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| author | Klaus Thoden <kthoden@mpiwg-berlin.mpg.de> |
|---|---|
| date | Wed, 29 Nov 2017 16:55:37 +0100 |
| parents | 22d6a63640c6 |
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<?xml version="1.0"?> <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></translator> <lang>la</lang> <cvs_file>delfi_fluxu_024_la_1559.xml</cvs_file> <cvs_version></cvs_version> <locator>024.xml</locator> </info> <text> <front> </front> <body> <chap> <pb xlink:href="024/01/001.jpg"></pb><p type="main"> <s><emph type="center"></emph>FEDERICI DELPHINI, <lb></lb>MATHEMATICI PRAESTANTISSIMI, <lb></lb>DE FLVXV ET REFLVXV AQVAE MARIS, <lb></lb>SVBTILIS ET ERVDITA DISPVTATIOI<emph.end type="center"></emph.end></s></p><p type="main"> <s><emph type="center"></emph>Eiuſdem<emph.end type="center"></emph.end><emph type="center"></emph>DE MOTV OCTAVAE SPHAERAE.<emph.end type="center"></emph.end></s></p><figure id="id.024.01.001.1.jpg" xlink:href="024/01/001/1.jpg"></figure><p type="main"> <s><emph type="center"></emph>IN ACADEMIA VENETA, <lb></lb>M D LIX.<emph.end type="center"></emph.end></s></p><pb xlink:href="024/01/002.jpg"></pb><pb xlink:href="024/01/003.jpg"></pb><p type="main"> <s><emph type="center"></emph>ILLVSTRISSIMO ET REVERENDISS.<emph.end type="center"></emph.end><emph type="center"></emph>CARDINALI TVRNONIO &c.<emph.end type="center"></emph.end></s></p><p type="main"> <s>VTINAM, uir præſtantiſsime, cogitationes hominum uirtute præ<lb></lb>ſtantium ſedem ac domicilium ita propinquum inuenirent in animis <lb></lb>Principum, & eorum, qui opibus abundant, ut ne diuturna peregri<lb></lb>natio, ante quàm ad agendum aggrederentur, uitam eorum termi<lb></lb>naret. </s> <s>atque utinam potius, ut omni benignitate ſubleuandi <expan abbr="ſuſten-tandiq́">ſuſten<lb></lb>tandique</expan>; ſunt, non contra multorum iniuriis uexarentur, <expan abbr="multaq́">multaque</expan>;, ab <lb></lb>iniquis ad impediendum excogitata, reperirent, quibus inſtitutus <expan abbr="cũ">cum</expan> <lb></lb>laude curſus interrumpitur, & omnis ad præclare agendum uia plane <lb></lb>præcluditur. </s> <s>non enim earum modo uirtutum copia fioreret ætas no<lb></lb>ſtra, quæ antiquam exornarunt, atque illuſtrarunt; ſed cum ueræ ac <lb></lb>diuinæ Chriſtianæ religionis, diuino quodam munere, patefacta co<lb></lb>gnitio ſit, qui fons uberrimus eſt, ex quo bona omnia, ex quo ma<lb></lb>nat ipſa felicitas; fructus ferret ita præſtantes, ut antiquis ſæculis lon<lb></lb>ge omnibus antecelleret. </s> <s>propterea uidemus euenire ut, cum in ali<lb></lb>qua orbis terrarum parte tanquam ex nubibus huiuſce corruptæ æta<lb></lb>tis lumen erumpit alicuius magnanimi <expan abbr="excelſiq́">excelſique</expan>; Principis; omnes <lb></lb>probitate ac uirtute præditi, non ſecus atque uolucres, poſt aliquod <lb></lb>dierum imbrem, lætæ ſolis radios excipientes, madefactas ac diſsi<lb></lb>patas pennas exiccant, <expan abbr="apteq́">apteque</expan>; conformant, recipiunt animos, <expan abbr="eosq́">eosque</expan>; <lb></lb>ad illorum nomina per illuſtres orbis terrarum partes geſtanda, & ad <lb></lb>eximias laudes longinquis nationibus ſignificandas inſtituunt. </s> <s>quæ <lb></lb>cum omnia, ut eſt non minus prudentia <expan abbr="omniq́">omnique</expan>; uirtute, quàm nobi<lb></lb>litate, excellens, Federicus Baduarius perſpicue uideret, <expan abbr="planeq́">planeque</expan>; <lb></lb>intelligeret; mentem intendit in eam curam, ut tam multa <expan abbr="tamq́">tamque</expan>; gra<lb></lb>uia, ingenuarum doctrinarum ſtudiis aduerſa, nouis conſiliis atque <lb></lb>inſtitutis, Deo duce, ſuperaret: & quemadmodum rapidis flumini<lb></lb>bus, inuſitato impetu extra ripas diffluentibus, obſiſtitur aggeribus <lb></lb>multiplici ſtrue lignorum compactis; ita multos in unum cœtum ui<lb></lb>ros coegit, Chriſtiana mente, <expan abbr="uitæq́">uitæque</expan> innocentia, & doctrinæ laude in <lb></lb>ſignes: quo ex cœtu noſtra exorta eſt Academia: quæ tum in ſer<lb></lb>monibus eruditis, ad litteras, aut ad præſentem rerum humana<lb></lb>narum ſtatum ſpectantibus, horas collocans, <expan abbr="ſuaq́">ſuaque</expan>;, aut aliorum <lb></lb>ſcripta, uel recentia, uel temporis uetuſtate abdita, ingenioſis cor<lb></lb>rectionibus aut commentariis illuſtrans<gap></gap>, & ad communem ſtudioſo<lb></lb>rum utilitatem diuulgans, ſperat edituram ſe gentibus exempla ita <lb></lb>præclara, ut præſidiis ita firmis, ubi res poſcere uidebitur, conſtitutis, <lb></lb>aut ita uitioſis moribus extinctis atque ſublatis, nouam imaginem, <lb></lb><expan abbr="nouamq́">nouamque</expan> formam, ſi nos tanto munere Deus impertiuerit, orbis ter<lb></lb>rarum accipiat. </s> <s>His noſtris conſiliis atque actionibus, minime dubi<pb xlink:href="024/01/004.jpg"></pb>tamus, quin & omnes Principes bona mente præditi, & quicunque <lb></lb>ſua uirtuti ſtudia dediderunt, magnopere faueant. </s> <s><expan abbr="iamq́">iamque</expan>; ſatis mani<lb></lb>feſta elucere ſigna cernimus. </s> <s>ex quo uoluptatem capimus eiuſmodi, <lb></lb>ut, cum honor quaſi pabulum ſit omnium artium, in hoc permanere <lb></lb>ſtatuamus excellenti inſtituto, donec res ad optatum exitum tota <lb></lb>perducatur. </s> <s>Nam quis ita rudi, aut ita demiſſo eſſet animo, qui cum <lb></lb>honorificum ſermonem à te, tam egregio Cardinali, tam graui ac ſa<lb></lb>piente uiro, noſtra cum dignitate habitum, quem nobis rara uirtute <lb></lb>uir inſignis Bernardus Taſſus narrauit, exaudiret, non ſe ipſe acue<lb></lb>ret, non quaſi lima poliret, & ad ſublimem ac nobilem rerum præ<lb></lb>clariſſimarum cupiditatem erigeret? </s> <s>Hæc tua ſingularis humanitas <lb></lb><expan abbr="eximiaq́">eximiaque</expan>; benignitas, uerbis amantiſsimis atque grauiſſimis decla<lb></lb>rata; tantum habet ponderis, <expan abbr="tantamq́">tantamque</expan>; uim, ut poſſit nos, pro eo <lb></lb>quod ipſi præſtare poſſumus, in iis actionibus confirmare, quæ ad <lb></lb>hanc uſque diem curſum annorum tuorum, <expan abbr="animumq́">animumque</expan>; tuum ita pro<lb></lb>ſecutæ ſunt, <expan abbr="itaq́">itaque</expan>; muniuerunt, ut multo magis tibi mentes homi<lb></lb>num deuinxerint, <expan abbr="clarioremq́">clarioremque</expan>; tuo nomini gloriam pepererint, quàm <lb></lb>ullus unquam Princeps uel immenſa exercituum, prouinciarum, re<lb></lb>gnorum multitudine ſit adeptus. </s> <s>quæ quidem eo præſtantior eſt, <expan abbr="eoq́">eoque</expan>; <lb></lb>magis expetenda, quòd, cum à uera uirtute fluxerit, perpetuam fore <lb></lb>conſtat: quæ uero pendet à terreſtribus rebus, inanis prorſus, cadu<lb></lb>ca, mortalis eſt. </s> <s>Neque tamen hæc tua tantum uerba præbere nobis <lb></lb>argumentum exiſtimes ſummæ tuæ uirtutis, <expan abbr="ſummæq́">ſummæque</expan>; probitatis. <lb></lb></s> <s>nam ſi pietas erga Deum infinita, non à te ad fictam ſpeciem, ſed ad <lb></lb>ueram fidem declarata; ſi erga inopes immenſa tua benignitas, ſem<lb></lb>per ex miſericordia, non ex ambitione, deriuata; ſi prudentiæ ſin<lb></lb>gularis in maximis maximorum Regum negociis, optimo ac laudabi<lb></lb>li mentis conſilio, non ob inanem aliquam laudis cupiditatem, exer<lb></lb>citata; ſi erga omnes, in quibus aliqua modo uirtus eniteat, eximia <lb></lb>liberalitas, ad uirtutem, non ad eam, quam aucupantur multi, famam <lb></lb>relata; ſi erga omnes homines immenſa humanitas, ex benignitate <lb></lb>potius, quàm ex animi humilitate, exorta, non ſolum te apud ma<lb></lb>ximum Regem tuum, <expan abbr="uniuerſamq́">uniuerſamque</expan>; Galliam, ſumma tua fide, <expan abbr="ſin-gulariq́">ſin<lb></lb>gularique</expan>; conſilio iam per tot annos adminiſtratam, tanta in exiſti<lb></lb>matione, atque auctoritate collocarunt, uerum etiam eos popu<lb></lb>los, qui obſeruantiam ignorant, ad te tamen non mediocriter ob<lb></lb>ſeruandum excitarunt, <expan abbr="feceruntq́">feceruntque</expan>; ut etiam inuidi, te admirentur, <lb></lb>omni procul amota & adulatione, & hominum intemperantium at<lb></lb>que improborum iniquitate: quo nos animo decet eſſe, quibus u<lb></lb>na propoſita uirtus eſt, <expan abbr="quiq́ue">quique</expan> in hac excelſa urbe uiuentes, ocu<lb></lb>lo quidem mentis Principes longe contemplamur, his autem cor<lb></lb>poreis facile cernimus quanta in exiſtimatione, atque obſeruantia <lb></lb>ſis apud hanc ſereniſſimam, ac ſapientiſſimam Rempublicam <expan abbr="apudq́">apudque</expan>; <lb></lb>hos omnes populos, quibus & nunc & antehac tantarum, quæ in <pb xlink:href="024/01/005.jpg"></pb>te ſunt, uirtutum liberalitate, <expan abbr="ſimulq́">ſimulque</expan>; tuæ Maieſtatis illo frui contigit <lb></lb>aſpectu, in quo, tanquam in lucidiſſimo cælo, ſplendent clariſſima <lb></lb>ſidera, uel potius tuæ beatæ mentis puriſſimus <expan abbr="pulcherrimusq́">pulcherrimusque</expan>; Sol. <lb></lb></s> <s>Nec tamen illud prætermittendum uidetur, quòd, cum tam illuſtri <lb></lb>editus è ſtirpe ſis; cum honoribus cunctis, <expan abbr="animiq́">animique</expan>; & corporis bo<lb></lb>nis abundes; <expan abbr="cumq́">cumque</expan>; tibi, tanta uirtute, tanta innocentia florenti, ſi<lb></lb>ne ulla ueneni ſuſpicione liceat, tanquam monoceroti, ex omnibus <lb></lb>potare aquis actionum humanarum; tamen, cum illud eſſe uerum <lb></lb><expan abbr="unumq́">unumque</expan>; bonum, quod ad Deum accedit, plane tibi perſuaſeris, ab<lb></lb>ducis te, quantum potes, à cunctis negociis, atque à tot ſplendori<lb></lb>bus, qui te ſequuntur inuitum; <expan abbr="nosq́">nosque</expan>; mones exemplo tuo, ut no<lb></lb>ſtrarum uoluntatum nauem conſilio regamus, ne illam fallaces abſor<lb></lb>beant fluctus, in quibus ipſe tam ſæpe, tanta tranquillitate, tam fe<lb></lb>lici curſu nauigaſti. </s> <s>Conſtantiam ergo tuebimur; <expan abbr="eaq́">eaque</expan>; duce, ſpera<lb></lb>mus fore, ut aliquando teſtatum apud omnes relinquamus, quem<lb></lb>admodum nemo te omnium, qui uiuunt, uirtute anteit, & à fortu<lb></lb>næ bonis egregie paratus es, ita neminem fore, qui aut iudicii teſti<lb></lb>monium illuſtrius, aut ueræ erga te præbeat obſeruantiæ. </s> <s>Quòd ſi <lb></lb>munus hoc, nunc à nobis ad te miſſum, minime tibi fuiſſe ingratum <lb></lb>cognouerimus: non modo iacta eſſe præclara operis à nobis inſtituti <lb></lb>fundamenta, uerum aditum etiam aliquem ad ſperatam perfectio<lb></lb>nem eſſe patefactum exiſtimabimus. </s> <s>Munus ipſum inſigne admodum <lb></lb>eſt, tum quia nobiliſſimum ac perdifficile continet argumentum, de <lb></lb>fluxu ſcilicet, & refluxu, <expan abbr="aliisq́">aliisque</expan>; præterea marinæ aquæ motibus; <lb></lb>quæ quàm non aperta, quàm ardua cognitio ſit, Ariſtotelis, <expan abbr="alio-rumq́">alio<lb></lb>rumque</expan>; philoſophorum induſtria declarat; ſed etiam quia rationes <lb></lb>non uulgares, nec à ueteribus perceptæ, in hoc libro exponuntur. <lb></lb></s> <s>Addidimus autem de motu octauæ ſphæræ ſubtilem & eruditam di<lb></lb>ſputationem, <expan abbr="idq́">idque</expan>; merito. </s> <s>ſi quidem tanti, <expan abbr="tamq́">tamque</expan>; uarii maris motus <lb></lb>non modo ad Solis <expan abbr="Lunæq́">Lunæque</expan>; curſum, ſed ad primum etiam mobile re<lb></lb>feruntur. </s> <s>Atque hæc eruditiſſima, <expan abbr="ualdeq́">ualdeque</expan>; à multis optata ſcripta <lb></lb>cum in tenebris laterent, fortaſſe, paulatim uetuſtate corrupta, pe<lb></lb>riiſlent, niſi præſtantis uiri, & doctrina clari, Lucæ Hieronymi Con <lb></lb>tareni, patricii Veneti, cui præceptor fuit Delphinus ipſe, horum <lb></lb>ſcriptorum auctor, ſingularis humanitas ea conceſſiſſet Academiæ <lb></lb>noſtræ: quæ ſtatim, cognito argumento, non minus iucundo, quàm <lb></lb>diflicili, munus ad te, ſuæ teſtimonium obſeruantiæ, mittendum <lb></lb>conſtituit: cum ipſam quidem rem, & pro tua excellenti doctrina, <lb></lb>& quia te in amœniſſimum Corneliani ſeceſſum, quietis, & ualetu<lb></lb>dinis cauſa, contuliſti, gratam fore opinaretur, animum tamen no<lb></lb>ſtrum tibi probari uehementius optaret, utpote qui ad tuam glo<lb></lb>riam multo ſublimiora cogitans, humilia tamen tuæ ſplendore di<lb></lb>gnitatis putauit illuſtranda. </s> <s>nec uero ſibi unquam ſatisfaciet, donec <lb></lb>plane peripiciat, neminem poſſe ipſo præſtantius ad tuum decus <pb xlink:href="024/01/006.jpg"></pb>amplificandum aut eloqui, aut agere, niſi qui te ipſum uirtute, <expan abbr="ani-moq́">ani<lb></lb>moque</expan>; adæquat. </s> <s>quod cum fieri uix poſsit: ideo ſequitur, ut actiones <lb></lb>noſtræ nequaquam tibi uulgares uideri debeant. </s> <s>quo fit, ut amore <lb></lb>tuo ac fauore complectendi ſimus, <expan abbr="gratiamq́">gratiamque</expan>; à te inire aliquam æ<lb></lb>quum ſit, quòd Academia noſtra, cum omnibus communem om<lb></lb>nium parentem Chriſtum pie colentibus, ab intimo corde preces <lb></lb>pie fundit, ut, ad noſtræ religionis utilitatem, ad ornamentum <lb></lb>omnium uirtutum, ad ætatis noſtræ gloriam, diuturnam tibi ui<lb></lb>tam cum optima ualetudine conſeruet. </s> <s>quandoquidem honores eos, <lb></lb>qui ab hominibus tribuuntur, iam nunc pleroſque poſſides, & quia <lb></lb>Cardinalis; & quòd ex Principum familia ortus es: reliquos uero poſ<lb></lb>ſediſſe iam primum propterea uideris, quia te iis maxime dignum <lb></lb>præſtitiſti quam rem ne quis in dubium uocet, ſpectet animo ueram <lb></lb>tui ſanguinis nobilitatem, <expan abbr="tuasq́">tuasque</expan>; actiones cæleſti fauore commen<lb></lb>datas; quarum ſublimitas dignitatem omnem, quæ conferri à mor<lb></lb>talibus poſſit, maxime ſuperat. </s></p><p type="main"> <s>Illuſtriſſimæ ac Reuerendiſſimæ D. tuæ deditiſſimi </s></p><p type="main"> <s>Mathematici Academiæ Venetæ. </s></p><pb xlink:href="024/01/007.jpg"></pb><p type="main"> <pb xlink:href="024/01/008.jpg"></pb> <s><emph type="center"></emph>ERRATA.<emph.end type="center"></emph.end></s></p><p type="main"> <s>2. falſe, falſe. </s> <s>5. quarta, quartam. </s> <s>10. notum, motum. </s> <s>a tergo argumen<lb></lb>tum, augmentum. </s> <s>12. aliquod fallunt, in aliquo uariant. </s> <s>13. die, diem. <lb></lb></s> <s>20. diferentis, deferentis. </s> <s>22. ſeptentrionale, ſeptentrionali. </s> <s>ibidem, ſe<lb></lb>ptione, ſectione. </s> <s>23. ſeptentrionale, ſeptentrionali. </s> <s>24. ſectione, ſectio<lb></lb>nem. </s> <s>a tergo idem erratum emenda. </s> <s>ibidem, diſtinguentem, diſtinguenti. <lb></lb></s> <s>ibidem. </s> <s>accederat, acceſſerat. </s> <s>25. tam, tamen. </s> <s>ibidem. </s> <s>que, quam. </s> <s>ibidem, <lb></lb>octaue, octaua. </s> <s>26. tabolariis, tabulariis. </s> <s>a tergo, aere, are ubique. </s> <s>ultima, <lb></lb>qui, quod. </s></p><pb xlink:href="024/01/009.jpg" pagenum="1"></pb><p type="main"> <s><emph type="center"></emph>FEDERICI DELPHINI, <lb></lb>ARTIVM, ET MEDICINAE<emph.end type="center"></emph.end><emph type="center"></emph>DOCTORIS, <lb></lb>mathematicarum diſciplinarum in celeberrimo gymnaſio <lb></lb>Patauino publici profeſſoris, <lb></lb>tractatus de FLVXV, & REFLVXV, ſeu cre<lb></lb>mento, & decremento, aut acceſſu, & receſ<lb></lb>ſu, & quiete falſa, ſeu motu inordi<lb></lb>nato aquæ maris.<emph.end type="center"></emph.end></s></p><p type="main"> <s>DE<gap></gap>O autem, quod ſuperius promiſeram me dicturum <lb></lb><gap></gap>e huius mei tractatus de ſphæra, uidelicet de motu, & <lb></lb>quiete falſa aquæ maris ad motum primi mobilis; nunc re<lb></lb>ſtat à me dicendum. </s> <s>& licet à præcedentibus magiſtris facta <lb></lb>fuerit tractatio motus, & quietis falſæ aquæ maris, uidelicet <lb></lb>fluxus, & refluxus, ſeu crementi, & decrementi eius; & in <lb></lb>tractatibus eorum includantur omnes cauſæ huiuſmodi mo<lb></lb>tus fluxus, & refluxus, ſeu crementi, & decrementi: quia <lb></lb>tamen non ſunt omnes ita manifeſte poſitæ in tractatibus <lb></lb>eorum; nec poſſunt ab omnibus legentibus tractatus eorum <lb></lb>ita bene elici ex dictis eorum: ideo ego Federicus Delphi<lb></lb>nus, artium, & medicinæ, & mathematicarum diſciplina<lb></lb>rum doctor, decreui in iſto meo tractatu eas diligenter & ſcri<lb></lb>bere, & bene, & clare exprimere: ut doctrina iſta fluxus, & <lb></lb>refluxus, ſeu crementi, & decrementi, & quietis falſæ, ſeu <lb></lb>motus inordinati aquæ maris, omnibus legentibus hunc <lb></lb>meum tractatum ſit manifeſtior. </s></p><p type="main"> <s>Pro facili autem intelligentia horum duorum modorum <lb></lb>motus aquæ maris, ſequentium motum ſolis, & lunæ ad mo<lb></lb>tum primi mobilis, eſt ſciendum, primo, quòd, ubicunque <lb></lb>ſit homo in terra, orizon eius, ſicut dictum eſt ſupra à me, <pb xlink:href="024/01/010.jpg"></pb>in tractatu meo de ſphera, ſemper ſecat ei cælum in duo me<lb></lb>dia, & medietas cæli ſemper eſt ſupra orizontem eius, & <lb></lb>medietas infra. </s> <s>cum autem in omni medietate corporis ſphe<lb></lb>rici contineantur duæ quartæ: duæ quartæ cæli ſemper e<lb></lb>runt ſupra orizontem eius, & duæ infra. </s> <s>quæ autem ſunt <lb></lb>ſupra orizontem, dicuntur quartæ diurnæ; & quæ ſunt ſub <lb></lb>orizonte, dicuntur quartæ nocturnæ. </s> <s>harum autem qua<lb></lb>tuor quartarum cæli duæ ſunt, in quibus fit fluxus, ſeu cre<lb></lb>mentum aquæ maris; & duæ, in quibus fit refluxus, ſeu de<lb></lb>crementum aquæ maris. </s> <s>quartæ, in quibus fit fluxus, ſeu <lb></lb>crementum, ſunt quarta, quæ eſt ab ortu ad meridiem ſupra <lb></lb>orizontem; quæ eſt quarta acceſſionis diurnæ, ſeu crementi <lb></lb>diurni: & quarta ei oppoſita, quæ eſt ab occaſu ad medium <lb></lb>noctis ſub orizonte: quæ eſt quarta acceſſionis nocturnæ. <lb></lb></s> <s>quartæ autem, in quibus fit refluxus, ſeu decrementum; <lb></lb>ſunt quarta, quæ eſt à meridie ad occaſum ſupra <expan abbr="orizontẽ">orizontem</expan>; <lb></lb>quæ eſt quarta acceſſionis diurnæ: & quarta ei oppoſita, <lb></lb>quæ eſt à medio noctis ad ortum ſub orizonte; quæ eſt quar<lb></lb>ta receſſionis nocturnæ. </s></p><p type="main"> <s>Sciendum eſt etiam ſecundo, quòd octo ſunt puncta in cælo <lb></lb>pro fluxu, & refluxu, ſeu cremento, & decremento aquæ <lb></lb>maris: quorum quatuor ſunt fortia, & quatuor debilia. </s> <s>de<lb></lb>bilium duo ſunt debilia pro fluxu, ſeu cremento, & duo pro <lb></lb>refluxu, ſeu decremento: debilia pro fluxu, ſeu cremento, <lb></lb>ſunt punctum orientis, & punctum occidentis, quæ ſunt <lb></lb>principia duarum quartarum fluxus. </s> <s>debilia pro refluxu, <lb></lb>ſeu decremento, ſunt punctum meridiei, & punctum me<lb></lb>diæ noctis, quæ ſunt principia duarum quartarum refluxus. <lb></lb></s> <s>& iſta quatuor puncta diſtant adinuicem per quartam cæli. <lb></lb></s> <s>fortium duo ſunt fortia pro fluxu, ſeu cremento, & duo pro <lb></lb>refluxu, ſeu decremento. </s> <s>fortia pro fluxu, ſeu cremento, <lb></lb>ſunt punctum medium inter orientem, & meridiem in quar<lb></lb>ta diurna fluxus, diſtans ab oriente per 45 gradus (& à me<lb></lb>ridie ſimiliter: & punctum medium inter occidentem, & <pb xlink:href="024/01/011.jpg" pagenum="2"></pb>medium noctis in quarta nocturna fluxus) diſtans ab occaſu <lb></lb>per 45 gradus, & à medio noctis ſimiliter. </s> <s>fortia pro refluxu <lb></lb>ſunt punctum medium inter meridiem, & occaſum in quarta <lb></lb>diurna refluxus, diſtans à meridie per 45 gradus, & ab occa <lb></lb>ſu ſimiliter: & punctum medium inter medium noctis, & or<lb></lb>tum, in quarta nocturni refluxus, diſtans à medio noctis per <lb></lb>45 gradus, & ab ortu ſimiliter: & ſicut puncta debilia diſtant <lb></lb>adinuicem per quartam cæli; ita iſta fortia diſtant adinuicem <lb></lb>per quartam cæli, habentibus orizontem rectum. </s></p><p type="main"> <s>Sciendum eſt etiam tertio, quòd, præter iſta octo puncta di<lb></lb>cta, habentibus orizontem rectum, ſunt multa alia puncta æ<lb></lb>quipotentia, ſeu æqualis uirtutis: & talia puncta ſunt omnia <lb></lb>puncta cæli æqualiter diſtantia, & quatuor punctis principali<lb></lb>bus cæli, quæ puncta principalia cæli ſunt puncta orientis, pun<lb></lb>ctum occidentis, punctum meridiei, & punctum mediæ no<lb></lb>ctis, uel à quatuor punctis fortibus cæli, quod eſt idem: in <lb></lb>quartis tamen contrariæ operationis. </s> <s>ſunt enim omnia talia <lb></lb>puncta æqualis uirtutis, ſeu æquipotentia in mouendo aquam <lb></lb>maris: in orizonte autem obliquo aliter eſt, ut infra uidebitur. </s></p><p type="main"> <s>Sciendum eſt quarto, quòd ſol, & luna omni menſe ſunt ſi<lb></lb>mul in eodem ſigno, gradu, & minuto; & iſte ſitus appella<lb></lb>tur coniunctio lunæ cum ſole. </s> <s>inde ad octo dies, uel circa lu<lb></lb>na eſt elongata à ſole per motum eius proprium per quartam <lb></lb>partem cæli: & hæc elongatio appellatur quadratura prima <lb></lb>lunæ cum ſole. </s> <s>inde ad 14 dies, uel circa, eſt elongata à ſole, <lb></lb>per aliam quartam partem cæli, & ſic per medietatem cæli. </s> <s>& <lb></lb>hæc diſtantia appellatur oppoſitio lunæ cum ſole, ſeu plenilu <lb></lb>nium. </s> <s>inde ad 21 dies, uel circa, eſt elongata ab oppoſitione <lb></lb>eius cum ſole, ſeu plenilunio, per aliam quartam partem cæ<lb></lb>li, accedens ad ipſam ſolem. </s> <s>& hæc diſtantia appellatur qua<lb></lb>dratura ſecunda lunæ cum ſole. </s> <s>& tunc luna diſtat à ſole per <lb></lb>quartam partem cæli, ſicut diſtabat in quadratura prima. <lb></lb></s> <s>accedit ad coniunctionem eius cum ſole. </s> <s>inde ad 20 dies, uel <lb></lb>circa luna eſt iterum cum ſole, & ei coniuncta, ſicut pri<lb></lb>mo fuit. </s></p><pb xlink:href="024/01/012.jpg"></pb><p type="main"> <s>Sciendum quinto & ultimo, quòd ſol, & luna ambo ſimul <lb></lb>omni die naturali, quæ eſt tempus 24 horarum ad motum pri<lb></lb>mi mobilis ſunt cauſæ fluxus, & refluxus, ſeu crementi, & <lb></lb>decrementi aquæ maris bis. </s> <s>iſtis declarationibus præmiſſis, et <lb></lb>bene memoriæ retentis, declaremus quomodo ſol, et luna am<lb></lb>bo ſimul omni die naturali ad motum primi mobilis ſunt cau<lb></lb>ſæ fluxus, et refluxus, ſeu crementi, et decrementi aquæ ma <lb></lb>ris bis. </s> <s>ſi enim declarationes præmiſſæ bene memoriæ tenean<lb></lb>tur, et maxime iſtæ, uidelicet quæ ſunt quartæ cæli; in qui<lb></lb>bus fit fluxus, ſeu crementum aquæ maris; et quæ ſunt quar<lb></lb>tæ cæli; in quibus fit refluxus, ſeu decrementum aquæ maris; <lb></lb>et quæ ſunt puncta fortia pro fluxu; et quæ ſunt puncta for<lb></lb>tia pro refluxu; et quæ ſunt debilia pro fluxu; et quæ ſunt <lb></lb>debilia pro refluxu, tota narratio motus, et quietis falſæ aquæ <lb></lb>maris clara erit. </s></p><p type="main"> <s>Sciendum eſt primo (quantum ad fluxum, et refluxum, ſeu <lb></lb>crementum, et decrementum aquæ maris ad motum primi <lb></lb>mobilis) quòd quando ſol, et luna ſunt coniuncti ſimul, quæ <lb></lb>coniunctio appellatur nouilunium, dum feruntur ad motum <lb></lb>primi mobilis ab ortu ad meridiem; quia ambæ uirtutes uide<lb></lb>licet ſolis, et lunæ ſunt unitæ ſimul; et ambo luminaria, uide<lb></lb>licet ſol, et luna feruntur continue ad motum primi mobilis <lb></lb>per quartam fluxus, ſeu crementi diurni; quæ eſt ab ortu ad <lb></lb>meridiem, fit continue fluxus, ſeu crementum diurnum a<lb></lb>quæ maris: et dum feruntur à meridie ad occaſum, quia fe<lb></lb>runtur continue per quartam refluxus, ſeu decrementi diur<lb></lb>ni, fit continue refluxus, ſeu decrementum diurnum: et dum <lb></lb>feruntur ab occaſu ad medium noctis; quia feruntur per quar<lb></lb>tam fluxus nocturni, iterum fit continue fluxus, ſeu cremen <lb></lb>tum ſcilicet nocturnum: et dum feruntur à medio noctis ad <lb></lb>ortum; quia feruntur per quartam refluxus, ſeu decrementi <lb></lb>nocturni, iterum fit continue refluxus, ſeu decrementum ſci<lb></lb>licet nocturnum. </s> <s>& ſic bis in die naturali fit fluxus, & bis re<lb></lb>fluxus, ſeu bis crementum, & bis decrementum aquæ maris. <lb></lb></s> <s>Sciendum ſecundo, quòd quando luna poſt coniunctionem <pb xlink:href="024/01/013.jpg" pagenum="3"></pb>eius cum ſole per motum eius proprium elongatur à ſole uer<lb></lb>ſus orientem ſecundum ordinem ſignorum eundo uerſus qua<lb></lb>draturam primam eius cum ſole, quam appellant Nautæ, il <lb></lb>Quartirone: ſemper antequam luna per motum eius pro<lb></lb>prium ueniat ad illam quartam primam, quæ eſt diſtantia lu<lb></lb>næ à ſole uerſus orientem ſecundum ordinem ſignorum per <lb></lb>quartam partem cæli, quando ſol eſt tantum ſuper orizon<lb></lb>tem ex parte orientis in quarta fluxus diurni, quantum luna <lb></lb>eſt ſub orizonte ex eadem parte orientis in quarta refluxus <lb></lb>nocturni; quia tunc ſol tantum diſtat à puncto forti fluxus ſu<lb></lb>per orizontem, quantum luna à puncto forti refluxus ſub ori<lb></lb>zonte ipſi ſunt æquipotentes: & ideo tunc nec fit fluxus, ne<lb></lb>que refluxus aquæ maris; ſed aqua maris uidetur ſtare, & <lb></lb>tunc Veneti dicunt, L'acqua è ſtanca. </s> <s>cum autem ſol per mo<lb></lb>tum primi mobilis accedit ad punctum forte fluxus, qui eſt ſu<lb></lb>pra orizontem in quarta diurna fluxus, luna per eundem mo<lb></lb>tum primi mobilis recedit, & elongatur. </s> <s><expan abbr="tantundẽ">tantundem</expan> à puncto for<lb></lb>ti refluxus, qui eſt ſub orizonte in quarta nocturni refluxus <lb></lb>accedendo uerſus punctum orientis debile fluxus: & tunc <lb></lb>quia ſol eſt magis propinquus puncto forte fluxus, qui eſt ſu<lb></lb>pra orizontem in quarta diurna fluxus, quàm luna puncto for <lb></lb>ti refluxus, qui eſt ſub orizonte in quarta nocturna refluxus: <lb></lb>debilitatur refluxus, & fortificatur fluxus, & aqua maris <lb></lb>tunc incipit fluere: & quanto magis ſol appropinquat puncto <lb></lb>forti fluxus, qui eſt ſupra orizontem in quarta diurna fluxus, <lb></lb>tanto magis luna elongatur à puncto forti refluxus, qui eſt <lb></lb>ſub orizonte in quarta nocturna refluxus appropinquando <lb></lb>puncto orientis debili fluxus; & ideo continuatur fluxus. <lb></lb></s> <s>cum autem ſol per motum primi mobilis peruenit ad <expan abbr="punctũ">punctum</expan> <lb></lb>fortem fluxus, qui eſt ſupra orizontem in quarta diurna flu<lb></lb>xus, luna eſt elongata à puncto forti refluxus, qui eſt ſupra <lb></lb>orizontem in quarta nocturna refluxus: & facta eſt propin<lb></lb>qua puncto orientis debili fluxus; & ideo adhuc continua<lb></lb>tur fluxus. </s> <s>cum autem luna uenerit ad punctum orientis <lb></lb>debile fluxus, ipſa tunc ad motum primi mobilis mouetur <pb xlink:href="024/01/014.jpg"></pb>per quartam diurnam fluxus accedendo ſcilicet ad punctum <lb></lb>forte fluxus, qui eſt ſupra orizontem: & ſol quia diſtat à lu<lb></lb>na, minus quarta ſimiliter mouetur per eandem quartam di<lb></lb>urnam fluxus accedendo ſcilicet ad punctum meridiei debile <lb></lb>refluxus: et ideo quia ambo mouentur per quartam diurnam <lb></lb>fluxus, continuatur fluxus: & cum ſol per motum primi mo<lb></lb>bilis peruenit ad punctum meridiei debile refluxus, quia luna <lb></lb>tunc eſt magis propinqua puncto forti fluxus, qui eſt ſupra, <lb></lb>quàm ſol puncto forti refluxus; qui eſt ſupra <expan abbr="orizontẽ">orizontem</expan> in quar<lb></lb>ta diurna refluxus, continuabitur adhuc fluxus: & cum luna <lb></lb>uenerit ad punctum forte fluxus in quarta diurna fluxus, ſol <lb></lb>non erit adhuc in puncto forti refluxus in quarta diurna reflu<lb></lb>xus, eo quia ſol diſtat à luna minus quarta, ſed accedet ad ip<lb></lb>ſum, et luna tunc recedet à puncto forti fluxus, & minus diſta<lb></lb>bit ab eo, quàm ſol à puncto forti refluxus, et ideo adhuc <lb></lb>continuabitur fluxus, donec ſol ſit tantum ultra meridiem uer<lb></lb>ſus occidentem in quarta diurna fluxus, quantum luna citra <lb></lb>meridiem uerſus orientem in quarta diurna fluxus: & tunc <lb></lb>ſol tantum diſtabit à puncto forti refluxus, qui eſt ſupra ori<lb></lb>zontem ultra meridiem in quarta diurna refluxus, quantum <lb></lb>luna à puncto forti fluxus, qui eſt ſupra orizontem ante meri<lb></lb>diem in quarta diurna fluxus: et ex continenti ſol, & luna e<lb></lb>runt æquipotentes, & non fiet fluxus, neque refluxus, ſicut <lb></lb>prius dictum eſt. </s> <s>cum autem ſol per motum primi mobilis ac<lb></lb>cedet ad punctum forte refluxus in quarta diurna refluxus, <lb></lb>luna per eundem motum primi mobilis elongabitur tantun<lb></lb>dem à puncto forti fluxus in quarta diurna fluxus acceden<lb></lb>do uerſus punctum meridiei debile refluxus, et tunc luna plus <lb></lb>diſtabit à puncto forti fluxus, quàm ſol à puncto forti reflu<lb></lb>xus; et ſic ſol erit potentior luna; et ideo tunc incipiet reflu<lb></lb>xus aquæ maris, et continuabitur ſecundum quod ſol appro<lb></lb>pinquabit puncto forti refluxus in quarta diurna refluxus; et <lb></lb>luna elongabitur à puncto forti fluxus in quarta diurna flu<lb></lb>xus; et cum ſol ueniet ad punctum forte refluxus, luna erit <lb></lb>elongata à puncto forti fluxus, et ideo adhuc continuabitur <pb xlink:href="024/01/015.jpg" pagenum="4"></pb>refluxus, et cum luna ueniet ad punctum meridiei debile re<lb></lb>fluxus, ſol erit elongatus à puncto forti refluxus in quarta di<lb></lb>urna refluxus accedendo uerſus punctum occidentis debile <lb></lb>fluxus; minus tamen diſtabit ſol à puncto forti refluxus, quàm <lb></lb>luna à puncto forti fluxus; & ideo adhuc continuabitur reflu<lb></lb>xus: & cum ſol ueniet ad punctum occidentis debile, fluxus <lb></lb>luna facta erit propinqua puncto forti refluxus, qui eſt ſupra <lb></lb>orizontem in quarta diurna refluxus, & minus diſtabit ab eo, <lb></lb>quàm ſol à puncto forti fluxus, qui eſt ſub orizonte in quar<lb></lb>ta nocturna fluxus; eo quia ipſa diſtat à ſole minus quarta par<lb></lb>te cæli, & ideo adhuc continuabitur refluxus, donec ſol fue<lb></lb>rit tantum infra orizontem ex parte occidentis in quarta no<lb></lb>cturna fluxus, quantum luna ſupra orizontem, ex parte occi <lb></lb>dentis in quarta nocturna fluxus, quantum luna ſupra orizon<lb></lb>tem ex eadem parte occidentis in quarta diurna refluxus: & <lb></lb>quia tunc ſol tantum diſtabit à puncto forti fluxus, qui eſt ſub <lb></lb>orizonte, ex parte occidentis in quarta nocturna fluxus, quar<lb></lb>tum luna à puncto forti refluxus, qui eſt ſupra orizontem ex <lb></lb>eadem parte occidentis in quarta diurna refluxus: tunc ſol, <lb></lb>& luna erunt æquipotentes, et non fiet fluxus, neque reflu<lb></lb>xus. </s> <s>cum autem ſol per motum primi mobilis accedet ad pun<lb></lb>ctum forte fluxus, qui eſt ſub orizonte in quarta nocturna flu<lb></lb>xus, luna per eundem motum primi mobilis elongabitur tan<lb></lb>tundem à puncto forti refluxus, qui eſt ſupra orizontem in <lb></lb>quarta diurna refluxus; & tunc ſol minus diſtabit à puncto <lb></lb>forti fluxus in quarta nocturna fluxus, quàm luna à puncto <lb></lb>forti refluxus in quarta diurna refluxus; & ideo ſol erit poten<lb></lb>tior luna: & tunc iterum incipiet fluxus, & continuabitur, ſi<lb></lb>cut dictum eſt prius, donec ſol ſit tantum ultra medium no<lb></lb>ctis uerſus orientem in quarta nocturna refluxus, quantum <lb></lb>luna citra medium noctis uerſus occidentem in quarta noctur<lb></lb>na fluxus: & tunc tantum diſtabit ſol à puncto forti refluxus, <lb></lb>quantum luna à puncto forti fluxus, & ex continenti tunc ſol, <lb></lb>& luna erunt æquipotentes, et non fiet fluxus, neque re<lb></lb>fluxus. </s> <s>cum autem ſol per motum primi mobilis accedit ad <pb xlink:href="024/01/016.jpg"></pb>punctum forte refluxus in quarta nocturna refluxus, luna <lb></lb>per eundem motum primi mobilis recedit, & elongatur tan<lb></lb>tundem à puncto forti fluxus in quarta nocturna fluxus ac<lb></lb>cedendo uerſus punctum mediæ noctis debile refluxus: & <lb></lb>tunc ſol minus diſtabit à puncto forti refluxus in quarta no<lb></lb>cturna refluxus, quàm luna à puncto forti fluxus in quarta <lb></lb>nocturna fluxus; & tunc debilitatur fluxus, & fortificatur re<lb></lb>fluxus; & aqua maris tunc iterum incipit refluere, & conti<lb></lb>nuabitur refluxus, ſicut dictum eſt prius, donec ſol ſit tantum <lb></lb>ſupra orizontem, ex parte orientis, quantum luna ſub ori<lb></lb>zonte, ex eadem parte orientis: & tunc ſol tantum diſtabit <lb></lb>à puncto forti fluxus, qui eſt ſupra orizontem in quarta diur<lb></lb>na fluxus, quantum luna à puncto forti refluxus; qui eſt ſub <lb></lb>orizonte in quarta nocturna refluxus: & tunc ſol, & luna e<lb></lb>runt æquipotentes, & non fiet fluxus, neque refluxus. </s> <s>dein<lb></lb>de quotidie, ideſt in qualibet die naturali ſimilis, ut iam dicta <lb></lb>eſt mutatio, redibit, donec luna per motum eius proprium <lb></lb>ueniat ad quadraturam primam eius cum ſole, quam appel<lb></lb>lant nauræ, il Quartirone. </s> <s>Cum uero luna uenerit ad qua<lb></lb>draturam primam eius cum ſole, tunc cum ſol erit in puncto <lb></lb>orientis debiti pro fluxu luna erit in puncto mediæ noctis de<lb></lb>biti pro refluxu; & tunc ſol tantum diſtabit à puncto forti flu<lb></lb>xus, qui eſt ſupra orizontem, ex parte orientis in quarta diur<lb></lb>na fluxus, quantum luna à puncto forti refluxus, qui eſt ſub <lb></lb>orizonte, ex eadem parte orientis in quarta nocturna reflu<lb></lb>xus: & ſic ſol, & luna erunt æquipotentes, & non fiet flu<lb></lb>xus, neque refluxus notabilis: ſcilicet ſed fient minime cre<lb></lb>menta, & minima decrementa. </s> <s>cum autem ſol per motum pri<lb></lb>mi mobilis accedet ad punctum forte fluxus, qui eſt ſupra o<lb></lb>rizontem, ex parte orientis in quarta diurna fluxus, luna per <lb></lb>eundem motum primi mobilis accedet ſimiliter tantundem <lb></lb>ad punctum forte refluxus, qui eſt ſub orizonte, ex eadem <lb></lb>parte orientis in quarta nocturna refluxus, & continue ad mo<lb></lb>tum diurnum tantum diſtabit ſol à puncto forti fluxus, qui eſt <lb></lb>ſupra orizontem in quarta diurna fluxus, quantum luna à <pb xlink:href="024/01/017.jpg" pagenum="5"></pb>puncto forti refluxus, qui eſt ſub orizonte in quarta noctur<lb></lb>na refluxus, & ex continenti ſol, & luna continue erunt æqui<lb></lb>potentes, donec ſol per motum primi mobilis ueniat ad pun<lb></lb>ctum forte fluxus, qui eſt ſupra orizontem: & tunc ſimiliter <lb></lb>luna ueniet ad punctum forte refluxus, qui eſt ſub orizon<lb></lb>te, eo quia iſta puncta diſtant adinuicem per quarta cæli, ſi<lb></lb>cut ſol, & luna diſtant adinuicem per quartam cæli: & cum ſol <lb></lb>per motum primi mobilis recedet à puncto forti fluxus, qui <lb></lb>eſt ſupra orizontem in quarta diurna fluxus accedendo uer<lb></lb>ſus punctum meridiei debile refluxus luna per eundem mo<lb></lb>tum primi mobilis recedet ſimiliter tantundem à puncto forti <lb></lb>refluxus, qui eſt ſub orizonte accedendo uerſus punctum o<lb></lb>rientis debile fluxus, & continue tantum diſtabit ſol à puncto <lb></lb>forti fluxus, qui eſt ſupra orizontem, quantum luna à pun<lb></lb>cto forti refluxus, qui eſt ſub orizonte, donec ſol ueniet ad <lb></lb>punctum meridiei debile refluxus, & tunc luna ſimiliter ue<lb></lb>niet ad punctum orientis debile fluxus: & ſol, & luna per to<lb></lb>tum iſtud tempus erunt æquipotentes continue, & ex conti<lb></lb>nenti non fiet fluxus, neque refluxus notabilis, ſcilicet eo<lb></lb>dem modo fiet, dum ſol ad motum primi mobilis mouebitur <lb></lb>à meridie ad occaſum, quia tunc luna per eundem motum pri<lb></lb>mi mobilis mouebitur ab ortu ad meridiem: & ſimiliter dum <lb></lb>ſol mouebitur ab occaſu ad medium noctis, quia tunc luna mo<lb></lb>uebitur à meridie ad occaſum; & ſimiliter dum ſol mouebitur <lb></lb>à medio noctis ad ortum, quia tunc luna mouebitur ab occa<lb></lb>ſu ad medium noctis: & ſic in toto tempore unius reuolutionis <lb></lb>cæli, quod eſt una dies naturalis 24 horarum, aqua maris nec <lb></lb>fluet, nec refluet ſenſibiliter, ſed uidebitur ſtare, quia ſol, & <lb></lb>luna in toto tempore illius reuolutionis cæli erunt æquipo<lb></lb>tentes ſemper ſine notabili diſparitate: & iſtud accidit circa <lb></lb>octauam diem poſt coniunctionem lunæ cum ſole: & iſtam <lb></lb>quietem falſam aquæ maris appellant Veneti, Acqua de fele. <lb></lb></s> <s>& utuntur iſto dicto, Da gli otto a i noue l'acqua non ſi <lb></lb>moue. </s></p><p type="main"> <s>Cum autem luna elongatur à ſole ultra quadraturam primam <pb xlink:href="024/01/018.jpg"></pb>tendendo uerſus oppoſitionem eius cum ſole, tunc ſemper do <lb></lb>nec luna ueniet ad oppoſitionem eius cum ſole, cum ſol erit <lb></lb>tantum ſupra orizontem ex parte orientis in quarta diurna <lb></lb>fluxus, quantum luna ſub orizonte ex eadem parte orientis <lb></lb>in quarta nocturna refluxus, ſol tantum diſtabit à puncto for<lb></lb>ti fluxus, qui eſt ſupra orizontem in quarta diurna fluxus re<lb></lb>cedendo ab eo per motum primi mobilis, & accedendo ad <lb></lb>punctum meridiei debile refluxus, quantum luna à puncto <lb></lb>forti refluxus, qui eſt ſub orizonte in quarta nocturna reflu<lb></lb>Xus accedendo ad ipſum per eundem motum primi mobilis, <lb></lb>& tunc ſol, & luna erunt æquipotentes, & non fiet fluxus, ne<lb></lb>que refluxus. </s> <s>cum autem ſol per motum' primi mobilis acce<lb></lb>det ad punctum meridiei debile refluxus, luna per eundem <lb></lb>motum primi mobilis accedet, ſeu appropinquabit tantun<lb></lb>dem puncto forti refluxus, qui eſt ſub orizonte in quarta no<lb></lb>cturna refluxus; & tunc luna erit magis propinqua puncto <lb></lb>forti refluxus, qui eſt ſub orizonte in quarta nocturna reflu<lb></lb>Xus, quàm ſol puncto forti fluxus, qui eſt ſupra orizontem in <lb></lb>quarta diurna fluxus: & ideo tunc incipiet refluxus; quia <lb></lb>luna erit potentior ſole: & ſecundum quòd ſol per <expan abbr="motũ">motum</expan> primi <lb></lb>mobilis appropinquabit puncto meridiei debili refluxus, luna <lb></lb>per eundem motum primi mobilis appropinquabit tantun<lb></lb>dem puncto forti refluxus, qui eſt ſub orizonte: & ſic conti<lb></lb>nuabitur refluxus, donec ſol ueniat ad punctum meridiei de<lb></lb>bile refluxus: & cum ſol per motum primi mobilis recedet à <lb></lb>puncto meridiei debili refluxus, & mouebitur per quartam <lb></lb>diurnam refluxus appropinquando puncto forti refluxus: lu<lb></lb>na per eundem motum primi mobilis elongabitur tantundem <lb></lb>à puncto forti refluxus, qui eſt ſub <expan abbr="orizõte">orizonte</expan> in quarta nocturna <lb></lb>refluxus; & mouebitur etiam ipſo per quartam refluxus, ſicut <lb></lb>ſol accedendo ad punctum orientis debile fluxus, eo quia ſol, <lb></lb>& luna diſtant adinuicem pluſquam per quartam cæli: & ſic <lb></lb>ambo mouebuntur per quartas refluxus; & propter hoc con<lb></lb>tinuabitur refluxus, donec ſol ſit tantum ultra meridiem uer<lb></lb>ſus occidentem in quarta diurna refluxus, <expan abbr="quantũ">quantum</expan> luna citra <pb xlink:href="024/01/019.jpg" pagenum="6"></pb>meridiem uerſus orientem in quarta diurna fluxus: & tunc <lb></lb>ſol tantum diſtabit à puncto forti refluxus in quarta diurna <lb></lb>refluxus recedendo ab eo per motum primi mobilis uerſus <lb></lb>occidentem, quantum luna à puncto forti fluxus; qui eſt ſu<lb></lb>pra orizontem in quarta diurna fluxus accedendo ad ipſum: <lb></lb>& ſic ſol, & luna erunt æquipotentes, & tunc non fiet fluxus, <lb></lb>neque refluxus. </s> <s>cum autem ſol per motum primi mobilis e<lb></lb>longabitur à puncto forti refluxus; qui eſt ſupra orizontem <lb></lb>in quarta diurna fluxus accedendo ad punctum occidentis <lb></lb>debile fluxus; luna per eundem motum primi mobilis appro<lb></lb>pinquabit tantundem puncto forti fluxus; qui eſt ſupra ori<lb></lb>zontem in quarta diurna fluxus: & luna tunc erit magis pro<lb></lb>pinqua puncto forti fluxus in quarta diurna fluxus, quàm ſol <lb></lb>puncto forti refluxus in quarta diurna refluxus: & ſic luna e<lb></lb>rit potentior ſole, & tunc incipiet fluxus: & ſicut ſol continue <lb></lb>elongabitur à puncto forti refluxus in quarta diurna reflu<lb></lb>xus, ita luna continue appropinquabit puncto forti fluxus in <lb></lb>quarta diurna fluxus, & ſic continuabitur fluxus; & cum ſol <lb></lb>ueniet ad punctum occidentis debili fluxus, luna adhuc mo<lb></lb>uebit per quartam diurnam fluxus, eo quia ſol, & luna di<lb></lb>ſtant ad inuicem pluſquam per quartam cæli: & tunc luna e<lb></lb>rit magis propinqua puncto forti fluxus in quarta diurna flu<lb></lb>xus, quàm ſol puncto forti fluxus, qui eſt ſub orizonte in <lb></lb>quarta nocturna fluXus; & ideo continuabitur fluXus: & cum <lb></lb>luna ueniet ad punctum meridiei debile refluXus, ſol tranſibit <lb></lb>punctum occidentis debile fluXus <expan abbr="appropinquãdo">appropinquando</expan> puncto for<lb></lb>ti fluXus, qui eſt ſub orizonte in quarta nocturna fluXus; & <expan abbr="tũc">tunc</expan> <lb></lb>ſol erit magis propinquus puncto forti fluXus, qui eſt ſub ori<lb></lb>zonte in quarta nocturna fluXus, quàm luna puncto forti re<lb></lb>fluXus, qui eſt ſupra orizontem in quarta diurna refluXus: & <lb></lb>ſic ſol erit potentior luna; & ideo continuabitur fluXus: & <expan abbr="cũ">cum</expan> <lb></lb>ſol ueniet ad <expan abbr="punctũ">punctum</expan> forte fluXus, qui eſt ſub orizonte in quar<lb></lb>ta nocturna fluXus; luna adhuc <expan abbr="nõ">non</expan> erit in <expan abbr="pũcto">puncto</expan> forti refluXus, <lb></lb>qui eſt ſupra <expan abbr="orizontẽ">orizontem</expan> in quarta diurna refluXus; eo quia luna <lb></lb>diſtat à ſole pluſquam per quartam cæli; & ideo adhuc conti<pb xlink:href="024/01/020.jpg"></pb>nuabitur fluxus, donec ſol ſit tantum ſub orizonte eX parte oc<lb></lb>cidentis in quarta nocturna fluxus, quantum luna ſupra orizon<lb></lb><expan abbr="tẽ">tem</expan> eX eadem parte occidentis in quarta diurna refluxus; & <expan abbr="tũc">tunc</expan> <lb></lb>ſol <expan abbr="tantũ">tantum</expan> diſtabit à puncto forti fluxus, qui eſt ſub orizonte in <lb></lb>quarta nocturna fluxus accedendo ad punctum mediæ noctis <lb></lb>debile refluxus, quantum luna à puncto forti refluxus, qui eſt <lb></lb>ſupra orizontem in quarta diurna refluxus accedendo ad ip<lb></lb>ſum: & ideo ſol, & luna erunt æquipotentes, & non fiet flu<lb></lb>Xus, neque refluxus. </s> <s>poſtea cum ſol per motum primi mo<lb></lb>tus elongabitur à puncto forti fluxus; qui eſt ſub orizonte, <lb></lb>ex parte occidentis in quarta nocturna fluxus accedendo uer<lb></lb>ſus punctum mediæ noctis debile refluxus, luna per eundem <lb></lb>motum primi mobilis appropinquabit tantundem puncto for<lb></lb>ti refluxus; qui eſt ſupra orizontem in quarta diurna reflu<lb></lb>Xus accedendo ad ipſum: & ſic luna erit magis propinqua <lb></lb>puncto forti refluxus, quàm ſol puncto forti fluxus; & ideo <lb></lb>incipiet refluxus, & continuabitur modo dicto; donec ſol ſit <lb></lb>tantum ultra medium noctis, uerſus orientem in quarta no<lb></lb>cturna refluxus; quantum luna ante medium noctis uerſus oc<lb></lb>cidentem in quarta nocturna fluxus; & tunc ſol tantum diſta<lb></lb>bit à puncto forti refluxus in quarta nocturna refluxus rece<lb></lb>dendo ab eo uerſus prædictum orientis debile fluxus, quan<lb></lb>tum luna à puncto forti fluxus in quarta nocturna fluxus acce<lb></lb>dendo ad ipſum; & tunc ſol, & luna erunt æquipotentes, & <lb></lb>non fiet fluxus, neque refluxus. </s> <s>cum autem ſol per motum <lb></lb>primi mobilis elongabitur à puncto forti refluxus ſub orizon<lb></lb>te; qui eſt in quarta nocturna refluxus accedendo uerſus pun<lb></lb>ctum orientis debile fluxus; luna per eundem motum primi <lb></lb>mobilis appropinquabit tantundem puncto forti fluxus; qui <lb></lb>etiam eſt ſub orizonte in quarta nocturna fluxus accedendo <lb></lb>ad ipſum: & quia luna tunc eſt magis propinqua puncto forti <lb></lb>fluxus; qui eſt in quarta nocturna fluxus, quàm ſol puncto <lb></lb>forti refluxus; qui eſt in quarta nocturna refluxus: tunc in<lb></lb>cipit fluxus, & continuatur modo dicto, donec ſol ſit tantum <lb></lb>ſuper orizontem, eX parte orientis in quarta diurna fluxus, <pb xlink:href="024/01/021.jpg" pagenum="7"></pb>quantum luna ſub orizonte ex eadem parte orientis in quar<lb></lb>ta nocturna refluxus: & quia ſol tantum diſtabit à puncto for<lb></lb>ti fluxus, qui eſt ſupra orizontem in quarta diurna fluxus ac<lb></lb>cedendo per motum primi mobilis uerſus punctum meridiei <lb></lb>debile refluxus, quantum luna à puncto forti refluxus; qui eſt <lb></lb>ſub orizonte in quarta nocturna refluxus accedendo per eun<lb></lb>dem motum primi mobilis uerſus ipſum: ipſi erunt æquipo<lb></lb>tentes, & non fiet fluxus, neque refluxus: & iſto modo con<lb></lb>tinuabitur fluxus, & refluxus in omni die naturali donec luna <lb></lb>ueniat ad oppoſitionem eius cum ſole. </s></p><p type="main"> <s>Quando autem luna ueniet ad oppoſitionem eius cum ſole: <lb></lb>tunc quando ſol erit in puncto orientis debili fluxus, luna erit <lb></lb>in puncto occidentis ſimiliter debili fluxus: & tunc incipiet <lb></lb>fluxus, & continuabitur, quamdiu ſol mouebitur ad motum <lb></lb>primi mobilis à puncto orientis debili fluxus per quartam di<lb></lb>urnam fluxus ad punctum meridiei debile refluxus: & luna <lb></lb>tunc in toto iſto tempore mouebitur ſimiliter ad motum pri<lb></lb>mi mobilis à puncto occidentis debili fluxus per quartam no<lb></lb>cturnam fluxus ad punctum mediæ noctis debile refluxus; & <lb></lb>tunc ceſſabit fluxus, & incipiet refluxus, & durabit quamdiu <lb></lb>ſol ad motum primi mobilis mouebitur à puncto meridiei de<lb></lb>bili refluxus per quartam diurnam refluxus, uſque ad pun<lb></lb>ctum occidentis debile fluxus; & luna tunc in toto iſto tem<lb></lb>pore mouebitur ſimiliter ad motum primi mobilis à puncto <lb></lb>mediæ noctis debili refluxus per quartam nocturnam reflu<lb></lb>xus, uſque ad punctum orientis debile fluxus, & tunc ceſſa<lb></lb>bit refluxus: & iterum incipiet fluxus, & durabit quamdiu <lb></lb>ſol ad motum primi mobilis mouebitur à puncto occidentis <lb></lb>debili fluxus per quartam nocturnam fluxus, uſque ad pun<lb></lb>ctum mediæ noctis debile refluxus; & tunc luna in toto iſto <lb></lb>tempore per eundem motum primi mobilis mouebitur à pun<lb></lb>cto orientis ſimiliter debili fluxus per quartam diurnam flu<lb></lb>Xus, uſque ad punctum meridiei debile refluxus; & tunc ceſ<lb></lb>ſabit fluxus, & incipiet refluxus, & durabit quamdiu ſol ad <lb></lb>motum primi mobilis mouebitur à puncto mediæ noctis debili <pb xlink:href="024/01/022.jpg"></pb>refluxus per quartam nocturnam refluxus, uſque ad pun<lb></lb>ctum orientis debile fluxus: & tunc luna in toto iſto tempore <lb></lb>per eundem motum primi mobilis mouebitur à puncto meri<lb></lb>diei ſimiliter debili refluxus per quartam diurnam refluxus, <lb></lb>uſque ad punctum occidentis debile fluxus, & tunc ceſſabit <lb></lb>refluxus. </s></p><p type="main"> <s>Cum autem luna tranſibit oppoſitionem eius cum ſole per mo<lb></lb>tum eius proprium tendendo ad quadraturam ſecundam eius <lb></lb>cum ſole; tunc quando luna fuerit tantum ſupra orizontem <lb></lb>ex parte orientis in quarta diurna fluxus, quantum ſol ſub <lb></lb>orizonte ex eadem parte orientis in quarta nocturna reflu<lb></lb>xus; quia luna tunc tantum diſtabit à puncto forti fluxus; qui <lb></lb>eſt ſupra orizontem in quarta diurna fluxus, quantum ſol à <lb></lb>puncto forti refluxus; qui eſt ſub orizonte ex eadem parte o<lb></lb>rientis in quarta nocturna refluxus; tunc ſol, & luna erunt <lb></lb>æquipotentes, & non fiet fluxus, neque refluxus. </s> <s>Cum au<lb></lb>tem luna per motum primi mobilis elongabitur à puncto for<lb></lb>ti fluxus, qui eſt ſupra orizontem in quarta diurna fluxus ac<lb></lb>cedendo uerſus punctum meridie debile refluxus: ſol per <lb></lb>eundem motum primi mobilis appropinquabit tantundem <lb></lb>puncto forti refluxus, qui eſt ſub orizonte in quarta noctur<lb></lb>na refluxus accedendo ad ipſum; & tunc quia ſol minus di<lb></lb>ſtabit à puncto forti refluxus, qui eſt ſub orizonte ex parte o<lb></lb>rientis in quarta nocturna refluxus, quàm luna à puncto for<lb></lb>ti fluxus, qui eſt ſupra orizontem ex eadem parte orientis in <lb></lb>quarta diurna fluxus incipiet refluxus, & continuabitur. </s> <s>& <lb></lb>cum luna per motum primi mobilis perueniet ad punctum <lb></lb>meridiei debile refluxus, ſol adhuc erit ſub orizonte in quar<lb></lb>ta nocturna refluxus, eo quia ſol, & luna diſtant adinuicem <lb></lb>pluſquam per quartam cæli: & luna tunc ad motum primi <lb></lb>mobilis mouebitur per quartam diurnam refluxus, ſicut e<lb></lb>tiam ſol modo per quartam nocturnam refluxus accedendo <lb></lb>ad punctum fortem refluxus in quarta diurna refluxus, & ſic <lb></lb>continuabitur refluxus; & cum luna appropinquabit puncto <lb></lb>forti refluxus in quarta diurna refluxus, ſol appropinquabit <pb xlink:href="024/01/023.jpg" pagenum="8"></pb>puncto orientis debili fluxus in quarta nocturna refluxus, & <lb></lb>magis diſtabit à puncto forti fluxus, qui eſt ſupra orizontem <lb></lb>in quarta diurna fluxus, quàm luna à puncto forti refluxus, <lb></lb>qui eſt ſimiliter ſuper orizontem in quarta diurna refluxus, & <lb></lb>ſic continuabitur refluxus, donec luna fit tantum ultra meri<lb></lb>diem uerſus occidentem in quarta diurna refluxus, quantum <lb></lb>ſol ante meridiem uerſus orientem in quarta diurna fluxus, & <lb></lb>tunc luna tantum diſtabit à puncto forti refluxus in quarta di<lb></lb>urna refluxus, quantum ſol à puncto forti fluxus in quarta <lb></lb>diurna fluxus: & ſic ſol, & luna erunt æquipotentes, & non <lb></lb>fiet fluxus, neque refluxus. </s> <s>cum autem luna per motum pri<lb></lb>mi mobilis elongabitur à puncto forti refluxus accedendo <lb></lb>uerſus punctum occidentis debile fluxus, ſol per eundem mo<lb></lb>tum primi mobilis appropinquabit tantundem puncto forti <lb></lb>fluxus in quarta diurna fluxus: & tunc quia ſol erit magis <lb></lb>propinquus puncto forti fluxus, qui eſt in quarta diurna flu<lb></lb>Xus, quàm luna puncto forti refluxus, qui eſt in quarta diur<lb></lb>na refluxus, incipiet fluxus, & continuabitur ſecundum quod <lb></lb>luna ad motum primi mobilis elongabitur à puncto forti reflu<lb></lb>xus in quarta diurna refluxus accedendo uerſus punctum oc<lb></lb>cidentis debile fluxus, & ſol appropinquabit puncto forti flu<lb></lb>xus in quarta diurna fluxus accedendo ad ipſum: & cum lu<lb></lb>na ueniet ad motum primi mobilis ad punctum occidentis de<lb></lb>bile fluxus, ſol adhuc per eundem motum primi mobilis mo<lb></lb>uebit per quartam diurnam fluxus, eo quia ſol, & luna diſtant <lb></lb>adinuicem pluſquam per quartam cæli, & ſol erit magis pro<lb></lb>pinquus puncto forti fluxus in quarta diurna fluxus, quàm lu<lb></lb>na puncto forti refluxus in quarta diurna refluxus, ideo con<lb></lb>tinuabitur fluxus: & cum ſol ueniet ad punctum meridiei de<lb></lb>bile refluxus, luna erit ſub orizonte eX parte occidentis in <lb></lb>quarta nocturna fluxus, & erit magis propinqua puncto for<lb></lb>ti fluxus, qui eſt ſub orizonte in quarta nocturna fluxus, <lb></lb>quàm ſol puncto forti refluxus, qui eſt ſupra orizontem in <lb></lb>quarta diurna refluxus: ideo adhuc continuabitur fluxus, <lb></lb>donec luna ſit tantum ſub orizonte eX parte occidentis in <pb xlink:href="024/01/024.jpg"></pb>quarta nocturna fluxus, quantum ſol ſupra orizontem ex <lb></lb>eadem parte occidentis in quarta diurna refluxus; & tunc lu<lb></lb>na tantum diſtabit à puncto forti fluxus ſub orizonte in quar<lb></lb>ta nocturna fluxus accedendo uerſus punctum mediæ noctis <lb></lb>debile refluxus, quantum ſol à puncto forti refluxus ſupra o<lb></lb>rizontem in quarta diurna refluxus accedendo ad ipſum, & <lb></lb>ſic ſol, & luna erunt æquipotentes & non fiet fluxus, neque <lb></lb>refluxus. </s> <s>cum autem luna per motum primi mobilis elonga<lb></lb>bitur à puncto forti fluxus ſub orizonte in quarta nocturna <lb></lb>fluxus accedendo uerſus punctum mediæ noctis debile reflu<lb></lb>xus, ſol per eundem motum primi mobilis appropinquabit <lb></lb>tantundem puncto forti refluxus, qui eſt ſupra orizontem in <lb></lb>quarta diurna refluxus accedendo ad ipſum, & tunc ſol erit <lb></lb>magis propinquus puncto forti refluxus, qui eſt ſupra orizon<lb></lb>tem in quarta diurna refluxus, quàm luna puncto forti flu<lb></lb>xus, qui eſt ſub orizonte in quarta nocturna fluxus, & ideo <lb></lb>tunc incipiet refluxus, & continuabitur ſecundum quod lu<lb></lb>na elongabitur à puncto forti fluxus, qui eſt ſub orizonte in <lb></lb>quarta nocturna fluxus appropinquando puncto mediæ noctis <lb></lb>debili refluxus, & ſol appropinquabit puncto forti refluxus, <lb></lb>qui eſt ſupra orizontem in quarta diurna refluxus: & cum lu<lb></lb>na per motum primi mobilis ueniet ad punctum mediæ noctis <lb></lb>debile refluxus, ſol adhuc erit ſupra orizontem ex parte oc<lb></lb>cidentis in quarta diurna refluxus accedens per motum pri<lb></lb>mi mobilis ad punctum occidentis debile fluxus, & eo quia <lb></lb>ſol, & luna diſtant adinuicem pluſquam per quartam, & tunc <lb></lb>ſol plus diſtabit à puncto forti fluxus, qui eſt ſub orizonte ex <lb></lb>parte occidentis in quarta nocturna fluxus, quàm luna à pun<lb></lb>cto forti refluxus, qui etiam eſt ſub orizonte ex parte orien<lb></lb>tis in quarta nocturna refluxus; & ideo continuabitur reflu<lb></lb>xus, donec luna ſit tantum ultra medium noctis uerſus orien<lb></lb>tem, quantum ſol ante medium noctis uerſus occidentem, & <lb></lb>tunc luna tantum diſtabit à puncto forti refluxus in quarta no<lb></lb>cturna refluxus recedendo ab eo per motum primi mobilis, <lb></lb>& accedendo ad punctum orientis debile fluxus, quantum ſol <pb xlink:href="024/01/025.jpg" pagenum="9"></pb>à puncto fluxus in quarta nocturna fluxus accedendo per eun<lb></lb>dem motum primi mobilis ad ipſum, & ſic ſol, & luna erunt <lb></lb>æquipotentes, & non fiet fluxus, neque refluxus. </s> <s>cum au<lb></lb>tem luna per motum primi mobilis elongabitur à puncto forti <lb></lb>refluxus, qui eſt ſub orizonte ex parte orientis in quarta no<lb></lb>cturna refluxus uerſus punctum orientis debile fluxus, ſol <lb></lb>per eundem motum primi mobilis appropinquabit tantun<lb></lb>dem puncto forti fluxus, qui eſt ſub orizonte ex parte occi<lb></lb>dentis in quarta nocturna fluxus accedendo ad ipſum, & <expan abbr="tũc">tunc</expan>, <lb></lb>quia luna erit magis remota à puncto forti refluxus, quàm <lb></lb>ſol à puncto forti fluxus, tunc incipiet fluxus, quia ſol erit po<lb></lb>tentior luna, & quanto magis luna elongabitur à puncto forti <lb></lb>refluxus in quarta nocturna refluxus, tanto magis ſol ap<lb></lb>propinquabit puncto forti fluxus in quarta nocturna flu<lb></lb>xus, & ſic continuabitur fluxus: & cum luna ueniet ad <lb></lb>punctum orientis debile fluxus, ſol adhuc erit in quarta no<lb></lb>cturna fluxus, eo quia ſol diſtat à luna pluſquam per quar<lb></lb>tam cæli, & erit ſol magis propinquus puncto forti fluxus <lb></lb>in quarta nocturna fluxus, quàm luna puncto forti refluxus, <lb></lb>qui eſt in quarta nocturna refluxus, & ſic adhuc continuabi<lb></lb>tur fluxus, donec luna ſit tantum ſupra orizontem ex parte <lb></lb>orientis, quantum ſol ſub orizonte ex eadem parte orientis, <lb></lb>& tunc luna tantum diſtabit à puncto forti fluxus, qui eſt ſu<lb></lb>pra orizontem in quarta diurna fluxus recedendo ab eo per <lb></lb>motum primi mobilis uerſus punctum meridiei debile reflu<lb></lb>xus, quantum ſol à puncto forti refluxus, qui eſt ſub orizon<lb></lb>te in quarta nocturna refluxus accedendo ad ipſum per eun<lb></lb>dem motum primi mobilis, & ſic ſol, & luna erunt æquipoten<lb></lb>tes, & non fiet fluxus, neque refluxus, & iterum prior diſ<lb></lb>poſitio redibit, & continuabitur talis fluxus, & refluxus o<lb></lb>mni die naturali iſto modo, donec luna ueniat ad quadratu<lb></lb>ram eius cum ſole. </s></p><p type="main"> <s>Cum uero luna erit in quadratura ſecunda tunc aqua maris <lb></lb>nec fluet, nec refluet, ſed uidebitur quieſcere, ut facie<lb></lb>bat in quadratura prima, in qua in tota reuolutione cæli <pb xlink:href="024/01/026.jpg"></pb>luna, & ſol ſemper erant æquipotentes propter cauſas ſibi di<lb></lb>ctas, quia eædem cauſæ adſunt in quadratura ſecunda, quæ <lb></lb>adſunt in quadratura prima, & iſtud eſt circa XXI dies, & i<lb></lb>ſtam quietem aquæ maris appellant Veneti, ſicut ſupra <expan abbr="dictũ">dictum</expan> <lb></lb>eſt, Acqua de fele. </s> <s>& utuntur iſto dicto, Da uent'uno à uen<lb></lb>tidue, l'acqua non ua ne ſu, ne giu. </s></p><p type="main"> <s>Cum autem luna pertranſibit motum eius proprium hanc <lb></lb>quadraturam ſecundam tendendo ad coniunctionem eius <lb></lb>cum ſole, tunc luna diſtabit à ſole minus quarta parte cæli, & <lb></lb>tunc cum ipſa fuerit tantum ſupra orizontem ex parte o<lb></lb>rientis in quarta diurna fluxus, quantum ſol ſub orizonte ex <lb></lb>eadem parte orientis in quarta nocturna refluxus, tunc lu<lb></lb>na tantum diſtabit à puncto forti fluxus, qui eſt ſupra orizon<lb></lb>tem in quarta diurna fluxus accedendo ad ipſum per motum <lb></lb>primi mobilis, quantum ſol à puncto forti refluxus, qui eſt ſub <lb></lb>orizonte in quarta nocturna refluxus recedendo ab ipſo per <lb></lb>eundem motum primi mobilis uerſus punctum orientis debile <lb></lb>fluxus, & tunc ſol, & luna erunt æquipotentes, & non fiet flu<lb></lb>xus, neque refluxus. </s> <s>cum autem luna per motum primi mo<lb></lb>bilis accedet ad punctum forte fluxus, qui eſt ſupra orizon<lb></lb>tem in quarta diurna fluxus, ſol per eundem motum primi <lb></lb>mobilis recedet, & elongabitur tantundem à puncto forti re<lb></lb>fluxus, qui eſt ſub orizonte in quarta nocturna refluxus <lb></lb>uerſus punctum orientis debile fluxus, & tunc quia luna mi<lb></lb>nus diſtabit à puncto forti fluxus, qui eſt ſupra orizontem in <lb></lb>quarta diurna fluxus, quàm ſol à puncto forti refluxus, qui <lb></lb>eſt ſub orizonte in quarta nocturna refluxus, luna erit po<lb></lb>tentior ſole, & ideo tunc incipiet fluxus, & quanto magis lu<lb></lb>na appropinquabit puncto forti fluxus, tanto magis ſol elon<lb></lb>gabitur à puncto forti refluxus appropinquando puncto o<lb></lb>rientis debili fluxus, & ideo continuabitur fluxus: & cum <lb></lb>ſol ueniet per motum primi mobilis ad punctum orientis <lb></lb>debile fluxus, quia luna adhuc erit in quarta diurna <lb></lb>fluxus, eo quia ipſa diſtat à ſole minus quarta parte cæ<lb></lb>li, ipſa minus diſtabit à puncto forti fluxus, qui eſt ſupra <pb xlink:href="024/01/027.jpg" pagenum="10"></pb>orizontem in quarta diurna fluxus, quàm ſol à puncto forti <lb></lb>refluxus, qui eſt ſub <expan abbr="orizõte">orizonte</expan> in quarta nocturna refluxus, ideo <lb></lb>adhuc continuabitur fluxus, & <expan abbr="cũ">cum</expan> luna ueniet ad <expan abbr="punctũ">punctum</expan> meri <lb></lb>diei debile refluxus, ſol erit ſupra orizontem in quarta diur<lb></lb>na fluxus, & erit magis propinquus puncto forti fluxus, quàm <lb></lb>luna puncto forti refluxus, qui eſt poſt meridiem in quarta <lb></lb>diurna refluxus, eo quia ſol diſtat à luna minus quarta parte <lb></lb>cæli, & ideo continuabitur fluxus donec luna ſit tantum ul<lb></lb>tra meridiem uerſus occidentem in quarta diurna refluxus, <lb></lb>quantum ſol ante meridiem uerſus orientem in quarta diurna <lb></lb>fluxus, & tunc luna tantum diſtabit à puncto forti refluxus in <lb></lb>quarta diurna refluxus accedendo ad ipſum per <expan abbr="motũ">motum</expan> primi <lb></lb>mobilis, <expan abbr="quantũ">quantum</expan> ſol à puncto forti fluxus in quarta diurna flu<lb></lb>xus recedendo ab ipſo per eundem <expan abbr="motũ">motum</expan> primi mobilis, & ſic <lb></lb>ſol, & luna erunt æquipotentes, & non fiet fluxus, neque reflu<lb></lb>xus. </s> <s>cum autem luna per <expan abbr="motũ">motum</expan> primi mobilis appropinquabit <lb></lb>puncto forti refluxus in quarta diurna refluxus, ſol per <expan abbr="eundẽ">eundem</expan> <lb></lb>motum primi mobilis recedet, & elongabitur <expan abbr="tantundẽ">tantundem</expan> à pun<lb></lb>cto forti fluxus in quarta diurna fluxus, & tunc luna erit ma<lb></lb>gis propinqua <expan abbr="pũcto">puncto</expan> forti refluxus in quarta diurna refluxus, <lb></lb>quàm ſol puncto forti fluxus in quarta diurna fluxus, & ſic lu<lb></lb>na erit potentior ſole, & ideo incipiet refluxus, & continuabi<lb></lb>tur fluxus, & refluxus eodem modo, quo dictum eſt, quando <lb></lb>luna recedit à coniunctione eius cum ſole, & nondum uenit ad <lb></lb>quadraturam eius cum ſole primam, ſed eſt inter coniunctio<lb></lb>nem, & quadraturam primam: & cum luna ueniet ad con<lb></lb>iunctionem eius cum ſole, iterum tota diſpoſitio iam narra<lb></lb>ta redibit eodem modo penitus, ſicut dictum eſt. </s> <s>iſte er<lb></lb>go motus aquæ maris, qui dictus eſt, eſt motus aquæ ma<lb></lb>ris inſequens motum ſolis, & lunæ ad motum ſcilicet pri<lb></lb>mi mobilis. </s> <s>nam ſi bene conſideraueris ea, quæ dicta ſunt <lb></lb>de fluxu, & refluxu, ſeu cremento, & decremento, aut <lb></lb>acceſſu, & receſſu aquæ maris, cognoſces, quòd initia <lb></lb>fluxus, & refluxus, ſeu crementi, & decrementi aquæ <lb></lb>maris, & ſimiliter quies eius diuerſificantur in horis diei, & <pb xlink:href="024/01/028.jpg"></pb>noctis: non enim ſemper eadem hora diei fiunt ſicut manife<lb></lb>ſtum eſt obſeruantibus huiuſmodi fluxum, & refluxum, ſeu <lb></lb>crementum, & decrementum, & quietem falſam aquæ maris. <lb></lb></s> <s>Ex dictis apparet, quòd aqua maris habet motum acceſſio<lb></lb>nis, ſeu crementi in die ſemel, & in nocte ſemel. </s></p><p type="main"> <s>Similiter apparet, quòd aqua maris habet motum receſſionis, <lb></lb>ſeu decrementi in die ſemel, & in nocte ſemel. </s></p><p type="main"> <s>Apparet etiam quòd acceſſio, ſeu crementum aquæ maris <expan abbr="nõ">non</expan> <lb></lb>incipit eadem hora diei, uel noctis ſemper, ſed diuerſis horis, <lb></lb>& ſimiliter receſſio, ſeu decrementum. </s></p><p type="main"> <s>Et etiam tempus, in quo tam acceſſio, ſeu crementum, quàm <lb></lb>receſſio, ſeu decrementum aquæ maris inordinate procedit, <lb></lb>quando ſcilicet luna eſt in quadraturis eius cum ſole prima, ſci <lb></lb>licet uel ſecunda. </s></p><p type="main"> <s>Fiunt aliquando maximi aquarum curſus, aliquando minimi, <lb></lb>& aliquando medio modo ſe habentes, ſeu mediocres, quan<lb></lb>do ſcilicet luna fuerit in omni alio loco à ſole, præter hæc qua<lb></lb>tuor, uidelicet in coniunctione, uel oppoſitione, aut quadra<lb></lb>tura eius prima, aut ſecunda cum ſole. </s></p><p type="main"> <s>Fiunt aliquando maxima crementa aquarum, aliquando mi<lb></lb>nima, & aliquando medio modo ſe habentia. </s></p><p type="main"> <s>Fiunt ſimiliter aliquando maxima decrementa aquarum, ali<lb></lb>quando minima, & aliquando medio modo ſe habentia. </s></p><p type="main"> <s>Incrementa, ſeu argumentationes aquarum fiunt aliquando <lb></lb>maiora, aliquando minora. </s></p><p type="main"> <s>Maximi curſus, ſeu motus aquarum fiunt luna coniuncta ſoli, <lb></lb>& maxima crementa, & decrementa. </s></p><p type="main"> <s>Maximi curſus, ſeu motus aquarum ſimiliter fiunt luna oppo<lb></lb>ſita ſoli, & maxima crementa, & decrementa, & maiora quàm <lb></lb>tempore coniunctionis luna cum ſole: corpora enim ſuperio<lb></lb>ra infundunt uir tutes ſuas in iſtis inferioribus per motum eo<lb></lb>rum, & lumen: quanto enim plus habent de lumine, tanto <lb></lb>plus, & fortius operantur: & quia in oppoſitione lunæ cum <lb></lb>ſole, luna eſt plena lumine, & lumen eius eſt uerſus nos, ideo <lb></lb>rationabile eſt, ut cauſentur maiora crementa, & decrementa <pb xlink:href="024/01/029.jpg" pagenum="11"></pb>aquarum, quàm in coniunctione eius cum ſole, quia tamen in <lb></lb>coniunctione eius cum ſole, ſol, & luna ſunt unici ſimul, & eo<lb></lb>rum uirtutes: ideo fiunt etiam crementa, & decrementa a<lb></lb>quarum magna, quia ambæ uirtutes, ſcilicet ſolis, & lunæ <lb></lb>ſunt unicæ ſimul, ſed maiora fiunt in oppoſitione, quàm in <lb></lb>coniunctione propter cauſam dictam. </s></p><p type="main"> <s>Luna exiſtente in quadraturis eius cum ſole aqua maris nul<lb></lb>lum habet determinatum tempus acceſſionis, uel receſſionis, <lb></lb>ſeu crementi, aut decrementi: & tunc fiunt minimi curſus a<lb></lb>quarum, & minima crementa, & decrementa: & talis motus <lb></lb>aquæ maris eſt dictus à Venetis, De fele. </s> <s>& tunc aqua maris <lb></lb>nullum habet terminatum principium acceſſionis, uel receſ<lb></lb>ſionis, ſeu crementi, aut decrementi, ſed diuerſimode, & in<lb></lb>ordinate mouetur: aliquando enim accedit, aliquando rece<lb></lb>dit. </s> <s>huius autem uarietatis cauſa eſt, quia ſol, & luna ubicun<lb></lb>que fuerint in mouendo aquam ſibi inuicem æqualiter, uel <lb></lb>quaſi æqualiter contradicunt in quocunque puncto fuerint: <lb></lb>in quocunque enim puncto fuerit ſol, luna erit in puncto uir<lb></lb>tutis oppoſitæ, & contrariæ loco ſolis, uel prope. </s></p><p type="main"> <s>Cum autem luna erit extra quatuor loca dicta tunc aqua ma<lb></lb>ris incipiet accedere, uel recedere: quando ſol, & luna erunt <lb></lb>in punctis æqualibus uirtutis quartarum contrariæ operatio<lb></lb>nis, erunt etiam curſus aquarum tanto maiores, quanto luna <lb></lb>fuerit propinquior coniunctioni eius cum ſole, uel oppoſitio<lb></lb>ni: & tanto minores, quanto luna fuerit propinquior qua<lb></lb>draturis: ſimiliter etiam erunt incrementa, & decrementa <lb></lb>tanto maiora. </s> <s>ſi enim luna erit inter coniunctionem eius cum <lb></lb>ſole, & quadraturam primam, tunc luna ad motum primi <lb></lb>mobilis ſequitur ſolem in ortu ſuo, & tunc erit principium ac<lb></lb>ceſſionis diurnæ aquæ maris de die. </s> <s>poſt ortum ſolis circa ho<lb></lb>ram tertiam, uel ante, quando ſcilicet ſol erit tantum ſupra o<lb></lb>rizontem ex parte orientis in quarta diurna fluxus, quantum <lb></lb>luna ſub orizonte ex eadem parte orientis in quarta nocturna <lb></lb>refluxus, eo quia tunc ſol, & luna erunt æquipotentes, quia <lb></lb>erunt in punctis æqualis uirtutis in quartis contrariæ opera<pb xlink:href="024/01/030.jpg"></pb>tionis: & principium acceſſionis nocturnæ aquæ maris erit de <lb></lb>nocte poſt occaſum ſolis, quando ſcilicet ſol erit tantum ſub <lb></lb>orizonte ex parte occidentis in quarta nocturna fluxus, quan<lb></lb>tum luna ſupra orizontem ex eadem parte occidentis in quar<lb></lb>ta diurna refluxus. </s> <s>principium autem receſſionis diurnæ erit <lb></lb>de die poſt meridiem, quando ſcilicet ſol erit tantum poſt me<lb></lb>ridiem in quarta diurna refluxus, quantum luna ante meri<lb></lb>diem in quarta diurna fluxus: & principium receſſionis no<lb></lb>cturnæ erit de nocte poſt medium noctis, quando ſcilicet ſol <lb></lb>erit tantum poſt punctum mediæ noctis in quarta nocturna re<lb></lb>fluxus, quantum luna ante ipſum in quarta nocturna fluxus. <lb></lb></s> <s>ſi autem luna fuerit inter quadraturam primam, & oppoſitio<lb></lb>nem, adhuc luna in ſuo ortu ſequitur ſolem, & tunc erit prin<lb></lb>cipium acceſſionis diurnæ de die poſt meridiem circa ueſpe<lb></lb>ras, uidelicet parum ante, uel poſt, quando ſcilicet ſol fuerit <lb></lb>tantum ſupra orizontem ex parte occidentis in quarta diurna <lb></lb>refluxus, quantum luna ſupra orizontem ex parte orientis in <lb></lb>quarta diurna fluxus. </s> <s>principium autem acceſſionis nocturnæ <lb></lb>erit de nocte ante diem, uidelicet circa matutinum ante, uel <lb></lb>poſt, quando ſcilicet ſol erit tantum ſub orizonte à parte ori<lb></lb>entis in quarta nocturna refluxus, quantum luna ſub orizon<lb></lb>te ex parte occidentis in quarta nocturna fluxus. </s> <s>principium <lb></lb>uero receſſionis diurnæ erit de die ante meridiem, quando ſci <lb></lb>licet ſol erit tantum ante punctum meridiei, quantum luna <lb></lb>poſt punctum mediæ noctis. </s> <s>principium autem receſſionis no<lb></lb>cturnæ erit de nocte ante medium noctis, quando ſcilicet ſol <lb></lb>fuerit tantum ante punctum mediæ noctis in quarta nocturna <lb></lb>fluxus, quantum luna poſt punctum meridiei in quarta diur<lb></lb>na refluxus. </s> <s>ſi autem luna fuerit inter oppoſitionem ſolis, & <lb></lb>quadraturam ſecundam eius cum ſole, tunc luna in ortu ſuo <lb></lb>antecedit ſolem, & tunc principia tam acceſſionis, quàm re<lb></lb>ceſſionis ſunt eodem modo ſicut fuerunt, quando luna fuit <lb></lb>inter coniunctionem, & quadraturam primam: nam princi<lb></lb>pium acceſſionis diurnæ erit de die circa tertiam ante, uel poſt, <lb></lb>quando ſcilicet ſol erit tantum ſupra orizontem ex parte <pb xlink:href="024/01/031.jpg" pagenum="12"></pb>orientis in quarta diurna fluxus, quantum luna ſupra orizon<lb></lb>tem ex parte occidentis in quarta diurna refluxus: & princi<lb></lb>pium acceſſionis nocturnæ erit de nocte, quando ſcilicet ſol e<lb></lb>rit tantum ſub orizonte ex parte occidentis in quarta noctur<lb></lb>na fluxus, quantum luna ſub orizonte ex parte orientis in <lb></lb>quarta nocturna refluxus: ſed principium receſſionis diurnæ <lb></lb>erit de die poſt meridiem, quando ſcilicet ſol fuerit <expan abbr="tantũ">tantum</expan> poſt <lb></lb>punctum meridiei in quarta diurna refluxus, quantum luna <lb></lb>ante punctum mediæ noctis in quarta nocturna fluxus. </s> <s>prin<lb></lb>cipium uero receſſionis nocturnæ erit de nocte, quando ſcili<lb></lb>cet ſol fuerit tantum poſt punctum mediæ noctis in quarta no<lb></lb>cturna refluxus, quantum luna ante punctum meridiei in quar<lb></lb>ta diurna fluxus. </s> <s>ſi autem luna fuerit inter quadraturam ſe<lb></lb>cundam, & coniunctionem eius cum ſole, tunc luna etiam in <lb></lb>ſuo ortu antecedit ſolem, & erunt tunc principia acceſſionis, <lb></lb>& receſſionis in eiſdem horis, ſicut ſunt quando luna eſt in<lb></lb>ter quadraturam primam, & oppoſitionem, quia principium <lb></lb>acceſſionis diurnæ erit de die poſt meridiem circa ueſperas, <lb></lb>ante, ſcilicet uel poſt, quando ſcilicet ſol erit tantum ſupra o<lb></lb>rizontem ex parte occidentis in quarta diurna refluxus, quan <lb></lb>tum luna ſub orizonte ex eadem parte occidentis in quarta <lb></lb>nocturna fluxus. </s> <s>principium uero acceſſionis nocturnæ erit <lb></lb>de nocte circa matutinum ante, uel poſt, quando ſcilicet ſol <lb></lb>fuerit tantum ſub orizonte ex parte orientis in quarta noctur<lb></lb>na refluxus, quantum luna ſupra orizontem ex eadem parte <lb></lb>orientis in quarta diurna fluxus: ſed principium receſſionis <lb></lb>diurnæ erit de die ante meridiem, quando ſcilicet luna erit <lb></lb>tantum poſt punctum meridiei in quarta diurna refluxus, <lb></lb>quantum ſol ante ipſum in quarta diurna fluxus: & principi<lb></lb>um receſſionis nocturnæ erit de nocte ante medium noctis, <lb></lb>quando ſcilicet luna erit tantum poſt punctum mediæ noctis <lb></lb>in quarta nocturna refluxus, quantum ſol ante punctum me<lb></lb>diæ noctis in quarta nocturna fluxus. </s> <s>ex iſtis dictis apparet, <lb></lb>quòd tam acceſſio, quàm receſſio aquæ maris non incipiunt <lb></lb>ſemper in eiſdem horis diei, uel noctis, quia principium <pb xlink:href="024/01/032.jpg"></pb>acceſſionis, aut eſt in principio diei, aut in principio noctis, <lb></lb>quod accidit luna exiſtente coniuncta uel oppoſita ſoli, uel eſt <lb></lb>ante diem à matutinis uerſus diem, uel de die, uſque ad ter<lb></lb>tiam, uel circa; uel eſt ante ſerum à ueſperis uerſus ſerum, uſ<lb></lb>que ad <expan abbr="galicãtum">galicantum</expan>, uel circa quod accidit, quando luna eſt in<lb></lb>ter coniunctionem, uel oppoſitionem eius cum ſole, & ali<lb></lb>quam ex quadraturis. </s> <s>principium autem receſſionis, aut eſt <lb></lb>in meridie, aut in medio noctis, quando ſcilicet luna eſt con<lb></lb>iuncta ſoli, uel ei oppoſita, aut eſt ante meridiem, uel poſt, <lb></lb>aut ante medium noctis, uel poſt, quando ſcilicet luna eſt in<lb></lb>ter coniunctionem, uel oppoſitionem eius cum ſole, & ali<lb></lb>quam ex quadraturis. </s> <s>apparet etiam, quòd aliquando aqua <lb></lb>maris nullum habet terminatum principium, nec ordinem <lb></lb>acceſſionis, uel receſſionis, quod accidit luna exiſtente in qua<lb></lb>draturis eius cum ſole. </s> <s>apparet etiam, quod omnis acceſſio <lb></lb>aquæ maris fit per reſpectum ad orizontem ex parte orientis, <lb></lb>uel occidentis: & omnis receſſio per reſpectum ad meridia<lb></lb>num, ſeu ad punctum meridiei, uel mediæ noctis. </s></p><p type="main"> <s>Aduertendum eſt etiam, quòd omnia, quæ dicta ſunt, maxime <lb></lb>habent ueritatem in orizonte recto, in obliquo uero aliquo <lb></lb>tempore aliquod fallunt, ſicut ſic infra dicetur. </s></p><p type="main"> <s>Contingit autem aquam maris à ſupra ſcripto ordine motus <lb></lb>deuiare: communiter tamen, & ut in pluribus debitum or<lb></lb>nem obſeruat. </s> <s>talis autem deuiatio à ſupraſcripto ordine du<lb></lb>plex eſt; aut enim eſt deuiatio, ſeu error in hora principii mo<lb></lb>tus acceſſionis, uel receſſionis, aut in medio motus, uidelicet <lb></lb>quòd maiores, uel minores curſus habeant ſolito, uel maio<lb></lb>ra, aut minora habeant incrementa, aut decrementa. </s> <s>error <lb></lb>ueniens in hora motus, triplici de cauſa poteſt accidere, aut <lb></lb>ratione ſitus regionis, aut ratione corporum ſuper cæleſtium, <lb></lb>aut propter mutationem aeris: ratione ſitus regionum accidit <lb></lb>diuerſitas ſolum in hora principii acceſſionis, eo quia princi<lb></lb>pium acceſſionis habet reſpectum ad orizontem, ſeu eſt per <lb></lb>reſpectum ad orizontem: in principio autem receſſionis nul<lb></lb>la eſt diuerſitas, nec error, eo quia principium receſſionis eſt <pb xlink:href="024/01/033.jpg" pagenum="13"></pb>per reſpectum ad circulum meridianum: ratione ſitus re<lb></lb>gionis accidit diuerſitas propter hoc, aut enim eſt regio ſub <lb></lb>æquinoctiali circulo, aut extra; ſi ſub æquinoctiali circulo, <lb></lb>quia illi habent orizontem rectum, & dies ibi ſemper ſunt <lb></lb>æquales noctibus ibi in omni tempore anni ea, quæ dicta <lb></lb>ſunt de diuerſis horis principii acceſſionis aquæ maris maxi<lb></lb>me habent ueritatem. </s> <s>regiones autem diſtantes ab æquino<lb></lb>ctiali, quia habent orizontem obliquum, in eis principia <lb></lb>acceſſionis aquæ ſunt, ſicut in regionibus, quæ ſunt ſub æ<lb></lb>quinoctiali ſolum in duobus temporibus anni, uidelicet in <lb></lb>tempore ueris, ſeu æquinoctii uernalis, & in tempore autum<lb></lb>ni, ſeu æquinoctii autumnalis, uidelicet circa medium men<lb></lb>ſis Martii, & circa medium menſis Septembris. </s> <s>in aliis au<lb></lb>tem temporibus anni, ſeu ab æquinoctio uernali per totam <lb></lb>æſtatem, uſque ad æquinoctium autumnale aliter eſt, quia <lb></lb>principium acceſſionis diurnæ ſi ipſa acceſſio eſt ante meri<lb></lb>diem, uidelicet circa mane, erit tardius, quàm eſſe debet, <lb></lb>uidelicet plus de die, quàm fiat in regionibus, quæ ſunt ſub <lb></lb>æquinoctiali: & hoc ideo eſt, quia in talibus regionibus dies <lb></lb>incipit prius, ſeu ſol oritur priuſquam in regionibus, quæ <lb></lb>ſunt ſub æquinoctiali propter obliquitatem orizontis obli<lb></lb>qui (quamuis regiones ipſæ ſint ſub eodem meridiano) quod <lb></lb>ſi principium acceſſionis diurnæ fuerit poſt meridiem, uide<lb></lb>licet circa ſerum, tunc tale principium erit citiuſquam ſit in <lb></lb>regionibus, quæ ſunt ſub æquinoctiali, ideſt in paucioribus <lb></lb>horis diei: & hoc ideo eſt, quia tunc ſol tardius occidit, <lb></lb>quàm in regionibus, quæ ſunt ſub æquinoctiali. </s> <s>principium <lb></lb>uero acceſſionis nocturnæ ſi eſt ante medium noctis, fit in di<lb></lb>ctis locis, ſeu regionibus citius, ideſt in minori tempore no<lb></lb>ctis, ſeu in breuiori tempore poſt occaſum ſolis, quàm fiat in <lb></lb>regionibus, quæ ſunt ſub æquinoctiali, quia tunc nox incipit <lb></lb>eis poſt, quòd ſi principium acceſſionis nocturnæ eſt poſt me<lb></lb>diam noctem, uidelicet uerſus diem, fiet tardius, ideſt ad plu<lb></lb>res horas noctis, ſeu magis prope die, quàm in regionibus, <lb></lb>quæ ſunt ſub æquinoctiali, & hoc ideo eſt, quia ſol citius eis <pb xlink:href="024/01/034.jpg"></pb>oritur, quàm eis, qui ſunt ſub æquinoctiali, & hæc diuerſitas <lb></lb>tantum creſcit, quod aliquando contingit uidere duas acceſ<lb></lb>ſiones aquæ in die, & nullam in nocte; quod quidem accidit <lb></lb>propter inæqualitatem dierum cum ſuis noctibus: quanto e<lb></lb>nim dies artificialis fuerit longior ſua nocte, tanto talis diuer<lb></lb>ſitas, & error euidentius creſcit. </s> <s>quare in longioribus diebus <lb></lb>anni talis diuerſitas apparebit manifeſte; ſed ab æquinoctio <lb></lb>autumnali per totam hiemem, uſque ad æquinoctium uerna<lb></lb>le fit contrarium, quia principium acceſſionis diurnæ ſi fuerit <lb></lb>ante meridiem, ſcilicet circa mane, tunc erit citius, quàm de<lb></lb>beret eſſe, ideſt in paucioribus horis diei, quàm fiat in orizon<lb></lb>te recto, quia tunc tardius incipit dies, ſeu tardius oritur ſol <lb></lb>habentibus orizontem obliquum, quàm habentibus orizon<lb></lb>tem rectum; quòd ſi talis acceſſus fuerit poſt meridiem, ſcili<lb></lb>cet circa ſerum, tunc principium talis acceſſionis erit tardius, <lb></lb>ideſt magis uerſus ſerum, ſeu magis iuxta occaſum ſolis, quàm <lb></lb>in regionibus, quæ ſunt ſub æquinoctiali, quia in orizonte <lb></lb>obliquo fit citius nox, & ſol citius occidit, quàm in recto. </s> <s>prin<lb></lb>cipium ueto acceſſionis nocturnæ ſi fuerit ante medium noctis <lb></lb>erit tardius, & plus in nocte, quàm in regionibus, quæ ſunt <lb></lb>ſub æquinoctiali; & hoc ideo eſt, quia tunc nox in orizonte <lb></lb>obliquo prius incipit, quàm in recto, quia ſol prius occidit in <lb></lb>orizonte obliquo, quàm in recto; quòd ſi principium acceſſio<lb></lb>nis nocturnæ fuerit poſt mediam noctem, ideſt uerſus diem, <lb></lb>tunc tale principium acceſſionis in orizonte obliquo fiet citi<lb></lb>us, ideſt in paucioribus horis noctis, ideſt magis ante diem, <lb></lb>ſeu ante ortum ſolis, quàm fiat in regionibus, quæ ſunt ſub æ<lb></lb>quinoctiali, eo quia ſol oritur tardius, quàm in regionibus, <lb></lb>quæ ſunt ſub æquinoctiali, & talis diuerſitas in tantum creſcit, <lb></lb>quòd aliquando fient duæ acceſſiones aquæ in nocte, & nullæ <lb></lb>in die: & hoc quidem accidet propter inæqualitatem, & augu<lb></lb>mentum noctis ſupra diem ſuam: quanto enim nox fuerit lon<lb></lb>gior ſua die, tanto magis creſcit talis diuerſitas: quare talis di<lb></lb>uerſitas apparebit maxima in longiori nocte anni. </s> <s>ex dictis er<lb></lb>go apparet, quòd quanto fuerimus propinquiores æquinoctio, <pb xlink:href="024/01/035.jpg" pagenum="14"></pb>tanto minor apparebit diuerſitas in hora principii acceſſionis <lb></lb>aquæ: & quanto ſol fuerit propinquior ſolſtitiis, ſeu longiori<lb></lb>bus diebus, & longioribus noctibus, tanto maior erit diuerſitas, <lb></lb>& certior, & manifeſtius apparebit. </s> <s>ratione autem corporum <lb></lb>cæleſtium etiam accidit diuerſitas, & error in principiis non ſo<lb></lb>lum acceſſionis, uerum etiam receſſionis. </s></p><p type="main"> <s>Cum enim aliqua ex ſtellis magnis, & luminoſis (ut ſunt Venus, <lb></lb>& Iuppiter) fuerit circa ſolem, uel lunam; illum, uel <expan abbr="illã">illam</expan> adiu<lb></lb>uant in mouendo aquam maris: quare relinquunt debitum or<lb></lb>dinem. </s> <s>ratione uero mutationis aeris, ſæpe contingit diuerſi<lb></lb>tas, & error in principiis acceſſionis, & receſſionis aquæ maris. <lb></lb></s> <s>impetuoſa enim diſpoſitio uentorum tam de prope, quàm de <lb></lb>longe inſuflantium remouet curſus aquarum à debito ordine <lb></lb>aliquando feſtinando acceſſus, aliquando receſſus. </s> <s>ſimiliter & <lb></lb>ipſos poſtponere faciendo. </s> <s>error etiam accidit in medio mo<lb></lb>tus aquarum, quia tam curſus aquarum, quàm etiam incre<lb></lb>menta, & decrementa earum aliquando non ſeruant <expan abbr="debitũ">debitum</expan> <lb></lb>motum. </s> <s>diſpoſitio enim uentorum ad maiores, uel minores <lb></lb>curſus augumentum præbent: quare & maiora incrementa, <lb></lb>& decrementa accidunt: maiores etiam curſus, & <expan abbr="diuerſitatẽ">diuerſitatem</expan> <lb></lb>maiorem euenire faciunt coarctationes, & ſtricturæ locorum <lb></lb>ratione inſularum, uel montium in aliquibus locis maximis exi<lb></lb>ſtentium; quia ubi arctius, ſeu ſtrictius exiſtit mare, ibi fortior <lb></lb>curſus exiſtit, ut circa Eubœam <expan abbr="inſulã">inſulam</expan> Nigropontis, & inter <lb></lb>Siciliam, & Calabriam ſæpe notari poteſt. </s> <s>impediunt etiam ta<lb></lb>les ſtricturæ augumentationes aquarum: per ſtrictum enim lo<lb></lb>cum modica quantitas aquæ tranſire poteſt. </s> <s>quare augumen<lb></lb>tationes, & diminutiones minores fiunt, & ideo accidit, quòd <lb></lb>in Oceano maxima fiunt crementa, & decrementa. </s> <s>nulla enim <lb></lb>ibi adeſt ſtrictura impediens curſus aquarum: quare ibi motus <lb></lb>aquarum eſt liber, & aqua ibi incedit ordine certiori: ſed in <lb></lb>mari noſtro Mediterraneo aliter eſt, quia quicquid in eo ingre<lb></lb>ditur, uel egreditur ex mari Oceano, per unum <expan abbr="ſolũ">ſolum</expan>, & <expan abbr="ſtrictũ">ſtrictum</expan> <lb></lb>locum à parte occidentis tranſit. </s> <s>quare non poteſt <expan abbr="multũ">multum</expan> in ac<lb></lb>ceſſu impleri, nec multum in receſſu euacuari. </s> <s>& ex conſequen<lb></lb>ti motus aquæ maris non ita certo ordine incedit. </s> <s>& hæc de <lb></lb>diuerſis motibus aquæ maris dicta ſufficiunt. </s></p><pb xlink:href="024/01/036.jpg"></pb><pb xlink:href="024/01/037.jpg"></pb><figure id="id.024.01.037.1.jpg" xlink:href="024/01/037/1.jpg"></figure><p type="caption"> <s>Figura oſtendens initium crementi diurni in <lb></lb>ortu ſolis, & initium decrementi diurni in <lb></lb>meridie, & initium crementi nocturni in oc<lb></lb>caſu ſolis, & initium decrementi nocturni in <lb></lb>medio noctis. </s></p><pb xlink:href="024/01/038.jpg"></pb><figure id="id.024.01.038.1.jpg" xlink:href="024/01/038/1.jpg"></figure><p type="caption"> <s>Figura oſtendens initium crementi diurni poſt or<lb></lb>tum ſolis ante, uel poſt horam tertiarum ſecun<lb></lb>dum quod luna diſteterit a ſole plus, uel minus, <lb></lb>& nondum uenerit ad <expan abbr="quadratutã">quadratutam</expan> eius cum ſole <lb></lb><expan abbr="primã">primam</expan>: & <expan abbr="initiũ">initium</expan> <expan abbr="decremẽti">decrementi</expan> diurni poſt <expan abbr="meridiẽ">meridiem</expan> ante <lb></lb>uel poſt horam <expan abbr="ueſperarũ">ueſperarum</expan>, & <expan abbr="initiũ">initium</expan> crementi nocturni <lb></lb>poſt occaſum ſolis, & <expan abbr="initiũ">initium</expan> <expan abbr="decremẽti">decrementi</expan> diurni poſt <lb></lb>mediam noctem ante, uel poſt horam matutini. </s></p><pb xlink:href="024/01/039.jpg"></pb><figure id="id.024.01.039.1.jpg" xlink:href="024/01/039/1.jpg"></figure><figure id="id.024.01.039.2.jpg" xlink:href="024/01/039/2.jpg"></figure><pb xlink:href="024/01/040.jpg"></pb><pb xlink:href="024/01/041.jpg"></pb><p type="caption"> <s>Figura oſtendens quietem ſalſam, & mo<lb></lb>tum inordinatum, & minimum cremen<lb></lb>ti, & decrementi aquæ matutini.</s></p><pb xlink:href="024/01/042.jpg"></pb><figure id="id.024.01.042.1.jpg" xlink:href="024/01/042/1.jpg"></figure><p type="caption"> <s>Figura oſtendens initium crementi circa matutini <lb></lb>ante, uel poſt: & initium decrementi poſt horam <lb></lb>tertiarum, & initium crementi poſt ueſperas, & <lb></lb>initium decrementi ante medium noctis. <pb xlink:href="024/01/043.jpg"></pb><figure id="id.024.01.043.1.jpg" xlink:href="024/01/043/1.jpg"></figure><pb xlink:href="024/01/044.jpg"></pb><figure id="id.024.01.044.1.jpg" xlink:href="024/01/044/1.jpg"></figure></s></p><pb xlink:href="024/01/045.jpg"></pb><figure id="id.024.01.045.1.jpg" xlink:href="024/01/045/1.jpg"></figure><p type="caption"> <s>Figura oſtendens initium <gap></gap><lb></lb>ortu <gap></gap>, <gap></gap> initium decrem<gap></gap><lb></lb>meridie, & initium crementi <gap></gap><lb></lb>caſu ſolis, & initium decrementi<gap></gap></s></p><pb xlink:href="024/01/046.jpg"></pb><figure id="id.024.01.046.1.jpg" xlink:href="024/01/046/1.jpg"></figure><p type="caption"> <s>Figura oſtendens initium crementi poſt ortum ſo<lb></lb>lis circa horam tertiarum, uel ante: & <expan abbr="initiũ">initium</expan> decre<lb></lb><expan abbr="mẽti">menti</expan> circa ueſperas, & <expan abbr="initiũ">initium</expan> crementi ante medi<lb></lb>um noctis, & initium <expan abbr="decremẽti">decrementi</expan> poſt <expan abbr="mediũ">medium</expan> nocti. </s></p><pb xlink:href="024/01/047.jpg"></pb><pb xlink:href="024/01/048.jpg"></pb><figure id="id.024.01.048.1.jpg" xlink:href="024/01/048/1.jpg"></figure><figure id="id.024.01.048.2.jpg" xlink:href="024/01/048/2.jpg"></figure><pb xlink:href="024/01/049.jpg"></pb><p type="caption"> <s>Figura oſtendens quietem ſalſam, & mo<lb></lb>tum<gap></gap> nord<gap></gap>natum, & minimum cr<gap></gap><lb></lb>ti, & d<gap></gap>crementi aquæ <gap></gap>.</s></p><pb xlink:href="024/01/050.jpg"></pb><figure id="id.024.01.050.1.jpg" xlink:href="024/01/050/1.jpg"></figure><p type="caption"> <s>Figura oſtendens initium crementi circa <lb></lb>matutinum ante ortum ſolis: & <expan abbr="initiũ">initium</expan> de<lb></lb>crementi poſt horam tertiarum, & ante <lb></lb>meridiem: & initium crementi ante occa<lb></lb>ſum ſolis poſt ueſperas: & initium decre<lb></lb>menti ante medium noctis.</s></p><pb xlink:href="024/01/051.jpg" pagenum="19"></pb><p type="main"> <s><emph type="center"></emph>FEDERICI DELPHINI <emph.end type="center"></emph.end><emph type="center"></emph>DE MOTV OCTAVAE<emph.end type="center"></emph.end><emph type="center"></emph> SPHAERAE<emph.end type="center"></emph.end><emph type="center"></emph> TRACTATVS.<emph.end type="center"></emph.end></s></p><p type="main"> <s>SCIENDVM eſt primo, quòd circa numerum ſphæra<lb></lb>rum cæleſtium tres ſunt opiniones diuerſæ: una eſt philoſo<lb></lb>phorum, & aſtrologorum Indorum, quæ eſt, quòd ſphæræ <lb></lb>cæleſtes ſint octo tantum, uidelicet ſeptem ſphæræ planeta<lb></lb>rum, & octaua ſphæra ſtellata, quæ eſt primum mobile ſecun<lb></lb>dum iſtam opinionem; quæ mouetur motu diurno, uidelicet <lb></lb>in una die naturale, quæ eſt tempus uiginti quatuor hora<lb></lb>rum, una reuolutione completa, ab oriente ſcilicet uerſus oc<lb></lb>cidentem, reuoluendo ſecum tali motu omnes alias ſphæras <lb></lb>inferiores. </s> <s>alia eſt Ptolomæi, Alfragræni Alchabitii, Ioannis <lb></lb>de Sacrobuſto, & Thebit; qui ſphæræ cæleſtes ſint nouem: <lb></lb>& hæc opinio eſt bipartita, quia Ptolemæus, Alfragrænus Al<lb></lb>chabitius, & Ioannes de Sacrobuſto dicunt, quòd nona ſphæ<lb></lb>ra eſt primum mobile, & quòd ipſa eſt illa, quæ mouetur mo<lb></lb>tu diurno, reuoluendo omnes alias ſphæras inferiores, uide<lb></lb>licet octauam, & ſeptimam ſphæram ſeptem planetarum ſe<lb></lb>cum: & quòd octaua ſphæra, & aliæ inferiores ei mouentur <lb></lb>duplici motu: uno uidelicet diurno, quo reuoluuntur à nona <lb></lb>omni die naturali, una reuolutione completa: & alio pro<lb></lb>prio octauæ tardo, ſcilicet ad contrarium nonæ ſphæræ ſuper <lb></lb>polis zodiaci ſui exiſtentibus in directo polorum zodiaci no<lb></lb>næ ſemper; adeo quòd ſemper zodiacus octauæ eſt ſub zodia<lb></lb>ci nonæ ſphæræ eclipticæ octauæ ſub ecliptica nonæ, & poli <lb></lb>zodiaci octauæ ſub polis zodiaci nonæ, in centum annis uno <lb></lb>gradu uerſus orientem contrariæ, & taliter, quòd ſemper e<lb></lb>clipticæ octauæ ſphæræ eſſent ſub ecliptica nonæ. </s> <s>aliæ autem <lb></lb>ſphæræ inferiores octauæ, ultra iſtos duos motus, habent <lb></lb>motus ſibi proprios ab occidente uerſus orientem, ut in <pb xlink:href="024/01/052.jpg"></pb>theoricis earum uidebitur. </s></p><p type="main"> <s>Thebit autem uolens ſaluare uariationem declinationis ſolis <lb></lb>ab æquinoctiali, qui ſemper, & continue mouetur motu pro<lb></lb>prio ab occidente uerſus orientem ſub ecliptica octauæ ſphæ<lb></lb>ræ; quam declinationem inuenit Ptolomæus tempore ſuo eſſe <lb></lb>XXIII graduum, LI minutorum, & XX ſecundorum, & Al<lb></lb>meon, & Albategni, qui fuerunt poſteriores Ptolomæo, inue<lb></lb>nerunt eam eſſe XXIII graduum, XXXIII minutorum, & <lb></lb>XXX ſecundorum dixit octauam ſphæram moueri, quòd à <lb></lb>motu titubationis, ſeu acceſſus, & receſſus in circumferentiis <lb></lb>duorum circulorum paruorum æqualium, quorum media, ſeu <lb></lb>poli, ſeu centra ſunt ipſa capita, ſeu principia arietis, & libræ <lb></lb>nonæ ſphæræ, ſeu primi mobilis; taliter ſcilicet, quòd duo pun<lb></lb>cta certa, & determinata octauæ ſphæræ, quæ capita arietis, & <lb></lb>& libræ, ſeu principia arietis, & libræ octauæ ſphæræ dicuntur <lb></lb>moueri in circumferentiis duorum circulorum paruorum di<lb></lb>ctorum, deſcribendo eas in concauitate nonæ ſphæræ, circa <lb></lb>principia arietis, & libræ eiuſdem nonæ ſphæræ, & arietis ecli<lb></lb>pticæ nonæ ſphæræ inter centra horum paruorum circulorum <lb></lb>dictorum, & circumferentias ſuas. eſt quatuor graduum, <lb></lb>XVIII minutorum, & XLIII ſecundorum, & tota diametra <lb></lb>eorum circulorum eſt VIII graduum, XXXVII <expan abbr="minutorũ">minutorum</expan>, <lb></lb>& XXVI ſecundorum. </s> <s>adeo quòd ſtellæ fixæ octaui cæli non <lb></lb>poſſunt perficere circulationem ſuam uerſus <expan abbr="oriẽtem">orientem</expan> ad con<lb></lb>trarium nonæ ſphæræ, ſeu primi mobilis, ſed poſſunt tranſmo <lb></lb>ueri uerſus orientem per VIII graduum, XXXVII minuto<lb></lb>rum, & XXVI ſecundorum, & redire uerſus occidentem tar<lb></lb>dum. </s> <s>alia eſt opinio illorum, qui tabulas Alphonſi compoſue<lb></lb>runt, & Petri de Apono, ſeu Conciliatoris, & domini Nico<lb></lb>lai Paduani comitis de Comitibus, & Georgii Parbachui, qui <lb></lb>uolunt quòd ſint in numero decem ſphæræ, uidelicet quòd ſu<lb></lb>pra ſeptem ſphæras ſeptem planetarum ſint tres ſphæræ, uideli<lb></lb>cet octaua, nona, & decima, quod ſic <expan abbr="oſtẽditur">oſtenditur</expan>. </s> <s>uidemus in ſtel<lb></lb>lis fixis, ſeu in octaua ſphæra triplicem motum: unum ſcilicet <lb></lb><expan abbr="diurnũ">diurnum</expan> <expan abbr="uelociſſimũ">uelociſſimum</expan>, quo octaua ſphæra <expan abbr="cũ">cum</expan> ſtellis fixis, quæ ſunt <lb></lb>in ea, reuoluitur omni die naturali una reuolutione completa <pb xlink:href="024/01/053.jpg" pagenum="20"></pb>ab oriente, ſcilicet uerſus occidentem: & alium tardum, de <lb></lb>quo octaua ſphæra mouetur cum ſtellis fixis, quæ ſunt in ea ab <lb></lb>occidente uerſus orientem: & tertium, quo mouetur octaua <lb></lb>ſphæra, taliter quòd declinatio ſolis; qui ſecundum omnes a<lb></lb>ſtrologos mouetur motu proprio ſui orbis differentis ipſum <lb></lb>uerſus orientem ſemper, & continue ſub ecliptica octauæ ſphæ<lb></lb>ræ, nuſquam ab ea recedendo; uariatur creſcendo, & decre<lb></lb>ſcendo: ideo dicimus ſupra octauam ſphæram eſſe duas alias <lb></lb>ſphæras nonam, & decimam, quæ una ſola ſphæra ſuperior ip<lb></lb>ſi octauæ non poteſt dare ſphæræ inferiori, ultra motum nonæ <lb></lb>proprium, duos motus: & quia omnes ſphæræ cæleſtes mouen<lb></lb>tur motu diurno, uidelicet in uiginti quatuor horis, una reuo<lb></lb>lutione completa ab oriente, ſcilicet uerſus occidentem, incon<lb></lb>ueniens eſt dicere, quòd ſphæra inferior moueatur motu diur<lb></lb>no ſibi proprio uelociſſimo ſcilicet & quòd ad <expan abbr="motũ">motum</expan> eius pro<lb></lb>prium moueat ſuperiorem ei, ſimiliter motu diurno uelociſſi<lb></lb>mo: ideo dicimus decimam ſphæram eſſe primum mobile: & <lb></lb>eam eſſe illam, quæ mouetur motu diurno uelociſſimo, ad cu<lb></lb>ius motum omnes aliæ ſphæræ inferiores mouentur ſimiliter <lb></lb>motu diurno, uidelicet omni die naturali, quæ eſt tempus xxiiii <lb></lb>horarum, una reuolutione completa. </s> <s>& quia uidimus ſtellas <lb></lb>fixas in octaua ſphæra moueri continue uerſus orientem ad <lb></lb>contrarium motum diurnum, motu quodam tardo ualde ſi <lb></lb>poneremus octauam ſphæram immediate ſub decima; & eam <lb></lb>habere talem motum tardum, continu<expan abbr="ũ">um</expan> uerſus <expan abbr="occidentẽ">occidentem</expan>, tan<lb></lb>quam <expan abbr="motũ">motum</expan> ſibi <expan abbr="propriũ">proprium</expan>, & IX <expan abbr="ſphærã">ſphæram</expan> eſſe ſub ea, & <expan abbr="eã">eam</expan> moueri <lb></lb>tali motu, quòd per eum declinatio ſolis ab æquatore, qui ſem<lb></lb>per, & continue mouetur ſub ecliptica octauæ ſphæræ, augeat, <lb></lb>minuatur, ſequeretur <expan abbr="ſphærã">ſphæram</expan> <expan abbr="inferiorẽ">inferiorem</expan> ad ſuum <expan abbr="motũ">motum</expan> <expan abbr="propriũ">proprium</expan> <lb></lb>mouere <expan abbr="octauã">octauam</expan> <expan abbr="ſuperiorẽ">ſuperiorem</expan>, ex quo per <expan abbr="ſuũ">ſuum</expan> <expan abbr="motũ">motum</expan> declinatio ſolis, <lb></lb>qui <expan abbr="cõtinue">continue</expan> mouetur, ſub ecliptica viii ſphæræ uariatur, quod <lb></lb>eſt <expan abbr="abſurdũ">abſurdum</expan>, ſi aut diceretur <expan abbr="octauã">octauam</expan> <expan abbr="ſphærã">ſphæram</expan> immediate collocari <lb></lb>ſub decima, & <expan abbr="eã">eam</expan> moueri tali motu, <expan abbr="tanquã">tanquam</expan> motu ſibi proprio, <lb></lb>ut per eum declinatio ſolis ſemper, & continue diſcurrentis ſub <lb></lb>ecliptica VIII ſphæræ ab æquatore augeatur, & minuatur: <expan abbr="tũc">tunc</expan> <pb xlink:href="024/01/054.jpg"></pb>oporteret dicere, quòd nona ſphæra, quæ eſt ſub ea, moue<lb></lb>tur motu illo tardo, continuo dicto uerſus orientem; ad cu<lb></lb>ius motum ſtellæ fixæ, quæ ſunt in octaua ſphæra, quæ eſt ſu<lb></lb>pra eam, moueantur uerſus orientem continue, & ſic ſphæra <lb></lb>inferior ad motum eius proprium moueret ſuperiorem. </s> <s>ne<lb></lb>ceſſarium eſt ergo dicere nonam ſphæram collocari immedia<lb></lb>te ſub decima: & ipſam eſſe illam, quæ mouetur continue ab <lb></lb>occidente uerſus orientem motu illo tardo ualde iam dicto, <lb></lb>defferendo ſecum octauam ſphæram cum ſtellis fixis, quæ ſunt <lb></lb>in ea, & alias ſphæras inferiores ei: & quòd octaua ſphæra ſit <lb></lb>ſub ea, & eam moueri tali motu, tanquam motu ſibi proprio, <lb></lb>ut per eum motum etiam aliæ ſphæræ inferiores octauæ mo<lb></lb>ueantur: & declinatio ſolis ſemper continue diſcurrentis ſub <lb></lb>ecliptica octauæ ſphæræ augeatur, & minuatur: & ſic ſituatas <lb></lb>tres ſphæras non ſequitur aliquod inconueniens. </s> <s>neceſſarium <lb></lb>eſt ergo propter reuolutiones dicere ſphæras cæleſtes eſſe de<lb></lb>cem in numero: & omnes eſſe ſic ordinatas, ut dictum eſt: <lb></lb>Thebit ergo, ut ſupra dictum eſt, duplicem octauæ ſphæræ <lb></lb>motum ineſſe dixit: unum ſcilicet à primo mobili, ſeu nona <lb></lb>ſphæra diurnum ſcilicet: alium uero ſibi proprium trepida<lb></lb>tionis, ſeu acceſſus, & receſſus, qui fit ſuper circumferentiis <lb></lb>duorum circulorum paruorum æqualium deſcriptorum in <lb></lb>concauitate nonæ ſphæræ circa principium arietis, & libræ e<lb></lb>iuſdem nonæ ſphæræ: duplicem etiam eclipticam aſſeruit fi<lb></lb>xam quidem in nona ſphæra, ſeu primo mobili: mobile au<lb></lb>tem in octaua ita, ut capita arietis, & libræ eclipticæ mobilis, <lb></lb>ſeu octauæ ſphæræ circumferantur in circumferentiis duorum <lb></lb>circulorum paruorum æqualium, quorum media, ſeu poli, <lb></lb>ſeu centra ſunt ipſa capita, ſeu principia arietis, & libræ ecli<lb></lb>pticæ fixæ, ſcilicet nonæ ſphæræ, ſeu primi mobilis: & arcus <lb></lb>eclipticæ fixæ, ſeu nonæ ſphæræ inter polos, ſeu centra ho<lb></lb>rum circulorum paruorum, & circumferentias ſuas eſt qua<lb></lb>tuor graduum, 18 minutorum, & 43. ſecundorum. </s> <s>dixit autem <lb></lb>Thebit capita, ſeu principia arietis, & libræ mobilia, ſeu o<lb></lb>ctauæ ſphæræ taliter circumferri in circumferentiis ſuorum <pb xlink:href="024/01/055.jpg" pagenum="21"></pb>circulorum paruorum, ut, cum caput arietis mobilis, ſcilicet <lb></lb>octauæ ſphæræ fuerit in ſectione circumferentiæ ſui parui cir<lb></lb>culi cum æquatore occidentali, ipſum mouebitur per medie<lb></lb>tatem circumferentia ſui parui circuli ſeptentrionalem ab æ<lb></lb>quatore. </s> <s>caput autem libræ mobilis mouebitur tunc per me<lb></lb>dietatem circumferentiæ ſui parui circuli meridionalem ab <lb></lb>æquatore: & cum caput arietis mobilis fuerit in ſectione cir<lb></lb>cumferentiæ ſui parui circuli cum æquatore orientali, ipſum <lb></lb>mouebitur per medietatem circumferentiæ ſui parui circuli <lb></lb>meridionalem ab æquatore. </s> <s>caput autem libræ mobilis mo<lb></lb>uebitur tunc per medietatem circumferentiæ ſui parui circu<lb></lb>li ſeptentrionalem ab æquatore: & cum caput arietis mobilis <lb></lb>fuerit in alterutro duorum punctorum ſectionis circumferen<lb></lb>tiæ ſui parui circuli cum ecliptica fixa, ſcilicet nonæ ſphæræ, <lb></lb>ſeu primi mobilis; caput libræ mobilis erit ſimiliter ſe habens <lb></lb>in circumferentia ſui parui circuli: & tunc ecliptica mobilis, <lb></lb>ſcilicet octauæ collocabitur in ſuperficie eclipticæ fixæ dire<lb></lb>ctæ ſub ecliptica fixa, ſcilicet nonæ ſphæræ, ſeu primi mobi<lb></lb>lis. </s> <s>& ſuperficies eclipticæ mobilis, ſcilicet octauæ eritin ſu<lb></lb>perficiæ eclipticæ fixæ, ſcilicet nonæ, tanquam pars in toto, <lb></lb>quod in una reuolutione capitis arietis mobilis, ſcilicet octa<lb></lb>uæ ſphæræ in circumferentia ſui parui circuli bis accedet. </s> <s>in <lb></lb>omnibus autem aliis locis, ſeu punctis exceptis, capite arietis <lb></lb>mobilis in circumferentia ſui parui circuli locato, ecliptica mo <lb></lb>bilis, ſcilicet octauæ ſecabit eclipticam fixam, ſcilicet nonæ <lb></lb>ſemper in punctis, ſeu principiis cancri, & capricorni mobi<lb></lb>libus. </s> <s>nam hæc duo puncta, uidelicet capita, ſeu principia <lb></lb>cancri, & capricorni eclipticæ mobilis, ſcilicet octauæ ſphæ<lb></lb>ræ ſemper circumferentiæ eclipticæ fixæ, ſcilicet nonæ ſphæ<lb></lb>ræ in hoc motu cohærent, ut nuſquam ab ea recedant: à capi<lb></lb>tibus tam cancri, & capricorni ſixorum, ſcilicet. </s> <s>nonæ ſphæ<lb></lb>ræ per quantitatem quatuor graduum, 18 minutorum, & 43 <lb></lb>ſecundorum ea elongari uerſus orientem, & uerſus occiden<lb></lb>tem contingit; & ubicunque fiat. </s> <s>ſectio eclipticæ octauæ cum <lb></lb>ecliptica nonæ, ipſam, neceſſe eſt, à principiis arietis, & libræ <pb xlink:href="024/01/056.jpg"></pb>mobilibus octauæ per quartam circuli magni diſtare: & licet <lb></lb>in una reuolutione capitis arietis mobilis, ſcilicet octauæ in <lb></lb>circumferentia ſui parui circuli capita, ſeu principia cancri, <lb></lb>& capricorni mobilia octauæ ſphæræ collocentur directa ſub <lb></lb>capitibus cancri, & capricorni fixorum, ſeu nonæ ſphæræ. <lb></lb></s> <s>nunquam tam capita, ſeu principia arietis, & libræ fixorum <lb></lb>peruenient. </s> <s>dum enim ecliptica mobilis, ſcilicet octauæ, con<lb></lb>trahet circumferentiam circuli parui paruæ ſectionis in pun<lb></lb>cto arietis mobilis; capita cancri, & capricorni mobilia ſunt <lb></lb>coniuncta cum capitibus cancri, & capricorni fixorum. </s> <s>& ſi<lb></lb>militer accidit in contactu meridiano: capita uero arietis, & <lb></lb>libræ mobilia nunquam uenient ſub capite arietis, & libræ fi<lb></lb>xorum: ſed ſemper à capitibus arietis, & libræ fixorum diſta<lb></lb>bunt per quantitatem quatuor graduum, XVIII minutorum, <lb></lb>XLIII ſecundorum, quia ſemper errant in circumferentiis <lb></lb>ſuorum circulorum paruorum, quæ diſtant à centris eorum <lb></lb>per quantitatem dictam. </s> <s>ecliptica autem fixa ſemper ſecat æ<lb></lb>quatorem in capitibus arietis, & libræ fixorum ad angulum <lb></lb>ſemper eundem, cuius anguli arcus coluri ei correſpondens <lb></lb>ſemper eſt XXIII graduum, XXXIII <expan abbr="minutorũ">minutorum</expan>, & ſecundo<lb></lb>rum, qui eſt arcus maximæ declinationis eclipticæ fixæ, ſed e<lb></lb>clipticæ mobilis, ſcilicet octauæ æquatorem ſucceſſiue ſecat in <lb></lb>ſingulis punctis æquatoris: et ipſe ſecatur ab æquatore in ſin<lb></lb>gulis punctis eius compræhenſis in duobus arcubus ei eclipti<lb></lb>cæ mobilis, quos arcus ecliptica mobilis excitentibus capiti<lb></lb>bus arietis, & libræ mobilibus in duobus punctis diſtinguen<lb></lb>tibus quartas ſuorum circulorum paruorum ab interſectioni<lb></lb>bus eorum cum æquatore ſeparat à toto reſiduo eclipticæ mo<lb></lb>bilis, & quantitas unius cuiuſque horum arcuum eſt circa <lb></lb>XXI graduum, & XXX minutorum. </s> <s>eſt maxima diſtantia ca<lb></lb>pitis arietis mobilis, quando eſt in puncto diſtinguenti quartas <lb></lb>ſui parui circuli ab interſectionibus eius cum æquatore ſepten<lb></lb>trionali à ſectione eclipticæ mobilis cum æquatore per gradu<lb></lb>um X, & 45 minutorum ecliptica mobilis, ſcilicet in piſcibus, <lb></lb>ſcilicet ecliptica mobilis: & quando eſt in puncto diſtinguente <pb xlink:href="024/01/057.jpg" pagenum="22"></pb>quartas ſui parui circuli ab interſectionibus eius cum æquato<lb></lb>re meridiano, eſt per gradus X, & XLV minutorum in arie<lb></lb>te ecliptica mobilis. </s> <s>ſimiliter dicendum eſt de capite libræ mo <lb></lb>bilis. </s> <s>quando enim caput arietis mobilis eſt in puncto ſui par<lb></lb>ui circuli diſtinguente quartas parui circuli ab interſectioni<lb></lb>bus eius cum æquatore ſeptentrionale: caput libræ mobilis <lb></lb>tunc eſt in puncto ſui parui circuli diſtinguente quartas parui <lb></lb>circuli ab interſectionibus eius cum æquatore ſeptentrionali. <lb></lb></s> <s>& tunc ſicut maxima diſtantia capitis arietis mobilis ab inter<lb></lb>ſectione ecliptica mobilis cum æquatore eſt per gradus de<lb></lb>cem, & XLV minutos in piſcibus eclipticæ mobilis; ita ma<lb></lb>xima diſtantia capitis libræ mobilis ab interſectione eclipticæ <lb></lb>mobili æquatore eſt per gradus X, & XLV minutos ecli<lb></lb>pticæ mobilis in uirgine eclipticæ mobilis. </s> <s>& quando caput <lb></lb>arietis mobilis eſt in puncto ſui parui circuli diſtinguente <lb></lb>quartas parui circuli ab interſectionibus eius cum æquatore <lb></lb>meridionali, tunc caput libræ mobilis eſt in puncto ſui parui <lb></lb>circuli diſtinguente quartas parui circuli ab interſectionibus <lb></lb>eius cum æquatore ſeptentrionali: & tunc ſicut maxima di<lb></lb>ſtantia capitis arietis mobilis à ſeptione ecliptica mobili cum <lb></lb>æquatore eſt per gradus X, & XLV minutos eclipticæ <lb></lb>mobilis in ariete eclipticæ mobilis; ita maxima diſtantia capi<lb></lb>tis libræ mobilis ab interſectione eclipticæ mobilis cum æqua<lb></lb>tore eſt per gradus X, & XLV minutos eclipticæ mobi<lb></lb>lis in libra ecliptica mobilis; & ſic ecliptica mobilis ſecatur ab <lb></lb>æquinoctiali in ſingulis punctis duorum arcuum eius: quos ar<lb></lb>cus exiſtentibus capitibus arietis, & libræ mobilibus in duo<lb></lb>bus punctis duorum circulorum paruorum diſtinguentibus <lb></lb>quartas eorum ab interſectionibus eorum cum æquinoctiali; <lb></lb>quorum unus eſt ab ſeptentrionale æquinoctionali, et alter <lb></lb>meridionalis ſeparat à toto reſiduo eclipticæ mobilis: quorum <lb></lb>arcuum unus eſt ex parte arietis mobilis à XIX gradus XV <lb></lb>minutos piſcium ecliptica mobilis, uſque ad X gradus, <lb></lb>et XLV minutos arietis eiuſdem eclipticæ mobilis, et ali<lb></lb>ter eſt XIX gradus, et XV minutos uirginis eclipticæ <pb xlink:href="024/01/058.jpg"></pb>mobilis, uſque ad X gradus, & XLV minutos in arietis e<lb></lb>iuſdem eclipticæ mobilis: & quantitas uniuſcuiuſque horum <lb></lb>graduum eſt XXI gradus, XXX minutos. </s> <s>maxima enim di<lb></lb>ſtantia capitis arietis, & libræ mobilium à ſeptione eclipticæ <lb></lb>mobilis cum æquinoctiali eſt per gradus X, & XLV minu<lb></lb>tos eclipticæ mobilis in piſcibus, & per X gradus, & XLV <lb></lb>minutos eclipticæ mobilis in ariete; qui aggregati faciunt <lb></lb>arcum XXI gradus, et XXX minutos eclipticæ mobi<lb></lb>lis: et idem eſt ex parte libræ mobilis: unde accidit, quòd <lb></lb>maxima declinatio eclipticæ mobilis, ideſt octauæ ſphæræ ua<lb></lb>riabilis eſt, maior quandoque declinatione eclipticæ fixæ, ideſt <lb></lb>quandoque minor eadem, quandoque ſibi æqualis. </s> <s>tunc enim <lb></lb>maxima declinatio eclipticæ octaua mobilis eſt æqualis maxi<lb></lb>mæ declinationi eclipticæ nonæ fixæ; quando ecliptica mobi<lb></lb>lis eſt collocata in ſuperficie eclipticæ fixæ; quod accidit capi<lb></lb>tibus arietis, et libræ mobilibus exiſtentibus in ſectionibus <lb></lb>ſuorum circulorum paruorum cum ecliptica fixa. </s> <s>maior uero <lb></lb>capitibus arietis, et libræ mobilibus exiſtentibus in ſectioni<lb></lb>bus contactuum. </s> <s>in punctis ſuorum circulorum paruorum <lb></lb>diſtinguentibus quartas eorum circulorum à ſectionibus eo<lb></lb>rum cum ecliptica fixa: unde eam Ptolomæus inuenit XXIII <lb></lb>gradus, LI minut. </s> <s>et XX ſecund. </s> <s>minor autem in ca<lb></lb>pite arietis, et libræ mobilia fuerint in punctis interſectionis <lb></lb>ſuorum circulorum paruorum cum æquinoctiali. </s> <s>tunc enim <lb></lb>interſectio eclipticarum erit in puncto eclipticæ mobilis, ideſt <lb></lb>octauæ: maxima declinatio ab æquinoctiali, qui minus decli<lb></lb>nabit, quàm caput cancri, et capricorni ecliptica fixa, ſeu no <lb></lb>næ. </s> <s>æquatio autem octauæ ſphæræ eſt arcus eclipticæ octauæ <lb></lb>ſphæræ, uſque ad interſectionem eclipticæ octauæ ſphæræ cum <lb></lb>æquinoctiali; ſed motus acceſſus, et receſſus eſt arcus circuli <lb></lb>parui ab interſectione circuli parui cum æquinoctiali occiden <lb></lb>tali per medietatem circuli parui ſeptentrionalem, progre<lb></lb>diendo, uſque ad caput arietis octauæ ſphæræ in ſuo circulo <lb></lb>paruo. </s> <s>hoc motu octauæ ſphæræ dicto contingit, ut ſtellæ fi<lb></lb>xæ in octauo cælo uideantur nunc moueri uerſus occidentem, <pb xlink:href="024/01/059.jpg" pagenum="23"></pb>nunc uerſus orientem, nunc motu ueloci, nunc motu tar<lb></lb>do propter diuerſum ſitum capitis arietis octauæ ſphæræ in <lb></lb>ſuo circulo paruo, & propter diuerſum motum ſectionis <lb></lb>æquinoctialis per eclipticam octauæ ſphæræ. </s> <s>nam in toto <lb></lb>tempore, in quo caput arietis octauæ ſphæræ recedit à <lb></lb>puncto ſui parui circuli diſtinguente quartas ab interſe<lb></lb>ctionibus eius cum æquatore meridionali, donec ueniat <lb></lb>ad punctum ſui parui circuli diſtinguentem quartas ab in<lb></lb>terſectionibus eius cum æquatore ſeptentrionale ſectio e<lb></lb>clipticæ octauæ ſphæræ cum æquinoctiali primi mobilis, <lb></lb>ſcilicet quæ mouetur continue per eclipticam octauæ ſphæ<lb></lb>ræ contra ſucceſſionem ſignorum à X grad. arietis eclipti<lb></lb>cæ octauæ ſphæræ, & XLV min. uſque ad XIX grad. pi<lb></lb>ſcium, & XV min. eclipticæ octauæ ſphæræ cum æquino<lb></lb>ctionali: recedit à ſtellis fixis octauæ ſphæræ, quæ eſt uer<lb></lb>ſus orientem ab ea eundo uerſus ſtellas fixas, quæ eſt uer<lb></lb>ſus occidentem ab ea appropinquando eis: & propter hoc <lb></lb>ſtellæ, quæ ſunt uerſus orientem, ab ea uidentur moue<lb></lb>ri ſupra ſucceſſionem ſignorum, ſcilicet uerſus orientem: <lb></lb>& ſtellæ, quæ ſunt uerſus occidentem, ab ea uidentur ſe<lb></lb>qui eas ſupra ſucceſſionem ſignorum: cum tamen in ue<lb></lb>ritate moueantur contra ſucceſſionem ſignorum, ſcilicet <lb></lb>uerſus occidentem: & tunc caput libræ octauæ ſphæræ re<lb></lb>cedit à puncto ſui parui circuli diſtinguente quartas eius <lb></lb>ab interſectionibus eius cum æquatore ſeptentrionali, & <lb></lb>uenit ad punctum ſui parui circuli diſtinguentem quartas <lb></lb>ſui parui circuli ab interſectionibus eius cum æquatore <lb></lb>meridionali, & ſectio eclipticæ octauæ ſphæræ cum æqui<lb></lb>noctionali primi mobilis mouetur ſimiliter continue per <lb></lb>eclipticam octauæ ſphæræ contra ſucceſſionem ſignorum <lb></lb>à X grad. libræ eclipticæ octauæ ſphæræ, & XLV mi<lb></lb>nut. </s> <s>uſque ad XIX grad. & XV minut. </s> <s>uirginis eiuſdem <lb></lb>eclipticæ octauæ ſphæræ: & tunc ſectio ecliptica octauæ <pb xlink:href="024/01/060.jpg"></pb>ſphæræ cum æquinoctionali ſimiliter recedit à ſtellis fixis, <lb></lb>quæ ſunt uerſus orientem ab ea eundo uerſus ſtellas fixas, <lb></lb>quæ ſunt uerſus occidentem, ab ea eis appropinquando, & <lb></lb>propter hoc ſimiliter ſtellæ fixæ, quæ ſunt uerſus orien<lb></lb>tem ab ea uidentur moueri ſecundum ſucceſſionem ſigno<lb></lb>rum ſcilicet uerſus orientem, & ſtellæ fixæ, quæ ſunt uer<lb></lb>ſus occidentem ab ea uidentur ſequi eas ſecundum ſucceſ<lb></lb>ſionem ſignorum, cum tamen in ueritate moueantur con<lb></lb>tra ſucceſſionem ſignorum, ſcilicet uerſus occidentem. </s></p><p type="main"> <s>Cum autem caput arietis octauæ ſphæræ recedit à puncto <lb></lb>ſui parui circuli diſtinguenti quartas eius ab interſectionibus <lb></lb>eius cum æquinoctionali ſeptentrionali, donec ueniat ad <lb></lb>punctum ſui parui circuli diſtinguentem quartas eius ab in<lb></lb>terſectionibus eius cum æquinoctionali meridionali: ſectio <lb></lb>ecliptica octauæ ſphæræ cum æquinoctionali mouetur con<lb></lb>tinue per eclipticam octauæ ſphæræ, ſecundum ſignorum <lb></lb>ſucceſſionem ad XIX grad. & XV min. piſcium ecliptica <lb></lb>octauæ ſphæræ, uſque ad X grad. & XLV min. arietis ecli<lb></lb>pticæ octauæ ſphæræ: & tunc ſectio ecliptica octauæ ſphæ<lb></lb>ræ cum æquinoctionali recedit à ſtellis fixis, quæ ſunt uer<lb></lb>ſus occidentem, ab ea eundo uerſus ſtellas fixas, quæ ſunt <lb></lb>uerſus orientem, ab ea appropinquando eis: & propter <lb></lb>hoc ſtellæ fixæ, quæ ſunt uerſus occidentem, ab ea uiden<lb></lb>tur moueri contra ſucceſſionem ſignorum, ſcilicet uerſus <lb></lb>occidentem: & ſtellæ, quæ ſunt uerſus orientem, ab ea ui<lb></lb>dentur ſequi eas, cum tamen in ueritate moueantur ſe<lb></lb>cundum ſucceſſionem ſignorum, ſcilicet uerſus orientem: <lb></lb>& tunc caput libræ octauæ ſphæræ recedit à puncto ſui par<lb></lb>ui circuli diſtinguente quartas eius ab interſectionibus e<lb></lb>ius, cum æquinoctiali, meridionali, & uenit ad pun<lb></lb>ctum ſui parui circuli diſtinguentem quartas eius ab inter<lb></lb>ſectionibus eius, cum æquinoctionali, meridionali: & ue<lb></lb>nit ad punctum ſui parui circuli diſtinguentem quar<lb></lb>tas eius ab interſectionibus eius, cum æquinoctionali, <pb xlink:href="024/01/061.jpg" pagenum="24"></pb>ſeptentrionali: & ſectio ecliptica octauæ ſphæræ cum æ<lb></lb>quinoctiali mouetur continue per eclipticam octauæ ſphæ<lb></lb>ræ à XIX grad. XV min. uirginis ecliptica octauæ ſphæ<lb></lb>ræ, uſque ad X grad. & XLV min. libræ eclipticæ octauæ <lb></lb>ſphæræ cum æquinoctionali recedit à ſtellis fixis, quæ ſunt <lb></lb>uerſus occidentem, ab ea eundo uerſus ſtellas fixas, quæ <lb></lb>ſunt uerſus orientem, ab ea appropinquando eis: & pro<lb></lb>pter hoc ſtellæ, quæ ſunt uerſus occidentem, ab ea uiden<lb></lb>tur moueri contra ſucceſſionem ſignorum, ſcilicet uerſus <lb></lb>occidentem: & quæ ſunt uerſus orientem ab ea uidentur <lb></lb>ſequi eas, cum iam in ueritate moueantur ſupra ſucceſſio<lb></lb>nem ſignorum, ſcilicet uerſus orientem. </s> <s>cum autem caput <lb></lb>arietis octauæ ſphæræ recedit à puncto ſui parui circuli di<lb></lb>ſtinguente quartas eius ab interſectionibus eius cum æqui<lb></lb>noctiali, meridionali uerſus orientem accedens: tunc ſectio <lb></lb>ecliptica octauæ ſphæræ mouetur per eclipticam octauæ ſphæ<lb></lb>ræ tarde uerſus orientem; quia æquatio octauæ ſphæræ, quam <lb></lb>ponit Thebit eſſe arcum. </s> <s>ecliptica octauæ ſphæræ à capite <lb></lb>arietis octauæ ſphæræ, uſque ad interſectionem eclipticæ o<lb></lb>ctauæ ſphæræ cum æquinoctionali parum decreſcit: & tunc <lb></lb>ſtellæ fixæ uidentur moueri uerſus occidentem tarde. </s> <s>cum <lb></lb>autem caput arietis octauæ ſphæræ eſt prope ſectione ſui par<lb></lb>ui circuli cum æquinoctionali orientali, ex utroque latere <lb></lb>eius ſectio ecliptica octauæ ſphæræ ibi, uel multum decre<lb></lb>ſcit, uel multum creſcit; & tunc ſtellæ fixæ uidentur mo<lb></lb>ueri uerſus occidentem uelociter. </s> <s>cum autem caput arie<lb></lb>tis octauæ ſphæræ appropinquat puncto ſui parui circuli di<lb></lb>ſtinguenti quartas eius ab interſectionibus eius cum æqui<lb></lb>noctionali, meridionali, donec ueniat ad ipſum, tunc ſectio <lb></lb>ecliptica octauæ ſphæræ mouetur per eclipticam octauæ <lb></lb>ſphæræ uerſus orientem tarde; quia æquatio octauæ ſphæræ <lb></lb>parum creſcit, & tunc ſtellæ uidentur moueri tarde uerſus <lb></lb>occidentem. </s></p><p type="main"> <s>Cum <expan abbr="autẽ">autem</expan> caput arietis octauæ ſphæræ recedit à <expan abbr="pũcto">puncto</expan> ſui par<lb></lb>ui circuli diſtinguenti quartas eius ab interſectionibus eius <expan abbr="cũ">cum</expan> <pb xlink:href="024/01/062.jpg"></pb>æquinoctiali, meridionali uerſus occidentem accedens, ſe<lb></lb>ctio eclipticæ octauæ ſphæræ mouetur per eclipticam octauæ <lb></lb>ſphæræ tarde uerſus occidentem, quia æquatio octauæ ſphæ<lb></lb>ræ ibi parum decreſcit, & ſtellæ fixæ uidentur moueri uerſus <lb></lb>orientem tarde. </s></p><p type="main"> <s>Cum autem caput arietis octauæ ſphæræ eſt prope ſectione ſui <lb></lb>parui circuli cum æquinoctiali, occidentali ex utroque latere <lb></lb>eius, ſectio ecliptica octauæ ſphæræ mouetur per eclipticam <lb></lb>octauæ ſphæræ uelociter uerſus occidentem. </s> <s>æquatio octa<lb></lb>uæ ſphæræ ibi multum creſcit, uel multum decreſcit: & tunc <lb></lb>ſtellæ fixæ uidentur moueri uerſus orientem uelociter. </s> <s>cum au<lb></lb>tem caput arietis octauæ ſphæræ appropinquat puncto ſui par<lb></lb>ui circuli diſtinguentem quartas ab interſectionibus eius cum <lb></lb>æquatore circuli, donec ueniat ad ipſum ſectio eclipticæ octa<lb></lb>uæ ſphæræ, mouetur per eclipticam octauæ ſphæræ uerſus oc<lb></lb>cidentem tarde, quia æquatio octauæ ſphæræ ibi parum cre<lb></lb>ſcit, & tunc ſtellæ fixæ uidentur moueri tarde uerſus orien<lb></lb>tem. </s> <s>idem fit per modum capitis libræ octauæ ſphæræ in cir<lb></lb>cumferentia ſui parui circuli: quod fit per motum capitis a<lb></lb>rietis libræ octauæ ſphæræ in circumferentia ſui parui circuli: <lb></lb>quod fit per motum capitis arietis in circumferentia ſui, niſi, <lb></lb>quòd motus eorum ſit in partibus ſuorum circulorum par<lb></lb>uorum contrariis. </s> <s>hinc inuenta eſt diuerſitas manifeſta in mo<lb></lb>tu ipſarum ſtellarum fixarum. </s> <s>Ptolomæus enim loca ſtella<lb></lb>rum fixarum inuenta ab ipſo tempore ſuo comparauit ad lo<lb></lb>ca earum inuenta ab Hipparcho, & aliis, & reperit ſtellas fi<lb></lb>xas non motas motu tardo, uidelicet in centum annis u<lb></lb>no gradu, & hoc ideo fiat, quia tunc caput arietis octauæ <lb></lb>ſphæræ erat ſeparatum à puncto ſui parui circuli diſtin<lb></lb>guente quartas eius ab interſectionibus eius cum æquatore <lb></lb>meridiano uerſus æquatorem accedens. </s> <s>poſteriores uero, <lb></lb>dum magis accederat uerſus æquatorem, inuenerunt eas <lb></lb>moueri in LXVI annis uno gradu: in anno autem domini <lb></lb>MCDLX factum eſt caput arietis octauæ ſphæræ ſeptentriona<lb></lb>lis ab æquatore, & diſtans à ſectione ſui parui circuli cum <pb xlink:href="024/01/063.jpg" pagenum="25"></pb>æquatore occidentali fere LXVI gradibus, & à ſectione ecli<lb></lb>ptica octauæ cum æquinoctionali IX gradibus, & XLV min. <lb></lb>fere eclipticæ octauæ diſtans: ſectio ergo eclipticæ octauæ <lb></lb>cum æquinoctionali fiebat ſuper XX grad. & XII min. in ſi<lb></lb>gno piſcium eclipticæ octauæ ſphæræ. </s> <s>maxima autem æquatio <lb></lb>octauæ ſphæræ motus ſecundum Thebit contingit, quando ca<lb></lb>put arietis octauæ ſphæræ fuerit in punctis diſtinguentibus <lb></lb>quartas ſui parui circuli ab interſectionibus eius cum æqua<lb></lb>tore, & eſt X grad. & XLV min. unde ſequitur quòd quodli<lb></lb>bet punctum eclipticæ octauæ ſphæræ à XIX grad. & XV min. <lb></lb>piſcium, uſque ad X grad. & XLV min. arietis eclipticæ o<lb></lb>ctauæ ſphæræ cum æquinoctionali, & ex conſequenti in eo fie<lb></lb>ri æquinoctium uernale. </s> <s>idem intelligendum eſt de puncto <lb></lb>æquinoctii, autumnali in arcu eclipticæ octauæ ſphæræ oppo<lb></lb>ſito, uidelicet à XIX gradu uirginis, & XV min. uſque ad X <lb></lb>grad. & XLV min. libræ. </s> <s>conſtat etiam per prædicta puncta <lb></lb>tropica, ſeu maximarum declinationum ſolis, ſeu eclipticæ o<lb></lb>ctauæ ſphæræ, ſub qua ſemper, & continue diſcurrit centrum <lb></lb>corporis ſolis ab æquinoctionali continue reſpectu æquino<lb></lb>ctionali uariari, nunc ei appropinquando, nunc ab eo elon<lb></lb>gando: ſimiliter conſtat ea ſemper numero eſſe in capite can<lb></lb>cri, & capricorni octauæ ſphæræ: ſed ſemper eſſe in punctis <lb></lb>eclipticæ octauæ ſphæræ diſtantibus à ſectionibus eclipticæ o<lb></lb>ctauæ ſphæræ cum æquinoctionali per quartam. </s> <s>Ptolomæus <lb></lb>itaque iudicans ſtellas fixas octaui cæli tempore ſuo moueri ab <lb></lb>occidente uerſus orientem, uidelicet ſecundum ſucceſſionem <lb></lb>ſignorum, credidit unum tantum eſſe zodiacum, ſcilicet no<lb></lb>næ ſphæræ, ſeu primi mobilis fixum, ſcilicet qui ſemper ha<lb></lb>beret eandem declinationem ab æquinoctionali ſub ecliptica, <lb></lb>cum ſemper, & continue moueretur ſol: ad quam credulita<lb></lb>tem ſequitur illud, quod ipſe dixit: nam ex quo ſtellæ fixæ <lb></lb>mobiles inuentæ ſunt tempore ſuo, receſſiſſe à tropico hiema<lb></lb>li, & acceſſiſſe uerſus æquinoctionalem: & quæ erant inter æ<lb></lb>quinoctionalem, et tropicum æſtiuum inuentæ ſunt: receſſiſſe <lb></lb>ab æquinoctionali in parte ſeptentrionis uerſus tropicum <pb xlink:href="024/01/064.jpg"></pb>æſtiuum iudicauit Ptolomæus; & propter hoc eas moueri <lb></lb>uerſus orientem, uidelicet ſecundum ſucceſſionem ſignorum <lb></lb>eclipticæ fixæ ſcilicet nonæ. </s> <s>uerum eſt tam quod propter æ<lb></lb>quationem octauæ ſphæræ tunc decreſcente, quia ſectio ecli<lb></lb>ptica octauæ ſphæræ cum æquinoctionali mouebantur tem<lb></lb>pore ſuo per eclipticam octauæ ſphæræ uerſus occidentem <lb></lb>appropinquando ſtellis fixis, quæ erant uerſus occidentem <lb></lb>ab ea, & elongando ſe à ſtellis fixis, quæ erant uerſus orien<lb></lb>tem ab ea, uiſæ ſunt Ptolomæo ſtellæ ipſæ moueri uerſus o<lb></lb>rientem ſecundum ſcilicet ſucceſſionem ſignorum: eo quia <lb></lb>Ptolomæus putabat interſectionem eclipticæ octauæ ſphæræ <lb></lb>cum æquinoctionali eſſe interſectionem eclipticæ fixæ nonæ <lb></lb>ſcilicet ſphæræ: quia ſolam eclipticam nonæ ſphæræ imagina<lb></lb>batur, quam interſectionem ſemper fixam exiſtimabat, & pu<lb></lb>tabat eam eſſe caput arietis zodiaci nonæ ſphæræ, ſeu primi <lb></lb>mobilis. </s> <s>Purbachius autem triplicem motum octauæ ſphæræ <lb></lb>ineſſe dixit: unum quidem à primo mobili, ſeu decima ſphæ<lb></lb>ra diurnum, ſcilicet quòd in una die naturali octauæ ſphæræ <lb></lb>cum aliis ſphæris inferioribus ei ſemel ſuper polis totius ma<lb></lb>chinæ mundi reuoluitur: alium à nona ſphæra, quæ ſecundum <lb></lb>mobile uocauit; quo motu nonæ ſphæræ, octaua ſphæra cum <lb></lb>aliis ſphæris inferioribus mouetur omnibus 69200 annis per <lb></lb>unum gradum, et XXVIII min. uerſus orientem regulari<lb></lb>ter contra motum decimi orbis, ſeu primi mobilis ſuper po<lb></lb>lis zodiaci nonæ ſphæræ exiſtentibus ſemper directo ſub polis <lb></lb>zodiaci decimæ, ſeu primi mobilis, adeo quòd zodiacus no<lb></lb>næ ſphæræ ſemper eſt directus ſub zodiaco decimæ, ſeu primi <lb></lb>mobilis, & ecliptica nonæ ſphæræ ſemper ſub ecliptica deci<lb></lb>mæ, taliter quòd ſuperficies eclipticæ decimæ, ſeu primi mo<lb></lb>bilis, tanquam pars in toto, nuſquam ab ea declinans, & iſte <lb></lb>motus nonæ ſphæræ datus octauæ, & aliis ſphæris inferiori<lb></lb>bus, octauæ appellatur motus augium, & ſtellarum fixarum <lb></lb>in tabulis: quia ad iſtum motum nonæ ſphæræ dictum octa<lb></lb>uæ, & aliis ſphæris inferioribus octauæ, mouetur octauæ ſphæ<lb></lb>ra cum ſtellis fixis, quæ ſunt in ea, & <expan abbr="mouẽtur">mouentur</expan> auges <expan abbr="planetarũ">planetarum</expan>, <pb xlink:href="024/01/065.jpg" pagenum="26"></pb>quæ ſunt in ſphæris inferioribus octauæ, de quibus augibus <lb></lb>dicam in theoricis planetarum ſequentibus hunc tractatum, <lb></lb>quem motum nonæ ſphæræ reuoluentis ſecum octauam ſphæ<lb></lb>ram cum aliis ſphæris inferioribus ei ab occidente uerſus o<lb></lb>rientem ad contrarium diurnæ, ſeu primi mobilis. </s> <s>Purbacus <lb></lb>dicit eſſe arcum zodiaci decimæ ſphæræ, ſeu primi mobilis <lb></lb>à capite arietis decimæ ſphæræ, ſeu primi mobilis, uſque ad <lb></lb>caput arietis nonæ ſphæræ; hoc autem uidetur mihi eſſe fal<lb></lb>ſum propter rationes, quas nunc dicam. </s> <s>ſi enim uerum eſſet, <lb></lb>quòd motus nonæ ſphæræ, qui à tabolariis appellatur mo<lb></lb>tus augium, & ſtellarum fixarum, eſſet arcus zodiaci mobi<lb></lb>lis, ſcilicet decimæ ſphæræ, inter caput arietis primi mobilis, <lb></lb>& caput arietis nonæ ſphæræ, oporteret, ut in principio, u<lb></lb>niuſcuiuſque ære ex æris poſitis in tabulis fuiſſet caput arietis <lb></lb>nonæ ſphæræ directæ ſub capite arietis decimæ præciſæ; & ſic <lb></lb>ſequeretur, quòd à principio uniuſcuiuſque ære ex æris poſi<lb></lb>tis in tabulis uſque ad principium huius uniuſcuiuſque alte<lb></lb>rius caput arietis nonæ ſphæræ feciſſet unam reuolutionem <lb></lb>præcedentem, & ſic, cum differentia unius ære ab alia ſit di<lb></lb>uerſa in tempore, ſequeretur nonam ſphæram irregulariter <lb></lb>facere ſ<gap></gap> reuolutionem, uidelicet quandoque in breuiori <lb></lb>tempore, quandoque in longiori, cuius contrarium ipſe dici<lb></lb>tur: & etiam apparet ex ipſa tabula motus nonæ ſphæræ, quæ <lb></lb>oſtendit motum eius eſſe regularem; & iſto modo tabula ip<lb></lb>ſa eſt falſa, quia ipſa dat modum regularem, & ſic uera loca <lb></lb>augium, & planetarum, quæ inueniuntur cum tabulis, eſſent <lb></lb>falſa, & tota ſcientia aſtrologiæ rueret. </s> <s>quod autem ſequatur <lb></lb>illud, quod dixi, ſic oſtendo, ſi calculamus motum nonæ ſphæ<lb></lb>ræ cum differentiæ ære diluuii, & incarnationis, inuenimus <lb></lb>eum eſſe XXII graduum, XLVII min. & IX ſecundorum, <lb></lb>et ſi calculamus cum differentiæ ære incarnationis, & ære Ara<lb></lb>bum, inuenimus eum eſſe IIII graduum, XXXIIII min. & <lb></lb>VIII ſecundorum. </s> <s>ſtantibus autem talibus calculationibus, <lb></lb>uel oportet dicere, quòd in principio ære diluuii caput arietis <lb></lb>nonæ ſphæræ erat directe ſub capite arietis decimæ, & quod <pb xlink:href="024/01/066.jpg"></pb>in 3101 annis, & 319 diebus, qui anni, & dies ſunt differentia <lb></lb>ære diluuii, & incarnationis, nonæ ſphæræ facit arcum XXII <lb></lb>graduum, & XLVII min. & XIX ſecundorum, & quod à <lb></lb>tempore incarnationis, uſque ad tempus Arabum, quod <lb></lb>tempus eſt 621 annorum, & 195 dierum, perfecit rationem <lb></lb>inchoatam in principio ære diluuii, & inchoauit aliam, & <lb></lb>de inchoata fecit IIII grad. XXXIIII min. & VIII ſecun<lb></lb>dos, & ſic in 621 annis, perfecit rationem inchoatam in prin<lb></lb>cipio ære diluuii, & inchoauit aliam, & ſic nona ſphæra ci<lb></lb>tius perficeret reuolutionem, quàm in 40000 annis, & plus <lb></lb>moueretur in 621 annis, & 195 diebus, quàm moueretur in <lb></lb>3101, & 319 diebus, quod eſt contra ſententiam Purbachi, & <lb></lb>contra calculum tabularum: quia reductis 49000 annis ad <lb></lb>4 3 2, & in calculando modum nonæ ſphæræ, cum eis <lb></lb>inuenimus rationem completam, & reductis 200 annis ad <lb></lb>4 3 2, & in calculando inuenimus motum nonæ ſphæræ <lb></lb>grad. I, min. XXVIII, uel oporteret dicere, quòd in <lb></lb>principio uniuſcuiuſque ære, caput arietis nonæ ſphæræ eſt <lb></lb>directo ſub capite arietis decimæ, & quod arcus, quem inue<lb></lb>nimus calculando cum tali ære ſit diſtantia capitis arietis no<lb></lb>næ ſphæræ à capite arietis decimæ, quod eſt manifeſte falſum: <lb></lb>quia calculando cum differentia ære diluuii, & incarnationis, <lb></lb>inuenimus in principio ære incarnationis motum augium, & <lb></lb>ſtellarum fixarum, ſeu motum nonæ ſphæræ eſſe grad. XXII, <lb></lb>min. XLVII, ſecundi XIX. ubi deberent eſſe ſigna . . . . <lb></lb>m. </s> <s>o. </s> <s>&c. </s> <s>dicendum eſt ergo, qui neſcitur locus capitis <lb></lb>ære X, neque locus capitis arietis nonæ, & qui motus augi<lb></lb>um, & ſtellarum fixarum: qui inuenitur calculando cum ali<lb></lb>qua ære, eſt arcus zodiaci, ſeu ecliptica decimæ ſphæræ, ſeu <lb></lb>primi mobilis deſcripti à capite arietis nonæ ſphæræ principio <lb></lb>cuiuſque ære uolueris, uſque ad tempus tuum propoſitum, <lb></lb>ideſt motus, ſeu arcus eclipticæ decimæ ſphæræ, per quem <lb></lb>motus eſt quilibet punctus eclipticæ nonæ ſphæræ à principio <lb></lb>cuiuſcunque ære tuæ propoſitæ, uſque ad tempus tuum pro<lb></lb>poſitum: & hoc ſufficit ad <expan abbr="inueniẽdum">inueniendum</expan> loca augium <expan abbr="planetarũ">planetarum</expan>, <pb xlink:href="024/01/067.jpg" pagenum="27"></pb>& alia contenta, quæ faciunt ad inuentionem locorum uero<lb></lb>rum planetarum: quia, addito tali arcu inuento, cum ara tua <lb></lb>propoſita ſuper radices auguum planetarum fundatas ad prin<lb></lb>cipium tuæ aræ poſitæ; habebis cum æquatione motum octa<lb></lb>uæ ſphæræ, ſicut dicta loca auguum ad tempus tuæ aræ propoſi<lb></lb>tæ, & cetera continentur: & ideo in principio tabulæ radicum <lb></lb>auguum, & ſtellarum fixarum, ideſt nonæ ſphæræ apponun<lb></lb>tur, cum unæ non ſint, ideſt cum non ſint aliquæ aræ poſitæ, & <lb></lb>ſine eis motus earum poſſit inueniri, quia inuenimus quan<lb></lb>tum motum facit nona ſphæra ab initio uniuſcuiuſque aræ uſ<lb></lb>que ad tempus propoſitum poſt principium illius aræ: & ex <lb></lb>conſequenti quantum motum fecerunt auges, & ſtellæ fixæ <lb></lb>per motum nonæ ſphæræ, qui motus additus ſuper radices au<lb></lb>guum in initio illius aræ ſimul cum æquatione motus octauæ <lb></lb>ſphæræ: ſi motus octauæ ſphæræ eſt minus ſemicirculo, uel ab <lb></lb>eo ſubtractæ prius æquatione motus octauæ ſphæræ eſt plus <lb></lb>ſemicirculo ab æra loca auguum ad tempus poſitum computa <lb></lb>tum ab initio illius aræ: & non eſt neceſſitas habendi radicem <lb></lb>aliquam, nec eſt neceſſitas ſciendi quantum diſtat caput arie<lb></lb>tis nonæ ſphæræ à capite arietis decimæ, ſeu primi mobilis, <lb></lb>& hoc uadit ad tale ſignum. </s></p><p type="main"> <s>Tertius autem motus octauæ ſphæræ eſt ſibi proprius, quia <lb></lb>motus trepidationis, ſeu acceſſus, & receſſus octauæ ſphæ<lb></lb>ræ uocatur, qui fit in circumferentiis duorum circulo<lb></lb>rum paruorum æqualium deſcriptorum in concauitate no<lb></lb>næ ſphæræ ſuper principia arietis, & libræ ipſius nonæ ſphæ<lb></lb>ræ, ſic quod duo puncta certa, & determinata ecliptica octa<lb></lb>uæ ſphæræ, quæ capita arietis, & libræ octauæ ſphæræ di<lb></lb>cuntur diametraliter oppoſita, circumferentias talium <expan abbr="duorũ">duorum</expan> <lb></lb>circulorum in concauitate nonæ ſphæræ regulariter deſcri<lb></lb>bantur, quorum media ſeu poli, ſeu centra ſint ipſa capita <lb></lb>arietis, & libræ nonæ ſphæræ, & arcus eclipticæ nonæ ſphæ<lb></lb>ræ inter polos, ſeu centra horum paruorum circulorum, & <lb></lb>circumferentias ſuas. </s> <s>eſt IX grad. eclipticæ nonæ ſphæræ: unde <lb></lb>fit, ut ecliptica octauæ ſphæræ quaſi ſemper ſecet eclipticam <pb xlink:href="024/01/068.jpg"></pb>nonæ, & quando ſecat eam, ſemper ſecat eam in capitibus ca<lb></lb>pricorni, & cancri octauæ. </s> <s>nam hæc duo puncta eclipticæ octa<lb></lb>uæ ſphæræ, uidelicet capita cancri, & capricorni octauæ utrin <lb></lb>que à capitibus cancri, & capricorni nonæ recedunt per quan<lb></lb>titatem IX grad. & reuertuntur; & in tali eorum motu ſemper <lb></lb>circumferentiæ eclipticæ nonæ <expan abbr="cohærẽt">cohærent</expan>, & nuſquam ab ea re<lb></lb>cedunt à capitibus cancri, & capricorni, quæ quantitate IX <lb></lb>grad. ut dictum eſt, recedunt. </s> <s>Purbachus autem dixit capita <lb></lb>cancri, & capricorni octauæ recedere ab ecliptica nonæ ſphæ<lb></lb>ræ, & deſcribere quaſdam figuras connidatas utrunque à ca<lb></lb>pitibus cancri, & capricorni, quæ <expan abbr="habẽtes">habentes</expan> pro baſilias curuas, <lb></lb>quod non uidetur mihi eſſe uerum: quia ex quo puncto ecli<lb></lb>pticæ octauæ ſphæræ, quæ incipiunt recedere ab ecliptica no<lb></lb>næ, ſunt capita arietis, & libræ octauæ ſphæræ. </s> <s>uidetur, quòd ip<lb></lb>ſa <expan abbr="debeãt">debeant</expan> eſſe <expan abbr="pũcta">puncta</expan> maximæ latitudinis eclipticæ octauæ ſphæ<lb></lb>ræ ab ecliptica nonæ: cum autem à puncto maximæ latitudinis <lb></lb>duorum circulorum maiorum ſe inuicem ſecantium ad utraſ<lb></lb>que ſectiones ſit quarta circuli à capitibus arietis, & libræ octa<lb></lb>uæ ſphæræ ad utraſque ſectiones ſemper erit quarta circuli; <lb></lb>ſed à capitibus arietis, & libræ octauæ ſphæræ ad capita cancri, <lb></lb>& capricorni, eiuſdem ſunt quarta eclipticæ octauæ. </s> <s>ergo ſectio <lb></lb>eclipticarum ſemper erit in capite cancri, & capricorni octauæ, <lb></lb>ut bene dixit Thebit. </s> <s>& etiam hoc conſidero, unde fit, quòd <lb></lb>quando unus dictorum punctorum duorum eclipticæ octauæ <lb></lb>ſphæræ, quæ principia arietis, & libræ eiuſdem uocantur, eſt im<lb></lb>mediate ſui circuli parui meridiana ab ecliptica nonæ ſphæræ: <lb></lb>alter eſt immediate ſui circuli parui ſeptentrionalis eclipticæ <lb></lb>etiam octauæ ſphæræ, quando ſecatur ab ecliptica nonæ, ſem<lb></lb>per ſecatur ab ea in partes æquales, uidelicet in duas medieta<lb></lb>tes: & quando ipſa ſecat circulos paruos, portiones circulo<lb></lb>rum paruorum ſectæ ab ea ſunt alternatim æquales, uidelicet <lb></lb>portio <expan abbr="ſeptẽtrionalis">ſeptentrionalis</expan> unius <expan abbr="eorũ">eorum</expan> eſt æqualis meridionali alteri<lb></lb>us: & meridionalis illius <expan abbr="ſeptẽtrionali">ſeptentrionali</expan> alterius. </s> <s>uelocitas autem <lb></lb>motus uniuſcuiuſque duorum capitum, uidelicet arietis, & <lb></lb>libræ octauæ ſphæræ in circumferentiis duorum circulo<lb></lb>rum paruorum eſt iſta, uidelicet quilibet duorum punctorum <pb xlink:href="024/01/069.jpg" pagenum="28"></pb>dictorum, quæ ſunt principia arietis, & principia libræ octa<lb></lb>uæ ſphæræ circumferentiam ſui parui circuli, in qua circum<lb></lb>fertur in 7000 annis præciſæ perficit. </s> <s>quanquam autem hoc <lb></lb>motu titubationis prædicta duo puncta eclipticæ octauæ ſphæ<lb></lb>ræ, quæ capita arietis, & libræ octauæ ſphæræ dicuntur, duas <lb></lb>æquales circumferentias circulorum deſcribant: nulla tamen <lb></lb>alia puncta eius deſcribunt circumferentiam circuli perfe<lb></lb>ctam. </s> <s>capita uero cancri, & capricorni octauæ mouentur per <lb></lb>eclipticam nonæ ſphæræ à XXI grad. geminorum eclipticæ <lb></lb>nonæ ſphæræ, uſque ad IX grad. cancri eiuſdem ſecundum <lb></lb>ſucceſſionem ſignorum, & contra ſucceſſionem ſignorum eun<lb></lb>do, & recedendo: & quandoque capita cancri, & capricorni <lb></lb>octauæ præcedunt capita cancri, & capricorni nonæ <expan abbr="ſecundũ">ſecundum</expan> <lb></lb>ſucceſſionem ſignorum: quandoque ſequuntur modo eundo <lb></lb>ad ea, modo recedendo ab eis ſecundum ſucceſſionem ſigno<lb></lb>rum, & contra ſucceſſionem ſignorum: & quandoque con<lb></lb>iunguntur. </s> <s>coniunguntur enim capita cancri, & capricorni <lb></lb>octauæ cum capitibus cancri, & capricorni nonæ, quando ca<lb></lb>pita arietis, & libræ octauæ ſphæræ erunt in punctis ſectionum <lb></lb>ſuorum circulorum paruorum cum circulo magno per polos <lb></lb>zodiaci nonæ, & centro ſuorum circulorum paruorum eun<lb></lb>te, ſeu in punctis ſuorum circulorum paruorum diſtantibus <lb></lb>per quartam à ſectionibus eorum cum ecliptica nonæ ſphæræ: <lb></lb>& tunc capita arietum, & librarum nonæ ſphæræ, & octauæ <lb></lb>ſunt coniuncta adinuicem ſecundum longitudinem: & licet ca<lb></lb>pita cancri, & capricorni octauæ ſphæræ quandoque ſtatuan<lb></lb>tur directe ſub capitibus cancri, & capricorni nonæ: <expan abbr="nunquã">nunquam</expan> <lb></lb><expan abbr="tamẽ">tamen</expan> capita arietis, & libræ octauæ ſphæræ <expan abbr="erũt">erunt</expan> collocata dire<lb></lb>cte ſub capitibus arietis, & libræ nonæ, quia ſemper erunt in cir<lb></lb>cumferentiis ſuorum circulorum paruorum, diſtantia à cen<lb></lb>tris eorum, quantitate IX grad. ſicut dictum eſt. </s> <s>poli autem e<lb></lb>clipticæ octauæ improprie dicti poli. </s> <s>& quia octaua ſphæra <lb></lb>non mouetur motu ſuo proprio ſuper eis per hunc motum ti<lb></lb>tubationis, quandoque accedunt ad polos zodiaci nonæ, & <lb></lb>decimæ, qui ſemper ſunt ſimul. </s> <s>unus uidelicet ſub alio: & <pb xlink:href="024/01/070.jpg"></pb>quandoque recedunt, ſeu remouentur ab eis per quantita<lb></lb>tem, ſcilicet IX grad. talis autem acceſſus, & receſſus fit ſu<lb></lb>per circulo magno per polos zodiaci nonæ, & centra circulo<lb></lb>rum paruorum eunte. </s> <s>Contingit itaque, quòd per motum <lb></lb>nonæ ſphæræ, qui in 49000 annis perficitur quod quilibet <lb></lb>punctus eclipticæ nonæ ſphæræ ſecat æquinoctioualem primi <lb></lb>mobilis, uidelicet decimæ in eodem puncto, in quo ecliptica <lb></lb>decima, ſeu primi mobilis, ſecat eum: ecliptica autem octauæ <lb></lb>ſphæræ ſub diuerſa eius habitudine, propter motum eius titu<lb></lb>bationis æquinoctialem primi mobilis prope caput arietis, et <lb></lb>etiam prope caput libræ primi mobilis ſecabit, et quandoque <lb></lb>in eo, quando ſcilicet omnes eclipticæ erunt ſimul, quod con<lb></lb>tingit, quando capite arietis, et libræ octauæ ſphæræ fuerint in <lb></lb>ſectionibus ſuorum circulorum paruorum cum ecliptica no<lb></lb>næ ſphæræ; quæ quidem ſectiones eclipticæ octauæ cum æqui<lb></lb>noctionali primi mobilis recedunt, quandoque ad capita arie <lb></lb>tis, & libræ primi mobilis, et quandoque ab eis recedunt, ali<lb></lb>quando ſecundum ſucceſſionem ſignorum; aliquando contra <lb></lb>progrediendo; unde fit per iſtam uariam ſectionem eclipticæ <lb></lb>octauæ cum æquinoctionali primi mobilis, ut maxime declina<lb></lb>tiones zodiaci, ſeu eclipticæ octauæ ſphæræ uariabiles exi<lb></lb>ſtant, et ob hoc contigiſſe uidetur in diuerſis temporibus à <lb></lb>diuerſis aſtronomis quantitates maximarum declinationum <lb></lb>zodiaci, ſeu eclipticæ octauæ ſphæræ fuiſſe inæqualiter inuen<lb></lb>tas maiores; nanque inuentæ ſunt à Ptolomæo, quam ab Al<lb></lb>meone, et Albatægni, qui cum ſimilibus uiis, et modis pro<lb></lb>ceſſerunt in inueniendo eas, non potuit hæc diuerſitas eueni<lb></lb>re, niſi propter talem motum titubationis, aut ſimilem huic <lb></lb>talem diuerſitatem aptum cauſare ad uariationem autem ſe<lb></lb>ctionis eclipticæ octauæ ſphæræ cum æquinoctiali primi mobi<lb></lb>lis neceſſarium eſt, ut ſolſtitia, et ſimiliter æquinoctia continue <lb></lb>diuerſificentur: unde non ſemper, cum ſol fuerit in capite a<lb></lb>rietis, uel libræ primi mobilis, neceſſe eſt æquinoctium eſſe, <lb></lb>ſed erat ante fuiſſe ſol, uel poſt futurum eſſe, cum fuerit in ſe<lb></lb>ctione eclipticæ octauæ cum æquinoctionali. </s> <s>ex quo enim ſic <pb xlink:href="024/01/071.jpg" pagenum="29"></pb>ſupra dictum eſt centrum corporis ſolis ſemper, et continue <lb></lb>diſcurrit ſub ecliptica octauæ ſphæræ: hæc autem ſæpe immo <lb></lb>frequenter eſt extra eclipticas nonæ, & decimæ, quæ ſemper <lb></lb>ſunt ſimul ex continenti, ipſa erit extra capitibus arietis, & li<lb></lb>bræ primi mobilis: quare ſequitur illud, quod dictum eſt. </s> <s>ſi<lb></lb>milis de uariatione ſolſtitiorum eſt ratio, uidelicet quod pro<lb></lb>pter uariationem continuam ſectionis eclipticæ octauæ cum <lb></lb>æquinoctionali reſpectu arietis, & libræ primi mobilis, ſub <lb></lb>qua ecliptica octaua continue mouetur ſol, non ſemper ſole <lb></lb>exiſtente in capite cancri, uel capricorni primi mobilis; neceſ <lb></lb>ſe eſt ſolſtitium accedere. </s> <s>cum enim ut plurimum ſuperficies <lb></lb>eclipticæ octauæ ſphæræ ſit extra ſuperficiem eclipticæ primi <lb></lb>mobilis, & ſolſtitia ſint in punctis eclipticæ octauæ ſphæræ me<lb></lb>diis inter duas ſectiones eclipticæ octauæ ſphæræ cum æquino<lb></lb>ctionali primi mobilis continue uarientur, neceſſe eſt, ut pun<lb></lb>cta eclipticæ octauæ ſphæræ ſolſtitialia, quæ ſunt puncta media <lb></lb>inter ipſas ſectiones ſimiliter continue uarientur; & <expan abbr="conſequẽ-ter">conſequen<lb></lb>ter</expan> ſolſtitia non ſint ſemper in capite cancri, & capricorni pri<lb></lb>mi mobilis, ſed in punctis, eclipticæ octauæ ſphæræ mediis in<lb></lb>ter ſectiones ipſas eclipticæ octauæ cum æquinoctionali: quia <lb></lb>talia puncta ſunt puncta maxime diſtantia ab æquinoctionali <lb></lb>inter omnia puncta eclipticæ octauæ ſphæræ: ex quibus con<lb></lb>cluditur non eſſe neceſſarium ſole exiſtente in capite arietis, <lb></lb>uel libræ primi mobilis ipſum nullam habere declinationem: <lb></lb>ab æquinoctionali ſimiliter ſequitur, non eſſe neceſſarium ſo<lb></lb>le exiſtente in capite cancri, uel capricorni primi mobilis, ip<lb></lb>ſum habere declinationem <expan abbr="maximã">maximam</expan> ab æquinoctiali. </s> <s>ſtat enim <lb></lb>ſolem eſſe in circulo magno per polos eclipticæ primi mobilis, <lb></lb>& caput arietis, & libræ eiuſdem tranſeunte, & tam ipſum eſſe <lb></lb>extra æquinoctialem: ſimiliter ſtat ſolem eſſe in circulo ma<lb></lb>gno per polos eclipticæ primi mobilis, & caput cancri, & ca<lb></lb>pricorni eiuſdem tranſeunte, & tamen tunc non habere decli<lb></lb>nationem maximam ab æquinoctionali, ſed ante eam habuiſ<lb></lb>ſe, uel poſtea eam habituram eſſe. </s> <s>ſequitur etiam circulos <lb></lb>tropicos continuos reſpectu æquinoctionali uariari, nunc ei <pb xlink:href="024/01/072.jpg"></pb>appropinquando, nunc ab eo elongando. </s> <s>ex his autem ſtel<lb></lb>larum motibus ſatis clarum eſt, motum ſtellarum fixarum ag<lb></lb>gregatum ex motu contrariæ, & motu trepidationis octauæ <lb></lb>ſphæræ quandoque eſſe ſecundum ſucceſſionem ſignorum, <lb></lb>& nunc uelociter, & nunc tarde: et quandoque eſſe ſtationa<lb></lb>rium: & quandoque eſſe, contra ſucceſſionem ſignorum ſupra <lb></lb>diuerſitatem, ſitum capitis arietis, et libræ octauæ ſphæræ <lb></lb>in ſuis paruis circulis, ſeu in circumferentiis ſuorum circulo<lb></lb>rum paruorum. </s> <s>difficile enim multum fuit antiquis huius mo<lb></lb>tus reperire modum: et ob hoc diuerſi diuerſos modos hu<lb></lb>ius motus imaginati ſunt. </s> <s>aliqui enim dicebant auges planeta<lb></lb>rum, et ſtellas fixas moueri per 900 annos continue uerſus <lb></lb>orientem uſque ad grad. VII. deinde per alios 900 annos tan<lb></lb>dem uerſus occidentem. </s> <s>Abategni uero dicebant eas moueri <lb></lb>in 66 annis, et 4 menſibus uerſus orientem continue per u<lb></lb>num gradum. </s> <s>Alphragranus autem putauit eas in 100 annis <lb></lb>unum gradum perficere uerſus orientem continue. </s> <s>meus er<lb></lb>go auguum motus, et ſtellarum fixarum ſecundum imagina<lb></lb>tionem dictam eſt arcus zodiaci, ſeu eclipticæ primi mobilis, <lb></lb>ſeu decimæ, deſcriptus à capite arietis nonæ ſphæræ, ſeu cen<lb></lb>tro parui circuli arietis octauæ à principio cuiuſcunque aræ <lb></lb>uolucris uſque ad tempus tuum propoſitum. </s> <s>ſed meus mo<lb></lb>tus acceſſus, et receſſus octauæ ſphæræ, et arcus circuli par<lb></lb>ui arietis octauæ ſphæræ, incipiendo à puncto circuli magni a<lb></lb>rietis octauæ ſphæræ ſeptentrionali diſtante à ſectionibus ip<lb></lb>ſius circuli parui cum ecliptica nonæ ſphæræ per quartas par<lb></lb>ui circuli uſque ad locum capitis arietis octauæ in ſuo paruo <lb></lb>circulo ad tempus tuæ aræ propoſitum ſecundum ordinem ſi<lb></lb>gnorum, ſeu uerſus orientem procedendo computat: æqua<lb></lb>tio autem octauæ ſphæræ eſt arcus eclipticæ nonæ ſphæræ in<lb></lb>ter centrum parui circuli, ſeu caput arietis nonæ ſphæræ, et <lb></lb>circulum magnum per polos zodiaci nonæ ſphæræ, et caput <lb></lb>arietis octauæ ſphæræ in ſuo circulo paruo tranſeunte in<lb></lb>terceptus. </s></p><p type="main"> <s>Cum autem meus motus acceſſus, et receſſus octauæ ſphæræ <pb xlink:href="024/01/073.jpg" pagenum="30"></pb>nihil fiunt, aut ſemicirculus præciſe, nulla eſt dicta æquatio, ſed <lb></lb>ſi XC grad. ante CCLXX fuerit, eſt maxima, & eſt IX grad. <lb></lb></s> <s>Cum autem meus motus acceſſus, & receſſus erit minus XC <lb></lb>grad. æquatio ſemper creſcit, & eſt addenda meo motui augu<lb></lb>um; & <expan abbr="cũ">cum</expan> erit plus XC grad. & minus CLXXX decreſcit, & eſt <lb></lb>ſimiliter <expan abbr="addẽda">addenda</expan>. </s> <s>et <expan abbr="cũ">cum</expan> fuerit plus CLXXX, & minus CCLXX <lb></lb>creſcit, et eſt minuenda: et cum fuerit plus CCLXX, donec <lb></lb>meus motus acceſſus, & receſſus fuerit, nihil decreſcit, et eſt <lb></lb>minuenda. </s> <s>hunc modum titubationis, ſeu acceſſus, et receſſus <lb></lb>octauæ ſphæræ ſequuntur omnes ſphæræ inferiores octauæ. </s> <s>ita <lb></lb>ut reſpectu eclipticæ octauæ ſphæræ ſint auges <expan abbr="differẽtium">differentium</expan> pla<lb></lb>netarum, et declinationes earum ſemper inuariabiles. </s> <s>et his ſit <lb></lb>finis mei tractatus de motu octauæ ſphæræ. </s></p><p type="main"> <s>QVOD corpus ſolis, et lunæ, et corpora cæterorum <expan abbr="planeta-rũ">planeta<lb></lb>rum</expan>, et corpora ſtellarum fixarum ſint ſphæræ, ſic oſtenditur. <lb></lb></s> <s>Vbicunque fuerit ſol, et aſpiciatur à nobis, ſemper apparet <lb></lb>nobis figura rotunda, ſiue ſit in parte orientis, ſiue in parte <lb></lb>meridiei, ſiue in parte occidentis; et tamen in iſtis locis diuer<lb></lb>ſus non aſpicitur à nobis ſemper ſecundum eandem partem e<lb></lb>ius præciſe. </s> <s>hoc autem arguit ipſum eſſe ſphæricæ figuræ: lu<lb></lb>nam etiam eſſe ſphæricam deprehendimus ab illuminatione e<lb></lb>ius à ſole, ſecundum quod ipſe à ſole <expan abbr="elõgatur">elongatur</expan>, et à ſuppoſitio<lb></lb>ne eius ſub eo in coniunctione, in qua fit eclipſis ſolis: non e<lb></lb>nim ſemper illuminatur à ſole ſecundum eandem partem eius <lb></lb>præciſe. </s> <s>Planetæ etiam delati à ſuis orbibus uario motu <expan abbr="nõ">non</expan> ſem<lb></lb>per ſpectantur à nobis ſecundum eandem partem eorum præ<lb></lb>ciſe; et tamen ſemper uidentur à nobis rotundæ figuræ. </s> <s>ad hoc <lb></lb>etiam adiuuat motus eorum à ſuis epicyclis. </s> <s>corpora enim <lb></lb>planetarum, et lunæ ſimiliter ita feruntur à ſuis epicyclis, qui <lb></lb>nunc ex una parte eorum, nunc ex alia à nobis aſpiciuntur; <lb></lb>ſemper tamen uidentur à nobis rotundæ figuræ, quod oſten<lb></lb>dit ea eſſe ſphærica. </s> <s>quòd ſi dicatur planetas reuolui in quibuſ<lb></lb>dam concauitatibus, in quibus recipiuntur, et taliter reuol<lb></lb>ui, quòd propter motus eorum in talibus concauitatibus ſem<lb></lb>per oſtendunt nobis eandem eorum partem præciſe; quod <pb xlink:href="024/01/074.jpg"></pb>tamen nos negamus, quia dicimus eas eſſe fixas in ſuis epicy<lb></lb>clis, ſicut nodi, ſeu claui in tabula; ſi tamen aſſentire uolu<lb></lb>mus, quòd planetæ habeant concauitatis in ipſis cælis, in qui<lb></lb>bus recipiantur, & reuoluantur; dico, quòd hoc non poteſt <lb></lb>eſſe niſi ſint corpora ſphærica; aliter enim non poſſent reuolui <lb></lb>in talibus concauitatibus, & ſi reuoluerentur, neceſſario da<lb></lb>rentur penetratio corporum; & ſicut eſt de ſole, & luna, & <lb></lb>aliis planetis; ita dicendum eſt de ſtellis fixis, quæ ſunt in o<lb></lb>ctauo cælo, uidelicet qui ſint corpora ſphærica cum ſint indi<lb></lb>uidua eiuſdem ſpeciei. </s></p><pb xlink:href="024/01/075.jpg"></pb> </chap> </body> <back></back> </text></archimedes>