <lb/>fluxus, quantum luna &longs;ub orizonte ex eadem parte orientis <lb/>in quarta nocturna refluxus, &longs;ol tantum di&longs;tabit à puncto for<lb/>ti fluxus, qui e&longs;t &longs;upra orizontem in quarta diurna fluxus re­<lb/>cedendo ab eo per motum primi mobilis, & accedendo ad <lb/>punctum meridiei debile refluxus, quantum luna à puncto <lb/>forti refluxus, qui e&longs;t &longs;ub orizonte in quarta nocturna reflu­<lb/>Xus accedendo ad ip&longs;um per eundem motum primi mobilis, <lb/>& tunc &longs;ol, & luna erunt æquipotentes, & non fiet fluxus, ne­<lb/>que refluxus. </s> <s>cum autem &longs;ol per motum' primi mobilis acce­<lb/>det ad punctum meridiei debile refluxus, luna per eundem <lb/>motum primi mobilis accedet, &longs;eu appropinquabit tantun­<lb/>dem puncto forti refluxus, qui e&longs;t &longs;ub orizonte in quarta no­<lb/>cturna refluxus; & tunc luna erit magis propinqua puncto <lb/>forti refluxus, qui e&longs;t &longs;ub orizonte in quarta nocturna reflu­<lb/>Xus, quàm &longs;ol puncto forti fluxus, qui e&longs;t &longs;upra orizontem in <lb/>quarta diurna fluxus: & ideo tunc incipiet refluxus; quia <lb/>luna erit potentior &longs;ole: & &longs;ecundum quòd &longs;ol per <expan abbr="motũ">motum</expan> primi <lb/>mobilis appropinquabit puncto meridiei debili refluxus, luna <lb/>per eundem motum primi mobilis appropinquabit tantun­<lb/>dem puncto forti refluxus, qui e&longs;t &longs;ub orizonte: & &longs;ic conti­<lb/>nuabitur refluxus, donec &longs;ol ueniat ad punctum meridiei de­<lb/>bile refluxus: & cum &longs;ol per motum primi mobilis recedet à <lb/>puncto meridiei debili refluxus, & mouebitur per quartam <lb/>diurnam refluxus appropinquando puncto forti refluxus: lu­<lb/>na per eundem motum primi mobilis elongabitur tantundem <lb/>à puncto forti refluxus, qui e&longs;t &longs;ub <expan abbr="orizõte">orizonte</expan> in quarta nocturna <lb/>refluxus; & mouebitur etiam ip&longs;o per quartam refluxus, &longs;icut <lb/>&longs;ol accedendo ad punctum orientis debile fluxus, eo quia &longs;ol, <lb/>& luna di&longs;tant adinuicem plu&longs;quam per quartam cæli: & &longs;ic <lb/>ambo mouebuntur per quartas refluxus; & propter hoc con­<lb/>tinuabitur refluxus, donec &longs;ol &longs;it tantum ultra meridiem uer­<lb/>&longs;us occidentem in quarta diurna refluxus, <expan abbr="quantũ">quantum</expan> luna citra <pb xlink:href="024/01/019.jpg" pagenum="6"/>meridiem uer&longs;us orientem in quarta diurna fluxus: & tunc <lb/>&longs;ol tantum di&longs;tabit à puncto forti refluxus in quarta diurna <lb/>refluxus recedendo ab eo per motum primi mobilis uer&longs;us <lb/>occidentem, quantum luna à puncto forti fluxus; qui e&longs;t &longs;u­<lb/>pra orizontem in quarta diurna fluxus accedendo ad ip&longs;um: <lb/>& &longs;ic &longs;ol, & luna erunt æquipotentes, & tunc non fiet fluxus, <lb/>neque refluxus. </s> <s>cum autem &longs;ol per motum primi mobilis e­<lb/>longabitur à puncto forti refluxus; qui e&longs;t &longs;upra orizontem <lb/>in quarta diurna fluxus accedendo ad punctum occidentis <lb/>debile fluxus; luna per eundem motum primi mobilis appro<lb/>pinquabit tantundem puncto forti fluxus; qui e&longs;t &longs;upra ori­<lb/>zontem in quarta diurna fluxus: & luna tunc erit magis pro­<lb/>pinqua puncto forti fluxus in quarta diurna fluxus, quàm &longs;ol <lb/>puncto forti refluxus in quarta diurna refluxus: & &longs;ic luna e­<lb/>rit potentior &longs;ole, & tunc incipiet fluxus: & &longs;icut &longs;ol continue <lb/>elongabitur à puncto forti refluxus in quarta diurna reflu­<lb/>xus, ita luna continue appropinquabit puncto forti fluxus in <lb/>quarta diurna fluxus, & &longs;ic continuabitur fluxus; & cum &longs;ol <lb/>ueniet ad punctum occidentis debili fluxus, luna adhuc mo­<lb/>uebit per quartam diurnam fluxus, eo quia &longs;ol, & luna di­<lb/>&longs;tant ad inuicem plu&longs;quam per quartam cæli: & tunc luna e­<lb/>rit magis propinqua puncto forti fluxus in quarta diurna flu­<lb/>xus, quàm &longs;ol puncto forti fluxus, qui e&longs;t &longs;ub orizonte in <lb/>quarta nocturna fluXus; & ideo continuabitur fluXus: & cum <lb/>luna ueniet ad punctum meridiei debile refluXus, &longs;ol tran&longs;ibit <lb/>punctum occidentis debile fluXus <expan abbr="appropinquãdo">appropinquando</expan> puncto for<lb/>ti fluXus, qui e&longs;t &longs;ub orizonte in quarta nocturna fluXus; & <expan abbr="tũc">tunc</expan> <lb/>&longs;ol erit magis propinquus puncto forti fluXus, qui e&longs;t &longs;ub ori­<lb/>zonte in quarta nocturna fluXus, quàm luna puncto forti re­<lb/>fluXus, qui e&longs;t &longs;upra orizontem in quarta diurna refluXus: & <lb/>&longs;ic &longs;ol erit potentior luna; & ideo continuabitur fluXus: & <expan abbr="cũ">cum</expan> <lb/>&longs;ol ueniet ad <expan abbr="punctũ">punctum</expan> forte fluXus, qui e&longs;t &longs;ub orizonte in quar<lb/>ta nocturna fluXus; luna adhuc <expan abbr="nõ">non</expan> erit in <expan abbr="pũcto">puncto</expan> forti refluXus, <lb/>qui e&longs;t &longs;upra <expan abbr="orizont&etilde;">orizontem</expan> in quarta diurna refluXus; eo quia luna <lb/>di&longs;tat à &longs;ole plu&longs;quam per quartam cæli; & ideo adhuc conti­<pb xlink:href="024/01/020.jpg"/>nuabitur fluxus, donec &longs;ol &longs;it tantum &longs;ub orizonte eX parte oc<lb/>cidentis in quarta nocturna fluxus, quantum luna &longs;upra orizon<lb/><expan abbr="t&etilde;">tem</expan> eX eadem parte occidentis in quarta diurna refluxus; & <expan abbr="tũc">tunc</expan> <lb/>&longs;ol <expan abbr="tantũ">tantum</expan> di&longs;tabit à puncto forti fluxus, qui e&longs;t &longs;ub orizonte in <lb/>quarta nocturna fluxus accedendo ad punctum mediæ noctis <lb/>debile refluxus, quantum luna à puncto forti refluxus, qui e&longs;t <lb/>&longs;upra orizontem in quarta diurna refluxus accedendo ad ip­<lb/>&longs;um: & ideo &longs;ol, & luna erunt æquipotentes, & non fiet flu­<lb/>Xus, neque refluxus. </s> <s>po&longs;tea cum &longs;ol per motum primi mo­<lb/>tus elongabitur à puncto forti fluxus; qui e&longs;t &longs;ub orizonte, <lb/>ex parte occidentis in quarta nocturna fluxus accedendo uer<lb/>&longs;us punctum mediæ noctis debile refluxus, luna per eundem <lb/>motum primi mobilis appropinquabit tantundem puncto for<lb/>ti refluxus; qui e&longs;t &longs;upra orizontem in quarta diurna reflu­<lb/>Xus accedendo ad ip&longs;um: & &longs;ic luna erit magis propinqua <lb/>puncto forti refluxus, quàm &longs;ol puncto forti fluxus; & ideo <lb/>incipiet refluxus, & continuabitur modo dicto; donec &longs;ol &longs;it <lb/>tantum ultra medium noctis, uer&longs;us orientem in quarta no­<lb/>cturna refluxus; quantum luna ante medium noctis uer&longs;us oc<lb/>cidentem in quarta nocturna fluxus; & tunc &longs;ol tantum di&longs;ta<lb/>bit à puncto forti refluxus in quarta nocturna refluxus rece­<lb/>dendo ab eo uer&longs;us prædictum orientis debile fluxus, quan­<lb/>tum luna à puncto forti fluxus in quarta nocturna fluxus acce<lb/>dendo ad ip&longs;um; & tunc &longs;ol, & luna erunt æquipotentes, & <lb/>non fiet fluxus, neque refluxus. </s> <s>cum autem &longs;ol per motum <lb/>primi mobilis elongabitur à puncto forti refluxus &longs;ub orizon<lb/>te; qui e&longs;t in quarta nocturna refluxus accedendo uer&longs;us pun<lb/>ctum orientis debile fluxus; luna per eundem motum primi <lb/>mobilis appropinquabit tantundem puncto forti fluxus; qui <lb/>etiam e&longs;t &longs;ub orizonte in quarta nocturna fluxus accedendo <lb/>ad ip&longs;um: & quia luna tunc e&longs;t magis propinqua puncto forti <lb/>fluxus; qui e&longs;t in quarta nocturna fluxus, quàm &longs;ol puncto <lb/>forti refluxus; qui e&longs;t in quarta nocturna refluxus: tunc in­<lb/>cipit fluxus, & continuatur modo dicto, donec &longs;ol &longs;it tantum <lb/>&longs;uper orizontem, eX parte orientis in quarta diurna fluxus, <pb xlink:href="024/01/021.jpg" pagenum="7"/>quantum luna &longs;ub orizonte ex eadem parte orientis in quar­<lb/>ta nocturna refluxus: & quia &longs;ol tantum di&longs;tabit à puncto for<lb/>ti fluxus, qui e&longs;t &longs;upra orizontem in quarta diurna fluxus ac­<lb/>cedendo per motum primi mobilis uer&longs;us punctum meridiei <lb/>debile refluxus, quantum luna à puncto forti refluxus; qui e&longs;t <lb/>&longs;ub orizonte in quarta nocturna refluxus accedendo per eun<lb/>dem motum primi mobilis uer&longs;us ip&longs;um: ip&longs;i erunt æquipo­<lb/>tentes, & non fiet fluxus, neque refluxus: & i&longs;to modo con­<lb/>tinuabitur fluxus, & refluxus in omni die naturali donec luna <lb/>ueniat ad oppo&longs;itionem eius cum &longs;ole. </s></p><p type="main"> <s>Quando autem luna ueniet ad oppo&longs;itionem eius cum &longs;ole: <lb/>tunc quando &longs;ol erit in puncto orientis debili fluxus, luna erit <lb/>in puncto occidentis &longs;imiliter debili fluxus: & tunc incipiet <lb/>fluxus, & continuabitur, quamdiu &longs;ol mouebitur ad motum <lb/>primi mobilis à puncto orientis debili fluxus per quartam di­<lb/>urnam fluxus ad punctum meridiei debile refluxus: & luna <lb/>tunc in toto i&longs;to tempore mouebitur &longs;imiliter ad motum pri­<lb/>mi mobilis à puncto occidentis debili fluxus per quartam no­<lb/>cturnam fluxus ad punctum mediæ noctis debile refluxus; & <lb/>tunc ce&longs;&longs;abit fluxus, & incipiet refluxus, & durabit quamdiu <lb/>&longs;ol ad motum primi mobilis mouebitur à puncto meridiei de­<lb/>bili refluxus per quartam diurnam refluxus, u&longs;que ad pun­<lb/>ctum occidentis debile fluxus; & luna tunc in toto i&longs;to tem­<lb/>pore mouebitur &longs;imiliter ad motum primi mobilis à puncto <lb/>mediæ noctis debili refluxus per quartam nocturnam reflu­<lb/>xus, u&longs;que ad punctum orientis debile fluxus, & tunc ce&longs;&longs;a­<lb/>bit refluxus: & iterum incipiet fluxus, & durabit quamdiu <lb/>&longs;ol ad motum primi mobilis mouebitur à puncto occidentis <lb/>debili fluxus per quartam nocturnam fluxus, u&longs;que ad pun­<lb/>ctum mediæ noctis debile refluxus; & tunc luna in toto i&longs;to <lb/>tempore per eundem motum primi mobilis mouebitur à pun<lb/>cto orientis &longs;imiliter debili fluxus per quartam diurnam flu­<lb/>Xus, u&longs;que ad punctum meridiei debile refluxus; & tunc ce&longs;<lb/>&longs;abit fluxus, & incipiet refluxus, & durabit quamdiu &longs;ol ad <lb/>motum primi mobilis mouebitur à puncto mediæ noctis debili <pb xlink:href="024/01/022.jpg"/>refluxus per quartam nocturnam refluxus, u&longs;que ad pun­<lb/>ctum orientis debile fluxus: & tunc luna in toto i&longs;to tempore <lb/>per eundem motum primi mobilis mouebitur à puncto meri­<lb/>diei &longs;imiliter debili refluxus per quartam diurnam refluxus, <lb/>u&longs;que ad punctum occidentis debile fluxus, & tunc ce&longs;&longs;abit <lb/>refluxus. </s></p><p type="main"> <s>Cum autem luna tran&longs;ibit oppo&longs;itionem eius cum &longs;ole per mo<lb/>tum eius proprium tendendo ad quadraturam &longs;ecundam eius <lb/>cum &longs;ole; tunc quando luna fuerit tantum &longs;upra orizontem <lb/>ex parte orientis in quarta diurna fluxus, quantum &longs;ol &longs;ub <lb/>orizonte ex eadem parte orientis in quarta nocturna reflu­<lb/>xus; quia luna tunc tantum di&longs;tabit à puncto forti fluxus; qui <lb/>e&longs;t &longs;upra orizontem in quarta diurna fluxus, quantum &longs;ol à <lb/>puncto forti refluxus; qui e&longs;t &longs;ub orizonte ex eadem parte o­<lb/>rientis in quarta nocturna refluxus; tunc &longs;ol, & luna erunt <lb/>æquipotentes, & non fiet fluxus, neque refluxus. </s> <s>Cum au­<lb/>tem luna per motum primi mobilis elongabitur à puncto for­<lb/>ti fluxus, qui e&longs;t &longs;upra orizontem in quarta diurna fluxus ac­<lb/>cedendo uer&longs;us punctum meridie debile refluxus: &longs;ol per <lb/>eundem motum primi mobilis appropinquabit tantundem <lb/>puncto forti refluxus, qui e&longs;t &longs;ub orizonte in quarta noctur­<lb/>na refluxus accedendo ad ip&longs;um; & tunc quia &longs;ol minus di­<lb/>&longs;tabit à puncto forti refluxus, qui e&longs;t &longs;ub orizonte ex parte o­<lb/>rientis in quarta nocturna refluxus, quàm luna à puncto for­<lb/>ti fluxus, qui e&longs;t &longs;upra orizontem ex eadem parte orientis in <lb/>quarta diurna fluxus incipiet refluxus, & continuabitur. </s> <s>& <lb/>cum luna per motum primi mobilis perueniet ad punctum <lb/>meridiei debile refluxus, &longs;ol adhuc erit &longs;ub orizonte in quar<lb/>ta nocturna refluxus, eo quia &longs;ol, & luna di&longs;tant adinuicem <lb/>plu&longs;quam per quartam cæli: & luna tunc ad motum primi <lb/>mobilis mouebitur per quartam diurnam refluxus, &longs;icut e­<lb/>tiam &longs;ol modo per quartam nocturnam refluxus accedendo <lb/>ad punctum fortem refluxus in quarta diurna refluxus, & &longs;ic <lb/>continuabitur refluxus; & cum luna appropinquabit puncto <lb/>forti refluxus in quarta diurna refluxus, &longs;ol appropinquabit <pb xlink:href="024/01/023.jpg" pagenum="8"/>puncto orientis debili fluxus in quarta nocturna refluxus, & <lb/>magis di&longs;tabit à puncto forti fluxus, qui e&longs;t &longs;upra orizontem <lb/>in quarta diurna fluxus, quàm luna à puncto forti refluxus, <lb/>qui e&longs;t &longs;imiliter &longs;uper orizontem in quarta diurna refluxus, & <lb/>&longs;ic continuabitur refluxus, donec luna fit tantum ultra meri­<lb/>diem uer&longs;us occidentem in quarta diurna refluxus, quantum <lb/>&longs;ol ante meridiem uer&longs;us orientem in quarta diurna fluxus, & <lb/>tunc luna tantum di&longs;tabit à puncto forti refluxus in quarta di­<lb/>urna refluxus, quantum &longs;ol à puncto forti fluxus in quarta <lb/>diurna fluxus: & &longs;ic &longs;ol, & luna erunt æquipotentes, & non <lb/>fiet fluxus, neque refluxus. </s> <s>cum autem luna per motum pri<lb/>mi mobilis elongabitur à puncto forti refluxus accedendo <lb/>uer&longs;us punctum occidentis debile fluxus, &longs;ol per eundem mo<lb/>tum primi mobilis appropinquabit tantundem puncto forti <lb/>fluxus in quarta diurna fluxus: & tunc quia &longs;ol erit magis <lb/>propinquus puncto forti fluxus, qui e&longs;t in quarta diurna flu­<lb/>Xus, quàm luna puncto forti refluxus, qui e&longs;t in quarta diur­<lb/>na refluxus, incipiet fluxus, & continuabitur &longs;ecundum quod <lb/>luna ad motum primi mobilis elongabitur à puncto forti reflu<lb/>xus in quarta diurna refluxus accedendo uer&longs;us punctum oc<lb/>cidentis debile fluxus, & &longs;ol appropinquabit puncto forti flu<lb/>xus in quarta diurna fluxus accedendo ad ip&longs;um: & cum lu­<lb/>na ueniet ad motum primi mobilis ad punctum occidentis de­<lb/>bile fluxus, &longs;ol adhuc per eundem motum primi mobilis mo<lb/>uebit per quartam diurnam fluxus, eo quia &longs;ol, & luna di&longs;tant <lb/>adinuicem plu&longs;quam per quartam cæli, & &longs;ol erit magis pro­<lb/>pinquus puncto forti fluxus in quarta diurna fluxus, quàm lu<lb/>na puncto forti refluxus in quarta diurna refluxus, ideo con­<lb/>tinuabitur fluxus: & cum &longs;ol ueniet ad punctum meridiei de­<lb/>bile refluxus, luna erit &longs;ub orizonte eX parte occidentis in <lb/>quarta nocturna fluxus, & erit magis propinqua puncto for­<lb/>ti fluxus, qui e&longs;t &longs;ub orizonte in quarta nocturna fluxus, <lb/>quàm &longs;ol puncto forti refluxus, qui e&longs;t &longs;upra orizontem in <lb/>quarta diurna refluxus: ideo adhuc continuabitur fluxus, <lb/>donec luna &longs;it tantum &longs;ub orizonte eX parte occidentis in <pb xlink:href="024/01/024.jpg"/>quarta nocturna fluxus, quantum &longs;ol &longs;upra orizontem ex <lb/>eadem parte occidentis in quarta diurna refluxus; & tunc lu­<lb/>na tantum di&longs;tabit à puncto forti fluxus &longs;ub orizonte in quar­<lb/>ta nocturna fluxus accedendo uer&longs;us punctum mediæ noctis <lb/>debile refluxus, quantum &longs;ol à puncto forti refluxus &longs;upra o­<lb/>rizontem in quarta diurna refluxus accedendo ad ip&longs;um, & <lb/>&longs;ic &longs;ol, & luna erunt æquipotentes & non fiet fluxus, neque <lb/>refluxus. </s> <s>cum autem luna per motum primi mobilis elonga­<lb/>bitur à puncto forti fluxus &longs;ub orizonte in quarta nocturna <lb/>fluxus accedendo uer&longs;us punctum mediæ noctis debile reflu­<lb/>xus, &longs;ol per eundem motum primi mobilis appropinquabit <lb/>tantundem puncto forti refluxus, qui e&longs;t &longs;upra orizontem in <lb/>quarta diurna refluxus accedendo ad ip&longs;um, & tunc &longs;ol erit <lb/>magis propinquus puncto forti refluxus, qui e&longs;t &longs;upra orizon<lb/>tem in quarta diurna refluxus, quàm luna puncto forti flu­<lb/>xus, qui e&longs;t &longs;ub orizonte in quarta nocturna fluxus, & ideo <lb/>tunc incipiet refluxus, & continuabitur &longs;ecundum quod lu­<lb/>na elongabitur à puncto forti fluxus, qui e&longs;t &longs;ub orizonte in <lb/>quarta nocturna fluxus appropinquando puncto mediæ noctis <lb/>debili refluxus, & &longs;ol appropinquabit puncto forti refluxus, <lb/>qui e&longs;t &longs;upra orizontem in quarta diurna refluxus: & cum lu<lb/>na per motum primi mobilis ueniet ad punctum mediæ noctis <lb/>debile refluxus, &longs;ol adhuc erit &longs;upra orizontem ex parte oc­<lb/>cidentis in quarta diurna refluxus accedens per motum pri­<lb/>mi mobilis ad punctum occidentis debile fluxus, & eo quia <lb/>&longs;ol, & luna di&longs;tant adinuicem plu&longs;quam per quartam, & tunc <lb/>&longs;ol plus di&longs;tabit à puncto forti fluxus, qui e&longs;t &longs;ub orizonte ex <lb/>parte occidentis in quarta nocturna fluxus, quàm luna à pun<lb/>cto forti refluxus, qui etiam e&longs;t &longs;ub orizonte ex parte orien<lb/>tis in quarta nocturna refluxus; & ideo continuabitur reflu­<lb/>xus, donec luna &longs;it tantum ultra medium noctis uer&longs;us orien­<lb/>tem, quantum &longs;ol ante medium noctis uer&longs;us occidentem, & <lb/>tunc luna tantum di&longs;tabit à puncto forti refluxus in quarta no<lb/>cturna refluxus recedendo ab eo per motum primi mobilis, <lb/>& accedendo ad punctum orientis debile fluxus, quantum &longs;ol <pb xlink:href="024/01/025.jpg" pagenum="9"/>à puncto fluxus in quarta nocturna fluxus accedendo per eun<lb/>dem motum primi mobilis ad ip&longs;um, & &longs;ic &longs;ol, & luna erunt <lb/>æquipotentes, & non fiet fluxus, neque refluxus. </s> <s>cum au­<lb/>tem luna per motum primi mobilis elongabitur à puncto forti <lb/>refluxus, qui e&longs;t &longs;ub orizonte ex parte orientis in quarta no­<lb/>cturna refluxus uer&longs;us punctum orientis debile fluxus, &longs;ol <lb/>per eundem motum primi mobilis appropinquabit tantun­<lb/>dem puncto forti fluxus, qui e&longs;t &longs;ub orizonte ex parte occi­<lb/>dentis in quarta nocturna fluxus accedendo ad ip&longs;um, & <expan abbr="tũc">tunc</expan>, <lb/>quia luna erit magis remota à puncto forti refluxus, quàm <lb/>&longs;ol à puncto forti fluxus, tunc incipiet fluxus, quia &longs;ol erit po<lb/>tentior luna, & quanto magis luna elongabitur à puncto forti <lb/>refluxus in quarta nocturna refluxus, tanto magis &longs;ol ap­<lb/>propinquabit puncto forti fluxus in quarta nocturna flu­<lb/>xus, & &longs;ic continuabitur fluxus: & cum luna ueniet ad <lb/>punctum orientis debile fluxus, &longs;ol adhuc erit in quarta no­<lb/>cturna fluxus, eo quia &longs;ol di&longs;tat à luna plu&longs;quam per quar­<lb/>tam cæli, & erit &longs;ol magis propinquus puncto forti fluxus <lb/>in quarta nocturna fluxus, quàm luna puncto forti refluxus, <lb/>qui e&longs;t in quarta nocturna refluxus, & &longs;ic adhuc continuabi­<lb/>tur fluxus, donec luna &longs;it tantum &longs;upra orizontem ex parte <lb/>orientis, quantum &longs;ol &longs;ub orizonte ex eadem parte orientis, <lb/>& tunc luna tantum di&longs;tabit à puncto forti fluxus, qui e&longs;t &longs;u­<lb/>pra orizontem in quarta diurna fluxus recedendo ab eo per <lb/>motum primi mobilis uer&longs;us punctum meridiei debile reflu­<lb/>xus, quantum &longs;ol à puncto forti refluxus, qui e&longs;t &longs;ub orizon­<lb/>te in quarta nocturna refluxus accedendo ad ip&longs;um per eun­<lb/>dem motum primi mobilis, & &longs;ic &longs;ol, & luna erunt æquipoten<lb/>tes, & non fiet fluxus, neque refluxus, & iterum prior di&longs;­<lb/>po&longs;itio redibit, & continuabitur talis fluxus, & refluxus o­<lb/>mni die naturali i&longs;to modo, donec luna ueniat ad quadratu­<lb/>ram eius cum &longs;ole. </s></p><p type="main"> <s>Cum uero luna erit in quadratura &longs;ecunda tunc aqua maris <lb/>nec fluet, nec refluet, &longs;ed uidebitur quie&longs;cere, ut facie­<lb/>bat in quadratura prima, in qua in tota reuolutione cæli <pb xlink:href="024/01/026.jpg"/>luna, & &longs;ol &longs;emper erant æquipotentes propter cau&longs;as &longs;ibi di­<lb/>ctas, quia eædem cau&longs;æ ad&longs;unt in quadratura &longs;ecunda, quæ <lb/>ad&longs;unt in quadratura prima, & i&longs;tud e&longs;t circa XXI dies, & i­<lb/>&longs;tam quietem aquæ maris appellant Veneti, &longs;icut &longs;upra <expan abbr="dictũ">dictum</expan> <lb/>e&longs;t, Acqua de fele. </s> <s>& utuntur i&longs;to dicto, Da uent'uno à uen­<lb/>tidue, l'acqua non ua ne &longs;u, ne giu. </s></p><p type="main"> <s>Cum autem luna pertran&longs;ibit motum eius proprium hanc <lb/>quadraturam &longs;ecundam tendendo ad coniunctionem eius <lb/>cum &longs;ole, tunc luna di&longs;tabit à &longs;ole minus quarta parte cæli, & <lb/>tunc cum ip&longs;a fuerit tantum &longs;upra orizontem ex parte o­<lb/>rientis in quarta diurna fluxus, quantum &longs;ol &longs;ub orizonte ex <lb/>eadem parte orientis in quarta nocturna refluxus, tunc lu­<lb/>na tantum di&longs;tabit à puncto forti fluxus, qui e&longs;t &longs;upra orizon<lb/>tem in quarta diurna fluxus accedendo ad ip&longs;um per motum <lb/>primi mobilis, quantum &longs;ol à puncto forti refluxus, qui e&longs;t &longs;ub <lb/>orizonte in quarta nocturna refluxus recedendo ab ip&longs;o per <lb/>eundem motum primi mobilis uer&longs;us punctum orientis debile <lb/>fluxus, & tunc &longs;ol, & luna erunt æquipotentes, & non fiet flu­<lb/>xus, neque refluxus. </s> <s>cum autem luna per motum primi mo­<lb/>bilis accedet ad punctum forte fluxus, qui e&longs;t &longs;upra orizon­<lb/>tem in quarta diurna fluxus, &longs;ol per eundem motum primi <lb/>mobilis recedet, & elongabitur tantundem à puncto forti re­<lb/>fluxus, qui e&longs;t &longs;ub orizonte in quarta nocturna refluxus <lb/>uer&longs;us punctum orientis debile fluxus, & tunc quia luna mi­<lb/>nus di&longs;tabit à puncto forti fluxus, qui e&longs;t &longs;upra orizontem in <lb/>quarta diurna fluxus, quàm &longs;ol à puncto forti refluxus, qui <lb/>e&longs;t &longs;ub orizonte in quarta nocturna refluxus, luna erit po­<lb/>tentior &longs;ole, & ideo tunc incipiet fluxus, & quanto magis lu­<lb/>na appropinquabit puncto forti fluxus, tanto magis &longs;ol elon­<lb/>gabitur à puncto forti refluxus appropinquando puncto o­<lb/>rientis debili fluxus, & ideo continuabitur fluxus: & cum <lb/>&longs;ol ueniet per motum primi mobilis ad punctum orientis <lb/>debile fluxus, quia luna adhuc erit in quarta diurna <lb/>fluxus, eo quia ip&longs;a di&longs;tat à &longs;ole minus quarta parte cæ­<lb/>li, ip&longs;a minus di&longs;tabit à puncto forti fluxus, qui e&longs;t &longs;upra <pb xlink:href="024/01/027.jpg" pagenum="10"/>orizontem in quarta diurna fluxus, quàm &longs;ol à puncto forti <lb/>refluxus, qui e&longs;t &longs;ub <expan abbr="orizõte">orizonte</expan> in quarta nocturna refluxus, ideo <lb/>adhuc continuabitur fluxus, & <expan abbr="cũ">cum</expan> luna ueniet ad <expan abbr="punctũ">punctum</expan> meri <lb/>diei debile refluxus, &longs;ol erit &longs;upra orizontem in quarta diur­<lb/>na fluxus, & erit magis propinquus puncto forti fluxus, quàm <lb/>luna puncto forti refluxus, qui e&longs;t po&longs;t meridiem in quarta <lb/>diurna refluxus, eo quia &longs;ol di&longs;tat à luna minus quarta parte <lb/>cæli, & ideo continuabitur fluxus donec luna &longs;it tantum ul­<lb/>tra meridiem uer&longs;us occidentem in quarta diurna refluxus, <lb/>quantum &longs;ol ante meridiem uer&longs;us orientem in quarta diurna <lb/>fluxus, & tunc luna tantum di&longs;tabit à puncto forti refluxus in <lb/>quarta diurna refluxus accedendo ad ip&longs;um per <expan abbr="motũ">motum</expan> primi <lb/>mobilis, <expan abbr="quantũ">quantum</expan> &longs;ol à puncto forti fluxus in quarta diurna flu­<lb/>xus recedendo ab ip&longs;o per eundem <expan abbr="motũ">motum</expan> primi mobilis, & &longs;ic <lb/>&longs;ol, & luna erunt æquipotentes, & non fiet fluxus, neque reflu­<lb/>xus. </s> <s>cum autem luna per <expan abbr="motũ">motum</expan> primi mobilis appropinquabit <lb/>puncto forti refluxus in quarta diurna refluxus, &longs;ol per <expan abbr="eund&etilde;">eundem</expan> <lb/>motum primi mobilis recedet, & elongabitur <expan abbr="tantund&etilde;">tantundem</expan> à pun­<lb/>cto forti fluxus in quarta diurna fluxus, & tunc luna erit ma­<lb/>gis propinqua <expan abbr="pũcto">puncto</expan> forti refluxus in quarta diurna refluxus, <lb/>quàm &longs;ol puncto forti fluxus in quarta diurna fluxus, & &longs;ic lu<lb/>na erit potentior &longs;ole, & ideo incipiet refluxus, & continuabi­<lb/>tur fluxus, & refluxus eodem modo, quo dictum e&longs;t, quando <lb/>luna recedit à coniunctione eius cum &longs;ole, & nondum uenit ad <lb/>quadraturam eius cum &longs;ole primam, &longs;ed e&longs;t inter coniunctio­<lb/>nem, & quadraturam primam: & cum luna ueniet ad con­<lb/>iunctionem eius cum &longs;ole, iterum tota di&longs;po&longs;itio iam narra­<lb/>ta redibit eodem modo penitus, &longs;icut dictum e&longs;t. </s> <s>i&longs;te er­<lb/>go motus aquæ maris, qui dictus e&longs;t, e&longs;t motus aquæ ma­<lb/>ris in&longs;equens motum &longs;olis, & lunæ ad motum &longs;cilicet pri­<lb/>mi mobilis. </s> <s>nam &longs;i bene con&longs;ideraueris ea, quæ dicta &longs;unt <lb/>de fluxu, & refluxu, &longs;eu cremento, & decremento, aut <lb/>acce&longs;&longs;u, & rece&longs;&longs;u aquæ maris, cogno&longs;ces, quòd initia <lb/>fluxus, & refluxus, &longs;eu crementi, & decrementi aquæ <lb/>maris, & &longs;imiliter quies eius diuer&longs;ificantur in horis diei, & <pb xlink:href="024/01/028.jpg"/>noctis: non enim &longs;emper eadem hora diei fiunt &longs;icut manife­<lb/>&longs;tum e&longs;t ob&longs;eruantibus huiu&longs;modi fluxum, & refluxum, &longs;eu <lb/>crementum, & decrementum, & quietem fal&longs;am aquæ maris. <lb/></s> <s>Ex dictis apparet, quòd aqua maris habet motum acce&longs;&longs;io­<lb/>nis, &longs;eu crementi in die &longs;emel, & in nocte &longs;emel. </s></p><p type="main"> <s>Similiter apparet, quòd aqua maris habet motum rece&longs;&longs;ionis, <lb/>&longs;eu decrementi in die &longs;emel, & in nocte &longs;emel. </s></p><p type="main"> <s>Apparet etiam quòd acce&longs;&longs;io, &longs;eu crementum aquæ maris <expan abbr="nõ">non</expan> <lb/>incipit eadem hora diei, uel noctis &longs;emper, &longs;ed diuer&longs;is horis, <lb/>& &longs;imiliter rece&longs;&longs;io, &longs;eu decrementum. </s></p><p type="main"> <s>Et etiam tempus, in quo tam acce&longs;&longs;io, &longs;eu crementum, quàm <lb/>rece&longs;&longs;io, &longs;eu decrementum aquæ maris inordinate procedit, <lb/>quando &longs;cilicet luna e&longs;t in quadraturis eius cum &longs;ole prima, &longs;ci <lb/>licet uel &longs;ecunda. </s></p><p type="main"> <s>Fiunt aliquando maximi aquarum cur&longs;us, aliquando minimi, <lb/>& aliquando medio modo &longs;e habentes, &longs;eu mediocres, quan­<lb/>do &longs;cilicet luna fuerit in omni alio loco à &longs;ole, præter hæc qua­<lb/>tuor, uidelicet in coniunctione, uel oppo&longs;itione, aut quadra­<lb/>tura eius prima, aut &longs;ecunda cum &longs;ole. </s></p><p type="main"> <s>Fiunt aliquando maxima crementa aquarum, aliquando mi­<lb/>nima, & aliquando medio modo &longs;e habentia. </s></p><p type="main"> <s>Fiunt &longs;imiliter aliquando maxima decrementa aquarum, ali­<lb/>quando minima, & aliquando medio modo &longs;e habentia. </s></p><p type="main"> <s>Incrementa, &longs;eu argumentationes aquarum fiunt aliquando <lb/>maiora, aliquando minora. </s></p><p type="main"> <s>Maximi cur&longs;us, &longs;eu motus aquarum fiunt luna coniuncta &longs;oli, <lb/>& maxima crementa, & decrementa. </s></p><p type="main"> <s>Maximi cur&longs;us, &longs;eu motus aquarum &longs;imiliter fiunt luna oppo­<lb/>&longs;ita &longs;oli, & maxima crementa, & decrementa, & maiora quàm <lb/>tempore coniunctionis luna cum &longs;ole: corpora enim &longs;uperio­<lb/>ra infundunt uir tutes &longs;uas in i&longs;tis inferioribus per motum eo­<lb/>rum, & lumen: quanto enim plus habent de lumine, tanto <lb/>plus, & fortius operantur: & quia in oppo&longs;itione lunæ cum <lb/>&longs;ole, luna e&longs;t plena lumine, & lumen eius e&longs;t uer&longs;us nos, ideo <lb/>rationabile e&longs;t, ut cau&longs;entur maiora crementa, & decrementa <pb xlink:href="024/01/029.jpg" pagenum="11"/>aquarum, quàm in coniunctione eius cum &longs;ole, quia tamen in <lb/>coniunctione eius cum &longs;ole, &longs;ol, & luna &longs;unt unici &longs;imul, & eo­<lb/>rum uirtutes: ideo fiunt etiam crementa, & decrementa a­<lb/>quarum magna, quia ambæ uirtutes, &longs;cilicet &longs;olis, & lunæ <lb/>&longs;unt unicæ &longs;imul, &longs;ed maiora fiunt in oppo&longs;itione, quàm in <lb/>coniunctione propter cau&longs;am dictam. </s></p><p type="main"> <s>Luna exi&longs;tente in quadraturis eius cum &longs;ole aqua maris nul­<lb/>lum habet determinatum tempus acce&longs;&longs;ionis, uel rece&longs;&longs;ionis, <lb/>&longs;eu crementi, aut decrementi: & tunc fiunt minimi cur&longs;us a­<lb/>quarum, & minima crementa, & decrementa: & talis motus <lb/>aquæ maris e&longs;t dictus à Venetis, De fele. </s> <s>& tunc aqua maris <lb/>nullum habet terminatum principium acce&longs;&longs;ionis, uel rece&longs;­<lb/>&longs;ionis, &longs;eu crementi, aut decrementi, &longs;ed diuer&longs;imode, & in­<lb/>ordinate mouetur: aliquando enim accedit, aliquando rece­<lb/>dit. </s> <s>huius autem uarietatis cau&longs;a e&longs;t, quia &longs;ol, & luna ubicun<lb/>que fuerint in mouendo aquam &longs;ibi inuicem æqualiter, uel <lb/>qua&longs;i æqualiter contradicunt in quocunque puncto fuerint: <lb/>in quocunque enim puncto fuerit &longs;ol, luna erit in puncto uir­<lb/>tutis oppo&longs;itæ, & contrariæ loco &longs;olis, uel prope. </s></p><p type="main"> <s>Cum autem luna erit extra quatuor loca dicta tunc aqua ma­<lb/>ris incipiet accedere, uel recedere: quando &longs;ol, & luna erunt <lb/>in punctis æqualibus uirtutis quartarum contrariæ operatio­<lb/>nis, erunt etiam cur&longs;us aquarum tanto maiores, quanto luna <lb/>fuerit propinquior coniunctioni eius cum &longs;ole, uel oppo&longs;itio­<lb/>ni: & tanto minores, quanto luna fuerit propinquior qua­<lb/>draturis: &longs;imiliter etiam erunt incrementa, & decrementa <lb/>tanto maiora. </s> <s>&longs;i enim luna erit inter coniunctionem eius cum <lb/>&longs;ole, & quadraturam primam, tunc luna ad motum primi <lb/>mobilis &longs;equitur &longs;olem in ortu &longs;uo, & tunc erit principium ac­<lb/>ce&longs;&longs;ionis diurnæ aquæ maris de die. </s> <s>po&longs;t ortum &longs;olis circa ho<lb/>ram tertiam, uel ante, quando &longs;cilicet &longs;ol erit tantum &longs;upra o­<lb/>rizontem ex parte orientis in quarta diurna fluxus, quantum <lb/>luna &longs;ub orizonte ex eadem parte orientis in quarta nocturna <lb/>refluxus, eo quia tunc &longs;ol, & luna erunt æquipotentes, quia <lb/>erunt in punctis æqualis uirtutis in quartis contrariæ opera­<pb xlink:href="024/01/030.jpg"/>tionis: & principium acce&longs;&longs;ionis nocturnæ aquæ maris erit de <lb/>nocte po&longs;t occa&longs;um &longs;olis, quando &longs;cilicet &longs;ol erit tantum &longs;ub <lb/>orizonte ex parte occidentis in quarta nocturna fluxus, quan­<lb/>tum luna &longs;upra orizontem ex eadem parte occidentis in quar<lb/>ta diurna refluxus. </s> <s>principium autem rece&longs;&longs;ionis diurnæ erit <lb/>de die po&longs;t meridiem, quando &longs;cilicet &longs;ol erit tantum po&longs;t me­<lb/>ridiem in quarta diurna refluxus, quantum luna ante meri­<lb/>diem in quarta diurna fluxus: & principium rece&longs;&longs;ionis no­<lb/>cturnæ erit de nocte po&longs;t medium noctis, quando &longs;cilicet &longs;ol <lb/>erit tantum po&longs;t punctum mediæ noctis in quarta nocturna re­<lb/>fluxus, quantum luna ante ip&longs;um in quarta nocturna fluxus. <lb/></s> <s>&longs;i autem luna fuerit inter quadraturam primam, & oppo&longs;itio­<lb/>nem, adhuc luna in &longs;uo ortu &longs;equitur &longs;olem, & tunc erit prin<lb/>cipium acce&longs;&longs;ionis diurnæ de die po&longs;t meridiem circa ue&longs;pe­<lb/>ras, uidelicet parum ante, uel po&longs;t, quando &longs;cilicet &longs;ol fuerit <lb/>tantum &longs;upra orizontem ex parte occidentis in quarta diurna <lb/>refluxus, quantum luna &longs;upra orizontem ex parte orientis in <lb/>quarta diurna fluxus. </s> <s>principium autem acce&longs;&longs;ionis nocturnæ <lb/>erit de nocte ante diem, uidelicet circa matutinum ante, uel <lb/>po&longs;t, quando &longs;cilicet &longs;ol erit tantum &longs;ub orizonte à parte ori­<lb/>entis in quarta nocturna refluxus, quantum luna &longs;ub orizon<lb/>te ex parte occidentis in quarta nocturna fluxus. </s> <s>principium <lb/>uero rece&longs;&longs;ionis diurnæ erit de die ante meridiem, quando &longs;ci <lb/>licet &longs;ol erit tantum ante punctum meridiei, quantum luna <lb/>po&longs;t punctum mediæ noctis. </s> <s>principium autem rece&longs;&longs;ionis no<lb/>cturnæ erit de nocte ante medium noctis, quando &longs;cilicet &longs;ol <lb/>fuerit tantum ante punctum mediæ noctis in quarta nocturna <lb/>fluxus, quantum luna po&longs;t punctum meridiei in quarta diur­<lb/>na refluxus. </s> <s>&longs;i autem luna fuerit inter oppo&longs;itionem &longs;olis, & <lb/>quadraturam &longs;ecundam eius cum &longs;ole, tunc luna in ortu &longs;uo <lb/>antecedit &longs;olem, & tunc principia tam acce&longs;&longs;ionis, quàm re­<lb/>ce&longs;&longs;ionis &longs;unt eodem modo &longs;icut fuerunt, quando luna fuit <lb/>inter coniunctionem, & quadraturam primam: nam princi­<lb/>pium acce&longs;&longs;ionis diurnæ erit de die circa tertiam ante, uel po&longs;t, <lb/>quando &longs;cilicet &longs;ol erit tantum &longs;upra orizontem ex parte <pb xlink:href="024/01/031.jpg" pagenum="12"/>orientis in quarta diurna fluxus, quantum luna &longs;upra orizon­<lb/>tem ex parte occidentis in quarta diurna refluxus: & princi­<lb/>pium acce&longs;&longs;ionis nocturnæ erit de nocte, quando &longs;cilicet &longs;ol e­<lb/>rit tantum &longs;ub orizonte ex parte occidentis in quarta noctur­<lb/>na fluxus, quantum luna &longs;ub orizonte ex parte orientis in <lb/>quarta nocturna refluxus: &longs;ed principium rece&longs;&longs;ionis diurnæ <lb/>erit de die po&longs;t meridiem, quando &longs;cilicet &longs;ol fuerit <expan abbr="tantũ">tantum</expan> po&longs;t <lb/>punctum meridiei in quarta diurna refluxus, quantum luna <lb/>ante punctum mediæ noctis in quarta nocturna fluxus. </s> <s>prin­<lb/>cipium uero rece&longs;&longs;ionis nocturnæ erit de nocte, quando &longs;cili­<lb/>cet &longs;ol fuerit tantum po&longs;t punctum mediæ noctis in quarta no<lb/>cturna refluxus, quantum luna ante punctum meridiei in quar<lb/>ta diurna fluxus. </s> <s>&longs;i autem luna fuerit inter quadraturam &longs;e­<lb/>cundam, & coniunctionem eius cum &longs;ole, tunc luna etiam in <lb/>&longs;uo ortu antecedit &longs;olem, & erunt tunc principia acce&longs;&longs;ionis, <lb/>& rece&longs;&longs;ionis in ei&longs;dem horis, &longs;icut &longs;unt quando luna e&longs;t in­<lb/>ter quadraturam primam, & oppo&longs;itionem, quia principium <lb/>acce&longs;&longs;ionis diurnæ erit de die po&longs;t meridiem circa ue&longs;peras, <lb/>ante, &longs;cilicet uel po&longs;t, quando &longs;cilicet &longs;ol erit tantum &longs;upra o­<lb/>rizontem ex parte occidentis in quarta diurna refluxus, quan <lb/>tum luna &longs;ub orizonte ex eadem parte occidentis in quarta <lb/>nocturna fluxus. </s> <s>principium uero acce&longs;&longs;ionis nocturnæ erit <lb/>de nocte circa matutinum ante, uel po&longs;t, quando &longs;cilicet &longs;ol <lb/>fuerit tantum &longs;ub orizonte ex parte orientis in quarta noctur­<lb/>na refluxus, quantum luna &longs;upra orizontem ex eadem parte <lb/>orientis in quarta diurna fluxus: &longs;ed principium rece&longs;&longs;ionis <lb/>diurnæ erit de die ante meridiem, quando &longs;cilicet luna erit <lb/>tantum po&longs;t punctum meridiei in quarta diurna refluxus, <lb/>quantum &longs;ol ante ip&longs;um in quarta diurna fluxus: & principi­<lb/>um rece&longs;&longs;ionis nocturnæ erit de nocte ante medium noctis, <lb/>quando &longs;cilicet luna erit tantum po&longs;t punctum mediæ noctis <lb/>in quarta nocturna refluxus, quantum &longs;ol ante punctum me­<lb/>diæ noctis in quarta nocturna fluxus. </s> <s>ex i&longs;tis dictis apparet, <lb/>quòd tam acce&longs;&longs;io, quàm rece&longs;&longs;io aquæ maris non incipiunt <lb/>&longs;emper in ei&longs;dem horis diei, uel noctis, quia principium <pb xlink:href="024/01/032.jpg"/>acce&longs;&longs;ionis, aut e&longs;t in principio diei, aut in principio noctis, <lb/>quod accidit luna exi&longs;tente coniuncta uel oppo&longs;ita &longs;oli, uel e&longs;t <lb/>ante diem à matutinis uer&longs;us diem, uel de die, u&longs;que ad ter­<lb/>tiam, uel circa; uel e&longs;t ante &longs;erum à ue&longs;peris uer&longs;us &longs;erum, u&longs;­<lb/>que ad <expan abbr="galicãtum">galicantum</expan>, uel circa quod accidit, quando luna e&longs;t in­<lb/>ter coniunctionem, uel oppo&longs;itionem eius cum &longs;ole, & ali­<lb/>quam ex quadraturis. </s> <s>principium autem rece&longs;&longs;ionis, aut e&longs;t <lb/>in meridie, aut in medio noctis, quando &longs;cilicet luna e&longs;t con­<lb/>iuncta &longs;oli, uel ei oppo&longs;ita, aut e&longs;t ante meridiem, uel po&longs;t, <lb/>aut ante medium noctis, uel po&longs;t, quando &longs;cilicet luna e&longs;t in­<lb/>ter coniunctionem, uel oppo&longs;itionem eius cum &longs;ole, & ali­<lb/>quam ex quadraturis. </s> <s>apparet etiam, quòd aliquando aqua <lb/>maris nullum habet terminatum principium, nec ordinem <lb/>acce&longs;&longs;ionis, uel rece&longs;&longs;ionis, quod accidit luna exi&longs;tente in qua­<lb/>draturis eius cum &longs;ole. </s> <s>apparet etiam, quod omnis acce&longs;&longs;io <lb/>aquæ maris fit per re&longs;pectum ad orizontem ex parte orientis, <lb/>uel occidentis: & omnis rece&longs;&longs;io per re&longs;pectum ad meridia­<lb/>num, &longs;eu ad punctum meridiei, uel mediæ noctis. </s></p><p type="main"> <s>Aduertendum e&longs;t etiam, quòd omnia, quæ dicta &longs;unt, maxime <lb/>habent ueritatem in orizonte recto, in obliquo uero aliquo <lb/>tempore aliquod fallunt, &longs;icut &longs;ic infra dicetur. </s></p><p type="main"> <s>Contingit autem aquam maris à &longs;upra &longs;cripto ordine motus <lb/>deuiare: communiter tamen, & ut in pluribus debitum or­<lb/>nem ob&longs;eruat. </s> <s>talis autem deuiatio à &longs;upra&longs;cripto ordine du­<lb/>plex e&longs;t; aut enim e&longs;t deuiatio, &longs;eu error in hora principii mo<lb/>tus acce&longs;&longs;ionis, uel rece&longs;&longs;ionis, aut in medio motus, uidelicet <lb/>quòd maiores, uel minores cur&longs;us habeant &longs;olito, uel maio­<lb/>ra, aut minora habeant incrementa, aut decrementa. </s> <s>error <lb/>ueniens in hora motus, triplici de cau&longs;a pote&longs;t accidere, aut <lb/>ratione &longs;itus regionis, aut ratione corporum &longs;uper cæle&longs;tium, <lb/>aut propter mutationem aeris: ratione &longs;itus regionum accidit <lb/>diuer&longs;itas &longs;olum in hora principii acce&longs;&longs;ionis, eo quia princi­<lb/>pium acce&longs;&longs;ionis habet re&longs;pectum ad orizontem, &longs;eu e&longs;t per <lb/>re&longs;pectum ad orizontem: in principio autem rece&longs;&longs;ionis nul­<lb/>la e&longs;t diuer&longs;itas, nec error, eo quia principium rece&longs;&longs;ionis e&longs;t <pb xlink:href="024/01/033.jpg" pagenum="13"/>per re&longs;pectum ad circulum meridianum: ratione &longs;itus re­<lb/>gionis accidit diuer&longs;itas propter hoc, aut enim e&longs;t regio &longs;ub <lb/>æquinoctiali circulo, aut extra; &longs;i &longs;ub æquinoctiali circulo, <lb/>quia illi habent orizontem rectum, & dies ibi &longs;emper &longs;unt <lb/>æquales noctibus ibi in omni tempore anni ea, quæ dicta <lb/>&longs;unt de diuer&longs;is horis principii acce&longs;&longs;ionis aquæ maris maxi­<lb/>me habent ueritatem. </s> <s>regiones autem di&longs;tantes ab æquino­<lb/>ctiali, quia habent orizontem obliquum, in eis principia <lb/>acce&longs;&longs;ionis aquæ &longs;unt, &longs;icut in regionibus, quæ &longs;unt &longs;ub æ­<lb/>quinoctiali &longs;olum in duobus temporibus anni, uidelicet in <lb/>tempore ueris, &longs;eu æquinoctii uernalis, & in tempore autum­<lb/>ni, &longs;eu æquinoctii autumnalis, uidelicet circa medium men­<lb/>&longs;is Martii, & circa medium men&longs;is Septembris. <!-- KEEP S--></s> <s>in aliis au­<lb/>tem temporibus anni, &longs;eu ab æquinoctio uernali per totam <lb/>æ&longs;tatem, u&longs;que ad æquinoctium autumnale aliter e&longs;t, quia <lb/>principium acce&longs;&longs;ionis diurnæ &longs;i ip&longs;a acce&longs;&longs;io e&longs;t ante meri­<lb/>diem, uidelicet circa mane, erit tardius, quàm e&longs;&longs;e debet, <lb/>uidelicet plus de die, quàm fiat in regionibus, quæ &longs;unt &longs;ub <lb/>æquinoctiali: & hoc ideo e&longs;t, quia in talibus regionibus dies <lb/>incipit prius, &longs;eu &longs;ol oritur priu&longs;quam in regionibus, quæ <lb/>&longs;unt &longs;ub æquinoctiali propter obliquitatem orizontis obli­<lb/>qui (quamuis regiones ip&longs;æ &longs;int &longs;ub eodem meridiano) quod <lb/>&longs;i principium acce&longs;&longs;ionis diurnæ fuerit po&longs;t meridiem, uide­<lb/>licet circa &longs;erum, tunc tale principium erit citiu&longs;quam &longs;it in <lb/>regionibus, quæ &longs;unt &longs;ub æquinoctiali, ide&longs;t in paucioribus <lb/>horis diei: & hoc ideo e&longs;t, quia tunc &longs;ol tardius occidit, <lb/>quàm in regionibus, quæ &longs;unt &longs;ub æquinoctiali. </s> <s>principium <lb/>uero acce&longs;&longs;ionis nocturnæ &longs;i e&longs;t ante medium noctis, fit in di­<lb/>ctis locis, &longs;eu regionibus citius, ide&longs;t in minori tempore no­<lb/>ctis, &longs;eu in breuiori tempore po&longs;t occa&longs;um &longs;olis, quàm fiat in <lb/>regionibus, quæ &longs;unt &longs;ub æquinoctiali, quia tunc nox incipit <lb/>eis po&longs;t, quòd &longs;i principium acce&longs;&longs;ionis nocturnæ e&longs;t po&longs;t me­<lb/>diam noctem, uidelicet uer&longs;us diem, fiet tardius, ide&longs;t ad plu<lb/>res horas noctis, &longs;eu magis prope die, quàm in regionibus, <lb/>quæ &longs;unt &longs;ub æquinoctiali, & hoc ideo e&longs;t, quia &longs;ol citius eis <pb xlink:href="024/01/034.jpg"/>oritur, quàm eis, qui &longs;unt &longs;ub æquinoctiali, & hæc diuer&longs;itas <lb/>tantum cre&longs;cit, quod aliquando contingit uidere duas acce&longs;­<lb/>&longs;iones aquæ in die, & nullam in nocte; quod quidem accidit <lb/>propter inæqualitatem dierum cum &longs;uis noctibus: quanto e­<lb/>nim dies artificialis fuerit longior &longs;ua nocte, tanto talis diuer­<lb/>&longs;itas, & error euidentius cre&longs;cit. </s> <s>quare in longioribus diebus <lb/>anni talis diuer&longs;itas apparebit manife&longs;te; &longs;ed ab æquinoctio <lb/>autumnali per totam hiemem, u&longs;que ad æquinoctium uerna­<lb/>le fit contrarium, quia principium acce&longs;&longs;ionis diurnæ &longs;i fuerit <lb/>ante meridiem, &longs;cilicet circa mane, tunc erit citius, quàm de­<lb/>beret e&longs;&longs;e, ide&longs;t in paucioribus horis diei, quàm fiat in orizon<lb/>te recto, quia tunc tardius incipit dies, &longs;eu tardius oritur &longs;ol <lb/>habentibus orizontem obliquum, quàm habentibus orizon­<lb/>tem rectum; quòd &longs;i talis acce&longs;&longs;us fuerit po&longs;t meridiem, &longs;cili­<lb/>cet circa &longs;erum, tunc principium talis acce&longs;&longs;ionis erit tardius, <lb/>ide&longs;t magis uer&longs;us &longs;erum, &longs;eu magis iuxta occa&longs;um &longs;olis, quàm <lb/>in regionibus, quæ &longs;unt &longs;ub æquinoctiali, quia in orizonte <lb/>obliquo fit citius nox, & &longs;ol citius occidit, quàm in recto. </s> <s>prin<lb/>cipium ueto acce&longs;&longs;ionis nocturnæ &longs;i fuerit ante medium noctis <lb/>erit tardius, & plus in nocte, quàm in regionibus, quæ &longs;unt <lb/>&longs;ub æquinoctiali; & hoc ideo e&longs;t, quia tunc nox in orizonte <lb/>obliquo prius incipit, quàm in recto, quia &longs;ol prius occidit in <lb/>orizonte obliquo, quàm in recto; quòd &longs;i principium acce&longs;&longs;io­<lb/>nis nocturnæ fuerit po&longs;t mediam noctem, ide&longs;t uer&longs;us diem, <lb/>tunc tale principium acce&longs;&longs;ionis in orizonte obliquo fiet citi­<lb/>us, ide&longs;t in paucioribus horis noctis, ide&longs;t magis ante diem, <lb/>&longs;eu ante ortum &longs;olis, quàm fiat in regionibus, quæ &longs;unt &longs;ub æ­<lb/>quinoctiali, eo quia &longs;ol oritur tardius, quàm in regionibus, <lb/>quæ &longs;unt &longs;ub æquinoctiali, & talis diuer&longs;itas in tantum cre&longs;cit, <lb/>quòd aliquando fient duæ acce&longs;&longs;iones aquæ in nocte, & nullæ <lb/>in die: & hoc quidem accidet propter inæqualitatem, & augu­<lb/>mentum noctis &longs;upra diem &longs;uam: quanto enim nox fuerit lon­<lb/>gior &longs;ua die, tanto magis cre&longs;cit talis diuer&longs;itas: quare talis di­<lb/>uer&longs;itas apparebit maxima in longiori nocte anni. </s> <s>ex dictis er<lb/>go apparet, quòd quanto fuerimus propinquiores æquinoctio, <pb xlink:href="024/01/035.jpg" pagenum="14"/>tanto minor apparebit diuer&longs;itas in hora principii acce&longs;&longs;ionis <lb/>aquæ: & quanto &longs;ol fuerit propinquior &longs;ol&longs;titiis, &longs;eu longiori­<lb/>bus diebus, & longioribus noctibus, tanto maior erit diuer&longs;itas, <lb/>& certior, & manife&longs;tius apparebit. </s> <s>ratione autem corporum <lb/>cæle&longs;tium etiam accidit diuer&longs;itas, & error in principiis non &longs;o<lb/>lum acce&longs;&longs;ionis, uerum etiam rece&longs;&longs;ionis. </s></p><p type="main"> <s>Cum enim aliqua ex &longs;tellis magnis, & lumino&longs;is (ut &longs;unt Venus, <lb/>& Iuppiter) fuerit circa &longs;olem, uel lunam; illum, uel <expan abbr="illã">illam</expan> adiu­<lb/>uant in mouendo aquam maris: quare relinquunt debitum or<lb/>dinem. </s> <s>ratione uero mutationis aeris, &longs;æpe contingit diuer&longs;i­<lb/>tas, & error in principiis acce&longs;&longs;ionis, & rece&longs;&longs;ionis aquæ maris. <lb/></s> <s>impetuo&longs;a enim di&longs;po&longs;itio uentorum tam de prope, quàm de <lb/>longe in&longs;uflantium remouet cur&longs;us aquarum à debito ordine <lb/>aliquando fe&longs;tinando acce&longs;&longs;us, aliquando rece&longs;&longs;us. </s> <s>&longs;imiliter & <lb/>ip&longs;os po&longs;tponere faciendo. </s> <s>error etiam accidit in medio mo­<lb/>tus aquarum, quia tam cur&longs;us aquarum, quàm etiam incre­<lb/>menta, & decrementa earum aliquando non &longs;eruant <expan abbr="debitũ">debitum</expan> <lb/>motum. </s> <s>di&longs;po&longs;itio enim uentorum ad maiores, uel minores <lb/>cur&longs;us augumentum præbent: quare & maiora incrementa, <lb/>& decrementa accidunt: maiores etiam cur&longs;us, & <expan abbr="diuer&longs;itat&etilde;">diuer&longs;itatem</expan> <lb/>maiorem euenire faciunt coarctationes, & &longs;tricturæ locorum <lb/>ratione in&longs;ularum, uel montium in aliquibus locis maximis exi<lb/>&longs;tentium; quia ubi arctius, &longs;eu &longs;trictius exi&longs;tit mare, ibi fortior <lb/>cur&longs;us exi&longs;tit, ut circa Eubœam <expan abbr="in&longs;ulã">in&longs;ulam</expan> Nigropontis, & inter <lb/>Siciliam, & Calabriam &longs;æpe notari pote&longs;t. </s> <s>impediunt etiam ta<lb/>les &longs;tricturæ augumentationes aquarum: per &longs;trictum enim lo<lb/>cum modica quantitas aquæ tran&longs;ire pote&longs;t. </s> <s>quare augumen<lb/>tationes, & diminutiones minores fiunt, & ideo accidit, quòd <lb/>in Oceano maxima fiunt crementa, & decrementa. </s> <s>nulla enim <lb/>ibi ade&longs;t &longs;trictura impediens cur&longs;us aquarum: quare ibi motus <lb/>aquarum e&longs;t liber, & aqua ibi incedit ordine certiori: &longs;ed in <lb/>mari no&longs;tro Mediterraneo aliter e&longs;t, quia quicquid in eo ingre<lb/>ditur, uel egreditur ex mari Oceano, per unum <expan abbr="&longs;olũ">&longs;olum</expan>, & <expan abbr="&longs;trictũ">&longs;trictum</expan> <lb/>locum à parte occidentis tran&longs;it. </s> <s>quare non pote&longs;t <expan abbr="multũ">multum</expan> in ac­<lb/>ce&longs;&longs;u impleri, nec multum in rece&longs;&longs;u euacuari. </s> <s>& ex con&longs;equen<lb/>ti motus aquæ maris non ita certo ordine incedit. </s> <s>& hæc de <lb/>diuer&longs;is motibus aquæ maris dicta &longs;ufficiunt. </s></p><pb xlink:href="024/01/036.jpg"/><pb xlink:href="024/01/037.jpg"/><figure id="id.024.01.037.1.jpg" xlink:href="024/01/037/1.jpg"/><p type="caption"> <s>Figura o&longs;tendens initium crementi diurni in <lb/>ortu &longs;olis, & initium decrementi diurni in <lb/>meridie, & initium crementi nocturni in oc<lb/>ca&longs;u &longs;olis, & initium decrementi nocturni in <lb/>medio noctis. </s></p><pb xlink:href="024/01/038.jpg"/><figure id="id.024.01.038.1.jpg" xlink:href="024/01/038/1.jpg"/><p type="caption"> <s>Figura o&longs;tendens initium crementi diurni po&longs;t or­<lb/>tum &longs;olis ante, uel po&longs;t horam tertiarum &longs;ecun­<lb/>dum quod luna di&longs;teterit a &longs;ole plus, uel minus, <lb/>& nondum uenerit ad <expan abbr="quadratutã">quadratutam</expan> eius cum &longs;ole <lb/><expan abbr="primã">primam</expan>: & <expan abbr="initiũ">initium</expan> <expan abbr="decrem&etilde;ti">decrementi</expan> diurni po&longs;t <expan abbr="meridi&etilde;">meridiem</expan> ante <lb/>uel po&longs;t horam <expan abbr="ue&longs;perarũ">ue&longs;perarum</expan>, & <expan abbr="initiũ">initium</expan> crementi nocturni <lb/>po&longs;t occa&longs;um &longs;olis, & <expan abbr="initiũ">initium</expan> <expan abbr="decrem&etilde;ti">decrementi</expan> diurni po&longs;t <lb/>mediam noctem ante, uel po&longs;t horam matutini. </s></p><pb xlink:href="024/01/039.jpg"/><figure id="id.024.01.039.1.jpg" xlink:href="024/01/039/1.jpg"/><figure id="id.024.01.039.2.jpg" xlink:href="024/01/039/2.jpg"/><pb xlink:href="024/01/040.jpg"/><pb xlink:href="024/01/041.jpg"/><p type="caption"> <s>Figura o&longs;tendens quietem &longs;al&longs;am, & mo­<lb/>tum inordinatum, & minimum cremen<lb/>ti, & decrementi aquæ matutini.</s></p><pb xlink:href="024/01/042.jpg"/><figure id="id.024.01.042.1.jpg" xlink:href="024/01/042/1.jpg"/><p type="caption"> <s>Figura o&longs;tendens initium crementi circa matutini <lb/>ante, uel po&longs;t: & initium decrementi po&longs;t horam <lb/>tertiarum, & initium crementi po&longs;t ue&longs;peras, & <lb/>initium decrementi ante medium noctis. <pb xlink:href="024/01/043.jpg"/><figure id="id.024.01.043.1.jpg" xlink:href="024/01/043/1.jpg"/><pb xlink:href="024/01/044.jpg"/><figure id="id.024.01.044.1.jpg" xlink:href="024/01/044/1.jpg"/></s></p><pb xlink:href="024/01/045.jpg"/><figure id="id.024.01.045.1.jpg" xlink:href="024/01/045/1.jpg"/><p type="caption"> <s>Figura o&longs;tendens initium <gap/><lb/>ortu <gap/>, <gap/> initium decrem<gap/><lb/>meridie, & initium crementi <gap/><lb/>ca&longs;u &longs;olis, & initium decrementi<gap/></s></p><pb xlink:href="024/01/046.jpg"/><figure id="id.024.01.046.1.jpg" xlink:href="024/01/046/1.jpg"/><p type="caption"> <s>Figura o&longs;tendens initium crementi po&longs;t ortum &longs;o­<lb/>lis circa horam tertiarum, uel ante: & <expan abbr="initiũ">initium</expan> decre<lb/><expan abbr="m&etilde;ti">menti</expan> circa ue&longs;peras, & <expan abbr="initiũ">initium</expan> crementi ante medi­<lb/>um noctis, & initium <expan abbr="decrem&etilde;ti">decrementi</expan> po&longs;t <expan abbr="mediũ">medium</expan> nocti. </s></p><pb xlink:href="024/01/047.jpg"/><pb xlink:href="024/01/048.jpg"/><figure id="id.024.01.048.1.jpg" xlink:href="024/01/048/1.jpg"/><figure id="id.024.01.048.2.jpg" xlink:href="024/01/048/2.jpg"/><pb xlink:href="024/01/049.jpg"/><p type="caption"> <s>Figura o&longs;tendens quietem &longs;al&longs;am, & mo­<lb/>tum<gap/> nord<gap/>natum, & minimum cr<gap/><lb/>ti, & d<gap/>crementi aquæ <gap/>.</s></p><pb xlink:href="024/01/050.jpg"/><figure id="id.024.01.050.1.jpg" xlink:href="024/01/050/1.jpg"/><p type="caption"> <s>Figura o&longs;tendens initium crementi circa <lb/>matutinum ante ortum &longs;olis: & <expan abbr="initiũ">initium</expan> de­<lb/>crementi po&longs;t horam tertiarum, & ante <lb/>meridiem: & initium crementi ante occa­<lb/>&longs;um &longs;olis po&longs;t ue&longs;peras: & initium decre­<lb/>menti ante medium noctis.</s></p><pb xlink:href="024/01/051.jpg" pagenum="19"/><p type="main"> <s><emph type="center"/>FEDERICI DELPHINI <emph.end type="center"/><!-- REMOVE S--><emph type="center"/>DE MOTV OCTAVAE<emph.end type="center"/><!-- REMOVE S--><emph type="center"/> SPHAERAE<emph.end type="center"/><!-- REMOVE S--><emph type="center"/> TRACTATVS.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> <s>SCIENDVM e&longs;t primo, quòd circa numerum &longs;phæra­<lb/>rum cæle&longs;tium tres &longs;unt opiniones diuer&longs;æ: una e&longs;t philo&longs;o­<lb/>phorum, & a&longs;trologorum Indorum, quæ e&longs;t, quòd &longs;phæræ <lb/>cæle&longs;tes &longs;int octo tantum, uidelicet &longs;eptem &longs;phæræ planeta­<lb/>rum, & octaua &longs;phæra &longs;tellata, quæ e&longs;t primum mobile &longs;ecun<lb/>dum i&longs;tam opinionem; quæ mouetur motu diurno, uidelicet <lb/>in una die naturale, quæ e&longs;t tempus uiginti quatuor hora­<lb/>rum, una reuolutione completa, ab oriente &longs;cilicet uer&longs;us oc<lb/>cidentem, reuoluendo &longs;ecum tali motu omnes alias &longs;phæras <lb/>inferiores. </s> <s>alia e&longs;t Ptolomæi, Alfragræni Alchabitii, Ioannis <lb/>de Sacrobu&longs;to, & Thebit; qui &longs;phæræ cæle&longs;tes &longs;int nouem: <lb/>& hæc opinio e&longs;t bipartita, quia Ptolemæus, Alfragrænus Al­<lb/>chabitius, & Ioannes de Sacrobu&longs;to dicunt, quòd nona &longs;phæ<lb/>ra e&longs;t primum mobile, & quòd ip&longs;a e&longs;t illa, quæ mouetur mo<lb/>tu diurno, reuoluendo omnes alias &longs;phæras inferiores, uide­<lb/>licet octauam, & &longs;eptimam &longs;phæram &longs;eptem planetarum &longs;e­<lb/>cum: & quòd octaua &longs;phæra, & aliæ inferiores ei mouentur <lb/>duplici motu: uno uidelicet diurno, quo reuoluuntur à nona <lb/>omni die naturali, una reuolutione completa: & alio pro­<lb/>prio octauæ tardo, &longs;cilicet ad contrarium nonæ &longs;phæræ &longs;uper <lb/>polis zodiaci &longs;ui exi&longs;tentibus in directo polorum zodiaci no­<lb/>næ &longs;emper; adeo quòd &longs;emper zodiacus octauæ e&longs;t &longs;ub zodia­<lb/>ci nonæ &longs;phæræ eclipticæ octauæ &longs;ub ecliptica nonæ, & poli <lb/>zodiaci octauæ &longs;ub polis zodiaci nonæ, in centum annis uno <lb/>gradu uer&longs;us orientem contrariæ, & taliter, quòd &longs;emper e­<lb/>clipticæ octauæ &longs;phæræ e&longs;&longs;ent &longs;ub ecliptica nonæ. </s> <s>aliæ autem <lb/>&longs;phæræ inferiores octauæ, ultra i&longs;tos duos motus, habent <lb/>motus &longs;ibi proprios ab occidente uer&longs;us orientem, ut in <pb xlink:href="024/01/052.jpg"/>theoricis earum uidebitur. </s></p><p type="main"> <s>Thebit autem uolens &longs;aluare uariationem declinationis &longs;olis <lb/>ab æquinoctiali, qui &longs;emper, & continue mouetur motu pro­<lb/>prio ab occidente uer&longs;us orientem &longs;ub ecliptica octauæ &longs;phæ­<lb/>ræ; quam declinationem inuenit Ptolomæus tempore &longs;uo e&longs;&longs;e <lb/>XXIII graduum, LI minutorum, & XX &longs;ecundorum, & Al­<lb/>meon, & Albategni, qui fuerunt po&longs;teriores Ptolomæo, inue­<lb/>nerunt eam e&longs;&longs;e XXIII graduum, XXXIII minutorum, & <lb/>XXX &longs;ecundorum dixit octauam &longs;phæram moueri, quòd à <lb/>motu titubationis, &longs;eu acce&longs;&longs;us, & rece&longs;&longs;us in circumferentiis <lb/>duorum circulorum paruorum æqualium, quorum media, &longs;eu <lb/>poli, &longs;eu centra &longs;unt ip&longs;a capita, &longs;eu principia arietis, & libræ <lb/>nonæ &longs;phæræ, &longs;eu primi mobilis; taliter &longs;cilicet, quòd duo pun<lb/>cta certa, & determinata octauæ &longs;phæræ, quæ capita arietis, & <lb/>& libræ, &longs;eu principia arietis, & libræ octauæ &longs;phæræ dicuntur <lb/>moueri in circumferentiis duorum circulorum paruorum di­<lb/>ctorum, de&longs;cribendo eas in concauitate nonæ &longs;phæræ, circa <lb/>principia arietis, & libræ eiu&longs;dem nonæ &longs;phæræ, & arietis ecli<lb/>pticæ nonæ &longs;phæræ inter centra horum paruorum circulorum <lb/>dictorum, & circumferentias &longs;uas. <!--neuer Satz-->e&longs;t quatuor graduum, <lb/>XVIII minutorum, & XLIII &longs;ecundorum, & tota diametra <lb/>eorum circulorum e&longs;t VIII graduum, XXXVII <expan abbr="minutorũ">minutorum</expan>, <lb/>& XXVI &longs;ecundorum. </s> <s>adeo quòd &longs;tellæ fixæ octaui cæli non <lb/>po&longs;&longs;unt perficere circulationem &longs;uam uer&longs;us <expan abbr="ori&etilde;tem">orientem</expan> ad con­<lb/>trarium nonæ &longs;phæræ, &longs;eu primi mobilis, &longs;ed po&longs;&longs;unt tran&longs;mo <lb/>ueri uer&longs;us orientem per VIII graduum, XXXVII minuto­<lb/>rum, & XXVI &longs;ecundorum, & redire uer&longs;us occidentem tar<lb/>dum. </s> <s>alia e&longs;t opinio illorum, qui tabulas Alphon&longs;i compo&longs;ue<lb/>runt, & Petri de Apono, &longs;eu Conciliatoris, & domini Nico­<lb/>lai Paduani comitis de Comitibus, & Georgii Parbachui, qui <lb/>uolunt quòd &longs;int in numero decem &longs;phæræ, uidelicet quòd &longs;u<lb/>pra &longs;eptem &longs;phæras &longs;eptem planetarum &longs;int tres &longs;phæræ, uideli<lb/>cet octaua, nona, & decima, quod &longs;ic <expan abbr="o&longs;t&etilde;ditur">o&longs;tenditur</expan>. </s> <s>uidemus in &longs;tel<lb/>lis fixis, &longs;eu in octaua &longs;phæra triplicem motum: unum &longs;cilicet <lb/><expan abbr="diurnũ">diurnum</expan> <expan abbr="ueloci&longs;&longs;imũ">ueloci&longs;&longs;imum</expan>, quo octaua &longs;phæra <expan abbr="cũ">cum</expan> &longs;tellis fixis, quæ &longs;unt <lb/>in ea, reuoluitur omni die naturali una reuolutione completa <pb xlink:href="024/01/053.jpg" pagenum="20"/>ab oriente, &longs;cilicet uer&longs;us occidentem: & alium tardum, de <lb/>quo octaua &longs;phæra mouetur cum &longs;tellis fixis, quæ &longs;unt in ea ab <lb/>occidente uer&longs;us orientem: & tertium, quo mouetur octaua <lb/>&longs;phæra, taliter quòd declinatio &longs;olis; qui &longs;ecundum omnes a­<lb/>&longs;trologos mouetur motu proprio &longs;ui orbis differentis ip&longs;um <lb/>uer&longs;us orientem &longs;emper, & continue &longs;ub ecliptica octauæ &longs;phæ<lb/>ræ, nu&longs;quam ab ea recedendo; uariatur cre&longs;cendo, & decre­<lb/>&longs;cendo: ideo dicimus &longs;upra octauam &longs;phæram e&longs;&longs;e duas alias <lb/>&longs;phæras nonam, & decimam, quæ una &longs;ola &longs;phæra &longs;uperior ip<lb/>&longs;i octauæ non pote&longs;t dare &longs;phæræ inferiori, ultra motum nonæ <lb/>proprium, duos motus: & quia omnes &longs;phæræ cæle&longs;tes mouen­<lb/>tur motu diurno, uidelicet in uiginti quatuor horis, una reuo­<lb/>lutione completa ab oriente, &longs;cilicet uer&longs;us occidentem, incon<lb/>ueniens e&longs;t dicere, quòd &longs;phæra inferior moueatur motu diur­<lb/>no &longs;ibi proprio ueloci&longs;&longs;imo &longs;cilicet & quòd ad <expan abbr="motũ">motum</expan> eius pro­<lb/>prium moueat &longs;uperiorem ei, &longs;imiliter motu diurno ueloci&longs;&longs;i­<lb/>mo: ideo dicimus decimam &longs;phæram e&longs;&longs;e primum mobile: & <lb/>eam e&longs;&longs;e illam, quæ mouetur motu diurno ueloci&longs;&longs;imo, ad cu­<lb/>ius motum omnes aliæ &longs;phæræ inferiores mouentur &longs;imiliter <lb/>motu diurno, uidelicet omni die naturali, quæ e&longs;t tempus xxiiii <lb/>horarum, una reuolutione completa. </s> <s>& quia uidimus &longs;tellas <lb/>fixas in octaua &longs;phæra moueri continue uer&longs;us orientem ad <lb/>contrarium motum diurnum, motu quodam tardo ualde &longs;i <lb/>poneremus octauam &longs;phæram immediate &longs;ub decima; & eam <lb/>habere talem motum tardum, continu<expan abbr="ũ">um</expan> uer&longs;us <expan abbr="occident&etilde;">occidentem</expan>, tan<lb/>quam <expan abbr="motũ">motum</expan> &longs;ibi <expan abbr="propriũ">proprium</expan>, & IX <expan abbr="&longs;phærã">&longs;phæram</expan> e&longs;&longs;e &longs;ub ea, & <expan abbr="eã">eam</expan> moueri <lb/>tali motu, quòd per eum declinatio &longs;olis ab æquatore, qui &longs;em<lb/>per, & continue mouetur &longs;ub ecliptica octauæ &longs;phæræ, augeat, <lb/>minuatur, &longs;equeretur <expan abbr="&longs;phærã">&longs;phæram</expan> <expan abbr="inferior&etilde;">inferiorem</expan> ad &longs;uum <expan abbr="motũ">motum</expan> <expan abbr="propriũ">proprium</expan> <lb/>mouere <expan abbr="octauã">octauam</expan> <expan abbr="&longs;uperior&etilde;">&longs;uperiorem</expan>, ex quo per <expan abbr="&longs;uũ">&longs;uum</expan> <expan abbr="motũ">motum</expan> declinatio &longs;olis, <lb/>qui <expan abbr="cõtinue">continue</expan> mouetur, &longs;ub ecliptica viii &longs;phæræ uariatur, quod <lb/>e&longs;t <expan abbr="ab&longs;urdũ">ab&longs;urdum</expan>, &longs;i aut diceretur <expan abbr="octauã">octauam</expan> <expan abbr="&longs;phærã">&longs;phæram</expan> immediate collocari <lb/>&longs;ub decima, & <expan abbr="eã">eam</expan> moueri tali motu, <expan abbr="tanquã">tanquam</expan> motu &longs;ibi proprio, <lb/>ut per eum declinatio &longs;olis &longs;emper, & continue di&longs;currentis &longs;ub <lb/>ecliptica VIII &longs;phæræ ab æquatore augeatur, & minuatur: <expan abbr="tũc">tunc</expan> <pb xlink:href="024/01/054.jpg"/>oporteret dicere, quòd nona &longs;phæra, quæ e&longs;t &longs;ub ea, moue­<lb/>tur motu illo tardo, continuo dicto uer&longs;us orientem; ad cu­<lb/>ius motum &longs;tellæ fixæ, quæ &longs;unt in octaua &longs;phæra, quæ e&longs;t &longs;u­<lb/>pra eam, moueantur uer&longs;us orientem continue, & &longs;ic &longs;phæra <lb/>inferior ad motum eius proprium moueret &longs;uperiorem. </s> <s>ne­<lb/>ce&longs;&longs;arium e&longs;t ergo dicere nonam &longs;phæram collocari immedia­<lb/>te &longs;ub decima: & ip&longs;am e&longs;&longs;e illam, quæ mouetur continue ab <lb/>occidente uer&longs;us orientem motu illo tardo ualde iam dicto, <lb/>defferendo &longs;ecum octauam &longs;phæram cum &longs;tellis fixis, quæ &longs;unt <lb/>in ea, & alias &longs;phæras inferiores ei: & quòd octaua &longs;phæra &longs;it <lb/>&longs;ub ea, & eam moueri tali motu, tanquam motu &longs;ibi proprio, <lb/>ut per eum motum etiam aliæ &longs;phæræ inferiores octauæ mo­<lb/>ueantur: & declinatio &longs;olis &longs;emper continue di&longs;currentis &longs;ub <lb/>ecliptica octauæ &longs;phæræ augeatur, & minuatur: & &longs;ic &longs;ituatas <lb/>tres &longs;phæras non &longs;equitur aliquod inconueniens. </s> <s>nece&longs;&longs;arium <lb/>e&longs;t ergo propter reuolutiones dicere &longs;phæras cæle&longs;tes e&longs;&longs;e de­<lb/>cem in numero: & omnes e&longs;&longs;e &longs;ic ordinatas, ut dictum e&longs;t: <lb/>Thebit ergo, ut &longs;upra dictum e&longs;t, duplicem octauæ &longs;phæræ <lb/>motum ine&longs;&longs;e dixit: unum &longs;cilicet à primo mobili, &longs;eu nona <lb/>&longs;phæra diurnum &longs;cilicet: alium uero &longs;ibi proprium trepida­<lb/>tionis, &longs;eu acce&longs;&longs;us, & rece&longs;&longs;us, qui fit &longs;uper circumferentiis <lb/>duorum circulorum paruorum æqualium de&longs;criptorum in <lb/>concauitate nonæ &longs;phæræ circa principium arietis, & libræ e­<lb/>iu&longs;dem nonæ &longs;phæræ: duplicem etiam eclipticam a&longs;&longs;eruit fi­<lb/>xam quidem in nona &longs;phæra, &longs;eu primo mobili: mobile au­<lb/>tem in octaua ita, ut capita arietis, & libræ eclipticæ mobilis, <lb/>&longs;eu octauæ &longs;phæræ circumferantur in circumferentiis duorum <lb/>circulorum paruorum æqualium, quorum media, &longs;eu poli, <lb/>&longs;eu centra &longs;unt ip&longs;a capita, &longs;eu principia arietis, & libræ ecli­<lb/>pticæ fixæ, &longs;cilicet nonæ &longs;phæræ, &longs;eu primi mobilis: & arcus <lb/>eclipticæ fixæ, &longs;eu nonæ &longs;phæræ inter polos, &longs;eu centra ho­<lb/>rum circulorum paruorum, & circumferentias &longs;uas e&longs;t qua­<lb/>tuor graduum, 18 minutorum, & 43. &longs;ecundorum. </s> <s>dixit autem <lb/>Thebit capita, &longs;eu principia arietis, & libræ mobilia, &longs;eu o­<lb/>ctauæ &longs;phæræ taliter circumferri in circumferentiis &longs;uorum <pb xlink:href="024/01/055.jpg" pagenum="21"/>circulorum paruorum, ut, cum caput arietis mobilis, &longs;cilicet <lb/>octauæ &longs;phæræ fuerit in &longs;ectione circumferentiæ &longs;ui parui cir­<lb/>culi cum æquatore occidentali, ip&longs;um mouebitur per medie­<lb/>tatem circumferentia &longs;ui parui circuli &longs;eptentrionalem ab æ­<lb/>quatore. </s> <s>caput autem libræ mobilis mouebitur tunc per me­<lb/>dietatem circumferentiæ &longs;ui parui circuli meridionalem ab <lb/>æquatore: & cum caput arietis mobilis fuerit in &longs;ectione cir­<lb/>cumferentiæ &longs;ui parui circuli cum æquatore orientali, ip&longs;um <lb/>mouebitur per medietatem circumferentiæ &longs;ui parui circuli <lb/>meridionalem ab æquatore. </s> <s>caput autem libræ mobilis mo­<lb/>uebitur tunc per medietatem circumferentiæ &longs;ui parui circu­<lb/>li &longs;eptentrionalem ab æquatore: & cum caput arietis mobilis <lb/>fuerit in alterutro duorum punctorum &longs;ectionis circumferen­<lb/>tiæ &longs;ui parui circuli cum ecliptica fixa, &longs;cilicet nonæ &longs;phæræ, <lb/>&longs;eu primi mobilis; caput libræ mobilis erit &longs;imiliter &longs;e habens <lb/>in circumferentia &longs;ui parui circuli: & tunc ecliptica mobilis, <lb/>&longs;cilicet octauæ collocabitur in &longs;uperficie eclipticæ fixæ dire­<lb/>ctæ &longs;ub ecliptica fixa, &longs;cilicet nonæ &longs;phæræ, &longs;eu primi mobi­<lb/>lis. </s> <s>& &longs;uperficies eclipticæ mobilis, &longs;cilicet octauæ eritin &longs;u­<lb/>perficiæ eclipticæ fixæ, &longs;cilicet nonæ, tanquam pars in toto, <lb/>quod in una reuolutione capitis arietis mobilis, &longs;cilicet octa­<lb/>uæ &longs;phæræ in circumferentia &longs;ui parui circuli bis accedet. </s> <s>in <lb/>omnibus autem aliis locis, &longs;eu punctis exceptis, capite arietis <lb/>mobilis in circumferentia &longs;ui parui circuli locato, ecliptica mo <lb/>bilis, &longs;cilicet octauæ &longs;ecabit eclipticam fixam, &longs;cilicet nonæ <lb/>&longs;emper in punctis, &longs;eu principiis cancri, & capricorni mobi­<lb/>libus. </s> <s>nam hæc duo puncta, uidelicet capita, &longs;eu principia <lb/>cancri, & capricorni eclipticæ mobilis, &longs;cilicet octauæ &longs;phæ­<lb/>ræ &longs;emper circumferentiæ eclipticæ fixæ, &longs;cilicet nonæ &longs;phæ­<lb/>ræ in hoc motu cohærent, ut nu&longs;quam ab ea recedant: à capi­<lb/>tibus tam cancri, & capricorni &longs;ixorum, &longs;cilicet. </s> <s>nonæ &longs;phæ­<lb/>ræ per quantitatem quatuor graduum, 18 minutorum, & 43 <lb/>&longs;ecundorum ea elongari uer&longs;us orientem, & uer&longs;us occiden­<lb/>tem contingit; & ubicunque fiat. </s> <s>&longs;ectio eclipticæ octauæ cum <lb/>ecliptica nonæ, ip&longs;am, nece&longs;&longs;e e&longs;t, à principiis arietis, & libræ <pb xlink:href="024/01/056.jpg"/>mobilibus octauæ per quartam circuli magni di&longs;tare: & licet <lb/>in una reuolutione capitis arietis mobilis, &longs;cilicet octauæ in <lb/>circumferentia &longs;ui parui circuli capita, &longs;eu principia cancri, <lb/>& capricorni mobilia octauæ &longs;phæræ collocentur directa &longs;ub <lb/>capitibus cancri, & capricorni fixorum, &longs;eu nonæ &longs;phæræ. <lb/></s> <s>nunquam tam capita, &longs;eu principia arietis, & libræ fixorum <lb/>peruenient. </s> <s>dum enim ecliptica mobilis, &longs;cilicet octauæ, con­<lb/>trahet circumferentiam circuli parui paruæ &longs;ectionis in pun­<lb/>cto arietis mobilis; capita cancri, & capricorni mobilia &longs;unt <lb/>coniuncta cum capitibus cancri, & capricorni fixorum. </s> <s>& &longs;i­<lb/>militer accidit in contactu meridiano: capita uero arietis, & <lb/>libræ mobilia nunquam uenient &longs;ub capite arietis, & libræ fi­<lb/>xorum: &longs;ed &longs;emper à capitibus arietis, & libræ fixorum di&longs;ta­<lb/>bunt per quantitatem quatuor graduum, XVIII minutorum, <lb/>XLIII &longs;ecundorum, quia &longs;emper errant in circumferentiis <lb/>&longs;uorum circulorum paruorum, quæ di&longs;tant à centris eorum <lb/>per quantitatem dictam. </s> <s>ecliptica autem fixa &longs;emper &longs;ecat æ­<lb/>quatorem in capitibus arietis, & libræ fixorum ad angulum <lb/>&longs;emper eundem, cuius anguli arcus coluri ei corre&longs;pondens <lb/>&longs;emper e&longs;t XXIII graduum, XXXIII <expan abbr="minutorũ">minutorum</expan>, & &longs;ecundo­<lb/>rum, qui e&longs;t arcus maximæ declinationis eclipticæ fixæ, &longs;ed e­<lb/>clipticæ mobilis, &longs;cilicet octauæ æquatorem &longs;ucce&longs;&longs;iue &longs;ecat in <lb/>&longs;ingulis punctis æquatoris: et ip&longs;e &longs;ecatur ab æquatore in &longs;in­<lb/>gulis punctis eius compræhen&longs;is in duobus arcubus ei eclipti­<lb/>cæ mobilis, quos arcus ecliptica mobilis excitentibus capiti­<lb/>bus arietis, & libræ mobilibus in duobus punctis di&longs;tinguen­<lb/>tibus quartas &longs;uorum circulorum paruorum ab inter&longs;ectioni­<lb/>bus eorum cum æquatore &longs;eparat à toto re&longs;iduo eclipticæ mo­<lb/>bilis, & quantitas unius cuiu&longs;que horum arcuum e&longs;t circa <lb/>XXI graduum, & XXX minutorum. </s> <s>e&longs;t maxima di&longs;tantia ca­<lb/>pitis arietis mobilis, quando e&longs;t in puncto di&longs;tinguenti quartas <lb/>&longs;ui parui circuli ab inter&longs;ectionibus eius cum æquatore &longs;epten­<lb/>trionali à &longs;ectione eclipticæ mobilis cum æquatore per gradu­<lb/>um X, & 45 minutorum ecliptica mobilis, &longs;cilicet in pi&longs;cibus, <lb/>&longs;cilicet ecliptica mobilis: & quando e&longs;t in puncto di&longs;tinguente <pb xlink:href="024/01/057.jpg" pagenum="22"/>quartas &longs;ui parui circuli ab inter&longs;ectionibus eius cum æquato­<lb/>re meridiano, e&longs;t per gradus X, & XLV minutorum in arie­<lb/>te ecliptica mobilis. </s> <s>&longs;imiliter dicendum e&longs;t de capite libræ mo <lb/>bilis. </s> <s>quando enim caput arietis mobilis e&longs;t in puncto &longs;ui par­<lb/>ui circuli di&longs;tinguente quartas parui circuli ab inter&longs;ectioni­<lb/>bus eius cum æquatore &longs;eptentrionale: caput libræ mobilis <lb/>tunc e&longs;t in puncto &longs;ui parui circuli di&longs;tinguente quartas parui <lb/>circuli ab inter&longs;ectionibus eius cum æquatore &longs;eptentrionali. <lb/></s> <s>& tunc &longs;icut maxima di&longs;tantia capitis arietis mobilis ab inter­<lb/>&longs;ectione ecliptica mobilis cum æquatore e&longs;t per gradus de­<lb/>cem, & XLV minutos in pi&longs;cibus eclipticæ mobilis; ita ma­<lb/>xima di&longs;tantia capitis libræ mobilis ab inter&longs;ectione eclipticæ <lb/>mobili æquatore e&longs;t per gradus X, & XLV minutos ecli­<lb/>pticæ mobilis in uirgine eclipticæ mobilis. </s> <s>& quando caput <lb/>arietis mobilis e&longs;t in puncto &longs;ui parui circuli di&longs;tinguente <lb/>quartas parui circuli ab inter&longs;ectionibus eius cum æquatore <lb/>meridionali, tunc caput libræ mobilis e&longs;t in puncto &longs;ui parui <lb/>circuli di&longs;tinguente quartas parui circuli ab inter&longs;ectionibus <lb/>eius cum æquatore &longs;eptentrionali: & tunc &longs;icut maxima di­<lb/>&longs;tantia capitis arietis mobilis à &longs;eptione ecliptica mobili cum <lb/>æquatore e&longs;t per gradus X, & XLV minutos eclipticæ <lb/>mobilis in ariete eclipticæ mobilis; ita maxima di&longs;tantia capi­<lb/>tis libræ mobilis ab inter&longs;ectione eclipticæ mobilis cum æqua­<lb/>tore e&longs;t per gradus X, & XLV minutos eclipticæ mobi­<lb/>lis in libra ecliptica mobilis; & &longs;ic ecliptica mobilis &longs;ecatur ab <lb/>æquinoctiali in &longs;ingulis punctis duorum arcuum eius: quos ar<lb/>cus exi&longs;tentibus capitibus arietis, & libræ mobilibus in duo­<lb/>bus punctis duorum circulorum paruorum di&longs;tinguentibus <lb/>quartas eorum ab inter&longs;ectionibus eorum cum æquinoctiali; <lb/>quorum unus e&longs;t ab &longs;eptentrionale æquinoctionali, et alter <lb/>meridionalis &longs;eparat à toto re&longs;iduo eclipticæ mobilis: quorum <lb/>arcuum unus e&longs;t ex parte arietis mobilis à XIX gradus XV <lb/>minutos pi&longs;cium ecliptica mobilis, u&longs;que ad X gradus, <lb/>et XLV minutos arietis eiu&longs;dem eclipticæ mobilis, et ali­<lb/>ter e&longs;t XIX gradus, et XV minutos uirginis eclipticæ <pb xlink:href="024/01/058.jpg"/>mobilis, u&longs;que ad X gradus, & XLV minutos in arietis e­<lb/>iu&longs;dem eclipticæ mobilis: & quantitas uniu&longs;cuiu&longs;que horum <lb/>graduum e&longs;t XXI gradus, XXX minutos. </s> <s>maxima enim di­<lb/>&longs;tantia capitis arietis, & libræ mobilium à &longs;eptione eclipticæ <lb/>mobilis cum æquinoctiali e&longs;t per gradus X, & XLV minu­<lb/>tos eclipticæ mobilis in pi&longs;cibus, & per X gradus, & XLV <lb/>minutos eclipticæ mobilis in ariete; qui aggregati faciunt <lb/>arcum XXI gradus, et XXX minutos eclipticæ mobi­<lb/>lis: et idem e&longs;t ex parte libræ mobilis: unde accidit, quòd <lb/>maxima declinatio eclipticæ mobilis, ide&longs;t octauæ &longs;phæræ ua­<lb/>riabilis e&longs;t, maior quandoque declinatione eclipticæ fixæ, ide&longs;t <lb/>quandoque minor eadem, quandoque &longs;ibi æqualis. </s> <s>tunc enim <lb/>maxima declinatio eclipticæ octaua mobilis e&longs;t æqualis maxi­<lb/>mæ declinationi eclipticæ nonæ fixæ; quando ecliptica mobi­<lb/>lis e&longs;t collocata in &longs;uperficie eclipticæ fixæ; quod accidit capi­<lb/>tibus arietis, et libræ mobilibus exi&longs;tentibus in &longs;ectionibus <lb/>&longs;uorum circulorum paruorum cum ecliptica fixa. </s> <s>maior uero <lb/>capitibus arietis, et libræ mobilibus exi&longs;tentibus in &longs;ectioni­<lb/>bus contactuum. </s> <s>in punctis &longs;uorum circulorum paruorum <lb/>di&longs;tinguentibus quartas eorum circulorum à &longs;ectionibus eo­<lb/>rum cum ecliptica fixa: unde eam Ptolomæus inuenit XXIII <lb/>gradus, LI minut. </s> <s>et XX &longs;ecund. </s> <s>minor autem in ca­<lb/>pite arietis, et libræ mobilia fuerint in punctis inter&longs;ectionis <lb/>&longs;uorum circulorum paruorum cum æquinoctiali. </s> <s>tunc enim <lb/>inter&longs;ectio eclipticarum erit in puncto eclipticæ mobilis, ide&longs;t <lb/>octauæ: maxima declinatio ab æquinoctiali, qui minus decli­<lb/>nabit, quàm caput cancri, et capricorni ecliptica fixa, &longs;eu no <lb/>næ. </s> <s>æquatio autem octauæ &longs;phæræ e&longs;t arcus eclipticæ octauæ <lb/>&longs;phæræ, u&longs;que ad inter&longs;ectionem eclipticæ octauæ &longs;phæræ cum <lb/>æquinoctiali; &longs;ed motus acce&longs;&longs;us, et rece&longs;&longs;us e&longs;t arcus circuli <lb/>parui ab inter&longs;ectione circuli parui cum æquinoctiali occiden <lb/>tali per medietatem circuli parui &longs;eptentrionalem, progre­<lb/>diendo, u&longs;que ad caput arietis octauæ &longs;phæræ in &longs;uo circulo <lb/>paruo. </s> <s>hoc motu octauæ &longs;phæræ dicto contingit, ut &longs;tellæ fi­<lb/>xæ in octauo cælo uideantur nunc moueri uer&longs;us occidentem, <pb xlink:href="024/01/059.jpg" pagenum="23"/>nunc uer&longs;us orientem, nunc motu ueloci, nunc motu tar­<lb/>do propter diuer&longs;um &longs;itum capitis arietis octauæ &longs;phæræ in <lb/>&longs;uo circulo paruo, & propter diuer&longs;um motum &longs;ectionis <lb/>æquinoctialis per eclipticam octauæ &longs;phæræ. </s> <s>nam in toto <lb/>tempore, in quo caput arietis octauæ &longs;phæræ recedit à <lb/>puncto &longs;ui parui circuli di&longs;tinguente quartas ab inter&longs;e­<lb/>ctionibus eius cum æquatore meridionali, donec ueniat <lb/>ad punctum &longs;ui parui circuli di&longs;tinguentem quartas ab in­<lb/>ter&longs;ectionibus eius cum æquatore &longs;eptentrionale &longs;ectio e­<lb/>clipticæ octauæ &longs;phæræ cum æquinoctiali primi mobilis, <lb/>&longs;cilicet quæ mouetur continue per eclipticam octauæ &longs;phæ­<lb/>ræ contra &longs;ucce&longs;&longs;ionem &longs;ignorum à X grad. <!-- REMOVE S-->arietis eclipti­<lb/>cæ octauæ &longs;phæræ, & XLV min. <!-- REMOVE S-->u&longs;que ad XIX grad. <!-- REMOVE S-->pi­<lb/>&longs;cium, & XV min. <!-- REMOVE S-->eclipticæ octauæ &longs;phæræ cum æquino­<lb/>ctionali: recedit à &longs;tellis fixis octauæ &longs;phæræ, quæ e&longs;t uer­<lb/>&longs;us orientem ab ea eundo uer&longs;us &longs;tellas fixas, quæ e&longs;t uer­<lb/>&longs;us occidentem ab ea appropinquando eis: & propter hoc <lb/>&longs;tellæ, quæ &longs;unt uer&longs;us orientem, ab ea uidentur moue­<lb/>ri &longs;upra &longs;ucce&longs;&longs;ionem &longs;ignorum, &longs;cilicet uer&longs;us orientem: <lb/>& &longs;tellæ, quæ &longs;unt uer&longs;us occidentem, ab ea uidentur &longs;e­<lb/>qui eas &longs;upra &longs;ucce&longs;&longs;ionem &longs;ignorum: cum tamen in ue­<lb/>ritate moueantur contra &longs;ucce&longs;&longs;ionem &longs;ignorum, &longs;cilicet <lb/>uer&longs;us occidentem: & tunc caput libræ octauæ &longs;phæræ re­<lb/>cedit à puncto &longs;ui parui circuli di&longs;tinguente quartas eius <lb/>ab inter&longs;ectionibus eius cum æquatore &longs;eptentrionali, & <lb/>uenit ad punctum &longs;ui parui circuli di&longs;tinguentem quartas <lb/>&longs;ui parui circuli ab inter&longs;ectionibus eius cum æquatore <lb/>meridionali, & &longs;ectio eclipticæ octauæ &longs;phæræ cum æqui­<lb/>noctionali primi mobilis mouetur &longs;imiliter continue per <lb/>eclipticam octauæ &longs;phæræ contra &longs;ucce&longs;&longs;ionem &longs;ignorum <lb/>à X grad. <!-- REMOVE S-->libræ eclipticæ octauæ &longs;phæræ, & XLV mi­<lb/>nut. </s> <s>u&longs;que ad XIX grad. <!-- REMOVE S-->& XV minut. </s> <s>uirginis eiu&longs;dem <lb/>eclipticæ octauæ &longs;phæræ: & tunc &longs;ectio ecliptica octauæ <pb xlink:href="024/01/060.jpg"/>&longs;phæræ cum æquinoctionali &longs;imiliter recedit à &longs;tellis fixis, <lb/>quæ &longs;unt uer&longs;us orientem ab ea eundo uer&longs;us &longs;tellas fixas, <lb/>quæ &longs;unt uer&longs;us occidentem, ab ea eis appropinquando, & <lb/>propter hoc &longs;imiliter &longs;tellæ fixæ, quæ &longs;unt uer&longs;us orien­<lb/>tem ab ea uidentur moueri &longs;ecundum &longs;ucce&longs;&longs;ionem &longs;igno­<lb/>rum &longs;cilicet uer&longs;us orientem, & &longs;tellæ fixæ, quæ &longs;unt uer­<lb/>&longs;us occidentem ab ea uidentur &longs;equi eas &longs;ecundum &longs;ucce&longs;­<lb/>&longs;ionem &longs;ignorum, cum tamen in ueritate moueantur con­<lb/>tra &longs;ucce&longs;&longs;ionem &longs;ignorum, &longs;cilicet uer&longs;us occidentem. </s></p><p type="main"> <s>Cum autem caput arietis octauæ &longs;phæræ recedit à puncto <lb/>&longs;ui parui circuli di&longs;tinguenti quartas eius ab inter&longs;ectionibus <lb/>eius cum æquinoctionali &longs;eptentrionali, donec ueniat ad <lb/>punctum &longs;ui parui circuli di&longs;tinguentem quartas eius ab in­<lb/>ter&longs;ectionibus eius cum æquinoctionali meridionali: &longs;ectio <lb/>ecliptica octauæ &longs;phæræ cum æquinoctionali mouetur con­<lb/>tinue per eclipticam octauæ &longs;phæræ, &longs;ecundum &longs;ignorum <lb/>&longs;ucce&longs;&longs;ionem ad XIX grad. <!-- REMOVE S-->& XV min. <!-- REMOVE S-->pi&longs;cium ecliptica <lb/>octauæ &longs;phæræ, u&longs;que ad X grad. <!-- REMOVE S-->& XLV min. <!-- REMOVE S-->arietis ecli­<lb/>pticæ octauæ &longs;phæræ: & tunc &longs;ectio ecliptica octauæ &longs;phæ­<lb/>ræ cum æquinoctionali recedit à &longs;tellis fixis, quæ &longs;unt uer­<lb/>&longs;us occidentem, ab ea eundo uer&longs;us &longs;tellas fixas, quæ &longs;unt <lb/>uer&longs;us orientem, ab ea appropinquando eis: & propter <lb/>hoc &longs;tellæ fixæ, quæ &longs;unt uer&longs;us occidentem, ab ea uiden­<lb/>tur moueri contra &longs;ucce&longs;&longs;ionem &longs;ignorum, &longs;cilicet uer&longs;us <lb/>occidentem: & &longs;tellæ, quæ &longs;unt uer&longs;us orientem, ab ea ui­<lb/>dentur &longs;equi eas, cum tamen in ueritate moueantur &longs;e­<lb/>cundum &longs;ucce&longs;&longs;ionem &longs;ignorum, &longs;cilicet uer&longs;us orientem: <lb/>& tunc caput libræ octauæ &longs;phæræ recedit à puncto &longs;ui par­<lb/>ui circuli di&longs;tinguente quartas eius ab inter&longs;ectionibus e­<lb/>ius, cum æquinoctiali, meridionali, & uenit ad pun­<lb/>ctum &longs;ui parui circuli di&longs;tinguentem quartas eius ab inter­<lb/>&longs;ectionibus eius, cum æquinoctionali, meridionali: & ue­<lb/>nit ad punctum &longs;ui parui circuli di&longs;tinguentem quar­<lb/>tas eius ab inter&longs;ectionibus eius, cum æquinoctionali, <pb xlink:href="024/01/061.jpg" pagenum="24"/>&longs;eptentrionali: & &longs;ectio ecliptica octauæ &longs;phæræ cum æ­<lb/>quinoctiali mouetur continue per eclipticam octauæ &longs;phæ­<lb/>ræ à XIX grad. <!-- REMOVE S-->XV min. <!-- REMOVE S-->uirginis ecliptica octauæ &longs;phæ­<lb/>ræ, u&longs;que ad X grad. <!-- REMOVE S-->& XLV min. <!-- REMOVE S-->libræ eclipticæ octauæ <lb/>&longs;phæræ cum æquinoctionali recedit à &longs;tellis fixis, quæ &longs;unt <lb/>uer&longs;us occidentem, ab ea eundo uer&longs;us &longs;tellas fixas, quæ <lb/>&longs;unt uer&longs;us orientem, ab ea appropinquando eis: & pro­<lb/>pter hoc &longs;tellæ, quæ &longs;unt uer&longs;us occidentem, ab ea uiden­<lb/>tur moueri contra &longs;ucce&longs;&longs;ionem &longs;ignorum, &longs;cilicet uer&longs;us <lb/>occidentem: & quæ &longs;unt uer&longs;us orientem ab ea uidentur <lb/>&longs;equi eas, cum iam in ueritate moueantur &longs;upra &longs;ucce&longs;&longs;io­<lb/>nem &longs;ignorum, &longs;cilicet uer&longs;us orientem. </s> <s>cum autem caput <lb/>arietis octauæ &longs;phæræ recedit à puncto &longs;ui parui circuli di­<lb/>&longs;tinguente quartas eius ab inter&longs;ectionibus eius cum æqui­<lb/>noctiali, meridionali uer&longs;us orientem accedens: tunc &longs;ectio <lb/>ecliptica octauæ &longs;phæræ mouetur per eclipticam octauæ &longs;phæ<lb/>ræ tarde uer&longs;us orientem; quia æquatio octauæ &longs;phæræ, quam <lb/>ponit Thebit e&longs;&longs;e arcum. </s> <s>ecliptica octauæ &longs;phæræ à capite <lb/>arietis octauæ &longs;phæræ, u&longs;que ad inter&longs;ectionem eclipticæ o­<lb/>ctauæ &longs;phæræ cum æquinoctionali parum decre&longs;cit: & tunc <lb/>&longs;tellæ fixæ uidentur moueri uer&longs;us occidentem tarde. </s> <s>cum <lb/>autem caput arietis octauæ &longs;phæræ e&longs;t prope &longs;ectione &longs;ui par­<lb/>ui circuli cum æquinoctionali orientali, ex utroque latere <lb/>eius &longs;ectio ecliptica octauæ &longs;phæræ ibi, uel multum decre­<lb/>&longs;cit, uel multum cre&longs;cit; & tunc &longs;tellæ fixæ uidentur mo­<lb/>ueri uer&longs;us occidentem uelociter. </s> <s>cum autem caput arie­<lb/>tis octauæ &longs;phæræ appropinquat puncto &longs;ui parui circuli di­<lb/>&longs;tinguenti quartas eius ab inter&longs;ectionibus eius cum æqui­<lb/>noctionali, meridionali, donec ueniat ad ip&longs;um, tunc &longs;ectio <lb/>ecliptica octauæ &longs;phæræ mouetur per eclipticam octauæ <lb/>&longs;phæræ uer&longs;us orientem tarde; quia æquatio octauæ &longs;phæræ <lb/>parum cre&longs;cit, & tunc &longs;tellæ uidentur moueri tarde uer&longs;us <lb/>occidentem. </s></p><p type="main"> <s>Cum <expan abbr="aut&etilde;">autem</expan> caput arietis octauæ &longs;phæræ recedit à <expan abbr="pũcto">puncto</expan> &longs;ui par­<lb/>ui circuli di&longs;tinguenti quartas eius ab inter&longs;ectionibus eius <expan abbr="cũ">cum</expan> <pb xlink:href="024/01/062.jpg"/>æquinoctiali, meridionali uer&longs;us occidentem accedens, &longs;e­<lb/>ctio eclipticæ octauæ &longs;phæræ mouetur per eclipticam octauæ <lb/>&longs;phæræ tarde uer&longs;us occidentem, quia æquatio octauæ &longs;phæ­<lb/>ræ ibi parum decre&longs;cit, & &longs;tellæ fixæ uidentur moueri uer&longs;us <lb/>orientem tarde. </s></p><p type="main"> <s>Cum autem caput arietis octauæ &longs;phæræ e&longs;t prope &longs;ectione &longs;ui <lb/>parui circuli cum æquinoctiali, occidentali ex utroque latere <lb/>eius, &longs;ectio ecliptica octauæ &longs;phæræ mouetur per eclipticam <lb/>octauæ &longs;phæræ uelociter uer&longs;us occidentem. </s> <s>æquatio octa­<lb/>uæ &longs;phæræ ibi multum cre&longs;cit, uel multum decre&longs;cit: & tunc <lb/>&longs;tellæ fixæ uidentur moueri uer&longs;us orientem uelociter. </s> <s>cum au<lb/>tem caput arietis octauæ &longs;phæræ appropinquat puncto &longs;ui par­<lb/>ui circuli di&longs;tinguentem quartas ab inter&longs;ectionibus eius cum <lb/>æquatore circuli, donec ueniat ad ip&longs;um &longs;ectio eclipticæ octa­<lb/>uæ &longs;phæræ, mouetur per eclipticam octauæ &longs;phæræ uer&longs;us oc<lb/>cidentem tarde, quia æquatio octauæ &longs;phæræ ibi parum cre­<lb/>&longs;cit, & tunc &longs;tellæ fixæ uidentur moueri tarde uer&longs;us orien­<lb/>tem. </s> <s>idem fit per modum capitis libræ octauæ &longs;phæræ in cir­<lb/>cumferentia &longs;ui parui circuli: quod fit per motum capitis a­<lb/>rietis libræ octauæ &longs;phæræ in circumferentia &longs;ui parui circuli: <lb/>quod fit per motum capitis arietis in circumferentia &longs;ui, ni&longs;i, <lb/>quòd motus eorum &longs;it in partibus &longs;uorum circulorum par­<lb/>uorum contrariis. </s> <s>hinc inuenta e&longs;t diuer&longs;itas manife&longs;ta in mo<lb/>tu ip&longs;arum &longs;tellarum fixarum. </s> <s>Ptolomæus enim loca &longs;tella­<lb/>rum fixarum inuenta ab ip&longs;o tempore &longs;uo comparauit ad lo­<lb/>ca earum inuenta ab Hipparcho, & aliis, & reperit &longs;tellas fi­<lb/>xas non motas motu tardo, uidelicet in centum annis u­<lb/>no gradu, & hoc ideo fiat, quia tunc caput arietis octauæ <lb/>&longs;phæræ erat &longs;eparatum à puncto &longs;ui parui circuli di&longs;tin­<lb/>guente quartas eius ab inter&longs;ectionibus eius cum æquatore <lb/>meridiano uer&longs;us æquatorem accedens. </s> <s>po&longs;teriores uero, <lb/>dum magis accederat uer&longs;us æquatorem, inuenerunt eas <lb/>moueri in LXVI annis uno gradu: in anno autem domini <lb/>MCDLX factum e&longs;t caput arietis octauæ &longs;phæræ &longs;eptentriona­<lb/>lis ab æquatore, & di&longs;tans à &longs;ectione &longs;ui parui circuli cum <pb xlink:href="024/01/063.jpg" pagenum="25"/>æquatore occidentali fere LXVI gradibus, & à &longs;ectione ecli­<lb/>ptica octauæ cum æquinoctionali IX gradibus, & XLV min. <lb/><!-- REMOVE S-->fere eclipticæ octauæ di&longs;tans: &longs;ectio ergo eclipticæ octauæ <lb/>cum æquinoctionali fiebat &longs;uper XX grad. <!-- REMOVE S-->& XII min. <!-- REMOVE S-->in &longs;i­<lb/>gno pi&longs;cium eclipticæ octauæ &longs;phæræ. </s> <s>maxima autem æquatio <lb/>octauæ &longs;phæræ motus &longs;ecundum Thebit contingit, quando ca<lb/>put arietis octauæ &longs;phæræ fuerit in punctis di&longs;tinguentibus <lb/>quartas &longs;ui parui circuli ab inter&longs;ectionibus eius cum æqua­<lb/>tore, & e&longs;t X grad. <!-- REMOVE S-->& XLV min. <!-- REMOVE S-->unde &longs;equitur quòd quodli­<lb/>bet punctum eclipticæ octauæ &longs;phæræ à XIX grad. <!-- REMOVE S-->& XV min. <lb/><!-- REMOVE S-->pi&longs;cium, u&longs;que ad X grad. <!-- REMOVE S-->& XLV min. <!-- REMOVE S-->arietis eclipticæ o­<lb/>ctauæ &longs;phæræ cum æquinoctionali, & ex con&longs;equenti in eo fie<lb/>ri æquinoctium uernale. </s> <s>idem intelligendum e&longs;t de puncto <lb/>æquinoctii, autumnali in arcu eclipticæ octauæ &longs;phæræ oppo­<lb/>&longs;ito, uidelicet à XIX gradu uirginis, & XV min. <!-- REMOVE S-->u&longs;que ad X <lb/>grad. <!-- REMOVE S-->& XLV min. <!-- REMOVE S-->libræ. </s> <s>con&longs;tat etiam per prædicta puncta <lb/>tropica, &longs;eu maximarum declinationum &longs;olis, &longs;eu eclipticæ o­<lb/>ctauæ &longs;phæræ, &longs;ub qua &longs;emper, & continue di&longs;currit centrum <lb/>corporis &longs;olis ab æquinoctionali continue re&longs;pectu æquino­<lb/>ctionali uariari, nunc ei appropinquando, nunc ab eo elon­<lb/>gando: &longs;imiliter con&longs;tat ea &longs;emper numero e&longs;&longs;e in capite can­<lb/>cri, & capricorni octauæ &longs;phæræ: &longs;ed &longs;emper e&longs;&longs;e in punctis <lb/>eclipticæ octauæ &longs;phæræ di&longs;tantibus à &longs;ectionibus eclipticæ o­<lb/>ctauæ &longs;phæræ cum æquinoctionali per quartam. </s> <s>Ptolomæus <lb/>itaque iudicans &longs;tellas fixas octaui cæli tempore &longs;uo moueri ab <lb/>occidente uer&longs;us orientem, uidelicet &longs;ecundum &longs;ucce&longs;&longs;ionem <lb/>&longs;ignorum, credidit unum tantum e&longs;&longs;e zodiacum, &longs;cilicet no­<lb/>næ &longs;phæræ, &longs;eu primi mobilis fixum, &longs;cilicet qui &longs;emper ha­<lb/>beret eandem declinationem ab æquinoctionali &longs;ub ecliptica, <lb/>cum &longs;emper, & continue moueretur &longs;ol: ad quam credulita­<lb/>tem &longs;equitur illud, quod ip&longs;e dixit: nam ex quo &longs;tellæ fixæ <lb/>mobiles inuentæ &longs;unt tempore &longs;uo, rece&longs;&longs;i&longs;&longs;e à tropico hiema­<lb/>li, & acce&longs;&longs;i&longs;&longs;e uer&longs;us æquinoctionalem: & quæ erant inter æ­<lb/>quinoctionalem, et tropicum æ&longs;tiuum inuentæ &longs;unt: rece&longs;&longs;i&longs;&longs;e <lb/>ab æquinoctionali in parte &longs;eptentrionis uer&longs;us tropicum <pb xlink:href="024/01/064.jpg"/>æ&longs;tiuum iudicauit Ptolomæus; & propter hoc eas moueri <lb/>uer&longs;us orientem, uidelicet &longs;ecundum &longs;ucce&longs;&longs;ionem &longs;ignorum <lb/>eclipticæ fixæ &longs;cilicet nonæ. </s> <s>uerum e&longs;t tam quod propter æ­<lb/>quationem octauæ &longs;phæræ tunc decre&longs;cente, quia &longs;ectio ecli­<lb/>ptica octauæ &longs;phæræ cum æquinoctionali mouebantur tem­<lb/>pore &longs;uo per eclipticam octauæ &longs;phæræ uer&longs;us occidentem <lb/>appropinquando &longs;tellis fixis, quæ erant uer&longs;us occidentem <lb/>ab ea, & elongando &longs;e à &longs;tellis fixis, quæ erant uer&longs;us orien­<lb/>tem ab ea, ui&longs;æ &longs;unt Ptolomæo &longs;tellæ ip&longs;æ moueri uer&longs;us o­<lb/>rientem &longs;ecundum &longs;cilicet &longs;ucce&longs;&longs;ionem &longs;ignorum: eo quia <lb/>Ptolomæus putabat inter&longs;ectionem eclipticæ octauæ &longs;phæræ <lb/>cum æquinoctionali e&longs;&longs;e inter&longs;ectionem eclipticæ fixæ nonæ <lb/>&longs;cilicet &longs;phæræ: quia &longs;olam eclipticam nonæ &longs;phæræ imagina­<lb/>batur, quam inter&longs;ectionem &longs;emper fixam exi&longs;timabat, & pu­<lb/>tabat eam e&longs;&longs;e caput arietis zodiaci nonæ &longs;phæræ, &longs;eu primi <lb/>mobilis. </s> <s>Purbachius autem triplicem motum octauæ &longs;phæræ <lb/>ine&longs;&longs;e dixit: unum quidem à primo mobili, &longs;eu decima &longs;phæ­<lb/>ra diurnum, &longs;cilicet quòd in una die naturali octauæ &longs;phæræ <lb/>cum aliis &longs;phæris inferioribus ei &longs;emel &longs;uper polis totius ma­<lb/>chinæ mundi reuoluitur: alium à nona &longs;phæra, quæ &longs;ecundum <lb/>mobile uocauit; quo motu nonæ &longs;phæræ, octaua &longs;phæra cum <lb/>aliis &longs;phæris inferioribus mouetur omnibus 69200 annis per <lb/>unum gradum, et XXVIII min. <!-- REMOVE S-->uer&longs;us orientem regulari­<lb/>ter contra motum decimi orbis, &longs;eu primi mobilis &longs;uper po­<lb/>lis zodiaci nonæ &longs;phæræ exi&longs;tentibus &longs;emper directo &longs;ub polis <lb/>zodiaci decimæ, &longs;eu primi mobilis, adeo quòd zodiacus no­<lb/>næ &longs;phæræ &longs;emper e&longs;t directus &longs;ub zodiaco decimæ, &longs;eu primi <lb/>mobilis, & ecliptica nonæ &longs;phæræ &longs;emper &longs;ub ecliptica deci­<lb/>mæ, taliter quòd &longs;uperficies eclipticæ decimæ, &longs;eu primi mo­<lb/>bilis, tanquam pars in toto, nu&longs;quam ab ea declinans, & i&longs;te <lb/>motus nonæ &longs;phæræ datus octauæ, & aliis &longs;phæris inferiori­<lb/>bus, octauæ appellatur motus augium, & &longs;tellarum fixarum <lb/>in tabulis: quia ad i&longs;tum motum nonæ &longs;phæræ dictum octa­<lb/>uæ, & aliis &longs;phæris inferioribus octauæ, mouetur octauæ &longs;phæ<lb/>ra cum &longs;tellis fixis, quæ &longs;unt in ea, & <expan abbr="mou&etilde;tur">mouentur</expan> auges <expan abbr="planetarũ">planetarum</expan>, <pb xlink:href="024/01/065.jpg" pagenum="26"/>quæ &longs;unt in &longs;phæris inferioribus octauæ, de quibus augibus <lb/>dicam in theoricis planetarum &longs;equentibus hunc tractatum, <lb/>quem motum nonæ &longs;phæræ reuoluentis &longs;ecum octauam &longs;phæ<lb/>ram cum aliis &longs;phæris inferioribus ei ab occidente uer&longs;us o­<lb/>rientem ad contrarium diurnæ, &longs;eu primi mobilis. </s> <s>Purbacus <lb/>dicit e&longs;&longs;e arcum zodiaci decimæ &longs;phæræ, &longs;eu primi mobilis <lb/>à capite arietis decimæ &longs;phæræ, &longs;eu primi mobilis, u&longs;que ad <lb/>caput arietis nonæ &longs;phæræ; hoc autem uidetur mihi e&longs;&longs;e fal­<lb/>&longs;um propter rationes, quas nunc dicam. </s> <s>&longs;i enim uerum e&longs;&longs;et, <lb/>quòd motus nonæ &longs;phæræ, qui à tabolariis appellatur mo­<lb/>tus augium, & &longs;tellarum fixarum, e&longs;&longs;et arcus zodiaci mobi­<lb/>lis, &longs;cilicet decimæ &longs;phæræ, inter caput arietis primi mobilis, <lb/>& caput arietis nonæ &longs;phæræ, oporteret, ut in principio, u­<lb/>niu&longs;cuiu&longs;que ære ex æris po&longs;itis in tabulis fui&longs;&longs;et caput arietis <lb/>nonæ &longs;phæræ directæ &longs;ub capite arietis decimæ præci&longs;æ; & &longs;ic <lb/>&longs;equeretur, quòd à principio uniu&longs;cuiu&longs;que ære ex æris po&longs;i­<lb/>tis in tabulis u&longs;que ad principium huius uniu&longs;cuiu&longs;que alte­<lb/>rius caput arietis nonæ &longs;phæræ feci&longs;&longs;et unam reuolutionem <lb/>præcedentem, & &longs;ic, cum differentia unius ære ab alia &longs;it di­<lb/>uer&longs;a in tempore, &longs;equeretur nonam &longs;phæram irregulariter <lb/>facere &longs;<gap/> reuolutionem, uidelicet quandoque in breuiori <lb/>tempore, quandoque in longiori, cuius contrarium ip&longs;e dici­<lb/>tur: & etiam apparet ex ip&longs;a tabula motus nonæ &longs;phæræ, quæ <lb/>o&longs;tendit motum eius e&longs;&longs;e regularem; & i&longs;to modo tabula ip­<lb/>&longs;a e&longs;t fal&longs;a, quia ip&longs;a dat modum regularem, & &longs;ic uera loca <lb/>augium, & planetarum, quæ inueniuntur cum tabulis, e&longs;&longs;ent <lb/>fal&longs;a, & tota &longs;cientia a&longs;trologiæ rueret. </s> <s>quod autem &longs;equatur <lb/>illud, quod dixi, &longs;ic o&longs;tendo, &longs;i calculamus motum nonæ &longs;phæ<lb/>ræ cum differentiæ ære diluuii, & incarnationis, inuenimus <lb/>eum e&longs;&longs;e XXII graduum, XLVII min. <!-- REMOVE S-->& IX &longs;ecundorum, <lb/>et &longs;i calculamus cum differentiæ ære incarnationis, & ære Ara­<lb/>bum, inuenimus eum e&longs;&longs;e IIII graduum, XXXIIII min. <!-- REMOVE S-->& <lb/>VIII &longs;ecundorum. </s> <s>&longs;tantibus autem talibus calculationibus, <lb/>uel oportet dicere, quòd in principio ære diluuii caput arietis <lb/>nonæ &longs;phæræ erat directe &longs;ub capite arietis decimæ, & quod <pb xlink:href="024/01/066.jpg"/>in 3101 annis, & 319 diebus, qui anni, & dies &longs;unt differentia <lb/>ære diluuii, & incarnationis, nonæ &longs;phæræ facit arcum XXII <lb/>graduum, & XLVII min. <!-- REMOVE S-->& XIX &longs;ecundorum, & quod à <lb/>tempore incarnationis, u&longs;que ad tempus Arabum, quod <lb/>tempus e&longs;t 621 annorum, & 195 dierum, perfecit rationem <lb/>inchoatam in principio ære diluuii, & inchoauit aliam, & <lb/>de inchoata fecit IIII grad. <!-- REMOVE S-->XXXIIII min. <!-- REMOVE S-->& VIII &longs;ecun<lb/>dos, & &longs;ic in 621 annis, perfecit rationem inchoatam in prin<lb/>cipio ære diluuii, & inchoauit aliam, & &longs;ic nona &longs;phæra ci­<lb/>tius perficeret reuolutionem, quàm in 40000 annis, & plus <lb/>moueretur in 621 annis, & 195 diebus, quàm moueretur in <lb/>3101, & 319 diebus, quod e&longs;t contra &longs;ententiam Purbachi, & <lb/>contra calculum tabularum: quia reductis 49000 annis ad <lb/>4 3 2, & in calculando modum nonæ &longs;phæræ, cum eis <lb/>inuenimus rationem completam, & reductis 200 annis ad <lb/>4 3 2, & in calculando inuenimus motum nonæ &longs;phæræ <lb/>grad. <!-- REMOVE S-->I, min. <!-- REMOVE S-->XXVIII, uel oporteret dicere, quòd in <lb/>principio uniu&longs;cuiu&longs;que ære, caput arietis nonæ &longs;phæræ e&longs;t <lb/>directo &longs;ub capite arietis decimæ, & quod arcus, quem inue­<lb/>nimus calculando cum tali ære &longs;it di&longs;tantia capitis arietis no­<lb/>næ &longs;phæræ à capite arietis decimæ, quod e&longs;t manife&longs;te fal&longs;um: <lb/>quia calculando cum differentia ære diluuii, & incarnationis, <lb/>inuenimus in principio ære incarnationis motum augium, & <lb/>&longs;tellarum fixarum, &longs;eu motum nonæ &longs;phæræ e&longs;&longs;e grad. <!-- REMOVE S-->XXII, <lb/>min. <!-- REMOVE S-->XLVII, &longs;ecundi XIX. ubi deberent e&longs;&longs;e &longs;igna . . . . <lb/>m. </s> <s>o. </s> <s>&c. </s> <s>dicendum e&longs;t ergo, qui ne&longs;citur locus capitis <lb/>ære X, neque locus capitis arietis nonæ, & qui motus augi­<lb/>um, & &longs;tellarum fixarum: qui inuenitur calculando cum ali­<lb/>qua ære, e&longs;t arcus zodiaci, &longs;eu ecliptica decimæ &longs;phæræ, &longs;eu <lb/>primi mobilis de&longs;cripti à capite arietis nonæ &longs;phæræ principio <lb/>cuiu&longs;que ære uolueris, u&longs;que ad tempus tuum propo&longs;itum, <lb/>ide&longs;t motus, &longs;eu arcus eclipticæ decimæ &longs;phæræ, per quem <lb/>motus e&longs;t quilibet punctus eclipticæ nonæ &longs;phæræ à principio <lb/>cuiu&longs;cunque ære tuæ propo&longs;itæ, u&longs;que ad tempus tuum pro­<lb/>po&longs;itum: & hoc &longs;ufficit ad <expan abbr="inueni&etilde;dum">inueniendum</expan> loca augium <expan abbr="planetarũ">planetarum</expan>, <pb xlink:href="024/01/067.jpg" pagenum="27"/>& alia contenta, quæ faciunt ad inuentionem locorum uero­<lb/>rum planetarum: quia, addito tali arcu inuento, cum ara tua <lb/>propo&longs;ita &longs;uper radices auguum planetarum fundatas ad prin­<lb/>cipium tuæ aræ po&longs;itæ; habebis cum æquatione motum octa­<lb/>uæ &longs;phæræ, &longs;icut dicta loca auguum ad tempus tuæ aræ propo&longs;i<lb/>tæ, & cetera continentur: & ideo in principio tabulæ radicum <lb/>auguum, & &longs;tellarum fixarum, ide&longs;t nonæ &longs;phæræ apponun­<lb/>tur, cum unæ non &longs;int, ide&longs;t cum non &longs;int aliquæ aræ po&longs;itæ, & <lb/>&longs;ine eis motus earum po&longs;&longs;it inueniri, quia inuenimus quan­<lb/>tum motum facit nona &longs;phæra ab initio uniu&longs;cuiu&longs;que aræ u&longs;­<lb/>que ad tempus propo&longs;itum po&longs;t principium illius aræ: & ex <lb/>con&longs;equenti quantum motum fecerunt auges, & &longs;tellæ fixæ <lb/>per motum nonæ &longs;phæræ, qui motus additus &longs;uper radices au<lb/>guum in initio illius aræ &longs;imul cum æquatione motus octauæ <lb/>&longs;phæræ: &longs;i motus octauæ &longs;phæræ e&longs;t minus &longs;emicirculo, uel ab <lb/>eo &longs;ubtractæ prius æquatione motus octauæ &longs;phæræ e&longs;t plus <lb/>&longs;emicirculo ab æra loca auguum ad tempus po&longs;itum computa <lb/>tum ab initio illius aræ: & non e&longs;t nece&longs;&longs;itas habendi radicem <lb/>aliquam, nec e&longs;t nece&longs;&longs;itas &longs;ciendi quantum di&longs;tat caput arie­<lb/>tis nonæ &longs;phæræ à capite arietis decimæ, &longs;eu primi mobilis, <lb/>& hoc uadit ad tale &longs;ignum. </s></p><p type="main"> <s>Tertius autem motus octauæ &longs;phæræ e&longs;t &longs;ibi proprius, quia <lb/>motus trepidationis, &longs;eu acce&longs;&longs;us, & rece&longs;&longs;us octauæ &longs;phæ­<lb/>ræ uocatur, qui fit in circumferentiis duorum circulo­<lb/>rum paruorum æqualium de&longs;criptorum in concauitate no­<lb/>næ &longs;phæræ &longs;uper principia arietis, & libræ ip&longs;ius nonæ &longs;phæ­<lb/>ræ, &longs;ic quod duo puncta certa, & determinata ecliptica octa<lb/>uæ &longs;phæræ, quæ capita arietis, & libræ octauæ &longs;phæræ di­<lb/>cuntur diametraliter oppo&longs;ita, circumferentias talium <expan abbr="duorũ">duorum</expan> <lb/>circulorum in concauitate nonæ &longs;phæræ regulariter de&longs;cri­<lb/>bantur, quorum media &longs;eu poli, &longs;eu centra &longs;int ip&longs;a capita <lb/>arietis, & libræ nonæ &longs;phæræ, & arcus eclipticæ nonæ &longs;phæ­<lb/>ræ inter polos, &longs;eu centra horum paruorum circulorum, & <lb/>circumferentias &longs;uas. </s> <s>e&longs;t IX grad. <!-- REMOVE S-->eclipticæ nonæ &longs;phæræ: unde <lb/>fit, ut ecliptica octauæ &longs;phæræ qua&longs;i &longs;emper &longs;ecet eclipticam <pb xlink:href="024/01/068.jpg"/>nonæ, & quando &longs;ecat eam, &longs;emper &longs;ecat eam in capitibus ca­<lb/>pricorni, & cancri octauæ. </s> <s>nam hæc duo puncta eclipticæ octa<lb/>uæ &longs;phæræ, uidelicet capita cancri, & capricorni octauæ utrin <lb/>que à capitibus cancri, & capricorni nonæ recedunt per quan<lb/>titatem IX grad. <!-- REMOVE S-->& reuertuntur; & in tali eorum motu &longs;emper <lb/>circumferentiæ eclipticæ nonæ <expan abbr="cohær&etilde;t">cohærent</expan>, & nu&longs;quam ab ea re­<lb/>cedunt à capitibus cancri, & capricorni, quæ quantitate IX <lb/>grad. <!-- REMOVE S-->ut dictum e&longs;t, recedunt. </s> <s>Purbachus autem dixit capita <lb/>cancri, & capricorni octauæ recedere ab ecliptica nonæ &longs;phæ­<lb/>ræ, & de&longs;cribere qua&longs;dam figuras connidatas utrunque à ca­<lb/>pitibus cancri, & capricorni, quæ <expan abbr="hab&etilde;tes">habentes</expan> pro ba&longs;ilias curuas, <lb/>quod non uidetur mihi e&longs;&longs;e uerum: quia ex quo puncto ecli­<lb/>pticæ octauæ &longs;phæræ, quæ incipiunt recedere ab ecliptica no­<lb/>næ, &longs;unt capita arietis, & libræ octauæ &longs;phæræ. </s> <s>uidetur, quòd ip<lb/>&longs;a <expan abbr="debeãt">debeant</expan> e&longs;&longs;e <expan abbr="pũcta">puncta</expan> maximæ latitudinis eclipticæ octauæ &longs;phæ<lb/>ræ ab ecliptica nonæ: cum autem à puncto maximæ latitudinis <lb/>duorum circulorum maiorum &longs;e inuicem &longs;ecantium ad utra&longs;­<lb/>que &longs;ectiones &longs;it quarta circuli à capitibus arietis, & libræ octa<lb/>uæ &longs;phæræ ad utra&longs;que &longs;ectiones &longs;emper erit quarta circuli; <lb/>&longs;ed à capitibus arietis, & libræ octauæ &longs;phæræ ad capita cancri, <lb/>& capricorni, eiu&longs;dem &longs;unt quarta eclipticæ octauæ. </s> <s>ergo &longs;ectio <lb/>eclipticarum &longs;emper erit in capite cancri, & capricorni octauæ, <lb/>ut bene dixit Thebit. <!-- KEEP S--></s> <s>& etiam hoc con&longs;idero, unde fit, quòd <lb/>quando unus dictorum punctorum duorum eclipticæ octauæ <lb/>&longs;phæræ, quæ principia arietis, & libræ eiu&longs;dem uocantur, e&longs;t im<lb/>mediate &longs;ui circuli parui meridiana ab ecliptica nonæ &longs;phæræ: <lb/>alter e&longs;t immediate &longs;ui circuli parui &longs;eptentrionalis eclipticæ <lb/>etiam octauæ &longs;phæræ, quando &longs;ecatur ab ecliptica nonæ, &longs;em­<lb/>per &longs;ecatur ab ea in partes æquales, uidelicet in duas medieta­<lb/>tes: & quando ip&longs;a &longs;ecat circulos paruos, portiones circulo­<lb/>rum paruorum &longs;ectæ ab ea &longs;unt alternatim æquales, uidelicet <lb/>portio <expan abbr="&longs;ept&etilde;trionalis">&longs;eptentrionalis</expan> unius <expan abbr="eorũ">eorum</expan> e&longs;t æqualis meridionali alteri­<lb/>us: & meridionalis illius <expan abbr="&longs;ept&etilde;trionali">&longs;eptentrionali</expan> alterius. </s> <s>uelocitas autem <lb/>motus uniu&longs;cuiu&longs;que duorum capitum, uidelicet arietis, & <lb/>libræ octauæ &longs;phæræ in circumferentiis duorum circulo­<lb/>rum paruorum e&longs;t i&longs;ta, uidelicet quilibet duorum punctorum <pb xlink:href="024/01/069.jpg" pagenum="28"/>dictorum, quæ &longs;unt principia arietis, & principia libræ octa­<lb/>uæ &longs;phæræ circumferentiam &longs;ui parui circuli, in qua circum­<lb/>fertur in 7000 annis præci&longs;æ perficit. </s> <s>quanquam autem hoc <lb/>motu titubationis prædicta duo puncta eclipticæ octauæ &longs;phæ­<lb/>ræ, quæ capita arietis, & libræ octauæ &longs;phæræ dicuntur, duas <lb/>æquales circumferentias circulorum de&longs;cribant: nulla tamen <lb/>alia puncta eius de&longs;cribunt circumferentiam circuli perfe­<lb/>ctam. </s> <s>capita uero cancri, & capricorni octauæ mouentur per <lb/>eclipticam nonæ &longs;phæræ à XXI grad. <!-- REMOVE S-->geminorum eclipticæ <lb/>nonæ &longs;phæræ, u&longs;que ad IX grad. <!-- REMOVE S-->cancri eiu&longs;dem &longs;ecundum <lb/>&longs;ucce&longs;&longs;ionem &longs;ignorum, & contra &longs;ucce&longs;&longs;ionem &longs;ignorum eun<lb/>do, & recedendo: & quandoque capita cancri, & capricorni <lb/>octauæ præcedunt capita cancri, & capricorni nonæ <expan abbr="&longs;ecundũ">&longs;ecundum</expan> <lb/>&longs;ucce&longs;&longs;ionem &longs;ignorum: quandoque &longs;equuntur modo eundo <lb/>ad ea, modo recedendo ab eis &longs;ecundum &longs;ucce&longs;&longs;ionem &longs;igno­<lb/>rum, & contra &longs;ucce&longs;&longs;ionem &longs;ignorum: & quandoque con­<lb/>iunguntur. </s> <s>coniunguntur enim capita cancri, & capricorni <lb/>octauæ cum capitibus cancri, & capricorni nonæ, quando ca<lb/>pita arietis, & libræ octauæ &longs;phæræ erunt in punctis &longs;ectionum <lb/>&longs;uorum circulorum paruorum cum circulo magno per polos <lb/>zodiaci nonæ, & centro &longs;uorum circulorum paruorum eun­<lb/>te, &longs;eu in punctis &longs;uorum circulorum paruorum di&longs;tantibus <lb/>per quartam à &longs;ectionibus eorum cum ecliptica nonæ &longs;phæræ: <lb/>& tunc capita arietum, & librarum nonæ &longs;phæræ, & octauæ <lb/>&longs;unt coniuncta adinuicem &longs;ecundum longitudinem: & licet ca<lb/>pita cancri, & capricorni octauæ &longs;phæræ quandoque &longs;tatuan­<lb/>tur directe &longs;ub capitibus cancri, & capricorni nonæ: <expan abbr="nunquã">nunquam</expan> <lb/><expan abbr="tam&etilde;">tamen</expan> capita arietis, & libræ octauæ &longs;phæræ <expan abbr="erũt">erunt</expan> collocata dire<lb/>cte &longs;ub capitibus arietis, & libræ nonæ, quia &longs;emper erunt in cir<lb/>cumferentiis &longs;uorum circulorum paruorum, di&longs;tantia à cen­<lb/>tris eorum, quantitate IX grad. <!-- REMOVE S-->&longs;icut dictum e&longs;t. </s> <s>poli autem e­<lb/>clipticæ octauæ improprie dicti poli. </s> <s>& quia octaua &longs;phæra <lb/>non mouetur motu &longs;uo proprio &longs;uper eis per hunc motum ti­<lb/>tubationis, quandoque accedunt ad polos zodiaci nonæ, & <lb/>decimæ, qui &longs;emper &longs;unt &longs;imul. </s> <s>unus uidelicet &longs;ub alio: & <pb xlink:href="024/01/070.jpg"/>quandoque recedunt, &longs;eu remouentur ab eis per quantita­<lb/>tem, &longs;cilicet IX grad. <!-- REMOVE S-->talis autem acce&longs;&longs;us, & rece&longs;&longs;us fit &longs;u<lb/>per circulo magno per polos zodiaci nonæ, & centra circulo­<lb/>rum paruorum eunte. </s> <s>Contingit itaque, quòd per motum <lb/>nonæ &longs;phæræ, qui in 49000 annis perficitur quod quilibet <lb/>punctus eclipticæ nonæ &longs;phæræ &longs;ecat æquinoctioualem primi <lb/>mobilis, uidelicet decimæ in eodem puncto, in quo ecliptica <lb/>decima, &longs;eu primi mobilis, &longs;ecat eum: ecliptica autem octauæ <lb/>&longs;phæræ &longs;ub diuer&longs;a eius habitudine, propter motum eius titu<lb/>bationis æquinoctialem primi mobilis prope caput arietis, et <lb/>etiam prope caput libræ primi mobilis &longs;ecabit, et quandoque <lb/>in eo, quando &longs;cilicet omnes eclipticæ erunt &longs;imul, quod con­<lb/>tingit, quando capite arietis, et libræ octauæ &longs;phæræ fuerint in <lb/>&longs;ectionibus &longs;uorum circulorum paruorum cum ecliptica no­<lb/>næ &longs;phæræ; quæ quidem &longs;ectiones eclipticæ octauæ cum æqui­<lb/>noctionali primi mobilis recedunt, quandoque ad capita arie <lb/>tis, & libræ primi mobilis, et quandoque ab eis recedunt, ali­<lb/>quando &longs;ecundum &longs;ucce&longs;&longs;ionem &longs;ignorum; aliquando contra <lb/>progrediendo; unde fit per i&longs;tam uariam &longs;ectionem eclipticæ <lb/>octauæ cum æquinoctionali primi mobilis, ut maxime declina­<lb/>tiones zodiaci, &longs;eu eclipticæ octauæ &longs;phæræ uariabiles exi­<lb/>&longs;tant, et ob hoc contigi&longs;&longs;e uidetur in diuer&longs;is temporibus à <lb/>diuer&longs;is a&longs;tronomis quantitates maximarum declinationum <lb/>zodiaci, &longs;eu eclipticæ octauæ &longs;phæræ fui&longs;&longs;e inæqualiter inuen­<lb/>tas maiores; nanque inuentæ &longs;unt à Ptolomæo, quam ab Al­<lb/>meone, et Albatægni, qui cum &longs;imilibus uiis, et modis pro­<lb/>ce&longs;&longs;erunt in inueniendo eas, non potuit hæc diuer&longs;itas eueni­<lb/>re, ni&longs;i propter talem motum titubationis, aut &longs;imilem huic <lb/>talem diuer&longs;itatem aptum cau&longs;are ad uariationem autem &longs;e­<lb/>ctionis eclipticæ octauæ &longs;phæræ cum æquinoctiali primi mobi­<lb/>lis nece&longs;&longs;arium e&longs;t, ut &longs;ol&longs;titia, et &longs;imiliter æquinoctia continue <lb/>diuer&longs;ificentur: unde non &longs;emper, cum &longs;ol fuerit in capite a­<lb/>rietis, uel libræ primi mobilis, nece&longs;&longs;e e&longs;t æquinoctium e&longs;&longs;e, <lb/>&longs;ed erat ante fui&longs;&longs;e &longs;ol, uel po&longs;t futurum e&longs;&longs;e, cum fuerit in &longs;e­<lb/>ctione eclipticæ octauæ cum æquinoctionali. </s> <s>ex quo enim &longs;ic <pb xlink:href="024/01/071.jpg" pagenum="29"/>&longs;upra dictum e&longs;t centrum corporis &longs;olis &longs;emper, et continue <lb/>di&longs;currit &longs;ub ecliptica octauæ &longs;phæræ: hæc autem &longs;æpe immo <lb/>frequenter e&longs;t extra eclipticas nonæ, & decimæ, quæ &longs;emper <lb/>&longs;unt &longs;imul ex continenti, ip&longs;a erit extra capitibus arietis, & li<lb/>bræ primi mobilis: quare &longs;equitur illud, quod dictum e&longs;t. </s> <s>&longs;i­<lb/>milis de uariatione &longs;ol&longs;titiorum e&longs;t ratio, uidelicet quod pro­<lb/>pter uariationem continuam &longs;ectionis eclipticæ octauæ cum <lb/>æquinoctionali re&longs;pectu arietis, & libræ primi mobilis, &longs;ub <lb/>qua ecliptica octaua continue mouetur &longs;ol, non &longs;emper &longs;ole <lb/>exi&longs;tente in capite cancri, uel capricorni primi mobilis; nece&longs; <lb/>&longs;e e&longs;t &longs;ol&longs;titium accedere. </s> <s>cum enim ut plurimum &longs;uperficies <lb/>eclipticæ octauæ &longs;phæræ &longs;it extra &longs;uperficiem eclipticæ primi <lb/>mobilis, & &longs;ol&longs;titia &longs;int in punctis eclipticæ octauæ &longs;phæræ me­<lb/>diis inter duas &longs;ectiones eclipticæ octauæ &longs;phæræ cum æquino<lb/>ctionali primi mobilis continue uarientur, nece&longs;&longs;e e&longs;t, ut pun­<lb/>cta eclipticæ octauæ &longs;phæræ &longs;ol&longs;titialia, quæ &longs;unt puncta media <lb/>inter ip&longs;as &longs;ectiones &longs;imiliter continue uarientur; & <expan abbr="con&longs;equ&etilde;-ter">con&longs;equen­<lb/>ter</expan> &longs;ol&longs;titia non &longs;int &longs;emper in capite cancri, & capricorni pri<lb/>mi mobilis, &longs;ed in punctis, eclipticæ octauæ &longs;phæræ mediis in­<lb/>ter &longs;ectiones ip&longs;as eclipticæ octauæ cum æquinoctionali: quia <lb/>talia puncta &longs;unt puncta maxime di&longs;tantia ab æquinoctionali <lb/>inter omnia puncta eclipticæ octauæ &longs;phæræ: ex quibus con­<lb/>cluditur non e&longs;&longs;e nece&longs;&longs;arium &longs;ole exi&longs;tente in capite arietis, <lb/>uel libræ primi mobilis ip&longs;um nullam habere declinationem: <lb/>ab æquinoctionali &longs;imiliter &longs;equitur, non e&longs;&longs;e nece&longs;&longs;arium &longs;o­<lb/>le exi&longs;tente in capite cancri, uel capricorni primi mobilis, ip­<lb/>&longs;um habere declinationem <expan abbr="maximã">maximam</expan> ab æquinoctiali. </s> <s>&longs;tat enim <lb/>&longs;olem e&longs;&longs;e in circulo magno per polos eclipticæ primi mobilis, <lb/>& caput arietis, & libræ eiu&longs;dem tran&longs;eunte, & tam ip&longs;um e&longs;&longs;e <lb/>extra æquinoctialem: &longs;imiliter &longs;tat &longs;olem e&longs;&longs;e in circulo ma­<lb/>gno per polos eclipticæ primi mobilis, & caput cancri, & ca­<lb/>pricorni eiu&longs;dem tran&longs;eunte, & tamen tunc non habere decli­<lb/>nationem maximam ab æquinoctionali, &longs;ed ante eam habui&longs;­<lb/>&longs;e, uel po&longs;tea eam habituram e&longs;&longs;e. </s> <s>&longs;equitur etiam circulos <lb/>tropicos continuos re&longs;pectu æquinoctionali uariari, nunc ei <pb xlink:href="024/01/072.jpg"/>appropinquando, nunc ab eo elongando. </s> <s>ex his autem &longs;tel­<lb/>larum motibus &longs;atis clarum e&longs;t, motum &longs;tellarum fixarum ag­<lb/>gregatum ex motu contrariæ, & motu trepidationis octauæ <lb/>&longs;phæræ quandoque e&longs;&longs;e &longs;ecundum &longs;ucce&longs;&longs;ionem &longs;ignorum, <lb/>& nunc uelociter, & nunc tarde: et quandoque e&longs;&longs;e &longs;tationa­<lb/>rium: & quandoque e&longs;&longs;e, contra &longs;ucce&longs;&longs;ionem &longs;ignorum &longs;upra <lb/>diuer&longs;itatem, &longs;itum capitis arietis, et libræ octauæ &longs;phæræ <lb/>in &longs;uis paruis circulis, &longs;eu in circumferentiis &longs;uorum circulo­<lb/>rum paruorum. </s> <s>difficile enim multum fuit antiquis huius mo<lb/>tus reperire modum: et ob hoc diuer&longs;i diuer&longs;os modos hu­<lb/>ius motus imaginati &longs;unt. </s> <s>aliqui enim dicebant auges planeta­<lb/>rum, et &longs;tellas fixas moueri per 900 annos continue uer&longs;us <lb/>orientem u&longs;que ad grad. <!-- REMOVE S-->VII. deinde per alios 900 annos tan<lb/>dem uer&longs;us occidentem. </s> <s>Abategni uero dicebant eas moueri <lb/>in 66 annis, et 4 men&longs;ibus uer&longs;us orientem continue per u­<lb/>num gradum. </s> <s>Alphragranus autem putauit eas in 100 annis <lb/>unum gradum perficere uer&longs;us orientem continue. </s> <s>meus er­<lb/>go auguum motus, et &longs;tellarum fixarum &longs;ecundum imagina­<lb/>tionem dictam e&longs;t arcus zodiaci, &longs;eu eclipticæ primi mobilis, <lb/>&longs;eu decimæ, de&longs;criptus à capite arietis nonæ &longs;phæræ, &longs;eu cen­<lb/>tro parui circuli arietis octauæ à principio cuiu&longs;cunque aræ <lb/>uolucris u&longs;que ad tempus tuum propo&longs;itum. </s> <s>&longs;ed meus mo­<lb/>tus acce&longs;&longs;us, et rece&longs;&longs;us octauæ &longs;phæræ, et arcus circuli par­<lb/>ui arietis octauæ &longs;phæræ, incipiendo à puncto circuli magni a­<lb/>rietis octauæ &longs;phæræ &longs;eptentrionali di&longs;tante à &longs;ectionibus ip­<lb/>&longs;ius circuli parui cum ecliptica nonæ &longs;phæræ per quartas par­<lb/>ui circuli u&longs;que ad locum capitis arietis octauæ in &longs;uo paruo <lb/>circulo ad tempus tuæ aræ propo&longs;itum &longs;ecundum ordinem &longs;i­<lb/>gnorum, &longs;eu uer&longs;us orientem procedendo computat: æqua­<lb/>tio autem octauæ &longs;phæræ e&longs;t arcus eclipticæ nonæ &longs;phæræ in­<lb/>ter centrum parui circuli, &longs;eu caput arietis nonæ &longs;phæræ, et <lb/>circulum magnum per polos zodiaci nonæ &longs;phæræ, et caput <lb/>arietis octauæ &longs;phæræ in &longs;uo circulo paruo tran&longs;eunte in­<lb/>terceptus. </s></p><p type="main"> <s>Cum autem meus motus acce&longs;&longs;us, et rece&longs;&longs;us octauæ &longs;phæræ <pb xlink:href="024/01/073.jpg" pagenum="30"/>nihil fiunt, aut &longs;emicirculus præci&longs;e, nulla e&longs;t dicta æquatio, &longs;ed <lb/>&longs;i XC grad. <!-- REMOVE S-->ante CCLXX fuerit, e&longs;t maxima, & e&longs;t IX grad. <lb/><!-- KEEP S--></s> <s>Cum autem meus motus acce&longs;&longs;us, & rece&longs;&longs;us erit minus XC <lb/>grad. <!-- REMOVE S-->æquatio &longs;emper cre&longs;cit, & e&longs;t addenda meo motui augu­<lb/>um; & <expan abbr="cũ">cum</expan> erit plus XC grad. <!-- REMOVE S-->& minus CLXXX decre&longs;cit, & e&longs;t <lb/>&longs;imiliter <expan abbr="add&etilde;da">addenda</expan>. </s> <s>et <expan abbr="cũ">cum</expan> fuerit plus CLXXX, & minus CCLXX <lb/>cre&longs;cit, et e&longs;t minuenda: et cum fuerit plus CCLXX, donec <lb/>meus motus acce&longs;&longs;us, & rece&longs;&longs;us fuerit, nihil decre&longs;cit, et e&longs;t <lb/>minuenda. </s> <s>hunc modum titubationis, &longs;eu acce&longs;&longs;us, et rece&longs;&longs;us <lb/>octauæ &longs;phæræ &longs;equuntur omnes &longs;phæræ inferiores octauæ. </s> <s>ita <lb/>ut re&longs;pectu eclipticæ octauæ &longs;phæræ &longs;int auges <expan abbr="differ&etilde;tium">differentium</expan> pla<lb/>netarum, et declinationes earum &longs;emper inuariabiles. </s> <s>et his &longs;it <lb/>finis mei tractatus de motu octauæ &longs;phæræ. </s></p><p type="main"> <s>QVOD corpus &longs;olis, et lunæ, et corpora cæterorum <expan abbr="planeta-rũ">planeta­<lb/>rum</expan>, et corpora &longs;tellarum fixarum &longs;int &longs;phæræ, &longs;ic o&longs;tenditur. <lb/></s> <s>Vbicunque fuerit &longs;ol, et a&longs;piciatur à nobis, &longs;emper apparet <lb/>nobis figura rotunda, &longs;iue &longs;it in parte orientis, &longs;iue in parte <lb/>meridiei, &longs;iue in parte occidentis; et tamen in i&longs;tis locis diuer<lb/>&longs;us non a&longs;picitur à nobis &longs;emper &longs;ecundum eandem partem e­<lb/>ius præci&longs;e. </s> <s>hoc autem arguit ip&longs;um e&longs;&longs;e &longs;phæricæ figuræ: lu­<lb/>nam etiam e&longs;&longs;e &longs;phæricam deprehendimus ab illuminatione e­<lb/>ius à &longs;ole, &longs;ecundum quod ip&longs;e à &longs;ole <expan abbr="elõgatur">elongatur</expan>, et à &longs;uppo&longs;itio­<lb/>ne eius &longs;ub eo in coniunctione, in qua fit eclip&longs;is &longs;olis: non e­<lb/>nim &longs;emper illuminatur à &longs;ole &longs;ecundum eandem partem eius <lb/>præci&longs;e. </s> <s>Planetæ etiam delati à &longs;uis orbibus uario motu <expan abbr="nõ">non</expan> &longs;em<lb/>per &longs;pectantur à nobis &longs;ecundum eandem partem eorum præ­<lb/>ci&longs;e; et tamen &longs;emper uidentur à nobis rotundæ figuræ. </s> <s>ad hoc <lb/>etiam adiuuat motus eorum à &longs;uis epicyclis. </s> <s>corpora enim <lb/>planetarum, et lunæ &longs;imiliter ita feruntur à &longs;uis epicyclis, qui <lb/>nunc ex una parte eorum, nunc ex alia à nobis a&longs;piciuntur; <lb/>&longs;emper tamen uidentur à nobis rotundæ figuræ, quod o&longs;ten­<lb/>dit ea e&longs;&longs;e &longs;phærica. </s> <s>quòd &longs;i dicatur planetas reuolui in quibu&longs;­<lb/>dam concauitatibus, in quibus recipiuntur, et taliter reuol­<lb/>ui, quòd propter motus eorum in talibus concauitatibus &longs;em<lb/>per o&longs;tendunt nobis eandem eorum partem præci&longs;e; quod <pb xlink:href="024/01/074.jpg"/>tamen nos negamus, quia dicimus eas e&longs;&longs;e fixas in &longs;uis epicy­<lb/>clis, &longs;icut nodi, &longs;eu claui in tabula; &longs;i tamen a&longs;&longs;entire uolu­<lb/>mus, quòd planetæ habeant concauitatis in ip&longs;is cælis, in qui­<lb/>bus recipiantur, & reuoluantur; dico, quòd hoc non pote&longs;t <lb/>e&longs;&longs;e ni&longs;i &longs;int corpora &longs;phærica; aliter enim non po&longs;&longs;ent reuolui <lb/>in talibus concauitatibus, & &longs;i reuoluerentur, nece&longs;&longs;ario da­<lb/>rentur penetratio corporum; & &longs;icut e&longs;t de &longs;ole, & luna, & <lb/>aliis planetis; ita dicendum e&longs;t de &longs;tellis fixis, quæ &longs;unt in o­<lb/>ctauo cælo, uidelicet qui &longs;int corpora &longs;phærica cum &longs;int indi­<lb/>uidua eiu&longs;dem &longs;peciei. </s></p><pb xlink:href="024/01/075.jpg"/> </chap> </body> <back/> </text></archimedes>