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