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version 1.6, 2003/11/17 15:30:57

version 1.13, 2005/09/30 08:55:28

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<?xml version="1.0"?>

<?xml version="1.0" encoding="UTF-8"?>

<!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" >

<archimedes xmlns:xlink="http://www.w3.org/1999/xlink"> <info> <author>Ghetaldus, Marinus</author> <title>Promotus Archimedis</title> <date>1603</date>

<info>

<place>Rome</place> <translator/> <lang>la</lang> <cvs_file>gheta_promo_029_la_1603.xml</cvs_file><cvs_version>1.11</cvs_version> <locator>029.xml</locator> </info> <text> <front> </front> <body> <chap> <pb id="p.0001"/>

<author>Fabri, Honoré</author>

<title>Dialogi physici in quibus de motu terrae disputatur</title>

<s>MARINI GHETALDI <lb/>PATRICII <lb/>RAGVSINI <lb/>PROMOTVS ARCHIMEDIS <lb/>SEV.De varijs corporum generibus <lb/>grauitate & magnitudine <lb/>comparatis.</s><figure/>

<s>ROM AE, <lb/>Apud Aloy&longs;ium Zannettum. </s>

<s>MDCIII. <lb/><emph type="italics"/>SVPERIORVM PERMISSV.<emph.end type="italics"/></s><pb/>

<cvs_file>fabri_dialo_025_la_1665.xml</cvs_file>

<cvs_version/>

<s>REVERENDISSIMO <lb/>SERAPHINO OLIVARIO <lb/>RAZZALIO. <lb/>PATRIARCH AE <lb/>ALEXANDRINO. <lb/>MARINUS GHETALDUS. S.P.D.</s>

</info>

<s>Egregia &longs;anè Reuerendi&longs;sime <lb/>PRÆSVL quod probe no&longs;ti, vete<lb/>rum &longs;apientum f&oelig;licitas fuit. </s>

<text>

<s>Eam <lb/>enim cum ingenij præ&longs;tantia, tum <lb/>prær<gap/>gatiua temporis laudem occu<lb/>parunt, <expan abbr="quã">quam</expan> vel &longs;perare po&longs;terioribus <lb/><expan abbr="temerari&utilde;">temerarium</expan> &longs;it. </s>

<body>

<chap>

<s>Et vero illis non &longs;olum nos plurimum de<lb/>bemus, quod plurima ip&longs;i perfecere: verum etiam quod <lb/>quædam qua&longs;i fundamenta iecere, quibus dum rerum <lb/><expan abbr="nouar&utilde;">nouarum</expan> molem conamur imponere, nos quoque experi<lb/>ri no&longs;tras vires, exercere indu&longs;triam, remque &longs;apientiæ <lb/>publicam amplificare po&longs;simus. </s>

<s>Quo in genere magno<lb/>rum ego virorum &longs;tudium potius, quam gloriam æmu<lb/>latus &longs;uper vnum ex Archimedeis fundamentis, de ra<lb/>tione, qua varia corporum genera inter &longs;e grauitate & <lb/>magnitudine comparantur, fabricatus nonnulla &longs;um: <pb/>quæ nunc omnium oculis expo&longs;iturus, vt eam <expan abbr="&longs;u&longs;tineã">&longs;u&longs;tineam</expan>, <lb/>per&longs;onam, quam &longs;emper recu&longs;aui, patrocinium huiu&longs;<lb/>modi quærendum mihi exi&longs;timaui, quod & imbecillita<lb/>tem meam contra obtrectatorum, &longs;i qui forte exi&longs;terent, <lb/>calumnias &longs;u&longs;tineret; & imminentem famæ, exi&longs;timatio <lb/>ni&longs;que iacturam auerteret. </s>

<s id="s.000001"><emph type="center"/>DIALOGI <lb/>PHYSICI, <lb/>IN QVIBVS <lb/>De Motu Terræ Di&longs;putatur, <lb/>MARINI ÆSTVS NOVA <lb/>cau&longs;a proponitur,<emph.end type="center"/></s>

<s>Vnus igitur tu occuri&longs;ti SE<lb/>RAPHINE qui & <expan abbr="cõmodi&longs;sime">commodi&longs;sime</expan> mihi patrocinari po&longs;<lb/>&longs;es, & quodam qua&longs;i iure deberes. </s>

<s id="s.000002"><emph type="center"/><emph type="italics"/>Nec non aquarum & Mercurij &longs;upra. </s>

<s>Cum enim tu me ad <lb/>emittendum id opus hortatu tuo compuleris, videbatur <lb/>quodam iure ad tuam fidem eius tutela pertinere. </s>

<s id="s.000003">libellam elevatio examinatur.<emph.end type="italics"/><emph.end type="center"/></s>

<s><expan abbr="Tuq;">Tuque</expan> <lb/>is es, quem non modo rudes, &longs;ed etiam docti &longs;u&longs;piciunt. </s>

<s id="s.000004"><emph type="center"/>AD EMINENTISSIMVM <lb/>CARDINALEM FACCHINETTVM.<emph.end type="center"/></s>

<s><lb/>Habetino&longs;tra bæc ætas, quos admitetur; habet quos ex<lb/>tollat præclaros viros, &longs;ed quos tibi anteponat, non facile <lb/>inueniet. </s>

<s>Degis ea in Vrbe, quæ laudis mediocritatem <lb/>vel nunquam agnouit, vel &longs;emper contemp&longs;it: neque in <lb/>tanta maie&longs;tate, tua deficit virtus, &longs;ed bono in lumine po <lb/>&longs;ita collucet magis. </s>

<s id="s.000005"><emph type="center"/><emph type="italics"/>Auctore<emph.end type="italics"/> R. P. HONORATO FABRI. <emph type="italics"/>Societatis<emph.end type="italics"/> IESU.<emph.end type="center"/></s>

<s>In primis enim tua vitæ integritas <lb/>elu&longs;modi e&longs;t, vt non conterita dome&longs;tico præcomo lati&longs;<lb/>&longs;ime peruagetur. </s>

<s>Habent omnes quod prædicent, & imi <lb/>tentur; habet quod excipiat grati&longs;sima memoria po&longs;te<lb/>ritas vniuer&longs;a. </s>

<s id="s.000006"><emph type="center"/><emph type="italics"/>LVGDVNI,<emph.end type="italics"/><lb/>Sumptibus CHRISTOPHORI FOVRMY, <lb/>in vico Mercatorio, &longs;ub &longs;igno Occa&longs;ionis.<emph.end type="center"/></s>

<s>Doctrinæ vero ea excellentia es, vt ea &longs;atis <lb/>omnibus clarus, & illu&longs;tris, non &longs;atis tibi, <gap/>cum a&longs;sidue <lb/>certes. </s>

<s id="s.000007"><emph type="center"/><emph type="italics"/>M. DC. LXV. <emph.end type="italics"/><lb/>CVM PERMISSV SVPERIORVM.<emph.end type="center"/></s>

<s>nec minum, qui vel à primis incunabulis ad &longs;um<lb/>ma contendebas, &longs;i prouecta iam ætate vix habeas, quo <lb/>altius contendas. </s>

<s>Præclarum &longs;anè & eximium vno do<lb/>ctrinæ genere; &longs;ublime, atque admirabile multiplici ex<lb/>cellere. </s>

<s id="s.000008"><emph type="center"/>IRREGULAR <lb/>PAGINATION<emph.end type="center"/></s>

<s>Tu vero în omni genere laudem egregiam a&longs;&longs;e<lb/>cutus es ab&longs;olutam videlicet tibî gloriam propo&longs;itam <lb/>volui&longs;ti; <expan abbr="quiq;">quique</expan> intelligebas hominem ad hone&longs;ta omnia <pb/>genitum, nullam tibi rerum glorio&longs;arum partem con<lb/>temnendam puta&longs;ti. </s>

<s>Placet incredibili rerum humana<lb/>num v&longs;ui diuinarum rerum cognitionem adiungere; vt <lb/>habeat animus à caducis ad æterna, &longs;e conferendo, vnde <lb/>oblectamentum capiat, & admirationem. </s>

<s>Philo&longs;ophiam <lb/>ita tenes, vt qui in maximis negocijs a&longs;sidue ver&longs;atus es, <lb/>videaris &longs;emper fui&longs;fe otio&longs;us. </s>

<s id="s.000009"><emph type="center"/>LECTORI.<emph.end type="center"/></s>

<s>Quid dicam de &longs;ingulari <lb/><expan abbr="caq;">caque</expan> eximia rerum c&oelig;le&longs;tium, <expan abbr="totiu&longs;q;">totiu&longs;que</expan> mundi cognitio<lb/>ne quam tu tanta cum auiditate ex reconditi&longs;simis Ma<lb/>thematicorum fontibus hau&longs;i&longs;ti, vt illud a&longs;&longs;ecutus in eo <lb/>genere iam &longs;is, quod alij in maxima tranquillitate, in <lb/>&longs;ummo otio vix au&longs;int optare? </s>

<s id="s.000010"><emph type="italics"/>REM i&longs;tam, provt ge&longs;ta e&longs;t fideli narratione tibi <lb/>expono, Candidi&longs;&longs;ime Lector, elap&longs;o proxime Iu<lb/>nio ab Eminenti&longs;&longs;ime<emph.end type="italics"/> CARDINALI FACCHI<lb/>NETTO, <emph type="italics"/>&longs;ub cujus au&longs;piciis, hoc ip&longs;um, quod <lb/>in manibus habes, opu&longs;culum in lucem prodire volui, pro <lb/>&longs;umma illa, qua pollet humanitate, ad prandium invitatus <lb/>&longs;um, vt deinde pomeridianis horis, cum eruditi&longs;&longs;imis homini<lb/>bus, de nonnullis experimentis Phy&longs;icis di&longs;&longs;ertationem in&longs;ti<lb/>tuerem, cui Eminenti&longs;&longs;imus pro eo, quo e&longs;t in rem literariam <lb/>affectu, intere&longs;&longs;et. </s>

<s>Exitum tuorum labor um <lb/>f&oelig;lici&longs;simum vides: gloria multiplici frueris, <gap/>eque illa <lb/>precaria &longs;ed tua & quibu&longs;dam qua&longs;i gradibus ad ampli&longs;<lb/>&longs;<gap/>mos: honores euehendus, in ea con&longs;titueris dignitate; in <lb/>qua pro &longs;acro&longs;ancta Eccle&longs;ia <gap/>quam non excubando, <lb/>in peramplo tot illu&longs;trium vitorum Theatro non alienæ <lb/>gloriæ &longs;pectator, &longs;ed actor tuæ con&longs;i&longs;tas. </s>

<s id="s.000011">Aliquid fortè de me inaudierat<gap/>, & vt <lb/>amici nunquam ferè de amico ni&longs;i hyperbolicè, illud, quod <lb/>in me &longs;entio, vel nullum, vel admodum tenue ingenium, <lb/>plus æquo efferre dignati &longs;uerant: parvi tamen, & hora <lb/>condicta adfui, quamvis alioquin tenuitatis meæ con&longs;cius, vt <lb/>morem Eminenti&longs;&longs;imo gererem; præ&longs;ertim; cùm opera pre<lb/>tium foret, Eminenti&longs;&longs;imum ab ea, quam per amicorum hy<lb/>perbolem, de me conceperat, opinione dimovere; quod mihi <lb/>&longs;anè pro votis &longs;ucce&longs;&longs;i&longs;&longs;e facilè crediderim, vbi me Emi<lb/>nenti&longs;&longs;imus vix balbutientem audivit. </s>

<s id="s.000012">Vt vt &longs;it, de va<lb/>riis à nobis actum e&longs;t; &longs;ed præ&longs;ertim de motu Terræ, Maris <lb/>æ&longs;tu Aquarum & Mercurij in tubis erectis elevatione, alii&longs;<lb/>que huc pertinentibus. </s>

<s>Tu vero, quod <lb/>rarum e&longs;t, laudem &longs;apientiæ, quæ vix vllos habet at ter<lb/>minos, humanitatis tuæ terminis circum&longs;cribis; & expo<lb/>nis omnibus<gap/> vt extanto &longs;onte perennes ad omnium or<lb/>dinum homines fiuuli deducantur. </s>

<s id="s.000013">Cum autem is, quem &longs;ub Augu&longs;tini no<lb/>mine in &longs;cenam induxi, à me po&longs;t aliquot men&longs;es, efflagita&longs;&longs;et,<emph.end type="italics"/><pb xlink:href="025/01/004.jpg"/><emph type="italics"/>vt ea, qu<gap/> nuda voce prolata à me acceperat, &longs;cripto tradi<lb/>ta ip&longs;i con&longs;ignarem, &longs;atius fore putavi, &longs;i publicam in lucem <lb/>Typis mandata prodirent; cùm &longs;æpè accidat, vt ex amanuen<lb/>&longs;ium incuria, multi næ vi ac f&oelig;di errores in ex&longs;cripta irre<lb/>pant. </s>

<s id="s.000014">Cæterùm more Platonico & Tulliano Dialogi formam <lb/>adhibui, tum quia magis expedita e&longs;t, tum quia hoc ferè mo<lb/>do res ip&longs;aperact<gap/> fuit illam autem &longs;ententiam meam e&longs;&longs;e <lb/>facile intelliges, quam &longs;ub nomine Antimi vel doceo, vel <lb/>approb<gap/>. </s>

<s>F&oelig;lix qui &longs;olidæ <lb/>f&oelig;licitatis car&longs;am & in&longs;tium in re con&longs;titutumita foues, <lb/>vt cum alijs illam communicando, non imminuas, &longs;ed <lb/>amplifices, prægrande videlicet non &longs;uccre&longs;centis, &longs;ed <lb/>adultæ iam virtutis f&oelig;nus honorem ex honore, laudem <lb/>ex laude con&longs;equi vberiorem, hæcilla &longs;apienti viro non <lb/>indigna liberalitas, quæ terum pre&longs;tanti&longs;simarum po&longs;<lb/>&longs;e&longs;sione non imminuta, in copia tenuitatem non inqui-<pb/>rens vbertatis ip&longs;a&longs;uæ dominæ nunquam debilitatur, <lb/>nunquam deficit. </s>

<s id="s.000015">Sihæc pauca tibi arri&longs;erint, dulci&longs;&longs;ime Lector, dabo <lb/>operam, vt alia quàm plurima iis &longs;uccedant; admi&longs;cui pau<lb/>ca Geometrica, non data opera &longs;ed ferè coastus, vt &longs;altem <lb/>inde videas, quantum Geometria, non modò vtilis, verùm <lb/>etiam nece&longs;&longs;aria &longs;it, ad res Phy&longs;icas pro dignitate pertractan<lb/>das. </s>

<s>Quin etiam i&longs;to loco con&longs;titutus bo<lb/>narum literarum &longs;tudio&longs;os complecteris, ac tueris. </s>

<s>Hæc <lb/>e&longs;t vera germanæ nota &longs;apientiæ, cum, quas vires nanci<lb/>fcitur, ijs &longs;apientiam alit, tuus animus & tuæ &longs;apientiæ, & <lb/>alienæ par e&longs;t. </s>

<s>Hæc &longs;unt firmi&longs;sima & &longs;olidi&longs;sima funda<lb/>menta ad æternam po&longs;teritatis memoriam, quam licer <lb/>profici&longs;ci iam videas ex ijsquibus abundas animi orna<lb/>mentis, ne&longs;cio tamen quo pacto gratior nobis acccidit, <lb/>cum ex alioium etiam prædonio &longs;u&longs;cipit in crementum. </s>

<s id="s.000017"><emph type="center"/>DIALOGVS PRIMVS.<emph.end type="center"/></s>

<s><lb/>Hinc domus tua floret docti&longs;simorum familiaritatibus; <lb/>hinc nulli ad tuam con&longs;uetudinom præcluditur aditus; <lb/>hinc plurimorum &longs;tudia commouentur; hinc illa &longs;apien <lb/>tum æmulatio & admiratio<gap/> hinc omnium omnino or<lb/>dinum ad te concur&longs;us; tanquam ad &longs;apienti&longs;simum hu<lb/>mani <expan abbr="diuiniq;">diuinique</expan> iuris paponum, & interpetem. </s>

<s id="s.000018"><emph type="center"/><emph type="italics"/>In quo argumenta pro ad&longs;truenda Copernici <lb/>hypothe&longs;i adducta, reijciuntur.<emph.end type="italics"/><emph.end type="center"/></s>

<s>Quid ego <lb/>igitur quem tibi &longs;excentis eximiæ beneuolenti&oelig; argu<lb/>mentis obligatum vo<gap/>&longs;ti, perexigitum hunc ingenij <lb/>mei partum exp<gap/>&longs;uiuus, vnum te nominis & exi&longs;tima<lb/>tionis meæ patronum non &longs;u&longs;eipiam<gap/> equide<gap/> in am<lb/>pli&longs;simi Theatri lucern &longs;apienti&longs;simorum<32> hominum <lb/>con&longs;pectum, quibus abundat hæd no&longs;tra ætas inferre me <lb/>non magnopere cogitabam <gap/>Tu hortatus es dubitan<lb/>tem impuli&longs;ti vel reluctamem<gap/> tuereigitur ob&longs;equen<lb/>tem. </s>

<s>iam nunc mihi videor in exigua vel nulla &longs;pe lau<lb/>dis ex ingenio meo; &longs;empiternam nominis immortali<lb/>tatem ex tuo patrocinio con&longs;ecutus. </s>

<s id="s.000019">ILLA dies aibo &longs;ignata lapillo, qua me immerentem <lb/>&longs;anè, lauto &longs;imul & literatio convivio excepi&longs;ti, <lb/>CARDINALIS EMINENTISSIME, Nunquam mihi <lb/>venit in mentem, ni&longs;i & &longs;ingularis humanitatis tuæ, qua <lb/>tibi omnium animos arcti&longs;&longs;imè devinxi&longs;ti, & docti&longs;&longs;imo<lb/>rum illorum hominum, qui congre&longs;&longs;ui no&longs;tro interfue<lb/>runt, jucundi&longs;&longs;ima recordatio &longs;uavi&longs;&longs;imo voluptatis &longs;en<lb/>&longs;u animum meum perfundat : ita enim confabulando am&oelig;nus, promptus <lb/>arguendo, &longs;olvendo &longs;ubtilis, explicando elegans & limpidus omnibus no<lb/>bis vi&longs;us es, vt conjuncta eloquentiæ &longs;apientia, ad fundenda oracula, tua <lb/>voce, tuis verbis vti videretur. </s>

<s id="s.000020">Vt autem perpetuum docti&longs;&longs;imi congre&longs;&longs;us <lb/>monumentum extet, cuius ego aliqua pars, licet exigua fui, literis illum & <lb/>typis con&longs;ignatum ad po&longs;teritatem tran&longs;mittere con&longs;titui; vt &longs;altem in<lb/>telligant homines, Eminenti&longs;&longs;imum Principem non politicis modò & gra<lb/>vioribus &longs;tudiis, verùm etiam am&oelig;nioribus literis plurimùm delectatum <lb/>fui&longs;&longs;e. </s>

<s id="s.000021">Sed in &longs;cenam per&longs;onatos Actores induco, quos in arena literaria <lb/>di&longs;ceptantes audire priùs volui&longs;ti: &longs;ingulos facilè agno&longs;ces, quamvis enim, <lb/>vt fieri &longs;olet, nomina tantulùm mutata fuerint, eos tamen, in quos &longs;ingula <lb/>optimè quadrant, nullo negotio per&longs;picies Sed ad rem venio. </s>

<s>Romæ VII. Kal. Maij. MDCIII. </s>

<s id="s.000022"><emph type="italics"/>Antimus.<emph.end type="italics"/> E&longs;t, quod mihi &longs;ummoperè gratuler, docti&longs;&longs;ime Augu&longs;tine, <lb/>quod jamdudum à me de&longs;ideratam, hodierna die, abundè, vt &longs;pero, tui <lb/>copiam mihi facturus &longs;is; mirum enim, quanto eruditæ con&longs;uetudinis <lb/>&longs;tudio tenerime &longs;entiam, quæ grati&longs;&longs;imos, di&longs;cendi nova, & a&longs;&longs;equendi <lb/>hactenus incomperta, igniculos in me accendit, & quadam, vt &longs;ic loquar, <lb/>vellicatione. </s>

<s id="s.000023">Ingenium &longs;timulat, ad ea nonnunquam expromenda, quæ lon<lb/>ga meditatione, & repetita cogitationum huc illuc ver&longs;atione, vix vnquam <lb/>elici potui&longs;&longs;ent. </s>

<s id="s.000024">A te igitur illa audire percupio, quæ & &longs;itim meam ex<lb/>tinguant, & opinionem de te meam, quamvis alioquin maximam longè <lb/>&longs;uperent & po&longs;t &longs;e relinquant. </s>

<pb/>

<s>BENEVOLO <lb/>LECTORI.</s><figure/>

<s id="s.000025"><emph type="italics"/>Augu&longs;tinus.<emph.end type="italics"/></s>

<s id="s.000026"> Hoc ip&longs;um tibi à me dictum e&longs;&longs;e puta; huc venis, Antimo, <lb/>vt doceas, non verò vt di&longs;cas; & &longs;i fortè identidem à me aliquid oppo-<pb pagenum="2" xlink:href="025/01/006.jpg"/>nendum &longs;it, eo dumtaxat fine hoc à me fiet, ad vberiorem explicationis <lb/>lucem extorquendam. </s>

<s>D<emph type="italics"/>iversa. corporum genera duplici ra<lb/>tione comparari inter &longs;e à Mathematicis <lb/>po&longs;&longs;unt mole ac pondere. </s>

<s id="s.000027">Eminenti&longs;&longs;imus Princeps, eo animo te invitavit, <lb/>vt cùm de te multa à nobis inaudii&longs;&longs;et, de rebus Philo&longs;ophicis di&longs;&longs;erentem <lb/>audiret; & non modico huiu&longs;ce rei de&longs;iderio teneri &longs;e, nobis &longs;emel atque <lb/>iterum &longs;ignificavit. </s>

<s id="s.000028"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>Pondere compara<lb/>tio fit, cum iuter corpora diuer&longs;i generis mo <lb/>le aqualia, quæritur, qu&ecedil; &longs;it tatioponderis: <lb/>quanto videlicet, vnum altero grauius, aut leuius &longs;it. </s>

<s id="s.000029"> Quid tandem à me expromi queat, quod Eminenti&longs;&longs;imi auri<lb/>bus dignum &longs;it, profectò non liquet; quicquid enim, etiam cum aliquo <lb/>mentis ni&longs;u excogito, nugas inter & qui&longs;quilias mihi &longs;emper huc v&longs;que <lb/>reponendum e&longs;&longs;e vi&longs;um e&longs;t, qua&longs;i verò mea pluris faciam, quàm me? </s>

<s>Ma<lb/>guitudine autem &longs;it collatio, cum po&longs;ita pari grauitate, quæ<lb/>ritur, que &longs;it ratio magnitudinis; quanto &longs;it alterum altero <lb/>maius, aut minus. </s>

<s id="s.000030"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>Quæ comparatio mihi cum videretur & <lb/>iucunda cognitu, & v&longs;um manullum habere, nee fu&longs;e à que <lb/>piam explicata, non ita pridem &longs;uper ea non nihil c&oelig;pi me <lb/>liris &longs;ed nihil de luce ac publico cogitabam l<gap/> enim ego &longs;um, <lb/>qui malim &longs;eire, quam ne&longs;cidi&longs;cere, quam decere. </s>

<s id="s.000031"> Dic, vt voles, illud &longs;altem con&longs;tat, quidquid vel ex tuis lu<lb/>cubrationibus, vel ex tuo di&longs;&longs;erentis ore accepi, mihi &longs;ummoperè pla<lb/>cui&longs;&longs;e: vnum tamen e&longs;t, ne quid di&longs;&longs;imulem, quod in te aliqui de&longs;ide<lb/>ra&longs;&longs;ent, ne &longs;cilicet tanto adversùs Copernicanam hypothe&longs;im odio flagra<lb/>res, in quo nonnullis paululùm excedere mihi vi&longs;us es; poteras haud du<lb/>biè oppo&longs;itam &longs;equi, quam & ego demi&longs;&longs;a fronte o&longs;culor, cum iis præ&longs;er<lb/>tim, qui Eccle&longs;ia&longs;ticam vitam amplexi, Pontificiis &longs;tare debent decretis, <lb/>quibus in Galileum eiu&longs;dem &longs;ententiæ egregium & nunquam &longs;atis lauda<lb/>tum propugnatorem animadver&longs;um e&longs;t; &longs;ed non erat, quod tam alienum <lb/>animum o&longs;tentares. </s>

<s>Sed ta<lb/>men cum Michael <gap/>gnetus in rebus. </s>

<s id="s.000032"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>Mathematicis ex<lb/>cellens vit, ac Magi&longs;ter meus, cui ego plurimum debere me <lb/>fateor, ab <gap/> enim prim a<gap/>menta habui, vepo&longs;cere à me pu<lb/>blicum aliquem doctrine &longs;ua fructum videretur ac Fede<lb/>ricus Samini atus auius <gap/>onum &longs;uauitatem, & beneuol&ecedil;n<lb/>tiam erga me diu, dum &longs;imul bi&longs;ce studijs condi&longs;cipuli ope<lb/>ram dedimus, expertus &longs;um, me cut aliquid auderem tum <lb/>oratione, tum exomplo&longs;uo excitaret, c&oelig;pi minus ab ea cogi<lb/>tatione alienus e&longs;&longs;e. </s>

<s id="s.000033"> Vix me teneo, Augu&longs;tine, dum hæc à te audio, præter omnem <lb/>expectationem meam: odium vocas contrarium &longs;en&longs;um, ab&longs;que vllo im<lb/>moderato affectu, in iis præ&longs;ertim, in quibus opinari, cuique liberum <lb/>e&longs;t. </s>

<s id="s.000034">Nullo, crede mihi, odio, nullo contentionis &longs;tudio ducor; &longs;ed cùm <lb/>quædam in hypothe&longs;i Copernicana di&longs;pliceant, quæ in oppo&longs;ita nullum <lb/>mihi negotium face&longs;&longs;unt, facere non potui, quia hanc illi anteponerem; <lb/>nunquam tamen inficias iturus, præclarum inventum e&longs;&longs;e; Copernicum <lb/>A&longs;tronomorum &longs;ui temporis principem jure cen&longs;eri, eumque Galileum <lb/>fui&longs;&longs;e, qui nulli, quod &longs;ciam, impar ingenio æ&longs;timandus &longs;it, quique eo no<lb/>mine vel maximam gloriam &longs;ibi comparavit, quod argumenta, quibus <lb/>præfata hypothe&longs;is impugnabatur, ita diluerit, vt maximo inde plau&longs;u re<lb/>lato, ii&longs;dem illam potiùs confirma&longs;&longs;e videatur, cùm vero certum &longs;it, nec <lb/>ip&longs;e Galileus hoc inficietur, nullam demon&longs;trationem hucu&longs;que excogi<lb/>tatam fui&longs;&longs;e, qua hypothe&longs;is Copernicana probetur, ab antiqua illa, quæ <lb/>terram in mundi centro immobilem ad&longs;truit, di&longs;cedendum e&longs;&longs;e non puta<lb/>vi; præ&longs;ertim cùm hæc novis argumentis, &longs;i non demon&longs;trari, plurimùm <lb/>&longs;altem confirmari po&longs;&longs;it, quibus, vt liberè dicam, quod &longs;entio, mihi valdè <lb/>per&longs;ua&longs;um e&longs;t, hanc multis nominibus alteri e&longs;&longs;e anteponendam. </s>

<s>Deinde vero &longs;ummos vixos habui <pb/>hortatores. </s>

<s>Etenim cum Clauium, quod tam diu cupiebam, <lb/>vidi&longs;&longs;em <gap/> minerem ta<gap/>ientia, & fama viri bent, <lb/>gmtatem <gap/>peri&longs;&longs;em. </s>

<s id="s.000035"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000036"> Docti&longs;&longs;imis illis, tui certè amantibus, & quos &longs;ingulari etiam <lb/>cultu per&longs;equeris, haud modicum ri&longs;um moveres, <gap/>i hæc fortè à te audi<lb/>rent, nec vllum mihi dubium e&longs;t, quin per jocum, vel ironiam hæc à te <lb/>dici putarent, vtpote qui apprimè &longs;cias, Copernicanam hypothe&longs;im iis <lb/>rationum momentis in&longs;tructam e&longs;&longs;e, quæ vt demon&longs;trationem Geometri<lb/>cam minimè adæquant, quod certè vltrò damus, ita proximè ad eam acce<lb/>dunt, atque adeò communi Doctorum omnium con&longs;en&longs;u longè aliâ pro<lb/>babiliorem jure cen&longs;eri. </s>

<s>Ab eo &longs;imul ac Theodo&longs;io. </s>

<s>Rubeo ba <lb/>mine mihi tum ex &longs;tudiorum &longs;imilitudine, tum pracipue ex <lb/>eius humanitate amici&longs;simo, ad Reuerendi&longs;simum Sera<lb/>phinum deductus &longs;um. </s>

<s id="s.000037"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>I&longs;qs me tantus Præ&longs;ul non &longs;olum <lb/>humani&longs;sime complexus est, ver <gap/> ets am ita bo<gap/>tus ad <lb/>eualganda, que &longs;crip&longs;eram; plane vt mihi nefas putauerim <lb/>non parere. </s>

<s id="s.000038"> Hebetiori, quæ&longs;o, ingenio igno&longs;ce, optime Augu&longs;tine, quod <lb/>energiam illam rationum, quæ pro Copernico militant, nondum a&longs;&longs;equi <lb/>potuit; nec mirum profectò, lippos enim oculos &longs;ubtilia fallunt, ac &longs;e&longs;e <lb/>iis &longs;ubducunt; quate vt &longs;um inprimis veritatis amans, me tibi plurimùm <lb/>ob&longs;trinxeiis, &longs;i præfatas rationes ea mihi claritudine exponas, quâ, vt mi<lb/>rificè vales, ita & mihi opus e&longs;&longs;e fateor, ad debiliores mentis oculos re<lb/>creandos. </s>

<s>Aecipeigitur & tu Lactor optime amico ac be<lb/>uigno auimo laborem hunc, quem à me tali<gap/><lb/>&longs;umma benignitas expre&longs;sit. </s>

<s id="s.000039"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>Argumentum quidem, vt <lb/>dicob am non iniucundum e&longs;t, nec ab v&longs;u alienam. </s>

<s id="s.000040"> Non legi&longs;ti apud Galileum, ita limpidè ac per&longs;picuè explica<lb/>tas, vt nihil meo judicio, clarius aut liquidius legi po&longs;&longs;it? </s>

<s>Huiu&longs;<lb/>medi enim comparatione Archimides mixtionem argemi <lb/>in aure deprebeudit, & furtum Auri&longs;itis in corona aurea <lb/>patefecit. </s>

<s id="s.000041"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>de quæ re &longs;uo leco ego tractabo, & facilem mon<lb/>strabo viam, quæ vel argentum in aure, vel quod visme<lb/>tallum in quolibet admistum diprebeudi queat, & alte <lb/><gap/> ab aliero di&longs;rerni & &longs;imul explicabo, quo pacto ex au<lb/>ri grauitate <gap/> qualiras, <gap/>perfectio intelligi po&longs;sit. </s>

<s id="s.000042"> Legi haud dubiè; Vt enim Authorem illum maximi facio, ita <lb/>nihil ab eo in publicam lucem editum fuit, quod &longs;tatim avidè &longs;æpè ac &longs;æ<lb/>piùs non legerim; hoc tamen tibi per&longs;uadeas, velim, prædictas rationes, <lb/>quamvis alioquin eleganti&longs;&longs;imè ab eo explicatas, illa vi & nervo, vt dicis, <lb/>pollere mihi non videri, &longs;ingulas accuratè perpendi & ponderavi, nec op<lb/>po&longs;itæ &longs;ententiæ &longs;tudium obfuit; nam crede mihi; vnius dumtaxat veri<lb/>tatis amore ducor, quam &longs;ive Copernicus porrigat, &longs;ive Ptolemæus, &longs;ive <lb/>Ari&longs;toteles, &longs;ive Democritus; illa æquè grata & chara mihi &longs;emper accidit. <lb/></s>

<s id="s.000043">Sed quæ&longs;o te, periculum faciamus, vt &longs;altem dum no&longs;tri venerint, hoc mo<lb/>dicum tempus cum æ&longs;tu fallamus. </s>

<s><lb/>Tati vere apu&longs;culo nomen ab Arthimede, quem Ducem &longs;e<lb/>quer impo&longs;ui Nam cum ille, vt erat &longs;ummus Magi&longs;ter, &longs;e<lb/>tis haliui&longs;&longs;et hunc, totem qu<gap/> fabr<gap/> pe&longs;ito fundumen<lb/>to delineare in primo lib.

vbi agit de i&longs;s quæ vt huntur in <lb/>a quæ. </s>

<s id="s.000044"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000045"> Per me licert &longs;ed cur&longs;im, iis tamen prætermi&longs;&longs;is, quæ inter <lb/>Academicos quidem, non tamen inter Philo&longs;ophos locum obtinent, quas <lb/>potiùs rationum vmbras, quàm veras rationes appellare &longs;oleo. </s>

<s>Opus egapra<gap/> <expan abbr="eiq;">eique</expan> fundamenta molem inyce<lb/>re conatus &longs;um p<gap/>ribus &longs;uis etaberatam, atque dictin<lb/>ctam. </s>

<s>Qua in re &longs;i quid a&longs;&longs;equutus &longs;um, quod publice pro<lb/>betur, gaudeo cau&longs;a & mea & publica illud quidem &longs;pe<lb/>rofere vt conatus non di&longs;pliceat.<emph.end type="italics"/></s><pb pagenum="1"/>

<s id="s.000046"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000047"> Optimè judicas, quid enim juvat, tantirem momenti levi&longs;&longs;imis <lb/>fulcire adminiculis: Nonnulla obiter indico. </s>

<s>MARINI GHETALDI <lb/>PROMOTVS ARCHIMEDES <lb/>SEU.<emph type="italics"/>DE VARIIS CORPORVM GENERIBVS <lb/>Grauitate, & magnitudine comparatis.<emph.end type="italics"/></s>

<s id="s.000048">Sol, inquiunt, tes inter cor<lb/>poreas nobili&longs;&longs;imus, in nobili&longs;&longs;imo loco, &longs;cilicet in mundi centro, collo<lb/>cari debuit; qua&longs;i verò infimus locus &longs;upremo nobilior reputandus &longs;it, & <lb/>tenebro&longs;us orcus radianti præferendus Empyreo: &longs;ed pergunt, qui&longs;quis <lb/>alterius operâ indiget, ad illum accedere debet, neque hunc, &longs;ed illum <lb/>moveri par e&longs;t; cùm igitur reliqua corpora benigno Solis influxu indi<lb/>geant, hunc certè immotum con&longs;i&longs;tere, illa verò circa perennem illum <lb/>beneficæ naturæ fontem ite oportuit. </s>

<s id="s.000049">Bellè profectò; Solem rerum crea<lb/>tarum Principem faciunt, qui tamen omnibus &longs;ervit, & non modò ani<lb/>mantibus, verùm etiam plantis dignitate cedit; Æquum igitur e&longs;t, vt circa <lb/>terram eat, cuius gratia conditus e&longs;t, non verò vt tellus eiu&longs;que incolæ <lb/>circa Solem ite cogantur. </s>

<s>THEOREMAI. PROPOS. I.</s>

<s id="s.000050">Denique ex culina ip&longs;a nova depromunt argu<lb/>menta; Videmus, inquiunt, <expan abbr="ver&utilde;">verum</expan> ad immotum ignem in gyros verti, quod <lb/>certè rationi con&longs;entaneum e&longs;&longs;e videtur; quidni ergo pariter terre&longs;tris <lb/>globus, qui calore Solis foveri & recreari debet, circa Solem, non Sol cir<lb/>ca terram volvatur? </s>

<s id="s.000051">Hoc argumentum culinam olet, vnde profectum e&longs;t. </s>

<s>Si duorum Grauium Corporum eiu&longs;dem ge<lb/>neris alterum alterius fuerit multiplex, quo<lb/>tuplex maius fuerit minoris, totuplex erit <lb/>maioris grauitas, grauitatis minoris. </s>

<s>SINT duo corpora eiu&longs;dem generis ABC, D, quorum grauita<lb/>tes, EFG, ip&longs;ius ABC, & H, ip<lb/>&longs;ius D, &longs;it autem corpus ABC, <lb/><figure id="fig1"/><lb/>multiplex corporis D. </s>

<s id="s.000052"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000053"> Sed hæc omittamus, quæ no&longs;tri per jocum potiùs, quàm &longs;eriò <lb/>dixerunt; ad &longs;eria igitur & gravia, quæ nobis non de&longs;unt, veniendum e&longs;t: <lb/>illud inprimis maximi ponderis e&longs;&longs;e videtur, quod in hypothe&longs;i no&longs;tra <lb/>(&longs;ic eam di&longs;putan di gratia deinceps appellabo) per &longs;implici&longs;&longs;imum eum<lb/>que proprium motum omnia explicemus, ablegatis alienis motibus, <lb/>illoque præ&longs;ertim, quem raptus vocant, primi &longs;cilicet mobilis, quo ab Ortu <pb pagenum="4" xlink:href="025/01/008.jpg"/>ad Occa&longs;um inferiores &longs;phæræ tanta velocitate ferri dicuntur, vt &longs;tella <lb/>fixa &longs;ub Æquatore, vnico temporis minuto leucarum miriadas conficiat, <lb/>quod certè non fidem modo, verùm etiam cogitationem ip&longs;am &longs;uperat. <lb/></s>

<s>Dico quo <lb/>tuplex e&longs;t corpus ABC, corporis <lb/>D, totuplicem e&longs;&longs;e grauitatem, <lb/>EFG, grauitatis H, diuidatur <lb/>enim corpus ABC, in partes ip<lb/>&longs;i D, æquales, quæ &longs;int A, B, C, <lb/>quoniam igitur corpus A, æqua<lb/>le e&longs;t corpori D, magnitudine, <lb/>& &longs;unt eiu&longs;dem generis, erit grauitas vnius æqualis grauitati alterius. </s>

<s id="s.000054">Hunc porrò motum ablegamus, & &longs;implici ac diurna telluris globi circa <lb/>&longs;uum centrum turbinatione, &longs;eu revolutione præfatum motum &longs;up<lb/>plemus. </s>

<s><lb/>Sumatur grauitas E, æqualis grauitati H, erit igitur corporis A, gra<lb/>uitas E, & reliqui corporis BC, grauitas FG. </s>

<s id="s.000055"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>Rur&longs;us quoniam cor<lb/>pora B, D, &longs;unt magnitudine æqualia, erunt æquè grauia, &longs;umatur <lb/>grauitati H, æqualis grauitas F, erit igitur corporis B, grauitas F, & <lb/>reliqui corporis C, grauitas G, & &longs;ic fiat, donec perueniatur ad vlti<lb/>mam partem corporis ABC, æqualem ip&longs;i D, &longs;it ea vltima pars C, quo <lb/>niam igitur corpus C, æquatur magnitudine ip&longs;i D, æquabitur, & gra<lb/>uitate, quare grauitas G, æqualis erit grauitati H, &longs;equitur igitur <lb/>quot partes &longs;unt in corpore ABC, æquales ip&longs;i D, tot e&longs;&longs;e partes in <lb/>grauitate EFG, æquales ip&longs;i H, quoties enim &longs;ump&longs;imus in corpore <lb/>ABC, corpus ip&longs;i D æquale, toties & in grauitate EFG, &longs;ump&longs;imus <pb pagenum="2"/>grauitatem æqualem ip&longs;i H. </s>

<s id="s.000056"> Ab hoc vltimo incipio; quia nonnulli multam vim in eo fa<lb/>ciunt; cum tamen me parum, aut nihil pro&longs;us afficiat; nempe diver&longs;as <lb/>motuum velocitates per comparationem quamdam optimè intelligimus; <lb/>Sit enim quodlibet terræ punctum in æquatore, &longs;uppo&longs;ita ve&longs;tra hypo<lb/>the&longs;i, illud, vt probè no&longs;ti, in turbinatione præfati globi, præ&longs;cindendo <lb/>a motu centri, ita movetur, a&longs;&longs;umpto &longs;cilicet, quodam medio motu, vt vo<lb/>cant, vt &longs;ingulis horis 900. circiter miliaria Italica conficiat, 15.verò &longs;in<lb/>gulis minutis primis, vno denique &longs;ecundo minuto, 250. pa&longs;&longs;us geome<lb/>tricos, hoc e&longs;t 1250. pedes; vt autem comparationem in&longs;tituam, con&longs;ide<lb/>ro motum glandis plumbeæ ex maiore catapulta explo&longs;æ, quæ vno &longs;ecun<lb/>do minuto 1000. pedes circiter conficit; vnde vides punctum illud paulò <lb/>dumtaxat velociùs moveri. </s>

<s>Si duorum igitur grauium corporum <lb/>eiuldem generis, & c. quod erat demon&longs;trandum. </s>

<s id="s.000057"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000058"> Su&longs;tine tanti&longs;per; ne&longs;cio quid intelligas per illum medium <lb/>motum. </s>

<s>THEOREMA II. PROPOS. II.</s>

<s id="s.000059"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>Corpora grauia eiu&longs;dem generis magnitudine com <lb/>men&longs;urabilia, eandem in grauitate rationem ha<lb/>bent, quam in magnitudine. </s>

<s id="s.000060"> Intelligo motum æquabilem, ita vt &longs;ingulis horis punctum <lb/>illud æquale &longs;patium decurrere cen&longs;eatur, cùm tamen &longs;ecus ac<lb/>cidat. </s>

<s>SINT corpora commen&longs;urabilia eiu&longs;dem generis A, B, quorum <lb/>grauitates C, ip&longs;ius A, & D, ip&longs;ius B, Dico e&longs;&longs;e vt A, ad B, ita C, ad D, <lb/>quouiam enim, A, B, commen&longs;ura<lb/>bilia &longs;unt, metietur ip&longs;a aliquod <lb/>corpus, metiatur, & &longs;it E, cuius <lb/><figure id="fig2"/><lb/><arrow.to.target n="note1"/> grauitas F, &longs;itque corpus E, <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> <lb/>generis cum corporibus A, B, *ergo <lb/>quotuplex e&longs;t corpus A, ip&longs;ius E, <lb/><arrow.to.target n="note2"/> totuplex erit grauitas C, grauitatis <lb/>F, & quotuplex B, ip&longs;ius E, *totuplex <lb/>D, ip&longs;ius F, &longs;i igitur diuidantur cor<lb/>pora A, B, in partes æquales ip&longs;i E, <lb/>& grauitates quoque C, D, in partes æquales ip&longs;i F, erit vt corporie <lb/>A, pars vna, ad corpus E, ita pars vna grauitatis C, ad grauitatem F, <lb/>æquale videlicet ad æquale, & æque multiplicatis antecedentibus <lb/>erit vt A, ad E, ita C, ad F, &longs;unt enim antecedentium, hoc e&longs;t, illarum <lb/>partium æque multiplicia A, C, eadem ratione, vt B, ad E, ita erit D, <lb/>ad F, & conuertendo vt E, ad B, ita F, ad D. quoniam igitur vt A, ad <lb/><arrow.to.target n="note3"/> E, ita e&longs;t C, ad F, & vt E, ad B, ita F, ad D, * erit ex æquali vt A, ad <lb/>B, ita C, ad D. corpora igitur commen&longs;urabilia eiu&longs;dem generis ean<lb/>dem in grauitate rationem habent, quam in magnitudine, quod erat <lb/>demon&longs;trandum. </s>

<s id="s.000061"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s><margin.target id="note1"/><emph type="italics"/>Ex an<lb/>teced.<emph.end type="italics"/></s>

<s id="s.000062"> Non capio, exi&longs;timo enim rem ita e&longs;&longs;è, & æqualibus tempo<lb/>ribus, æqualia &longs;patia decurri. </s>

<s><margin.target id="note2"/><emph type="italics"/>Ex an<lb/>teced.<emph.end type="italics"/></s>

<s id="s.000063"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000064"> Ita &longs;anè nobis apparet, id tamen haud dubiè per errorem; <lb/>nempe punctum illud motu quodam mixto movetur, ex motibus orbis <lb/>& centri, &longs;ic enim vocare &longs;oles; Vnde fit, vt pro diver&longs;o ad &longs;olem a&longs;pectu, <lb/>modò tardiùs, modò velociùs moveatur; quia motus orbis ab hora &longs;exta <lb/>ve&longs;pertina ad &longs;extam oppo&longs;itam matutinam additur motui centri, ab hac <lb/>verò ad illam detrahitur; ac proinde punctum illud in meridie collocatum <lb/>tardi&longs;&longs;imè in a&longs;pectu oppo&longs;ito, &longs;cilicet, mediænoctis, veloci&longs;&longs;imè movetur <lb/>quod vt ad rudiores calculos reducam, &longs;uppono, exempligratia, diametrum <lb/>magni orbis, quem Sol&longs;ecundùm meam, & terra &longs;ecundùm ve&longs;tram hypo<lb/>the&longs;im decurrit, continere diametros terræ 2000. hoc po&longs;ito, motu centri, <lb/>vno &longs;ecundo minuto, decurruntur pedes circiter 6942. & motu orbis pe<lb/>des 1250. adde vnum alteri, venient pedes 8192.hoc e&longs;t &longs;patium, quod di<lb/>ctum punctum decurritin media nocte, tempore vnius &longs;ecundi minuti <lb/>detrahe verò, erunt pedes 5692. hoc e&longs;t, &longs;patium, quod eodem tempore, <lb/>decurrit in meridie; Vides inæqualitatem. </s>

<s id="s.000065">Semoto igitur illo inæquali <lb/>motu, ex motibus orbis & centri re&longs;ultante, æqualem tantummodò con&longs;i<lb/>dero motum orbis, quo punctum terre&longs;tris globi in Æquatore, &longs;ingulis mi<lb/>nutis &longs;ecundis, pedes circiter 1250.decurrit. </s>

<s>THEOREMA III. PROPOS. III.</s>

<s>Et incommen&longs;urabilia corpora eiu&longs;dem generis <lb/>eandem in grauitate rationem habent, quam in <lb/>magnitudine. </s>

<s id="s.000066"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>SINT incommen&longs;urabilia corpora A, BC, quorum grauitates <lb/>D, ip&longs;ius A, & EF, ip&longs;ius BC. </s>

<s id="s.000068">Non video, quid tibi velis, ad infirmandum <lb/>illud argumentum, quod ab incredibili velocitate motus raptus, &longs;eu <pb pagenum="5" xlink:href="025/01/009.jpg"/>primi mobilis contra ve&longs;tram hypothe&longs;im ducitur. </s>

<s>Dico e&longs;&longs;e vt A, ad BC, ita D, ad EF, &longs;i <pb pagenum="3"/>enim non e&longs;t vt A, ad BC, ita D, ad EF, erit vt A, ad BC, ita D, vel ad <lb/><figure id="fig3"/><lb/>minorem quam EF, <lb/>vel ad maiorem, &longs;it <lb/>primum ad minoré, <lb/>pempe ad EG, & ex<lb/>ponatur aliquod cor <lb/>pus K, eiu&longs;dem gene<lb/>ris cum corporibus <lb/>A, B C, cuius graui<lb/>tas &longs;it æqualis ip&longs;i <lb/>GF, & à corpore BC, <lb/>auferatur aliqua <lb/>pars HC, quæ &longs;it mi<lb/>nor corpore K, ita vt reliquæ pars. </s>

<s id="s.000069"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>BL, &longs;it commen&longs;urabilis ip&longs;i A. & <lb/>&longs;it partis HC, grauitas IF, ergo reliquæ partis BL, grauitas erit EI. </s>

<s id="s.000070"> Jam iam videbis. </s>

<s id="s.000071">Suppone terre&longs;tem globum in mundi centro, <lb/>eo motu orbis torqueri, de quo &longs;upra; &longs;uppone radium à centro terræ <lb/>in Æquatoris plano ductum indefinitè, vt aiunt, id e&longs;t, ad quamcumque <lb/>longitudinem productum, eatque per centra Lunæ, Solis, lovis, Satur<lb/>ni, & cuiu&longs;piam &longs;tellæ fixæ, ac &longs;imul totus radius, eo, quo dixi orbis mo<lb/>tu, moveatur circa immobile centrum; certè po&longs;ito quod Luna di&longs;tet a <lb/>terra 50. &longs;emidiametris terre&longs;tris globi, velocitas motus Lunæ ad veloci<lb/>tatem puncti Æquatoris in quo dictus radius terræ &longs;uperficiem &longs;ecat e&longs;t <lb/>in ratione <gap/> & ad velocitatem motus Solis, po&longs;ito quod Sol di&longs;tet à <lb/>centro terræ 2000. &longs;emidiametris e&longs;t in ratione <gap/> Solis verò motus ad <lb/>Iovis motum, erit in rationne <gap/> & ad motum Saturni in ratione <gap/> de<lb/>nique ad &longs;tellæ fixæ motum in ratione, &longs;tatue, vt voles, an fortè <gap/> ita <lb/>vt fixarum di&longs;tantia à mundi centro &longs;it dupla di&longs;tantia Saturnij, tibi non <lb/>&longs;ufficit? </s>

<s><lb/>Quoniam igitur corpus A, commen&longs;urabile e&longs;t ip&longs;i BL,* erit vt A, ad<arrow.to.target n="note4"/><lb/>BL, ita D, ad EI, &longs;ed vt A, ad BC, ita e&longs;t D, ad EG, atque A, primus, <lb/>proportionalium terminus in &longs;erie prima, * maiorem habet<arrow.to.target n="note5"/> ratio<lb/>nem ad BL, &longs;ecundum terminum, quam A, primus terminus in &longs;erie <lb/>&longs;ecunda ad BC, &longs;ecundum; ergo & D, tertius terminus in &longs;erie prima <lb/>ad EI, quartum, maiorem habebit rationem quam D, tertius termi<lb/>nus in &longs;erie &longs;ecunda ad EG, quartum, quoniam igitur D, maiorem<arrow.to.target n="note6"/><lb/>habet rationem ad EI, quam ad EG,* erit EI, minor quam EG, quod <lb/>e&longs;t ab&longs;urdum. </s>

<s id="s.000072">Ponamus <gap/> ita vt &longs;it quintupla, aut majorem adhuc, &longs;i voles; <lb/>an verò cogitationem omnem &longs;uperat, vnum motum e&longs;&longs;e ad alium in ra<lb/>tione quater decupla, immò centupla & millecupla? </s>

<s id="s.000073">Crede mihi, hi &longs;unt <lb/>effectus imaginationis in fraudem inductæ; Vbi enim &longs;emel &longs;tatuitur vnus <lb/>motus, & huius cum aliis comparatio, huiu&longs;modi terricula illicò eva<lb/>ne&longs;cunt. </s>

<s>non igitur e&longs;t vt A, ad BC, ita D, ad minorem quam EF. </s>

<s><margin.target id="note4"/>E<emph type="italics"/>x an<lb/>teced<gap/><emph.end type="italics"/></s>

<s id="s.000074"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000075"> Rem probè intelligo; & &longs;anè miror, nonnullos in hoc argu<lb/>mento tantam vim & energiam agnovi&longs;&longs;e, vt præ cæteris ad illam hypo<lb/>the&longs;im confirmandam adhibendum e&longs;&longs;e putarint: non erat etiam <lb/>quod aliqui antiqui &longs;y&longs;tematis a&longs;&longs;ertores, & acerrimini propugnato<lb/>res ad divinam potentiam confugerent, licèt illa in tanta motuum <lb/>velocitate mirificè &longs;plende&longs;cere nec non &longs;uas partes agere vi<lb/>deatur. </s>

<s id="s.000076"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000077"> Rectè mones, Augu&longs;tine, huc divina potentia accer&longs;enda <lb/>non e&longs;t, cùm ex mera motus naturalis acceleratione, hæc eadem pe&longs;picua <lb/>e&longs;&longs;e con&longs;tet; &longs;ic enim v. g. motus glandis ex catapulta explo&longs;æ, vt dictum <lb/>e&longs;t &longs;upra, quo &longs;cilicet vno &longs;ecundo minuto, glans pedes circiter 1000. <lb/>decurrit, æquabilis e&longs;&longs;e &longs;upponitur; iam verò &longs;i eadem catapulta &longs;ursùm <lb/>rectà explodatur, de 500.dumtaxat pedes motu retardato glans perveniet, <lb/>& in de&longs;cen&longs;u eundem velocitatis gradum motu accelerato acquiret; <lb/>cùm igitur quælibet altitudo a&longs;&longs;umi queat ad libitum, ex qua corpus <lb/>grave de&longs;cendat motu accelerato, quilibet etiam velocitatis gradus ob<lb/>tineri pote&longs;t; quo dato tempore, datum quodlibet &longs;patium, motu æqua<lb/>bili decurratur, igitur prædicta motuum velocitas inter præcipua divi<lb/>næ potentiæ miracula minimè reponenda e&longs;&longs;e videtur; quamquam, ne<lb/>que hîc dee&longs;t, vnde divinam potentiam homines laudent, cùm id in &longs;a<lb/>cris literis nobis innuatur, laudet que P&longs;almi&longs;ta Dominum, ex pernici&longs;&longs;i<lb/>mo Solis motu, nec e&longs;t, quod Heterodoxi, qui &longs;acræ Scripturæ ita &longs;e ad<lb/>hærere patant, a literali eiu&longs;dem &longs;en&longs;u, vnius Copernici gratia di&longs;cedant, <lb/>ea&longs;que laudes ex eo capite &longs;upremo c&oelig;lorum Conditori atque motori <lb/>Deo, gratis, vt aiunt, recu&longs;ent. </s>

<s>Deinde &longs;it vt A, ad BC, ita D, ad maiorem quam EF, nempe ad <lb/><figure id="fig4"/><lb/>EG, & expo&longs;ito cor<lb/>pore K, vt dictum <lb/>e&longs;t, cuius grauitas, <lb/>&longs;it æqualis grauita<lb/>ti FG, addatur cor<lb/>pori BC, aliquod <lb/>corpus CH, quod &longs;it <lb/>minus corpore K, & <lb/>eiu&longs;dem generis cú <lb/>corporibus A, BC, <lb/>ita vt totum corpus <lb/>BL, &longs;it commen&longs;urabile ip&longs;i A, & &longs;it ip&longs;ius CH, grauitas FI, ergo to<lb/>tius corporis BL, grauitas erit EI; Quoniam igitur corpori A, com<lb/>men&longs;urabile e&longs;t corpus BL,* erit vt A, ad BL, ita D, ad EI, &longs;ed vt A, ad<arrow.to.target n="note7"/><lb/>BC, ita e&longs;t D, ad EG, atque A, primus proportionalium terminus in <lb/>&longs;erie prima, * minorem habet rationem ad BL, &longs;ecundum terminum, <pb pagenum="4"/>quam A, primus terminus in &longs;erie &longs;ecunda ad BC, &longs;ecundum, ergo, & <lb/>D, tertius terminus in &longs;erie prima ad EI, quartum, minorem habebi<gap/><lb/>rationem quam D, tertius terminus in &longs;erie &longs;ecunda ad EG, quartum. </s>

<s><lb/>Quoniam igitur D, minorem habet rationem ad EI, quam ad EG, <lb/><arrow.to.target n="note8"/> erit * EI, maior quam EG, quod e&longs;t ab&longs;urdum. </s>

<s id="s.000078"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>Non igitur e&longs;t vt A, <lb/>ad BC, ita D, ad maiorem quam EF, o&longs;ten&longs;um autem e&longs;t neque ad mi<lb/>norem; quare vt A, ad BC, ita erit D, ad EF. & incommen &longs;urabilia igi<lb/>tur corpora eiu&longs;dem generis eandem in grauitate rationem habent, <lb/>quam in magnitudine, quod erat demon&longs;trandum. </s>

<s id="s.000079"> Benè e&longs;t, in hoc vterque convenimus, &longs;ecùs fortè in alio <lb/>puncto, à me propo&longs;ito, quod à facilitate & &longs;implicitate &longs;y&longs;thematis peti<lb/>tur; vno enim, vel altero terre&longs;tis globi motu no&longs;tra hypothe&longs;is con&longs;tat, <lb/>cùm tamen ve&longs;tra motus ita multiplicet, etiam &longs;ibi invicem contrarios, vt <lb/>res illa, vel omnino impo&longs;&longs;ibilis, vel &longs;altem maximè difficilis e&longs;&longs;e videa<lb/>tur. </s>

<s><margin.target id="note7"/><emph type="italics"/>Ex an <lb/>teced..<emph.end type="italics"/><lb/><gap/><emph type="italics"/>Ele<emph.end type="italics"/></s>

<s id="s.000080"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000081"> Primo &longs;anè a&longs;pectu, rem i&longs;tam minùs &longs;edulò con&longs;ideranti, ita <lb/>e&longs;&longs;e videtur; &longs;i tamen penitiùs illam in&longs;piciamus; primum errorem faci<lb/>lè ca&longs;tigabimus: & verò vt in vno Solis &longs;y&longs;temate periculum facia<lb/>mus, quotuplice motus opus e&longs;&longs;e putas ad &longs;alvanda omnia phæno<lb/>mena? </s>

<s>ID QVOD nos duobus præcedentibus Theorematis de<lb/>mon&longs;trauimus, <expan abbr="nõnulli">nonnulli</expan>, vt per &longs;e notum, & vt commune quod<lb/>dam axioma &longs;upponunt, quam bene & rationabiliter ip&longs;i vide<lb/>rint; melius enim Euclides propo&longs;itionem 20. primi libri Ele<lb/>mentorum &longs;uppo&longs;ui&longs;&longs;et vt pronunciatum; vnicuique enim no<lb/>tius e&longs;t duo trianguli latera reliquo e&longs;&longs;e maiora (cum & Afino <lb/>illud &longs;it notum) quam corpora grauia ciu&longs;dem generis eandem <lb/>in grauitate rationem habere, quam in magnitudine, & tamen <lb/>illam propo&longs;itionem demon&longs;trat Euclides, non &longs;upponit, non <lb/>igitur hæc, quæ minus ad principij rationem accedit, &longs;uppo<lb/>nenda fuit, &longs;ed demon&longs;tranda. </s>

<s id="s.000082"><emph type="italics"/>Augu&longs;lin.<emph.end type="italics"/></s>

<s>THEOREMA IV. PROPOS. IV.</s>

<s id="s.000083"> Duo motus, ni fallor, omnia &longs;alvant, orbis &longs;cilicet & centri, <lb/>terre&longs;tris globi, quie&longs;cente Sole in mundi centro. </s>

<s>Si quatuor corporum grauium primum ad <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <lb/>eandem in magnitudine rationem habeat, quam <lb/>tertium ad quartum, primum autem, & &longs;ecundum &longs;int <lb/>eiu&longs;dem generis, itidem tertium, & quartum; & in gra<lb/>uitate primum ad &longs;ecundum eandem rationem habebit, <lb/>quam tertium ad quartum. </s>

<s id="s.000084"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>PRIMVM enim A, ad &longs;ecundum B, eandem in magnitudine ra<lb/>tionem habeat, quam tertium C, ad quartum D, &longs;int autem A, B, <lb/>eiu&longs;dem generis, itidem C, D. Dico. </s>

<s id="s.000085"> Tibi omnino impo&longs;itum fuit, vel vt verius puto, tibi excidit, <lb/>Primò enim, motu <expan abbr="c&etilde;tri">centri</expan> opus e&longs;t; annuo, &longs;cilicet in Ecliptica, iuxta &longs;eriem <lb/>&longs;ignorum, nec qui&longs;quam hoc negat: Secundò, motu orbis diurno, quo <lb/>terra ita rotatur, vt pars &longs;uperior globi tendat in ortum; hîc autem mo<lb/>tus fit circa axem mundi, vel plani Æquatoris. </s>

<s id="s.000086">Terrius motus nece&longs;&longs;a<lb/>rius e&longs;t, annuus &longs;cilicet, quo terra ita &longs;emel voluitur circa Axem Eclipticæ, <lb/>vt pars inferior, quæ Solem &longs;pectat, tendát in ortum; hoc enim motu obti<lb/>netur, vt Axis Æquatoris &longs;ibi ip&longs;i &longs;emper maneat parallelus; aliquis fortè <lb/>per incogitantiam quartum motum etiam adhiberet, quo &longs;cilicet Axis <lb/>Æquatoris vtrimque de&longs;cribit circulos polares, circa polos Eclipticæ, &longs;ed <lb/>hic motus à tertio diver&longs;us non e&longs;t, vt con&longs;ideranti patebit, & licèt aliqui <lb/>etiam ex iis, qui terram mobilem ad&longs;truunt, hunc diver&longs;um motum &longs;ta<lb/>tuant, ego tamen, vt &longs;incerè tecum ago, diver&longs;um à motu orbis annuo mi<lb/>nimè &longs;tatuo. </s>

<s>& in grauitate primum A, ad <lb/>&longs;ecundum B, eandem rationem habere, quam tertium C, ad D, quar<lb/>tum. </s>

<s id="s.000087">Addo denique quartum motum Solis, circa proprium cen<lb/>trum, axemque immobilem, & inclinatum ad planum Eclipticæ, &longs;ine quo <lb/>macularum motus 27. circiter dierum explicari nequit: hunc etiam ne<lb/>mo ve&longs;trum inficiatur. </s>

<s>Sint enim earum grauitates E, ip&longs;ius A, & F, ip&longs;ius B, ip&longs;ius <lb/>vero C, &longs;it grauitas G, & ip&longs;ius D, grauitas H, quoniam igitur cor-<pb pagenum="5"/><figure id="fig5"/><lb/>pora A, B, eiu&longs;dem &longs;unt generis, <lb/>&longs;imiliter, & corpora C, D,* erit <lb/>vt A, ad B, ita E, ad F,* & vt<arrow.to.target n="note9"/><lb/>C, ad D, ita G, ad H. </s>

<s id="s.000088"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>Sed poni<lb/>tur vt A, ad B, ita e&longs;&longs;e C, ad D, <lb/>ergo vt E, ad F, ita erit G, ad <lb/>H. </s>

<s id="s.000089"> Cuncta hæc et&longs;i vltro damus, nihil tamen ob&longs;tat, quin adhuc <lb/>&longs;y&longs;tema no&longs;trum &longs;implicius e&longs;&longs;e dicamus, & ex paucioribus motibus, <lb/>quàm ve&longs;trum componi. </s>

<s id="s.000090">Ve&longs;trum enim, &longs;i rectè memini, in vno Solo 7. <lb/>vel 8. motus po&longs;tulat. </s>

<s>Si igitur quatuor corporum <lb/>grauium, primum ad &longs;ecundum <lb/>eandem in magnitudine ratio<lb/>nem habeat: etcæt. </s>

<s id="s.000091">Primus e&longs;t motus raptus, &longs;eu primi Mobilis ab or<lb/>tu ad occa&longs;um, &longs;cilicet diurnus: &longs;ecundus, motus in Ecliptica annuus; <lb/>tertius, motus Solis circa proprium axem inclinatum, ferè men&longs;truus: <lb/>quartus motus eju&longs;dem circa axem erectum ad planum Eclipticæ, an<lb/>nuus: quintus motus prioris axis inclinati, de&longs;cribentis vtrinque circellos <lb/>circa Solarem axem erectum ad planum Eclipticæ, item annuus: &longs;extus, <lb/>motus Apogæi Solis iuxta &longs;eriem &longs;ignorum: &longs;eptimus motus præce&longs;&longs;io<lb/>nis Æquinoctiorum; octavus motus obliquitatis Zodiaci, vt vocant: et&longs;i <lb/>fortè mutetur excentricitas, de quo nonnulli dubitarunt: nonus motus <lb/>adjiciendus e&longs;&longs;et; vides, quantam motuum farraginem &longs;y&longs;tema ve&longs;trum <lb/>po&longs;tulet: quorum aliqui, cùm &longs;int oppo&longs;iti, vt annuus & men&longs;truus &longs;olaris <lb/>globi, quantumvis circa diver&longs;os axes, nec aliunde in &longs;olarem &longs;phæram <pb pagenum="7" xlink:href="025/01/011.jpg"/>traducantur, &longs;ed vterque per &longs;e, vt aiunt, Soli competat, inde &longs;ortè <lb/>ture cuipiam impo&longs;&longs;ibiles videbuntur. </s>

<s>quod demon<lb/>&longs;trare oportebat. </s>

<s id="s.000092"><emph type="italics"/>Antimus,<emph.end type="italics"/> Ita luditis &longs;impliciorum animos maioris &longs;implicitatis obtentu; <lb/>& dubito, an &longs;eriò, an verò per iocum hæc dicas; tu quoque imponere <lb/>mihi cogitabas; Apage igitur prefatam motuum farraginem; ego enim <lb/>vnum dumtaxat, cumque &longs;implici&longs;&longs;imum motum admitto in &longs;olari &longs;y&longs;te<lb/>mate, quod ne&longs;cio, an mirum tibi accidat. </s>

<s><margin.target id="note9"/>2. & <gap/>. <lb/><emph type="italics"/>huius<emph.end type="italics"/></s>

<s>THEOREMA V. PROPOS. V.</s>

<s id="s.000093"><emph type="italics"/>Augu&longs;lin.<emph.end type="italics"/></s>

<s id="s.000094"> Mirum pror&longs;us, immò fal&longs;um, neque id, opinor mihi vn<lb/>quam per&longs;uadebis; cum per&longs;picuum &longs;it (neque ve&longs;tri hoc negant) ad Sal<lb/>vanda cuncta phænomena, prædictos omnes motus, &longs;i fortè vltimum ex<lb/>cipias, quem non ita omnes a&longs;&longs;everanter ad&longs;truunt, nece&longs;&longs;arios e&longs;&longs;e. </s>

<s>Solida corpora liquido grauiora demi&longs;&longs;a in liquidum <lb/>ferentur deoríum, donec de&longs;cendant, & erunt in li<lb/>quido tanto leuiora, quanta e&longs;t grauitas liquidi magni<lb/>tudinem habentis &longs;olido corpori æqualem. </s>

<s>HOC autem demon&longs;tratum e&longs;t ab Archimede propo&longs;.7. primi li<lb/>bri de ijs, quæ vehuntur in aqua. </s>

<s id="s.000095"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000096"> Ne quæ&longs;o dubites, vbi rem a me intellexetis, tibi fortè per<lb/>&longs;uaderi &longs;ines; ea quippe dicam quæ, ni fallor, luce meridiana clariora &longs;int. <lb/></s>

<s>THEOREMA VI. PROPOS. VI.</s>

<s id="s.000097">Sol vno Eodemque motu &longs;implici&longs;&longs;imo movetur ab ortu ad occa&longs;um, &longs;ub <lb/>Ecliptica <expan abbr="s&etilde;per">semper</expan> mobili, circa axem mundi cum duplici inclinatione, <expan abbr="&longs;urs&utilde;">&longs;ursum</expan>, <lb/>deor&longs;um, &longs;ini&longs;tro&longs;um; & rotatione, &longs;eu turbinatione, circa axem æquè in<lb/>clinatum ad planum Eclipticæ, ac &longs;ibi &longs;emper parallelum. </s>

<s id="s.000098">En tibi mo<lb/>tum &longs;implicidimum, quo &longs;uppo&longs;ito, cuncta facile ac planè explicantur. </s>

<s>Si quatuor grauium corporum primum, & &longs;ecundum <lb/>fuerint magnitudine æqualia, tertium vero, & quar<lb/>tum æque grauia, fuerint autem primum, & tertium <lb/>eiu&longs;dem generis, itidem &longs;ecundum, & quartum; erit, vt <lb/>grauitas corporis primi, ad grauitatem &longs;ecundi, ita gra<lb/>uitas liquidi æqualis magnitudine corpori quarto, ad gra<lb/>uitatem liquidi tertio corpori æqualis. </s>

<s>SINT quatuor corpora A, B, C, D, quorum A, primum, & B, &longs;e<lb/>cundum &longs;int magnitudine æqualia, tertium vero C, & D, quartum <lb/>æque grauia, &longs;int autem A, & C, eiu&longs;dem generis, itidem B, & D. </s>

<s id="s.000099"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000100"> Non intelligo; immò hæc mihi ab&longs;urda & repugnantia e&longs;&longs;e <lb/>videntur; nec capere po&longs;&longs;um, quî fiat vt omnia facile & plané hoc modò <lb/>explice utur. </s>

<s>Di<lb/>eo vt grauitas corporis A, ad grauitatem corporis B, ita e&longs;&longs;e grauita<lb/>tem liquidi æqualis magnitudine corpori D, ad grauitatem liquidi <lb/>magnitudine corpori C, æqualis. </s>

<s>Accipiantur enim tria eiu&longs;dem ge-<pb pagenum="6"/>neris liquidi corpora E, F, G, quorum E, &longs;it æquale corpori A, vel B, <lb/><figure id="fig6"/><lb/>magnitudine, ip&longs;um vero F, æqua <lb/>le corpori C, & ip&longs;um G, æquale <lb/>corpori D. </s>

<s id="s.000101"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000102"> Cuncta &longs;eor&longs;im explico, Cogita, &longs;i vis, Solem à puncto Æqui<lb/>noctij verni ab ortu ad occa&longs;um ita ferri, vt po&longs;t 24. horarum motum, <lb/>orbem &longs;uum nondum ab&longs;olverit, &longs;uper&longs;itque vnus ferè gradus, paulò <lb/>minùs; fing<gap/> tantula &longs;imul Solem inclinatione ire versùs Boream, & <lb/>&longs;igna vtriu&longs;que loci in c&oelig;lo ve&longs;tigia, atque ita deinceps moveri Solem <lb/>puta, &longs;ignatis &longs;ingulorum locorum ve&longs;tigiis; vbi verò Sol ad Tropicum <lb/>Cancri pervenerit, &longs;uppone qua&longs;i repercu&longs;&longs;um versùs Au&longs;trum eodem <lb/>modo deflectere, multiplicatis revolutionibus, donec ad Tropicum Ca<lb/>pricorni perveniat, a quo eodem modo versùs Boream deflectat donec <lb/>tandem ad Æquatorem denuò redeat; per &longs;ignata ve&longs;tigia &longs;i ducas circu<lb/>lum,, erit Ecliptica, quam circa mundi Axem finges moveri, & ab eius <lb/>polis circulos polares de&longs;cribi; ita autem &longs;ol attemperat reciprocam il<lb/>lam inclinationem, &longs;eu declinationem versùs Au&longs;trum & Boream, vt <lb/>nunquam à prædicto Eclipticæ circulo di&longs;cedat, quod quomodò obtineat, <lb/>paulò po&longs;t dicam. </s>

<s>Quoniam igitur e&longs;t vt <lb/>D, ad G, ita B, ad E, æquale vi<lb/>delicet ad æquale, erit permutan<lb/>do vt D, ad B, ita G, ad E, & quo<lb/>niam &longs;unt eiu&longs;dem generis corpo<lb/>ra D, B, &longs;imiliter & corpora G, E, <lb/><arrow.to.target n="note10"/> erit * vt grauitas corporis D, hoc <lb/>e&longs;t ip&longs;ius C, ponuntur enim æque <lb/>grauia corpora C, D, ad grauita<lb/>tem corporis B, ita liquidi G, gra<lb/>uitas ad grauitatem liquidi E. </s>

<s><lb/>Similiter quoniam e&longs;t vt A, ad E, <lb/>ita C, ad F, æquale videlicet ad <lb/>æquale, erit permutando vt A, ad <lb/>C, ita E, ad F, & quoniam ponuntur eiu&longs;dem generis corpora A, C, <lb/><arrow.to.target n="note11"/> itidem E, F,* erit vt grauitas corporis A, ad grauitatem ip&longs;ius C, ita <lb/>liquidi E, grauitas ad grauitatem liquidi F, &longs;ed vt grauitas corporis <lb/>C, ad grauitatem corporis B; ita e&longs;t grauitas liquidi G, ad grauita<lb/><arrow.to.target n="note12"/>tem liquidi E, vt e&longs;t demon&longs;tratum, ergo * in perturbata proportione <lb/>erit vt grauitas corporis A, ad ip&longs;ius corporis B, grauitatem, ita liqui <lb/>di G, grauitas, ad grauitatem liquidi F. &longs;i igitur quatuor grauium <lb/>corporum primum, & &longs;ecundum, & c. quod erat demon&longs;trandum. </s>

<s id="s.000103"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000104"> Sed i&longs;ti &longs;unt duo motus, alter cuiu&longs;dam qua&longs;i librationis, al<lb/>ter circularis. </s>

<s><margin.target id="note10"/>2. & 3. <lb/><emph type="italics"/>huius.<emph.end type="italics"/></s>

<s id="s.000105"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000106"> Vnicus e&longs;t motus, augu&longs;tine, &longs;ed per modum &longs;piræ; quis enim <lb/>negat turbinem proiectum &longs;implici motu moveri, id e&longs;t, eodem impetu <lb/>ad talem lineam determinato; nempe hoc &longs;uppono cerrum, ex alibi firma<lb/>ta motuum doctrina, eundem impetum ad diver&longs;as lineas determinati po&longs;<lb/>&longs;e, &longs;ic pila repercu&longs;&longs;a &longs;implici motu movetur, licet linea motus per quam <lb/>feretur, duplicem determinationem &longs;upponat &longs;cilicet à linea motus <lb/>directi, & à plano reflectente; Non e&longs;t igitur dubium, quin prædictus <pb pagenum="8" xlink:href="025/01/012.jpg"/>Solis motus &longs;implici&longs;&longs;imus &longs;it. </s>

<s><margin.target id="note11"/>2. & 3. <lb/><emph type="italics"/>huius.<emph.end type="italics"/></s>

<s id="s.000107">Pati modo cogita Solem &longs;imul inclinari <lb/>ab Apogeo ad Perigeum, & vici&longs;&longs;im, hæc &longs;ecunda determinatio, vel in<lb/>clinatio &longs;implici motui non obe&longs;t, vt patet: In hoc porrò motu, Ecliptica <lb/>etiam mo<gap/>ri fingitur circa Axem mundi, ac proinde Eclipticæ &longs;ectio in <lb/>Solari globo eadem &longs;emper e&longs;t; denique, finge, Solem circa &longs;uum cen<lb/>trum ita revolvi 27. circiter dierum &longs;patio, ab ortu in occa&longs;um, ratione il<lb/>lius hemi&longs;phærij, quod ad terram &longs;pectat, vt axis, circa quem voluitur, in<lb/>clinatus &longs;it ad Eclipticæ planum, & &longs;ibi &longs;emper parallelus; quod &longs;anè &longs;im<lb/>plicitatem motus non de&longs;truit; &longs;ic enim &longs;æpè ac &longs;æpiùs globos projicimus; <lb/>imò hic naturalis e&longs;t globorum motus. </s>

<s id="s.000108"><emph type="italics"/>Augu&longs;tinus.<emph.end type="italics"/></s>

<s>THEOREMA VII. PROPOS. VII.</s>

<s id="s.000109"> Duo &longs;unt motus, ni fallor, orbis, &longs;cilicet, & centri &longs;implex <lb/>igitur motus non e&longs;t. </s>

<s>Si quatuor grauium corporum primum, & <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan>, <lb/>fuerint magnitudine æqualia, tertium vero, & quar<lb/>tum æque grauia, fuerint autem primum, & tertium <lb/>eiu&longs;dem generis, itidem &longs;ecundum, & quartum; primum <lb/>ad &longs;ecundum eandem in grauitate rationem habebit, <lb/>quam habet in magnitudine quartum ad tertium. </s>

<s id="s.000110"><emph type="italics"/>Antimus.<emph.end type="italics"/></s>

<s>SINT quatuor grauia corpora A, B, C, D, quorum A, primum, <lb/>& B, &longs;ecundum &longs;int magnitudine æqualia, tertium vero C, & D, quar<lb/>tum æque grauia, &longs;int autem A, & C, eiu&longs;dem generis, itidem B, & <lb/>D. </s>

<s id="s.000111"> Igitur motus naturalis, quo corpus grave, v.g. globus fertur <lb/>deor&longs;um non e&longs;t motus &longs;implex, &longs;ed mixtus, quod nemo dixerit, cum &longs;im<lb/>plici&longs;&longs;imus &longs;it, vtpote ab eodem principio, &longs;cilicet à gravitate: &longs;i enim de<lb/>mittas globum, primò quidem per planum inclinatum, ex quo inde per li<lb/>berum aëra perpendiculariter de&longs;cendat, videbis illicò duos illos motus <lb/>quos dicis, centri & orbis; qui tamen reverà duo motus non &longs;unt, &longs;ed vnus <lb/>ab vna eademque gravitate profectus. </s>

<s>Dico corpus A, eandem in grauitate rationem habere ad corpus <pb pagenum="7"/>B, quam corpus D, habet in magnitudine ad C, corpus. </s>

<s id="s.000112"><emph type="italics"/>Augu&longs;tinus.<emph.end type="italics"/></s>

<s>Sit enim li<lb/><figure id="fig7"/><lb/>quidi magnitudine æqualis corpo<lb/>ri C, grauitas E, &longs;imiliter, & liqui<lb/>di æqualis magnituline corpori D, <lb/>grauitas F, quoniam igitur gra<lb/>uia corpora eiu&longs;dem generis, ean<lb/>dem in magnitudine rationem*<arrow.to.target n="note13"/> ha<lb/>bent, quam in grauitate, erit vt ma<lb/>gnitudo liquidi æqualis corpori D, <lb/>ad magnitudinem liquidi æqualis <lb/>corpori C, hoc e&longs;t, vt magnitudo <lb/>corporis D, ad magnitudinem cor<lb/>poris C, ita grauitas F, ad grauita<lb/>tem E, &longs;ed vt grauitas F, ad grauitatem E, * ita e&longs;t grauitas corporis<arrow.to.target n="note14"/><lb/>A, ad grauitatem corporis B,* ergo vt grauitas corporis A, ad graui<lb/>tatem corporis B, ita erit magnitudo corporis D, ad corporis C, ma<lb/>gnitudinem. </s>

<s id="s.000113"> Nonnulli ex ve&longs;tris, vt &longs;alvent paralleli&longs;mum illius axis, cir<lb/>ca quem Sol revolvitur, adhibent alium motum revolutionis annuum cir<lb/>ca Solis axem, axi Eclipticæ parallelum. </s>

<s>Si quatuor igitur grauium corporum primum, & &longs;ecun<lb/>dum, & c. quod erat demon&longs;trandum. </s>

<s id="s.000114"><emph type="italics"/>Antimus.<emph.end type="italics"/></s>

<s id="s.000115"> Ita pror&longs;us. </s>

<s id="s.000116">Sed e&longs;t motus fictus, eo fine, vt meliùs res illa in<lb/>telligatur: vt enim terra circa axem axi Elipticæ parallelum revolui dici<lb/>tur annuo motu, in ve&longs;tra hypothe&longs;i ab occa&longs;u ad ortum, ratione hemi<lb/>&longs;phærij ad Solem ver&longs;i, vt axem, circa quem fit motus diurnus, &longs;emper pa<lb/>rallelum &longs;ervet, ita pror&longs;us &longs;olaris globus revolui dicendus e&longs;t annuo mo<lb/>tu, ad prædictum ph&oelig;nomenum Axis paralleli &longs;alvandum; &longs;ed vtrimque <lb/>hic motus fictitius e&longs;t, cùm &longs;implex turbinationis motus &longs;ufficiat, circa <lb/>Axem inclinatum ad planum Eclipticæ, &longs;emper &longs;ibi ip&longs;i parallelum. </s>

<s><margin.target id="note13"/>2. & 3. <lb/><emph type="italics"/>huius.<emph.end type="italics"/></s>

<s id="s.000117">Ana<lb/>logiam habes in acu magnetica, quæ cum pixide &longs;ua ita movetur, vt &longs;ine <lb/>novo motu, &longs;ibi parallela &longs;emper maneat. </s>

<s><margin.target id="note14"/><emph type="italics"/>Ex an<lb/>teced.<emph.end type="italics"/><lb/>11. 5. <lb/><emph type="italics"/>Elem.<emph.end type="italics"/></s>

<s id="s.000118"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>PROBLEMA I. PROPOS. VIII.</s>

<s id="s.000119"> Igitur non tres, aut quatuor motus in <expan abbr="nõ&longs;tra">no&longs;tra</expan> hypothe&longs;i &longs;ta<lb/>tuendi &longs;unt, vt &longs;upra dicebas; cum vnus duntaxat, eo quo explicas modo <lb/>&longs;ufficiat: cur ergo quatuor nece&longs;&longs;arios e&longs;&longs;e fingis? </s>

<s>Propo&longs;itis duobus corporibus magnitudine æquali<lb/>bus, vno &longs;olido, altero liquido, data &longs;olidi corporis <lb/>grauitate, grauitatem liquidi inuenire. </s><figure/>

<s id="s.000120"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>SINT duo propo&longs;ita corpo<lb/>ra magnitudine æqualia A, B, <lb/>quorum A, &longs;it &longs;olidum, B, vero <lb/>liquidum, & &longs;it &longs;olidi data graui<lb/>tas CD, Oportet inuenire quan<lb/>ta erit grauitas liquidi B. </s>

<s id="s.000121"> Iuxta morem ve&longs;trorum, & aliorum locutus &longs;um, qui prædictos <lb/>motus di&longs;tingunt; fateor tamen, in ve&longs;tra hypothe&longs;i, duos motus &longs;uffice<lb/>re, alterum turbinationis in terre&longs;tri globo, &longs;ervato, vt dixi, paralleli&longs;mo <lb/>Axis; alterum &longs;implicis revolutionis in Sole, circa Axem pariter inclina<lb/>tum, vt dixi, ad planum Eclipticæ. </s>

<s id="s.000122">In no&longs;tra verò vnus duntaxat motus <lb/>&longs;ufficit turbinationis, circa axem pariter inclinatum ad planum Eclipticæ, <lb/>& &longs;ibi &longs;emper parallelum, cum gemina illa inclination ereciproca, in Bo<lb/>ream, & Au&longs;trum, & &longs;ur&longs;um atque deor&longs;um; &longs;ic turbo actus, orbes &longs;uos <lb/>ita de&longs;cribit, vt aliquando majores, aliquando minores &longs;int; quod certè, <lb/>vt dixi, &longs;implicitati motus turbinationis non ob&longs;tat: Ex his autem, vt <pb pagenum="9" xlink:href="025/01/013.jpg"/>per&longs;picuè vides, no&longs;tra hypothe&longs;is &longs;implicior cen&longs;enda e&longs;t, ac proinde ex <lb/>hoc &longs;altem primo capite, ve&longs;træ anteponenda. </s>

<s>Si &longs;o<lb/>lidum A, grauius &longs;it liquido, de<lb/>mittatur in <expan abbr="liquid&utilde;">liquidum</expan>, & habeat in <lb/>liquido grauitatem ED, quoniam <lb/>igitur &longs;olidum A, grauius e&longs;t li<lb/>quido, demi&longs;&longs;um in liquidum <lb/>erit* in liquido tanto leuius,<arrow.to.target n="note15"/> <expan abbr="quã-ta">quan<lb/>ta</expan> e&longs;t grauitas liquidi magnitu<lb/>dine æqualis &longs;olido A, &longs;ed <expan abbr="&longs;olid&utilde;">&longs;olidum</expan> <lb/>A, leuius e&longs;t in liquido, quanta <pb pagenum="8"/>e&longs;t grauitas CE, ergo grauitas liquidi magnitudine æqualis &longs;olido A, <lb/>erit CE. </s>

<s id="s.000123"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000124"> Omittis duos alios motus, quos adhibent, &longs;cilicet obli<lb/>quitatis Zodiaci, præce&longs;&longs;ionis Æquinoctiorum, & fortè mutationem <lb/>excentricitatis. </s>

<s>Si vero &longs;olidum A, &longs;it leuius liquido, accipiatur aliquod aliud cor<lb/>pus &longs;olidum F, grauius liquido, ita vt &longs;olidum con&longs;tans ex vtri&longs;que <lb/>&longs;olidis A, F, demi&longs;&longs;um in liquidum feratur deor&longs;um, & &longs;it &longs;olidi F, <lb/>grauitas DG, item eiu&longs;dem &longs;olidi F, in liquido videlicet exi&longs;tentis &longs;it <lb/><arrow.to.target n="note16"/> grauitas HG,* ergo liquidi magnitudine æqualis &longs;olido F, erit gra<lb/>uitas DH. </s>

<s><margin.target id="note16"/>5.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s id="s.000125"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000126"> Vobis æquè atque nobis prædicti motus explicandi e&longs;&longs;ent; &longs;ed <lb/>negotium neutri parti face&longs;&longs;unt, cùm &longs;emper eadem maneat Zodiaci <lb/>obliquitas, &longs;emper eadem excentricitas; quod verò &longs;pectat ad Æquino<lb/>ctorium præce&longs;&longs;ionem, tu illam explicare potes, adhibito tardi&longs;&longs;imo &longs;tel<lb/>larum motu, ortum versùs, ego verò, &longs;i dicam, paulò tardiùs &longs;tellas move<lb/>ri ab Ortu ad Occa&longs;um, quàm <expan abbr="prim&utilde;">primum</expan> Mobile, ac proinde videri &longs;emper or<lb/>tum versùs recedere à punctis Æquinoctiorum, id e&longs;t à &longs;ectionibus Æqua<lb/>toris & Æclipticæ; neque in hoc alia re&longs;tat difficultas, atque adeò, tuum <lb/>illud primum argumentum &longs;olutum manet; iam propone alia, &longs;i quæ <lb/>habes. </s>

<s>Et quoniam &longs;olidi A, grauitas e&longs;t CD, &longs;olidi vero F, grauitas DG, <lb/>erit vtrorumque &longs;olidorum A, F, grauitas CG. coniungantur &longs;olida <lb/>A, F, & &longs;olidum ex vtri&longs;que con&longs;tans demittatur in liquidum, & ha<lb/>beat in liquido grauitatem GI, (habebit autem in liquido minorem <lb/>grauitatem, quam &longs;olum &longs;olidum F, quoniam &longs;olidum F, grauius li<lb/>quido fertur deor&longs;um nullo prohibente, & coniunctum cum &longs;olido A, <lb/>leuiori liquido ab eo &longs;u&longs;tinetut, ne deor&longs;um feratur <expan abbr="tãta">tanta</expan> vi, qua &longs;eiun<lb/>ctum) quoniam igitur &longs;olidi, quod con&longs;tat ex vtri&longs;que &longs;olidis A, F, <lb/><arrow.to.target n="note17"/> grauitas e&longs;t CG, in liquido vero exi&longs;tentis grauitas GI, * erit liquidi <lb/>habentis magnitudinem æqualem vtri&longs;que &longs;olidis A, F, grauitas CI, <lb/>&longs;ed grauitas liquidi æqualis magnitudine &longs;olido F, e&longs;t DH, ergo reli<lb/>qui liquidi æqualis &longs;olido A, erit grauitas CD, IH, &longs;ed liquidum B, <lb/>æquatur magnitudine &longs;olido A, ergo grauitas liquidi B, erit CD, IH, <lb/>inuenta igitur e&longs;t liquidi corporis B, grauitas CD, IH, de qua quæ<lb/>rebatur. </s>

<s><margin.target id="note17"/>5.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s id="s.000127"><emph type="italics"/>Augu&longs;tinus.<emph.end type="italics"/></s>

<s id="s.000128"> Vt vt &longs;it, Negari non pote&longs;t, quin no&longs;tra hypothe&longs;is ad <lb/>calculos A&longs;tronomicos magis accommodata &longs;it. </s>

<s>Placet huic Problemati exemplum apponere, vt vnicuique <lb/>etiam di&longs;ciplinæ Mathematicæ experto ad v&longs;um pateat adi<lb/>tus; quare etiam &longs;equentibus Problematis apponemus &longs;imilia <lb/>exempla. </s>

<s>Exemplum.</s>

<s id="s.000129"><emph type="italics"/>Antimu.<emph.end type="italics"/> E&longs;to, demus hoc, quod tamen facilè à me negari po&longs;&longs;et; cum <lb/>vtrinque &longs;imiles ferè calculi adhibendi &longs;int, ad quem finem, non realibus <lb/>& veris, &longs;ed fictitiis orbibus vtimur; omi&longs;&longs;o diurno Solis motu, fingimus <lb/>Solem moveri in Ecliptica motu annuo, item Apogæi motum, cum fictitio <lb/>circulo, &longs;eu circello ad calculos reducimus; &longs;ic calculis vtimur ad rationes <lb/>dati & accepti firmandas; cuncta igitur hæc ad calculationem adhiben<lb/>tur, cùm res perinde &longs;e habeat. </s>

<s id="s.000130">atque &longs;i ita e&longs;&longs;et. </s>

<s>Qvidam proponit aliquod corpus &longs;olidum notæ <lb/>grauitatis, & vult &longs;cire quanta erit grauitas liqui<lb/>di, magnitudinem habentis propo&longs;ito Corpori &longs;olido æ<lb/>qualem. </s>

<s id="s.000131">In quo, vt vides, nulla e&longs;t <lb/>difficultas. </s>

<s id="s.000132">Sed de hoc argumento plura infra, &longs;i hoc tibi gratum accidat: <lb/>iam verò reliqua exprome, &longs;i quæ habes adversùm nos. </s>

<s><emph type="italics"/>Sit primum propo&longs;itum aliquod corpus plumbeum A, euius graui<lb/>tas &longs;it<emph.end type="italics"/> 23. <emph type="italics"/>& oporteat &longs;cire quanta erit grauitas aquæ magnitudinem <lb/>habentis æqualem propo&longs;ito plumbo A, ponderetur plumbum A, in <lb/>aqua (modum quo ponderanda &longs;int corpora &longs;olida in aqua, inferius <lb/>apponemus) & habeat grauitatem<emph.end type="italics"/> 21. <emph type="italics"/>quoniam igitur numerus<emph.end type="italics"/> 23. <pb pagenum="9"/><emph type="italics"/>juperat numerum<emph.end type="italics"/> 21, <emph type="italics"/>numero 2, erit grauitàs aquæ magnitudinem <lb/>habentis æqualem plumbo A, 2.<emph.end type="italics"/></s>

<s>Eadem via omnium liquidorum inuenitur grauitas, quan<lb/>do nimirum corpus &longs;olidum &longs;it grauius liquido, cuius liquidi <lb/>quærenda e&longs;t grauitas, hoc e&longs;t quando corpus &longs;olidum demi&longs;<lb/>&longs;um in liquidum feratur deor&longs;um. </s>

<s id="s.000133"><emph type="italics"/>Augi&longs;tinus.<emph.end type="italics"/></s>

<s id="s.000134"> Crede mihi, Antime, abundè &longs;uppetunt, illudque in <lb/>primis, quod in hac mea hypothe&longs;i planetarum pa&longs;&longs;iones ea facilitate ex<lb/>plicantur. </s>

<s>Quando vero corpus &longs;olidum fuerit leuius liquido, hoc e&longs;t <lb/>demi&longs;&longs;um in liquidum non de&longs;cendat, per adiectionem alicuius <lb/>alius &longs;olidi corporis liquido grauioris, quæ&longs;ita liquidi grauitas <lb/>inuenietur. </s>

<s id="s.000135">quá ne&longs;cio an major ex cogitari po&longs;&longs;it; puta &longs;tationes, retrogre&longs;<lb/>fiones, accelerationes &c. </s>

<s><emph type="italics"/>Sit igitur propo&longs;itum aliquod ccreum corpus A, cuius grauitas &longs;it<emph.end type="italics"/><lb/>21. <emph type="italics"/>& oporteat &longs;cire quanta erit grauitas aquæ magnitudinem haben<lb/>tis æqualem ceræ A. </s>

<s id="s.000136"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>Quoniam cera leuior est, quam aqua, &longs;i demitta<lb/><gap/>ur in aquam non feretur deor&longs;um, accipiatur aliquod corpus &longs;olidum <lb/>F, grauius quam aqua, ita vt corpus constans ex vtri&longs;que corporibus <lb/>A, F, demi&longs;&longs;um in aquam feratur deor&longs;um, &longs;it igitur corpus F, plum<lb/>beum, cuius grauitas &longs;it v.g.<emph.end type="italics"/> 23, <emph type="italics"/>& eiu&longs;dem in aqua ponderati<emph.end type="italics"/> 21, <lb/><emph type="italics"/><gap/>go aquæ magnitudinem habentis <expan abbr="æqual&etilde;">æqualem</expan> plumbo F, erit grauitas<emph.end type="italics"/> 2, </s>

<s id="s.000137"> Hic profectò Achilles ve&longs;ter e&longs;t; &longs;ed non invictus, meo iudi<lb/>cio; faveor explicari po&longs;&longs;e alicuius planetæ, puta Saturni, retrogre&longs;&longs;ionem <lb/>v.g. (figuram tecum non adhibeo, qui res i&longs;tas facilè intelligis) &longs;i enim ter<lb/>ram colloces in eo Eclipticæ gradu, qui ab alio di&longs;tet, in quo e&longs;t Saturnus <lb/>vno quadrante integro circuli, Saturnus in eo loco, in quo e&longs;t, non videbi<lb/>tur &longs;ed in alio remotiore. </s>

<s><emph type="italics"/>Et quoniam ceræ A, grauitas est<emph.end type="italics"/> 21, <emph type="italics"/>plumbi vero F,<emph.end type="italics"/> 23, <emph type="italics"/>erit vtro<lb/>rumque corporum A, F, ceræ nimirum, & plumbi grauitas<emph.end type="italics"/> 44, <emph type="italics"/>coniun <lb/>gatur cera, & plumbum, & ita coniuncta ponderentur in aqua, & <lb/>habeant grauitatem<emph.end type="italics"/> 20, <emph type="italics"/>quoniam igitur numerus<emph.end type="italics"/> 44, <emph type="italics"/>&longs;uperat nume<lb/>rum<emph.end type="italics"/> 20, <emph type="italics"/>numero<emph.end type="italics"/> 24, <emph type="italics"/>erit grauitas aquæ habentis magnitudinem æqua<lb/>lem vtri&longs;que corporibus ceræ & plumbi<emph.end type="italics"/> 24, <emph type="italics"/>&longs;ed grauitas aquæ magni<lb/>tudinem habentis æqualem plumbo F, est<emph.end type="italics"/> 2, <emph type="italics"/>ergo reliquum quod est<emph.end type="italics"/><lb/>22, <emph type="italics"/>erit grauitas, aquæ magnitudine æqualis propo&longs;itæ ceræ A.<emph.end type="italics"/></s>

<s id="s.000138"><emph type="italics"/>Augu&longs;tinus<emph.end type="italics"/> Adhibe quæ&longs;o aliquid &longs;chematis, vt res i&longs;ta clariùs à me <lb/>intelligatur. </s>

<s>At vero &longs;i propo&longs;itum fuerit aliquod corpus &longs;olidum ma<lb/>gni ponderis, ita vt difficile po&longs;&longs;it ponderari in aqua, hac via <lb/>inuenietur aquæ quæ&longs;ita grauitas. </s>

<s><emph type="italics"/>Sit aliquod corpus <expan abbr="plumbe&utilde;">plumbeum</expan> A, cuius grauitas<emph.end type="italics"/> 2300, <emph type="italics"/>& oporteat in <lb/>uenire grauitatem aquæ magnitudinem habentis <expan abbr="æqual&etilde;">æqualem</expan> plumbo A, <lb/>accipiatur aliquod paruum plumbi corpus F, cuius grauitas &longs;it v.g.<emph.end type="italics"/><lb/>23, <emph type="italics"/>& inueniatur grauitas aquæ magnitudine æqualis plumbo F, vt <lb/>dictum est, quæ &longs;it.<emph.end type="italics"/> 2, <emph type="italics"/>& fiat vt<emph.end type="italics"/> 23, <emph type="italics"/>ad<emph.end type="italics"/> 2, <emph type="italics"/>ita<emph.end type="italics"/> 2300, <emph type="italics"/>ad alium numerum <lb/>qui &longs;it<emph.end type="italics"/> 200. <emph type="italics"/>grauitas igitur aquæ magnitudinem habentis æqualem <lb/>plumbo A, erit<emph.end type="italics"/> 200. </s>

<s><emph type="italics"/>Similiter &longs;it aliquod cereum corpus A, cuius grauitas<emph.end type="italics"/> 2100, <emph type="italics"/>& opor <lb/>teat facere, quod imperatum e&longs;t. </s>

<s id="s.000139"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000140"> Schemate opus e&longs;&longs;e non putarem, quia tamen ita iubes, tibi <lb/>morem geram. </s>

<s>accipiatur aliquod paruum ceræ cor<lb/>pus F, cuius grauitas &longs;it v.g.<emph.end type="italics"/> 21, <emph type="italics"/>& inuenta grauitate aquæ magni-<emph.end type="italics"/><pb pagenum="10"/><emph type="italics"/>tudinem habentis æqualem ceræ F, quæ &longs;it<emph.end type="italics"/> 12, <emph type="italics"/>fiat vt<emph.end type="italics"/> 21, <emph type="italics"/>ad<emph.end type="italics"/> 22, <emph type="italics"/>ita<emph.end type="italics"/><lb/>2100, <emph type="italics"/>ad alium numerum qui &longs;it<emph.end type="italics"/> 2200; <emph type="italics"/>erit igitur grauitas aquæ ma <lb/>gnitudinem habentis æqualem ceræ A,<emph.end type="italics"/> 2200. </s>

<s id="s.000141">Sit A. centrum vniver&longs;i, &longs;itque BCDE magnus Orbis, <lb/>vt vocant, in quo, primo loco, iuxta tuam hypothe&longs;im, terre&longs;trem globum <lb/>moveri &longs;uppono; &longs;it orbita Martis FRPS. </s>

<s id="s.000142">Terra moveatur ex C. per B. <lb/>in con&longs;equentia, vt vocant, id e&longs;t, iuxta&longs;eriem Signorum; Item Mars ex F <lb/>per R. &longs;upponatur Mars in F, & terra in B; Supponamus lineam AF pro<lb/>ductam ad &longs;tellas, terminari ad principium Cancri, ac proinde AB. pro<lb/>ductam ad initium Libræ; ex puncto B, Mars videbitur per lineam BFL. <lb/></s>

<s>Neque nece&longs;&longs;e e&longs;t, vt illud corpus &longs;olidum magni ponderis <lb/>reip&longs;a proponatur, &longs;ufficit enim vt eius grauitas notificetur <lb/>numero tantum. </s>

<s id="s.000143">Igitur in eo Zodiaci puncto, quod, a principio Cancri versùs Occa&longs;um di<lb/>&longs;tat, toto angulo BFA, vel quod idem e&longs;t, FAM. </s>

<s id="s.000144">Item &longs;i &longs;tatuamus initio <lb/>Terram in D, Martem in S. erit Mars in Perigæo, & in oppo&longs;itione; &longs;patio <lb/>vorò &longs;ex men&longs;ium, circiter, Mars ab S. pervenit ad F, & Terra à D.ad IB; <lb/>tunc autem Mars e&longs;t in mediocri di&longs;tantia, & videtur retrogredi à puncto <lb/>in, quo non videtur ex B, &longs;ed in quo e&longs;t, ad punctum L, vel K, in quo non e&longs;t, <lb/>&longs;ed in quo videtur ex B. </s>

<s>Si autem propo&longs;itum fuerit inuenire quanta erit graui<lb/>tas argenti viui magnitudine æqualis propo&longs;ito corpori &longs;o<lb/>lido A; ratione qua &longs;upra, non inuenietur ip&longs;a grauitas, quo<lb/>niam nullum corpus demi&longs;&longs;um in argentum viuum fertur <lb/>deor&longs;um, ni&longs;i aurum, aurum vero in ip&longs;o argento viuo perrum<lb/>pitur, &longs;ed qua ratione inuenienda &longs;it ip&longs;a argenti viui graui<lb/>tas, dicemus ad finem exempli propo&longs;itionis decimæquartæ. </s>

<s>Quomodo ponderanda &longs;int corpora &longs;olida in aqua. </s>

<s id="s.000145">In no&longs;tra comnunique hypothe&longs;i, hæc æquè facilè explicantur, &longs;it enim <lb/>Terra in Centro A &longs;it BCDE orbita Solis, &longs;it FRPS, deferens centrum <lb/>Epicych Marris; &longs;it demum ONCM, Epicyclus Martis, cuius motus, cir-<pb pagenum="11" xlink:href="025/01/015.jpg"/>ca proptium centrum, &longs;it ab Oin N, id e&longs;t, in con&longs;equentia, &longs;ecundùm <lb/>partem &longs;uperiorem, nec non eodem cum centro motu; Sit igitur centrum <lb/>Epicycli in S. planeta in D, id e&longs;t in Perigæo ; <expan abbr="centr&utilde;">centrum</expan> S feratur in P, erit Plane<lb/>ta in M ; igitur ex A videtur in K ; ergo videtur retrogredi: &longs;upponamus au<lb/>tem motum Martis e&longs;&longs;e duorum annorum; in ve&longs;tra hypothe&longs;i ; Terra ex <lb/>D prefecta, redit in idem punctum D. decur&longs;o orbe, eo tempore, quo <lb/>Mars ex S. profectus pervenit in R ; in S autem erat in Perigæo ; in R verò <lb/>e&longs;t in Apogæo ; videtur denique Mars retrogradus, quando e&longs;t in S. & <lb/>acceleratus quando e&longs;t in R. </s>

<s id="s.000146">Pari modo in no&longs;tra hypothe&longs;i, eodem tem<lb/>pore, centrum Epicycli ex S pervenit in R, & planeta pervenit in I, & vt <lb/>in D e&longs;t Perigæus, ita in T e&longs;t Apogæus, di&longs;tantiis verinque ferè æquali<lb/>bus. </s>

<s>C<emph type="italics"/>orpus quod ponderandum proponitur &longs;eta equina ex altera li<lb/>bræ lance appendatur, in altera lance ponantur pondera, & cor<lb/>pus appen&longs;um demittatur in aquam, ita vt in aqua libere pendeat, ne<lb/>que lancem, cui appen&longs;um est corpus, neque aliam in qua &longs;unt <expan abbr="ponderã">ponderam</expan> <lb/>aqua contingat, & ita ponderetur propo&longs;itum corpus, ac &longs;i in aere pen <lb/>deret.<emph.end type="italics"/></s>

<s id="s.000147">Mars item in D. e&longs;t retrogradus, in I verò acceleratus. </s>

<s id="s.000148">Vtrùm verò <lb/>hæc ob&longs;ervationibus con&longs;entiant, hoc loco minimè di&longs;puto; hoc tantùm <lb/>demon&longs;tra&longs;&longs;e contentus, vtrimque fore &longs;imilia pa&longs;&longs;ionum phænomena, <lb/>accelerationum; &longs;cilicet, &longs;tationum, repre&longs;&longs;ionum &c. </s>

<s><emph type="italics"/>Dixi &longs;eta e quina corpus ponder andum debere appendi, quia fere <lb/>æque grauis e&longs;t atque aqua, & ideo nihil addet, vel minuet grauita<lb/>tis in ip&longs;o corpore ponderando.<emph.end type="italics"/></s>

<s id="s.000149">Vter verò explican<lb/>di modus magis aptus &longs;it, magi&longs;que naturæ ip&longs;i congruat, demon&longs;trandum <lb/>re&longs;tat. </s>

<s><emph type="italics"/>Quod &longs;i corpus ponderandum fuerit, tam graue, vt &longs;eta &longs;implici &longs;u<lb/>stineri nequeat, appendatur pluribus &longs;imul iunctis &longs;etis, & ne aliquid <lb/>grauitatis &longs;etarum coniunctio addat corpori ponderando, ponantur <lb/>in altera lance totidem &longs;etæ æquales eis, quæ ex lance, cui appen&longs;um e&longs;t <lb/>corpus pendent, v&longs;que ad corpus appen&longs;um, hac igitur &longs;etarum addi<lb/>tione æque ponderabunt lances, & quamuis illæ &longs;etæ, quibus appen<lb/>&longs;um est corpus, &longs;int longiores, quam aliæ alteri lanci addilæ, longitudi<lb/>ne partium, quibus ligatum est corpus, tamen quoniam illæ partes <lb/>æque graues &longs;unt, atque aqua, exi&longs;tentes cum ip&longs;o corpore in aqua, nul<lb/>lam grauitatem habebunt, & ideo illæ &longs;etæ, quæ alias &longs;uperant dictis <lb/>partibus, & &longs;i longiores, non erunt grauiores quam aliæ, existenti<lb/>bus, nempe, vt dictum e&longs;t, illis partibus cum ip&longs;o corpore in aqua. </s>

<s id="s.000150"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>Sic <lb/>igitur in aqua ponderanda erunt &longs;olida corpora, quod animaduerti&longs;&longs;e <lb/>fuit operæ pretium.<emph.end type="italics"/></s><pb pagenum="11"/>

<s id="s.000151"> Nemini profectò dubium &longs;it, quin res tota planior in no<lb/>&longs;tra hypothe&longs;i cen&longs;eatur, in qua &longs;implex & vnica Martis orbita &longs;tatui<lb/>tur, cùm tamen in tua, duos circulos ponas, deferentem &longs;cilicet, <lb/>& Epicyclum; ac proinde duos etiam motus; in mea vnicum dumtaxat <lb/>agno&longs;cis. </s>

<s>PROBLEMA II. PROPOS. IX.</s>

<s id="s.000152"><emph type="italics"/>Antim.<emph.end type="italics"/> Haec quæ dicis, ad &longs;peciem vera & per&longs;picua e&longs;&longs;e videntur; <lb/>cùm tamen &longs;ecus &longs;it; nam in tua quoque hypothe&longs;i, gemin<gap/> orbes, & <lb/>totidem motus ponendi &longs;unt; ni&longs;i enim terræ motum &longs;imul cum Martis <lb/>motu ad calculos reducas, nunquam prædicta phænomena invenies; vn<lb/>de motum pro motu, circulum pro circulo reddimus; Orbitam Martis <lb/>eandem vterque ponimus, &longs;cilicet FRPS, diver&longs;imode tamen illa vti<lb/>mur; tu enim vis ab ea deferri planetam, ego verò centrum Epicycli. </s>

<s>Propo&longs;itis duobus corporibus magnitudine æquali<lb/>bus, vno &longs;olido, altero liquido, data corporis li<lb/>quidi grauitate, grauitatem &longs;olidi inuenire. </s>

<s id="s.000153">Tu <lb/>magnum orbem accer&longs;is, in quo terram moveri decernis, ego Epicyclum <lb/>Martis, eiu&longs;dem omnino &longs;emidiametri in quo planeta movetur; vterque <lb/>igitur geminos orbes & circulos ponimus. </s>

<s>SINT duo propo&longs;ita corpora <lb/>magnitudine æqualia, A, quidem &longs;o<lb/><figure id="fig8"/><lb/>lidum, B, vero liquidum, &longs;it autem li<lb/>quidi B, data grauitas F, & oporteat <lb/>inuenire grauitatem &longs;olidi A, accipia <lb/>tur aliquod corpus &longs;olidum D, <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> <lb/>generis, cum &longs;olido A, cuius grauitas <lb/>&longs;it H, deinde liquidi eiu&longs;dem generis <lb/>cum liquido B, magnitudine æqualis <lb/>&longs;olido D,* inueniatur grauitas quæ &longs;it<arrow.to.target n="note18"/><lb/>G, & fiat vt G, ad H, ita F, ad aliam <lb/>grauitatem, quæ &longs;it C. </s>

<s id="s.000154"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>Dico &longs;olidi A, <lb/>grauitatem e&longs;&longs;e C, accipiatur enim aliquod corpus liquidum E, eiu&longs;<lb/>dem generis cum liquido B, grauitatem habens æqualem &longs;olido D. </s>

<s id="s.000155"> Magnus orbis etiam a te ponendus e&longs;t, in quo Sol ip&longs;e mo<lb/>veatur; orbes igitur multiplicas. </s>

<s><lb/>Quoniam igitur &longs;unt quatuor corpora grauia B, A, E, D, quorum pri<lb/>mum B, & &longs;ecundum A, &longs;unt magnitudine æqualia, tertium vero E, <lb/>& quartum D, æquegrauia, & &longs;unt eiu&longs;dem generis corpora B, E, &longs;i<lb/>militer, & corpora A, D,*erit vt grauitas liquidi æqualis<arrow.to.target n="note19"/> magnitudi<lb/>ne &longs;olido D, hoc e&longs;t vt G, ad grauitatem liquidi E; hoc e&longs;t ad H, <expan abbr="pon&utilde;-tnr">ponun<lb/>tnr</expan> enim æque grauia corpora D, E, ita grauitas F, ad &longs;olidi A, graui<lb/>tatem, &longs;ed vt grauitas G, ad grauitatem H, ita e&longs;t grauitas F, ad C, <lb/>grauitatem, ergo grauitas C, æqualis erit grauitati &longs;olidi A. </s>

<s id="s.000156"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>Inuenta <lb/>igitur e&longs;t &longs;olidi A, grauitas C, quod facere oportebat. </s>

<s id="s.000157"> Magnus orbis ad prædictarum pa&longs;&longs;ionum phænomena, mihi <lb/>nece&longs;&longs;arius non e&longs;t; &longs;tatuta terra immobili in centro A, cum orbita Mar<lb/>i, & Epicyclo, eo modo, quo dixi; nam etiam &longs;emoto magno illo orbe, <lb/>prædicta phænomena, regre&longs;&longs;ionum, accelerationum, &longs;tationum &c. </s>

<s id="s.000158">nece&longs;<lb/>&longs;ariò con&longs;equentur. </s>

<s><margin.target id="note19"/>6.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s id="s.000159"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000160"> Pace tua dixerim, Antime; ni&longs;i enim magnum orbem &longs;ta<lb/>tuas, & in eo Solem moveri, &longs;upponas, nunquam obtinebis, vt <lb/>Mars Perigæus, &longs;it &longs;emper oppo&longs;itus; Apogæus verò, Soli &longs;emper coniun<lb/>ctus &longs;it. </s>

<s>Exemplum.</s>

<s>Qvidam proponit aliquod corpus liquidum notæ <lb/>grauitatis, & vult &longs;cire quanta erit grauitas alicu<lb/>ius &longs;olidi, magnitudinem habentis propo&longs;ito Corpori li<lb/>quido æqualem. </s>

<s id="s.000161"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000162"> Equidem nunquam habemus Martem Soli coniunctum, vel <lb/>oppo&longs;itum, ni&longs;i Solem e&longs;&longs;e &longs;upponamus; nec etiam e&longs;&longs;e pote&longs;t, ni&longs;i alicu-<pb pagenum="12" xlink:href="025/01/016.jpg"/>bi &longs;it; &longs;it in B etiam immobilis, & Mars in D. hic erit Perigæus & oppo<lb/>&longs;itus: moveatur autem tum centrum Epicicli S, tum ip&longs;e Epicyclus, eo <lb/>modo, quo diximus, quando centrum Epicycli erit in R, planeta erit in T; <lb/>igitur Apogæus & coniunctus; atque ita deinceps emen&longs;is revolutioni<lb/>bus iuxta præ&longs;criptum motum, Mars &longs;emper erit Perigæus in oppo&longs;itio<lb/>ne, Apogæus in coniunctiono; Iam &longs;umus ergo pares, & vtrinque par <lb/>numerus e&longs;t circulorum & motuum: vter verò modus rationi & naturæ <lb/>magis con&longs;entaneus &longs;it, videndum re&longs;tat. </s>

<s><emph type="italics"/>Sitpropo&longs;itum aliquod corpus aqueum B, euius grauitas &longs;it 100. &<emph.end type="italics"/><pb pagenum="12"/><emph type="italics"/>oporteat &longs;cire quanta erit grauitas plumbi magnitudinem habentis <lb/>æqualem propo&longs;itæ aquæ B, verbi gratia &longs;it vas aliquod plenum aqua, <lb/>cuius aquæ grauitas &longs;it 100, & oporteat &longs;cire, &longs;i illud <expan abbr="id&etilde;">idem</expan> vas replea<lb/>tur plumbo, quanta illius plumbi erit grauitas. </s>

<s>Accipiatur aliquod <lb/>plumbeum corpus D, cuius grauitas &longs;it<emph.end type="italics"/> 23<emph type="italics"/>, deinde aquæ <expan abbr="magnitudin&etilde;">magnitudinem</expan> <lb/>habentis æqualem plumbo D, inueniatur grauitas, quod quomodo fie<lb/>ri oporteat iam dictum e&longs;t in antecedentis problematis exemplo: &longs;it igi <lb/>tur ea inuenta grauitas<emph.end type="italics"/> 2<emph type="italics"/>, & fiat vt<emph.end type="italics"/> 2<emph type="italics"/>, ad<emph.end type="italics"/> 23<emph type="italics"/>, ita<emph.end type="italics"/> 100<emph type="italics"/>, ad alium nume<lb/>rum qui &longs;it<emph.end type="italics"/> 1150<emph type="italics"/>, is igitur numerus erit grauitas plumbi magnitu<lb/>dinem habentis propo&longs;itæ aquæ B, æqualem, hoc est illius plumbi, quod <lb/>in va&longs;e continetur.<emph.end type="italics"/></s>

<s id="s.000163"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000164"> Vtrique parti, &longs;uus videbitur in rem i&longs;tam magis quadrare; <lb/>quid enim pro tua cau&longs;a dici po&longs;&longs;it, non video, quod pro mea æquè non <lb/>militet. </s>

<s>At vero &longs;i <expan abbr="propo&longs;it&utilde;">propo&longs;itum</expan> fuerit inuenire <expan abbr="quãta">quanta</expan> erit grauitas ceræ, <lb/>aut ligni, aut <expan abbr="cuiu&longs;c&utilde;que">cuiu&longs;cunque</expan> &longs;olidi leuioris quam aqua, nihil diuer<lb/>&longs;i in opere accidet, ni&longs;i quod ratio inueniendi grauitatem <lb/>aquæ magnitudinem habentis æqualem corpori &longs;olido leuio<lb/>ri, quàm aqua, differt in aliquo à ratione, qua inuenitur graui<lb/>tas aquæ magnitudinem habentis æqualem &longs;olido corpori <lb/>grauiori, quam aqua, &longs;ed vtramque rationem exemplo ante<lb/>cedentis Problematis illu&longs;trauimus, in eo enim &longs;atis explica<lb/>tum e&longs;t de vtraque. </s>

<s><emph type="italics"/>Sed ne exemplorum inopia laborare videamur, &longs;it inuenienda gra<lb/>uitas ceræ magnitudinem habentis æqualem propo&longs;itæ aquæ B, acci<lb/>piatur aliquod cereum corpus D, cuius grauitas &longs;it<emph.end type="italics"/> 21, <emph type="italics"/>deinde aquæ <lb/>magnitudinem habentis æqualem ceræ D, inueniatur grauitas, vt in <lb/>antecedentis Problematis exemplo dictum est, quæ grauitas &longs;it<emph.end type="italics"/> 22, <emph type="italics"/>& <lb/>fiat vt<emph.end type="italics"/> 22<emph type="italics"/>, ad<emph.end type="italics"/> 21<emph type="italics"/>, ita<emph.end type="italics"/> 100<emph type="italics"/>, hoc est grauitas aquæ B, ad alium numerum <lb/>qui &longs;it<emph.end type="italics"/> 95 5/11. <emph type="italics"/>is igitur numerus indicabit quanta erit grauitas ceræ <lb/>magnitudinem habentis æqualem propo&longs;itæ aquæ B.<emph.end type="italics"/></s>

<s id="s.000165"><emph type="italics"/>Antimus.<emph.end type="italics"/></s>

<s id="s.000166"> Secus e&longs;&longs;e crediderim; nempe<gap/> ille modus veritati, rationi, & <lb/>naturæ magis con&longs;entaneus e&longs;t, qui nec &longs;en&longs;um, nec intellectum in erro<lb/>rem inducit, &longs;ed exhibet planetam in eo loco, in quo revera e&longs;t; is enim <lb/>poti&longs;&longs;imùm oculorum finis, vt objectum, & tale quale e&longs;t, & in loco in <lb/>quo e&longs;t, exhibeant. </s>

<s>Similiter &longs;i propo&longs;itum liquidum corpus B, fuerit olei, aut <lb/>vini, aut cuiu&longs;cumque liquidi, præter argenti viui, eadem om<lb/>nino via, qua ante, inuenietur quæ&longs;ita corporis &longs;olidi grauitas, <lb/>&longs;ed de argento viuo tractabimus ad finem propo&longs;itionis deci<lb/>mæ quartæ. </s>

<s id="s.000167">Atqui iuxta no&longs;trum modum, video ex A Martem in <lb/>M, per lineam rectam productam ad verum locum Eclipticæ, in quo e&longs;t, <lb/>cùm tamen iuxta tuum, ex B, videam Martem in eodem loco Eclipticæ, in <lb/>quo tamen non e&longs;t, &longs;ed in alio, ad quem terminatur recta AF. </s>

<s id="s.000168">Igitur in <lb/>mea hypothe&longs;i, nec &longs;en&longs;us fallitur, nec intellectus; & provt terum natura <lb/>po&longs;tulat, videtur Planeta in eo loco, in quo e&longs;t; in tua verò, & &longs;en&longs;us fal<lb/>litur, & per &longs;en&longs;um intellectus; Licit hic deinde ex aliis notionibus &longs;en<lb/>&longs;um corrigat; & contra rerum naturam & rectæ rationis ordinem, plane<lb/>ta &longs;emper in eo loco videtur, in quo non e&longs;t, & nunquam in eo, in quo e&longs;t, <lb/>citra puncta oppo&longs;itionum & conjunctionum. </s>

<s>PROBLEMA III. PROPOS. X.</s>

<s id="s.000169">Fateor vltrò, &longs;en&longs;us ali<lb/>quando falli, & multis &longs;ubjici fallaciis; &longs;ed profectò id accidit, vt aiunt, per <lb/>accidens; nam per &longs;e &longs;en&longs;us non fallit, nec fallitur; &longs;ed meo iudicio, ab<lb/>&longs;urdum dictu e&longs;t, naturam oculis &longs;emper illudere volui&longs;&longs;e, quod tamen <lb/>ex tua hypothe&longs;i nece&longs;&longs;ariò &longs;equitur; Video Solem moveri, ac Terram &longs;ta<lb/>re, turpiter erro, Sol enim quie&longs;cit, Terra movetur; terre&longs;trem globum in <lb/>centro Vniver&longs;i e&longs;&longs;e video, & Solem in ætherea regione extra medium; <lb/>&longs;ed oculi hallucinantur; nam Sol in centro e&longs;t, atque inter Sydera Tellus: <lb/>Video Martem in 20. gradu Geminorum, oculo minimè impedito, <expan abbr="etiã">etiam</expan> ex <lb/>centro ter<gap/>; fallor, erroque toto c&oelig;lo; cùm Mars reverâ &longs;it in principio <lb/>Cancri; &longs;ic nobis Natura gratis impo&longs;uit, & in perpetuo errore ver&longs;ari <lb/>voluit, quis hoc credat? </s>

<s id="s.000170">Quis homini cordato per&longs;uadeat? </s>

<s>Propo&longs;itis duobus corporibus æque grauibus, vno <lb/>&longs;olido, altero liquido, data &longs;olidi corporis magnitu-<pb pagenum="13"/>dine, magnitudinem liquidi inuenire. </s>

<s id="s.000171">præ&longs;ertim vbi <lb/>nulla nece&longs;&longs;itas vrget, nulla ratio po&longs;tulat, nulla cogunt phænomena. </s>

<s>SINT duo propo&longs;ita corpora <lb/>æque grauia, A, quidem &longs;olidum B, <lb/>vero liquidum, &longs;it autem &longs;olidi A, da<lb/><figure id="fig9"/><lb/>ta magnitudo C, & oporteat inuenire <lb/>quanta erit magnitudo liquidi B, Ac<lb/>cipiatur aliquod corpus &longs;olidum D, <lb/>eiu&longs;dem generis cuni &longs;olido A, & &longs;it <lb/>eius grauitas G, & liquidi, quod &longs;it E, <lb/>eiu&longs;dem gener is cum liquido B, ma<lb/>gnitudinem habentis æqualem &longs;olido <lb/>D,* inueniatur grauitas quæ &longs;it H, &<arrow.to.target n="note20"/><lb/>fiat vt grauitas H, ad grauitatem G, <lb/>ita magnitudo C, ad aliam magnitudinem quæ &longs;it F. </s>

<s id="s.000172"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>Quoniam igitur <lb/>&longs;unt quatuor corpora grauia E, D, B, A, quorum primum E, & &longs;ecun<lb/>dum D, &longs;unt æqualia magnitudine, tertium vero B, & quartum A, <lb/>æque grauia, & &longs;unt eiu&longs;dem generis corpora E, B, &longs;imiliter, & corpo<lb/>ra D, A, *erityt grauitas H, ad grauitatem G, ita magnitudo C, ad<arrow.to.target n="note21"/> li<lb/>quidi B, magnitudinem, &longs;ed vt grauitas H, ad grauitatem G, ita e&longs;t <lb/>magnitudo C, ad magnitudinem F, ergo magnitudo F, æqualis erit <lb/>magnitudini liqudi B, inuenta igitur e&longs;t liquidi corporis B, magni<lb/>tudo F, quod facere oportebat. </s>

<s id="s.000173"> Illa facilitas Apogæi ac Perigæi, quæ in no&longs;tra hypothe&longs;i <lb/>mirabilis e&longs;t, negari profectò nequit. </s>

<s><margin.target id="note20"/>8.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s id="s.000174"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s><margin.target id="note21"/>7.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s id="s.000175"> Quæ major facilitas excogitari pote&longs;t, quàm illa, qua res Apo<lb/>gæi ac Perigæi per Epicyclum explicatur? </s>

<s id="s.000176">Quis &longs;tatim non capiat, Mar<lb/>tem in O e&longs;&longs;e Apogæum, in C verò Perigæum ? Quis non videt, eodem <lb/>modo terram ab E, per EBC, accedere ad Martem F, quo Mars ab O <lb/>per ONC, accedit ad terram A, &longs;cilicet ab O in N, & ab E in B, iuxta <lb/>rationem &longs;inuum ver&longs;orum, ab N verò in C, & à B in C, iuxta rationem &longs;i-<pb pagenum="13" xlink:href="025/01/017.jpg"/>nuum rectorum arcuum decur&longs;orum: In his, crede mihi, nulla e&longs;t diffi<lb/>cultas, &longs;ed par vtrinque facilitas; no&longs;ter tamen modus naturæ, veritati, <lb/>& rationi congruit, ve&longs;ter errori & fallaciis patrocinatur. </s>

<s>Sed quoniam corporum regularium magnitudo quo<lb/>que exprimitur latere eiu&longs;dem corporis, vel diametro, &longs;i <lb/>propo&longs;ita duo corpora A, B, fuerint regularia, vtpote &longs;ph&ecedil; <lb/>rica, fuerit autem &longs;phæræ A, data diameter C, & oporteat <lb/>inuenire quanta erit diameter &longs;phæræ B. ita faciendum <lb/>erit. </s>

<s id="s.000177">Hic autem ac<lb/>curatas revolutionum men&longs;uras non definio, &longs;ed illud duntaxat intendo <lb/>æquè facilè in no&longs;tra hypothe&longs;i, atque in tua, explicari illa omnia, quæ ad <lb/>Planetarum pa&longs;&longs;iones &longs;pectant, licet no&longs;tra hypothe&longs;is naturæ ac rationi <lb/>magis congruat. </s>

<s id="s.000178">Sed ne in hoc quidem pares e&longs;&longs;e videamur, per te mihi <lb/>liceat, quæro, rem i&longs;tam paulò minutiùs enucleare. </s>

<s>Accepto, vt diximus, aliquo corpore &longs;olido D, eiu&longs;dem generis <expan abbr="c&utilde;">cum</expan> <lb/>&longs;phæra A, & inuenta grauitate liquidi E, vt &longs;upra, fiat vt grauitas H, <lb/>ad grauitatem G, ita cubus ex C, ad alium cubum, cuius latus &longs;it F, <lb/>dico ip&longs;um latus F, æquale e&longs;&longs;e diametro &longs;phæræ B. </s>

<s id="s.000179">Suppone, Martem, <lb/>cum eo velocitatis gradu, quo velociùs Sole movetur, moveri ab ortu in <lb/>occa&longs;um, haud dubiè Solem po&longs;t &longs;e relinquit, & po&longs;t aliquot revolutio<lb/>nes, modò e&longs;t in Quadraturis, modò in oppo&longs;itione, modò in Coniunctio<lb/>ne; &longs;it enim v.g. Sol in C, Mars in F, & vterque versùs occa&longs;um eat, &longs;ci<lb/>licet Sol à C, versùs D, Mars ab F, versùs S ; haud dubiè Mars Solem à <lb/>tergo relinquit versùs ortum, atque adeò po&longs;t aliquot revolutiones Mars <lb/>erit in F ; & Solem a&longs;piciet in B, tum in F ; po&longs;tea in D, ac demum <lb/>eum a&longs;&longs;equetur in C, redibitque Conjunctio; Vides, vtrumque moveri <lb/>&longs;implici&longs;&longs;imo motu; Cogita duos equos in duobus circulis currentes, <lb/>quorum alter velociùs &longs;uum orbem ab&longs;oluit; Hinc Mars &longs;emper a&longs;&longs;equi<lb/>tur partem ortivam di&longs;ci Solaris; hinc &longs;emper ve&longs;pertinus occidit He<lb/>liacè, id e&longs;t, immergitur in radios Solis, ac proinde de&longs;init videri; Matuti<lb/>nus verò Heliacè oritur; id e&longs;t, emergit ex radiis &longs;olaribus, Sole po&longs;t &longs;e <lb/>relicto versùs ortum; ac proinde incipit videri. </s>

<s>Quoniam enim <lb/>eadem ratione qua &longs;upra demon&longs;trabitur, vt grauitas H, ad grauita<lb/>tem G, ita e&longs;&longs;e magnitudinem &longs;phæræ A, ad &longs;phæræ B, magnitudinem, <lb/>&longs;ed magnitudo &longs;phæræ A, ad magnitudinem &longs;phæræ B,* triplicatam<arrow.to.target n="note22"/><lb/>rationem habet eius, quam C, diameter &longs;phæræ A, ad diametrum <lb/>&longs;phæræ B, &longs;imiliter & cubus ex C, ad cubum ex diametro &longs;phæræ B, <pb pagenum="14"/><arrow.to.target n="note23"/> tripiicatam* rationem habet eius, quam C, ad diametrum &longs;phæræ, <lb/>B, ergo vt grauitas H, ad grauitatem G, ita erit cubus ex C, ad cubum <lb/>ex diametro &longs;phæræ B, &longs;ed vt grauitas H, ad grauitatem G, &longs;ta e&longs;t cu <lb/>bus ex C, ad cubum ex F, ergo cubus ex F, æqualis erit cubo diame<lb/>tri&longs;phæræ B; quare & latus F, æquabitur &longs;phæræ B, diametro. </s>

<s id="s.000180"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>inuen<lb/>ta igitur e&longs;t quantitas diametri liquidæ &longs;phæræ, B, quod facere opor<lb/>tebat. </s>

<s id="s.000181"> Optimè &longs;anè intelligo, quomodò ex diver&longs;o velocitatis gra<lb/>du, &longs;uppo&longs;ito etiam motu &longs;implici&longs;&longs;imo, vtriu&longs;que Planetæ diver&longs;i a&longs;pe<lb/>ctus &longs;equantur, & &longs;uppleatur vtriu&longs;que motus ortum versùs, motu illo <lb/>diurno; &longs;ed quæ&longs;o te, quomodò Apogæum & Perigæum explicabis? </s>

<s id="s.000182"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000183"> Per&longs;picuè omninò; &longs;uppo&longs;ito enim illo velocitatis gradu, <lb/>quem Mars motu recto acqui&longs;ivit, eo temporis <gap/>momento, quo c&oelig;pit agi <lb/>in orbem, &longs;imul vna cum Sole, retinuit tantulam inclinationem primus <lb/>ille impetus deor&longs;um, ab Apogæo, &longs;cilicet, in quo tune erat, cum volui <lb/>c&oelig;pit, eamque ad in&longs;tar motus accelerati, v&longs;que ad mediocrem di&longs;tan<lb/>tiam, & ab hac v&longs;que ad Perigæum ad in&longs;tar motus retardati; atque ita <lb/>deinceps: Ita porrò hæc inclinatio, qua Planeta deor&longs;um &longs;ur&longs;umque vi<lb/>bratur, eo modo, quo dixi, attemperata e&longs;t, vt men&longs;ura illius periodi, qua <lb/>&longs;cilicet Planeta ab Apogæo ad Apagæum redit, &longs;it ferè æqualis, priori pe<lb/>riodo, quæ &longs;cilicet intercedit, ab vna Conjunctione ad aliam Conjunctio<lb/>nem, ac proinde, po&longs;ito quod, Mars initio, cum primùm c&oelig;pit moveri mo<lb/>tu circulari, e&longs;&longs;et in Apogæo & in conjunctione, nece&longs;&longs;atiò &longs;equitur oppo<lb/>&longs;itionem fieri, cùm e&longs;t in Perigæo, ac &longs;imul deinde ad Coniunctionem & <lb/>Apogæum redire. </s>

<s id="s.000184">Cur autem prædictæ inclinationis &longs;it talis men&longs;ura, vel <lb/>periodus, facilè dictu e&longs;t; po&longs;ito &longs;cilicet, quod Naturæ Auctor ita di&longs;po<lb/>nere voluerit; nempe negari non pote&longs;t, quin res &longs;ecus e&longs;&longs;e potuerit, ac <lb/>diver&longs;us motuum & revolutionum modus; &longs;ed &longs;tatuto &longs;emel hoc ordi<lb/>ne, finis Planetæ fuit, ita volvi, & ad Solem componere &longs;e&longs;e; proportio<lb/>nata igitur fuit ad hunc finem prædicta inclinatio, imò & talis medio-<pb pagenum="14" xlink:href="025/01/018.jpg"/>cris di&longs;tantia, &longs;uppo&longs;ito tali velocitatis gradu acqui&longs;ito, &longs;ive à Motore <lb/>extrin&longs;eco, &longs;ive per motum acceleratum prævium. </s>

<s>Exemplum.</s>

<s>Qvidam proponit aliquod corpus &longs;olidum notæ <lb/>magnitudinis, & vult &longs;cire quanta erit magnitudo <lb/>alicuius liquidi, grauitatem habentis propo&longs;ito corpori <lb/>&longs;olido æqualem. </s>

<s id="s.000185"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/> Hæc &longs;anè in rem i&longs;tam optimè quadrarent, &longs;i Mars Perigæus <lb/>&longs;emper e&longs;&longs;et oppo&longs;itus, & Apogæus &longs;emper coniunctus, quod tamen cum <lb/>veritate <expan abbr="nõ">non</expan> con&longs;entit; Nam &longs;æpè extra oppo&longs;itionem e&longs;t Perigæus & Apo<lb/>gæus extra coniunctionem; quod certè in hac tua hypothe&longs;i ab&longs;urdi&longs;&longs;imum <lb/>e&longs;&longs;et; &longs;upponamus enim Martis Apogæum in O, Perigæum in E, & con<lb/>iunctionem citiùs fieri, quàm Mars perveniat ad Apogæum ; haud dubiè <lb/>coniunctio non fiet in O, &longs;ed versùs ortum, id e&longs;t, versùs R. </s>

<s id="s.000186">Igitur po&longs;t <lb/>alteram revolutionem punctum coniunctionis promovebitur vltra, versùs <lb/>ortum, atque ita deinceps; igitur po&longs;t multas revolutiones, eveniet tan<lb/>dem, vt coniunctio fiat in Perigæo, & Mars in Solem fortè impingat. </s>

<s><emph type="italics"/>Sit propo&longs;itum aliquod corpus plumbeum A, cuius magnitudo &longs;it<emph.end type="italics"/><lb/>10<emph type="italics"/>, & oporteat &longs;cire quanta erit magnitudo aquæ grauitatem haben<lb/>tis æqualem propo&longs;ito plumbo A, accipiatur aliquod corpus <expan abbr="plumbe&utilde;">plumbeum</expan> <lb/>D, cuius grauitas<emph.end type="italics"/> 23<emph type="italics"/>, deinde aquæ magnitudinem habentis æqualem <lb/>plumbo D, inueniatur grauitas, vt in exemplo propo&longs;. </s>

<s>8. dictum e&longs;t, <lb/>quæ &longs;it<emph.end type="italics"/> 2<emph type="italics"/>, & fiat vt<emph.end type="italics"/> 2<emph type="italics"/>, ad<emph.end type="italics"/> 23<emph type="italics"/>, ita<emph.end type="italics"/> 10<emph type="italics"/>, ad alium numerum qui&longs;it 115, is <lb/>igitur indicabit quanta erit magnitudo aquæ grauitatem habentis <lb/>æqualem propo&longs;ito plumbo A.<emph.end type="italics"/></s>

<s id="s.000187"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000188"> Nodus i&longs;te nullo negotio &longs;olvitur; &longs;i enim Sol &longs;emper e&longs;&longs;et in <lb/>mediocri di&longs;tantia, haud dubiè coniunctio &longs;emper fieret in Apogæo, & <lb/>oppo&longs;itio in Perigæo ; &longs;i autem Sol &longs;emper e&longs;&longs;et in Perigæo, oppo&longs;itio fie<lb/>ret vltra Perigæum, citrà verò &longs;i Sol &longs;emper e&longs;&longs;et in Apogæo ; nempe Sol <lb/>circa &longs;uum Apogæum ver&longs;ans, maiores orbes decurrit, igitur tardiùs <lb/>ab&longs;olvit; Quid mirum igitur, &longs;i Mars citiùs illum a&longs;&longs;equatur? </s>

<s>Quod &longs;i <expan abbr="propo&longs;it&utilde;">propo&longs;itum</expan> corpus plumbeum A &longs;it regulare vt po<lb/>te &longs;phæricum, cuius &longs;phæræ diameter &longs;it 10, & oporteat inue<lb/>nire quanta erit diameter &longs;phæræ ex aqua, grauitatem haben<lb/>tis æqualem propo&longs;itæ &longs;phæræ A, ita faciendum erit. </s>

<s id="s.000189">cùm ta<lb/>men Sol Perigæus paulò minores circulos de&longs;cribat, citiùs igitur illos ab<lb/>&longs;oluit, Mais igitur tardiùs illum a&longs;&longs;equitur: At cùm Sol &longs;emper recurrat <lb/>ab Apogæo ad Perigæum per mediocrem di&longs;tantiam, & vici&longs;&longs;im, iu&longs;ta fit <lb/>compen&longs;atio breviorum & maiorum orbium, & pro diver&longs;a coniuga<lb/>tione vtriu&longs;que Apogæi & Perigæi, e&longs;t enim diver&longs;a vtrinque revolutio<lb/>num periodus modò præit Coniunctio Apogæum, modò &longs;ub&longs;equitur, <lb/>v. g. &longs;i Sol circa Apogæum ver&longs;etur cum tardiùs orbes &longs;uos, vtpote ma<lb/>iores decurrat, citiùs illum Mars a&longs;&longs;equitur; ac proinde coniunctio præit <lb/>Apogæum ; &longs;i verò circa Perigæum, citiùs &longs;uos orbes conficit, ac pro<lb/>inde tardiùs illum Mars a&longs;&longs;equitur, ac proinde &longs;equitur po&longs;t Apogæum <lb/>coniunctio. </s>

<s id="s.000190">Hæc ni&longs;i facilia &longs;int & ex &longs;implici&longs;&longs;imis principiis deducta, <lb/>quid &longs;implex &longs;it & facile, nequit intelligi. </s>

<s><emph type="italics"/>Atcipiatur, vt diximus, aliquod corpus plumbeum D, cuius gra<lb/>uitas<emph.end type="italics"/> 23<emph type="italics"/>, deinde aquæ habentis magnitudinem æqualem plumbo D, <lb/>inueniatur grauitas quæ &longs;it<emph.end type="italics"/> 2<emph type="italics"/>, & fiat vt<emph.end type="italics"/> 2<emph type="italics"/>, ad<emph.end type="italics"/> 23<emph type="italics"/>, ita cubus ex<emph.end type="italics"/> 10<emph type="italics"/>, qui <lb/>e&longs;t 1000, ad alium numerum qui &longs;it<emph.end type="italics"/> 11500<emph type="italics"/>, is igitur numerus erit <lb/>cubus diametri &longs;phæræ ex aqua grauitatem habentis æqualem propo<lb/>&longs;itæ &longs;phæræ A, quare eius latus cubicum, quod est<emph.end type="italics"/> 22 57/100. <emph type="italics"/><expan abbr="proxim&utilde;">proximum</expan> <lb/>vero indicabit ip&longs;am diametrum.<emph.end type="italics"/></s>

<s id="s.000191">Suppono hoc loco Solem in <lb/>Apogæo po&longs;itum, maiorem orbem de&longs;cribere, &longs;cilicet diurnum, mi<lb/>nimum verò in Perigæo, licèt &longs;ecus aliquando accidat, de quo infra; <lb/>Sed ad rem hanc &longs;ufficit, Solem aliquando maiores, aliquando mino<lb/>res, aliàs mediocres orbes per annum decurrere; exempli autem gra<lb/>tia, &longs;uppono, maiores e&longs;&longs;e in Apogæo, minores in Perigæo, medio<lb/>cres in mediocri di&longs;tantia. </s>

<s><emph type="italics"/>Similiter &longs;i propo&longs;itum corpus plumbeum A, fuerit cubicum, vel <lb/>alicuius alterius formæ regularis, eadem ratione inueniemus latus cu <lb/>bi ex aqua grauitatem habentis æqualem propo&longs;ito cubo A, nam &longs;i cu<lb/>bi A, datum &longs;it latus<emph.end type="italics"/> 10<emph type="italics"/>, erit numerus 11500, cubus ex aqua æqualis <lb/>grauitate propo&longs;ito cubo A, quare latus cubicum numeri<emph.end type="italics"/> 11500<emph type="italics"/>, quod<emph.end type="italics"/><pb pagenum="15"/><emph type="italics"/>e&longs;t<emph.end type="italics"/> 22 17/100. <emph type="italics"/><expan abbr="proxim&utilde;">proximum</expan> vero indicabit quæ&longs;itum latus eubi ex aqua.<emph.end type="italics"/></s>

<s id="s.000192"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>Neque di&longs;&longs;imili ratione inuenietur magnitudo olei, aut ar<lb/>genti viui, aut cuiu&longs;cumque generis liquidi grauitatem habe<lb/>tis propo&longs;ito corpori &longs;olido æqualem, &longs;ed quomodo inuenien<lb/>da &longs;it grauitas argenti viui magnitudinem habentis æqualem <lb/>corpori &longs;olido, docebimus po&longs;t exemplum propo&longs;itionis de<lb/>cimæ quartæ. </s>

<s id="s.000193"> Negari non pote&longs;t, quin hæc &longs;int facillima; at vnum &longs;cire <lb/>averem, cur Mars aliquando matutinus bis emergat, & &longs;emel occul<lb/>tetur. </s>

<s>PROBLEMA IV. PROPOS. XI.</s>

<s id="s.000194"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>Propo&longs;itis duobus corporibus æque grauibus, vno &longs;o<lb/>lido, altero liquido, data liquidi corporis magnitu<lb/>dine, magnitudinem &longs;olidi inuenire. </s>

<s id="s.000195"> Vnus Keplerus, &longs;altem quod &longs;ciam, hoc a&longs;&longs;erit, cui tamen <lb/>parum fidei habendum e&longs;&longs;e puto; Vt vt &longs;it, hoc etiam facilè explicari <lb/>pote&longs;t; nam &longs;i Coniunctio præcedat Apogæum, cùm Mars &longs;uos orbes <lb/>citiùs ab&longs;oluat, quàm Sol &longs;uos, Solem po&longs;t &longs;erelinquit versùs ortum, at<lb/>que adeò emergit; quia verò paulò po&longs;t proximè accedit ad Apogæum, & <lb/>Sol ad Perigæum, Mars tardiùs, Sol citiùs &longs;uum orbem decurrit, hinc <pb pagenum="15" xlink:href="025/01/019.jpg"/>Sol Martem a&longs;&longs;equitur; hinc Martem occultari nece&longs;&longs;e e&longs;t; quia verò <lb/>po&longs;t aliquod tempus, Sol à Perigæo, & Mars ab Apogæo recedunt, Mars <lb/>citiùs &longs;uos orbes decurrit; hinc Solem po&longs;t &longs;e relinquit; hinc demum <lb/>emergit. </s>

<s id="s.000196">Si hoc phænomenum verum e&longs;t, vix puto aliam illius cau&longs;am <lb/>a&longs;&longs;ignari po&longs;&longs;e; &longs;ed vt iam indicavi, Kepleri dictis parum fidei haben<lb/>dum e&longs;&longs;e putarem; præterquàm quòd fieri potuit, vt cra&longs;&longs;iores vapores <lb/>Martem circa horizontem ortivum oculis &longs;ubduxerint per aliquot dies, <lb/>quibus deinde di&longs;cu&longs;&longs;is, &longs;e&longs;e iterum Planeta videndum præbuerit, ac <lb/>proinde non fuerit vera immer&longs;io, vel emer&longs;io; Vt vt &longs;it, nec enim de <lb/>hoc laboramus, &longs;i phænomenum verum e&longs;t, in no&longs;tra etiam hypothe&longs;i <lb/>&longs;ua cau&longs;a & ratione non caret, & vix &longs;cio, quonam pacto in ve&longs;tra ex<lb/>plicari po&longs;&longs;it. </s>

<s>SINT propo&longs;ita duo corpora æ<lb/>quæ grauia, A, quidem &longs;olidum, B, <lb/>vero liquidum, &longs;it autem, liquidi B; <lb/><figure id="fig10"/><lb/>data magnitudo F, & oporteat &longs;olidi <lb/>A, magnitudinem inuenire. </s>

<s>Accipia<lb/>tur aliquod corpus &longs;olidum D, <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> <lb/>generis cum corpore &longs;olido A, cuius <lb/>grauitas &longs;it G, deinde liquidi quod &longs;it <lb/>E, eiu&longs;dem generis cum corpore liqui <lb/>do B, magnitudinem æqualem<arrow.to.target n="note24"/> haben<lb/>tis &longs;olido D, *inueniatur grauitas, <lb/>quæ &longs;it H, & fiat vt grauitas G; ad gra<lb/>uitatem H, ita F, magnitudo, ad aliam magnitudinem, quæ &longs;it C; <lb/>quoniam igitur &longs;unt quatuor corpora D, E, A, B, quorum primum D, <lb/>& &longs;ecundum E, &longs;unt magnitudine æqualia, tertium vero A, & <expan abbr="quart&utilde;">quartum</expan> <lb/>B, æquæ grauia, & &longs;unt eiu&longs;dem generis &longs;olida D, A, &longs;imiliter, & liqui<lb/>da E, B,* erit vt grauitas G, ad grauitatem H, ita F, magnitudo ad ma<arrow.to.target n="note25"/><lb/>gnitudinem &longs;olidi A, &longs;ed vt grauitas G, ad grauitatem H, ita e&longs;t ma<lb/>gnitudo F, ad C, magnitudinem, ergo magnitudo C, æqualis erit ma<lb/>gnitudini corporis &longs;olidi A, inuenta igitur e&longs;t corporis &longs;olidi A, ma<lb/>gnitudo C, quod erat faciendum. </s>

<s id="s.000197"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000198"> Rectè omnia explicas, <emph type="italics"/>Antime,<emph.end type="italics"/> nec etiam dubito, quin <lb/>ablegato etiam ve&longs;tro Epicyclo, retardationem, accelerationem, retro <lb/>gradationem, &longs;tationem Martis explices; &longs;upponamus enim, Martei <lb/>motu &longs;emper æquabili &longs;uos agere orbes, cum maiorem circulum de&longs;cri<lb/>bat in Apogæo, & minorem in Perigæo, hunc citiùs, tardiùs illum per<lb/>ficit; Supponamus autem, versùs Apogæum &longs;uum orbem decurrere tar<lb/>diùs, quàm &longs;tellas, citiùs verò ver&longs;us Perigæum; haud dubiè versùs Apo<lb/>gæum, longè retro à &longs;tellis relinquitur versùs ortum, vnde progredi vi<lb/>detur in con&longs;equentia &longs;ignorum, idque maiore intervallo, quò propiùs <lb/>ad Apogæum accedit; minore verò, quo longiùs ab eo recedit; at verò <lb/>versùs Perigæum &longs;tellas ver&longs;us ortum po&longs;t &longs;e relinquit; igitur versùs oc<lb/>ca&longs;um progredi videtur, id e&longs;t, à &longs;tella recedere, quod retrogredi vocant; <lb/>vbi demum &longs;uum orbem æquè citò conficit atque &longs;tella, &longs;tare dicitur: Hæc <lb/>&longs;atis bene intelligo, etiam, ex principiis Phy&longs;icis, quæ per optica tan<lb/>tùm in no&longs;tra hypothe&longs;i, explicantur; nonnulla tamen à te &longs;cire de&longs;ide<lb/>ro, v. g. vtrùm Mars in mediocri di&longs;tantia citiùs &longs;uum orbem decurrat, <lb/>quàm &longs;tellæ, an verò tardiùs; deinde, cur Mars &longs;it retrogradus breuiori <lb/>tempore, & longiore directus; cur ab Apogæo ad Quadraturam plus <lb/>temporis ponat, quàm ab i&longs;ta ad Perigæum. </s>

<s><margin.target id="note24"/>8.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s><margin.target id="note25"/>7.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s id="s.000199"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000200"> Mars haud dubiè in mediocri di&longs;tantia tardiùs &longs;uum orbem <lb/>quàm &longs;tellæ, & non procul à Perigæo æquè citò illum decurrit; vnde <lb/>non mirum e&longs;t, &longs;i cum ab vna coniunctione ad aliam dies circiter 780. &longs;eu <lb/>revolutiones &longs;pirales intercurrant, &longs;it directus in 705. retrogradus in 73. <lb/>in 2. demum &longs;tationarius. </s>

<s>Qvod &longs;i propo&longs;ita duo corpora æque grauia A, B, fue<lb/>rint regularia vtpote &longs;phærica, fuerit autem liqui-<pb pagenum="16"/>dæ &longs;phæræ B, data diameter F, & oporteat inuenire quan<lb/>ta erit diameter &longs;olidæ &longs;phæræ A, ita faciendum erit. </s>

<s id="s.000201">Si autem in mediocri di&longs;tantia &longs;uum orbem <lb/>æquè citò ac &longs;tella conficeret, æque diu e&longs;&longs;et retrogradus, ac </s>

<s id="s.000202">directus; <lb/>ac proinde nunquam ad oppo&longs;itionem pervenire po&longs;&longs;et, & in Perigæo <lb/>e&longs;&longs;et etiam Soli coniunctus, vt Venus; vnde parum omnino regreditur, <lb/>&longs;i ob&longs;ervationes con&longs;ulamus, quibus haud dubiè &longs;tandum e&longs;t, non verò <lb/>fictitio Sy&longs;temati. </s>

<s>Accepto vt &longs;upra corpore &longs;olido D, & liquid E, inuenta grauitate, <lb/>vt dictum e&longs;t, fiat vt grauitas G, ad prauitatem H, ita cubus ex F, ad <lb/>alium cubum, cuius latus &longs;it C, Quoniam igitur eadem ratione qua <lb/>fupra o&longs;tendetut, vt grauitas G, ad grauitatem H, ita e&longs;&longs;e magnitudi<lb/>nem &longs;phæræ B, ad &longs;phæræ A, magnitudinem, &longs;ed magnitudo &longs;phæræ B, <lb/><arrow.to.target n="note26"/> ad magnitudinem &longs;phæræ A, *triplicatam rationem habet eius, quam <lb/>F, diameter &longs;phæræ B, ad diametrum &longs;phæræ A, &longs;imiliter, & cubus ex <lb/><arrow.to.target n="note27"/> F, ad cubum ex diametro &longs;phæræ A, <expan abbr="triplicatã*">triplicatan*</expan> rationem liabet eius, <lb/>quam F, ad diametrum &longs;phæræ A, ergo, vt grauitas G, ad <expan abbr="grauitat&etilde;">grauitatem</expan> <lb/>H, ita erit cubus ex F, ad cubum ex diametro &longs;phæræ A, &longs;ed vt graui<lb/>tas G, ad grauitatem H, ita e&longs;t cubus ex F, ad cubum ex C, ergo cubus <lb/>ex C, æqualis erit eubo diametri &longs;phæræ A, quare, & latus C, æquabi<lb/>tur ip&longs;ius &longs;phæræ A, diametro, inuenta igitur e&longs;t quantitas diametri <lb/>&longs;olidæ &longs;phæræ A, quod facere oportebat. </s>

<s id="s.000203"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000204"> Sy&longs;tema ex ob&longs;eruationibus &longs;tatuitur, ac proinde his &longs;tan<lb/>tibus, &longs;y&longs;tema etiam &longs;tare nece&longs;&longs;e e&longs;t. </s>

<s>Exemplum.</s>

<s id="s.000205"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000206"> Vis liberè dicam, quod &longs;entio; cum ex multis ob&longs;ervationi<lb/>bu: &longs;y&longs;tema &longs;tatuatur, eo &longs;emel &longs;tatuto, reliquas ad illud vt plurimùm <pb pagenum="16" xlink:href="025/01/020.jpg"/>accommodant v.g. ad explicandas huiumodi pa&longs;&longs;iones planetarum, puta <lb/>Martis, nonnulli cum Ptolemæo Epicyclum po&longs;uerunt, alij cum Tycone <lb/>circulum cuius centrum in Sole &longs;emper fixum e&longs;&longs;et; alij cum Copernico <lb/>orbem excentricum circa Solem immobilem in centro mundi; his autem <lb/>&longs;tatutis, ac definitis circulorum diametris; periodis, &longs;itu, &c. </s>

<s>Qvidam proponit aliquod corpus liquidum notæ <lb/>magnitudinis, & vult inuenire quanta erit magni<lb/>tudo alicuius &longs;olidi grauitatem habentis propo&longs;i<lb/>to corpori liquido æqualem. </s>

<s id="s.000207">omnes ob<lb/>&longs;ervationes ad prædicta &longs;y&longs;temata, vt dixi, accommodant, licèt vt pluri<lb/>mum, aliquæ parum congruant. </s>

<s id="s.000208">Hinc non mirum, &longs;i fortè &longs;upponant, Mar<lb/>tem pluribus gradibus retrogredi, quam re ip&longs;a retrogrediatur. </s>

<s><emph type="italics"/>Sit propo&longs;itum aliquod corpus aqueum B, cuius magnitude &longs;it 115, <lb/>& oporteat inuenire quanta erit magnitudo plumbi grauitatem ha<lb/>bentis æqualem propo&longs;itæ aquæ B, accipiatur aliquod corpus <expan abbr="plumbe&utilde;">plumbeum</expan> <lb/>D, cuius grauitas &longs;it verbi gratia<emph.end type="italics"/> 23<emph type="italics"/>, deinde aquæ magnitudinem ba<lb/>bentis æqualem plumbo D, inueniatur grauitas quæ &longs;it<emph.end type="italics"/> 2. <emph type="italics"/>id autem do<lb/>cuit propo&longs;itionis octauæ exemplum, & fiat vt<emph.end type="italics"/> 23<emph type="italics"/>, ad<emph.end type="italics"/> 2<emph type="italics"/>, ita 115, ad <lb/>alium numerum qui &longs;it<emph.end type="italics"/> 10<emph type="italics"/>, is igitur numerus indicabit quanta erit <lb/>magnitudo plumbi grauitatem habentis æqualem propo&longs;itæ aquæ B.<emph.end type="italics"/></s>

<s id="s.000209">Sed iam ad <lb/>alia tua po&longs;tulata gradum fac<gap/></s>

<s>Quod &longs;i propo&longs;itum corpus aqueum B, &longs;it &longs;phæricum, cuius <lb/>&longs;phæræ diameter &longs;it 10, & oporteat inuenire quanta erit dia<lb/>meter &longs;phæræ ex plumbo, grauitatem habentis æqualem pro<lb/>po&longs;itæ &longs;phæræ B, ita faciendum erit. </s>

<s id="s.000210"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s><emph type="italics"/>Accepto, vt diximus aliquo corpore plumbeo D, cuius grauitas<emph.end type="italics"/> 23, <lb/><emph type="italics"/>& aquæ magnitudinem habentis æqualem plumbo D, inuenta graui<emph.end type="italics"/><pb pagenum="17"/><emph type="italics"/>tate 2, fiat vt<emph.end type="italics"/> 23<emph type="italics"/>, ad<emph.end type="italics"/> 2<emph type="italics"/>, ita cubus ex<emph.end type="italics"/> 10<emph type="italics"/>, hoc est<emph.end type="italics"/> 1000<emph type="italics"/>, ad alium nume<lb/>rum qui &longs;it<emph.end type="italics"/> 86 22/2<gap/><31> <emph type="italics"/>is igitur numerus erit cubus diametrs &longs;phæræ ex <lb/>plumbo, grauitatem æqualem habentis propo&longs;ite ex aqua &longs;phæræ B, <lb/>quare eius latus cubicum, quod est<emph.end type="italics"/> 4 41/100<31> <emph type="italics"/>ferè, indicabit ip&longs;am <lb/>diametrum.<emph.end type="italics"/></s>

<s id="s.000211"> Su&longs;tine parumper, vnum exciderat, quod jam in mentem <lb/>venit; dixi&longs;ti enim paulò ante, ni fallor, Solem in Perigæo &longs;uum orbem <lb/>citiùs, in Apogæo tardiùs conficere; dies igitur no&longs;tri &longs;unt inæquales. </s>

<s><emph type="italics"/>Similiter &longs;i propo&longs;itum corpus aqueum B, fuerit cubicum, vel alicu <lb/>las alterius formæ regularis, eadem ratione vtemur ad inueniendum <lb/>latus cubi ex plumbo, grauitatem habentis æqualem propo&longs;ito ex aqua <lb/><gap/>bo B, nam &longs;i ex aqua cubi B, datum &longs;it latus<emph.end type="italics"/> 10<emph type="italics"/>, erit numerus<emph.end type="italics"/><lb/>86 22/2<gap/><31> <emph type="italics"/>cubus ex plumbo æqualis grauitate propo&longs;ito ex aqua cubo B, <lb/>quare latus cubicum numeri<emph.end type="italics"/> 86 22/2<gap/><31> <emph type="italics"/>quod e&longs;t<emph.end type="italics"/> 4 41/100<31> <emph type="italics"/>ferè, indicabit <lb/>quæ&longs;itum latus cubi ex plumbo.<emph.end type="italics"/></s>

<s id="s.000212"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>Neque di&longs;&longs;imili ratione inuenienda erit magnitudo auri, <lb/>argenti, ceræ, aut cuiu&longs;cunque &longs;olidi, grauitatem habentis <lb/>propo&longs;ito corpori liquido æqualem. </s>

<s id="s.000213"> Novum profectò dictu non e&longs;t; nempe in antiqua etiam hypo<lb/>the&longs;i Ptolemaica, ex duplici capite illa dierum inæqualitas petitur; primò <lb/>ex eo quod Sol in Apogæo excentrici in con&longs;equentia versùs ortum videa<lb/>tur tardiùs promoveri, contra verò velociùs in Perigæo ; igitur in Apogæo <lb/>citiùs orbem &longs;uum ab&longs;olvit, diurnum &longs;cilicet, ab ortu ad occa&longs;um, tardiùs <lb/>verò in Perigæo: Igitur circa Sol&longs;titium æ&longs;tivum, ex hoc capite &longs;unt bre<lb/>viores, & circa brumale, longiores. </s>

<s id="s.000214">Secundò ex a&longs;cen&longs;ione recta & obli<lb/>qua Eclipticæ, nempe æquali tempore major arcus a&longs;cendit obliquæ, quàm <lb/>rectæ; Igitur Sol in Sol&longs;titiis in quibus e&longs;t a&longs;cen&longs;io recta, tardiùs, in Æqui<lb/>noctiis, in quibus e&longs;t obliqua velociùs orbem diurnum ab&longs;olvit. </s>

<s>PROBLEMA V. PROPOS. XII.</s>

<s id="s.000215">Sed his <lb/>rejectis, ex alio capite, prædictam inæqualitatem etiam duci po&longs;&longs;e dicimus; <lb/>&longs;cilicet ex inæqualibus circulis, &longs;eu &longs;piris à Sole decur&longs;is, cum eodem &longs;ci<lb/>licet velocitatis gradu; vnde reverà fit, vt Apogæus majorem, & tardiùs, <lb/>Perigæus verò breviorem & citiùs orbem decurrat; Vellem, vt fideli fune<lb/>pendulo inæqualitatem illam probares, numerato &longs;cilicet vibrationum nu<lb/>mero, idque &longs;ub initium Iulij & Ianuarij: Tunc enim e&longs;t aliqua, etiam for<lb/>tè &longs;en&longs;ibilis circulorum in æqualitas, igitur & dierum; & plures vibratio<lb/>nes numerantur intra &longs;patium &longs;emihoræ &longs;ub initium Iulij, Sole in Apogæo <lb/>exi&longs;tente, quàm &longs;ub initium Ianuarij, quo tempore Sol in Perigæo ver<lb/>&longs;atur; & his vibrationibus, crede mihi, aliquam differentiam invenires, <lb/>minimam certè, at, ni&longs;i &longs;allor, &longs;en&longs;ibilem. </s>

<s>Propo&longs;itis duobus &longs;olidis corporibus magnitudine <lb/>æqualibus, data grauitate vnius, grauitatem al<lb/>terius inuenire. </s>

<s id="s.000216"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>SINT propo&longs;ita duo corpora &longs;o<lb/>lida magnitudine æqualia A, B, &longs;it au<lb/><figure id="fig11"/><lb/>tem vnius, vtpote ip&longs;ius A, data gra<lb/>uitas C, & oporteat inuenire grauita<lb/>tem ip&longs;ius B. </s>

<s id="s.000217"> Si hæc cum veritate con&longs;entiant, nullus dubitat, quin A&longs;tro<lb/>nomos plurimùm tibi ob&longs;trinxeris, &longs;ed antequam meis po&longs;tulatis facias <lb/>&longs;atis, &longs;i tibi grave non e&longs;&longs;et, vellem, vt rude &longs;altem tui &longs;y&longs;tematis Solaris <lb/>&longs;chema mihi exhiberes. </s>

<s>Accipiatur aliquod &longs;oli<lb/>dum corpus D, eiu&longs;dem generis cum <lb/>corpore &longs;olido A, cui æquale grauita<lb/>te accipiatur alterum E, eiu&longs;dem ge<lb/>neris cum corpore B, deinde liquidi <lb/>magnitudine æqualis corpori D,<arrow.to.target n="note28"/> *in<lb/>ueniatur grauitas, quæ &longs;it G, item li<lb/>quidi eiu&longs;dem generis, æqualis ma<lb/>gnitudine corpori E,* inueniatur grauitas, quæ &longs;it H, & fiat vt H, ad<arrow.to.target n="note29"/><lb/>G, ita C, ad aliam grauitatem, quæ &longs;it F. </s>

<s id="s.000218"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>Quoniam igitur &longs;unt qua<lb/>tuor corpora A, B, D, E, quorum A, B, primum videlicet, & &longs;ecundum <lb/>&longs;unt æqualia magnitudine, tertium vero D, & E, quartum æque gra<lb/>uia, & &longs;unt <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> generis &longs;olida A, D, itidem &longs;olida B, E, *erit vt<arrow.to.target n="note30"/> gra<lb/>uitas C, ad &longs;olidi B, grauitatem, ita grauitas H, ad grauitatem G, &longs;ed <pb pagenum="18"/>vt grauitas H, ad <expan abbr="grauitat&etilde;">grauitatem</expan> G, ita e&longs;t grauitas C, ad F, grauitatem; er<lb/>go grauitas F, æqualis erit grauitati &longs;olidi B, inuenta igitur e&longs;t cor<lb/>poris &longs;olidi B, grauitas F, quod &longs;acere oportebat. </s>

<s id="s.000219"> Prolixior reverà e&longs;&longs;em, &longs;i rem hanc, vt par e&longs;t, explicandam <lb/>&longs;u&longs;ciperem; &longs;ed quandoquidem rudiorem dumtaxat delineationem fla<lb/>gitas, eò libentiùs tibi morem geram. <pb pagenum="17" xlink:href="025/01/021.jpg"/><figure id="id.025.01.021.1.jpg" xlink:href="025/01/021/1.jpg"/><lb/>Sit igitur centrum mundi A, Axis <lb/>mundi BC, diameter Æquatoris KF, <lb/>diameter Tropici Cancri ID, Capri<lb/>corni LH, Apogæum D, Perigæum L, <lb/>mediocris di&longs;tantia AQ, quæ di&longs;po<lb/>&longs;itio fortè fuit anno mundi 5400. Sit <lb/>angulus obliquitatis Zodiaci DAF, <lb/>item HAF, &longs;upponamus Solem in <lb/>Apogæo cum tali velocitatis gradu, <lb/>quo circa Axem mundi æquabili mo<lb/>tu &longs;uum orbem diurnum decurrit ab <lb/>Ortu ad Occa&longs;um, cum duplici in<lb/>clinatione, altera &longs;cilicet versùs <lb/>centrum A, ad in&longs;tar motus accelerati, <lb/>v&longs;que ad mediocrem di&longs;tantiam, & <lb/>retardati ab hac ad Perigæum, atque <lb/>ita deinceps; altera verò versùs E, ad <lb/>in&longs;tar pariter motus accelerati v&longs;que <lb/>ad Æquatorem, & retardati ab Æqua<lb/>tore ad Tropicum, atque ita deinceps; <lb/>cùm autem circuli &longs;int, vt diametri, <lb/>vel &longs;emidiametri, erunt orbes decur<lb/>&longs;i, &longs;i tamen decurruntur orbes, vt B <lb/>D, AQ, CH; & cùm AQ, &longs;it haud <lb/>dubiè major, quàm BD, maximus <lb/>circulus decurritur circa Æquatorem <lb/>quod certè in hac hypothe&longs;i &longs;ingulare non e&longs;t, cùm etiam in Ptolemaica, <lb/>& Tyconica locum habeat Dixi, cautè, &longs;i tamen decurrantur orbes, quia <lb/>orbes non decurruntur, &longs;ed &longs;piræ, quæ ita componuntur, per majorem aut <lb/>minorem di&longs;tractionem, vt &longs;ingulæ æquales ferè &longs;ingulis evadant, dico <lb/>ferè, quia non nego, aliquam ine&longs;&longs;e inæqualitatem, vt &longs;upra dictum e&longs;t. <lb/></s>

<s id="s.000220">Finge igitur, &longs;epo&longs;ito motu circulari, Solem duplici inclinatione, eo modo, <lb/>quo &longs;uprà dictum e&longs;t, in&longs;tructum, ite, ac redire, tum versùs centrum mun<lb/>di A, tum à D ad E per arcum DE, & vtraque &longs;uo gaudeat acce&longs;&longs;u & <lb/>rece&longs;&longs;u; hoc quidem motum retardatum, illo verò acceleratum imitante, <lb/>&longs;itque men&longs;ura acce&longs;&longs;us primæ inclinationis FQ, vel EV, & rece&longs;&longs;us VH; <lb/>Secundæ verò, acce&longs;&longs;us DF, & rece&longs;&longs;us FE, atque ita vici&longs;&longs;im; finge igi<lb/>tur, inquam, Solem ita moveri, &longs;epo&longs;ito motu circulari diurno; ibit haud <lb/>dubiè per lineam curvam DQH. </s>

<s><margin.target id="note28"/>8.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s><margin.target id="note29"/>5.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s id="s.000221"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000222"> Quis amabo &longs;ciat, lineam illam curvam e&longs;&longs;e? </s>

<s><margin.target id="note30"/>6.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s id="s.000223">quid &longs;i dixe<lb/>rim e&longs;&longs;e rectam in latere cylindri, vel coni? </s>

<s id="s.000224">Deinde &longs;i curva e&longs;t, quis de<lb/>finiat, quæ & qualis &longs;it? </s>

<s>Hoc Problema magni momenti e&longs;t, pleri&longs;que artificibus <lb/>maximo v&longs;ui e&longs;&longs;e pote&longs;t. </s>

<s id="s.000225">vide, quàm ab&longs;tru&longs;a & ob&longs;cura nobis obtru<lb/>das. </s>

<s>in arte fu&longs;oria propo&longs;ito operis modu <lb/>lo, ex illius grauitate, facile metalli ad opus faciendum, gra<lb/>uitatem inueniet, &longs;i enim hoc ignoret artifex, periculum e&longs;t, ne <lb/>metallum, aut deficiat, vel &longs;i multum e&longs;t, ob nimiam graui<lb/>tatem difficile tractetur. </s>

<s id="s.000226"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>Neque tormenti bellici magi&longs;tro inutile erit, is enim cogni<lb/>ta grauitate alicuius globi, exempli gratia ex plumbo, &longs;tatim <lb/>alterius globi eiu&longs;dem magnitudinis, vel &longs;it ex lapide, vel ex <lb/>fcrro, vel ex quacunque alia materia, grauitatem inueniet. </s>

<s id="s.000227"> Recta e&longs;&longs;e non pote&longs;t in latere cylindri: &longs;it enim DE recta, &longs;i <lb/>fieri pote&longs;t; erit AE æqualis, AD; igitur Perigæum æquè di&longs;tabit a <pb pagenum="18" xlink:href="025/01/022.jpg"/>Apògæum, quod repugnat; nec etiam in latere coni. </s>

<s id="s.000228">Sit enim DH re<lb/>cta; &longs;itque exempli gratia HE <gap/> ferè totius AE; haud dubiè AX e&longs;t <lb/>brevior AH vt con&longs;tat ex Trigonometria; accedit enim propiùs ad per<lb/>pendicularem; omitto calculos, quia res e&longs;t per&longs;picua, etiam tyronibus <lb/>Geometris; dixi <gap/> exempli gratia, cùm re ip&longs;a minor &longs;it. </s>

<s>Exemplum.</s>

<s>Qvidam proponit aliquod corpus &longs;olidum notæ <lb/>grauitatis, & vult &longs;cire quanta erit grauitas alicu<lb/>ius &longs;olidi, alterius generis, magnitudinem habentis pro<lb/>po&longs;ito corpori &longs;olido æqualem. </s>

<s id="s.000229"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000230"> Quæ&longs;o te, Antime, tibi per&longs;picuum e&longs;t, aliis fortè non <lb/>item, memini aliquando à magno Geometra, tibi haud ignoto, audii&longs;&longs;e, <lb/>cum de te, tua que hypothe&longs;i &longs;ermo incidi&longs;&longs;et, DH, e&longs;&longs;e latus coni. </s>

<s><emph type="italics"/>Sit propo&longs;itum aliquod corpus plumbeum A, cuius grauitas &longs;it<emph.end type="italics"/><lb/>1150<emph type="italics"/>, & oporteat inuenire quanta erit grauitas stanni <expan abbr="magnitudin&etilde;">magnitudinem</expan> <lb/>habentis æqualem propo&longs;ito plumbo A. </s>

<s>Accipiantur duo corpora æque <lb/>grauia, D, plumbeum, E, stinncum, deinde duarum quantitatum, <lb/>aquæ, quarum una &longs;it æqualis magnitudine plumbo D, altera &longs;tanno <lb/>E, <expan abbr="inueniãtur">inueniantur</expan> grauitates, quæ &longs;int, primæ videlicet quantitatis aquæ<emph.end type="italics"/><lb/>74, <emph type="italics"/>&longs;ecundæ vero<emph.end type="italics"/> 115<emph type="italics"/>, & fiat vt<emph.end type="italics"/> 115<emph type="italics"/>, ad<emph.end type="italics"/> 74<emph type="italics"/>, ita<emph.end type="italics"/> 1150<emph type="italics"/>, ad alium nume<lb/>rum, qui &longs;it<emph.end type="italics"/> 740<emph type="italics"/>, is igitur numerus indicabit grauitatem stanni, ma<lb/>gnitudinem habentis propo&longs;ito plumbo A.<emph.end type="italics"/></s>

<s id="s.000231"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000232"> Scio, quem intelligas, hoc etiam mihi primùm, ne quid tibi di&longs;<lb/>&longs;imulem in mentem venerat, & maximè in votis hoc erat; &longs;i enim DH &longs;it <lb/>latus coni, volvaturque BDEC, circa Axem BC, <expan abbr="genit&utilde;">genitum</expan> erit fru&longs;tum ma<lb/>jus coni, quod &longs;i &longs;ecetur per Axem DL, erit &longs;ectio elliptica &longs;imul, & <lb/>ecliptica, vnde Kepleri & aliorum ellip&longs;is ex Phy&longs;icis principiis demon<lb/>&longs;trata maneret; &longs;ed, vt iam dixi, DH non e&longs;t linea recta; &longs;i enim, &longs;i <lb/>fieri pote&longs;t, ducatur recta DGE; igitur AX e&longs;t minor AH, quod re<lb/>pugnat, vt dixi; cùm enim angulus DAF &longs;it gradus 23.30. min. erit. </s>

<s>Etiam &longs;i non accipiantur duo corpora, plumbeum videlicet <lb/>& &longs;tanneum, æque grauia, &longs;ed grauitate quacunque, grauitas <lb/>&longs;tanni magnitudinem habentis æqualem propo&longs;ito plumbo <lb/>D, inuenietur &longs;ic. </s>

<s id="s.000233">DG <lb/>illius &longs;inus rectus; igitur AG &longs;inus complementi; iam verò in hoc libel<lb/>lo tabularum &longs;inuum, invenio, vt vides, GA e&longs;&longs;e æqualem &longs;inui recto <lb/>anguli grad 66.30 minut. </s>

<s id="s.000234">qui e&longs;t ad <expan abbr="&longs;in&utilde;">&longs;inum</expan> totum, vt 91706.ad 100000.Igi<lb/>tur GF erit vt 8794.Igitur fere <gap/> totius AD. </s>

<s><emph type="italics"/>Accipiantur duo corpora D, plumbeum, E, &longs;tanneum grauitate <lb/>quacunque, &longs;it vcrbi gratia plumbi D, grauitas<emph.end type="italics"/> 23<emph type="italics"/>, &longs;tanni vero E, <lb/>grauitas<emph.end type="italics"/> 37<emph type="italics"/>, deinde duarum quantitatum aquæ, quarum vna &longs;it ma<lb/>gnitudine æqualis plumbo D, altera stanno E, inueniantur graui<lb/>tates, quæ &longs;int, primæ videlicet quantitatis<emph.end type="italics"/> 2<emph type="italics"/>, &longs;ecundæ vero<emph.end type="italics"/> 5<emph type="italics"/>, & fiat,<emph.end type="italics"/><pb pagenum="19"/><emph type="italics"/>ot 23, ad 2, ita 37, ad<emph.end type="italics"/> 3 5/21. <emph type="italics"/>grauitas igitur aquæ, magnitudinem <lb/>habentis æqualem plumbo, cuius grauitas est 37, erit<emph.end type="italics"/> 3 5/21. </s>

<s id="s.000235">Sed HE &longs;upponitur <gap/> Igi<lb/>tur AH e&longs;t maior AG, & potiori iure maior AX, quæ minor e&longs;t AG: <lb/>quanquam, vt dixi, fortè E e&longs;t minor <gap/> AE. </s>

<s><emph type="italics"/>Et quoniam aquæ, magnitudinem habentis æqualem stanno E, cu<lb/>ius grauitas est 37, e&longs;t grauitas<emph.end type="italics"/> 5, <emph type="italics"/>erunt grauitates duarum quan<lb/>titatum aquæ<emph.end type="italics"/> 3 5/21, & 5, <emph type="italics"/>quarum quantitatum prima e&longs;t æqualis <lb/>magnitudine corpori plumbeo, &longs;ecunda stanneo, que &longs;unt æque gra<lb/>uia, vtriu&longs;que enim grauitas est<emph.end type="italics"/> 37. <emph type="italics"/>Fiatigitur vt<emph.end type="italics"/> 5, <emph type="italics"/>ad<emph.end type="italics"/> 3 5/21, <emph type="italics"/>it a<emph.end type="italics"/><lb/>1150, <emph type="italics"/>ad alium numerum, qui &longs;it<emph.end type="italics"/> 740, <emph type="italics"/>tantaigitur erit grauitas <lb/>&longs;tanni, magnitudinem habentis æqualem propo&longs;ito plumbo A, quanta <lb/><gap/>iam inueniebatur & &longs;upra.<emph.end type="italics"/></s>

<s id="s.000236"><emph type="italics"/>Angu&longs;tinus.<emph.end type="italics"/></s>

<s>Quod &longs;i propo&longs;itum &longs;it cereum corpus aliquod, aut cuiu&longs;<lb/>cunque generis &longs;olidi, &longs;iue leuioris quam aqua, &longs;iue grauio<lb/>ris, & oporteat inuenire grauitatem alicuius &longs;olidi alterius <lb/>generis, magnitudine æqualis propo&longs;ito corpori &longs;olido. </s>

<s id="s.000237"> Satis e&longs;t; igno&longs;ce, hæc Geometrica pene mihi exciderunt; <lb/>&longs;ed &longs;i linea DQH curva e&longs;t, vix &longs;ciri pote&longs;t, quænam & qualis <lb/>&longs;it. </s>

<s>Ea<lb/>dem ratione qua &longs;upra inuenietur quæ&longs;ita &longs;olidi grauitas, &longs;ed <lb/>hoc &longs;olum animaduertendum e&longs;t, quod non eadem ratione <lb/>inuenitur grauitas aquæ, magnitudinem habentis æqualem <lb/>propo&longs;ito cuiu&longs;cunque generis &longs;olido, alia enim tenenda e&longs;t <lb/>ratio ad inueniendam grauitatem prædictæ aquæ, quando <lb/>propo&longs;itum &longs;olidum &longs;it grauius quam aqua, alia vero quando <lb/>leuius, &longs;ed &longs;iue &longs;it leuius, &longs;iue grauius, de inuentione huiu&longs;<lb/>modi grauitatis, in exemplo propo&longs;itionis octauæ, &longs;atis e&longs;t ex<lb/>plicatum. </s>

<s id="s.000238"><emph type="italics"/>Antimus.<emph.end type="italics"/></s>

<s>PROBLEMA VI. PROPOS. XIII.</s>

<s id="s.000239"> Hoc etiam &longs;ciri pote&longs;t; e&longs;t enim linea quædam motus mix<lb/>ti, à magno Archimede iam olim inuenta; fac enim radium DA volui in <lb/>hoc plano circa A, motu quidem accelerato, donec perveniat ad AF, <lb/>retardato verò donec veniat ad AE, & &longs;imul vna punctum D ire versùs A <lb/>in radio AD mobili, motu quidem accelerato, donec decurrerit &longs;egmen<lb/>tum radij æquale VE, retardato verò, tantundem; dictum punctum D <lb/>ibit per curvam DQH modò acce&longs;&longs;us & rece&longs;&longs;us vtriu&longs;que motus &longs;int <lb/>æquè diuturni; vnde vides curvam DQH e&longs;&longs;e veram &longs;piralem Archi<lb/>medis; ac proinde Sectio per axem DL, in &longs;olido genito à plano BDQ <lb/>HC circa axem BC revoluto, quæ munere Eclipticæ defungitur, non <lb/>e&longs;t vera ellip&longs;is, cuius tractatio ad præ&longs;entem quæ&longs;tionem non pertinet. </s>

<s>Propo&longs;itis duobus &longs;olidis corporibus æque graui<lb/>bus, data magnitudine vnius, magnitudinem alte<lb/>rius inuenire. </s>

<s id="s.000240"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>SINT propo&longs;ita duo corpora &longs;olida æque grauia A, B, &longs;it au<lb/><gap/>m vnius, vtpote ip&longs;ius A, data magnitudo C, & oporteat inueni<lb/>re magnitudinem ip&longs;ius B, Accipiatur aliquod &longs;olidum corpus D, <lb/>ciu&longs;dem generis cum &longs;olido A, & &longs;it eius grauitas G, deinde &longs;olidi <lb/>corporis quod &longs;it E, eiu&longs;dem generis cum &longs;olido B, magnitudine <lb/>æqualis ip&longs;i D, inueniatur grauitas, quæ &longs;it H, hoc autem, Proble<lb/>ma antecedens docuit, & fiat vt grauitas H, ad grauitatem G, ita <lb/>magnitudo C, ad aliam magnitudinem, quæ &longs;it F. </s>

<s id="s.000241"> Iam vtcumque tuam Solarem hypothe&longs;im concipio, vis <lb/>enim Solem &longs;implici motu æquabili diurno ferri ab Ortu ad Occa&longs;um, <expan abbr="c&utilde;">cum</expan> <lb/>gemina inclinatione, eo modo, quo dixi&longs;ti; & cum vno ferè gradu &longs;in<lb/>gulis diebus à &longs;tellis retroagatur, videtur &longs;emper inhærere prædictæ el<lb/>lipticæ mobili circa eundem Mundi Axem; ita tamen vt &longs;patio 24. hora<lb/>rum quodlibet illius punctum &longs;uum integrum orbem decurrat, itemque <lb/>in ea moveri ab Occa&longs;u ad Ortum, ita vt &longs;patio vnius anni totam decur<lb/>rat; &longs;ed hic motus non e&longs;t realis, vt vocant, &longs;ed tantùm apparens, ita<lb/>que hæc &longs;atis bene intelligo; &longs;ed non levis difficultas mihi e&longs;&longs;e videtur, <pb pagenum="19" xlink:href="025/01/023.jpg"/>tum in explicando Apogæi motu, tum in excogitanda aliqua ratione Ano<lb/>maliæ Solis; Sol enim, vt nemo ne&longs;cit, &longs;tatuto Apogæo in D, plures dies <lb/>ponit à Tropico Cancri ad Æquatorem, quàm ab Æquatore ad Tropicum <lb/>Capricorni. </s>

<s>Quoniam igitur <pb pagenum="20"/>&longs;unt quatuor corpora grauia E, D, B, <lb/>A, quorum E, D, primum videlicet, <lb/><figure id="fig12"/><lb/>& &longs;ecundum, &longs;unt æqualia magnitu<lb/>dine, tertium vero B, & quartum A, <lb/>æquegrauia, & &longs;unt eiu&longs;dem generis <lb/>corpora E, B, &longs;imiliter & corpora <lb/><arrow.to.target n="note31"/> D, A, * erit vt grauitas H, ad graui<lb/>tatem G, ita magnitudo C, ad corpo<lb/>ris B, magnitudinem, &longs;ed vt grauitas <lb/>H, ad grauitatem G, ita e&longs;t magnitu<lb/>do C, ad F, magnitudinem, ergo ma<lb/>gnitudo F, æqualis erit magnitudini <lb/>corporis B. inuenta igitur e&longs;t corporis B, magnitudo F, quod facere <lb/>oportebat. </s>

<s id="s.000242"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s><margin.target id="note31"/>7.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s id="s.000243"> Rectè omninò: Hinc vides, ni fallor, duo triangula ABD, <lb/>ACH e&longs;&longs;e proportionalia, quia æquiangula; ac proinde, vt AD ad AH, <lb/>ita BA ad AC; igitur AC e&longs;t minor AB; igitur breviore tempore de<lb/>curritur: &longs;epo&longs;ito enim motu circulari, cum prima inclinatione, &longs;it mo<lb/>tus acceleratus à B ad A, & retardatus ab A versùs C, &longs;i &longs;patia &longs;int, vt <lb/>lineæ BA, AC, &longs;itque inter BA, AC media proportionalis BY, erunt <lb/>tempora vt YB, AB; &longs;unt enim &longs;patia in duplicata ratione tempo<lb/>rum. </s>

<s id="s.000244">Hoc autem ex duplici analogia facilè intelligitur; Prima e&longs;t; <lb/><figure id="id.025.01.023.1.jpg" xlink:href="025/01/023/1.jpg"/><lb/>Sit corda ten&longs;a BC, tendatur vltrà in BAC, affixo <lb/>gemino clavo in FG, redit in BC motu accelerato; hic <lb/>e&longs;t acce&longs;&longs;us; per rece&longs;&longs;um verò pervenit in FEG; ita vt <lb/>DE &longs;it ad DA, vt DF ad DB; tempus autem acce&longs;&longs;us <lb/>e&longs;t ad tempus rece&longs;&longs;us, vt AD ad DE. </s>

<s>Quod &longs;i propo&longs;ita duo corpora æque grauia A, B, fue<lb/>rint regularia, vtpote &longs;phærica, fuerit autem &longs;phæræ A, <lb/>data diameter C, & oporteat inuenire, quanta erit dia<lb/>meter &longs;phær&ecedil; B, ita faciendum erit. </s>

<s id="s.000245">Alia verò &longs;it <lb/>hæc; &longs;it BI funependulum in perpendiculo, pendens ex <lb/>B, &longs;itque affixus clavus in F, ita prima &longs;emivibratio fiat per <lb/>arcum AI, altera verò per IE, &longs;it inter AD, DE, media <lb/>proportionalis AO, tempus vibrationis AI erit ad tem<lb/>pus vibrationis IE, vt AD ad AO; &longs;unt enim tempora in <lb/>&longs;ubduplicata ratione &longs;patiorum, vt con&longs;tat ex doctrina mo<lb/>tuum. </s>

<s id="s.000247">Vtraque analogia facilè applicatur. </s>

<s>Accepto corpore &longs;olido D, & inuenta &longs;olidi corporis E, grauita<lb/>te, vt &longs;upra dictum e&longs;t, fiat vt grauitas H, ad grauitatem G, ita cu<lb/>bus ex C, ad alium cubum, cuius latus &longs;it F. </s>

<s id="s.000248">Quod verò &longs;pe<lb/>ctat ad rationem motus accelerati, vt ad calculos reduca<lb/>tur, fortè po&longs;&longs;et accipi quadrans circuli BZ, qui repræ&longs;en<lb/>tet tempus acce&longs;&longs;us divi&longs;um in quotcunque partes æqua<lb/>les. </s>

<s id="s.000249">v. g. accipiatur (<emph type="italics"/>in Figura priore<emph.end type="italics"/>) BN, arcus 30. <lb/>graduum demittatur NM perpendicularis, acce&longs;&longs;us pro<lb/>motus e&longs;t illo tempore &longs;egmento BM, vel vt ad Phy&longs;icas <lb/>cau&longs;as propiùs accedatur, acciperet aliquis &longs;emiparabo<lb/>lam ABZ, cuius Axis &longs;it BA, applicata quælibet, &longs;eu <lb/>&longs;emiba&longs;is AZ, hæc &longs;i dividatur in quotcumque partes <lb/>æquales, puta in 90. repræ&longs;entat tempus acce&longs;&longs;us, v.g. ab initio acce&longs;&longs;us <lb/>&longs;it tempus AO 45.graduum; ducatur ON parallela Axi AB, tum appli<lb/>cata NM, applicatæ AZ parallela, BM erit men&longs;ura &longs;patij decur&longs;i in <lb/>acce&longs;&longs;u, nec fortè vna progre&longs;&longs;io multùm differt ab alia, vt patet ex <lb/>calculatione; vix enim a&longs;&longs;umptis quotcunque partibus temporis, diffe<lb/>rentia &longs;patiorum acce&longs;&longs;us vnum gradum integrum adæquat; &longs;ed profectò, <lb/>vt A&longs;tronomicè vtramque probo, ita neutram phy&longs;ice admitto; germa<lb/>nam dabimus &longs;uo loco & Phy&longs;icam. </s>

<s>Quoniam igitur eadem <lb/>ratione, qua &longs;upra, demon&longs;trabitur, vt grauitas H, ad grauitatem G, <lb/>ita e&longs;&longs;e magnitudinem &longs;phæræ A, ad &longs;phæræ B, magnitudinem, &longs;ed <lb/><arrow.to.target n="note32"/> magnitudo &longs;phæræ A, ad &longs;phæræ B, magnitudinem*triplicatam ra<lb/>tionem habet eius, quam C, diameter &longs;phæræ A, ad diametrum &longs;phæ<lb/><arrow.to.target n="note33"/>ræ B. </s>

<s id="s.000250">Hæc enim obiter quatenus ad rem <lb/>no&longs;tram facit, hîc tantùm indico; &longs;ed alibi ju&longs;tum cúmque integrum tra<lb/>ctatum edemus </s>

<s>Similiter & cubus ex C, ad cubum, ex diametro &longs;phæræ B, *tri<lb/>plicatam rationem habet eius, quam C, ad &longs;phæræ B, diametrum; er<lb/>go vt grauitas H, ad grauitatem G, ita erit cubus ex C, ad cubum ex <lb/>diametro &longs;phæræ B, &longs;ed vt grauitas H, ad grauitatem G, ita e&longs;t cubus <lb/>ex C, ad cubum ex F; ergo cubus ex F, æqualis erit cubo diametri <lb/>&longs;phæræ B; quare & latus F, æquabitur &longs;phæræ B, diametro. </s>

<s id="s.000251"><emph type="italics"/>Augu&longs;tinus.<emph.end type="italics"/></s>

<s>inuenta <lb/>igitur e&longs;t quantitas diametri &longs;phæræ B, quod facere oportepat. </s>

<s id="s.000252"> Acce&longs;&longs;us ab Apogæo ad Perigæum, & vici&longs;&longs;im, eodem <lb/>modo ad calculos reducitur, a&longs;lumpta &longs;emiparabola &longs;ub Axe EV; item-<pb pagenum="20" xlink:href="025/01/024.jpg"/>que rece&longs;&longs;us &longs;ub Axe HV, applicata qualibet ba&longs;i, quæ in partes qua&longs;<lb/>cunque divi&longs;a repræ&longs;entat tempus, tum acce&longs;&longs;us, tum rece&longs;&longs;us. </s>

<s id="s.000253"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000254"> Optimè; vnum tamen ob&longs;erva, in acce&longs;&longs;u ita dividi tempus, <lb/>quod repræ&longs;entatur per lineam AZ, vt incipiat ab A & terminetur in Z; <lb/>in rece&longs;&longs;u verò incipiat à Z, & de&longs;inat in A: idem dico de acce&longs;&longs;u & re<lb/>ce&longs;&longs;u Apogæi. </s>

<s id="s.000255">Iam verò ad id, quod de motu Apogæi quæ&longs;iveras re&longs;pon<lb/>deo, periodum inclinationis, &longs;eu motus Apogæi, æqualem non e&longs;&longs;e perio<lb/>do alterius inclinationis; ita vt, Sol citiùs redeat ad Tropicum Cancri, <lb/>vnde di&longs;ce&longs;&longs;erat, ab&longs;oluto totius Eclipticæ motu, quàm ad Apogæum, <lb/>quod tantùm attingit paulo pò&longs;t: igitur interea Sol tantulùm promove<lb/>tur in Ecliptica, hinc Apogæum videtur moveri &longs;ecundùm &longs;eriem Signo<lb/>rum, &longs;ed adeò lentè, vt vix &longs;ingulis annis 1. minutum conficiat; & hic <lb/>motus e&longs;t tantùm apparens. </s>

<s>Neque hoc Problema inutile erit tormenti bellici magi&longs;tro, <lb/>is enim cognita diametro alicuius globi, excmpli gratia, ex <lb/>plumbo, &longs;tatim alterius globi eandem habentis grauitatem, <lb/>diametrum inueniet, &longs;it globus ille, vel ex lapide, vel ex fer<lb/>ro, vel ex quocunque alio &longs;olidorum genere. </s><pb pagenum="21"/>

<s id="s.000256">Hæc dixi ad reducendum ad calculos Ano<lb/>maliæ motum; nam re ip&longs;a AD habet minorem proportionem ad AH. <lb/>&longs;eu BD ad CH, quàm tempus, quo Sol Apogæus in Cancro decurrit <lb/>arcum Eclipticæ æ&longs;tivum, à principio &longs;cilicet Cancri ad Libram, ad tem<lb/>pus quo arcum autumnalem de&longs;cribit, &longs;unt enim &longs;piræ paulò laxiores in <lb/>hoc arcu; ac proinde pauciores; igitur pauciores dies; quod ideò fit, vt <lb/>vna &longs;pira diurna Solis &longs;it ferè æqualis alteri diurnæ; &longs;ic enim &longs;upplet natu<lb/>ra æqualitatem motuum; quod &longs;anè multis aliis exemplis comprobare <lb/>po&longs;&longs;em, &longs;i fortè ita iuberes. </s>

<s id="s.000257">Ex his reliqua, ni fallor, quæ ad Solare <lb/>no&longs;trum &longs;y&longs;tema pertinent, facilè intelliges. </s>

<s>Exemplum.</s>

<s>Qvidam proponit aliquod corpus &longs;olidum notæ <lb/>magnitudinis, & vult inuenire, quanta erit magni <lb/>tudo alicuius &longs;olidi alterius generis, grauitatem <lb/>habentis propo&longs;ito corpori &longs;olido æqualem. </s>

<s id="s.000258"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000259"> Ita e&longs;t: quare ad prima illa po&longs;tulata de Marte redeo; vnum, <lb/>ni fallor, &longs;upererat, cur &longs;cilicet Mars à coniunctione, vel Apogæo <lb/>ad Quadraturam, plus temporis ponat, quàm à Quadratura, &longs;cilicet re&longs;<lb/>pectu Solis, ad Oppo&longs;itionem, vel Perigæum. </s>

<s><emph type="italics"/>SIT propo&longs;itum aliquod corpus plumbeum A, cuius magnitudo<emph.end type="italics"/><lb/>740, <emph type="italics"/>& oporteat inuenire quanta erit magnitudo &longs;tanni, grauita<lb/>tem habentis æqualem propo&longs;ito plumbo A. </s>

<s>Accipiatur aliquod cor<lb/>pus plumbeum D, cuius grauitas &longs;it 115, deinde stanni, magnitudi<lb/>ne æqualis plumbo D, inueniatur grauitas, quæ &longs;it<emph.end type="italics"/> 74, <emph type="italics"/>quod quomo<lb/>do fieri oportent, dictum est in antecedentis Problematis exemplo, & <lb/>fiat vt<emph.end type="italics"/> 74, <emph type="italics"/>ad<emph.end type="italics"/> 115. <emph type="italics"/>ita<emph.end type="italics"/> 740, <emph type="italics"/>ad alium numerum qui &longs;it<emph.end type="italics"/> 1150, <emph type="italics"/>is igitur <lb/>numcrus indicabit quanta erit magnitudo &longs;tanni, grauitatem haben<lb/>tis æqualem propo&longs;ito plumbo A.<emph.end type="italics"/></s>

<s id="s.000260"><emph type="italics"/>Antimus.<emph.end type="italics"/></s>

<s id="s.000261"> Miror à te, qui adeò per&longs;picax es, non videri; cùm enim <lb/>Mars ab Apogæo & Coniunctione ad mediocrem di&longs;tantiam orbes &longs;uos <lb/>tardiùs conficiat; haud dubiè minoribus intervallis Solem po&longs;t &longs;e relin<lb/>quit, quàm dum à mediocri di&longs;tantia tendit ad Perigæum; quia orbes <lb/>&longs;uos citiùs decurrit; igitur maioribus intervallis Solem po&longs;t &longs;e relinquit; <lb/>igitur cum æqualibus temporibus, ab Apogæo ad mediocrem di&longs;tantiam, <lb/>& ab hac ad Perigæum perveniat, & cum eo tempore, quo ab Apogæo <lb/>pervenit ad mediocrem di&longs;tantiam, minore arcu Solem po&longs;t &longs;e relinquat, <lb/>maiore verò æquali tempore, quo à mediocri di&longs;tantia pervenit ad Pe<lb/>rigæum; inde &longs;equitur, vt arcus hinc inde &longs;int æquales, provt reverà <lb/>æquales apparent, à Coniunctione ad Quadraturam, & ab hac ad Oppo&longs;i<lb/>tionem, a&longs;&longs;umenda e&longs;&longs;e inæqualia temporum intervalla, maius &longs;cilicet <lb/>ab Apogæo ad Quadraturam, minus verò ab hac ad Perigæum. </s>

<s>Quod &longs;i propo&longs;itum corpus plumbeum A, &longs;it &longs;phæricum, cu <lb/>ius &longs;phæræ diameter &longs;it 10, & oporteat inuenire quanta erit <lb/>diameter &longs;phæræ ex &longs;tanno, grauitatem habentis æqualem <lb/>propo&longs;itæ &longs;phæræ A, ita faciendum erit. </s>

<s><emph type="italics"/>Accipiatur vt diximus aliquod corpus plumbeum D, cuius graui<lb/>tas &longs;it 115, & &longs;tanni, magnitudinem habentis æqualem plumbo D, in<lb/>ueniatur grauitas, quæ &longs;it<emph.end type="italics"/> 74. <emph type="italics"/>& fiat vt 74, ad<emph.end type="italics"/> 115, <emph type="italics"/>ita cubus ex 10, <lb/>qui e&longs;t 1000, ad alium numerum qui &longs;it<emph.end type="italics"/> 1554 2/17, <emph type="italics"/>is igitur numerus <lb/>erit cubus diametri &longs;phæræ ex stanno, grauitatem habentis æqualem <lb/>propo&longs;itæ ex plumbo &longs;phæræ A, quare eius latus cubicum, quod est<emph.end type="italics"/><lb/>11 52/100, <emph type="italics"/>vero proximum, indicabit ip&longs;am diametrum.<emph.end type="italics"/></s>

<s id="s.000262"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/> Hæc adeò facilia Sunt, vt nimia facilitas non nihil de pre<lb/>tio detrahere videatur; iam verò mihi facilè per&longs;uadeo, reliqua omnia, <lb/>quæ ad alias pa&longs;&longs;iones &longs;uperiorum Planetarum pertinent, pari facilitate ex <lb/>iactis à te principiis explicari<gap/> po&longs;&longs;e. </s>

<s><emph type="italics"/>Similiter &longs;i propo&longs;itum corpus plumbeum A, fuerit cubicum, vel <lb/>alicuius alterius formæ regularis, eadem ratione inuenietur latus cu <lb/>bi ex stanno, grauitatem bab<gap/>ntis æqualem propo&longs;ito plumbto cu<lb/>bo A, &longs;i enim ip&longs;ius cubi plumbti A, datum &longs;it latus 10, erit numerus<emph.end type="italics"/><lb/>1554 2/17<31> <emph type="italics"/>cubus ex &longs;tanno æqualis grauitate propo&longs;ito plumbeo Cu <lb/>bo A, quare latus. </s>

<s id="s.000263"><emph type="italics"/>Antimus.<emph.end type="italics"/></s>

<s>cubitum numeri<emph.end type="italics"/> 1554 2/17<31> <emph type="italics"/>quod est<emph.end type="italics"/> 11 52/100<31> <emph type="italics"/>pro <lb/>ximum vero; indicabit quæ &longs;itum latus.<emph.end type="italics"/></s>

<s id="s.000264"> Ita e&longs;t pror&longs;us; nam res eodem modo explicatur in Iove & <lb/>Saturno; ni&longs;i quod cùm Iupiter maioribus intervallis Solem po&longs;t &longs;e relin-<pb pagenum="21" xlink:href="025/01/025.jpg"/>quat, quàm Mars, illum citiùs à tergo a&longs;&longs;equatur; ac proinde à Coniun<lb/>ctione ad Oppo&longs;itionem minus temporis excurrat; atque adeò, cùm il<lb/>lud temporis intervallum, æquè dividatur à mediocris di&longs;tantiæ momen<lb/>to, ad eundem finem obtinendum, Iovis &longs;cilicet Apogæi, in Coniunctio<lb/>ne, & Perigæi in Oppo&longs;i<gap/>; brevior e&longs;t <expan abbr="acce&longs;&longs;u&utilde;">acce&longs;&longs;uum</expan> & <expan abbr="rece&longs;&longs;u&utilde;">rece&longs;&longs;uum</expan> periodus in <lb/>Iove quàm in Marte; vnde frequentiùs recurrunt Coniunctiones in Iove, <lb/><expan abbr="qu&amacr;">quam</expan> in Marte; cur verò Iupiter matutinus emergat, ve&longs;pertinus verò immer<lb/>gatur, cur plus temporis ponat à Coniunctione ad Quadraturam, quàm <lb/>ab hac ad Perigæum; cur aliquando retrogredi, & &longs;tare aliquando vi<lb/>deatur, eodem modo in Iove explicamus, quo iam in Marte explicuimus; <lb/>item cur Iupiter citiùs in con&longs;equentia moveri videatur circa Apogæum ; <lb/>hic porro Planeta dies ponit in &longs;ua revolutione integra, nimirum à Con<lb/>iunctione ad Coniunctionem 399. ita vt diebus 283. directo motu feratur, <lb/>&longs;cilicet apparenter; diebus 118. retrogrado; 4. verò &longs;it &longs;tationarius. </s>

<s id="s.000265">In <lb/>Saturno cuncta hæc locum habent; ni&longs;i quod maioribus adhuc intervallis <lb/>Solem po&longs;t &longs;e relinquit versus Ortum; ac proinde pariodus revolutionis <lb/>à Coniunctione ad Coniunctionem brevior e&longs;t, illa autem e&longs;t dierum 378. <lb/>ita vt &longs;it directus diebus 244. retrogradus 136. &longs;tationarius fere 8. Hæc <lb/>omnia ex ii&longs;dem no&longs;tris principiis nece&longs;&longs;ariò con&longs;equuntur. </s>

<s>Neque di&longs;&longs;imili ratione inuenienda erit magnitudo auri, <lb/>argenti, cæræ, aut cuiu&longs;cumque &longs;olidi, grauitatem habentis <lb/>propo&longs;ito corpori &longs;olido æqualem. </s><pb pagenum="22"/>

<s>PROBLEMA VII. PROPOS. XIV.</s>

<s id="s.000266"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000267"> Inaudij non nihil de motu Apogæi; trium &longs;uperiorum Plane<lb/>tarum; ne&longs;cio, vtrùm in tua hypothe&longs;i rectè illud explicare po&longs;&longs;is. </s>

<s>Propo&longs;itis duobus liquidis corporibus magnitudine <lb/>&ecedil;qualibus, data grauitate vnius, grauitatem alte<lb/>rius inuenire. </s><figure/>

<s>SINT propo&longs;ita duo cor<lb/>ra liquida, magnitudine æqualia <lb/>A, B, &longs;it autem vnius, vtpote li<lb/>quidi A, data grauitas G, & <lb/>oporteat alterius liquidi B, gra<lb/>uitatem inuenire. </s>

<s id="s.000268"><emph type="italics"/>Antimus.<emph.end type="italics"/></s>

<s id="s.000269"> Recti&longs;&longs;ime Nam &longs;upponamus, Apogæum Marris coniuncti <lb/>e&longs;&longs;e in primo Arietis gradu; cùm illius revolutio ab Apogæo ad Apogæum, <lb/>duret diebus 780. Sol bis redit ad idem punctum diebus fere 731. quibus <lb/>detractis ex 780. re&longs;tant adhuc 49. ac proinde po&longs;t 49. ferè dies, Mars tan<lb/>tùm a&longs;&longs;equitur Solem, quibus per totidem ferè gradus Eclipticæ Sol pro<lb/>gredi videtur; Igitur Apogæum Martis tunc erit circa gradus 19. Tauri. <lb/></s>

<s>Accipiatur <lb/>aliquod corpus &longs;olidum C, & li<lb/>quidi, quod &longs;it H, eiu&longs;dem ge<lb/>neris cum liquido A, magnitu<lb/><arrow.to.target n="note34"/> dine æqualis &longs;olido C, *inuenia<lb/>tur grauitas, quæ &longs;it D, &longs;imiliter <lb/>& liquidl, quod &longs;it I, ciu&longs;dem <lb/>generis cum liquido B, magni<lb/>tudine æqualis eidem &longs;olido C, <lb/><arrow.to.target n="note35"/> * inueniatur grauitas, quæ &longs;it E, <lb/>& fiat vt D, ad E, ita G, ad aliam grauitatem, quæ &longs;it F. </s>

<s id="s.000270">Igitur &longs;ingulis annis & diebus 25. Apogæum Martis 25. circiter gradi<lb/>bus in con&longs;equentia moveri videtur. </s>

<s id="s.000271">In Iove autem, cum illius revolutio <lb/>fiat diebus 399. detractis 365. &longs;uper&longs;unt adhuc 34. quibus Sol totidem <lb/>decurrere videtur; Igitur Apogæum Iovis po&longs;ito quod prior Coniunctio <lb/>fuerit in primo gradu Arietis, erit in 4. gradu Tauri. </s>

<s>Quoniam <lb/>igitur e&longs;t vt A, ad B, ita H, ad I, æquale videlicet ad æquale, erit per<lb/>mutando vt A, ad H, ita B, ad I, & quoniam eiu&longs;dem &longs;unt generis cor<lb/><arrow.to.target n="note36"/> pora A, H, &longs;imiliter & corpora B, I, * erit vt grauitas G, ad grauita<lb/>tem D, ita liquidi B, grauitas, ad grauitatem E, & permutando vt <lb/>grauitas G, ad grauitatem liquidi B, ita D, grauitas, ad grauitatem <lb/>E, &longs;ed vt grauitas D, ad grauitatem E, ita e&longs;t grauitas G, ad graui<lb/>tatem F; ergo grauitas F, æqualis erit grauitati liquidi B. inuenta <lb/>igitur e&longs;t liquidi corporis B, grauitas F, quod facere oportebat. </s>

<s id="s.000272">Igitur &longs;ingulis annis <lb/>& diebus 34. Apogæum Iovis moveri videtur in con&longs;equentia 34. grad. <lb/></s>

<s id="s.000273">In Saturno denique, cùm eius revolutio fiat diebus 378. ex his &longs;i detrahas <lb/>365. &longs;uper&longs;unt 13. Igitur, ne idem repetam, &longs;ingulis annis, diebus 13. <lb/>Apogæum Saturni moveri videtur in con&longs;equentia gradibus 13. circiter <lb/>Sunt autem huiu&longs;modi motus apparentes tantùm, in mea hypothe&longs;i, vt <lb/>tute&longs;cis, qui ramen ex illo reali &longs;implici&longs;&longs;imo nece&longs;&longs;ariò con&longs;equuntur, <lb/>nec alio Apogæo excentrici opus e&longs;&longs;e crediderim. </s>

<s><margin.target id="note34"/>2.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s><margin.target id="note35"/>3.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s id="s.000274"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000275"> Dubito, an po&longs;&longs;is alia explicare in tua hypothe&longs;i, quæ no<lb/>&longs;træ tantum hominum plau&longs;um conciliarunt, v. g. quod Saturnus <lb/>directus Iovi & Marti conjungi non po&longs;&longs;it, ni&longs;i hi &longs;int directi; nec Marti <lb/>retrogrado, alij duo, ni&longs;i &longs;int retrogradi, licèt Saturno retrogrado alij <lb/>duo conjungi po&longs;&longs;int, licèt directi &longs;int, & Iovi retrogrado Mars dire<lb/>ctus. </s>

<s><margin.target id="note36"/>4.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s>Exemplum.</s>

<s id="s.000276"><emph type="italics"/>Antim.<emph.end type="italics"/> Hæc &longs;unt ve&longs;træ hypothe&longs;eos miracula; &longs;ed hæc in no&longs;tra hy<lb/>pothe&longs;i facilè explicantur. </s>

<s>Qvidam proponit aliquod corpus liquidum notæ <lb/>grauitatis, & vult &longs;cire, quanta erit grauitas alte<lb/>rius liquidi, magnitudinem habentis propo&longs;ito corpori <lb/>liquido æqualem. </s>

<s><emph type="italics"/>Sit propo&longs;itum aliquod olei corpus A, cuius grauitas<emph.end type="italics"/> 550, <emph type="italics"/>& <lb/>oporteat inuenire, quanta erit grauitas aquæ, magnitudinem haben<emph.end type="italics"/><pb pagenum="23"/><emph type="italics"/>tis æqualem propo&longs;ito oleo A, Accipiatur aliquod corpus &longs;olidum C, <lb/>vtpote plumbeum, & aquæ, magnitudinem habentis æqualem plumb<gap/><lb/>C, inueniatur grauitas, quæ &longs;it 12, vt in exemplo propo&longs;. </s>

<s id="s.000277">Sit enim Saturnus in I, Mars in M, Sol in C, cùm &longs;ingulis diebus, &longs;eu dìur<lb/>nis revolutionibus Mars relinquatur à Stellis Ortum versùs 3 ò. </s>

<s>8. <expan abbr="dict&utilde;">dictum</expan> e&longs;t. </s>

<s id="s.000278">circiter, <lb/>dum &longs;cilicet directus e&longs;t, & Saturnus. </s>

<s id="s.000279">2. Sit arcus FM, grad. 22. 15. minutis <lb/>circiter; po&longs;t 45. dies Mars erit in F, Saturnus verò di&longs;tabit à puncto I, <lb/>Ortum versùs grad. 3. igitur &longs;eptimo po&longs;t die, Mars Saturno conjungetur, <lb/>directus directo; item Iupiter Marti; crat autem Saturnus in Apogæo, <lb/>vt con&longs;tat, conjunctus &longs;cilicet Soli. </s>

<s><lb/>Similiter & olei, magnitudinem æqualem habentis, eidem plumbo C, <lb/>inueniatur grauitas, quæ &longs;it 11, & fiat, vt<emph.end type="italics"/> 11, <emph type="italics"/>ad<emph.end type="italics"/> 12, <emph type="italics"/>ita 550, ad <expan abbr="ali&utilde;">alium</expan> <lb/>numerum qui &longs;it<emph.end type="italics"/> 600. <emph type="italics"/>is igitur numerus indicabit quanta erit graui<lb/>tas aquæ, magnitudinem habentis æqualem propo&longs;ito oleo A.<emph.end type="italics"/></s>

<s id="s.000280">Supponamus autem Martem oppo<lb/>&longs;itum in R, Solem in D, Saturnum in I, cùm Saturnus à &longs;tatione haud pro<lb/>cul ab&longs;it, e&longs;t enim juxta Quadraturam, tanto intervallo Mars regredi ne<lb/>quit versùs F, vt Saturno directo jungatur; quia &longs;tatim Saturnus &longs;tatio<lb/>nem attingit, & paucis po&longs;t diebus, fit retrogradus: eadem ratio facit <lb/>pro Iove, vt &longs;cilicet nunquam Saturno directo, retrogradus jungatur. <lb/></s>

<s id="s.000281">Sed vt hæc paulò accuratiùs di&longs;cutiamus; cùm Saturni & Solis conjun-<pb pagenum="23" xlink:href="025/01/027.jpg"/>ctiones &longs;æpiùs recur<gap/>ant, quia &longs;cilicet &longs;ingulis annis, Saturnus minoris <lb/>arcus intervallo, à Stellis versùs Ortum relinquitur, ac proinde revolu<lb/>tionis Conjunctionum periodus brevior e&longs;t; igitur citiùs ab Apogæo ad <lb/>Perigæum de&longs;cendit, imo inter di&longs;tantias Saturni Apogæi & Perigæi à <lb/>centro mundi, longè minor e&longs;t proportio inæqualitatis, quàm inter di<lb/>&longs;tantias Martis Apogæi & Perigæi, ab eodem mundi centro; etiam a&longs;&longs;um<lb/>ptis Axibus acce&longs;&longs;uum & rece&longs;&longs;uum æqualibus, v. g. &longs;it di&longs;tantia Saturni <lb/>Apogæi 100. Perigæi 90. Martis vero Apogæi 50. Perigæi 40. vtrinque <lb/>a&longs;&longs;umitur idem Axis, id e&longs;t, eadem differentia di&longs;tantiarum, &longs;cilicet 10. <lb/>e&longs;t autem major ratio 50. ad 40. &longs;cilicet 1/4 quam ad 90. &longs;cilicet <gap/> &longs;ed ita <lb/>&longs;e habent motus, vt di&longs;tantiæ; igitur vt Saturnus in Apogæo tantulùm <lb/>versùs Ortum excurrit, ita & in Perigæo versùs Occa&longs;um; Hîc enim Stel<lb/>lam po&longs;t &longs;e relinquit; illic verò à Stella retro relinquitur; igitur modicum <lb/>arcum in &longs;ingulis revolutionibus, tum directo, tum retrogrado motu <lb/>decurrit: Mars verò longè majorem. </s>

<s><emph type="italics"/>Si vero propo&longs;itum &longs;it aliquod argenti viui corpus A, cuius <lb/>grauitas<emph.end type="italics"/> 95, <emph type="italics"/>& oporteat inuexire, quanta erit grauitas aquæ, magni<lb/>tudincm habentis æqualem propo&longs;ito argento viuo A. </s>

<s id="s.000282">Sit ergo Mars directus in M, Sa<lb/>turnus in I, cùm Mars longè majorem arcum directus decurrat, quàm <lb/>Saturnus, conjungitur tandem Saturno versùs Ortum, ita vt primùm pars <lb/>ortiva Martis cum occidua Saturni coëant: Sit verò Saturnus retrogra<lb/>dus in I, &longs;itque Mars in N etiam retrogradus, cùm hic etiam longè ma<lb/>jorem arcum decurrat retrogrado motu, jungetur Saturno versùs Occa<lb/>&longs;um, pars &longs;cilicet Occidua Martis, cum Ortiva Saturni: Si vero Mars &longs;it <lb/>directus in M, exi&longs;tente Sole inter CB, alter versùs alterum fertur, <lb/>jungentúrque inter FM, quo loco Mars directus e&longs;&longs;e pote&longs;t, & Saturnus <lb/>retrogradus, nempe Martis &longs;tatio e&longs;t infrà trigonum a&longs;pectum, Saturni <lb/>verò paulò infrà quadratum; hinc motus Saturni retrogradus diuturnio&longs; <lb/>e&longs;t, licèt in minore arcu fiat; quid mirum igitur, &longs;i in eodem loco con<lb/>juncti e&longs;&longs;e po&longs;&longs;int Mars & Saturnus; licèt hic &longs;it retrogradus, ille directus; <lb/>eadem ratio probat Saturno retrogrado etiam Iovem directum jungi po&longs;&longs;e; <lb/>& Iovi retrogrado Martem directum. </s>

<s>Accipiatur ali<lb/>quod vas vitreum mundum, & politum, cuius grauitas &longs;it v. g.<emph.end type="italics"/> 91. <lb/><emph type="italics"/><expan abbr="ip&longs;umq;">ip&longs;umque</expan> vas plenum aqua ponderetur in aqua, & habeat grauitatem<emph.end type="italics"/><lb/>55, <emph type="italics"/>quoniam igitur numerus<emph.end type="italics"/> 91, <emph type="italics"/>&longs;uperat <expan abbr="numer&utilde;">numerum</expan><emph.end type="italics"/> 55, <emph type="italics"/>numero<emph.end type="italics"/> 36, <emph type="italics"/>* erit<emph.end type="italics"/><arrow.to.target n="note37"/><lb/><emph type="italics"/>grauitas aquæ, magnitudinem habentis æqualem ip&longs;i va&longs;i, hoc est &longs;oli<lb/>ditati ip&longs;ius va&longs;is<emph.end type="italics"/> 36, <emph type="italics"/>ponatur deinde in ip&longs;um vas propo&longs;itum argen<lb/>tum <expan abbr="viu&utilde;">viuum</expan> A, nihil interest, vt vas &longs;it plenum, vel non, & quoniam ar <lb/>genti viui A, grauitas est<emph.end type="italics"/> 95, <emph type="italics"/>& va&longs;is vitrei grauitas<emph.end type="italics"/> 91, <emph type="italics"/>erit argenti <lb/>viui &longs;imul cum ip&longs;o va&longs;e, grauitas<emph.end type="italics"/> 186. <emph type="italics"/>ponderetur itaque ip&longs;um vas, <lb/>&longs;imul cum argento viuo A, in aqua, ita vt aqua repleat va&longs;is partem <lb/>vacuam, & &longs;it va&longs;is grauitas in aqua &longs;imul cum argento viuo<emph.end type="italics"/> 143, <lb/><emph type="italics"/>quoniam igitur numerus<emph.end type="italics"/> 186, <emph type="italics"/>&longs;uperat numerum<emph.end type="italics"/> 143, <emph type="italics"/>numero<emph.end type="italics"/> 43, <emph type="italics"/>* erit<emph.end type="italics"/><arrow.to.target n="note38"/><lb/><emph type="italics"/>grauitas aquæ, <expan abbr="magnitudin&etilde;">magnitudinem</expan> <expan abbr="bib&etilde;tis">bibentis</expan> æqualem argento viuo, &longs;imul <expan abbr="c&utilde;">cum</expan> <lb/>va&longs;e<emph.end type="italics"/> 43, <emph type="italics"/>&longs;ed grauitas aquæ habentis magnitudinem æqualem va&longs;i est<emph.end type="italics"/><lb/>36, <emph type="italics"/>ergo reliquum quod est<emph.end type="italics"/> 7, <emph type="italics"/>erit grauitas aquæ, magnitudinem ba<lb/>bentis æqualem propo&longs;ito argento viuo A.<emph.end type="italics"/></s>

<s id="s.000283"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000284"> Nunquam profectò mihi per&longs;ua&longs;i&longs;&longs;em ex principiis Phy&longs;icis, <lb/>hæc tam facilè demon&longs;trari potui&longs;&longs;e; tota res eò reducitur, Saturnum eo <lb/>velocitatis gradu moveri, vt paulò infrà mediocrem di&longs;tantiam, æquè <lb/>citò &longs;uum circulum diurnum decurrat, ac Stellæ &longs;uum. </s>

<s id="s.000285">Iupiter verò <lb/>adhuc infrà, qua&longs;i in trigono; Mars demùm infrà trigonum; idem autem <lb/>futuris &longs;æculis futurum e&longs;t; cùm eundem velocitatis gradum hi Planetæ <lb/>&longs;ervaturi &longs;int, cum gemina illa inclinatione, de qua &longs;uprà; ex hoc enim <lb/>illa, de quibus huiu&longs;que di&longs;&longs;eruimus, nece&longs;&longs;ariò con&longs;equuntur; nam <lb/>Saturnus altior motum retrogradum diuturniorem habet; licèt in mino<lb/>re arcu, quàm Iupiter & Mars, directus verò breviorem, Idem dicitur <lb/>de Iove re&longs;pectu Martis; hinc revolutio &longs;eu temporis periodus Saturni, <lb/>illa &longs;cilicet, quæ inter duas Conjunctiones intercipitur, brevior e&longs;t, <lb/>quàm Iovis, & huius etiam, quàm Martis brevior; hinc frequentiores <lb/>recurrunt &longs;tationes in Saturno, quàm in Iove, & in hoc, quà in in Mar<lb/>te; hinc Saturnus minorem arcum Eclypticæ decurrit, tum directo, tum <lb/>retrogrado motu; quia &longs;cilicet parum differt illius circulus diurnus confe-<pb pagenum="24" xlink:href="025/01/028.jpg"/>ctus in Perigæo, à circulo decur&longs;o in Apogæo ; E&longs;t enim minor propor<lb/>tio vnius ad alium; hinc per plures dies &longs;tare videtur; quia licèt reip&longs;a <lb/>non &longs;tet, tam parum tamen promovetur & recedit à Stella, seu versùs <lb/>Ortum, &longs;eu versùs Occa&longs;um, vt eandem à Stella di&longs;tantiam &longs;ervare vi<lb/>deatur; Cuncta hæc ita per&longs;picua &longs;unt, vt negari profectò non po&longs;&longs;int, quale <lb/>do vltrò in hac tua hypothe&longs;i, huiu&longs;modi pa&longs;&longs;iones Planetarum æquè facilè <lb/>explicari atque in mea. </s>

<s id="s.000286"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000287"> Imò longè faciliùs & cum multiplici prærogativa: Nam pri<lb/>mò &longs;implici&longs;&longs;imum motum adhibeo; realem &longs;cilicet & æquabilem, circa <lb/>mundi Centrum; tu verò duos, & fortè plures, eó&longs;que minimè æquabi<lb/>les; vtrumque in Excentrico circa centra ad libitum excogitata & ficta. <lb/></s>

<s>Sed &longs;i propo&longs;itum fuerit aliquod magnum argenti viui cor <lb/>pus, ita vt difficile po&longs;&longs;it ponderari in aqua, hac via inuenietur <lb/>aquæ quæ&longs;ita grauitas. </s>

<s id="s.000288">Secundo, nunquam vides Planetam extrà Perigæum & Apogæum, in eo <lb/>vero loco in quo e&longs;t, ac proinde perpetuæ fallaciæ &longs;ubjaces; ego in eo <lb/>loco, in quo reverà e&longs;t, Planetam video. </s>

<s id="s.000289">Tertiò, tu &longs;en&longs;um decipi <lb/>a&longs;&longs;eris, quamvis rectè applicatum; ego vt & in aliis minimè falli repo<lb/>no, nec qui&longs;quam hoc jure ad&longs;truat, ni&longs;i aliqua ratione fretus. </s>

<s><emph type="italics"/>Sit propo&longs;itum aliquod magnum argenti viui corpus A, cuius gra<lb/>uitas<emph.end type="italics"/> 5700. <emph type="italics"/>& oporteat facere, quod imperatum e&longs;t. </s>

<s id="s.000290">Quartò; <lb/>denique habeo in mea cau&longs;as Phy&longs;icas, eá&longs;que tritas & vulgares in doctri<lb/>na motuum, i&longs;torum omnium effectuum, Apogæi &longs;cilicet, Perigæi, accelera<lb/>tionis, retardationis, &c. </s>

<s id="s.000291">Tu verò meras fallacias, & oculorum illu&longs;iones <lb/>e&longs;&longs;e contendis. </s>

<s>Accipiatur ali<lb/>quod paruum argenti viui corpus C, cuius grauitas &longs;it<emph.end type="italics"/> 95, <emph type="italics"/>& aquæ, <lb/>magnitudinem habentis æqualem argento viuo C, inueniatur graui<lb/>tas, eo modo quo dictum est, quæ &longs;it<emph.end type="italics"/> 7, <emph type="italics"/>& fiat vt<emph.end type="italics"/> 95, <emph type="italics"/>ad<emph.end type="italics"/> 7, <emph type="italics"/>ita<emph.end type="italics"/> 5700, <emph type="italics"/>ad <lb/>alium numerum, qui &longs;it<emph.end type="italics"/> 420, <emph type="italics"/>is igitur numerus indicabit quanta erit <lb/>grauitas aquæ, magnitudinem habentis æqualem propo&longs;ito argento <lb/>viuo A.<emph.end type="italics"/></s>

<s id="s.000292">Igitur non æquè facilè in tua hypothe&longs;i, ac in mea, res i&longs;ta ex<lb/>plicatur, &longs;ed in mea longè faciliùs, planiùs, &, vt &longs;ic loquar, connaturaliùs. </s>

<s><emph type="italics"/>Contra, &longs;it propo&longs;itum aliquod corpus aqueum A, cuius grauitas<emph.end type="italics"/><lb/>420, <emph type="italics"/>& oporteat inuenire quanta erit grauitas argenti viui, magni<lb/>tudine æqualis propo&longs;itæ aquæ A. facto, vt &longs;upra, & inuenta graui<lb/>tate<emph.end type="italics"/> 7, <emph type="italics"/>aquæ &longs;cilicet magnitudinem habentis æqualem <expan abbr="arg&etilde;to">argento</expan> viuo C,<emph.end type="italics"/><pb pagenum="24"/><emph type="italics"/>flat vt<emph.end type="italics"/> 7, <emph type="italics"/>ad<emph.end type="italics"/> 95, <emph type="italics"/>ita<emph.end type="italics"/> 420, <emph type="italics"/>ad alium numerum, qui &longs;it<emph.end type="italics"/> 5700, <emph type="italics"/>is igi<lb/>tur indicabit quanta erit grauitas argenti viui, magnitudine æqua<lb/>lis propo&longs;itæ aquæ A.<emph.end type="italics"/></s>

<s id="s.000293"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>Inueniemus etiam aliter, & expeditius grauitatem <lb/>aquæ, magnitudinem habentis æqualem propo&longs;ito ar<lb/>gento viuo A. </s>

<s id="s.000294"> Vt vt &longs;it, quoad hæc, antequam ad alia, quæ fortè magis vrgent, <lb/>accedam, ex te &longs;cire vellem, quonam modo latitudinem Planetarum in tua <lb/>hypothe&longs;i explices; quod eò libentiùs audiam, quò mirabilior mihi videtur <lb/>ille modus, quo in hypothe&longs;i no&longs;tra explicatur; in qua &longs;uppo&longs;ita orbitæ ex<lb/>centricæ Planetæ inclinatione ad planum Eclypticæ, latitudinis variatio per <lb/>diver&longs;um terræ mobilis <expan abbr="&longs;it&utilde;">&longs;itum</expan> optimè explicatur; nempè arcus, qui maximam <lb/>latitudinem metitur, in limitibus &longs;ub majore vel minore angulo apparet, <lb/>quo remotior, vel propior oculus &longs;tatuetur; quod vt in &longs;chemate explicem, <lb/><figure id="id.025.01.028.1.jpg" xlink:href="025/01/028/1.jpg"/><lb/>Sit centrum mundi A, planum ecli<lb/>pticæ EGKH, excentricus FGI <lb/>H, cuius centrum e&longs;t in D ; nodi G <lb/>H, arcus inclinationis excentrici F <lb/>E, IK, Tellnris orbita BLCM. <lb/></s>

<s id="s.000295">Sit Terra in B, Planeta in limite Bo<lb/>reali F ; apparebit prædictus arcus <lb/>&longs;ub angulo FBE, po&longs;ita verò Terra <lb/>in C, apparebit &longs;ub angulo FCE, <lb/>qui priore minor e&longs;t; Si verò &longs;tatua<lb/>tur in limite Au&longs;trali, I & Terra &longs;it <lb/>in C, videbitur arcus IK &longs;ub an<lb/>gulo ICK, & ex B &longs;ub angulo <lb/>IBK, &longs;ed ex Optica, per&longs;pi<lb/>cuum e&longs;t, angulum ICK majorem <lb/>e&longs;&longs;e angulo FBE, quia CI minor <pb pagenum="25" xlink:href="025/01/029.jpg"/>e&longs;t BF; hinc phænomena illa, &longs;en potiùs generalia pronuntiata clari&longs;&longs;imè <lb/>explicantur, &longs;cilicet Planetæ oppo&longs;iti in eodem limite majorem e&longs;&longs;e Lati<lb/>tudinem, quàm conjuncti; item Planetæ oppo&longs;iti in limite Au&longs;trino, La<lb/>titudinem majorem e&longs;&longs;e quàm in Boreali; vides, quàm clarè & per&longs;picuè <lb/>in mea hypothe&longs;i hæc explicentur. </s>

<s><emph type="italics"/>Accipiatur enim aliquod corpus aurcum, cui &longs;uperinducatur ce<lb/>rea tunica tenui&longs;&longs;ima, ne fiat argento viuo leuius, neue ab <expan abbr="eod&etilde;">eodem</expan> di&longs;&longs;ol<lb/>uatur, deinde aquæ, magnitudinem habentis æqualem ip&longs;i corpori au <lb/>reo inueniatur grauitas, vt dictum est in propo&longs;.<emph.end type="italics"/> 8. <emph type="italics"/>exemplo, quæ &longs;it<emph.end type="italics"/> 7, <lb/><emph type="italics"/>&longs;imiliter & argenti viui, vt aquæ, magnitudinem habentis æqualem <lb/>eidem corpori aureo, inueniatur grauitas, quæ &longs;it<emph.end type="italics"/> 95, <emph type="italics"/>& fiat vt<emph.end type="italics"/> 95, <emph type="italics"/>ad<emph.end type="italics"/><lb/>7, <emph type="italics"/>ita<emph.end type="italics"/> 5700, <emph type="italics"/>ad<emph.end type="italics"/> 420, <emph type="italics"/>grauitas igitur aquæ, magnitudinem habentis æ<lb/>qualem argento viuo A, erit<emph.end type="italics"/> 420. </s>

<s><emph type="italics"/>Contra. </s>

<s id="s.000296"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000297"> Fateor, hæc non &longs;ine plau&longs;u ab hominibus excepta fui&longs;&longs;e; &longs;ed <lb/>re penitiùs con&longs;iderata, &longs;ummæ difficultates etiamnum re&longs;tant, quibus <lb/>&longs;uperandis tuæ hypothe&longs;eos a&longs;&longs;ertores fru&longs;trà omninò de&longs;udârunt, immò <lb/>nequidem inter &longs;e conveniunt, &longs;i rectè memini, in definienda huiu&longs;mo<lb/>di Planetarum latitudine, excentricorum inclinatione, Nodorum, & <lb/>Apogæi motu, limitum libratione; atque adeò vltro fatentur, adhuc opus <lb/>e&longs;&longs;e novis Ob&longs;ervationibus, ad rem hanc meliùs &longs;tatuendam. </s>

<s>&longs;it propo&longs;itum aliquod corpus aqueum, cuius grauitas<emph.end type="italics"/><lb/>420, <emph type="italics"/>& oporteat inuenire, quanta erit grauitas argenti viui, magni<lb/>tudine æqualis propo&longs;itæ aquæ A. </s>

<s id="s.000298">In mea <lb/>hypothe&longs;i res &longs;atis expeditè explicatur, per &longs;ecundam illam inclinationem <lb/>à Tropicis ad Æquatorem, & vici&longs;&longs;im, juxtà rationem motus accelerati <lb/>& retardati; cùm autem Mars modò citiùs, modò tardiùs orbem &longs;uum <lb/>decurrat, quàm Stellæ &longs;uum, &longs;emper verò citiùs quàm Sol, ni&longs;i fortè <lb/>Mars &longs;it in Apogæo, & Sol in Perigæo, & cùm motus &longs;ecundæ inclina<lb/>tionis tardiùs fiat in Marte quàm in Sole; cùm demùm Mars ab Æqua<lb/>tore declinare po&longs;&longs;it versùs Boream & Au&longs;trum, gradib. </s>

<s id="s.000299">circiter 25. ex <lb/>his &longs;equitur, latitudo Martis, eaque varia, cùm aliquando relinquat <lb/>Eclipticam versùs Boream, vbi di&longs;cedit à Nodo, in Signis de&longs;cendenti<lb/>bus, in a&longs;cendentibus verò, versùs Au&longs;trum; variatur etiam Latitudo ex <lb/>varia di&longs;tantia Martis. </s>

<s>Superinducta corpori aureo cerea <lb/>tunica, vt &longs;upra, & inuentis grauitatibus<emph.end type="italics"/> 7, & 95, <emph type="italics"/>aquæ nimirum, & <lb/>argenti viut, magnitudine æqualium prædicto aureo corpori, fiat vt<emph.end type="italics"/><lb/>7, <emph type="italics"/>ad 95, ita<emph.end type="italics"/> 430, <emph type="italics"/>ad<emph.end type="italics"/> 5700 <emph type="italics"/>grauitas igitur argenti viui, magnitudin<gap/><lb/>æqualis propo&longs;ito corpori aqueo A, erit<emph.end type="italics"/> 5700. </s>

<s id="s.000300">Cæterùm vnum ob&longs;erves velim, optime Augu<lb/>&longs;tine, nullum mortalium hactenùs ad iu&longs;tos calculos minorum Planeta<lb/>rum, immò nec fortè Lunæ latitudinem reduxi&longs;&longs;e; præ&longs;ertim Martis, vt <lb/>vel ip&longs;e Keplerus vltrò fatetur, qui vult, hæc latere in pandectis <lb/>æternitatis; hinc tot excentrici, epicycli, circelli, deviationes, incli<lb/>nationes, reflexiones, librationes, centra diver&longs;a, excentricitates; ne<lb/>que adhuc Martem A&longs;tronomi tot tamque variis & multiplicatis retibus <lb/>comprehendere potuerunt; vtor igitur, ad calculos, qualibet hypothe&longs;i, <lb/>vt A&longs;trologus; vt Philo&longs;ophus eam dumtaxat admitto, quæ cum princi<lb/>piis Phy&longs;icis con&longs;entit; calculi verò difficultas ex eo provenit, quod &longs;int <lb/>ferè innumeræ combinationes Apogæorum Solis & Martis; <expan abbr="Nodor&utilde;">Nodorum</expan> item, <lb/>qui versùs Ortum in con&longs;equentia promoveri videntur; nempè ex diver<lb/>&longs;o Nodorum & Apogæorum loco ac &longs;itu, diver&longs;a Latitudinis mutatio ne<lb/>ce&longs;&longs;ariò &longs;equitur. </s>

<s id="s.000301">Hæc in Saturno & Iove etiam locum habent; atque <lb/>adeò, ni fallor, ex dictis habes, in mea hypothe&longs;i, trium &longs;uperiorum <lb/>Planetarum pa&longs;&longs;iones haud difficulter explicari, idque per principia Phy<lb/>&longs;ica, quæ ex doctrina moruum &longs;upponimus: quare &longs;i me audis, ac tibi <lb/>putas à me factum e&longs;&longs;e &longs;atis, exprome alia argumenta, &longs;i quæ &longs;uppetunt <lb/>pro tua hypothe&longs;i. </s>

<s>Qua ratione inuenienda &longs;it grauitas argenti viui, ma<lb/>gnitudinem habentis propo&longs;ito cuicunque corpori &longs;oli<lb/>do æqualem. </s>

<s><emph type="italics"/>Sit propo&longs;itum aliquod corpus &longs;olidum, vtpote plumbeum A, cuius <lb/>grauitas<emph.end type="italics"/> 161, <emph type="italics"/>& oporteat inuenire quanta erit grauitas argenti viui <lb/>magnitudine æqualis propo&longs;ito plumbo A. inueniatur grauitas aquæ <lb/>magnitudinem habentis æqualem plumbo A, vt in exemplo propo&longs;i<lb/>tionis<emph.end type="italics"/> 8, <emph type="italics"/>dictum e&longs;t, quæ &longs;it<emph.end type="italics"/> 14, <emph type="italics"/>& inuenta grauitate argenti viui, ma<lb/>gnitudine æqualis ip&longs;i aquæ, ea erit de qua quæritur, &longs;it enim inuen<lb/>ta argenti viui grauitas<emph.end type="italics"/> 190. <emph type="italics"/><expan abbr="Quoniã">Quoniam</expan> igitur argentum viuum, cuius <lb/>grauitas est<emph.end type="italics"/> 190, <emph type="italics"/>magnitudine æquatur aquæ, cuius grauitas e&longs;t<emph.end type="italics"/> 14, <lb/><emph type="italics"/>ip&longs;ique aquæ æquatur magnitudine plumbum A, erit argentum vi<lb/>uum, cuius grauitas 190, magnitudine propo&longs;ito plumbo A, æquale; <lb/>quare inuenta est grauitas argenti viui, magnitudine æqualis propo<lb/>&longs;ito plumbo A, quod facere oportebat.<emph.end type="italics"/></s>

<s id="s.000302"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000303"> Veneris & Mercurij Conjunctiones in Copernicana hypo<lb/>the&longs;i, ea claritudine explicantur, qua ne&longs;cio, an major excogitari po&longs;&longs;it, <lb/>itémque Apogæa & Perigæa, tum etiam aliorum Planetarum &longs;uperiorum, <lb/>&longs;ed jam prævideo, quid pro tua hypothe&longs;i de hoc argumento dicturus &longs;is. </s>

<s>Quomodo inuenienda &longs;it grauitas cuiu&longs;cunque cor-<pb pagenum="25"/>poris &longs;olidi, magnitudinem habentis propo&longs;ito corpori <lb/>ex argento viuo æqualem. </s>

<s><emph type="italics"/>Sit propo&longs;itum aliquod corpus ex argento viuo A, cuius grauitas <lb/>190, & oporteat inuenire quanta erit grauitas plumbi, magnitudine <lb/>æqualis propo&longs;ito argento viuo A. inueniatur grauitas aquæ, magni<lb/>tudinem habentis æqualem argento viuo A, quæ &longs;it<emph.end type="italics"/> 14, <emph type="italics"/>deinde inuen<lb/>ta grauitate plumbi, magnitudine æqualis ip&longs;i aquæ, vt in exemplo <lb/>propo&longs;. </s>

<s id="s.000304"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>9. dictum est, ea erit de qua quæritur. </s>

<s id="s.000305"> Apogæa & Perigæa facillimè in mea hypothe&longs;i explicantur per <lb/>&longs;implicem motum æquabilem realiter, vt aiunt, inæqualem verò appa<lb/>renter, prima illa inclinatione, de qua &longs;uprà, in&longs;tructum; Apogæum au<lb/>tem e&longs;t &longs;emper circa Conjunctionem, & Perigæum circa Oppo&longs;itionem; <lb/>quia ii di&longs;tantiæ fines &longs;upponuntur, i&longs;que velocitatis gradus impre&longs;&longs;us vel <lb/>acqui&longs;itus, quibus &longs;uppo&longs;itis, æqualia &longs;int tempora acce&longs;&longs;us atque re<lb/>ce&longs;&longs;us, & &longs;emirevolutionis Conjunctionum & Oppo&longs;itionum; Sed hæc <lb/>abundè &longs;uprà explicata &longs;unt; quare ad Venerem & Mercurium iam venio; <lb/>quorum motus in mea hypothe&longs;i æquè facilè explicantur. </s>

<s>&longs;it enim inuenta plum<lb/>bigrauitas<emph.end type="italics"/> 161, <emph type="italics"/>quoniam igitur aqua, cuius grauitas est<emph.end type="italics"/> 14, <emph type="italics"/>æqua<lb/>tur magnitudine plumbo, cuius grauitas est<emph.end type="italics"/> 161, <emph type="italics"/>& æquatur quoque <lb/>argento viuo A, plumbum cuius grauitas e&longs;t<emph.end type="italics"/> 161, <emph type="italics"/>æquabitur magni<lb/>tudine argento viuo A. quare inuenta, e&longs;t grauitas plumbi, magnitu<lb/>dine æqualis propo&longs;ito argento viuo A, quod facere oportebat.<emph.end type="italics"/></s>

<s>PROBLEMA VIII. PROPOS. XV.</s>

<s id="s.000306">Sit enim centrum mundi B, <lb/>orbita Solis ADCE, Apo<lb/>gæum Veneris S, Perigæum I, <lb/>mediocris di&longs;tantia D: &longs;uppo<lb/>namus Venerem eo gradu ve<lb/>locitatis moveri, qui minor <lb/>&longs;it illo, quo Sol movetur, ita <lb/>vt inter di&longs;tantias BS, BN, <lb/>tardiùs quàm Sol &longs;uum orbem <lb/>decurrat, citiùs verò inter <lb/>di&longs;tantias BN, BI. </s>

<s id="s.000307">Itaque <lb/>&longs;it Venus in Apogæo S, mo<lb/>vetur Occa&longs;um versùs &longs;impli<lb/>ci&longs;&longs;imo motu, &longs;imúlque ac<lb/>cedit ad mediocrem <expan abbr="di&longs;tãtiam">di&longs;tantiam</expan> <lb/>BD, relinquitur autem à Sole <lb/>versùs Ortum, a&longs;&longs;umptòque <lb/>&longs;egmento acce&longs;&longs;us SO, Ve<lb/>nus erit in P, digre&longs;&longs;a &longs;cilicet <lb/>à Sole angulo DBP; addito <lb/>verò &longs;egmento acce&longs;&longs;us OD, erit Venus in mediocri di&longs;tantia, digre&longs;&longs;a <lb/>à Sole arcu DL; a&longs;&longs;umpto porrò &longs;egmento rece&longs;&longs;us DN, erit in M ter<lb/>mino maximæ digre&longs;&longs;ionis, quam metitur angulus DBM grad. circiter 47. <lb/>in M erit &longs;tationaria re&longs;pectu Solis, cùm nec ab eo vltrà digredi, nec ad <lb/>illum accedere videatur; Dum verò ab&longs;olvit aliud &longs;egmentum rece&longs;&longs;us <lb/>NI, redire ad Solem videtur, quia &longs;uos orbes citiùs decurrit vtpote mi<lb/>nores, donec tandem ad Perigæum I perveniat; MI accedit proximè ad <lb/>lineam rectam; idem &longs;tatuatur pro acce&longs;&longs;u ab I, ad D, & rece&longs;&longs;u à D ad <lb/>S, eritque figura integra cuius &longs;emifiguram tantùm hîc habes. </s>

<s>Propo&longs;itis duobus liquidis corporibus æquè graui<lb/>bus, data magnitudine vnius, magnitudinem alte<lb/>rius inuenire. </s><figure/>

<s>SINT propo&longs;ita duo cor<lb/>pora liquida æquè grauia A, <lb/>B, &longs;it autem vnius vt pote li<lb/>quidi A, data magnitudo G, <lb/>& oporteat inuenire quanta <lb/>erit magnitudo liquidi B. </s>

<s id="s.000308"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000309"> Cur amabo cum Tyconicis Epicyclum FHKG non a&longs;&longs;umis, <lb/>in quo eadem &longs;alvabis phænomena, non verò figuram irregularem & in<lb/>cognitam? </s>

<s>Ac<lb/>cipiatur aliquod &longs;olidum cor <lb/>pus C, & liquidi quod &longs;it H, <lb/>eiu&longs;dem generis cum liquido <lb/>A, magnitudinem habentis <lb/>æqualem &longs;olido C, *<arrow.to.target n="note39"/> inuenia<lb/>tur grauitas quæ &longs;it D, &longs;imili. </s>

<s><lb/>ter & liquidi, quod &longs;it I, eiu&longs;dé <lb/>generis cum liquido B, magni <lb/>tudinern habentis æqualem eidem &longs;olido C, * inueniatur grauitas,<arrow.to.target n="note40"/><lb/>quæ &longs;it E, & fiat vt grauitas E, ad grauitatem D, ita magnitudo G, ad <lb/>ad aliam <expan abbr="magnitadin&etilde;">magnitadinem</expan>, quæ &longs;ie F. </s>

<s id="s.000310"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000311"> Multa ob&longs;tant, quo minùs Epicyclum adhibeam. </s>

<s>Quoniam igitur &longs;unt quatuor cor<lb/>pora grauia I, H, B, A, quorum primum, & &longs;ecundum &longs;unt magnitu<lb/>dine æqualia, tertium vero, & quartum æque grauia, & &longs;unt eiu&longs;dem <lb/>generis primum videlicet, & tertium, &longs;imiliter eiu&longs;dem generis &longs;e<pb pagenum="26"/><arrow.to.target n="note41"/> cundum & quartum, * Erit vt grauitas E, ad grauitatem D, ita ma<lb/>gnitudo G, ad liquidi B, magnitudinem, &longs;ed vt grauitas E, ad graui<lb/>tatem D, ita e&longs;t magnitudo G, ad F, magnitudinem; ergo magnitudo <lb/>F, æqualis erit magnitudini liquidi B. inuenta igitur e&longs;t corporis li<lb/>quidi B, magnitudo F, quod &longs;acere oportebat. </s>

<s id="s.000312">Primò, <lb/>Licet Venus plus temporis ponat ab Apogæo ad maximam digre&longs;&longs;ionem, <lb/>quàm ab hac ad Perigæum, non tamen iuxtà proportionem acceptam in <lb/>Epicyclo: Sit enim arcus DV 45. grad. ducatur BV, tum perpendicularis <pb pagenum="27" xlink:href="025/01/031.jpg"/>DR, hæc erit &longs;emidiameter Epicycli, quanquam a&longs;&longs;umpto angulo maxi<lb/>mæ digre&longs;&longs;ionis grad. 47. &longs;emidiameter Epicycli erit paulo maior quàm <lb/>DR; &longs;ed &longs;it vt DR; haud dubiè arcus FHR e&longs;t triplus arcus RK. Igitur <lb/>tempus po&longs;itum ab Apogæo ad maximam digre&longs;&longs;ionem triplum e&longs;t illius, <lb/>quod ponitur à maxima digre&longs;&longs;ione ad Perigæum, &longs;ed reverà triplum non <lb/>e&longs;t, &longs;ed in minore proportione. </s>

<s id="s.000313">Secundò BF e&longs;t ad BK ferè vt 12. ad 2. <lb/>Igitur cùm circuli &longs;int vt diametri, circulus quem Venus decurtit in Apo<lb/>gæo F, e&longs;&longs;et dodecuplus illius, quem conficit in Perigæo K ; immo & in <lb/>maiore proportione, cum angulus maximæ digre&longs;&longs;ionis &longs;it maior angulo <lb/>grad.45. nempe ad gradus 48. immò & 49. nonnunquam accedit. </s>

<s><margin.target id="note39"/>8.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s><margin.target id="note40"/>8.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s id="s.000314"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/> Hæc eadem ratio contra te militat, na<gap/> &longs;uppo&longs;ita tua hy<lb/>pothe&longs;i, BS erit &longs;altem dupla BI, igitur circulus, quem Venus decurrit <lb/>&longs;ub radio BS, e&longs;t duplus illius, quem decurrit &longs;ub radio BI, hunc igitur <lb/>&longs;uppo&longs;ito motu &longs;emper æquabili, vt dicis, &longs;ub duplo etiam tempore Ve<lb/>nus decurrit, quod tamen Phænomenis non con&longs;entit. </s>

<s><margin.target id="note41"/>7.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s id="s.000315"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>Quod &longs;i propo&longs;ita duo corpora æque grauia fuerint <lb/>regularia, vtpote &longs;phærica, fuerit autem &longs;ph&ecedil;ræ A, data <lb/>diameter G, & oporteat inuenire, quanta erit diameter <lb/>&longs;phæræ B, ita faciendum erit. </s><figure/>

<s id="s.000316"> Mentem meam omnino a&longs;&longs;ecutus es, & rectè contra me con<lb/>cluderes, &longs;i radium BS duplum radij BI ponere cogerer; &longs;ed vt tute &longs;cis, <lb/>in exemplis non requiritur veritas; re igitur ip&longs;a provt diver&longs;a ratio motus <lb/>po&longs;tularit, Apogæum & Perigæum ad D propiùs &longs;tatuam: ex his autem <lb/>vides, quàm facilè omnia explicentur, primò po&longs;t Conjunctionem Apo<lb/>gæam, Venus versùs ortum à Sole digreditur, quia tardiùs Sole movetur <lb/>versùs occa&longs;um. </s>

<s id="s.000317">Secundò Venus vbi ad mediocrem di&longs;tantiam pervenit, <lb/>puta in L, adhuc vltra digreditur, quia tardiùs Sole movetur. </s>

<s>ACCEPTO aliquo cor <lb/>pore &longs;olido C, & inuentis <lb/>grauitatibus D, E, <expan abbr="liquidor&utilde;">liquidorum</expan> <lb/>H, I, vt &longs;upra, fiat vt grauitas <lb/>E, ad grauitatem D, ita cu<lb/>bus ex G, ad alium cubum, <lb/>cuius latus &longs;it F. </s>

<s id="s.000318">Tertiò nun<lb/>quam opponitur Soli; quia antequam perveniat ad <expan abbr="Quadraturã">Quadraturam</expan> cum Sole, <lb/>citiùs quàm Sol orbem &longs;uum decurrit; igitur à Sole vltra non digreditur. <lb/></s>

<s id="s.000319">Quartò plus temporis ponit ab Apogæo S, ad maximam digre&longs;&longs;ionem M, <lb/>quàm ab hac ad Perigæum; quia tempus acce&longs;&longs;us SL, æquale e&longs;t tempori <lb/>rece&longs;&longs;us LMI, &longs;ed MI citiùs decurritur quàm LMI; e&longs;t enim pars mi<lb/>nor toto. </s>

<s>Quoniam <lb/>igitur eadem ratione, qua <lb/>&longs;upra o&longs;tendetur, vt grauitas <lb/>E, ad grauitatem D, ita e&longs;&longs;e <lb/>magnitudinem &longs;phæræ A, ad <lb/>&longs;phæræ B, magnitudinem, &longs;ed <lb/>magnitudo &longs;phæræ A, ad <lb/><arrow.to.target n="note42"/> &longs;phæræ B, magnitudinem; * <lb/><expan abbr="triplicatã">triplicatam</expan> rationem habet eius, quam G, diameter &longs;phæræ A, ad dia<lb/>metrum &longs;phæræ B, &longs;imiliter & cubus ex G, ad cubum diametri &longs;phæ<lb/><arrow.to.target n="note43"/>ræ B, * triplicatam rationem habet eius, quam G, ad &longs;phæræ B, dia<lb/>metrum; ergo vt grauitas E, ad grauitatem D, ita erit cubus ex G, ad <lb/>cubum diametri &longs;phæræ B, &longs;ed vt grauitas D, ita grauitatem D, ita <lb/>e&longs;t cubus ex G, ad cubum ex F; ergo cubus ex F, æqualis erit cubo <lb/>diametri &longs;phæræ B; quare & latus F, æquabitur diametro ip&longs;ius &longs;phæ<lb/>ræ B. inuenta igitur e&longs;t quantitas diametri &longs;phæræ B, quod facere <lb/>oportebat. </s>

<s id="s.000320">Secundò versùs Apogæum promoveri videtur in con&longs;equentia; <lb/>versùs Perigæum in an<gap/>cedentia; quia versùs Apogæum tardiùs, versùs <lb/>Perigæum citiùs orbem &longs;uum ab&longs;olvit, ab ortu &longs;cilicet ad occa&longs;um. </s>

<s id="s.000321">Sextò <lb/>Emer&longs;io Veneris po&longs;t Conjunctionem Apogæam, e&longs;t ve&longs;pertina; quia Ve<lb/>nus à Sole versùs ortum digreditur, po&longs;t Conjunctionem Perigæam, e&longs;t <lb/>matutina; quia Venus Solem po&longs;t &longs;e relinquit ver&longs;us ortum: ergo in illa <lb/>apparet ve&longs;pere, in hac verò mane; &longs;ed paulò ante Apogæum fit immer&longs;io <lb/>matutina; quia cum Venus tunc &longs;pectet Solem versùs ortum, mane appa<lb/>ret, & cùm Sol eam a&longs;&longs;equatur, mane immergitur; at paulo po&longs;t ante Pe<lb/>rigæum, fit immer&longs;io ve&longs;pertina; quia cùm Venus tunc Solem &longs;pectet <lb/>ver&longs;us occa&longs;um, ve&longs;pere apparet, & cùm Solem a&longs;&longs;equatur, ve&longs;pere im<lb/>mergitur. </s>

<s id="s.000322"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000323"> Sed quid de hac linea SPL, aliquis &longs;ortè putaret e&longs;&longs;e para<lb/>bolam; hoc enim aliquando &longs;altem amicis innuere vi&longs;us es. </s>

<s>Exemplum.</s>

<s>Qvidam proponit aliquod corpus liquidum notæ <lb/>magnitudinis, & vult inuenire, quanta erit ma<lb/>gnitudo liquidi alterius generis, grauitatem </s><pb pagenum="27"/>

<s id="s.000324"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000325"> Multa haud dubiè con&longs;ideranda &longs;unt, vt ritè definiatur, quæ <lb/>& qualis &longs;it hæc linea: in modico arcu orbis va&longs;ti&longs;&longs;imi, qui ad in&longs;tar lineæ <lb/>rectæ a&longs;&longs;umi pote&longs;t, pro parabola, phy&longs;icè loquendo, accipi pote&longs;t, & <pb pagenum="28" xlink:href="025/01/032.jpg"/>hoc ip&longs;um e&longs;t, quod iam aliàs innui cùm de Saturno confabularer; nem<lb/>pe ex duplici motu recto, altero &longs;cilicet naturaliter accelerato, altero <lb/>æquabïli, hæc linea parabolica na&longs;citur, vt multi demon&longs;trarunt. </s>

<s>habentis propo&longs;ito corpori liquido æqualem.</s>

<s id="s.000326">Dixi <lb/>phy&longs;icè loquendo, quia neque arcus circuli e&longs;t linea recta, neque lineæ <lb/>ductæ ad idem centrum &longs;unt parallelæ, neque fortè motus apparens in <lb/>illo arcu e&longs;t æquabilis. </s>

<s id="s.000327">At verò in Venere, in qua longè maior arcus a&longs;&longs;u<lb/>mitur, vt DL, cùm hic a&longs;&longs;umi non po&longs;&longs;it, vt linea recta, quæ &longs;it ba&longs;is &longs;emi<lb/>parabolæ, linea SPL non e&longs;t, etiam phy&longs;icè loquendo, parabolica. </s>

<s><emph type="italics"/>Sit propo&longs;itum aliquod olei corpus A, cuius magnitudo<emph.end type="italics"/> 600. <emph type="italics"/>& <lb/>oporteat inuenire quanta srit magnitudo aquæ, grauitatem habentis <lb/>æqualem propo&longs;ito oleo A, accipiatur aliquod &longs;olidum corpus C, vt <lb/>pote plumbeum, & aquæ magnitudinem habentis æqualem plumbo <lb/>C, inueniatur grauitas, vt in exemplo prop.<emph.end type="italics"/> 8, <emph type="italics"/>dictum e&longs;t, quæ &longs;it<emph.end type="italics"/> 12. <lb/><emph type="italics"/>&longs;imiliter & olei æqualem habentis magnitudinem eidem plumbo C, <lb/>inueniatur grauitas quæ &longs;it 11, & fiat vt 12, ad<emph.end type="italics"/> 11, <emph type="italics"/>ita<emph.end type="italics"/> 600, <emph type="italics"/>ad alium <lb/><expan abbr="numer&utilde;">numerum</expan> qui &longs;it<emph.end type="italics"/> 550. <emph type="italics"/>is igitur numerus indicabit quanta erit magni<lb/>tudo aquæ grauitatem habentis æqualem propo&longs;ito oleo A.<emph.end type="italics"/></s>

<s id="s.000328">Vt <lb/>autem nonnihil, obiter &longs;altem, indicem, &longs;it BN radius illius circuli, quem <lb/>Venus æquali tempore cum Sole decurrit, &longs;it vt BS ad SN, ita circulus <lb/>&longs;ub radio BC ad arcum SX; &longs;it SO &longs;egmentum acce&longs;&longs;us ducto ex B <lb/>arcu OP, ducetur linea per punctum P: pari modo alia puncta habebun<lb/>tur; cogita punctum S moveri per SD motu accelerato, & &longs;imul cum axe <lb/>BS versùs X, circa centrum B, initio, velociùs: &longs;ub finem, tardiùs; de&longs;cri<lb/>bet curvam SPL, quæ e&longs;t &longs;pecies quædam &longs;piralis, &longs;eu fortè nova quæ<lb/>dam &longs;pecies parabolæ, in qua, arcus paralleli in locum applicatarum <lb/>&longs;ub&longs;tituuntur; ita vt v.g. quadratum OP ad quadratum DL, &longs;it vt SO, <lb/>ad SD, & vt tantulum Geometrizemus, cùm hæc figura &longs;it homogenea <lb/>&longs;emiparabolæ, &longs;unt enim arcus vt applicatæ, &longs;i ducatur arcus LD in <gap/> SD, <lb/>habebitur area dictæ figuræ: &longs;i autem idem arcus DL ducatur in <gap/> DB, <lb/>habebitur &longs;ector BLD. </s>

<s id="s.000329">Igitur figura SLD e&longs;t ad dictum &longs;ectorem, vt <lb/><gap/> SD ad <gap/> DB. </s>

<s><emph type="italics"/>Similiter &longs;i <expan abbr="propo&longs;it&utilde;">propo&longs;itum</expan> &longs;it aliquod corpus aqueum A, cuius magnitu<lb/>do<emph.end type="italics"/> 5700, <emph type="italics"/>& oporteat inuenire, quanta erit magnitudo argenti viui, <lb/>grauitatem habentis æqualem propo&longs;itæ aquæ A. </s>

<s id="s.000330">Sit etiam vt BD ad BS, ita BS ad tertiam BF, erit &longs;ector <lb/>BLD ad &longs;ectorem BHS, vt BD ad BF; &longs;unt enim &longs;ectores &longs;imiles in <lb/>duplicata; igitur &longs;ector BLD ad reliquum trapezium LHSD vt BD <lb/>ad DF, vel vt <gap/> BD ad <gap/> DF. </s>

<s id="s.000331">Igitur LSD ad dictum trapezium vt <gap/> SD <lb/>ad <gap/> FD; igitur LSD ad reliquum triangulum SHL vt <gap/> DS ad <gap/> DF <lb/>minùs <gap/> SD. </s>

<s>Accipiatur aliquod <lb/>corpus &longs;olidum C &longs;i aureum, &longs;uper inducatur ei cerea tunica propter <lb/>iam <expan abbr="dictã">dictam</expan> rationem, deinde argenti viui, magnitudine æqualis ip&longs;i C, <lb/>inueniatur grauitas quæ &longs;it<emph.end type="italics"/> 95, <emph type="italics"/>&longs;imiliter & aquæ <expan abbr="magnitudin&etilde;">magnitudinem</expan> ha<lb/>bentis equalem eidem C, inueniatur grauitas quæ &longs;it<emph.end type="italics"/> 7, <emph type="italics"/>& fiat vt<emph.end type="italics"/> 95, <lb/><emph type="italics"/>ad<emph.end type="italics"/> 7, <emph type="italics"/>ita<emph.end type="italics"/> 5700, <emph type="italics"/>ad alium numerum, qui &longs;it<emph.end type="italics"/> 420, <emph type="italics"/>is igitur numerus in<lb/>dicabit quanta erit magnitudo argenti viui grauitatem habentis <lb/>æqualem propo&longs;itæ aquæ A.<emph.end type="italics"/></s>

<s>Quod &longs;i propo&longs;itum corpus aqueum A, &longs;it &longs;phæricum, culus <lb/>&longs;phæræ diameter &longs;it 10, & oporteat inuenire quanta erit dia<lb/>meter &longs;phæræ ex argento viuo, grauitatem habentis æqualem <lb/>propo&longs;itæ &longs;phæræ A, ità faciendum erit. </s>

<s id="s.000332"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/> Hæc mihi non parum arrident; &longs;ed omitte quæ&longs;o hæc Geo<lb/>metrica, alioquin vix ab iis te ab&longs;trahere potero; probè igitur intelligo, <lb/>quomodo in hac tua hypothe&longs;i, omnia quorum huc v&longs;que memini&longs;ti Ve<lb/>neris Phænomena explicentur; nonnulla tamen &longs;uper&longs;unt, quæ fortè plus <lb/>negotij face&longs;&longs;unt v.g. cur maxima Veneris declinatio modò maior &longs;it, <lb/>modò minor, cur Venus aliquando matutina, &longs;imul & ve&longs;pertina eodem <lb/>die videatur; cur eiu&longs;dem latitudo Borealis &longs;it maior quàm Au&longs;tralis, alia<lb/>que huju&longs;modi. </s>

<s><emph type="italics"/>Accepto vt diximus aliquo corpore &longs;olido C, & inuentis grauita<lb/>tibus <expan abbr="liquidor&utilde;">liquidorum</expan> aquæ &longs;cilicet & argent viui magnitudinem æqua<lb/>lem habentium corpori C, quæ &longs;int<emph.end type="italics"/> 14, <emph type="italics"/>grauitas aquæ, &<emph.end type="italics"/> 190, <emph type="italics"/>graui<lb/>tas argenti viui, fiat vt<emph.end type="italics"/> 190, <emph type="italics"/>ad<emph.end type="italics"/> 14, <emph type="italics"/>ita cubus ex 10, hoc est ita 1000, <lb/>ad alium numerum, qui &longs;it<emph.end type="italics"/> 73 11/19, <emph type="italics"/>is igitur numerus erit cubus dia<lb/>metri &longs;phæræ ex argento viuo, grauitatem habentis æqualem propo<lb/>&longs;itæ ex aqua &longs;phæræ A: quare latus cubicum numeri<emph.end type="italics"/> 73 11/19, <emph type="italics"/>quod e&longs;t<emph.end type="italics"/><lb/>4 19/100 <emph type="italics"/>proxime indicabit ip&longs;am diametrum.<emph.end type="italics"/></s>

<s id="s.000333"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s><emph type="italics"/>Similiter &longs;i propo&longs;itum corpus aqueum A, fuerit cubicum, aut <lb/>alicuius alterius formæ regularis, eadem ratione, qua &longs;upra inuenit<lb/>tur latus cubi ex argento viuo, grauitate æqualis propo&longs;ito ex aqua <lb/>cubo A, nam &longs;i ip&longs;ius cabi A, <expan abbr="dat&utilde;">datum</expan> &longs;it latus<emph.end type="italics"/> 10, <emph type="italics"/>erit numerus<emph.end type="italics"/> 73 11/19, <lb/><emph type="italics"/>cubus ex argento viuo æqualis grauitate propo&longs;ito ex aqua cubo A; <lb/>quare latus cubicum numeri<emph.end type="italics"/> 73 11/19, <emph type="italics"/>quod est<emph.end type="italics"/> 4 19/100 <emph type="italics"/>proxime in<lb/>dicabit quæ&longs;itum latus cubi, ex argento viuo.<emph.end type="italics"/></s><pb pagenum="28"/>

<s id="s.000334"> Parum negotij cuncta hæc mihi face&longs;&longs;unt, &longs;ecus fortè vobis <lb/>ac proinde tot epicyclos, excentricos, circellos, librationes arcus, Ellip&longs;<lb/>&longs;es, Epicyclorum Epicyclos multiplicatis; quibus etiam admi&longs;&longs;is, vix fi<lb/>nem vobis propo&longs;itum obtinetis; itaque illa omnia cum meo &longs;implici&longs;&longs;imo <lb/>motu facillimè explico: vbi enim Venus pervenit ad M, id e&longs;t, ad illum <lb/>circulum ineundum quem æquali cum Sole tempore decurrit, dum hic <lb/>e&longs;t in mediocri di&longs;tantia D ; &longs;i Sol &longs;it in Apogæo, cum in con&longs;equentia, <lb/>id e&longs;t versùs Ortum Sol plus promoveri videatur, quia maiorem circu<lb/>lum de&longs;cribit, igitur tardiùs, haud dubiè Venus à Sole minùs digredi <lb/>videtur ad quàm Sol propiùs accedit, igitur in hoc ca&longs;u, maxima digre&longs;-<pb pagenum="29" xlink:href="025/01/033.jpg"/>&longs;io Veneris minor erit; &longs;ecus accidet, &longs;i tunc Sol degat in Perigæo, quia <lb/>&longs;cilicet breviorem circulum, ac proinde citiùs decurrit. </s>

<s id="s.000335">Igitur versùs Oc<lb/>ca&longs;um longiùs à Venere amovetur, hinc maior huius digre&longs;&longs;io, quæ dein<lb/>de pro diver&longs;o loco Solis diver&longs;a erit. </s>

<s>Neque di&longs;&longs;imili ratione inuenietur magnitudo reliquo<lb/>rum omnium liquidorum, grauitate propo&longs;ito corpori cuiu&longs;<lb/>cumque generis liquidi, æqualium, quare dicta &longs;ufficiant. </s>

<s id="s.000336">Minima igitur inter maximas fiet <lb/>Sole exi&longs;tente in Apogæo ; exempli gratia; maxima verò Sole exi&longs;tente <lb/>in Perigæo, media denique, Sole mediocrem di&longs;tantiam tenente, variæ <lb/>deinde pro variis locis, in quibus Sol ab Apogæo vel Perigæo plùs, vel <lb/>minùs di&longs;tat. </s>

<s id="s.000337">Quod verò &longs;pectat ad alterum po&longs;tulatum, æquè facile<gap/> ex<lb/>plico; cùm enim latitudo Borealis veneris maior &longs;it quàm au&longs;tralis, &longs;up<lb/>ponamus Venerem non procul à Perigæo cum latitudine Boreali 9. grad. <lb/></s>

<s>Dvm adhuc Opu&longs;culum &longs;ub prælo e&longs;&longs;et, dubitandi an&longs;am, <lb/>ex eo vir docti&longs;simus, cui percurrendum illud tradi<lb/>deram, arripuit, quod ex grauitate, corporum in aqua <lb/>exi&longs;tentium, non po&longs;&longs;et vera ratio, quam habent diuer&longs;a <lb/>ip&longs;orum corporum genera in grauitate, deprehendi, ni&longs;i <lb/>corpora fuerint &longs;imilia. </s>

<s id="s.000338">Sole v. g. exi&longs;tente iuxta Tropicum Capricorni, arcus diurnus Veneris, <lb/>longè maior e&longs;t, arcu diurno Solis, vt patet ex vulgaribus tabulis; quid <lb/>mirum; igitur, &longs;i & ante Solem oriatur, & po&longs;t illum occidat; ac pro<lb/>inde mane & &longs;ero &longs;e&longs;e videndam præbeat? </s>

<s id="s.000339">neque hic re&longs;tat vlla difficultas, <lb/>ni&longs;i fortè cur latitudo Borealis Veneris &longs;it maior au&longs;trali, cum tamen Mer<lb/>curij latitudo Au&longs;tralis Boreali maior &longs;it; partim à Sole ratio petenda e&longs;t, <lb/>cuius &longs;cilicet Apogæum modò e&longs;t in &longs;ignis Borealibus, modo in Au&longs;tra<lb/>libus, partim à diver&longs;is Coniunctionum & maximarum digre&longs;&longs;ionum lo<lb/>cis, ex quibus diver&longs;æ latitudinis ratio &longs;equitur; v. g. &longs;upponamus ma<lb/>ximam digre&longs;&longs;ionem ve&longs;pertinam in. </s>

<s>&longs;i enim (aiebat) accipiantur duo <lb/>corpora eiu&longs;dem generis, & grauitatis, quorum vnum &longs;it <lb/>planum, alterum conicam formam habens, & ponderen<lb/>tur in aqua, ita vt coni vertex deor&longs;um ver&longs;us <gap/> deat, ba&longs;is <lb/>vero ip&longs;ius coni, & latæ corporis plani &longs;uperficies æquidi&longs;tent <lb/>horizonti conus in aqua maiorem habebit grauitatem, cor<lb/>pore plano, quia corpus planum magis ab aqua &longs;u&longs;tentatur, <lb/>quam conus, & hoc quidem manife&longs;tum e&longs;t, quoniam &longs;i am<lb/>bo demittantur eodem tempore in aquam, conus citius ad <lb/>imum de&longs;cendet, quam corpus planum. </s>

<s id="s.000340">1. gradu Acietis ab&longs;que vlla latitu<lb/>dine, erit Sol v.g. in grad. 15. Pi&longs;cium, cùm autem hinc Venus cendat <lb/>versùs Perigæum, & &longs;uos orbes citiùs Sole perficiat, haud dubiè &longs;tatim <lb/>relinquit Eclipticam ver&longs;us Ortum & Au&longs;trum; vnde &longs;equitur latitudo <lb/>Borealis & tardi&longs;&longs;imus motus in con&longs;equentia, donec tandem fiat re<lb/>trograda, & paulò po&longs;t Coniungatur Soli Perigæa, nec non tamdiu du<lb/>ret retrogradatio po&longs;t Coniunctionem, quamdiu duravit ante Coniun<lb/>ctionem, cre&longs;cente &longs;emper latitudine Boreali; donec ad maximam di<lb/>gre&longs;&longs;ionem matutinam perveniat, modò &longs;it in &longs;ignis a&longs;cedentibus, id e&longs;t <lb/>à principio Capricorni ad principium Cancri. </s>

<s id="s.000341">Si autem &longs;upponamus ibi<lb/>dem Planetam, &longs;cilicet in 1. grad. Arietis ab&longs;que latitudine, in digre&longs;<lb/>&longs;ione maxima matutina, Sol erit v. g. in gr. 15. Geminorum, vt patet, <lb/>& cùm Venus hinc tendat ver&longs;us Apogæum, Orbes &longs;uos tardiùs Sole <lb/>decurrere incipit; Igitur relinquit Eclipticam versùs Occa&longs;um & Bo<lb/>ream vnde &longs;equitur latitudo Au&longs;tralis, quæ continuo cre&longs;cit versùs Can<lb/>crum: hæc forte regula generalis &longs;tatui po&longs;&longs;et, Venetis latitudo Borea<lb/>lis, quamdiu movetur tardiùs Sole, id e&longs;t à maxima digre&longs;&longs;ione matutina <lb/>v&longs;que ad maximam ve&longs;pertinam, in Signis a&longs;cendentibus, decre&longs;cit, in de&longs;<lb/>cendentibus cre&longs;cit; contra verò Au&longs;tralis in a&longs;cendentibus cre&longs;cit, & <lb/>decre&longs;cit in de&longs;centibus; quamdiu verò movetur citiùs Sole, latitudo bo<lb/>realis in a&longs;cendentibus cre&longs;cit, in de&longs;cendentibus decre&longs;cit, in his demum <lb/>Au&longs;tralis cre&longs;cit & decre&longs;cit in illis; cùm autem &longs;int ferè innumeræ con<lb/>iugationes, Signorum a&longs;cendentium & de&longs;cendentium, coniunctionum, <lb/>digre&longs;&longs;ionum, itemque Apogæi & Perigæi; Veneris & Solis; quid mi<lb/>rum, &longs;i tanta varietas in Phænomenis deprehen&longs;a A&longs;tronomos eò adegerit, <lb/>vt fateantur vltro, certum Sy&longs;tema Veneris, in quo omnia Phænomena <pb pagenum="30" xlink:href="025/01/034.jpg"/>explicentur nondum &longs;tatui po&longs;&longs;e, ri&longs;i plures & magis accuratæ Ob&longs;erva<lb/>tiones fiant. </s>

<s>Hoc argumentum <lb/>licet primo a&longs;pectu probabile videatur, tamen fal&longs;o concludit. </s>

<s id="s.000342">Porrò cum Venus proximè ad terram accedat, & circa hori-<lb/>zontem vt plurimum Ob&longs;ervetur, non e&longs;t dubium, quin refractio eius La<lb/>titudinem non parum mutet, ac proinde valde difficile &longs;it, certam regu<lb/>lam ex Ob&longs;ervationibus, quæ tot fallaciis oculorum &longs;ubjiciuntur &longs;tatuere; <lb/>&longs;ed ne &longs;im prolixior, & &longs;altem extra chorum, hæc omitto, cùm manife&longs;tè <lb/>con&longs;tet, in qualibet hypothe&longs;i ; hæc valde difficilè explicari; in ea tamen, <lb/>quam indicavi longè faciliùs. </s>

<s id="s.000343">De Mercurio nihil dico, quia eadem pro <lb/>illo faciunt, quæ de Venere diximus, ni&longs;i quòd &longs;uas revolutiones citiùs <lb/>ab&longs;olvit, minu&longs;que digreditur à Sole, quàm Venus; ac proinde illius Ob<lb/>&longs;ervationes longè difficiliores. </s>

<s><lb/>verum e&longs;t quod aqua &longs;u&longs;tentat magis corpus planum, quam <lb/>conum, ip&longs;um tamen &longs;u&longs;tentat, netanta velocitate feratur <lb/>deor&longs;um, non ideo ip&longs;ius grauitati aliquid detrahit, neque <lb/>enim ex velociori motu &longs;impliciter inferri pote&longs;t maior gra<lb/>uitas, illud enim valeret etiam in aere, quod e&longs;t fal&longs;um, &longs;ed <lb/>ne huiu&longs;modi dubitatio veritatis &longs;pecie aliquem decipiat, &longs;e<lb/>quenti Theoremate eam de&longs;truere agrediar. </s>

<s id="s.000344">De diver&longs;is pha&longs;ibus horum Planetarum <lb/>nihil etiam dico; quia non dubitas; opinor, quin facillimè citra ve&longs;tram <lb/>hypothe&longs;im explicentur: quare his peractis, vide quæ&longs;o, vtrùm alia pro <lb/>tua hypothe&longs;i &longs;uppetant argumenta. </s>

<s>THEOR EMA VIII. PROPOS. XVI.</s>

<s id="s.000345"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>Corpora eiu&longs;dem generis, & grauitatis giauiora <lb/>quam aqua, et&longs;i di&longs;similia, æqualem in aqua <lb/>grauitatem habent. </s>

<s id="s.000346"> Omi&longs;&longs;is A&longs;tronomis, quæ haud dubiè &longs;atis feliciter &longs;olvi&longs;ti, <lb/>alia duo &longs;unt, quæ magnum no&longs;træ hypothe&longs;i plau&longs;um pepererunt, pri<lb/>mùm petitur à maris æ&longs;tu, alterum à Magnete: quod ad primum &longs;pectat, <lb/>&longs;upponimus, Terram moveri motu quodam mixto ex motu orbis & cen<lb/>tri, qua&longs;i ad in&longs;tar rotæ in plano, vt iam &longs;upra in&longs;inua&longs;ti, ac proinde par<lb/>tes illius inæquali motu ferri, alias tardiùs, alias velociùs. </s>

<s id="s.000347">Suppono præ<lb/>tereà aquam in va&longs;e, &longs;eu cymba vectam, vbi cymba motum remittit, ex<lb/>currere versùs illam partem, in quam cymba tendit; in oppo&longs;itam verò, <lb/>vbi cymba motum accelerat, cogita quæ&longs;o aquam Occani, qua&longs;i in va&longs;ti&longs;<lb/>&longs;ima concha, à Globo Terræ delatam & circumactam, &longs;ed dicto motu <lb/>inæquali, haud dubiè vbi motus acceleratur, aqua versù; Occa&longs;um ex<lb/>currit, vbi remittitur, versùs Ortum: En tibi germanam cau&longs;am æ&longs;tus <lb/>marini, quæ certè, vt cum no&longs;tra hypothe&longs;i optimè con&longs;entit, ita in aliis <lb/>explicari non pote&longs;t. </s>

<s>SINT duo eiu&longs;dem generis, & grauitatis corpora A, B, grauiora <lb/>quam aqua, & &longs;int di&longs;&longs;imilia, dico ip&longs;a corpora æqualem in aqua <lb/>grauitatem habere. </s>

<s>&longs;it enim &longs;i &longs;ieri pote&longs;t corpus A, leuius corpore B, <pb pagenum="29"/>& accipiatur aliquod corpus L, leuius quam aqua, ita vt cum ip&longs;i <lb/>corpori L, appendatur, corpus B, & ambo &longs;imul demittantur in <expan abbr="aquã">aquam</expan>, <lb/>&longs;int æque grauia atque aqua, neque &longs;ur&longs;um, neque deor&longs;um &longs;eran<lb/>tur, &longs;imiliter accipiatur alterum corpus M, eiu&longs;dem generis cum <lb/>corpore L, ip&longs;ique &longs;imile, & <lb/><figure id="fig13"/><lb/>æquale, & corpori M, appen <lb/>datur corpus A. </s>

<s id="s.000348"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000349"> Negare non po&longs;&longs;um, quin hoc fuerit ingenio&longs;um inventum, <lb/>fictum tamen & commentitium. </s>

<s>Deinde in<lb/>teligatur aqua con&longs;i&longs;tens, & <lb/>manens, eiu&longs;que &longs;uper&longs;i<lb/>cies &longs;phærica C D E, cuius <lb/>&longs;phæræ centrum K, aquæ <lb/>enim con&longs;i&longs;tentis, atque <lb/>manentis &longs;uperficies &longs;phæ<lb/>rica e&longs;t, cui <gap/> &longs;phæræ cen<lb/>trum idem <gap/>, quod <expan abbr="centr&utilde;">centrum</expan> <lb/>terræ, hoc autem demon&longs;tratum e&longs;t ab Archimede Prop. 2. lib.

<s id="s.000350">Primo enim ita æ&longs;tus diurnus &longs;uas pe<lb/>riodos metitur, vt ad motum Lunæ dumtaxat, diurnum &longs;cilicet, non <lb/>Solis aut Terræ &longs;e&longs;e componat; nam &longs;ummi æ&longs;tus, vel &longs;ummæ aquarum <lb/>elevationis terminus e&longs;t Luna meridiana, tum in hoc, tum in oppo&longs;ito <lb/>hemi&longs;phærio; principium verò e&longs;t eadem Luna, Quadrante circuli di<lb/>&longs;tans à Meridiano: Igitur Luna exi&longs;tente in Meridiano, æ&longs;tus cre&longs;cere <lb/>de&longs;init, decre&longs;cere incipit, remota vero Quadrante circuli à Meridiano, <lb/>hinc inde æ&longs;tus decre&longs;cere de&longs;init, & cre&longs;cere incipit: rem ita fieri per <lb/>&longs;e con&longs;tanti&longs;&longs;imum e&longs;t, habeturque ex indubitatis Ob&longs;ervationibus; licèt <lb/>autem per accidens fieri po&longs;&longs;it, vt crementum decremento inæquale &longs;it; <lb/>hoc tamen non ob&longs;tat, quin po&longs;tero die dementum incipiat eadem hora <lb/>Lunari, ac proinde 48. minutis tardiùs, quàm pridie. </s>

<s id="s.000351">Quid autem ad <lb/>hæc, Augu&longs;tine mi, Terræ motus conferat, nemo capiat; cùm enim ea<lb/>dem motus inæqualitas, eadem &longs;emper hora, eidem Æquatoris terre&longs;tris <lb/>globi puncto in&longs;it, idem &longs;emper effectus ex eadem inæqualitate, ca<lb/>dem hora &longs;equi deberet: igitur eadem hora &longs;emper e&longs;&longs;et &longs;ummum cre-<pb pagenum="31" xlink:href="025/01/035.jpg"/>mentum æ&longs;tus, eadem, &longs;ummum decrementum; quod tamen omnibus <lb/>Ob&longs;ervationibus repugnat: &longs;i enim hac ip&longs;a die, Luna in Meridie &longs;ci<lb/>licet exi&longs;tente, &longs;it &longs;ummum crementum æ&longs;tus hora meridiana, vt &longs;it in no<lb/>vilunio, cra&longs;tina die, idem &longs;ummum crementum erit minutis 48. circiter <lb/>po&longs;t Meridiem; & tertio po&longs;t die hora, 1. 36. minutis po&longs;t Meridiem, at<lb/>que ita deinceps; idem de Plenilunio dicendum e&longs;t. </s>

1. de <lb/>ijs, quæ vehuntur in aqua. </s>

<s>Inteligantur etiam duæ pyramides con<lb/>iunctæ, & continuatæ, æquales, & &longs;imiles KCD, KDE, pro ba&longs;ibus <lb/>habentes in &longs;uperficie aquæ parallelogramma, vertices autem pun<lb/>ctum K, & corpora L, B, comprehendantur à pyramide KDE, corpo<lb/>ra vero M, A, à pyramide KCD, & &longs;ub corporibus L, B, de&longs;cribatur <lb/>quædam alterius &longs;phæræ &longs;uperficies FGH, in aqua, circa centrum K, <lb/>poterit autem huiu&longs;modi &longs;uperficies &longs;ub corporibus L, B, de&longs;cribi, <lb/>quoniam & &longs;i ip&longs;i corpora demerguntur tota, non ideo feruntur <lb/>deor&longs;um, ponuntur enim æque grauia atque aqua. </s>

<s id="s.000352"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000353"> Ita fortè di&longs;poni po&longs;&longs;unt prædicti duo motus, orbis &longs;cilicet <lb/>& centri, vt motus mixtus inde re&longs;ultans tales in æ&longs;tu mutationes pro<lb/>ducat. </s>

<s>Quoniam <lb/>igitur eiu&longs;dem generis ponuntur corpora M, L, & æqualia, & &longs;imilia, <lb/>erunt æque grauia, cum in aqua, tum in aere, & quoniam corpus <lb/>A, leuins e&longs;t in aqua, corpore B, erunt corpora M, A, &longs;imul, in aqua <lb/>leuiora corporibus L, B, &longs;ed corpora L, B, &longs;imul, æque grauia &longs;unt at<lb/>que aqua, ergo corpora M, A, &longs;imul, leuiora erunt quam aqua; quare <lb/>corpus M, non demergetur totum, &longs;ed aliqua pars ip&longs;ius ex aquæ &longs;u<lb/>per&longs;icie extabit. </s>

<s>Et quoniam eiu&longs;dem generis, & grauitatis ponuntur corpora A, B, <lb/>erunt magnitudine æqualia, & per additionem æqualium æquali<lb/>bus, corpora M, A, erunt æqualia corporibus L, B, </s>

<s id="s.000354"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000355"> Nullo &longs;ané modo id fieri po&longs;&longs;e, omni a&longs;&longs;everatione affirmo; quod <lb/>vt clariùs exponam. </s>

<s>Quoniam igitur corpora M, A, æqualia &longs;unt corporibus L, B, pars <lb/>autem corporis M, extat ex aquæ &longs;uperficie, & corpora L, B, tota de<lb/>merguntur, minus loci ocupabunt in aqua corpora M, A, quam cor<lb/>pora L, B, quare maior erit grauitas corporum M, A, & aquæ conti<lb/>nentis ip&longs;a corpora, quæ e&longs;t in loco pyramidis CDGF, quam corpo<lb/>rum L, B, & aquæ ip&longs;a corpora <expan abbr="contin&etilde;tis">continentis</expan> in loco pyramidis DEHG, <pb pagenum="30"/>magis igitur aquæ pars premetur, quæ e&longs;t &longs;ub &longs;uperficie FG, quam <lb/>ca quæ e&longs;t &longs;ub &longs;uperficie GH; quare expellet partem minus pre&longs;&longs;am, <lb/>(æqualiter enim & continuatæ iacent inter &longs;e&longs;e) & <expan abbr="nõ">non</expan> manebit aqua, <lb/>quod e&longs;t ab&longs;urdum, ponebatur enim manens. </s>

<s>non igitur corpus A, <lb/>leuius e&longs;t in aqua corpore B. eadem ratione o&longs;tendetur neque corpus <lb/>B, leuius e&longs;&longs;e in aqua corpore A, quare con&longs;tat propo&longs;itum. </s>

<s id="s.000356">Sit A Centrum mundi, DBLC orbita terræ, vel magnus orbis, D cen<lb/>trum terræ, quam paulò majorem de&longs;cribo, ne parvitas orbis confu&longs;io<lb/>nem patiat; dum centrum D movetur versùs B, ita volvitur circulus cir<lb/>ca D, vt Eversùs I, & F, versùs H tendat. </s>

<s>ALITER.</s>

<s id="s.000357">Vnde re&longs;ultat ex vtroque mo<lb/>tu æquabili motus mixtus omnino inæqualis; nempe ab H in I, per E; <lb/>additur motus orbis, motui centri; id e&longs;t &longs;patio decur&longs;o &longs;olo motu cen<lb/>tri, &longs;patium æquale diametro IH ; ab I verò in H per F, idem &longs;patium <lb/>detrahitur &longs;patio decur&longs;o mot<gap/> centri, hinc ab H in E, acelerationis cre<lb/>menta, &longs;uprà motum centri, &longs;unt in ratione &longs;inuum ver&longs;orum arcuum <lb/>decur&longs;orum; ab E in I, in ratione &longs;inuum rectorum; decrementa pariter <lb/>ab I in F, &longs;unt in ratione &longs;inuum ver&longs;orum; ab F verò in H, in ratione <pb pagenum="32" xlink:href="025/01/036.jpg"/>&longs;inuum rectorum: Vnde in E e&longs;t maxima acceleratio; in F maxima retar<lb/>datio, in I & H merus motus centri con&longs;ideratur: itaque ab H in I per E, <lb/>aqua Oceani juxta ea, quæ dicis, versùs Occa&longs;um excurrere deberer; ab <lb/>I verò in H per F, versùs Ortum; Igitur in E &longs;emper e&longs;&longs;et maximus excur<lb/>&longs;ionis motus versùs Occa&longs;um; in F versùs Ortum; in I & H quies; quan<lb/>tum hæc Ob&longs;ervationibus repugnent, omnibus rerum i&longs;tarum peritis cogi<lb/>tandum relinquo. </s>

<s>Sint duo eiu&longs;dem generis, & grauitatis corpora A, B, grauiora <lb/>quam aqua, & &longs;int di&longs;&longs;imilia. </s>

<s id="s.000358"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>o&longs;tendendum e&longs;t ip&longs;a corpora æqualem <lb/>in aqua grauitatem habere, &longs;it enim corporis A, vel ip&longs;ius B, graui<lb/>tas CD, aquæ vero magni<lb/><figure id="fig14"/><lb/>tudinem habentis æqua<lb/>lem ip&longs;i A, vel B, &longs;it graui<lb/>tas C, & accipiatur ali<lb/>quod corpus L, leuius <expan abbr="quã">quam</expan> <lb/>aqua, cuius grauitas &longs;it <lb/>ip&longs;i C, æqualis, aquæ ve<lb/>ro, magnitudinem haben<lb/>tis æqualem corpori L, &longs;it <lb/>grauitas æqualis ip&longs;i CD, <lb/>itaque appen&longs;o corpore <lb/>B, corpori L, corpus ex <lb/>vtri&longs;que con&longs;tans æque graue erit atque aqua, grauitas enim vtro<lb/>runque corporum B, L, e&longs;t æqualis vtri&longs;que grauitatibus CD, & C, & <lb/>grauitas aquæ, magnitudinem habentis æqualem <expan abbr="vtri&longs;q;">vtri&longs;que</expan> corporibus <lb/>L, B, æqualis e&longs;t ei&longs;dem grauitatibus CD, & C, corpora igitur B, L, <lb/>demi&longs;&longs;a in aquam, neque &longs;ur&longs;um, neque deor&longs;um ferentur, quia cor<lb/>pus B, grauius quam aqua fertur dcor&longs;um tanta vi, quanta à corpo<lb/>re <emph type="italics"/>L,<emph.end type="italics"/> &longs;ur&longs;um retrahitur. </s>

<s id="s.000359"> Quid &longs;i aliquis diceret, Nautis in hoc fidem habendam non <lb/>e&longs;&longs;e, qui forte ad libitum prædictas ad Lunam habitudines marino æ&longs;tui <lb/>affinxerunt? </s>

<s>Rur&longs;us accipiatur alterum corpus &longs;olidum M, eiu&longs;dem generis <lb/>cum corpore L, ip&longs;ique &longs;imile, & æquale, & corpore A, appen&longs;o ip&longs;i <lb/>M, & demi&longs;&longs;is ambobus in aquam, eadem ratione qua &longs;upra o&longs;ten<lb/>detur, corpora A, M, &longs;imul, e&longs;&longs;e æque grauia atque aqua, & corpus <lb/>A, tanta vi deor&longs;um ferri, quanta retrahitur &longs;ur&longs;um à corpore M, <lb/>&longs;ed corpora M, L, æqualem vim habent retrahendi &longs;ur&longs;um, cum <lb/>&longs;int eiu&longs;dem generis, & æqualia, & &longs;imilia, ergo æquali vi retra<lb/>hentur corpora A, B, ne de&longs;cendant; quare con&longs;tat ip&longs;a corpora A, <lb/>B, æqualem in aqua grauitatem habere quod erat o&longs;tendendum. </s><pb pagenum="31"/>

<s id="s.000360"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>THEOREMA IX. PROPOS. XVII.</s>

<s id="s.000361"> Cuique &longs;uæ artis perito credendum e&longs;&longs;e, optima ratio po&longs;tu<lb/>lat, præ&longs;ertim &longs;i periti omnes illius artis aliquid a&longs;&longs;erant, quod alioquin <lb/>nihil illorum intere&longs;t. </s>

<s id="s.000362">Cùm igitur Naucleri omnes periti, & principes illi <lb/>autores, qui de hoc argumento &longs;crip&longs;erunt, omni a&longs;&longs;everatione affirment, <lb/>rem ita e&longs;&longs;e, nemo prudens fidem iis detrectet; accedit, quod illi om<lb/>nes, qui in litore Oceani Gallici, Britannici, Anglici, Belgici habitant <lb/>(neque te ad Antipodas vel Garamantas amando) omnimodam huiu&longs;ce <lb/>rei te&longs;tificationem facere po&longs;&longs;unt, cùm illam præ oculis habeant; omitto <lb/>alia innumera argumenta, quibus hoc ve&longs;trum commentum refutatur; <lb/>quia &longs;upervacaneum puto, actum iam agere, illud tamen non omitto, <lb/>quod præ cæteris vrgere videtur; &longs;uppono enim cum iis omnibus, qui <lb/>vel delibârunt hanc materiam, maximam e&longs;&longs;e vim æ&longs;tus in Plenilunio, <lb/>magnam etiam in Novilunio, in Quadraturis perexiguam; Quid porro ad <lb/>hæc terræ motus? </s>

<s>Sphære eiu&longs;dem generis inter &longs;e &longs;unt in grauitate, vt <lb/>diametrorum cubi in magnitudine. </s>

<s id="s.000363">Nihil pror&longs;us. </s>

<s>SINT &longs;phæræ eiu&longs;dem gene<lb/><figure id="fig15"/><lb/>ris ABC, DEF, quarum diame<lb/>tri BC, EF. dico vt &longs;ph&ecedil;ra ABC, <lb/>&longs;e habet in grauitate, ad &longs;phæram <lb/>DEF, ita &longs;e habere in maguitudi<lb/>ne cubum ex BC, ad cubum ex <lb/>EF, &longs;it enim &longs;phæræ ABC, graui<lb/>tas G, & &longs;phæræ DEF, grauitas H, <lb/>quoniam igitur eiu&longs;dem generis <lb/>ponuntur &longs;phæræ ABC, DEF, <lb/>erit^{*} vt &longs;phæra ABC, ad &longs;phæram DEF, ita grauitas G, ad H,<arrow.to.target n="note44"/> graui<lb/>tatem, &longs;ed &longs;phæra ABC, ad &longs;phæram DEF,^{*} triplicatam habet<arrow.to.target n="note45"/> ra<lb/>tionem eius, quam diameter BC, ad EF, diametrum, orgo & graui<lb/>tas G, ad grauitatem H, triplicatam habebit rationem eius, quam <lb/>habet BC, ad EF, &longs;ed & cubus ex BC, ad cubum ex EF,^{*} triplicatam<arrow.to.target n="note46"/><lb/>rationem habeteius, quam BC, ad EF, ergo vt grauitas G, ad graui<lb/>tatem H, ita erit cubus ex BC, ad cubum ex EF. &longs;phæræ igitur eiu&longs;<lb/>dem generis inter &longs;e &longs;unt in grauitate, vt diametrorum cubi in ma<lb/>gnitudine, quod erat demon&longs;trandum. </s><pb pagenum="32"/>

<s id="s.000364"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s><margin.target id="note44"/>2. & 3. <lb/><emph type="italics"/>huius.<emph.end type="italics"/></s>

<s id="s.000365"> In Novilunio Luna propios ad Solem accedit, & minores <lb/>arcus decurrit, contraverò in Plenilunio. </s>

<s id="s.000366"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000368">An fortè Luna &longs;uos motus in Terram derivat? </s>

<s>Ad comparandum inter &longs;e duodecim corporum genera <lb/>grauitate, & magnitudine tabella.</s>

<s id="s.000369">Mi<lb/>nimè verò, alioquin maior æ&longs;tus e&longs;&longs;etin Quadraturis, quàm in Novilunio, <lb/>quod certè cum veritate minimè con&longs;entit: deinde Terra ip&longs;a in Novilu<lb/>nio tardiùs moveretur, quod nemo vnquam &longs;omniavit. </s>

<s>TABELLE WAR HIER</s>

<s id="s.000370"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæro exempli gratia, quam habet rationem in grauitate plumbum ad aurum. </s>

<s id="s.000371"> Saltem negari non pote&longs;t, quin terræ aut Solis motus ali<lb/>quid conferat ad mutationem illam æ&longs;tuum, quam omnes huiu&longs;que cir<lb/>ca Æquinoctia Ob&longs;ervarunt; nihil enim ad hæc Luna. </s>

<s>In<lb/>teligatur plumbum, quoniam leuius est auro, grauitatem habere 1, & in linea plumbi, <lb/>in prima columna nominati &longs;ub titulo auri, quæratur aurt grauitas, ea erit<emph.end type="italics"/> 1 11/21. <emph type="italics"/>plum<lb/>bum igitur ad aurum rationem habebit in grauitate vt 1, ad 1 1<gap/>/21, &longs;i enim &longs;umantur <lb/>duo corpora magnitudine æqualia, vnum plumbeum alterum aureum, &longs;it autem plum<lb/>bei corporis grauitas<emph.end type="italics"/> 1, <emph type="italics"/>aurei erit<emph.end type="italics"/> 1 1<gap/>/21, <emph type="italics"/>quare corpus plumbeum ad rorpus aureum <lb/>eiu&longs;dem magnitudinis rationem habebit in grauitate vt 1, ad 1 1<gap/>/21. comparantur an<lb/>tem inter &longs;e genera diuer&longs;a grauitate, in corporibus magnitudine æqualibus.<emph.end type="italics"/></s>

<s id="s.000372"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s><emph type="italics"/>Rur&longs;us, quæro quam habet rationem in grauitate aqua ad argentum viuum. </s>

<s id="s.000373"> Sed quid quæ&longs;o ad hæc terræ motus? </s>

<s id="s.000374">equidem in diurno ter<lb/>ræ motu, illa revolutio annua Globi, ad retinendum Axis Paralleli&longs;mum, <lb/>aliquid facit, quod tamen &longs;ub &longs;en&longs;um non cadit: nempe motui orbis <lb/>opponi videtur: &longs;ed reverà hoc nihil e&longs;t, nec quidquam ad hanc rem fa<lb/>cit, vt con&longs;ideranti patebit. </s>

<s>inteli<lb/>gatur aqua, vt leuior argento viuo grauitatem habere 1, & in linea aqua, &longs;ubtitulo ar<lb/>genti viui, quæratur argenti viui grauitas, ea erit<emph.end type="italics"/> 13 4/7, <emph type="italics"/>aqua igitur ad argentum <expan abbr="viu&utilde;">viuum</expan> <lb/>rationem habebit in grauitate vt 1, ad 13 4/7.<emph.end type="italics"/></s>

<s><emph type="italics"/>Contra, quæro quomodo &longs;e habent in magnitudine aurum, & plumbum. </s>

<s id="s.000375"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000376"> Quid autem ad hæc Luna, quis hominum aliquando dicat? </s>

<s>inteligatur <lb/>aurum, quoniam grauius e&longs;t plumbo, magnitudinem habere 1, & in linea plumbi, &longs;ub ti<lb/>tulo auri, quæratur plumbi magnitudo, ea erit 1 1<gap/>/21, aurum igitur ad plumbum &longs;e ba-<emph.end type="italics"/><pb pagenum="33"/><emph type="italics"/><gap/>bit in magnitudine vt 1, ad 1 19/21, &longs;i enim &longs;umantur duo corpora æque grauia, vnum <lb/>aureum, alterum plumbeum, &longs;it autem corporis aurei magnitudo 1, plumbei erit 1 1<gap/>/21, <lb/>quare corpus aureum ad corpus plumbeum eiu&longs;dem grauitatis &longs;e habebit in magnitudi<lb/>ne vt 1, ad 1 19/21, comparantur autem inter &longs;e genera diuer&longs;a magnitudine, in corpori<lb/>bus æque grauibus.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæro denique quomodo &longs;e habent in magnitudine ferrum, & aqua, ponatur ferrum, <lb/>vt grauius aqua, magnitudinem habere 1, & in linea aquæ, &longs;ub titulo ferri, quæratur <lb/>aquæ magnitudo, ea erit<emph.end type="italics"/> 8, <emph type="italics"/>ferrum igitur ad aquam &longs;e habebit in magnitudine vt 1, ad<emph.end type="italics"/> 8. </s>

<s id="s.000377"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000378"> Ego fortè minimus hominum; illam enim æ&longs;tus marini cau<lb/>&longs;am affero, quæ & communibus principiis nittitur, & ad quam cuncta <lb/>phænomena, quæ per &longs;e ex marino æ&longs;tu &longs;equuntur, facilè reduci po&longs;&longs;unt: <lb/>&longs;ed cùm altioris indaginis res &longs;it, in alium congre&longs;&longs;um remittendam illam <lb/>e&longs;&longs;e putarem, ne c&oelig;pta di&longs;ceptatio intermittatur: itaque omi&longs;&longs;o maris <lb/>æ&longs;tu, quid tandem de Magnete dicis? </s>

<s>Altera, ad comparandum inter &longs;e duodecim corporum genera, <lb/>grauitate, & magnitudine, tabella.</s>

<s>TABELLE WAR HIER</s>

<s id="s.000379"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæro exempli gratia, quæ nam &longs;it ratio in grauitate, auri ad argentum. </s>

<s id="s.000380"> Facilè opinor conjicies; terram enim maiorem Magnetem <lb/>e&longs;&longs;e dicimus cum Gilberto; vnde manife&longs;tam cau&longs;am ducimus perpetui <lb/>Axis paralleli&longs;mi; &longs;ic enim polorum Magneticorum axis, Axi mundi <lb/>&longs;emper e&longs;t parallelus, id e&longs;t, ad eandem &longs;emper fixam vniver&longs;i plagam <lb/>conver&longs;i &longs;unt, immo nullum alium ab i&longs;to Axem mundi agno&longs;cimus. </s>

<s>intelliga<lb/>tur aurum, quoniam grauius est argento, grauitatem habers 100, & in line a auri, &longs;ub <lb/>titulo argenti, reperietur argenti grauitas<emph.end type="italics"/> 54 22/57, <emph type="italics"/>aurum igitur ad argentum rationem <lb/>habebit in grauitate vt<emph.end type="italics"/> 100, <emph type="italics"/>ad<emph.end type="italics"/> 54 22/57, <emph type="italics"/>&longs;ienim &longs;umantur duo corpora, magnitudine <lb/>aqualia, vnum aureum, alterum argenteum, &longs;it autem aurei corporis grauitas<emph.end type="italics"/> 100, <emph type="italics"/>erit<emph.end type="italics"/><pb pagenum="34"/><emph type="italics"/>argentei<emph.end type="italics"/> 54 22/57, <emph type="italics"/>quare corpus aureum ad corpus argenteum eiu&longs;dem <lb/>magnitudinis, rationem habebit in grauitate, vt<emph.end type="italics"/> 100, <emph type="italics"/>ad<emph.end type="italics"/> 54 22/57. </s>

<s id="s.000381"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæro, quomodo &longs;e habet in grauitate aqua ad vinum. </s>

<s id="s.000382"> Terram Magnetem e&longs;&longs;e non pauci communiter negant; neque <lb/>rationes efficaces de&longs;unt; &longs;ed demus hoc in tui gratiam, & terra, vt vis, <lb/>&longs;it va&longs;tus Magnes: igitur illius poli ad fixa c&oelig;li puncta &longs;emper &longs;pectant; <lb/>rectè, quis hoc negat? </s>

<s id="s.000383">Vnde &longs;i fortè vi ab extrin&longs;eco impre&longs;&longs;a, ab hoc <lb/>a&longs;pectu & &longs;itu amoveretur, illico &longs;e&longs;e re&longs;titueret; optimè; quid inde? <lb/></s>

<s>quoniam <lb/>æqua grauior est vino, intelligatur eius grauitas<emph.end type="italics"/> 100, <emph type="italics"/>& quoniam in <lb/>linea aquæ, &longs;ub titulo vint, datur vini grauitas<emph.end type="italics"/> 98 <gap/>, <emph type="italics"/>aqua ad vinum <lb/>&longs;e habebit in grauitate, vt<emph.end type="italics"/> 100, <emph type="italics"/>ad<emph.end type="italics"/> 98 <gap/>. </s>

<s id="s.000384">Ergo, inquies, terra movetur in orbe magno, quia illius Axis, circa <lb/>quem diurnos agit orbes, &longs;ibi ip&longs;i Parallelus &longs;emper e&longs;t; nego con&longs;e<lb/>quentiam; &longs;ive enim terra moveatur, &longs;ive quie&longs;cat, ille Axis ad fixa &longs;em<lb/>per c&oelig;li puncta &longs;pectat: ergo ex hoc neutra hypothe&longs;is probari pote&longs;t; <lb/>immò potiori iure mea, quàm tua inde probatur. </s>

<s><emph type="italics"/>Contra quæro quomodo &longs;e habent in magnitudine argentum, & <lb/>aurum. </s>

<s id="s.000385"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>intelligatur argentum, vt leuius auro, magnitudinem balere<emph.end type="italics"/><lb/>100, <emph type="italics"/>& in linea auri &longs;ub titulo argenti, quæratur auri magnitudo, <gap/><lb/>erit<emph.end type="italics"/> 54 22/57, <emph type="italics"/>argentum igitur ad aurum &longs;e habebit in magnitudine, vt<emph.end type="italics"/><lb/>100, <emph type="italics"/>ad<emph.end type="italics"/> 54 22/57, <emph type="italics"/>&longs;i enim &longs;umantur duo corpora æque grauia, vnum <lb/>argenteum, alterum aureum, &longs;it autem argentei corporis magnitudo<emph.end type="italics"/><lb/>100, <emph type="italics"/>erit aurei<emph.end type="italics"/> 54 22/57, <emph type="italics"/>quare corpus argenteum, ad corpus aureum <lb/>eiu&longs;dem grauitatis, &longs;e habebit in magnitudine, vt 100, ad<emph.end type="italics"/> 54 22/57. </s>

<s id="s.000386"> Fortè illam &longs;ubaudis demon&longs;trationem, qua ex tuis aliquis <lb/>no&longs;tram hypothe&longs;im labefactare molitus e&longs;t. </s>

<s id="s.000387">Fru&longs;trà licet: cùm illam <lb/>Ga&longs;&longs;endus vir toto orbe literario notus illam in Docti&longs;&longs;imorum homi<lb/>num congre&longs;&longs;u, cui &longs;ummus quidam Princeps præerat, egregiè refutavit. </s>

<s><emph type="italics"/>Quæro denique quomodo &longs;e bab <gap/> in magnitudine aqua & ar<lb/>gentum viuum. </s>

<s>quoniam aqua leu<gap/> est argento viuo, intelligatur <lb/>eius magnitudo<emph.end type="italics"/> 100, <emph type="italics"/>& in linea argenti viui, &longs;ub titulo aquæ, quæ<lb/>ratur argenti viui magnitudo, & reperietur<emph.end type="italics"/> 7 7/29, <emph type="italics"/>aqua igitur ad <lb/>argentum viuum &longs;e habebit in magnitudine, vt 100, ad<emph.end type="italics"/> 7 7/29. </s>

<s id="s.000388"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000389"> Certè illam demon&longs;trationis loco non habeo; nam nec terram <lb/>magnum Magnetem e&longs;&longs;e, puto, nec etiam &longs;i magnes e&longs;&longs;et, ad alia quæ<lb/>dam c&oelig;li puncta, exceptis polis, re&longs;pectum haberet, volebat enim vir <lb/>ille de re Magnetica optimè meritus, Magnetem in &longs;phæram tornatum, <lb/>in eo &longs;emper &longs;itu manere, vt omnia illius puncta ad eadem &longs;emper vni<lb/>ver&longs;i puncta &longs;pectare debeant; quod certè variis experimentis, ii&longs;que <lb/>&longs;electi&longs;&longs;imis probare conatur; non tamen meo iudicio convincit, hoc <lb/>enim provenit à communi partium Magneticarum ni&longs;u, quæ Magneti <lb/>ita in&longs;unt, vt &longs;ingulæ &longs;phæræ Magneticæ portiones æquali vi non pol<lb/>leant, &longs;ed aliæ plus, aliæ minùs; vnde fit vt ex communi omnium ni&longs;u. <lb/></s>

<s>Hic &longs;equitur tabula, ad inueniendas &longs;phærarum grauita<lb/>tes, ex data diametrorum magnitudine, cuius hæc e&longs;t <lb/>explicatio. </s>

<s id="s.000390">vnde tantùm &longs;itus haberi po&longs;&longs;it; vnde &longs;i &longs;phæra illa Magnetica æquales <lb/>vires in omnibus &longs;uis partibus haberet, æquè ille communis ni&longs;us &longs;uum <lb/>effectum &longs;ortiretur, &longs;ive hoc punctum versùs Ortum, &longs;ive Occa&longs;um ver<lb/>sùs collocetur: &longs;ed, vt verum fatear, licèt ex Magnete neutra hypothe&longs;is <lb/>demon&longs;tretur, no&longs;træ tamen potiùs, quàm tuæ Magnes favet; primò <lb/>enim licèt non demus terram Magnetem e&longs;&longs;e, hoc tamen tecum &longs;uppo<lb/>nere po&longs;&longs;umus, aut &longs;altem cum aliis, multas illi particulas Magneticas <lb/>ine&longs;&longs;e, quod certè ex multis experimentis probatur: præ&longs;ertim ex de<lb/>clinatione acus Magneticæ; &longs;ufficienti igitur virtute in&longs;tructa e&longs;t, vt ta<lb/>lem a&longs;pectum &longs;emper retineat; virtute inquam particularum Magneti<lb/>carum, quæ in&longs;unt, quarum etiam communi ni&longs;u, cùm inæqualiter <lb/>ac difformiter terre&longs;tri globo admixtæ &longs;int, obtinebitur, vt non modò <lb/>duo terræ poli ad polos Mundi, &longs;ed etiam idem punctum &longs;emper ad Or<lb/>tum, idem ad Occa&longs;um &longs;emper conver&longs;um &longs;it. </s>

<s><emph type="italics"/>In dimetiendis &longs;phærarum diametris vtimur pede Romano anti<lb/>quo, cuius men&longs;uram in margine appo&longs;uimus, eaque re&longs;pondet ad Ro<lb/>mani palmi, quo bodie vtimur, men&longs;uram vt 4, ad 3, buiu&longs;modipe<lb/>dem diuidimus in duodeeim partes æquales, &longs;eu vncias, quas inutnies <lb/>in prima Columna &longs;ub titulo magnitudinis.<emph.end type="italics"/></s>

<s id="s.000391"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s><emph type="italics"/>Ponderibus autem vtimur hac nostra tempe&longs;tate v&longs;itatis, <gap/>bram <lb/>enim diuidimus in<emph.end type="italics"/> 12, <emph type="italics"/>vncias vnciam vero in<emph.end type="italics"/> 24, <emph type="italics"/>&longs;crupula, & &longs;cru<lb/>pulum in<emph.end type="italics"/> 24, <emph type="italics"/>grana. </s>

<s id="s.000392"> Hanc igitur Grandamici demon&longs;trationem tuo calculo do<lb/>nas, quam tamen viri Docti&longs;&longs;imi & Sapienti&longs;&longs;imi rejecerunt. </s>

<s>Ad inueniendas igitur &longs;phærarum grauitates ex <lb/>data diametrorum magnitudine, bæc erit ratio.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæris grauitatem &longs;phæræ plumbeæ, diametrum habentis<emph.end type="italics"/> 3, <emph type="italics"/>vn<lb/>ciarum, in&longs;pice tabulam, & in linea trium vnciarum, &longs;ub titulo gra<lb/>uitatis plumbeæ &longs;phæræ, deprebendes ip&longs;am &longs;phæram grauitætem ba<lb/>bere lib.<emph.end type="italics"/> 7, <emph type="italics"/>vnc.<emph.end type="italics"/> 4, <emph type="italics"/>&longs;eru.<emph.end type="italics"/> 13, <emph type="italics"/>gran.<emph.end type="italics"/> 22 29/57. </s>

<s id="s.000393"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000394"> Non habeo, vt iam dixi, pro demon&longs;tratione; quia nemo <lb/>huiu&longs;que probavit, terram Magnetem e&longs;&longs;e; aut &longs;altem tot particulis <lb/>Magneticis in&longs;tructam, quæ &longs;ufficiant, ad tantam molem volvendam; <lb/>hoc tamen &longs;uppo&longs;ito, cum iam ex aliis corporibus Magneticis con&longs;ter, <lb/>virtutem illam Magneticam per totam &longs;phæram vniformiter di&longs;tributam <lb/>non e&longs;&longs;e, ex hoc nece&longs;&longs;ariò &longs;equeretur, terram ab Occa&longs;u ad Ortum, mi<lb/>nimè moveri: vnde non crat, quòd vir ille docti&longs;&longs;imus non modo de <lb/>re Magnetica, verùm etiam de Chronologica optimè meritus, à nonnul<lb/>lis adeò exploderetur; hoc enim argumentum ab illo excogitatum, ad <lb/>hominem, vt vocant, contra Gilbertum & alios, qui terram magnum <lb/>Magnetem e&longs;&longs;e dixerunt, rem i&longs;tam omnino evincit; &longs;ecus tamen contra <lb/>illos, qui terram Magnetem e&longs;&longs;e negant, aut &longs;ufficienti virtute magnetica <lb/>in&longs;tructam, qua tanta moles agi queat. </s>

<s><emph type="italics"/>Rur&longs;us, quæris grauitatem &longs;phæræ aureæ, diametrum habentis<emph.end type="italics"/> 6, <lb/><emph type="italics"/>vnciarum. </s>

<s>in linea<emph.end type="italics"/> 6, <emph type="italics"/>vnciarum, &longs;ub titulo grauitatis aureæ &longs;phæræ<emph.end type="italics"/><pb pagenum="35"/><emph type="italics"/>datur quæ&longs;ita grauitas lib.<emph.end type="italics"/> 97, <emph type="italics"/>vnc.<emph.end type="italics"/> 6, <emph type="italics"/>&longs;crup. </s>

<s id="s.000395"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000396"> Ne&longs;cio quid aliud indicâras; hoc enim tantum primum <lb/>caput e&longs;t, ex quo Magnetem tuæ potiùs, quàm meæ hypothe&longs;i favere di<lb/>cebas, &longs;i primum e&longs;t, cur ad &longs;ecundum non venis? </s>

<s><emph type="italics"/>Quæris denique grauitatem &longs;phæræ stanneæ, diametrum habentis <lb/>vnius pedis. </s>

<s id="s.000397"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000398"> Res ferè e&longs;t nullius momenti, dicam tamen, illam hypothe&longs;im <lb/>ad rem magneticam potiùs facere, in qua terræ Axis fixa &longs;emper eadem<lb/>que vniver&longs;i puncta re&longs;picit, quàm illam, in qua terræ Axis per tot mil<lb/>liarium myriades in magno orbe circumfertur; Licèt enim &longs;ibi ip&longs;i &longs;em<lb/>per parallelus &longs;it, de&longs;cribit tamen vtroque termino, circulum æqualem <lb/>magno orbi; in no&longs;tra fixus e&longs;t Axis, fixa c&oelig;li puncta, neutrum in tua <lb/>habetur, quare vt fateor vltero, neutram ex Magnete demon&longs;trari, ita &longs;anè <lb/>nemo retum i&longs;tarum rectus æ&longs;timator inficias eat, quin no&longs;tra regulis <lb/>magneticis magis con&longs;entiat; &longs;ed de hoc &longs;atis, quare vide vtrùm pro tua <lb/>hypothe&longs;i aliquid aliud &longs;uppetat. </s>

<s>in linea vnius pedis, &longs;eu 12, vnciarum, &longs;ub titulo graui<lb/>tatis &longs;phæræ &longs;tanneæ, datur quæ&longs;ita &longs;phæræ grauitas lib.<emph.end type="italics"/> 304, <emph type="italics"/>adun<lb/>quem. </s>

<s>Atque ita reliquarum &longs;phærarum in tabula nominatarum, ex <lb/>data diametrorum magnitudine, grauitates inuenies.<emph.end type="italics"/></s>

<s id="s.000399"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000400"> Suppetunt quidem multa, &longs;ed ex iis, quæ à te adducta &longs;unt, <lb/>&longs;at video, quàm facilè illa &longs;olvere po&longs;&longs;is; quare de hoc argumento &longs;atis <lb/>&longs;uperque dictum e&longs;&longs;e puto. </s>

<s>Qua ratione hanc Tabulam compo&longs;uimus. </s>

<s><emph type="italics"/>Primum inueniendam curauimus grauitatem alicuius &longs;phæræ, da<lb/>tem habentis diametrum, & ad hoc faciendum, oportebat aliquam <lb/>&longs;pbæram efficere, &longs;ed quoniam ad illam efficiendam, exactam buman<gap/><lb/>diligentia non &longs;ufficit, fieri curauimus Cylindrum ex &longs;tanno, altitu<lb/>dine aqualem diametro circuli, qui ba&longs;is e&longs;t ip&longs;ius Cylindri, is enim <lb/>torno &longs;ieri pote&longs;t multo exactior quam &longs;pbæra, & facilius. </s>

<s id="s.000401"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000402"> Egregiè &longs;anè; &longs;ic æquis armis pugnamus. </s>

<s>huius au<lb/>tem Cylindri altitudo, vel diameter ip&longs;ius ba&longs;is, erat duarum vncia<lb/>rum prædicti pedis Romani, grauitas vero duarum librarum, cum <lb/>vna vncia, & octo &longs;crupulis, &longs;iue vt hoc pondus ad grana reducamus, <lb/>Cylindri grauitas erat Gran. 14592. abstulimns ab hac Cylindri <lb/>grauitate partem tertiam. </s>

<s id="s.000403">Huiu&longs;que meam <lb/>hypothe&longs;im tuis argumentis impugna&longs;ti, nec dixi vnquam &longs;atis; iam <lb/>verò ex arena pedem efferre velles, ne mihi copia detur tuam impugnandi. </s>

<s id="s.000404"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/> Æquum e&longs;t, per me licet; &longs;ed obiter quæ&longs;o, ne iu&longs;to lo<lb/>quaciores e&longs;&longs;e videamur. </s>

<s>id est<emph.end type="italics"/> 4864, <emph type="italics"/>reliquum, quod est<emph.end type="italics"/> 9728. <emph type="italics"/>&longs;er<lb/>uauimus, pro grauitate &longs;phæræ, diametrum habentis æqualem altitu<lb/>dini Cylindri, o&longs;ten&longs;um enim est ab Arcbimede propo&longs;.<emph.end type="italics"/> 32, <emph type="italics"/>lib.<emph.end type="italics"/> 1, <emph type="italics"/>de <lb/>&longs;pbæra, & Cylindro, Cylindrum, qui ba&longs;im habeat maximo in &longs;pbæra <lb/>circulo equalem, & altitudinem æqualem diametro &longs;phæræ, ad ip&longs;am <lb/>&longs;pbæram &longs;e&longs;quialterum e&longs;&longs;e; itaque grauitatem &longs;phæræ, diametrum <lb/>habentis duarum vnciarum inuenimus e&longs;&longs;e gran.<emph.end type="italics"/> 9728. </s>

<s><emph type="italics"/>Inuenta igitur grauitate &longs;phæræ, cuius diameter est duarum vn<lb/>ciarum, facile inuenientur reliquarum <expan abbr="&longs;pbærar&utilde;">&longs;phærarum</expan> grauitates, &longs;i enim <lb/>inuenienda &longs;it grauitas &longs;phæræ stannea habentis diametrum<emph.end type="italics"/> 1/4. <emph type="italics"/>vn<lb/>ciæ, fiat vt cubus ex<emph.end type="italics"/> 2, <emph type="italics"/>ad cubum ex<emph.end type="italics"/> 1/4, <emph type="italics"/>hoc est vt<emph.end type="italics"/> 512, <emph type="italics"/>ad 1, ita<emph.end type="italics"/> 9728, <lb/><emph type="italics"/>ad alium numerum, qui &longs;it<emph.end type="italics"/> 19, <emph type="italics"/>&longs;phæræ igitur cuius diameter e&longs;t<emph.end type="italics"/> 1/4, <lb/><emph type="italics"/>vnciæ, grauitas erit gran. 19, osten&longs;um enim est prop.

<s id="s.000405"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000406"> Obiter, inquis, non pauciora certè, immo longè plura argu<lb/>menta contra tuam hypothe&longs;im habeo, quàm tu contra meam igitur, &longs;i <lb/>non plus, tantumdem &longs;altem temporis, ad hanc provinciam exequen<lb/>dam, iure meo po&longs;tulo. </s>

17, huius, &longs;phæ<lb/>ras eiu&longs;dem generis inter &longs;e e&longs;&longs;e in grauitate, vt diametrorum cubi in <lb/>magritudine.<emph.end type="italics"/></s>

<s id="s.000407"><emph type="italics"/>Augu&longs;t.<emph.end type="italics"/></s>

<s id="s.000408"> Crede mihi, Antime, certamen non detrecto, nec vinci metuo, <lb/>timeo tamen ne prolixior di&longs;ceptatio nonnihil tædij <expan abbr="circ&utilde;&longs;tantibus">circun&longs;tantibus</expan> afferat </s>

<s><emph type="italics"/>Rur&longs;us &longs;it inuenienda grauitas &longs;phæræ stannæ habentis diame<lb/>trum<emph.end type="italics"/> 1/2, <emph type="italics"/>vnciæ, fiat vt cubus ex<emph.end type="italics"/> 1/4, <emph type="italics"/>ad cubum ex<emph.end type="italics"/> 1/2, <emph type="italics"/>hoc est vt<emph.end type="italics"/> 1, <emph type="italics"/>ad<emph.end type="italics"/> 8, <lb/><emph type="italics"/>ita<emph.end type="italics"/> 19, <emph type="italics"/>ad<emph.end type="italics"/> 152, <emph type="italics"/>&longs;phæra igitur, cuius diameter e&longs;t<emph.end type="italics"/> 1/2, <emph type="italics"/>vnciæ, habebit gra<lb/>uitatem gran.<emph.end type="italics"/> 152. </s>

<s><emph type="italics"/>Sit denique inuenienda grauitas &longs;phæræ stannæ, diametrum ha<lb/>bentis<emph.end type="italics"/> 1/4, <emph type="italics"/>vnciæ, fiat vt cubus ex<emph.end type="italics"/> 1/4, <emph type="italics"/>ad cubum ex<emph.end type="italics"/> 1/4, <emph type="italics"/>hoc e&longs;t vt<emph.end type="italics"/> 1, <emph type="italics"/>ad<emph.end type="italics"/> 27, <lb/><emph type="italics"/>ita<emph.end type="italics"/> 19, <emph type="italics"/>ad<emph.end type="italics"/> 513, <emph type="italics"/>grauitas igitur &longs;phæræ habentis diametrum<emph.end type="italics"/> 1/4, <emph type="italics"/>vnciæ,<emph.end type="italics"/></s><pb pagenum="36"/>

<s id="s.000409"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000410"> Rectè mones remittamus in <expan abbr="proxim&utilde;">proximum</expan> congre&longs;&longs;um, per me licet. </s>

<s>Ad inueniendas &longs;phæra<lb/>diametrorum <lb/>T A B </s>

<s>TABELLE WAR HIER</s><pb pagenum="37"/>

<s id="s.000411"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000412"> Ne tamen aliquid fortè quod &longs;upere&longs;t huic congre&longs;&longs;ui detra<lb/>hatur; tuam illam de marino æ&longs;tu &longs;ententiam exponere poteris, vt am&oelig;<lb/>niùs hæc di&longs;ceptatio terminetur; tenes enim, ni &longs;allor, ex lis aliquam, quæ <lb/>iam ab aliis excogitatæ fuerunt. </s>

<s>rum grauitates ex data <lb/>magnitudine <lb/>V L A. </s>

<s>TABELLE WAR HIER</s><pb/>

<s id="s.000413"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>TABELLE WAR HIER</s><pb/>

<s id="s.000414"> Minimè verò; Nova e&longs;t omnino mea &longs;ententia, & à me pri<lb/>mùm excogitata, & i&longs;tarum temporis angu&longs;tiarum impatiens; quare, vt <lb/>iam indicavi &longs;upra, integrum congre&longs;&longs;um implebit. </s>

<s>TABELLE WAR HIER</s><pb pagenum="40"/>

<s id="s.000415"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>TABELLE WAR HIER<lb/><emph type="italics"/>erit gran. 513. & &longs;ic reliquarum &longs;phærarum ex &longs;tanno, diametros <gap/><lb/>bentium magnitudine quacunque, inuenientur grauitates.<emph.end type="italics"/></s>

<s id="s.000416"> Illa opinion Carte&longs;ij mihi &longs;tatim venerat in mentem, qui <lb/>vult à circumfluente Luna comprimi aëra, & Oceani &longs;uperficiem, ex qua <lb/>pre&longs;&longs;ione, aquarum motus &longs;equatur, quem vocat æ&longs;tum; te fortè huic ad<lb/>hærere putabam; quando quidem Lunæ mentionem feci&longs;ti. </s>

<s id="s.000417"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s><emph type="italics"/>Aliter quoque & expeditius reliquarum &longs;phærarum ex &longs;tanno i<gap/><lb/>uenientur grauitates.<emph.end type="italics"/></s>

<s id="s.000418"> Toto c&oelig;lo erras; illam &longs;ententiam minimè approbo, quæ & <lb/>phænomenis & veritati non con&longs;entit; ex illa enim &longs;equitur. </s>

<s id="s.000419">Primò à <lb/>Luna meridiana illum maximè comprimi maris tractum, qui tali meri<lb/>diano &longs;ubjacet, aqua verò compre&longs;&longs;a &longs;ub&longs;idit, & quoquo ver&longs;um fluit; <lb/>igitur non &longs;ummum aquæ tumorem, &longs;ed maximam depre&longs;&longs;ionem meri<lb/>diana Luna conciliaret; quod repugnat ob&longs;ervationibus. </s>

<s><emph type="italics"/>Inuenta grauitate &longs;phæræ, diametrum habentis<emph.end type="italics"/> 1/4, <emph type="italics"/>vnciæ, &longs;im<gap/><lb/>tiplicetur ip&longs;a grauitas, per<emph.end type="italics"/> 8, <emph type="italics"/>hoc est per cubum ex<emph.end type="italics"/> 2, <emph type="italics"/>numerus pro <lb/>ductus dabit grauitatem &longs;phæræ, diametrum habentis<emph.end type="italics"/> 2/4, <emph type="italics"/>vnciæ, b<gap/><emph.end type="italics"/><lb/><arrow.to.target n="note47"/> <emph type="italics"/>e&longs;t<emph.end type="italics"/> 1/2, <emph type="italics"/>&longs;phæræ^{*} enim inter &longs;e in triplicata &longs;unt ratione &longs;uarum di<gap/><lb/>metrorum. </s>

<s id="s.000420">Secundò Præ<lb/>dictam aëris pre&longs;&longs;ionem omnino &longs;entiremus. </s>

<s id="s.000421">Tertiò In Plenilunio non <lb/>e&longs;&longs;et maior pre&longs;&longs;io, tunc enim Luna vicinior non e&longs;t, quàm in Novilu<lb/>nio & Quadraturis, igitur in Plenilunio maior æ&longs;tus non e&longs;&longs;et. </s>

<s>deinde &longs;i multiplicetur eadem grauitas per<emph.end type="italics"/> 27, <emph type="italics"/>hoc est p<gap/><lb/>cubum ex<emph.end type="italics"/> 3, <emph type="italics"/>numerus productus dabit grauitatem &longs;phæræ, habent<gap/><lb/>diametrum<emph.end type="italics"/> 3/4, <emph type="italics"/>vnciæ, & &longs;i multiplicetur per<emph.end type="italics"/> 64, <emph type="italics"/>hoc est per cub<gap/><lb/>ex<emph.end type="italics"/> 4, <emph type="italics"/>numerus productus dabit grauitatem &longs;phæræ, cuius diameter<gap/><emph.end type="italics"/><lb/>4/4, <emph type="italics"/>hoc est vnius vnciæ, & eo deinceps continuo ordine,<emph.end type="italics"/></s>

<s id="s.000422">Quartò <lb/>nullus æ&longs;tus e&longs;&longs;et in oppo&longs;ita parte terre&longs;tris Globi; quia nulla ibi pre&longs;<lb/>&longs;io; omitto reliqua cum hæc ad refutandum illud commentum, &longs;int &longs;atis. </s>

<s id="s.000423"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/> Hæc etiam, vt vis, in alium congre&longs;&longs;um remittamus; avidè <lb/>tamen ex te audire cupio, quid tamen novi de hoc argumento dicturus <lb/>&longs;is. </s>

<s><emph type="italics"/>Porro ad inueniendas grauitates &longs;phærarum ex reliquis metallis <lb/>vel ex quacunquæ alia materia, hæc erit ratio.<emph.end type="italics"/></s>

<s id="s.000424">Interea antequam hunc congre&longs;&longs;um terminemus nonnulla ex te per<lb/>cunctabor, quæ licèt à te dicta &longs;int circa tuam hypothe&longs;im, vereor tamen, <lb/>vt ea rectè, vt par e&longs;t, à me fuerint intellecta. </s>

<s id="s.000425">Dixi&longs;ti Solem inclinati <lb/>&longs;ur&longs;um ac deor&longs;um motu accelerato, ac retardato in reciproco acce&longs;&longs;u <lb/>& rece&longs;&longs;u; quæro ex te, vtrùm Sol novum producat impetum. </s>

<s><emph type="italics"/>Fiat vt<emph.end type="italics"/> 1, <emph type="italics"/>ad<emph.end type="italics"/> 1 41/74, <emph type="italics"/>hoc e&longs;t vt<emph.end type="italics"/> 74, <emph type="italics"/>ad<emph.end type="italics"/> 115, (<emph type="italics"/>&longs;i degrauitate &longs;phæræ<lb/><expan abbr="pl&umacr;beæ">plumbeæ</expan> quæritur cuius diameter est<emph.end type="italics"/> 1/4, <emph type="italics"/>vnciæ) ita 19. grauitas vi<gap/><lb/>licet &longs;phæræ stanneæ <expan abbr="diametr&umacr;">diametrum</expan> habentis<emph.end type="italics"/> 1/4, <emph type="italics"/>vnciæ, ad <expan abbr="ali&umacr;">alium</expan> numer<gap/><lb/>qui &longs;it<emph.end type="italics"/> 29 19/74, <emph type="italics"/>grauitas igitur &longs;phæræ plumbeæ, diametrum haben<lb/>tis<emph.end type="italics"/> 1/4, <emph type="italics"/>vnciæ, erit gran.<emph.end type="italics"/> 29 39/74. <emph type="italics"/>&longs;tannum enim ad plumbum ration<gap/><lb/>habet in grauitate vt<emph.end type="italics"/> 1, <emph type="italics"/>ad<emph.end type="italics"/> 1 41/74, <emph type="italics"/>vt con&longs;picitur in prima tabelle <lb/>quam ad comparandum inter &longs;e duodecim corporum genera, grauita<lb/>te, & magnitudine, appo&longs;uimus.<emph.end type="italics"/></s>

<s><emph type="italics"/>Si vero quæratur de grauitate &longs;phæræ plumbeæ, diametrum <lb/>habentis<emph.end type="italics"/> 2, <emph type="italics"/>vnciarum, fiat vt<emph.end type="italics"/> 74, <emph type="italics"/>ad<emph.end type="italics"/> 115, <emph type="italics"/>ita<emph.end type="italics"/> 9728, <emph type="italics"/>id est gra<gap/><emph.end type="italics"/></s><pb pagenum="41"/>

<s id="s.000426"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000427"> Nullo modo; alioquin &longs;i per tres continuos men&longs;es (tandum<lb/>dem enim acce&longs;&longs;us ab Apogæo ad mediocrem di&longs;tantiam) motu accele<lb/>rato moveretur, immen&longs;um penè &longs;patium percurreret; igitur non pro<lb/>ducit novum impetum, &longs;ed impetus, quem habet, vel à &longs;e acqui&longs;itum <lb/>vel aliunde impre&longs;&longs;um, huic inclinationi &longs;ervit &longs;imul & alteri; idque, vt <lb/>dixi, ad in&longs;tar motûs accelerati & retardati; &longs;ed valdè lentè, quia maior <lb/>& poti&longs;&longs;ima inclinatio, &longs;eu determinatio illius impetûs motui circulari <lb/>&longs;ervit; quòd autem idem impetus duas aut plures determinationes ha<lb/>beat, res nova non e&longs;t, &longs;ed trita; cùm hoc cuilibet motui mixto & re<lb/>flexo competat. </s>

<s>TABELLE WAR HIER<lb/><emph type="italics"/>&longs;phæræ stanneæ, cuius diameter est<emph.end type="italics"/> 2, <emph type="italics"/>vnciarum, ad alium numerum, <lb/>qui &longs;it<emph.end type="italics"/> 15 117 <gap/>, <emph type="italics"/>&longs;phæra igitur plumbea, cuius diameter est<emph.end type="italics"/> 2, <emph type="italics"/>vn<lb/><gap/>iarum grauitatem habebit gran. 15 117 <gap/>, atque hæc erit ob&longs;er<lb/>uanda in reliquis ratio.<emph.end type="italics"/></s>

<s id="s.000428"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/> E&longs;tne tibi quodpiam aliud exemplum, in quo &longs;imilem in<lb/>clinationum ad rectum acceleratum, & ad circularem æquabilem com<lb/>po&longs;itionem habeamus. </s>

<s><emph type="italics"/>Vel &longs;i ip&longs;a grauitas<emph.end type="italics"/> 29 19/74, <emph type="italics"/>multiplicetur per &longs;ingulos cubos, vt <lb/>dictum est de &longs;phera &longs;tannea, numeri producti dabunt grauitates <lb/>&longs;phærarum ex plumbo, ad quaram diametros latera cubica rationem <lb/>habebunt vt<emph.end type="italics"/> 4, <emph type="italics"/>ad<emph.end type="italics"/> 1, <emph type="italics"/>quoniam<emph.end type="italics"/> 29 19/74, <emph type="italics"/>est grauitas &longs;phæræ plumbeæ, <lb/>diametrum habentis<emph.end type="italics"/> 1/4, <emph type="italics"/>vnciæ.<emph.end type="italics"/></s>

<s id="s.000429"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>Sequitur, ad inueniendas diametrorum <lb/>magnitudines ex data &longs;phæ<lb/>rarum grauitate, <lb/>tabula.</s><pb pagenum="42"/>

<s id="s.000430"> Non de&longs;unt, eáque plurima, duo in mentem veniunt, omnino <lb/>&longs;imilia; primum tale e&longs;t. </s>

<s id="s.000431">Sit longior tubus vitreus altera dumtaxat ex<lb/>tremitate peruius, infundatur aqua, donec &longs;emipalmus dumtaxat circiter <lb/>vacuus re&longs;tet, & &longs;uppo&longs;ito ad extremum apertum arctè digito, tubus <lb/>invertatur, tunc cylindrus aëris lentè ac &longs;en&longs;im a&longs;&longs;urgit, à graviore aquâ <lb/>&longs;ur&longs;um extru&longs;us, dum hæc per tubilatera, <gap/>id e&longs;t per cavam tubi &longs;uper<lb/>ficiem, &longs;piratim ita de&longs;cendit, quod ip&longs;is oculis per&longs;picuum e&longs;t, vt hic <pb pagenum="36" xlink:href="025/01/040.jpg"/>motus ex recto accelerato & circulari compo&longs;itus e&longs;&longs;e videatur; hinc <lb/>initio &longs;pi&longs;&longs;iores & pre&longs;&longs;iores &longs;piræ, deinde verò di&longs;tractiores fiunt; e&longs;t <lb/>tamen tantùm vnus impetus ad motum deor&longs;um rectum per &longs;e determi<lb/>natus, qui cùm in linea recta finem &longs;uum obtinere non po&longs;&longs;it compen&longs;at <lb/>in circulari, retenta &longs;emper prima illa inclinatione ad rectum, cui quan<lb/>tum pote&longs;t, &longs;atisfacit, cùm autem etiam &longs;ecundùm id acceleratus &longs;it, in<lb/>de &longs;piras di&longs;trahi nece&longs;&longs;e e&longs;t. </s>

<s>TABELLE WAR HIER</s><pb pagenum="43"/>

<s>TABELLE WAR HIER</s><pb pagenum="44"/>

<s id="s.000432"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000433"> Iam capio, quod ante dixeras, naturam &longs;upplere æquali<lb/>tatem motuum: nempe aqua, &longs;eu corpus grave toto illo tempore, quo <lb/>præfatus cylindrus aëris &longs;en&longs;im a&longs;&longs;urgit, motu accelerato deor&longs;um, re<lb/>moto impedimento, longum &longs;patium in perpendiculari decurreret; &longs;ed <lb/>ob&longs;tante impedimento, cùm eadem vis impetus ad&longs;it, motum rectum <lb/>&longs;pirali compen&longs;at; atque adeò &longs;i tota illa &longs;pirarum congeries in lineam <lb/>rectam explicaretur, æqualis e&longs;&longs;et lineæ rectæ in perpendiculo eodem <lb/>tempore motu accelerato confectæ, &longs;ed applica quæ&longs;o ad &longs;piras Solares. </s>

<s>TABELLE WAR HIER</s><pb pagenum="45"/>

<s>TABELLE WAR HIER</s><pb pagenum="46"/>

<s id="s.000434"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000435"> Repete igitur figuram 2. & con&longs;idera primo loco primam in<lb/>clinationem &longs;eor&longs;im, quâ Sol ab Apogæo ad Perigæum, & vici&longs;&longs;im, per <lb/>mediocrem di&longs;tantiam, reciprocis acce&longs;&longs;ibus & rece&longs;&longs;ibus, ad imitatio<lb/>nem motus accelerati & retardati tendit reditque. </s>

<s>TABELLE WAR HIER</s><pb pagenum="47"/>

<s>TABELLE WAR HIER</s><pb pagenum="48"/>

<s id="s.000436">Et cogita radium AE moveri cir<lb/>ca AC, dum punctum E motu ac<lb/>celerato tendit ad V, & retardato, <lb/>ab V ad H, radius AE de&longs;cribet <lb/>&longs;uo motu &longs;uperficiem coni, cuius <lb/>ba&longs;is diameter, erit EL, punctum <lb/>verò E de&longs;cribet tot &longs;piras in dicta <lb/>&longs;uperficie coni, quot revolutiones <lb/>ab&longs;olventur, toto illo tempore, <lb/>quo ab E, pervenit in H ; hæc au<lb/>tem &longs;pira erit conica, cuius Helices <lb/>di&longs;tractiores erunt circa V, pre&longs;<lb/>&longs;iores circa E & H. </s>

<s>TABELLE WAR HIER</s><pb pagenum="49"/>

<s id="s.000437">Pari modo, co<lb/>gita triangulum ADE in orbem <lb/>agi, circa Axem BC dum D, motu <lb/>accelerato, tendit ad F, & retar<lb/>dato ab F, ad E; arcus DFE de<lb/>&longs;cribet partem &longs;uperficiei &longs;phæricæ, <lb/>punctum verò &longs;piram &longs;phæricam, <lb/>cuius Helices pre&longs;&longs;iores erunt cir<lb/>ca DE, di&longs;tractiores verò circa F. <lb/></s>

<s id="s.000438">Si verò D iret per lineam rectam <lb/>DGE, de&longs;cribet DGE &longs;uperfi<lb/>ciem cylindricam, & D &longs;piram cylin<lb/>dricam. </s>

<s>TABELLE WAR HIER</s>

<s id="s.000439">Iam verò <expan abbr="cõponaturvtraque">componatur vtraque</expan> <lb/>inclinatio, ita vt D partim versùs F, <pb pagenum="37" xlink:href="025/01/041.jpg"/>partim versùs A tendat, &longs;emoto motu circulari, ibit, vt dixi, per lineam &longs;pi<lb/>ralem DQH; volvatur ADQH circa Axem BC de&longs;cribet curva DQH <lb/>&longs;uperficiem &longs;olidi cuiu&longs;dam &longs;piralis; & &longs;i interea dum punctum de&longs;cribit <lb/>eo duplici motu curua DQH moveatur circa eundem Axem BC, <lb/>de&longs;cribet in dicta &longs;uperficie &longs;piram compo&longs;itam ex totidem Helicibus; <lb/>vt autem Helices omnes &longs;int ferè inter &longs;e æquales, ob&longs;ervabis præclarum <lb/>Naturæ in&longs;titutum; &longs;upponamus Apogæum Solis in D, initio Cancri <lb/>cùm DI plus di&longs;tet ab FK quàm hæc ab HL, haud dubiè plus temporis <lb/>ponit à Cancro ad Libram, quàm à Libra ad Capricornum; en tibi ratio<lb/>nem Anomaliæ Solis; quod verò &longs;pectat ad circulos diurnos, quos &longs;in<lb/>gulæ Helices, &longs;eu &longs;p<gap/>æ repræ&longs;entant; à D ad Q tantulùm cre&longs;cunt, &longs;cili<lb/>cet vt &longs;emidiametri paralleli BD, <expan abbr="Aq;">Aque</expan> à Q verò, v&longs;que ad illud pun<lb/>ctum, in quo recta DGE &longs;ecat curvam DQH ita decre&longs;cunt, vt de&longs;cri<lb/>ptus ab illo puncto &longs;it æqualis primo; ab eo verò puncto versùs H, fiunt <lb/>minores & minores circuli, ita vt vltimus, cuius radius e&longs;t CH, &longs;it ad <lb/>primum, cuius radius e&longs;t BD, vt AC ad AB, vel CH ad BD; e&longs;t <lb/>autem HE iuxta communem Anomaliæ men&longs;uram ferè <gap/> AE, ac proin<lb/>de circulus ille vltimus e&longs;&longs;et minor primo <gap/> igitur cum Sol &longs;upponatur <lb/>æquali &longs;emper motu agi, longè citiès perficiet &longs;uum orbem in H quàm <lb/>in D, &longs;i movetur in circulo, nempè illo iam ab&longs;oluto, &longs;uper&longs;unt huius <lb/>12. grad. igitur tempus, quo circulus diurnus decurritur in H, e&longs;t brevius <lb/>tempore, quo decurritur in D 48. minutis horæ. </s>

<s id="s.000440">Sed hoc e&longs;t ab&longs;urdum, <lb/>imò ab&longs;urdi&longs;&longs;imum; & vt natura huic incommodo occurreret, licet &longs;pa<lb/>tium CA &longs;it minus &longs;patio AB, &longs;egmentum tamen curvæ QH vix minus <lb/>e&longs;t &longs;egmento <expan abbr="Dq;">DQ</expan> igitur tantùm temporis à Q ad H, quantum à D ad <lb/>Q ponere deberet; quia tamen ex hoc &longs;equeretur ab&longs;urda circulorum diur<lb/>norum inæqualitas, contra finem à Natura intentum, hæc enim &longs;pirarum <lb/>diurnarum æqualitatem intendit, cùm cir culi diurni omnium reliquorum <lb/>men&longs;ura &longs;int, ita di&longs;trahuntur &longs;piræ in &longs;egmento QH, vt pauciores &longs;int, <lb/>quàm in &longs;egmento <expan abbr="Dq;">DQ</expan> ita tamen vt &longs;ingulæ ferè æquales &longs;int &longs;ingulis; <lb/>Cogita explicatam vtramque &longs;pirarum congeriem in duas lineas rectas, <lb/>maior erit ad minorem ferè vt 92.<gap/> ad 89.<gap/>, &longs;eu vt 1103. ad 1077. So<lb/>lers igitur Natura ita attemperavit vtramque inclinationem, vt &longs;ingulæ <lb/>&longs;ingulis æquales &longs;int in quantitate, & in tempore; atque ita motum <lb/>vnum alio motu compen&longs;at, adhibita maiore, aut minore &longs;pirarum di&longs;tra<lb/>ctione. </s>

<s>E<emph type="italics"/>st hæc tabula, quemadmodum & eius v&longs;us, præcedentis con<lb/>nuer&longs;a, in ea enim inueniuntur &longs;phærarum grauitates ex data <lb/>diametrorum magnitudine, in hac vero deprehenduntur diametro<lb/>rum magnitudines ex data &longs;phærarum grauitate.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæro exempli gratia magnitudinem diametri &longs;phæræ aureæ, <lb/>grauitatem habentis 10, lib. </s>

<s id="s.000441"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000442"> Fru&longs;trà laboras, Antime, vt dierum æqualitatem retineas. </s>

<s>Numeri in prima columna &longs;ub titulo <lb/>grauitatis denotant &longs;phærarum grauitates, reliqui vero in reliquis <lb/>columnis denotant diametrorum magnitudines; itaque in linea<emph.end type="italics"/> 10, <lb/><emph type="italics"/>lib.

&longs;ub titulo magnitudinis diametri &longs;phæræ aureæ, datur quæ&longs;ita <lb/>diametri magnitudo partium<emph.end type="italics"/> 2 21/100: <emph type="italics"/>qualium pes vnus est<emph.end type="italics"/> 12. </s>

<s id="s.000443"><emph type="italics"/>Antim.<emph.end type="italics"/> Hæc paulò fu&longs;iùs edi&longs;&longs;erere volui, vt intelligatur quonam mo<lb/>do naturaliter vnus motus alio compen&longs;etur, quando &longs;cilicet impeditur fi<lb/>nis Naturæ. </s>

<s id="s.000444">Finis autem Naturæ e&longs;t primò, vt in connaturali di&longs;tantia <lb/>Sol circa Terram eat; data enim mole vtriu&longs;que globi, dubium non e&longs;t, <lb/>quin prædicta di&longs;tantia po&longs;&longs;it e&longs;&longs;e major, aut minor, connaturali; &longs;i major, <lb/>cuncta rigerent; &longs;i minor, conflagrarent omnia; igitur majorem inter & <lb/>minorem connaturalis, &longs;eu mediocris, aut media definienda e&longs;t; hinc <lb/>manife&longs;ta ratio primæ inclinationis, per quam Sol ab Apogæo ad mediam <pb pagenum="38" xlink:href="025/01/042.jpg"/>di&longs;tantiam tendit motu recto, qui e&longs;t ad in&longs;tar accelerati; non &longs;i&longs;tit autem <lb/>in dicta di&longs;tantia, vbi obtinet illam; &longs;ed propter determinationem ac<lb/>qui&longs;itam, licèt obluctetur eadem inclinatio, pervenit v&longs;que ad Peri<lb/>gæum, &longs;imili motu recto, &longs;ed propter reluctantiam, ad in&longs;tar retarda<lb/>ti. </s>

<s><emph type="italics"/>Quæro magnitudinem diametri &longs;phæræ ferreæ, grauitatem haben<lb/>tis 50, lib.

<s id="s.000445">Secundò, finis Naturæ e&longs;t, vt Sol lumen &longs;uum æqualiter, quantum <lb/>fieri pote&longs;t, di&longs;tribuat; vnde petitur ratio &longs;ecundæ inclinationis, quâ Sol <lb/>à Tropico ad Æquatorem tendit, eo modo, quo dixi; nempe definito <lb/>&longs;emel Axe mundi, circa quem &longs;phærarum c&oelig;le&longs;tium revolutiones fiant, <lb/>cuius extremitates &longs;unt Poli, vi huius inclinationis Sol à D, v.g. tendit <lb/>versùs F per arcum DF, qui cadit perpendiculariter in AD; cùm enim <lb/>à D duci po&longs;&longs;int infinitæ lineæ, versùs Æquatorem, & vna tantùm per<lb/>pendicularis, quæ e&longs;t tangens, vel arcus, cùm radius AD continuò ten<lb/>dat versùs F ; &longs;i vna e&longs;t, determinata e&longs;t; Nec dicas, rectam DG cade<lb/>re perpendiculariter in planum Æquatoris; nam non cadit perpendicula<lb/>riter in AD; cùm tamen arcus DF vtrumque præ&longs;tet; cadit enim perpen<lb/>diculariter in vtramque, &longs;cilicet in AD, AF. Accedit, quòd Sol, quan<lb/>tum e&longs;t ex &longs;e, &longs;uppo&longs;ita di&longs;tantia connaturali à centro mundi, ad eam re<lb/>tinendam inclinat; &longs;ed &longs;i in arcu DF feratur, eadem &longs;emper manebit di<lb/>&longs;tantiæ ab A. Tertiò, finis Naturæ e&longs;t, vt omnes revolutiones diurnæ So<lb/>lis &longs;int æquales, & con&longs;equenter æquè diuturnæ, cùm hæ &longs;int commu<lb/>nis men&longs;ura omnium motuum, & temporis externi munere defungantur. <lb/></s>

<s id="s.000446">Porrè vt dictos fines Sol obtineat, gemina illa inclinatio ita &longs;e&longs;e attempe<lb/>rat, vt & ab Apogæo ad Perigæum Sol eat, & diurnæ revolutiones æqua<lb/>les ferè &longs;int, &longs;i tantùm habeatur ratio primæ inclinationis, &longs;piræ fient in <lb/>eodem plano, & omnes inæquales erunt, &longs;iverò &longs;ecundæ tantùm, &longs;piræ <lb/>fient in &longs;uperficie &longs;phærica, eruntque omnes inæquales, vt patet ad ocu<lb/>lum, cui figura &longs;ubjacet. </s>

in linea 50, lib. &longs;ub titulo magnitudinis diametri &longs;phæræ <lb/>ferreæ, datur quæ&longs;ita diametri magnitudo<emph.end type="italics"/> 6 40/100. </s>

<s id="s.000447">Itaque &longs;ecunda inclinatio ca&longs;tigat inæqualita<lb/>tem à prima inductam, deflexo Sole versùs Æquatorem; & prima par pari <lb/>referens, corrigit inæqualitatem, quam alioqui prima induceret depre&longs;&longs;o <lb/>Sole versùs centrum A; & cùm tantùm ferè temporis à Q ad H, ponendum <lb/>e&longs;&longs;et, quantum à D ad Q &longs;unt enim &longs;egmenta DQ, QH, fere æqualia; haud <lb/>dubiè tot &longs;piræ &longs;egmento QH, ine&longs;&longs;e deberent, quot &longs;egmento DQ in&longs;unt, <lb/>vt æquè di&longs;tractæ vtrimque e&longs;&longs;ent; quia tamen tunc &longs;piræ &longs;egmenti QH <lb/>minores e&longs;&longs;ent, ac proinde inæquales &longs;piris alterius &longs;egmenti, haud dubiè <lb/>tota &longs;pirarum QH congeries brevioritempore decurreretur, quàm teta &longs;pi<lb/>rarum DQ, eodem &longs;cilicet & æquabili motu; &longs;ed &longs;upponuntur totidem <lb/>vtrimque dies; igitur dies intra &longs;egmentum QH, breviores e&longs;&longs;ent; igitur to<lb/>tum tempus, quod complectitur dies intra &longs;egmentum QH, decur&longs;os, bre<lb/>vius e&longs;&longs;et tempore, quod complectitur dies decur&longs;os intra &longs;egmentum <expan abbr="Dq.">DQ</expan> <lb/>Sed æqualia tempora &longs;upponuntur: itaque vt huic incommodo occurra<lb/>tur, di&longs;trahuntur &longs;piræ &longs;egmenti QH, ita vt pauciores re&longs;tent, &longs;ed ferè æqua<lb/>les, atque ita in motu per QH Compen&longs;atur ille motus, qui alioqui per &longs;pi<lb/>ras obtineri non pote&longs;t, cùm breviores &longs;int, quàm par &longs;it. </s>

<s id="s.000448"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæro magnitudinem diametri &longs;phæræ argenteæ, grauitatem ha<lb/>bentis 60, lib.

<s id="s.000449"> An fortè Sol &longs;entit, <gap/>ut cogno&longs;cit, &longs;piras à &longs;e decur&longs;as <lb/>e&longs;&longs;e majores aut minores? </s>

<s id="s.000450">Minimè verò; Quomodo igitur tam &longs;ollicitè <pb pagenum="39" xlink:href="025/01/043.jpg"/>& accuratè inæqualitatis periculum avertit? </s>

in linea 60, lib. &longs;ub titulo magnitudinis diametri &longs;phæræ <lb/>argenteæ, datur ip&longs;a magnitudo<emph.end type="italics"/> 6 25/100. </s>

<s id="s.000451"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000452"> Quæro à te, Augu&longs;tine, An fortè aqua illa tubi vitrei &longs;entit <lb/>progre&longs;&longs;um in motu deor&longs;um &longs;ibi præcludi, & impediri, vt motum re<lb/>ctum in &longs;pirabilem convertat? </s>

<s><emph type="italics"/>Quæro denique magnitudinem diametri &longs;phæræ stanneæ, graui<lb/>tatem habentis 38, lib.

<s id="s.000453">Minimè verò; &longs;ed cùm habeat vim atque <lb/>impetum, eo &longs;anè motu movetur, quo & faciliùs moveri pote&longs;t, & in <lb/>quo dictus impetus totam &longs;uam vim exerit; modò vel minima determi<lb/>natio intercedat ad talem lineam motus; &longs;ic aqua in dicto tubo ad li<lb/>neam &longs;piralem determinatur à minima inæqualitate, vel inclinatione <lb/>tubi, & corpus grave, quod non pote&longs;t moveri in perpendiculari deor<lb/>&longs;um, movetur per Planum inclinatum, aut per arcum in funependulo, <lb/>aut per parabolam, vel aliam lineam in projectione; item corpus refle<lb/>xum, quod per eandem lineam motum pro&longs;equi non pote&longs;t, movetur <lb/>per aliam, ad quam determinatur partim à corpore reflectente, partim <lb/>à primo motu; &longs;ic etiam, vt alterum exemplum tibi ante à me promi&longs;<lb/>&longs;um adducam: Calamus volatilis, quem vos Italicè vocatis <emph type="italics"/>Grillo,<emph.end type="italics"/> im<lb/>pre&longs;&longs;o &longs;ibi per rectam impetu, cùm motum rectum, obluctantibus pen<lb/>nis, quæ aeri facilè cedunt, totum habere non po&longs;&longs;it, qui &longs;cilicet im<lb/>pre&longs;&longs;o impetui alioquin competeret, accito &longs;pirali motu, iacturam motus <lb/>recti compen&longs;at; cur verò in hanc potiùs, quàm in illam partem <lb/>eant &longs;piræ, à pennis in eam ab aëre deflexis, &longs;eu detortis omni<lb/>no procedit; quòd autem maior impetus dicto calamo in&longs;it, quàm qui <lb/>in eo motu recto, qui re&longs;tat, impenditur, vel ex eo liquidò con&longs;tat, <lb/>quod avul&longs;is ex theca, ca&longs;u aliquo, pennis, dum in medio aëre &longs;pira<lb/>tim movetur, theca ip&longs;a, præ&longs;ertim &longs;i o&longs;&longs;ea e&longs;t, longiùs aucto motu <lb/>recto, projici videatur; igitur ille impetus inerat. </s>

<s id="s.000454">Sed vt ad rem no<lb/>&longs;tram redeam, cùm Sol à Q ad H totum &longs;uum motum, in &longs;piris ha<lb/>bere non po&longs;&longs;it &longs;uppo&longs;itis temporibus æqualibus di&longs;trahit &longs;piras, com<lb/>pen&longs;ans &longs;pirarum motum, motu per &longs;egmentum QH, quod breviore <lb/>tempore decurrit, quam DQ, non tamen proptereà &longs;piratim motus re<lb/>mittitur &longs;ed æqualis &longs;emper remanet; nempe cum Sol in Q non tendat <lb/>ad Tropicum, per curuam QH, &longs;ed per arcum interceptum inter AF, <lb/>AE, minorem arcu FE, atque adeo per arcus &longs;emper minores, donec <lb/>tandem perveniat in H, & cùm arcus minores citiùs perficiar, eadem <lb/>vi motus; quid mirum &longs;i citiùs perveniat à Q ad H, quàm à D ad Q, ac <lb/>proinde &longs;i &longs;piræ di&longs;trahantur in &longs;egmento QH, atque adeò pauciores <lb/>maneant licèt enim QH. Æqualis &longs;it DQ, non tamen per QH &longs;ecunda <lb/>inclinatio &longs;uam vim exerit, &longs;ed per arcus concentricos minores, quos <lb/>citiùs decurrit, licèt à prima inclinatione ad curvam QH detorqueatur. <lb/></s>

in linea 38, lib. &longs;ub titulo magnitudinis dia<lb/>metri &longs;phæræ stanneæ, datur quæ&longs;ita diametri magnitudo 6, ad <lb/>vnguem.<emph.end type="italics"/></s>

<s id="s.000455">Hinc &longs;emoto motu circulari, & relicta gemina illa inclinatione, adhuc <lb/>&longs;ecunda inclinatio decurreret citiùs QH, q<gap/>àm <expan abbr="Dq.">DQ</expan> Ex his ni fallor <lb/>&longs;equi vides, tum di&longs;tractionem maiorem &longs;pirarum, tum imminutum &longs;pi<lb/>rarum numerum, tum compen&longs;ationem talem motuum, ex qua perfecta <lb/>ferè &longs;pirarum diurnarum æqualitas nece&longs;&longs;ariò con&longs;equitur. </s>

<s id="s.000456"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s><emph type="italics"/>Notandum autem est, quod numeri, qui diametrorum magnitu<lb/>dines denotant, non &longs;unt veri, ac certi, &longs;ed veris bene proximi, <expan abbr="quoniã">quoniam</expan> <lb/>numeri, quorum ip&longs;i &longs;unt radices cubicæ, non &longs;unt cubi, & ideo ip&longs;a <lb/>radices non explicantur accurate, &longs;ed vel veris maiores, vel minores, <lb/>atque vt cogno&longs;cantur quæ &longs;int maiores, queue minores, maioribus <lb/>duo puncta adiecimus, minoribus vnum, accuratis nullum. </s>

<s id="s.000457"> Si Apogæum &longs;it in Æquatore, quid tandem fieret? </s>

<s>inter om<lb/>nes autem vnus est accuratus, is &longs;cilicet, qui magnitudinem indicat <lb/>diametri &longs;phæræ stanneæ, grauitatem habentis<emph.end type="italics"/> 38, <emph type="italics"/>lib.<emph.end type="italics"/>De compo&longs;itione huius Tabulæ. </s>

<s id="s.000458"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s><emph type="italics"/>Huius tabulæ compo&longs;itio pendet ex præcedenti tabula, & ex pro<lb/>po&longs;.<emph.end type="italics"/> 17, <emph type="italics"/>huius, &longs;i enim fiat vt grauitas &longs;phæræ stanneæ, diametrum <lb/>habentis vnius vnciæ, id est, vt grana<emph.end type="italics"/> 1216, <emph type="italics"/>ad grauitatem &longs;phæræ <lb/>vnius libræ, idest, adgrana<emph.end type="italics"/> 6912, <emph type="italics"/>ita cubus diametri vnius vnciæ, <lb/>hoc e&longs;t, ita<emph.end type="italics"/> 1, <emph type="italics"/>ad alium numerum, qui &longs;it<emph.end type="italics"/> 5 11/19 <emph type="italics"/>is erit cubus diametri <lb/>&longs;phæræ stanneæ, grauitatem habentis 1, lib.

<s id="s.000459"> Planum Troprci DI tantulùm accederet ad Æquatorem FK, <pb pagenum="40" xlink:href="025/01/044.jpg"/>à quo planum Tropici HL tantulùm æquè recederet, vt æqualis vtrinque <lb/>effet di&longs;tantia, &longs;ub æqualibus tamen &longs;emper angulis DAF, EAF. </s>

<s id="s.000460">Tunc <lb/>autem po&longs;ito quod Apogæum &longs;it in principio Ar<gap/>tis, plus temporis po<lb/>netur ab Ariete ad Cancrum, quàm à Cancro ad Libram; & minus à Li<lb/>bra ad Capricornum, quàm ab hoc ad Arietem; tempora tamen erunt <lb/>æqualia à Cancro ad Libram, à Libra ad Capricornum, &longs;cilicet à me<lb/>diocri di&longs;tantia ad Perigæum: & ab hoc ad mediam di&longs;tantiam; erunt <lb/>item æqualia inter &longs;e tempora à Capricorno ad Arietem, & ab hoc ad <lb/>Cancrum. </s>

demonstratum enim <lb/>est prop.<emph.end type="italics"/> 17, <emph type="italics"/>huius, &longs;phæras eiu&longs;dem generis inter &longs;e e&longs;&longs;e in grauitate, <lb/>vt diametrorum cubi in magnitudine; quare radix cubica numeri<emph.end type="italics"/><lb/>5 13/19, <emph type="italics"/>dabit ip&longs;am diametrum, &longs;ed quoniam numerus<emph.end type="italics"/> 5 13/19, <emph type="italics"/>non est <lb/>præci&longs;e cubus, eius radix non explicabitur accurata, &longs;ed vt explicetur <lb/>veræ bene proxima, multiplicetur<emph.end type="italics"/> 5 13/19, <emph type="italics"/>per<emph.end type="italics"/> 1000000. <emph type="italics"/>& ex producto<emph.end type="italics"/><lb/>5684210 10/19, <emph type="italics"/>neglecto fracto<emph.end type="italics"/> 10/19, <emph type="italics"/>eruatur radix, tanquam ex accu<lb/>rato numero cubo, ea erit<emph.end type="italics"/> 173. <emph type="italics"/>proxime, & erit centupla radicis nu<lb/>meri<emph.end type="italics"/> 5 13/19, <emph type="italics"/>nam numerus<emph.end type="italics"/> 1000000, <emph type="italics"/>per quem fuit multiplicatus<emph.end type="italics"/><lb/>5 13/19, <emph type="italics"/>cubus e&longs;t ex<emph.end type="italics"/> 100<emph type="italics"/>; magnitudo igitur diametri &longs;phæræ &longs;tanneæ, <lb/>grauitatem habentis 1, lib.

erit<emph.end type="italics"/> 1 78/100. <emph type="italics"/>reliquarum autem ex &longs;tanno <lb/>&longs;phærarum, grauitatem habentium duplam primæ, triplam, quadru<lb/>plam &c. </s>

<s id="s.000461"><emph type="italics"/>Angu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000462"> Ille tuus calamus volatilis, vt vocas, mihi &longs;ummopere ar<lb/>ridet, itemque de&longs;cen&longs;i ille aquæ in tubo; aliquid &longs;imile in mentem <lb/>venit, cùm &longs;cilicet aqua, &longs;eu vinum per infundibulum in dolium mitti<lb/>tur; nam circa os infundibuli vinum in &longs;piras agitur, propter illam ra<lb/>tionem, quam attuli&longs;ti. </s>

<s>ita inuenientur diametri.<emph.end type="italics"/></s>

<s id="s.000463">Idem accidit in quibu&longs;dam fluminibus, &longs;eu la<lb/>cubus, ex quibus aqua in profundum hiatum &longs;eu voraginem &longs;piratim de&longs;<lb/>cendit, &longs;imulque à vortice naves ab&longs;orbentur, &longs;i quæ mala &longs;ua &longs;orte eò <lb/>appellantur. </s>

<s><emph type="italics"/>Duplum numeri<emph.end type="italics"/> 5684210 10/19, <emph type="italics"/>id est<emph.end type="italics"/> 11368421 1/19, <emph type="italics"/>erit cubus <lb/>centupli diametri &longs;pheræ stanneæ, grauitatem habentis duplam pri<lb/>mæ, hoc est<emph.end type="italics"/> 2, <emph type="italics"/>lib.

<s id="s.000464"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

ex &longs;upra nominata enim prop.<emph.end type="italics"/> 17, <emph type="italics"/>huius, e&longs;t vt gra<lb/>uitas &longs;phæræ vnius libræ, ad grauitatem &longs;phæræ duarum librarum, <lb/>ita cubus diametri primæ &longs;phæræ, ad cubum diametri &longs;ecundæ. </s>

<s id="s.000465"> Aliud omittis longè iucundius, vidi&longs;ti enim aliquando venti <lb/>turbinem, qui fe&longs;tucas, folia, pulverem in orbem agit ac vorticem; <lb/>immo & naves in medio mari &longs;ic à Typhone mi&longs;erum in modum abri<lb/>piuntur; vnde putas hunc venti vorticem &longs;eu turbinem ortum ducere? </s>

<s>Si <lb/>vero triplicetur numerus<emph.end type="italics"/> 5684210 10/19, <emph type="italics"/>eius triplum, quod est<emph.end type="italics"/><lb/>17052631 11/19, <emph type="italics"/>erit cubus centupli diametri &longs;phæræ &longs;tanneæ, graui<lb/>tatem habentis triplam primæ, idest<emph.end type="italics"/> 3, <emph type="italics"/>lib.

<s id="s.000466"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

& &longs;i quadruplicetur, eius<emph.end type="italics"/><pb pagenum="51"/><emph type="italics"/>quadruplum erit cubus centupli diametri &longs;phæræ stanneæ, grauita<lb/>tem habentis quadruplam primæ, & &longs;ic deinceps. </s>

<s id="s.000467"> Certè no&longs;tri Philo&longs;ophi communiter docent, hunc effe<lb/>ctum à varia reflexione procedere, quæ in circuma&longs;&longs;urgentibus monti<lb/>bus fiat. </s>

<s>itaque &longs;i ex eius <lb/>multiplicibus, neglectis fractis, <expan abbr="eruãtur">eruantur</expan> radices, tanquam ex accura<lb/>tis numeris cubis, ip&longs;æ indicabunt diametrorum magnitudines in <lb/>ratione centupla. </s>

<s id="s.000468"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>Sed vt etiam euitetur labor multiplicandi prædi<lb/>ctum numerum<emph.end type="italics"/> 5684210 10/19, <emph type="italics"/>hac ratione inuenientur eius multi<lb/>plicia.<emph.end type="italics"/></s>

<s id="s.000469"> Sat &longs;cio. </s>

<s id="s.000470">Sed quænam reflexio in va&longs;ta terrarum & Oceani <lb/>planitie fieri pote&longs;t? </s>

<s><emph type="italics"/>Prædicto numero<emph.end type="italics"/> 5684210 10/19, <emph type="italics"/>addatur eius duplum, id est,<emph.end type="italics"/><lb/>11368421 1/19, <emph type="italics"/>&longs;umma<emph.end type="italics"/> 17052631 11/19, <emph type="italics"/>dabit eius triplum, &longs;i vero ei <lb/>addatur eius triplum, id e&longs;t,<emph.end type="italics"/> 17052631 11/19, <emph type="italics"/>&longs;umma<emph.end type="italics"/> 22736842 2/19, <lb/><emph type="italics"/>dabit eius quadruplum, & &longs;i eius quadruplum ei addatur, &longs;umma <lb/>dabit eius quintuplum, & &longs;ic &longs;ola additione inuenientur eius quot<lb/>cunque multiplicia.<emph.end type="italics"/></s>

<s id="s.000471">in qua nulli montes a&longs;&longs;urguat. </s>

<s id="s.000472">Alia profectò ratio <lb/>e&longs;t, ex eodem no&longs;tro principio petita; nempe vbi aliqua portio aëris &longs;u<lb/>perioris tractus den&longs;atur (den&longs;ari autem pote&longs;t multiplici ca&longs;u) gravior <lb/>redditur inferiore; cùm autem deor&longs;um cadere non po&longs;&longs;it, ni&longs;i inferio<lb/>rem exten&longs;ione æqualem &longs;ur&longs;um extrudat, nec tam citò extrudere po&longs;<lb/>&longs;it, &longs;piratim per illius latera de&longs;cendit; Hinc turbo & vortex, cujus rei <lb/>analogiam habes in adductis &longs;upra exemplis, ad hunc porrò effectum <lb/>perinde e&longs;t, &longs;ive aër Superioris tractus conden&longs;etur, &longs;ive inferioris rare&longs;<lb/>cat: Hinc cum igne Typhon, aliàs cum aqua conjunctus e&longs;t; igne qui<lb/>dem quo inferioris aëris tractus &longs;tatim rare&longs;cat, ac proinde maximo im<lb/>petu aër Superioris tractus &longs;piratim ruat; aqua verò &longs;i magna Vaporum <lb/>vis expre&longs;&longs;a cum igne, caloris vi, in &longs;uperiori aëris tractu &longs;tatim conden<lb/>&longs;etur, ac proinde aqua &longs;piratim etiam & præceps deor&longs;um ruat. </s>

<s><emph type="italics"/>Eadem ratione inuenientur diametri &longs;phærarum ex quacunque <lb/>alia materia, &longs;i enim quæratur de magnitudine diametri verbi gra<lb/>tia &longs;phæræ ferreæ, grauitatem habentis 1, lib.

fiat vt grana<emph.end type="italics"/> 1314 22/37, <lb/><emph type="italics"/>id est vt grauitas &longs;phæræ ferreæ, cuius diameter e&longs;t vnius vnciæ, ad <lb/>grauitatem vnius libræ, id est ad grana 6912, ita cubus diametri <lb/>vnius vnciæ, hoc e&longs;t ita 1, ad alium numerum qui &longs;it<emph.end type="italics"/> 5 49/190, <emph type="italics"/>is igi<lb/>tur numerus * erit cubus diametri &longs;phæræ ferreæ, grauitatem haben<emph.end type="italics"/><arrow.to.target n="note48"/><lb/><emph type="italics"/>tis<emph.end type="italics"/> 1, <emph type="italics"/>lib.

<s id="s.000473"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000474"> Inde fortè imber guttatim de&longs;cendit, cùm enim &longs;ur&longs;um ex<lb/>trudendus &longs;it aër, humor in de&longs;cen&longs;u in guttas dividitur ad faciliorem <lb/>de&longs;cen&longs;um. </s>

quare radix cubica numeri<emph.end type="italics"/> 5 49/190, <emph type="italics"/>dabit quæ&longs;itam dia<lb/>metrum, & quoniam numerus<emph.end type="italics"/> 5 49/190, <emph type="italics"/>non e&longs;t præci&longs;e cubus, & ideo <lb/>non explicabitur eius radix accurate, multiplicetur per 1000000, & <lb/>ex producto<emph.end type="italics"/> 5257894 14/19, <emph type="italics"/>neglecto fracto<emph.end type="italics"/> 14/19, <emph type="italics"/>eruatur radix, tan<lb/>quam ex accurato numero cubo, ea erit<emph.end type="italics"/> 174: <emph type="italics"/>ferè, & erit centupla ra<lb/>dicis numeri<emph.end type="italics"/> 5 49/190, <emph type="italics"/>quia numerus<emph.end type="italics"/> 5 49/190, <emph type="italics"/>multiplicatus fuit per <lb/>cubum ex 100; diameter igitur &longs;phæræ ferreæ, grauitatem habentis <lb/>1, lib.

erit<emph.end type="italics"/> 1 74/100: <emph type="italics"/>deinde &longs;i duplicetur<emph.end type="italics"/> 5257894 24/19, <emph type="italics"/>& ex ita du<lb/>plicato eruatur radix cubica<emph.end type="italics"/> 219, <emph type="italics"/>ea dabit centuplum diametri &longs;phæ<lb/>ra ferreæ, grauitatem habentis<emph.end type="italics"/> 2, <emph type="italics"/>lib.

<s id="s.000475"><emph type="italics"/>Antim.<emph.end type="italics"/> A vero aberras, Augu&longs;tine, nec i&longs;ta, quam dicis, vera ratio <lb/>e&longs;t, nam & gutta maior ex &longs;ublimiore tractu de&longs;cendit, vt non rarò <lb/>æ&longs;tate accidit; quia forvente æ&longs;tu, altiùs vapores a&longs;&longs;urgunt, & perexiguæ <lb/>guttæ lenti&longs;&longs;imè de&longs;cendent, vt &longs;æpè vidi&longs;ti in nebula, dum re&longs;olvitur: <pb pagenum="41" xlink:href="025/01/045.jpg"/>tantulum porrò vaporis in guttulam re&longs;olvitur, hæc initio lento de&longs;cen<lb/>dit gradu, intereà multæ aliæ guttulæ minores occurrunt in de&longs;cen&longs;u, <lb/>quas ip&longs;a colligit, vnde major evadit, & motus cre&longs;cit, donec tandem <lb/>in Terram labatur: hinc cæteris paribus, illæ gurtæ maiores &longs;unt, quæ <lb/>ex &longs;ublimiore tractu de&longs;cendunt; plures enim colligunt in de&longs;cen&longs;u mi<lb/>nores guttas, nempe ex mutuo contactu duarum guttarum &longs;equitur, vt <lb/>ex duabus vnica fiat; trita res e&longs;t, &longs;ed ratio &longs;atis ab&longs;tru&longs;a: hinc æ&longs;tate, <lb/>vt plurimum, guttæ imbris maiores &longs;unt, quàm hieme, hinc demum ali<lb/>quando accidit, vt iuxta verticem montis &longs;it nebula, imber verò in infe<lb/>riore tractu; &longs;ed quæ&longs;o ad rem no&longs;tram redeamus longiùs enim excur<lb/>rimus. </s>

& &longs;i triplicetur, triplicati radix <lb/>cubica<emph.end type="italics"/> 250<gap/> <emph type="italics"/>dabit centuplum diametri &longs;phæræ ferreæ, cuius grauitas <lb/>crit<emph.end type="italics"/> 3, <emph type="italics"/>lib.

<s id="s.000476"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

& &longs;ic reliquarum &longs;phærarum in infinitum inuenientur <lb/>diametri. </s>

<s id="s.000477"> Circa tuam hypothe&longs;im multa e&longs;&longs;ent in accuratius examen <lb/>vocanda, &longs;ed per tempus non licet, aliqua tamen obiter percunctabor, <lb/>ac primum quidem illud, quid tibi velles, cùm &longs;upra diceres, gradum il<lb/>lum velocitatis acqui&longs;itum à Marte & à Sole, produci vel à Motore extrin<lb/>&longs;eco, vel ab ip&longs;i &longs;in et Planetis per motum acceleratum prævium. </s>

<s>multiplicia autem numeri<emph.end type="italics"/> 5257894 14/19, <emph type="italics"/>&longs;ola additione in<lb/>uenientur, vt dictum est &longs;upra de inuentione multiplicium numeri<emph.end type="italics"/><lb/>5684210 10/19. <emph type="italics"/>Atque hac ratione prædictam tabulam compo&longs;uimus.<emph.end type="italics"/></s>

<s id="s.000478"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s><margin.target id="note48"/>17<emph type="italics"/>: <lb/>huius.<emph.end type="italics"/></s>

<s id="s.000479"> Magnum certè hîc my&longs;terium non latet; cùm enim velim, pri<lb/>mum illum impetum Soli modò ine&longs;&longs;e, qui eidem initio inerat, eumque <lb/>motui æquabili, quo huiu&longs;que Sol movetur, movebiturque impo&longs;terum, <lb/>æqualem &longs;emper & eundem velocitatis gradum conciliare, cur enim & à <lb/>quo dictus impetus de&longs;trueretur, cùm nunquam fru&longs;tra &longs;it? </s>

<s id="s.000480">perinde &longs;anè <lb/>mihi fuit, &longs;ive ab ip&longs;o Sole per motum acceleratum prævium acqui&longs;itus <lb/>fuerit, &longs;ive à Deo, vel Angelo eidem impre&longs;&longs;us; Dic, vt voles, vtrum<lb/>que enim fieri potuit; nec qui&longs;quam, opinor, hoc negaverit, nec dif<lb/>ficile e&longs;&longs;et, definite altitudinem illam, ex qua Sol ad hunc velocitatis <lb/>gradum acquirendum de&longs;cenderit, cognita &longs;cilicet Solis Apogæi vel <lb/>Perigæi di&longs;tantia; immo & tempus in tali de&longs;cen&longs;u po&longs;itum; cum emin ve<lb/>locitate<gap/> vt tempora, & &longs;patia decur&longs;a in duplicata rat. </s>

<s>Qvomodo Archimedes argenti mixtionem depre<lb/>hendit in auro. </s>

<s id="s.000481">temporum, <lb/>&longs;cio, v.g. vno &longs;ecundo minuto corpus grave decurrere in perpendiculo <lb/>12. pedes, & velocitatem eodem &longs;ecundo minuto acqui&longs;itam &longs;ufficere, <lb/>vt motu æquabili 24. pedes decurrantur; &longs;cio quoque punctum Æqua<lb/>toris terre&longs;tris globi &longs;i hic motu orbis agatur, vno &longs;ecundo minuto con<lb/>ficere circiter 1250. pedes. </s>

<s id="s.000482">Sit verò di&longs;tantia Solis à centro terræ 2000. <lb/>circiter &longs;emidiametrorum, &longs;i hic numerus ducatur in illum, productus <lb/>veniet hic tertius 2500000; Sol igitur vno &longs;ecundo minuto conficit to<lb/>tidem pedes: ducatur hic numerus in 60. productus erit, 150000000. <lb/>tot pedes conficit vno primo minuto: ducatur etiam hic in 60. produ<lb/>ctus erit 9000000000. tot pedes conficiet vna hora; hic demum duca<lb/>tur in 24. productus erit 216000000000. tot pedes conficiet vno die; <lb/>accipiatur &longs;ubduplus &longs;cilicet 108000000000. tot pedes decurri; vno die <lb/>corpus grave motu naturaliter accelerato in perpendiculo deor&longs;um; Iam <lb/>duco 24. in 60. & productum in 60. hic productus erit 864000. tot &longs;ci<lb/>licet minuta &longs;ecunda, quot in 24. horas, ducatur hic in &longs;e ip&longs;um, pro<lb/>ductus erit 7464960000. per quem &longs;i dividas 108000000000. quotiens <lb/>erit 14 1/2 circiter, tot pedes conficit corpus grave motu deor&longs;um, vno <pb pagenum="42" xlink:href="025/01/046.jpg"/>minuto &longs;ecundo, vnde corriges Mer&longs;ennum, qui tantùm pedes 12. a&longs;&longs;i<lb/>gnat, itemque alium, qui vult corpus grave decurrere vno &longs;ecundo mi<lb/>nuto 15. pedes; quanquam hic ad verum proximè acce&longs;&longs;it, quod certè <lb/>in tanto numero 12. cifrarum, qui &longs;cilicet 200. & 16. millia milliorum <lb/>complectitur, parum e&longs;t. </s>

<s><emph type="italics"/>Hiero (referente Vitruuio lib.<emph.end type="italics"/> 9. <emph type="italics"/>Cap.<emph.end type="italics"/> 3.<emph type="italics"/>) Siracu&longs;is auctus regia<emph.end type="italics"/><pb pagenum="52"/><emph type="italics"/>pote&longs;tate, rebus bene ge&longs;tis, cum auream coronam votiuam, dys im<lb/>mortalibus in quodam fano con&longs;titui&longs;&longs;et ponendam, immani precia <lb/>locauit faciendam, & aurum ad &longs;acoma appendit redemptori. </s>

<s id="s.000483">Hæc porrò eo animo dico, vt quorumdam <lb/>hallucinatio ca&longs;tigetur, qui cùm hoc, eo, quo par e&longs;t, modo non di&longs;<lb/>cu&longs;&longs;erint, multa ab&longs;urda &longs;uper hac re pronunciant. </s>

<s id="s.000484">Immo, vt iam fortè <lb/>mecum ob&longs;ervas, &longs;i præcisè habeamus, quot pedes corpus grave in de&longs;<lb/>cen&longs;u decurrat vno &longs;ecundo minuto, habebimus haud dubiè quantum <lb/>decurrere debeat vno die integro, in linea recta deor&longs;um; quæ &longs;i du<lb/>plicetur, & inflectatur in circulum, hæc for&longs;itan erit, &longs;altem proximè, <lb/>magni orbis men&longs;ura; ita vt Sol motu recto prævio 24. horis decur<lb/>rerit &longs;patium æquale &longs;emicirculo magni orbis; &longs;ed quidquid &longs;it, &longs;ive <lb/>hic impetus accedat ab extrin&longs;eco, &longs;ive ab ip&longs;o Sole in &longs;e producatur, <lb/>perinde e&longs;t ad rem no&longs;tram; cùm Soli maximè connaturalis &longs;it, quate<lb/>nus &longs;cilicet Solaris globus ad talem finem à natura ip&longs;a, & naturæ ip&longs;ius <lb/>Autore ordinatus e&longs;t; quem vt obtineret tali tantoque impetu illi opus <lb/>erat; tantum igitur & talem vel ab extrin&longs;eco accepit, vel in &longs;e pro<lb/>duxit. </s>

<s>is ad <lb/>tempus opus manufactum &longs;ubtiliter, regi approbauit, & ad &longs;acoma <lb/>pondus coronæ vi&longs;us e&longs;t præ&longs;titi&longs;&longs;e. </s>

<s>Po&longs;tea quam inditium e&longs;t factum, <lb/>dempto auro, tantundem argenti in id coronarium opus admixtum <lb/>e&longs;&longs;e: indignatus Hiero &longs;e contemptum, neque inueniens, qua ratione <lb/>id furtum deprehenderet, rogauit Arcbimedem, vti in &longs;e &longs;umeret de <lb/>eo cogitationem. </s>

<s id="s.000485"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000486"> Sed quis Solern docuit in Occa&longs;um ferri, non verò in Or<lb/>tum; ire versùs di&longs;tantiam mediam, ad Æquatoris planum accedere, & <lb/>turbinis in&longs;tar circa &longs;uum axem inclinatum moveri, idque in hanc partem, <lb/>potiùs quàm illam? </s>

<s>tunc is cum baberet eius rei curam, ca&longs;u venit in <lb/>balneum, ibique cum in &longs;olium de&longs;cenderet, animaduertit quantum <lb/>corporis &longs;ui in eo in&longs;ideret, tantum aquæ extra &longs;olium effluere. </s>

<s><expan abbr="itaq;">itaque</expan> <lb/>cum eius rei rationem explicationis offendi&longs;&longs;et non est moratus, &longs;ed <lb/>exiliuit gaudio motus de &longs;olio, & nudus vadens domum ver&longs;us, &longs;igni <lb/>ficabat clara voce inueni<32>e quod quærerct. </s>

<s id="s.000487"><emph type="italics"/>Antim.<emph.end type="italics"/> Hæc aperire nolebam, &longs;ed profectò me cogis: &longs;i Sol ab Au<lb/>tore movetur extrin&longs;eco, nimirum à Deo, Angelorum mini&longs;terio, vt <lb/>no&longs;tri Schola&longs;tici communiter docent, nec ego inficias eo, ab eodem <lb/>motore cuncta hæc recipit; at ex hypothe&longs;i, quod à &longs;e ip&longs;o moveatur, <lb/>quod certè tanti non e&longs;&longs;et, cùm id cuipiam corpori gravi competat; di<lb/>cerem, Solem conditum à Deo fui&longs;&longs;e &longs;upra di&longs;tantiam mediam, multis <lb/>terræ &longs;emidiametris, vt dixi, ex quo loco de&longs;cendit versus mundi cen<lb/>trum, obtenta verò media & connaturali di&longs;tantia, motu circulari mo<lb/>veri c&oelig;pit, versùs Occa&longs;um: cur, inquis, potiùs quàm versùs Ortum? <lb/></s>

<s id="s.000488">Quia cum creatus fuerit in Tropico Cancri circa 180. grad. longitudinis <lb/>eo poti&longs;&longs;imum fine, vt in terræ &longs;uperficiem ageret, à maiori dictæ &longs;uper<lb/>ficiei tractu versùs Occa&longs;um inde excurrente ad hanc lineam determina<lb/>rus fuit, ex qua profectò prima determinatione, &longs;equuntur aliæ, &longs;cilicet, <lb/>Axis mundi, polorum, Æquatoris &c. </s>

<s>nam currens identidem <lb/>grece clamabat<emph.end type="italics"/> <foreign lang="greek"><gap/></foreign> <emph type="italics"/>tum vero ex eo inuentionis ingre&longs;&longs;u <lb/>duas dicitur feci&longs;&longs;e ma&longs;&longs;as æquo pondere, quo etiam fuerat coro<lb/>na, vnam ex auro, alteram ex argento. </s>

<s id="s.000489">& cùm tantulum primæ determi<lb/>nationis deor&longs;um retinuerit, debilis tamen, tota enim ferè in circularem <lb/>motum ivit, quid mirum, &longs;i ad Perigæum tendat? </s>

<s id="s.000490">à quo rur&longs;um eodem <lb/>modo versùs Apogæum regreditur; adde &longs;ecundam inclinationem, de <lb/>qua iam &longs;upra, & quia globorum more, deor&longs;um in morem turbinis <lb/>de&longs;cendit, retinuit illum motum orbis circa eundem Axem &longs;ibi ip&longs;i <lb/>&longs;emper parallelum, vbi motu circulari agi c&oelig;pit, cui prædicta turbinatio <lb/>non ob&longs;tat, Vides, cuncta hæc ex communibus illis principiis deduci, <lb/>per quæ aliorum corporum motus explicantur. </s>

<s>cum ita feci<32>et, vas <expan abbr="ampl&utilde;">amplum</expan> <lb/>ad &longs;umma labra impleuit aqua, in quo demi&longs;it argenteam ma&longs;&longs;am, <lb/>cuius quanta magnitudo in va&longs;e depre&longs;&longs;a est, tantum aquæ effluxit. </s>

<s><lb/>ita exempta ma&longs;&longs;a, quanto minus factum fuerat refudit, &longs;extario <lb/>men&longs;us, vt eodem modo, quo prius fuerat, ad labra æquaretur. </s>

<s id="s.000491"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>ita ex <lb/>eo inuenit, quantum ad certum pondus argenti certa aquæ men&longs;ura <lb/>re&longs;ponderet.<emph.end type="italics"/></s>

<s id="s.000492"> Rectè, illud &longs;altem commodi ex hac tua hypothe&longs;i acci<lb/>dit, quod primi orbis incolæ diem primum integrum habuerunt, Sol <lb/>nempe in ortiuo horizontis illorum limbo conditus fuit; id e&longs;t, in &longs;emi<lb/>circulo ortiuo magni Meridiani; & verò æquum fuit, vt Sol, qui pro<lb/>pter hominem creatus e&longs;t, no&longs;tro huic primum hemi&longs;phærio, in quo & <lb/>primus homo conditus, præfulgeret: &longs;ed fortè nobilem coronam diutius <lb/>quam par e&longs;&longs;et detinemus; tuam illam, quam contra no&longs;tram hypothe<lb/>&longs;im adorna&longs;ti, di&longs;putationem, in proximum congre&longs;&longs;um remittimus. </s>

<s><emph type="italics"/>Cum id experius e&longs;&longs;et tum auream ma&longs;&longs;am &longs;imiliter pleno va&longs;e <lb/>demi&longs;it, & ea exempta, eadem ratione men&longs;ura addita, inuenit ex <lb/>aqua non tantum deftuxi&longs;&longs;e, &longs;ed tantum minus, quantum minus ma <lb/>gno corpore eodem pondere auri ma&longs;&longs;a e&longs;&longs;et quam argenti. </s>

<s id="s.000493"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>Postea <lb/>vero repleto va&longs;e, in <expan abbr="ead&etilde;">eadem</expan> aqua ip&longs;a corona demi&longs;&longs;a, inuenit plus aqua <lb/>defluxi&longs;&longs;e in coronam, quam in auream. </s>

<s id="s.000494"> Sit, vt voles, adero cra&longs;tina die, ni&longs;i tibi fortè grave &longs;it; multi <lb/>etiam ex nobili&longs;&longs;imis auditoribus futurum congre&longs;&longs;um &longs;ua præ&longs;entia ho<lb/>ne&longs;tabunt. </s>

<s>eodem pondere ma&longs;&longs;am, & <lb/>ita ex eo quod plus deftuxerat aquæ in corona, quam in ma&longs;&longs;a ratio<lb/>cinatus, deprehendit argenti in auro mixtionem, & manifestum fur<lb/>tum redemptoris.<emph.end type="italics"/></s><s> Hactenus Vitruuius. </s>

<s>Mirum certe Archimedis fuit inuentum, ip&longs;ius tamen <lb/>modus ad inueniendam illam aquæ men&longs;uram, quæ ad <lb/>certum pondus auri, vel argenti, vel coronæ re&longs;ponderet, <lb/>maiori diligentia indiget, quam quæ ab hominibus adhiberi <lb/>pote&longs;t, impo&longs;&longs;ibile enim e&longs;t, exempta corona, vel aurea ma&longs;&longs;a, <lb/>vel argentea, tantum aquæ refundere, quantum è va&longs;e efflu<lb/>xerat ad vnguem, nam repo&longs;ita aqua in va&longs;e, non po&longs;&longs;umus <pb pagenum="53"/>affirmare ip&longs;um vas e&longs;&longs;e plenum, ni&longs;i aqua incipiat effluere, <lb/>cum autem incipit, effiuit aliquando totus ferè cumulus, ita<lb/>que vel plus aquæ additur eo, quod deficit, vel minus, ni&longs;i <lb/>coniectura a&longs;&longs;equatur: at vero conicctura pro veritate non ac<lb/>cipitur. </s>

<s id="s.000495"><emph type="center"/>DIALOGVS SECVNDVS.<emph.end type="center"/></s>

<s>præterea exempta corona, vel aurea ma&longs;&longs;a, vel argen<lb/>tea, eximitur etiam &longs;imul cum ip&longs;a aliquantum aquæ, quæ cir<lb/>cum ip&longs;am remanet, atque huiu&longs;modi defectus errorem indu<lb/>cit &longs;en&longs;ibilem. </s>

<s id="s.000496"><emph type="center"/><emph type="italics"/>In quo valida contra Copernici hypothe&longs;im <lb/>argumenta proponuntur.<emph.end type="italics"/><emph.end type="center"/></s>

<s>Neque per collectionem quæ&longs;ita aquæ men&longs;ura inueniri <lb/>pote&longs;t: æquè enim impo&longs;&longs;ibile e&longs;t vniuer&longs;am illam æquam col<lb/>ligere, quæ extra vas effluit, quando corona, vel aurea ma&longs;&longs;a <lb/>vel argentea in ip&longs;o va&longs;e deprimitur, cum enim aqua è va&longs;e <lb/>effluat, pars ip&longs;ius aquæ va&longs;i, ex quo effluit, pars va&longs;i in quod <lb/>influit adhæret, & &longs;i vniuer&longs;a omnino &longs;emper non colligatur, <lb/>erit non parui erroris cau&longs;a, præter quam quod, non &longs;emper <lb/>adeo facile inuenitur par auri, argentique ma&longs;&longs;a, quando eo<lb/>rona, vel alia auri ma&longs;&longs;a, quæ examinanda proponitur, medio<lb/>crem excederet magnitudinem. </s>

<s>Neque præterea pote&longs;t di&longs;cerni prædicta argenti portio in <lb/>aliqua auri parua ma&longs;&longs;a, differentiæ enim aquarum, quæ ex<lb/>tra vas effluunt, &longs;unt adeo exiguæ, vt ne cogno&longs;ci quidem <lb/>po&longs;&longs;int, quod &longs;i cogno&longs;cerentur, non &longs;emper erunt veræ, <lb/>&longs;iquidem non &longs;emper in va&longs;is medio in cumulum cre&longs;cens <lb/>æqualis aquæ copia remanet, &longs;ed maior interdum, inter<lb/>dum minor, vt con&longs;picitur. </s>

<s id="s.000497">DVBIVM mihi non e&longs;t, hanc di&longs;putationem ineunti, quin <lb/>pleri&longs;que fortè iam actum agere videar, CARDINALIS <lb/>EMINENTISSIMS, quotus enim qui&longs;que invenitur, vel Philo<lb/>&longs;ophorum in tractatione de Corpore C&oelig;le&longs;ti; vel Theologo<lb/>rum in Opere &longs;ex dierum enucleando;; vel &longs;acri Textus Interpretum, in <lb/>eorum locorum expo&longs;itione, in quibus Terra &longs;tare, Sol & A&longs;tra <lb/>pa&longs;&longs;im moveri dicuntur; vel denique A&longs;tronomorum, in mundi &longs;y&longs;tema<lb/>te definiendo, qui hanc partam non adornet, &longs;uam falcem in hanc me&longs;<lb/>&longs;em non mittat, ac de mi&longs;ero Copernico novos triumphos agere nolit. <lb/></s>

<s id="s.000498">Scribimus indocti, doctique poëmata: quanquam, vt ingenuè dicam, <lb/>maxima illorum argumentorum pars, quibus nonnulli præfatam Coper<lb/>nici opinionem petierunt, non parum laudis & plau&longs;us eidem concilia<lb/>vit; ita enim ab illius defen&longs;oribus rejecta fuere, vt &longs;olutionis, &longs;eu re<lb/>&longs;pon&longs;ionis facilitas qua&longs;i ad in&longs;tar <gap/>novæ demon&longs;trationis novum &longs;plendo<lb/>re in eidem &longs;ententia conciliârit, illud &longs;anè commune e&longs;t præliis etiam li<lb/>terariis, vt qui&longs;quis ho&longs;tem malè aggre&longs;&longs;us e&longs;t, & in ca&longs;&longs;um adortus, <lb/>pro &longs;emivicto haben<gap/>tur; ne igitur eundem errorem admittam, illa dum<lb/>taxat adducam, quæ &longs;i non fortè ho&longs;tem omninò conficere, plurimùm <lb/>tamen labefactare videntur; tuum erit, Eminenti&longs;&longs;ime, qui per&longs;pica<lb/>ci&longs;&longs;ima ingenij acie vales, quam nihil quantumvis arduum, vel ab&longs;tru<lb/>&longs;um effugiat, &longs;i non de integra victoria, de potioribus &longs;altem partibus à <lb/>nobis in hac cau&longs;a, vt benè &longs;pero, referendis, judicare, necnon æqui&longs;&longs;i<lb/>mam ferre &longs;ententiam. </s>

<s>fit enim vt aliquando cumulus <lb/>ille frangatur pluribus in locis, & ideo aqua diffundatur, vt <lb/>ferè nihilip&longs;ius cumuli &longs;uper&longs;it, aliquando vero frangatur <lb/>in vno tantum loco, & aqua colligens &longs;e in cumulum, parum <lb/>diffluat. </s>

<s id="s.000499">Sed initium di&longs;&longs;ertationi demus. </s>

<s>Sed ponderandis corporibus in aere & aqua, eo modo, quo <lb/>dictum e&longs;t in fine exempli prop.

8. inuenitur quæ&longs;ita aquæ, <lb/>grauitas, ita exactè, vt requiritur, fiue &longs;it corpus illud paruum, <lb/>&longs;iue magnum nihilintere&longs;t, & præterea facillima e&longs;t operatio, <lb/>nec adinueniendæ &longs;unt auri, & argenti ma&longs;&longs;æ æque graues, ac <pb pagenum="54"/>corona, &longs;ed quælibet particulæ, grauitate quacunque, etiam <lb/>differentes inter &longs;e, &longs;ufficiunt. </s>

<s id="s.000500"><emph type="italics"/>Antimus.<emph.end type="italics"/></s>

<s id="s.000501"> Omittam, vt prudenter feci&longs;ti, argumentorum qui&longs;quilias, <lb/>quæ nonnulli, præ&longs;ertim ex antiquioribus rerum Mathematicarum & <lb/>Phy&longs;icarum minùs peritis contra tuam hypothe&longs;im adduxerunt, quæ pe<lb/>tita &longs;cilicet petunt à ventis, & nubibus, motu projectorum, de&longs;cen&longs;u <lb/>gravium, domorum ruina & lap&longs;u; quanquam nonnihil ad hominem ex <lb/>his eliciam; vt enim vis, ex motu orbis retardato, in Ortum &longs;equi aqua<lb/>rum excur&longs;ionem, per quam marinum æ&longs;tum ve&longs;tri explicant, quia &longs;cili<lb/>cet obimpre&longs;&longs;um ante impetum, quem facilè aqua retinet, nec enim ni&longs;i <lb/>à contrario impediri pote&longs;t, eundem pro&longs;equitur motum versùs Ortum; <lb/>cuius rei præclaram certè analogiam habetis in aqua, quæ cymba vehi<lb/>tur; cymba enim motum valdè retardante, aqua versùs portum excurrit; <lb/>hoc vnum e&longs;t ex præcipuis &longs;ententiæ ve&longs;træ argumentis. </s>

<s>De ratione autem, qua Archimedes, cognitis grauitatibus <lb/>trium corporum ex aqua, magnitudine æqualium, coronæ <lb/>&longs;cilicet vnum, alterum ma&longs;&longs;æ aure&ecedil;, tertium argenteæ, potue<lb/>rit furtum aurificis in regia corona deprehendere, atque ar<lb/>gentum quod erat in ea permixtum ab auro di&longs;cernere, pluri<lb/>mi &longs;crip&longs;erunt, modos etiam ad id faciendum excogitarunt <lb/>varios, longa tamen methodo, atque difficili v&longs;i &longs;unt, & quod <lb/>maximam confu&longs;ionem, & ob&longs;curitatem parit, nullum opera<lb/>tionis tradunt præceptum firmum, ac &longs;tabile. </s>

<s>ego autem vni<lb/>ca tantum proportionis ratiocinatione, &longs;eu regula trium (vt <lb/>vulgo dicitur) breuiter, & expedite idem con&longs;equor, eamque <lb/>geometrica ratione demon&longs;tro. </s>

<s id="s.000502"><emph type="italics"/>Augu&longs;tinus.<emph.end type="italics"/></s>

<s id="s.000503"> Ita e&longs;t, & licèt ad ea, quæ repo&longs;ui&longs;ti, obmutire & ma<lb/>nus dare vi&longs;us &longs;im, quia illa omnia, quæ ad tabulas æ&longs;tus marini eiú&longs;que <lb/>phænomena pertinent, minùs calleo, vereor tamen, vt rerum i&longs;tarum peri<lb/>ris per&longs;uadere valeas; illud autem &longs;ilentium mihi poti&longs;&longs;imum impo&longs;uit, <lb/>quòd &longs;anctè jura&longs;ti, in adluc<gap/>tis à te phænomenis, omnes ad vnum æ&longs;tus <lb/>marini peritos, &longs;ive Naucleri &longs;int, &longs;ive alij, imò & ip&longs;os litorum Oceani <lb/>vel idiotas incolas &longs;umma tor&longs;en&longs;ione convenire; itaque licèt ex &longs;ola ter<lb/>re&longs;tris globi circuitione æ&longs;tus marini adæquata cau&longs;a petenda non &longs;it, &longs;ed <lb/>ex alia quapiam, negari tamen non pote&longs;t, quin prædictus motus aliquid <lb/>conferat. </s>

<s>Problema igitur ad hoc facien <lb/>dum ita concipio & ab&longs;oluo. </s>

<s>PROBLEMA IX. PROPOS. XVIII.</s>

<s id="s.000504"><emph type="italics"/>Antim:<emph.end type="italics"/> A&longs;&longs;igna priùs aliam cau&longs;am, vt videamus, an &longs;ufficiat ad hunc <lb/>mirabilem effectum; &longs;i enim &longs;ufficit, nihil &longs;anè e&longs;t, quod ille Terræ motus <lb/>conferat; &longs;i verò non &longs;ufficit, o&longs;tende id, ad quod non &longs;ufficit, & illius <lb/>motus opem po&longs;tulat; &longs;emper enim recurret propo&longs;itum argumentum; <lb/>totum illud, quidquid tandem &longs;it, quod à præfato motu efficitur, circa <lb/>maximæ inæqualitatis cardines; id e&longs;t, circa Meridiem & mediam noctem, <lb/>vi&longs;um &longs;emper iri; quod tamen Ob&longs;ervationibus repugnat: itaque certum <lb/>e&longs;t, & per&longs;picuum ex Maris æ&longs;tu Terræ motum minimè probari; certum <lb/>tamen e&longs;&longs;e dicitis, ex illo inæquali motu, varium &longs;equi aquarum motum; <lb/>quod certè ad hominem &longs;ic vrgeo; &longs;i reverà e&longs;&longs;et hic motus, ex illius inæ<lb/>qualitate, varius aquarum motus &longs;equeretur, &longs;cilicet ex retardatione aqua<lb/>rum excur&longs;io versùs Ortum, ex acceleratione, excur&longs;io versùs Occa&longs;um; <lb/>hoc non negatis, &longs;ed conceditis vltrò; idque in cardinibus maximæ in<lb/>æqualitatis, aut &longs;altem &longs;emper in ii&longs;dem, cùm eadem cau&longs;a idem &longs;em<lb/>per præ&longs;tet; &longs;ed in nullo certo ac fixo temporis puncte huiu&longs;modi aqua<lb/>rum excur&longs;iones fiunt, quod nemo neger, &longs;i cæcus & &longs;urdus; nullus e&longs;t <lb/>igitur Terræ motus, ex quo alioqui prædicti effectus nece&longs;&longs;ariò &longs;eque<lb/>rentur. </s>

<s>Portionem metalli, alterimetallo mi&longs;tam, ponde<lb/>ris ratiocinatione di&longs;cernere. </s>

<s id="s.000505"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>QVONIAM de Hieronis corona facta e&longs;t mentio, &longs;it ea B, <lb/>eiu&longs;que grauitas EK, & oporteat argentum, quod &longs;it in ea <expan abbr="permixt&utilde;">permixtum</expan>, <lb/>ab auro di&longs;cernere, hoc e&longs;t oporteat inuenire quanta erit portio ar<lb/><figure id="fig16"/><lb/>genti, & quanta auri. </s>

<s id="s.000506"> Facilis re&longs;pon&longs;io nobis &longs;uppetit, qualem etiam ve&longs;tri adhi<lb/>bent, &longs;cilicet illam inæqualitatem motus, e&longs;&longs;e tantùm apparentem, iis <lb/>&longs;cilicet, qui ex Solari &longs;phæra oculos in Terram conjicerent; &longs;icut C&oelig;le<lb/>&longs;tium &longs;phærarum motus nobis è Terra ob&longs;ervantibus inæquales apparent; <lb/>cùm tamen re ip&longs;a æquabiles &longs;int, igitur po&longs;ita reali motus æqualitate, <pb pagenum="45" xlink:href="025/01/049.jpg"/>vt no&longs;træ hypothe&longs;i hoc argumentum à marino æ&longs;tu petitum non prode&longs;t, <lb/>ita nec obe&longs;t: iam &longs;umus ergo pares. </s>

<s>In<lb/>telligantur duo corpora <lb/>A, D, vnum aureum, al<lb/>terum argenteum æque <lb/>grauia atque corona, <lb/>deinde trium corporum <lb/>ex aqua, magnitudine <lb/>æqualium, aureo &longs;cili<lb/>cet corpori vnum, alte<lb/>rum coronæ, tertium <lb/>corpori argenteo, inue<lb/>niantur grauitates, id autem poterit fieri facillime, &longs;i <expan abbr="accipiãtur">accipiantur</expan> duo <lb/>corpora vnum ex auro, alterum ex argento, grauitate quacunque, vt <pb pagenum="55"/>dictum e&longs;t in propo&longs;itionis octauæ exemplo, non enim nece&longs;&longs;e e&longs;t ha<lb/>bere duo corpora ex auro & argento, grauitatem habentia eandem <lb/>quam & corona, & hac de cau&longs;a diximus &longs;upra <expan abbr="intelligãtur">intelligantur</expan> duo cor<lb/>pora, non autem accipiantur. </s>

<s id="s.000507"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>&longs;it igitur primi corporis aquei æqualis <lb/>aureo A, inuenta grauitas G, &longs;ecundi vero æqualis coronæ B, graui<lb/>tas F, & tertij æqualis corpori argenteo D, grauitas H, & fiat vt dif<lb/>ferentia inter G, & H, ad EK, ita differentia inter G, & F, ad aliam <lb/>grauitatem, quæ &longs;it K. </s>

<s id="s.000508"> Merum effugium e&longs;t; cùm &longs;it vera & realis, vt aiunt, motus <lb/>inæqualitas; & vt ad tuam figuram veniam. </s>

<s>Dico K, grauitatem e&longs;&longs;e portionis argenti, <lb/>quod e&longs;t in corona, E vero grauitatem auri. </s>

<s>Vel &longs;i pro tertio proportionis termino &longs;umatur differentia inter F, <lb/>& H, & quartus terminus &longs;it E, Dico E, grauitatem e&longs;&longs;e portionis au<lb/>ri, K vero argenti. </s>

<s id="s.000509">Punctum E longè velociùs movetur, quàm F ; nam E in Ortum fertur, <lb/>vtroque motu, centri &longs;cilicet atque orbis, cùm tamen F toto quidem motu <lb/>centri feratur in Ortum, &longs;ed cum toto motu orbis feratur in Occa&longs;um, ex <lb/>vtriu&longs;que motus maxima oppo&longs;itione, motus ex vtroque mixtus maximè <lb/>retardatur, vt ex certi&longs;&longs;imis doctrinæ motuum principiis liquidò con&longs;tat. <lb/></s>

<s id="s.000510">Prætereà non tantùm aquarum excur&longs;io ex dicta motus inæqualitate &longs;eque<lb/>retur, verùm etiam alia, quæ facilè cadere po&longs;&longs;ent, reverà caderent, &longs;ive in <lb/>Ortum in maxima retardatione, &longs;ive in maxima acceleratione versùs Occa<lb/>&longs;um; & ad hoc eadem facit analogia tranantis cymbæ; vbi enim hæc ad li<lb/>tus appellitur, homines parum cauti, qui in illa &longs;unt, non versùs puppim re<lb/>pelluntur à littore, &longs;ed versùs proram proni ruunt; cymba enim retinet <lb/>fixa ve&longs;tigia, dum interim impetus ante impre&longs;&longs;us reliquum corpus an<lb/>tror&longs;um agit; in quo etiam aliquam rationem vectis ob&longs;ervo, hinc quo <lb/>altiores &longs;unt homines, in dicto ca&longs;u, faciliùs ruunt; quia vectis longior <lb/>e&longs;t; &longs;ed Augu&longs;tine, hoc minimè fieri videmus. </s>

<s>Quartus autem vtriu&longs;que proportionis terminus * minor e&longs;t<arrow.to.target n="note49"/> &longs;e<lb/>cundo EK, quod & tertius minor e&longs;t primo, primus enim terminus <lb/>e&longs;t differentia inter G, & H, tertius vero, vel e&longs;t differentia inter G, & <lb/>F, vel differentia inter F, & H, vterque minor primo. </s>

<s>Exemplis autem <lb/>res fiet illu&longs;trior. </s>

<s id="s.000511"><emph type="italics"/>Chry&longs;ocomus.<emph.end type="italics"/></s>

<s id="s.000512"> Hoc tuum argumentum, Antime, equidem ad homi<lb/>nem, vt aiunt, maximi momenti e&longs;t; nec video quonam pacto illi, qui <lb/>ex dicta inæqualitate motus, eiu&longs;modi aquarum excur&longs;iones &longs;e qui volunt, <pb pagenum="46" xlink:href="025/01/050.jpg"/>ab eo &longs;e&longs;e expediant; No&longs;tri tamen eo non vtuntur, vtpote qui &longs;ciant, <lb/>ex dicta inæqualitate, etiam &longs;uppo&longs;ita, minimè &longs;equi aquarum excur<lb/>&longs;iones, nempè eo motu &longs;ingulæ partes illius globi moventur, &longs;eu tardiùs, <lb/>&longs;eu velociùs, quo totius motus ratio illas moveri po&longs;tulàt; ac proinde il<lb/>lud globi punctum, quod ad Solem directè &longs;pectat de Meridie, tardè <lb/>movetur in Ortum, celeriter verò, vbi e&longs;t oppo&longs;itum in ip&longs;a media no<lb/>cte; quia totus globus ita moveri po&longs;tulat &longs;ingulas &longs;ui partes, imò etiam <lb/>in iis, quæ va&longs;e vehuntur, & ab extrin&longs;eco motum & impetum recipiunt, <lb/>inæqualitas motus non ex abrupto, at &longs;en&longs;im &longs;ine &longs;en&longs;u inducta nullum <lb/>alium effectum præter eandem rationem motus inducit; &longs;ic cymba qua <lb/>vehitur aqua celeri motu, &longs;i &longs;en&longs;im remittit, ac retardat motum, aut <lb/>certè tardiorem primum paulatim deinde accelerat, neque huc, neque <lb/>illuc aqua excurrit, nec &longs;tantes in navi huc aut illuc inclinari &longs;e &longs;entiunt. </s>

<s>Exemplum. </s>

<s id="s.000513"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000514"> Ita e&longs;t; vt dicis; hoc argumentum contra illos ad hominem, <lb/>vt aiunt, à me adductum e&longs;t, qui præfatos effectus ex illa motuum inæ<lb/>qualitate &longs;equi a&longs;&longs;erunt; at per te, mihi quæ&longs;o, liceat, idem argumen<lb/>tum etiam contra illos pro&longs;equi & vrgere, vt aiunt, qui negant dictos <lb/>effectus ex dicta inæqualitate &longs;equi, quorum ego; vt vereor &longs;en&longs;a, ita <lb/>illis, opinor, ingratum non accidet, quod rem hanc paulò accura<lb/>tiùs di&longs;cutiam, & ad certi&longs;&longs;ima doctrinæ motuum principia reducam; <lb/>Primò ergo quidem &longs;uppono ex dicta doctrina, impetum &longs;emel impre&longs;<lb/>&longs;um non de&longs;trui, quamdiu fru&longs;trà non e&longs;t, & con&longs;equi pote&longs;t &longs;uum ef<lb/>fectum, &longs;cilicet motum, qui & finis illius e&longs;t, &longs;eu per eandem lineam, <lb/>&longs;eu per aliam, ad quam e&longs;t nova determinatio; nulla enim e&longs;t alia ratio, <lb/>propter quam impetus de&longs;truatur; &longs;ic turbo v.g. di&longs;cus æneus, Axe vtrim<lb/>que extante, in levigato plano diuti&longs;&longs;imè &longs;uos orbes agit, & &longs;i nullus <lb/>e&longs;&longs;et attritus partium, & Axis ad perfectam libellam, per di&longs;ci centrum <lb/>iret, nunquam hic motus ce&longs;&longs;aret. </s>

<s id="s.000515">Prætereà, &longs;i globus tornatus de&longs;cen<lb/>dat per planum declive probè lævigatum, quod po&longs;t tantulam incurvatio<lb/>nem &longs;ur&longs;um ex adver&longs;o, &longs;ub eodem inclinationis angulo deflectatur; haud <lb/>dubiè ad imum primi plani declivis globus non &longs;i&longs;tet, &longs;ed per aliud ad <lb/>æqualem ferè altitudinem a&longs;cendet, virtute impetus, in primo de&longs;cen&longs;u <lb/>acqui&longs;iti, ad hanc portò lineam ab eodem plano determinatur; analo<lb/>giam perfectam in vibrato funependulo etiam habes, & in ip&longs;a corporum <lb/>repercu&longs;&longs;ione; de&longs;truitur tamen aliquid impetus in illo a&longs;cen&longs;u, &longs;cilicet <lb/>à quodam impetu innato, non acqui&longs;ito, qui gravibus ine&longs;t, &, vt fa<lb/>cilè vobis per&longs;uaderem, ab ip&longs;a gravitate non di&longs;tinguitur; &longs;ic etiam ab <lb/>alio impetu ob&longs;tante, vel ad aliam lineam trahente, vnde &longs;equitur de<lb/>terminatio quædam mixta, &longs;en&longs;im de&longs;truitur; &longs;ed ne longiùs excurram, <lb/>illa omnia doctrinæ motuum principia hoc loco dumtaxat &longs;upponam, quæ <lb/>huius doctrinæ petiti facilè concedunt, & fusè alibi pertractata nec non <lb/>firmata fuêre. </s>

<s id="s.000516">Primo igitur loco &longs;uppono, impetum nunquam de&longs;trui, <lb/>ni&longs;i quando e&longs;t fru&longs;trà, id e&longs;t, quando motus omnis impeditur, à quo<lb/>cunque tandem &longs;it ille impetus, &longs;ive impre&longs;&longs;us ab extrin&longs;eco, &longs;ive ab ip&longs;o <lb/>corpore in &longs;e productus, &longs;ive à toto, parti, &longs;ive toti à parte, &longs;ive parti ab alia <lb/>parte, nam perinde e&longs;t, quoad hoc principium. </s>

<s><emph type="italics"/>Sit coronæ grauitas<emph.end type="italics"/> 95, <emph type="italics"/>lib.

& oporteat facere quod imperatum e&longs;t. </s>

<s id="s.000517"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s><lb/>Intelligantur duo corpora, vnum aureum, alterum argenteum, æque <lb/>grauia atque corona, deinde trium corporum ex aqua, magnitudine <lb/>æqualium, aureo &longs;cilicet corporivnum, alterum coronæ, tertium cor<lb/>pori argenteo, inueniantur grauitates, vt in exemplo prop.<emph.end type="italics"/> 8. <emph type="italics"/>dictum <lb/>est, quæ &longs;int primi nimirum corporis aquei<emph.end type="italics"/> 5, <emph type="italics"/>&longs;ecundi vero 6, & terty<emph.end type="italics"/><lb/>9 6/31, <emph type="italics"/>& fiat vt differentia inter<emph.end type="italics"/> 5, & 9 6/32, <emph type="italics"/>hoc e&longs;t vt<emph.end type="italics"/> 4 6/31, <emph type="italics"/>ad<emph.end type="italics"/> 95, <lb/><emph type="italics"/>grauitatem videlicet coronæ, ita differentia inter<emph.end type="italics"/> 5, & 6, <emph type="italics"/>hoc est 1, ad<emph.end type="italics"/><lb/>22 17/26, <emph type="italics"/>ergo<emph.end type="italics"/> 22 17/26, <emph type="italics"/>erit grauitas portionis argenti quod est in coro<lb/>na, qua detracta ex totali grauitate coronæ, reliquum<emph.end type="italics"/> 72 9/26, <emph type="italics"/>erit <lb/>grauitas portionis auri.<emph.end type="italics"/></s>

<s id="s.000518"> Hoc facilè damus, imò hoc pro generali axiomate libenter <lb/>admitto, nihil vnquam de&longs;trui, ni&longs;i quando e&longs;&longs;e non pote&longs;t, ni&longs;i fru&longs;trà <lb/>&longs;it. </s>

<s id="s.000519">Sic anima, quæ defectu corrupti organi non pote&longs;t ampliùs operari <lb/>in corpore, de&longs;init e&longs;&longs;e, omninò quidem, &longs;i extrà organum operari <lb/>non pote&longs;t, vt de animabus brutarum animantium Philo&longs;ophi docent, non <lb/>tamen omninò & ab&longs;olutè, &longs;ed in corpore tantùm, &longs;i extrà organum opera<lb/>ri pote&longs;t, vt anima rationalis. </s>

<s><emph type="italics"/>Vel &longs;i pro tertio proportionis termino &longs;umatur differentia inter<emph.end type="italics"/> 6, <lb/>& 9 6/31, <emph type="italics"/>quæ e&longs;t<emph.end type="italics"/> 3 6/31, <emph type="italics"/>quartus terminus<emph.end type="italics"/> 72 9/26, <emph type="italics"/>erit grauitas por<lb/>tionis auri, quæ &longs;i dematur ex totali grauitate coronæ, remanebit<emph.end type="italics"/><lb/>22 17/26, <emph type="italics"/>pro grauitate portionis argenti.<emph.end type="italics"/></s>

<s>Exemplum. </s>

<s id="s.000520"><emph type="italics"/>Chry&longs;ec.<emph.end type="italics"/></s>

<s id="s.000521"> Hoc idem principium ad alias qualitates etiam extendi pote&longs;t; <lb/>caloris v.g. frigoris, &c. </s>

<s id="s.000522">quæ quamdiu &longs;uum finem con&longs;equi, & præ&longs;ta<lb/>re effectum po&longs;&longs;unt, in &longs;ubjecto, cui inhærent, tamdiu in eo permanent <lb/>intactæ; vt &longs;i per actionem qualitatis contrariæ novus effectus inducitur, <lb/>ac proinde, vel totus prior, vel pars illius de&longs;init, tunc prima illa qualitas <lb/>in &longs;ubjecto illo fru&longs;tra e&longs;&longs;e dicitur, ac proinde vel &longs;ecundùm &longs;e totam, <lb/>&longs;i totus effectus abactus e&longs;t, vel &longs;ecundùm &longs;ui partem, pro rata effectus <lb/>de&longs;tructi, e&longs;&longs;e de&longs;init. </s>

<s><emph type="italics"/>Sit aliquod corpus mistum ex auro. </s>

<s id="s.000523"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>& ære, & habeat grauitatem <lb/>171. lib.

<s id="s.000524"> Ad &longs;peciem hæc fortè cuipiam vera e&longs;&longs;e videntur; at profectò <lb/>res &longs;ecus &longs;e habet in præfatis qualitatibus, de quibus modò di&longs;putatio <lb/>in&longs;tituta non e&longs;t, &longs;atis mihi e&longs;t, &longs;i in no&longs;tro impetu res ita &longs;e habeat; ad<lb/>mitto etiam ea, quæ dixi&longs;ti, Augu&longs;tine, de anima rationali; de brutorum <lb/>animabus aliqua fortè difficultas e&longs;&longs;et, &longs;ed huius loci non e&longs;t. </s>

<s id="s.000525">Sit igitur <lb/>&longs;ecundum principium ex eadem doctrina motuum huc derivatum, cor<lb/>pus eo motu movetur, quo faciliùs moveri pote&longs;t, minore &longs;cilicet &longs;um<lb/>ptu, & cum minore difficultate, compen&longs;atque vt plurimum in vno, <lb/>quod in alio difficiliùs tantùm obtinere po&longs;&longs;et; hæc iam &longs;upra indicavi in <lb/>primo congre&longs;&longs;u; &longs;ic cylindrus, vel in plano lævigato iacens, vel humido <lb/>innatans ab altera extremitate pul&longs;us, vel tractus etiam per lineam per<lb/>pendiculariter incidentem, motu recto non movetur. </s>

& oporteat inuenire quanta erit portio æris in ip&longs;o corpore,<emph.end type="italics"/><pb pagenum="56"/><emph type="italics"/>& quanta auri. </s>

<s id="s.000526">&longs;ed circulari, circa <lb/>centrum, quod terminat mediam proportionalem totam inter & dimi<lb/>diam, ita vt major quantitas &longs;it versùs illam extremitatem, cui potentia <lb/>motrix applicata e&longs;t. </s>

<s>Intelligantur duo corpori, vnum ex auro puro, al<lb/>terum ex ære, æque grauia atque corpus mistum, & trium corporum <lb/>ex aqua, quorum vnum &longs;it æquale corpori aureo magnitudine, alte<lb/>rum misto, tertium aureo, inueniantur grauitates, vt in exemplo pro<lb/>po&longs;.<emph.end type="italics"/>8.<emph type="italics"/>dictum est, quæ &longs;int<emph.end type="italics"/> 9, 11, <emph type="italics"/>& 19, & fiat vt differentia inter<emph.end type="italics"/> 9, & <lb/>19, <emph type="italics"/>ad<emph.end type="italics"/> 171, <emph type="italics"/>grauitatem videlicet corporis misti, ita differentia inter<emph.end type="italics"/><lb/>9, & 11, <emph type="italics"/>ad<emph.end type="italics"/> 34 1/5, <emph type="italics"/>portio igitur corporis mi&longs;ti ærea grauitatem babebit<emph.end type="italics"/><lb/>34 1/5, <emph type="italics"/>quæ &longs;i auferatur ex totali corporis misti grauitate, remanebit<emph.end type="italics"/><lb/>136 4/5, <emph type="italics"/>pro grauitate portionis auri.<emph.end type="italics"/></s>

<s id="s.000527"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s><emph type="italics"/>Vel &longs;i pro tertio proportionis termino &longs;umatur differentia inter<emph.end type="italics"/> 11, <lb/><emph type="italics"/>& 19, quartus terminus<emph.end type="italics"/> 136 4/5, <emph type="italics"/>erit grauitas portionis auri, qua ab<lb/>lata ex totali corporis mi&longs;ti grauitate, reliquum<emph.end type="italics"/> 34 1/5, <emph type="italics"/>dabit grauita<lb/>tem portionis æreæ.<emph.end type="italics"/></s>

<s id="s.000528"> Licèt fortè in parergum incidamus, tantulum &longs;chematis de<lb/>&longs;idero, vt rem à te &longs;olo auditam meliùs intelligam. </s>

<s>At vero huiu&longs;modi ratio cinationem ad di&longs;cernendum ar<lb/>gentum ab auro, vel aliud metallum ab altero metallo, recte <lb/>e&longs;&longs;e in&longs;titutam, &longs;equenti Theoremate demon&longs;trabitur. </s>

<s id="s.000529"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>THE OREMA X. PROPOS. XIX.</s>

<s id="s.000530"> Non opus e&longs;t alio &longs;chemate: Supponamus enim cylindrum <lb/>BC (<emph type="italics"/>in Fig. pag.<emph.end type="italics"/>45.) innatantem humido, pul&longs;um in B, &longs;itque vt BC <lb/>ad BK, ita hæc ad BA, & ex K ducantur arcus BG, CN &longs;imiles, duca<lb/>turque GKN; cylindrus pul&longs;us, vt dixi ex B, de&longs;cribit &longs;uo motu duos <lb/>&longs;ectores BKG, CKN, quia &longs;cilicet &longs;patium vtroque contentum e&longs;t om<lb/>nium po&longs;&longs;ibilium minimum, &longs;uppo&longs;ito quolibet alio arcu, non minore <lb/>BG, & duobus radiis, qui &longs;imul coniuncti &longs;int æquales toti BC, quod <lb/>aliàs demon&longs;traui, nempe à &longs;ectoribus &longs;imilibus ad triangula propor<lb/>tionalia, & ab his ad &longs;implicem lineam gradum faciens, reduxi rem ad <lb/>hoc problema, datam quantitatem ita &longs;ecare, vt maius &longs;egmentum &longs;it <lb/>ad minus, vt hoc ad tertium, & compo&longs;ita ex duabus extremis &longs;it om<lb/>nium po&longs;&longs;ibilium minima; vel &longs;ic Datæ quantitati vnam partem detra<lb/>here, & aliam addere, vt re&longs;idua &longs;it ad detractam, vt detracta ad addi-<pb pagenum="48" xlink:href="025/01/052.jpg"/>tam, & compo&longs;ita ex re&longs;idua, & addita &longs;it omnium po&longs;&longs;ibilium minima; <lb/>&longs;ed his omi&longs;&longs;is & &longs;uppo&longs;itis, eo motu hic cylindrus, atque adeò c&oelig;teris <lb/>paribus, quodlibet corpus movetur, &longs;ive ab intrin&longs;eco, &longs;ive ab extrin<lb/>&longs;eco, quo faciliùs moveri pote&longs;t; idem ob&longs;ervamus in &longs;agittis alii&longs;que <lb/>corporibus oblongis, &longs;i vel aliquando &longs;ponte &longs;ua cadunt, vel projiciun<lb/>tur; &longs;ed luculentum exemplum omittere non po&longs;&longs;um, globi &longs;cilicet per <lb/>planum declive de&longs;cendentis, cùm enim duobus modis deor&longs;um ferri <lb/>po&longs;&longs;it. </s>

<s id="s.000531">Primò vno dumtaxat motu centri, quo &longs;ingulæ partes per lineas <lb/>plano inclinato parallelas eant. </s>

<s>Si trium corporum æque grauium primum & ter<lb/>tium fuerint generis diuer&longs;i, &longs;ecundi autem portio <lb/>fuerit eiu&longs;dem generis cum corpore primo, reliqua ve<lb/>ro eiu&longs;dem generis cum corpore tertio, fuerint etiam <lb/>tres quantitates aquæ prædictis corporibus æquales, pri<lb/>ma videlicet corpori primo, &longs;ecunda &longs;ecundo, & tertia <lb/>tertio. </s>

<s id="s.000532">Secundo motu rotationis, mixto &longs;cilicet <lb/>ex motibus centri & orbis; hoc &longs;ecundo modo movetur, non verò pri<lb/>mo, quem multus partium affrictus maximoperè retardaret. </s>

<s>erit vt differentia grauitatum primæ & tertiæ <lb/>quantitatis aquæ, ad grauitatem corporis &longs;ecundi, ita <lb/>differentia grauitatum primæ & &longs;ecundæ quantitatis <lb/>aquæ, ad grauitatem portionis corporis &longs;ecundi, quæ e&longs;t <lb/>eiu&longs;dem generis cum corpore tertio. </s>

<s id="s.000533"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/> Hæc concedere non po&longs;&longs;um; ideò enim movetur hoc motu, <lb/>quia cùm centrum gravitatis globi &longs;it extra perpendiculum, quid mirum, &longs;i <lb/>eò inclinet, vnde motus orbis nece&longs;&longs;ariò &longs;equitur; vt facilè etiam &longs;ine <lb/>figura quivis intelligat? </s>

<s>Et ita differentia grauitatum &longs;ecundæ & tertiæ quan <lb/>titatis aquæ, ad grauitatem portionis eiu&longs;dem generis <lb/>cum corpore primo. </s><pb pagenum="57"/>

<s>SINT tria corpora æque grauia A, BC, D, quorum A, primum, <lb/>& tertium D. &longs;int generis diuer&longs;i, portio vero &longs;ecundi B, &longs;it eiu&longs;dem <lb/>generis cum corpore A, & portio C, ein&longs;dem generis cum corpore <lb/><figure id="fig17"/><lb/>D, &longs;int etiam alia tria <lb/>corpora aquea P, OL, <lb/>& Q, <expan abbr="quor&utilde;">quorum</expan> <gap/>, &longs;it æqua<lb/>le corpori A, magnitu<lb/>dine, ip&longs;um vero OL, <lb/>æquale corpori BC, & <lb/>ip&longs;um Q, æquale cor<lb/>pori D, & &longs;int earum <lb/>grauitates, G, ip&longs;ius P, <lb/>& FV, ip&longs;ius OL, & H, <lb/>ip&longs;ius <expan abbr="q.">que</expan> Dico vt diffe<lb/>rentia granitatum G, <lb/>H, ad grauitatem cor<lb/>poris BC, ita e&longs;&longs;e diffe<lb/>rentiam grauitatum <lb/>G, FV, ad grauitatem <lb/>portionis C; & ita differentiam grauitatum FV, H, ad portionis B, <lb/>grauitatem. </s>

<s id="s.000534"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000535"> Nonnihil tamen figuræ adhibeo, vt maximam difficultatem, <lb/>quam ego quidem &longs;entio, in eo, quod dicis, mihi excutias. </s>

<s>Sit enim portionis B, grauitas E, & portionis C, gra<lb/>uitas K; ergo totius corporis BC grauitas erit EK, &longs;i<gap/><expan abbr="q;">que</expan> portionis O, <lb/>quæ &longs;it æqualis portioni B, grauitas F, ergo reliquæ portionis L, <lb/><gap/>qualis portioni C, grauitas erit V, Quoniam igitur e&longs;t, vt A, ad P, <lb/>ita B, ad O, æquale videlioet ad æquale, erit permutando, vt A, ad B, <lb/>ita p.ad O, & quoniam &longs;unt eiu&longs;dem generis A, B, fimiliter & P, O, <lb/>* erit vt grauitas corporis A, hoc e&longs;t vt EK, (ponuntur enim<arrow.to.target n="note50"/> cor<lb/>pora A, BC, D, æque grauia,) ad E, ita G, ad F, quod igitur fit ex EK, <lb/>& F, nempe ex extremis, æquale erit ei, quod fit ex E, & G, hoc eft <lb/>ex medijs. </s>

<s><margin.target id="note50"/>4.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s id="s.000536">Sit planum inclinatum DH, & in eo <lb/>globus gravis, tangens planum in D, per<lb/>pendicularis AF, à centro globi ducta; <lb/>&longs;intque aliæ duæ lineæ BAG, CI, plano <lb/>parallelæ, de&longs;cendit globus A, vt dixi, <lb/>non quidem primo modo, ita vt punctum <lb/>C &longs;equatur lineam CI, & punctum D <lb/>lineam DH. </s>

<s>Similiter quoniam e&longs;t, vt D, ad Q, ita C, ad E, æquale videlicet ad <lb/>æquale, erit permutando, vt D, ad C, ita Q, ad L, & quoniam &longs;unt <lb/>eiu&longs;dem ge net is D, C, &longs;imiliter & Q, L, * erit vt grauitas ip&longs;ius D,<arrow.to.target n="note51"/><lb/>hoc e&longs;t vt EK, ad K, ita H, ad V; quare quod fit ex EK, & V, ex extre<lb/>mis, æquabitur ei, quod ex H, fit & K, ex medijs. </s>

<s id="s.000537">Sed per rotationem, vt <lb/>aiunt, ita vt circa centrum A, aliæ par<lb/>tes moveantur, quia, inquis, centrum <lb/>globi A e&longs;t extra perpendiculum; de quo amabò perpendiculo intelligis <gap/><lb/>an de BD ducto à puncto contactus, an verò de AF. </s>

<s><margin.target id="note51"/>4.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s id="s.000538"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>Sed o&longs;ten&longs;um e&longs;t id quod ex EK, fit & F. æquale e&longs;&longs;e ei quod fit ex <lb/>G, & E, ergo quo<gap/> fit ex EK, & F, vna cum eo, quod ex BK, & V, hoc <lb/>e&longs;t id quod fit ex EK, & FV, æquale erit ei quod ex G, fit & E, vna <lb/>eum eo quod ex H, & K, &longs;ed quod ex G, fit & E, æquale e&longs;t ei quod fit <lb/>ex G, & EK, minus eo quod ex G, & K, quod enim additur, idem & <pb pagenum="58"/>minuitur; ergo quod fit ex EK, & FV. æquale erit ei quod fit ex G, & <lb/>EK, vna cumeo quod ex H, & K, minus eo quod fit ex G, & K. aufe<lb/>ratur vtrinque id quod fit ex G, & EK, quod igitur fit ex FV, & EK, <lb/><figure id="fig18"/><lb/>minus eo quod ex G, & <lb/>EK, æquabitur ei quod <lb/>ex H, & K, minus eo <lb/>quod fit ex G, & K, &longs;ed <lb/>quod fit ex H, & K, <lb/>minus eo quod fit ex <lb/>G, & K, æquale e&longs;t ei <lb/>quod ex differentia ip<lb/>&longs;arum H, G, fit & K, <lb/>&longs;imiliter, & quod fit ex <lb/>FV, & EK, minus eo <lb/>quod ex G, & EK, <lb/>æquale e&longs;t ei quod ex <lb/>differentia ip&longs;arum <lb/>FV, G, fit & EK, ergo <lb/>quod ex differentia <lb/>ip&longs;acum H, G, fit & K, æquale erit ei quod ex differentia ip&longs;arum <lb/>FV, G, fit & EK; æqualitatem ad proportionem reuocando, erit vt <lb/>differentia grauitatum. </s>

<s id="s.000539"> Vtrumque intelligo; vt enim globus &longs;u&longs;tineatur in plano <lb/>DH, perpendiculum, quod ducitur a puncto contactus B, per centrum <lb/>A ite deberet; vnde certè planum e&longs;&longs;et horizonti parallelum; quando <lb/>verò vnum perpendiculum cum alio non concurrit, vt in hoc ca&longs;u, <lb/>tunc planum e&longs;t inclinatum; igitur cùm centrum A per lineam perpendi<lb/>cularem AE non &longs;u&longs;tineatur à plano, vlteriùs enim ad F pertingit, de&longs;cen<lb/>dat nece&longs;&longs;e e&longs;t, cùm de&longs;cendere po&longs;&longs;it; in aliis omnibus corporibus, per<lb/>fectam analogiam habes. </s>

<s id="s.000540">Sit enim planum horizontale CN, & in eo <lb/><figure id="id.025.01.052.2.jpg" xlink:href="025/01/052/2.jpg"/><lb/>rectangulum CB, cuius centrum gravitatis F, ita <lb/>inclinetur rectangulum CB, donec perveniat ad <lb/>&longs;itum DI, exi&longs;tente centro gravitatis in H, ac <lb/>proinde cùm perpendiculam HL cadat extrà <lb/>punctum contactus D, deor&longs;um tendit, & to<lb/>tum rectangulum ruit. </s>

<s>H, G, ad grauitatem EK, ita differentia <lb/>grauitatum FV, G, ad graui<gap/> tom K, quod erat primo loco: demon<lb/>&longs;trandum. </s>

<s id="s.000541">Idem prorsùs de globo <lb/>dicendum e&longs;t. </s>

<s>Dico quoque vt differentia grauitatum H, G, ad grauitatem EK, <lb/>ita e&longs;&longs;e differenti <gap/> grauitatum H, FV, ad grauitatem E. </s>

<s id="s.000542"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>Quoniam <lb/>enim o&longs;ten&longs;um e&longs;t, quod fit ex EK, & FV, æquale e&longs;&longs;e ei quod ex G. fit <lb/>& E, vna cum eo quod ex H, & K; quod autem fit ex H, & K, æquat<gap/><lb/><gap/>i quod, ex H, fit & EK, minus eo quod ex H, & E, quod onim additur <lb/>idem & minuitur: ergo quod fit ex EK, & FV, æquale erit ei quod fit <lb/>ex H, & EK, vna cum eo quod ex G, & E, minus eo quod ex H, & E. <lb/>addatur vtrin que quod ex H, fit & E, & &longs;ubducantur ea quæ fiunt ex <lb/>G, & E, & ox EK, & FV; quod igitur fit ex H, & E, minus eo quod ex <lb/>G, & E, æquabitur ei quod ex H, fit & EK, minus eo quod ex FV, & <lb/>EK, &longs;ed quod fit ex H, & E, minus eo quod ex G, & E, æquale e&longs;t ei <lb/>quod ex, differ entia ip&longs;arum H, G, fit & E, &longs;imiliter, & quod ex H, fit <lb/>& EK, minus eo quod ex FV, & EK, æquale e&longs;t eiquod ex differentia <lb/>ip&longs;arum H, FV, fit & EK; ergo quod ex differentia ip&longs;arum H, G, fit <lb/>& E, æquabitur ei quod ex differentia ip&longs;arum H, FV, fit & EK; qua<lb/>re æqualitatem ad <expan abbr="proportion&etilde;">proportionem</expan> reuocando erit v<gap/> differen tia graui<pb pagenum="59"/>tatum H, G, ad grauitatem EK, ita differentia gra<gap/>tatum H, FV, <lb/>zd grauitatem E. quod &longs;ecundo loco fuit demon&longs;trandum. </s>

<s id="s.000543"> Crede mihi, Augu&longs;tine, multi &longs;æpè <lb/>ac &longs;æpiùs paralogi&longs;mis, & fal&longs;is præoccupatio-<pb pagenum="49" xlink:href="025/01/053.jpg"/>nibus abripi &longs;e &longs;inunt, quod in præ&longs;enti ca&longs;u, meo &longs;altem iudicio, acci<lb/>dit; vt enim in tua &longs;i&longs;tamus figura; non negabis, opinor, centrum H <lb/>minimè de&longs;cen&longs;urum, &longs;i fortè propiùs ad planum CN accedere non po&longs;<lb/>&longs;et, cùm ex ip&longs;is terminis idem &longs;it de&longs;cendere, & propriùs ad planum DN <lb/>accedere; At verò centrum A (<emph type="italics"/>in Figura perultima<emph.end type="italics"/>) propiùs ad planum in cli<lb/>natum DH accedere non pote&longs;t, à quo æquali &longs;emper di&longs;tantiæ men&longs;ura <lb/>di&longs;tat, &longs;cilicet radio, vnus autem radius alteri æqualis e&longs;t; hinc nunquam <lb/>di&longs;cedit à linea AG parallela Plano DH, & quodlibet perpendiculum ad <lb/>planum terminatum à centro A ductum lineæ AF æquale e&longs;t. </s>

<s>Alia breuior Theorematis demon&longs;tratio. </s>

<s id="s.000544"><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s>

<s>RESVMATVR eadem figuta vt &longs;upra. </s>

<s id="s.000545"> Proptereà globus de&longs;cendit, quia eius centrum A non <lb/>&longs;u&longs;tinetur in puncto contactus, cùm &longs;u&longs;tineri non po&longs;&longs;it ni&longs;i in perpen<lb/>diculo AF. </s>

<s>Qhoniam igitur <lb/>corpus D, æquale e&longs;t corpori Q, magnitudine, & portio C, æqualis <lb/>portioni Lerit vt D, ad Q, ita C, ad L, & permutando vt D, ad C, ita <lb/>Q, ad L, & quoniam eiu&longs;dem &longs;unt genoris D, C, &longs;imiliter & Q, L, * erit<arrow.to.target n="note52"/><lb/>vt grauitas corporis D, hoc e&longs;t vt EK; ad K, ita H, ad V. </s>

<s id="s.000546"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s><margin.target id="note52"/>4.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s id="s.000547"> Rectè, Proptereà globus de&longs;cendit; &longs;ed profectò non pro<lb/>pterea globus volvitur, &longs;ive enim volvatur deor&longs;um, &longs;ive de&longs;cendat iux<lb/>ta primum modum in &longs;itu, in quo e&longs;t, centrum A per eandem lineam <lb/>AG, deor&longs;um tendit, nec vnquam ab ea di&longs;cedit, aut di&longs;cedere pote&longs;t; <lb/>cur igitur cum vtroque modo, per eandem lineam de&longs;cendere po&longs;&longs;it, hoc <lb/>&longs;ecundo potiùs, quàm illo primo de&longs;cendit? </s>

<s id="s.000548">quod enim dicis, Augu&longs;ti<lb/>ne, centrum gravitatis A e&longs;&longs;e extra perpendiculum, ac proptereà de&longs;<lb/>cendere, id totum verum e&longs;t, & à me admittitur, vndè reverà de&longs;cen<lb/>dit; &longs;ed per lineam AG, infrà quam de&longs;cendere nequit ; &longs;ed cùm per eam <lb/>vtroque modo ire po&longs;&longs;it, ac proinde de&longs;cendere, cur, quæ&longs;o, vno <lb/>potiùs quàm alio? </s>

<s>Similiter quoniam ponuntur æqualia magnitudine corpora A, P, <lb/>& æquales quoque portiones B, O, erit vt A, ad P, ita B, ad O, & per<lb/>mutando vt A, ad B, ita P, ad O, &longs;ed eiu&longs;dem &longs;unt generis A, B, &longs;imili<lb/>ter & P, O, * vt igitur grauitas corporis A, id e&longs;t vt EK, ad E, ita erit<arrow.to.target n="note53"/><lb/>G, ad F, & per conuer&longs;ionem rationis erit vt EK, ad K, ita G, ad G, <lb/>minus F, &longs;ed demon&longs;tratum e&longs;t, vt EK, ad K, ita e&longs;&longs;e H, ad V, ergo vt <lb/>H, ad V, ita erit G, ad G, minus F, & permutando vt H, ad G, ita V, <lb/>ad G, minus F, & diuidendo vt H, minus G, ad G, ita erit FV, minus <lb/>G, ad G, minus F, rur&longs;us permutando erit vt H, minus G, ad FV, mi<lb/>nus G, ita G, ad G, minus F, &longs;ed vt EK, ad K, ita e&longs;t G, ad G, minus F, <lb/>vt e&longs;t demon&longs;tratum, ergo vt H, minus G, ad FV, minus G, ita erit <lb/>EK, ad K, quare permutando vt H, minus G, ad EK, ita erit FV, mi<lb/>nus G, ad K, quod e&longs;tò primum. </s>

<s id="s.000549">Sed hoc alio exemplo fortè luculentiore clari&longs;&longs;imè <lb/>o&longs;tendo. </s>

<s><margin.target id="note53"/>4.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s>Dico quoque vt H, minus G, ad EK, ita e&longs;&longs;e H, minus FV, ad E. </s>

<s id="s.000550">Sit planum inclinatum AB, &longs;it rectan<lb/>gulum C in eo collocatum; certè &longs;i &longs;up<lb/>ponatur vtrumque lævigatum, de&longs;cen<lb/>det rectangulum, per dictum planum, <lb/>ibitque centrum gravitatis C per CP <lb/>parallelam plano; nec enim aliter per &longs;e <lb/>de&longs;cendere pote&longs;t, nec volvi circa angu<lb/>lum D, quod fieri deberet, vt <gap/>iueret; <lb/>alioquin centrum C in revolutione a&longs;cen<lb/>deret, quod dici non pote&longs;t; <gap/>Sit enim <lb/>CD perpendiculum, & CN horizontalis, haud dubie &longs;i C volvatur <lb/>circa D, radio DC, tangens decta à puncto C, perpendicularis in <lb/>CD, ibit &longs;uprà horizontalem CN, vt patet ad oculum: Dixi per &longs;e, <lb/>nam per accidens, cùm à plani &longs;cabutie impediri po&longs;&longs;it, latus AD, &longs;u<lb/>perior p<gap/>o quæ libera e&longs;t, impetus vi acqui&longs;iti, prævalens, deor<lb/>&longs;um circum volvitur circa angulum D ; &longs;ed hoc per accidens fit. </s>

<s id="s.000551">Sit autem <lb/>aliud rectangulam F in eodem plano in<gap/>linato, perpendiculum, FH, ho<lb/>rizontalis FO; certè &longs;i ducatur tangens FK perpendicularis<gap/> MF; &longs;i <lb/>centium F circa M radio MF volvatur, ibit infra FO, igitur non a&longs;cen<gap/><lb/>det &longs;ed de&longs;cendet. </s>

<s><lb/>Quoniam enim o&longs;ten&longs;um e&longs;t vt EK, ad K, ita e&longs;&longs;e H, ad V, erit per <lb/>conuer&longs;ionem rationis vt EK, ad E, ita H, ad H, minus V, &longs;ed demon<lb/>&longs;tratum e&longs;t vt EK, ad E, ita e&longs;&longs;e G, ad F, ergo vt H, ad H, minus V, ita <lb/>erit G, ad F, & permutando vt H, ad G, ita H, minus V, ad F, & diui<lb/>dendo vt H, minus G, ad G, ita erit H, minus FV, ad F, & permutan<lb/>do vt H, minus G, ad H, minus FV, ita G, ad F, &longs;ed vt EK, ad E, ita e&longs;t <lb/>G, ad F, vt e&longs;t demon&longs;tratum, ergo vt H, minus G, ad H, minus FV, <lb/>ita erit EK, ad E, quare permutando, erit vt H, minus G, ad EK, ita <lb/>H, minus FV, ad E, quod erat &longs;ecundo loco demon&longs;trandum. </s>

<s id="s.000552">itaque vt ad no&longs;t<gap/> globum redeat or<gap/>atio cùn. </s>

<s id="s.000553">nec <lb/>circa punctum D volvi po&longs;&longs;it centrum A, (<emph type="italics"/>in Figura antipe<gap/>ima<emph.end type="italics"/>) ni&longs;i in-<pb pagenum="50" xlink:href="025/01/054.jpg"/>frà rectam AG de&longs;cendat, nec ab hac po&longs;&longs;it di&longs;cedere; certè non ideò <lb/>globus volvitur, vt centrum A de&longs;cendat, cùm de&longs;cendere po&longs;&longs;it, etiam&longs;i <lb/>non volvatur; igitur ideò volvitur, &longs;eu rotatur, quia cum vtroque modo <lb/>de&longs;cendere valeat centrum A, per eandem &longs;cilicet lineam AG, & cùm pri<lb/>mo modo difficiliùs de&longs;cendat, propter affrictum partium; ideò &longs;ecundo <lb/>modo de&longs;cendit, quia &longs;ic faciliùs de&longs;cendit; &longs;ic enim corpus grave non mo<lb/>do determinatum e&longs;t ad motum, &longs;ed etiam ad faciliorem, cæteris paribus, <lb/>motum. </s>

<s>Svpere&longs;t igitur vt dicamus, qua ratione ex grauitate aúri <lb/>cogno&longs;ci po&longs;&longs;it eius qualitas; id quod ex ijs, quæ dicta <lb/>&longs;unt facilè colligitur; &longs;i videlicet nota fiat cuiu&longs;uis ma&longs;&longs;æ auri <lb/>grauitas, quam habet tum in aere, tum in aqua. </s>

<s>Sed ante <lb/>omnia, duo nobis &longs;unt præmittenda, & explicanda. </s>

<s id="s.000554"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000555"> Audivi hactenus, in rotis valere rationem vectis; e&longs;t enim <lb/>vectis quidam perpetuus; vnde manife&longs;ta petitur ratio, cur majoribus <lb/>rotis currus in&longs;truantur; nempe inde cre&longs;cit mechanicæ potentiæ mo<lb/>mentum. </s>

<s>nimirum <lb/>quid &longs;it aurum 24. partium, &longs;eu (vt vulgo dicitur) di 24. ca<pb pagenum="60"/>ratti, quidue pauciorum, hoc e&longs;t penes quid attendatur di <lb/>uer&longs;a auri qualitas. </s>

<s>Deinde quomodo aurum alligent Auri <lb/>fices, vel alij ad quos alligandi officium &longs;pectat. </s>

<s id="s.000556"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000557"> Quis negat, in rotis haberi rationem vectis in vecte tamen &longs;up<lb/>ponitur aliquod punctum qua&longs;i immobile, quod in ip&longs;o Hypomoclio col<lb/>locatur; quod vt meliùs intelligatur. </s>

<s>His enim <lb/>cognitis, non erit difficile, id quod proponitur, certa aliqua <lb/>ratione, a&longs;&longs;equi. </s>

<s><emph type="italics"/>Aurum igitur<emph.end type="italics"/> 24. <emph type="italics"/>partium appellatur aurum purum, pauciorum <lb/>vero dicitur non purum, &longs;ed aliquo alio metallo, vel pluribus affe<lb/>ctum. </s>

<s id="s.000558">Supponatur planum DH e&longs;&longs;e horizon<lb/>tale, in quo &longs;it rota, eaque trahatur fune <lb/>AG, in&longs;erto &longs;cilicet axe per <expan abbr="centr&utilde;">centrum</expan> illius <lb/>A, haud dubiè &longs;i æquè facile <expan abbr="vtraq;">vtraque</expan> extre<lb/>mitas diametri rotæ DC adduci po&longs;&longs;et à <lb/>potentia trahente per AG vtraque extre<lb/>mitas, ac proinde reliquæ omnes partes <lb/>rotæ per parallelas AG adducerentur, & <lb/>omnes æquè citò <expan abbr="mover&etilde;tur">moverentur</expan>, vt reverà fit, <lb/>&longs;i rota humido innatet; at <expan abbr="c&utilde;">cum</expan> propter <expan abbr="af-frict&utilde;">af<lb/>frictum</expan> planirota; detur D, ac proinde difficiliùs accedat<gap/><expan abbr="punct&utilde;">punctum</expan> C longè faci<lb/>liùs accedit; item A. &c. </s>

<s>& quia hæc affectio multiplex e&longs;t, ide<gap/> etiam auri qualitas, <lb/>qua ex varia mixtione na&longs;citur, varia &longs;it est nece&longs;&longs;au quamuis vna <lb/>tantum&longs;it qualitas auri puri. </s>

<s id="s.000559">ac proinde citiùs <expan abbr="acced&utilde;t">accedunt</expan>, ex quo inæquali acce&longs;&longs;u, <lb/>propter partium nexum, motus orbis nece&longs;&longs;ariò &longs;equitur: Iam vero &longs;uppo<lb/>ne planum inclinatum, & nullam potentiam extrin&longs;ecam applicatam e&longs;&longs;e <lb/>centro A, &longs;ed &longs;olam ine&longs;&longs;e gravitatem rotæ, quæ à centro A exeritur ab <lb/>intrin&longs;eco, eodem pror&longs;us modo, quo ante à potentia, fune applicata <lb/>in plano horrizontali, & vt potentia extrin&longs;eca movet rotam eo motu, quo <lb/>faciliùs moveri pote&longs;t, mixto &longs;cilicet ex motu centri & orbis, in hoc plano, <lb/>ita & propria rotæ gravitas in inclinato; quid clarius? </s>

<s id="s.000560">maneat igitur illud <lb/>principium, quòd &longs;cilicet corpora eo motu moveantur, cæteris paribus, quo <lb/>faciliùs moveri po&longs;&longs;unt. </s>

<s>Qualitas enim auri in quouis cor <lb/>pore propo&longs;ito, exprimitur partibus auripuri, qua &longs;unt in ip&longs;o corpo<lb/>re, non in magnitudine, &longs;ed in grauitate &longs;umptis, qualibus totum cor<lb/>pus constat<emph.end type="italics"/> 24<emph type="italics"/>: vel quod idem est, auri qualitas exprimitur in ra<lb/>tione quam babent illæ partes in grauitate ad totum corpas: quod <lb/>exemplo clarius explicabitur in hunc modum.<emph.end type="italics"/></s>

<s><emph type="italics"/>Sit aliquod corpus aureum, exempli gratia<emph.end type="italics"/> 24. <emph type="italics"/>vnciarum, quod <lb/>expurgatum & ad aurum purum reductum, ami&longs;erit ex pri&longs;tina <lb/>grauitate nempe ex<emph.end type="italics"/> 24, <emph type="italics"/>vncys, quatuor vncias, ita vt reman&longs;erint <lb/>tantum<emph.end type="italics"/> 20, <emph type="italics"/>vnciæ auri puri, reliquum vero vel euanuerit in fumum, <lb/>vel fuerit alterius metalli. </s>

<s id="s.000561"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000562"> Do manus, & rem optimè capio, &longs;ed antequam vlteriùs per<lb/>gas, vnum ex te, Antime; re&longs;cire velim, circa ca, quæ in he&longs;terno con<lb/>gre&longs;&longs;u à te accepi. </s>

<s>Totum igitur illud corpus aureum ab <lb/>initio propo&longs;itum, &longs;i adbuc intelligatur tale quale fuit ante expurga<lb/>tionem, appellabitur<emph.end type="italics"/> 20. <emph type="italics"/>partium, &longs;eu, (vt vulgo dicitur) di<emph.end type="italics"/> 20. <emph type="italics"/>ca<lb/>ratti. </s>

<s id="s.000563">Illico probavi, vbi di&longs;ce&longs;&longs;i&longs;ti, pulcherrimum illud expe<lb/>rimentum tubi vitrei, in quo aqua per &longs;piras de&longs;cendit, dum &longs;ur&longs;um extru<lb/>dit, eo, quo dixi&longs;ti, modo inclu&longs;am illam aëtis portionem; ob&longs;ervavi <lb/>enim. illam aëris portionem in cylindrum priore contractiorem, vt labenti <lb/>aquæ &longs;ecus <gap/> tubi &longs;uperficiem locus detur, conformari, ita vt tamen <lb/>&longs;upicma pars &longs;it convexa &longs;phærica infima verò ba&longs;is, omnino plana, &longs;altem <lb/>provt oculo &longs;ubjicitur. </s>

<s>eo quod tota illa ma<32>a mista,<emph.end type="italics"/> 20. <emph type="italics"/>tantum vncias auri puri con<lb/>tinuerit. </s>

<s>I mmo non &longs;olum illa ma&longs;&longs;a auri, &longs;ed etiam illa cuius ip&longs;a <lb/>fui&longs;&longs;et pars, vel que ip&longs;ius fui&longs;&longs;et quæcunque pars dicetur<emph.end type="italics"/> 20, <emph type="italics"/>par<lb/>tium. </s>

<s id="s.000564"><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s>

<s id="s.000565"> Memini me legi&longs;&longs;e vel audii&longs;&longs;e præclari&longs;&longs;imam huius Phæno<lb/>neni rationem, nempe illa portio aëtis, aqua levior, vt in a&longs;cen&longs;u aquæ vim <lb/>& re&longs;i&longs;tentiam faciliùs frangat & &longs;uperet, huiu&longs;modi qua&longs;i cuncatam figu<lb/>ram induit. </s>

<s>Neque enim in alligationibus metallorum, alia est alli<lb/>gatio partium, alia totius, &longs;ed vtrorunque vna eademque e&longs;t qua<lb/>litas.<emph.end type="italics"/></s>

<s><emph type="italics"/>Et hoc est quod Aurifices in inaestigatione quali<gap/>atis auri ob<lb/>&longs;eruant. </s>

<s id="s.000566"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000567"> An fortè pro demon&longs;tratione hoc venditares? </s>

<s>Non enim purificant totum corpus propo&longs;itum, &longs;ed ali<lb/>quam eius particulam etiam perexiguam, quam &longs;olam ad aurum pu<lb/>rum reducunt. </s>

<s id="s.000568">Sed vnde, quæ&longs;o, <lb/>& qua vi, &longs;eu virtute aër in hanc formam &longs;e&longs;e fa&longs;tigiat? </s>

<s id="s.000569">Certè &longs;i ad per<lb/>rumpendum &longs;ur&longs;um faciliùs, mucronem illum nimis obtu&longs;um, &longs;phæricum <lb/>&longs;cilicet, in acutiorem conicum attenuare & acuere debuerat, cunei enim <lb/>eò validiores &longs;unt, quò acutiores. </s>

<s>hac enim reducta, non &longs;olum recte definiunt cuius <lb/>fuerit qualitatis particula illa purificata ante purificationem; ve<lb/>rum etiam cuius fuerit qualitatis, & quot partium fuerit illud cor<lb/>pus, à quo eadem particula detracta fuit, & illud, quod adbuc &longs;u<lb/>pere&longs;t, diminutum &longs;cilicet illa parte purificata, vt in eodem exemplo <lb/>propo&longs;ito, corporis aurei<emph.end type="italics"/> 24. <emph type="italics"/>vnciarum apparet. </s>

<s id="s.000570">Deinde æquè facilè aqua &longs;uperficiem <lb/>&longs;phæricam aëris dividere pote&longs;t ac planam: præterea cur minor aëris portio <lb/>aquæ re&longs;i&longs;tentiam citiùs perrumpit, & &longs;ur&longs;um emergit? </s>

<s id="s.000571">Nempe vt corpus <lb/>grave majus gravitatem &longs;uam potentiùs exerit, ita & leve majus &longs;uam le<lb/>vitatem; &longs;ed cur aqua &longs;imiliter cuneum cuneo minimè opponit? </s>

<s>Eius enim quali<lb/>tatem &longs;i forte aurifices inuestigare velint, detrabent ex eo particu<lb/>lam, verbi gratia, vnius vnciæ, vel qued idem est particulam<emph.end type="italics"/> 24. <pb pagenum="61"/><emph type="italics"/>&longs;<gap/>puforam; & banc particulam exeoquent ad qualitatem o&longs;que <lb/>c<gap/>ripuri. </s>

<s id="s.000572">an fortè <lb/>in ratione gravis corporis aëri cedit, quatenus hic corpus leve e&longs;t? </s>

<s id="s.000573">itaque <lb/>alia omnino rati<gap/>; cùm enim aqua tendat vt: sùs latera tubi, per quæ <lb/>deinde &longs;uas &longs;p<gap/>agens, vt dixi, de&longs;cendit, eo certè ex medio tubo, <lb/>&longs;en&longs;im ruere non pore&longs;t, ni&longs;i quoquo versùm cylindri aeris &longs;uperiorem <lb/>marginem qua&longs;i excutiat, & qua&longs;i &longs;e&longs;e in novam cunei formam induat, e&longs;t <lb/>enim cuneus latior in &longs;ummo, in imo acutior; neque in hoc vlla e&longs;t difficul<lb/>tas; multa &longs;anè eaque &longs;citu digna &longs;uper hoc experimento inihi dicenda e&longs;<lb/>&longs;ent, &longs;ed omitto, ne in parergis toti &longs;imus; inferior verò portio, &longs;eu ba&longs;is <lb/>plana e&longs;t; quia nullum aquæ pondu illam emarginat. </s>

<s>Bt &longs;t quidem inuenerint, ex priori grauitate<emph.end type="italics"/> 24. <emph type="italics"/>&longs;or<gap/><lb/>pulorum, deperi&longs;&longs;e nihil: pronunciabunt aurum sllud, hoc est, non <lb/>&longs;olum partieulam illam excoctam, &longs;ed etiam illud d quo fuit dotr<gap/><lb/>sta, nec non & illud quod reman&longs;it post &longs;ubiractionim e&longs;&longs;e vel &longs;ui&longs;<gap/><lb/>&longs;e aurum prima qualitatis &longs;eu<emph.end type="italics"/> 24, <emph type="italics"/>partiam; vel quod idem est au<lb/>tum purum. </s>

<s>Sivero deprebendirine gra<gap/>m diminuta<gap/>, ver<lb/>bi gratia, n<gap/>e e&longs;&longs;e<emph.end type="italics"/> 20. <emph type="italics"/>&longs;crupulorum, quæ ante defæcationem fuit<emph.end type="italics"/> 24. <lb/><emph type="italics"/>dicturi &longs;unt aurum propo&longs;itam<emph.end type="italics"/> 24. <emph type="italics"/>vnciarum fui&longs;&longs;e<emph.end type="italics"/> 20. <emph type="italics"/>partium & <lb/>illud quod teman&longs;it e&longs;&longs;e<emph.end type="italics"/> 20. <emph type="italics"/>partium & d<gap/>nique particul<gap/> expur<lb/>gatam nunc quidem e&longs;&longs;e aurum purum, fui&longs;&longs;e vero particulam auri<emph.end type="italics"/><lb/>20. <emph type="italics"/>partium.<emph.end type="italics"/></s>

<s id="s.000574"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000575"> Sed quid &longs;i oleum aquæ loco adhibeas; aut certè non <lb/>aëris, &longs;ed olei portionem tubo includas, aut demum oleum &longs;imul & <lb/>aëra? </s>

<s><emph type="italics"/>Et eodem modo pronunclabunt de quibafeunque alys auri quali<lb/>atibus, &longs;ecundum partes auri puri, quas in qualibet ma&longs;&longs;a auri in<lb/>uenerint, ea&longs;que vige&longs;imas quartai tutius grauitatis, non magnita<lb/>dinis. </s>

<s>Nam cum in hac comparatione qualitatum, &longs;eor&longs;im habe a<lb/>tar ratio partium auri, & &longs;eor&longs;im metallorum alligatorum; manife<lb/>stum est &longs;i grauitas totius corporis intelligatur diui&longs;a in<emph.end type="italics"/> 24. <emph type="italics"/>partes <lb/>equales, ex quibus<emph.end type="italics"/> 20. <emph type="italics"/>&longs;int auri, duæ argenti, & duæ æris; quumli<lb/>bet partem auri cum qualibet parte argenti & æris collatam, magni<lb/>tudine e&longs;&longs;e minorem; & &longs;imiliter partem argenti minorem parte <lb/>aris; propterea quod aurum omnia reliqua metalla &longs;uperet grauita<lb/>te quemadmodum & argentum ip&longs;uon as, vt constat experi<gap/>nt<gap/><lb/>atque hinc constat quam apte ac conuenienter Aurifices vtantur <lb/>voeabulo parlium. </s>

<s id="s.000576"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000577"> Si oleum loco aquæ, idem fiet; quanquam paulò lentiùs aëris <lb/>portio &longs;ur&longs;um evadet; &longs;i verò aëris loco, eodem modo, & &longs;ub eadem <lb/>forma, &longs;ed multò lentius; quia &longs;cilicet oleum e&longs;t longè gravius aëre: &longs;i <lb/>demum &longs;imul vtrumque, aër oleum longè po&longs;t &longs;e relinquet; &longs;i tamen dum <lb/>olei patricula mediam tubi altitudinem decurrit, po&longs;tquam aër iam emer<lb/>&longs;it tubum inverta;, aër certè oleum facilè a&longs;&longs;equitur, nec non per medium <lb/>oleum perrumpit, &longs;ervata eadem figura; quanquam tunc oleum &longs;e&longs;e non pa<lb/>rum dilatat, vt &longs;ur&longs;um aëra extrudat; aut &longs;altem vt eidem, vtpote leviori, <lb/>tran&longs;itum cedat. </s>

<s>bao enim ratione <gap/>dem numero exprimunt vnam <lb/>quamque qualitatem auri cuiuslibet ma&longs;&longs;æ propo&longs;itæ. </s>

<s>Sednunc ad <lb/>&longs;<gap/>undum veniamus & modum alligationis. </s>

<s id="s.000578"><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s>

<s id="s.000579"> Aliquando accidit in eo conflictu, vt aëris bullula &longs;upremæ <lb/>olei &longs;uperficiei adhæ&longs;erit & qua&longs;i captiva reman&longs;erit; tunc verò, vt <lb/>fidelis ob&longs;ervator refert, paulo citiùs oleum emer&longs;it, aër enim addidit <lb/>alas. </s>

<s>quem ydem ob&longs;eruant <lb/>breuiter adnotemus.<emph.end type="italics"/></s>

<s><emph type="italics"/>Inter varias autem & multiplices auri compo&longs;itiones quibus <lb/>cum alys metallis alligari potest, eam retinuere aurifices, quam diu<lb/>turna experientia deprehenderunt omnibus alys e&longs;&longs;e commodiorem, <lb/>eam nimirum quæ ab auri &longs;imilitudine vel minimum di&longs;cedat; qua<lb/>lis e&longs;t quæ &longs;olius argenti atque æris mixtione perficitur. </s>

<s id="s.000580"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000581"> Oleum, vt probè tenetis, &longs;ua vligine particulam aëris intra <lb/>buliam continere potuit, nempe bullæ ex materia vligino&longs;a tornantur; <lb/>quod autem totum illud corpus ex aëre & oleo con&longs;tans, paulò faciliùs ab <lb/>aqua &longs;ur&longs;um extrudatur, vel à levitate viribus auctis feratur, mirum e&longs;&longs;e <lb/>non debet: de levitate hoc loco non di&longs;puto, aio tamen, ex hoc experi<lb/>mento, minime probari, immo potiùs, vt patet, ex iis, quæ dicta &longs;unt, <lb/>impugnari. </s>

<s>Et quidem <lb/>&longs;ipartes auri excipias, aris atquo argenti partes, quæ auro &longs;unt per<lb/>mi&longs;cendæ &longs;emper volunte&longs;&longs;e æquales in grauitate: propterea quod <lb/>eadem experientia Magi&longs;tra didicerunt hunc e<32>e mixtionis modum <lb/>longe optimum.<emph.end type="italics"/></s>

<s id="s.000582">Sed ad alia principia ex doctrina motuum accer&longs;enda pergen-<pb pagenum="52" xlink:href="025/01/056.jpg"/>dum e&longs;t, Dico igitur tertio loco, in tantum corpus vnum ab alio moveri, <lb/>præ&longs;cindendo à magneticis, & electricis, in quantum illud aliquem mo<lb/>tum impedit; &longs;i enim id quod movetur nullo modo ab alio impeditur, <lb/>nullam vim pror&longs;us contra illud retorquet; & hoc nemo negaverit, qui hu<lb/>ius doctrinæ peritus &longs;it; &longs;ic directus ictus vegetior e&longs;t, obliquus verò debi<lb/>lior; in globulis, qui adhiberi &longs;olent in ludo minoris tudiculæ, res e&longs;t om<lb/>nino per&longs;picua. </s>

<s><emph type="italics"/>Quando ergo aurifices volunt producere aurum cuiu&longs;cunque <lb/>qualitatis, accipiunt tot partes auri puri æquales, quot partium fu<lb/>turum e&longs;t aurum producendum, pauciores tamen partibus<emph.end type="italics"/> 24, & <pb pagenum="62"/><emph type="italics"/>veliquas partes quæ d &longs;unt ad<emph.end type="italics"/> 24, <emph type="italics"/>explent argento & <gap/>e, &longs;umendo <lb/>exvtreque metallo parles aquales in grauite; atque bis rite inter &longs;e <lb/>permixtis componunt aurum de&longs;ideratæ qualitatis: eamque deno<lb/>minant à partibus auripuri in mixtione a&longs;umptis. </s>

<s id="s.000583"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>Et quoniam <lb/>non prodiret <gap/>ale pror&longs;us quale facere intendunt, &longs;ed paulo perfe<lb/>ctius; propterea quod <gap/> quidem partes in wixtione <gap/>antant, ex <lb/>argenta vero & are aliquid deperdatur, &longs;olen<gap/> Aucifices tanto plue <lb/><gap/>i&longs;cere argenti & aris quantum perdi po&longs;&longs;e deprehenderunt.<emph.end type="italics"/></s>

<s id="s.000584"> Videtur e&longs;&longs;e quoddam paradoxum, quod dicis cau&longs;am &longs;cilicet <lb/>potentiùs agere, quando magis impeditur, erit fortè quædam antiperi&longs;ta&longs;is; <lb/>&longs;ic ignis <gap/>calidior e&longs;t. </s>

<s><emph type="italics"/>Veru<gap/> nostra iutentio non est omnia quæ ad ciu&longs;modi mixtione <lb/>pertinent hoc loco expon<gap/>e; &longs;ed illud tantum vt recept<gap/> apud o<gap/><lb/><gap/>es ad ferre voluimus, ex quo manifeste constat, qu<gap/> metallorum <lb/>mixtio in &longs;ingulis qualitatum generibus statuatur: quaquidem e&longs;t <lb/>illa quam add<gap/>ximus <gap/>mpe in auro<emph.end type="italics"/> 23, <emph type="italics"/>partium, partes<emph.end type="italics"/> 23, <emph type="italics"/>e&longs;&longs;e <lb/>auripuri & reliquamq <gap/>deest ad<emph.end type="italics"/> 24, <emph type="italics"/>partes con&longs;tare dimidia <lb/>parte argenti, & dimidia <gap/>ris in grauitate. </s>

<s id="s.000585"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>In auro vero<emph.end type="italics"/> 22, <emph type="italics"/>par<lb/>tium, auri e&longs;&longs;e<emph.end type="italics"/> 23, <emph type="italics"/>argenti vnam, & æris vnam, &longs;ie enim iterum <lb/>&longs;amma omnium partium est<emph.end type="italics"/> 240 <emph type="italics"/>cademqus est ratio de reliquis ita <lb/><gap/>t numerus partium auri, &longs;e<gap/>per denovinet qualitatem auri, & <lb/>vna medietas reliquarum partium, quæ partibus a<gap/>ri de&longs;unt ad <lb/><gap/>omplendas partes<emph.end type="italics"/> 24, <emph type="italics"/>&longs;it argenti, & reliqua medictas &longs;it æris. </s>

<s id="s.000586"> Ita e&longs;t, paradoxum e&longs;&longs;e videtur; &longs;i quis tamen rectè perpendat, <lb/>impetum eum dumtaxat finem, vel effectum habere, ac præ&longs;tare immo<lb/>bili, cui ine&longs;t, vt hoc moveatur, tali &longs;cilicet motu & modo, qui offectus <lb/>&longs;i non impeditur ab alio. </s>

<s id="s.000587">fru&longs;tra certè contra illud vim &longs;uam exerit, &longs;i v. <lb/>g. corpori dum movetur, à tergo manum admoveas, aut certè à frontè, ea <lb/>ea tamen lege, vt manum admotam æquè citò moveas, nullam <lb/>vim, nullum impetum manui tuæ imprimi &longs;enties; quia hæc nullo modo <lb/>impedit illius corporis motum; &longs;i verò mobile in aliud corpus impinga<lb/>tur, quod motui obe&longs;t, in illud agit, impre&longs;&longs;oque impetu, illud amovet, vnde, <lb/>vt dixi, finis primarius impetus e&longs;t mobilis, cui ine&longs;t, motus; &longs;ecundarius <lb/>verò, & quem dumtaxat propter primum ponit, e&longs;t motus alterius cor<lb/>poris, quod dictum motum impedit; nec mirum, &longs;i impetus alium impetum <lb/>producit, in eo &longs;cilicet, quod proprij mobilis motum impedit: Hinc &longs;i Phi<lb/>lo&longs;opho in verbis ludere liceret, dici à me po&longs;&longs;et <emph type="italics"/>impetus,<emph.end type="italics"/> qua&longs;i <emph type="italics"/>impedi<lb/>tur,<emph.end type="italics"/> cùm nunquam agat, & &longs;uam vim exerat, ni&longs;i impediatur. </s>

<s>hac <lb/>enim &longs;atis est &longs;uppo&longs;ui&longs;&longs;e, ad nouum illud artificium, quo paulo po&longs;t <lb/>inuestig aturi &longs;umus auri qualitat<gap/> ex &longs;ola grauitate quam babe<gap/><lb/>in aere & aqua, eamque qualitatem dupliei via inuestigabimus <gap/><lb/>vnape<gap/> calculum, par tabellam altera: & quia ad calculum &longs;pe<lb/>stant ea, quæ &longs;uperi<gap/> inu<gap/>imus, de grauitate metallorum bucre<lb/>ferenda cen&longs;uimus quæ bic &longs;unt nece&longs;&longs;aria, cuiu&longs;modi &longs;unt auri, <lb/>argenti, atque æris grauitas, quam obtinent in aere, & aqua, qu<gap/><lb/>quidem ita &longs;e habet vt &longs;equitur.<emph.end type="italics"/></s>

<s id="s.000588">His præ<lb/>mi&longs;&longs;is, ad rem venio, Augu&longs;tine; Repetamus figuram Sextam, & primo <lb/>quidem loco vnum dicam, quod vix apud vos fidem inveniat, licèt cer<lb/>ti&longs;&longs;imum &longs;it, geometrica &longs;cilicet demon&longs;tratione confirmatum; illud <lb/>autem ad incredibilem proportionem inæqualitatis motus rotæ, in <lb/>diver&longs;is illius punctis con&longs;iderati pertinet; dico iterum incredi<lb/>bilem. </s>

<s><emph type="italics"/>Auripuri grauitas, quæ in aere e&longs;t<emph.end type="italics"/> 19, <emph type="italics"/>erit in aqua<emph.end type="italics"/> 18. </s>

<s id="s.000589"><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/> locaris, Antime: quis Auriga, Rhedarius, Carpentarius hoc <lb/>ne&longs;cit? </s>

<s><emph type="italics"/>Argenti greuitas, quæ in aert e&longs;t<emph.end type="italics"/> 31, <emph type="italics"/>erit in aqua<emph.end type="italics"/> 28. </s>

<s id="s.000590">quis oculos figens non videt, &longs;uperius rotæ punctum à plano, in <lb/>quo rota volvitur, tota rotæ diametro di&longs;tans, velociùs agi, quàm infimuru, <lb/>in quo &longs;cilicet rota planum tangit. </s>

<s><emph type="italics"/>Aeris grauitas; quæ in aere est<emph.end type="italics"/> 9, <emph type="italics"/>erit in aqua<emph.end type="italics"/> 8. </s>

<s id="s.000591"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000592"> Serio loquor, Chry&longs;ocome, non iocor; vident omnes e&longs;&longs;e quidem <lb/>inæquales motus, &longs;ed nemo crederet tantam inæqualitatis propor<lb/>tionem. </s>

<s><emph type="italics"/>Aurum ad aquam &longs;e habet in grauitate vt<emph.end type="italics"/> 19, <emph type="italics"/>ad<emph.end type="italics"/> 1. </s>

<s id="s.000593"><emph type="italics"/>Augu&longs;t.<emph.end type="italics"/></s>

<s><emph type="italics"/>Argentum ad aquam &longs;e habet in grauitate vt<emph.end type="italics"/> 31, <emph type="italics"/>ad<emph.end type="italics"/> 3. </s>

<s id="s.000594"> Quanta porrò illa erit? </s>

<s id="s.000595">fac &longs;upremum illud punctum moveri <lb/>duplo citiùs infimo, aut etiam triplo, quadruplo, decuplo, vt voles; quid <lb/>tandem erit? </s>

<s><emph type="italics"/>Aes ad aquam &longs;e habet in grauitate vt<emph.end type="italics"/> 9, <emph type="italics"/>ad<emph.end type="italics"/> 1. </s>

<s><emph type="italics"/>Ex quibus clari&longs;&longs;ime colligitur, &longs;i aliquod corpus mistum con<lb/>stet partibus æqualibus argenti, & aeris in grauitate, quantam <lb/>grauitatem habeat in aqua & que &longs;it ratio in grauitate ip&longs;ius mi<lb/>sti ad aquam &longs;i enim grauitas aeris in aere &longs;it<emph.end type="italics"/> 9, <emph type="italics"/>eius grauitas in <lb/>aqua erit<emph.end type="italics"/> 8, <emph type="italics"/>& &longs;i grauitas argenti in aere &longs;it quoque<emph.end type="italics"/> 9, <emph type="italics"/>erit eius gra<gap/><emph.end type="italics"/><pb pagenum="63"/><emph type="italics"/>vitas in àqua<emph.end type="italics"/> 8 4/11, <emph type="italics"/>est enim vt 9, ad<emph.end type="italics"/> 8 4/11 <emph type="italics"/>vt<emph.end type="italics"/> 31, <emph type="italics"/>ad<emph.end type="italics"/> 28: <emph type="italics"/>Quare &longs;i <lb/>grauitas corporis mi&longs;ti ex argento, & ære iuncta mixtionem prædi<lb/>ctam, quæ etiam &longs;ubinte<gap/>genda erit in &longs;equantibus, in aere fuerit<emph.end type="italics"/><lb/>18, <emph type="italics"/>erit id aqua<emph.end type="italics"/> 16<gap/> <emph type="italics"/>& còn&longs;eq<gap/> grauitas aquæ magnitu<emph.end type="italics"/><arrow.to.target n="note54"/><lb/><emph type="italics"/>dinem habentis æqualem <gap/> eor por<gap/> misto<gap/><emph.end type="italics"/> <gap/>; <emph type="italics"/>quare corpus <lb/><gap/>stum ex argento & are ad carpui aqueum eia&longs;dem magnitudi<lb/><gap/>is, rationem habe<gap/>it <gap/> grauitate vt<emph.end type="italics"/> 18, <emph type="italics"/>ad<emph.end type="italics"/> 1 22/11, <emph type="italics"/>vel vt<emph.end type="italics"/> 1, <emph type="italics"/>ad<emph.end type="italics"/><lb/><gap/>, <emph type="italics"/>vet <gap/> nique in numerit integrinvt<emph.end type="italics"/> 299, <emph type="italics"/>ad<emph.end type="italics"/> 29, <emph type="italics"/>omnium enim <lb/>i&longs;torum numerorum eadem e&longs;t ratie.<emph.end type="italics"/></s>

<s id="s.000596"><emph type="italics"/>Antim.<emph.end type="italics"/> videbis paulò po&longs;t; &longs;ed amabo te, Augu&longs;tine, cogita maximam <lb/>quam potes proportionem inæqualitatis; & videbis vtrùm illa, quam e&longs;&longs;e <lb/>con&longs;tat in rigore geometrico, &longs;it incredibilis. </s>

<s><margin.target id="note54"/>5. <emph type="italics"/>huius<emph.end type="italics"/></s>

<s id="s.000597"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quibus &longs;ic con&longs;titutis inuenietur qualitas auri cuiu&longs;cumque hoc <lb/>modo. </s>

<s id="s.000598"> Si centuplam e&longs;&longs;e dixero, vera haud dubiè longè maior erit, & <pb pagenum="53" xlink:href="025/01/057.jpg"/>vix vllus tantam e&longs;&longs;e crediderit. </s>

<s>Sit <gap/>xemp: gratia propo&longs;ita aliqua <gap/> e&longs;&longs;a aurea, cuius gra<lb/>uitas in aere &longs;it vnc<emph.end type="italics"/> 24, <emph type="italics"/>& oporte at in<gap/> euius qualitatis &longs;it ip<lb/>su<gap/> aurum. </s>

<s id="s.000599"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>Ponderetur ea ma&longs;&longs;a in aqua & habeat grauitatem <lb/>vnciarum<emph.end type="italics"/> 22 2<gap/>/5301, <emph type="italics"/>ergo * grauitas aquæ magnitudinem babe <gap/><emph.end type="italics"/><arrow.to.target n="note55"/><lb/><emph type="italics"/><gap/>is <gap/>qualem propo&longs;itæ ma&longs;&longs;æ erit vnc.<emph.end type="italics"/> 1 2431/5301. </s>

<s id="s.000600"> At &longs;i maiorem centupla, immo & millecupla, & centena mille<lb/>cupla e&longs;&longs;e dicerem, omnem fidem omnino detrectares? </s>

<s id="s.000601">&longs;i dicerem majorem <lb/>e&longs;&longs;e quacumque de&longs;ignabili, illico iocari me diceres, Chry&longs;ocome, vt tamen <lb/>verbo dicam, res ita &longs;e habet, vt facilè demon&longs;tratur. </s>

<s><margin.target id="note55"/>5.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s><emph type="italics"/>Deinde inueniatur grauitas aquæ magnitudine æqualis aur<gap/><lb/>puro<emph.end type="italics"/> 24, <emph type="italics"/>vnciarum: hoc e&longs;t vt 19, ad 1, ita fiat<emph.end type="italics"/> 24, <emph type="italics"/>ad alium, nempe ad <lb/>vnciam<emph.end type="italics"/> 1 9/19, <emph type="italics"/>hic enim numerus erit grauitas illius aquæ.<emph.end type="italics"/></s>

<s id="s.000602"><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s>

<s id="s.000603"> Sed quæ&longs;o te, noli nos vltra in geometrica retia & Labyrinthos <lb/>deducere, hæc enim totam congre&longs;&longs;ui gratiam & am&oelig;nitatem &longs;enticeta eri<lb/>piunt. </s>

<s><emph type="italics"/>Fiat denique ot<emph.end type="italics"/> 279, <emph type="italics"/>ad<emph.end type="italics"/> 29, <emph type="italics"/>ita <gap/>ur&longs;ue<emph.end type="italics"/> 24, <emph type="italics"/>vntiæ, ad alium, numi<lb/>rus enim quartus, nempe vnc.<emph.end type="italics"/> 2<gap/> <emph type="italics"/>erit grauitas aquæ, magnitu<lb/><gap/>ine æqualis corport mi&longs;to ex argento & ære, euius grauitas est in <lb/>ærè vnc.<emph.end type="italics"/> 24, <emph type="italics"/>corp<gap/>s enim ita mi&longs;tum, ad corpus aqueum eiu&longs;dem ma<lb/><gap/> nitudin<gap/> rationem babet in grauitate vt<emph.end type="italics"/> 279, <emph type="italics"/>ad<emph.end type="italics"/> 29. </s>

<s><emph type="italics"/>Atque ita habebuntur tres gravitates <gap/> aquæ quantitatum, <lb/>quarum prima æquatur auro puro<emph.end type="italics"/> 24, <emph type="italics"/>vuctarum, &longs;<gap/>unda ma&longs;&longs;<gap/><lb/>propo&longs;itæ<emph.end type="italics"/> 24, <emph type="italics"/>vnciarum, & reliqua corpori mi&longs;to ex argento & <gap/><lb/>&longs;imiliter<emph.end type="italics"/> 24, <emph type="italics"/><gap/>vnciarum quæ quidem tres grauitates in numeris di<lb/>&longs;ponantur eo ordine, quo &longs;equitur.<emph.end type="italics"/></s>

<s id="s.000604"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000605"> Si quando illis retibus aliquam veritatem nos f&oelig;liciter expi<lb/>&longs;cari contingat, crede mihi Chry&longs;ocome, illa retia non &longs;unt adeò inam&oelig;na, <lb/>&longs;ed vt tibi morem geram, nihil ferè dicam quod etiam ab A geometris facilè <lb/>intelligi non po&longs;&longs;it. </s>

<s>TABELLE WAR HIER</s>

<s><emph type="italics"/>Deinde quteratur differentia inter primam & tertiam aquæ gra<lb/>uitatem, quæ est vnc.<emph.end type="italics"/> 1 1227/5302, <emph type="italics"/>& hæc differentia statuatur pro <lb/>primo proportionis termino, pro &longs;ecundo termino ponatur grauitas <lb/><gap/>a&longs;&longs;æ propo&longs;itæ idest vnc.<emph.end type="italics"/> 24, <emph type="italics"/>& protertio denique termino ponatur <lb/>different<gap/> inter &longs;ecundam aquæ grauitatem & tertiam, quæ est <lb/>vnc.<emph.end type="italics"/> 1 <gap/> <emph type="italics"/>quart<gap/> enim proportionalium terminus nempe<emph.end type="italics"/> 20, </s><pb pagenum="64"/>

<s id="s.000606">Sit ergo Rota D, quæ volvitur in plano FG, punctum E &longs;upre<lb/>mum, F infimum, ita autem moveatur, vt motus orbis, &longs;eu rotæ <lb/>circa centrum D, &longs;it æqualis motui eiu&longs;dem centri D ; ac proinde eodem <lb/>tempore, quo E v.g. integrum &longs;uum orbem circa D decurrit, centrum D. <lb/>lineam rectam decurrat æqualem peripheriæ eiu&longs;dem rotæ, vel circuli, mo<lb/>vetur autem E motu illo mixto per lineam curuam EQV, quam haud <lb/>improprio nomine cycloidem vocatis, cuius &longs;ubduplam dumtaxat figuram <lb/>delineavi; nam petinde e&longs;t, &longs;ive punctum Rotæ ab E &longs;upremo perveniat <lb/>ad infimum V per curvam EQV, &longs;ive ab imo V ad &longs;upremum E per <lb/>VQE. </s>

<s>TABELLE WAR HIER<lb/><emph type="italics"/>erit de<gap/>ominator qualitatis auri de qua <gap/>uaritur quia ille termi<lb/><gap/>ut indicat partes auri pari i<gap/> grauitate, qualibus ma&longs;&longs;a propo&longs;ita <lb/>constat<emph.end type="italics"/> 24. <emph type="italics"/>Hoc autem de<gap/>onstratum e&longs;t prop.<emph.end type="italics"/> 19, <emph type="italics"/>huius.<emph.end type="italics"/></s>

<s><emph type="italics"/>Et quia inpropo&longs;ito exemplo bæ partes, nempe vnc.<emph.end type="italics"/> 20, <emph type="italics"/>&longs;unt par<lb/>tes vige&longs;<gap/> quartæ<emph.end type="italics"/> 24, <emph type="italics"/>onciarum, quæ constituunt grauitatem to<lb/>tius ma&longs;&longs;æ. </s>

<s id="s.000607"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/> Hæc e&longs;t cyclois illa, quæ tot ac tanto<gap/> excitavit tumultus, <lb/>de qua etiam opu&longs;culum geometricum edidi&longs;ti; &longs;ub nomine Antimi <lb/>Parbij. </s>

<s>binc fit quod eædem<emph.end type="italics"/> 20. <emph type="italics"/>vnc. </s>

<s>immediate denominent au<lb/>rum propo&longs;itum e<32>e<emph.end type="italics"/> 20, <emph type="italics"/>partium. </s>

<s id="s.000608"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000609"> Non agno&longs;cerem pro in ea lucubratiuncolam illam, ni<lb/>&longs;i me <expan abbr="grat&imacr;">gratim</expan> animi ratio &longs;timularet; enim verò facere non po&longs;&longs;um, <lb/>quin hoc loco in&longs;ignem pro&longs;ectò Geometram <gap/> Stephanum De An<lb/>gelis digni&longs;&longs;imum magni illius Cavalerij di&longs;cipulum appellem, ei<lb/>que gratias, quam po&longs;&longs;um maximas agam, pro iis laudibus, qui<lb/>bus liberaliùs certè quàm par fui&longs;&longs;et, cùm iis longè inferior &longs;im, pro &longs;ua <lb/>humanitate, me alioquin pror&longs;us incognitum, ratione præfati opu&longs;culi cu<lb/>mulavit; &longs;ed ad rem no&longs;tram. </s>

<s>Quando vero grauitas totius ma&longs;<lb/>&longs;anon exprimitur per numerum<emph.end type="italics"/> 24, <emph type="italics"/>tunc opus erit inquirere quot <lb/>partes vige&longs;imas quartas totius grauitatis efficiat quartus ille pro<lb/>portionis terminus vt in &longs;equenti <gap/>mplo clarius appar<gap/>bit.<emph.end type="italics"/></s>

<s id="s.000610">Comparemus vtriu&longs;que puncti motus, &longs;u<lb/>premi &longs;cilicet atque infimi; quod vt clariùs &longs;uccedat, &longs;it arcus EP. trigin<lb/>ta grad. punctum E, dum prædictum arcum decurrit, deferturque à cen<lb/>tro D &longs;ini&longs;tror&longs;um, &longs;cilicet versùs V, acquirit &longs;ini&longs;tror&longs;um ratione vtriu&longs;<lb/>que motus, totum &longs;patium OQ, &longs;cilicet ratione motus orbis, rectam OP, <lb/>id e&longs;t &longs;inum rectum EP, quem &longs;uppono e&longs;&longs;e 30. grad. & ratione motus <lb/>centri, rectam PQ æqualem ip&longs;i arcui ER, tantumdem enim Spatij cen<lb/>trum decurrit, ergo ratione vtriu&longs;que totum &longs;patium <expan abbr="Oq.">OQ</expan> Iam verò &longs;it <lb/>FR arcus æqualis 30. &longs;cilicet grad. punctum R eodem tempore motu or<lb/>bis acquirit dextror&longs;um <expan abbr="&longs;pati&utilde;">&longs;patium</expan> RS, & motu centri <expan abbr="&longs;&utilde;">&longs;ini&longs;tror&longs;um</expan> &longs;patium FT <lb/>æquale arcui FR. exi&longs;tis autem duobus motibus re&longs;ultat R T. </s>

<s id="s.000611">Iam compa<lb/>remus hæc duo &longs;patia, &longs;cilicet. </s>

<s><emph type="italics"/>Sit euim propo&longs;ita a lia auri ma&longs;&longs;a cuius grauitas in aere &longs;it<emph.end type="italics"/> 5301 <lb/><emph type="italics"/>in aqua vero<emph.end type="italics"/> 4988, <emph type="italics"/>&longs;i igitur hic <gap/>erus &longs;ubtrabatur ex numero to<emph.end type="italics"/><lb/><arrow.to.target n="note56"/><emph type="italics"/>tius grauitatis<emph.end type="italics"/> 5301, <emph type="italics"/>r<gap/>liquus numerus<emph.end type="italics"/> 313, * <emph type="italics"/>erit grauitas aquæ <lb/>propo&longs;itæ ma&longs;&longs;æ magnitudine æqualis. </s>

<s id="s.000612">EQ, & RT, vel OQ, & differentiam <lb/>SR, FT, &longs;it DE 100000. OP, &longs;ubdupla DE erit 50000. vt autem 7. ad <lb/>11.ita DE ad arcum EI, id e&longs;t ad 157143.cuius terti ars &longs;cilicet 52381. <lb/>erit æqualis arcui EP, vel rectæ <expan abbr="Pq;">PQ</expan> igitur tota OQ, addito vno nume<lb/>ro alteri, erit 102381. ducatur deinde per punctum R, &longs;ecans DR, haud <lb/>dubiè cadet vltra punctum T, versùs V, nempe tangens, quæ terminatur <lb/>ad dictam &longs;ecantem e&longs;t &longs;emilatus polygoni circum&longs;cripti; igitur major <lb/>arcu FR; igitur &longs;egmentum illud &longs;ecantis &longs;eu differentia &longs;ecantis, & &longs;inus <lb/>totius e&longs;t maior &longs;patio RT; igitur &longs;i &longs;upponamus æqualem, faciemus mo<lb/>tú R maiorem vero; accipio igitur &longs;ecantem arcus FR, & in canone inve<lb/>nio 115470. ex quo numero detraho &longs;inum totum 100000. re&longs;iduum erit <lb/>15470. hæc e&longs;t RT, qùæ ferè e&longs;t vna 7.igitur motus puncti E ad motum <lb/>puncti R toto tempore quo decurritur arcus FP, vel RS e&longs;t vt 7. <lb/>ad 1. </s>

<s>Inueniantur <expan abbr="quoq;">quoque</expan> duæ aliæ <lb/>grauitates aquæ, vna re&longs;pondentis auro puro magnitudine, altera <lb/>corpori mi&longs;to ex argento & ære, ita tamen vt grauitas tum auri pu<lb/>ri, tum corporis misti &longs;it eadem quæ ma&longs;&longs;æ propo&longs;itæ, non &longs;ecus ac in <lb/>præcedenti oxemplo factitatum est. </s>

<s id="s.000613"><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s>

<s>hoc e&longs;t primo fiat vt<emph.end type="italics"/> 19, <emph type="italics"/>ad<emph.end type="italics"/> 1, <emph type="italics"/>ita<emph.end type="italics"/><lb/>5301, <emph type="italics"/>ad<emph.end type="italics"/> 279, <emph type="italics"/>hic enim numerus erit grauitas aquæ magnitudinem <lb/>habentis æqualem auro puro, <gap/>uius grauitas e&longs;t<emph.end type="italics"/> 5301. <emph type="italics"/>Deinde fia<gap/><lb/>vt<emph.end type="italics"/> 279, <emph type="italics"/>ad<emph.end type="italics"/> 29, <emph type="italics"/>ita rur&longs;um grauitas<emph.end type="italics"/> 5301, <emph type="italics"/>ad aliam, hac enim ratione <lb/>producetur nu<gap/>erus<emph.end type="italics"/> 551, <emph type="italics"/>debitus grauitati aquæ, magnitudine <lb/>aqualis corpori mi&longs;to ex argento & ære grauitatem habenti eandem <lb/>cum eadem ma<32>a propo&longs;ita. </s>

<s id="s.000614"> Sed vbinam illa tua millecupla inæqualitatis proportio? <lb/></s>

<s id="s.000615">ad populum phaleras; vos &longs;anè Mathematici, multa promittitis, pau<lb/>ca præ&longs;tatis; totum orbem movetis, & vix murum in ruinam præcipitem <lb/>&longs;u&longs;tinetis. </s>

<s>Atque ba tre<gap/> grauitates aquæ &longs;criban<lb/>tur ordine quo &longs;upra; inuenti&longs;que differentys inter primam &<emph.end type="italics"/></s>

<s><margin.target id="note56"/>5.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s id="s.000616"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000617"> Parciùs i&longs;ta viris, Chry&longs;ocome, nam fortè aliquando incides in <lb/>manus cuiu&longs;piam ex iis, quos puros Geometras vocant, à quo immi&longs;ericor<lb/>diter vapulabis, iis arma profectò non de&longs;unt, &longs;agittæ &longs;cilicet, &longs;ecantes, <lb/>&longs;ecures, cunei, ro&longs;tra & vngues; expecta igitur parumper, nam pedeten<lb/>tim cum i&longs;ta rota progredimur, accipe arcum 15. grad. id e&longs;t &longs;ubduplam <pb pagenum="55" xlink:href="025/01/059.jpg"/>PQ, erit æqualis 26190. cui &longs;i addas &longs;inum rectum eiu&longs;dem arcus, &longs;cili<lb/>cet.25038. erit compo&longs;ita ex vtraque 51228. rejecta minutia, hic erit mo<lb/>tus punct<gap/>E, eo tempore, quo decurrit arcum 15.grad. iam verò accipe <lb/>&longs;ecantem eiu&longs;dem anguli 103290. ex qua, &longs;i &longs;ub&longs;trahas &longs;inum totum, re&longs;i<lb/>duum erit 3290. hic e&longs;t motus puncti F, eodem tempore, qui ad priorem <lb/>habet rationem <gap/> iam verò &longs;i accipias arcum 3. grad. &longs;cilicet 5238. eiu&longs;<lb/>dem &longs;inum rectum 5233. compo&longs;ita ex vtraque erit 10471. differentia ve<lb/>rò &longs;ecantis & &longs;inus totius eju&longs;dem anguli 137. Cùm igitur motus E per <lb/>arcum 3. grad. &longs;it ad motum F per arcum æqualem vt 10471. ad 137. erit <lb/>vt 75.ad 1.&longs;it motus per arcum 1.grad.erit compo&longs;ita ex arcu & &longs;inu 3491. <lb/>differentia &longs;ecantis & &longs;inus totius 15.igitur ratio maioris motus ad <expan abbr="mino-r&etilde;">mino<lb/>rem</expan> <gap/>. </s>

<s>TABELLE WAR HIER<lb/><emph type="italics"/>tertiam, nec noninter &longs;ecund am & tertiam, quæ &longs;unt<emph.end type="italics"/> 272, 238; <emph type="italics"/>sta<lb/>tuatur pro primo proportionis termino prior differentia<emph.end type="italics"/> 272, <emph type="italics"/>& pro <lb/>tertio posterior<emph.end type="italics"/> 238. <emph type="italics"/>grauitas vero ma&longs;&longs;æ propo&longs;itæ<emph.end type="italics"/> 5301, <emph type="italics"/>ponatur <lb/>pro&longs;ecundo termino, & quæratur terminus quartus, qui in præ-<emph.end type="italics"/></s>

<s id="s.000618">Accipe arcum 30.minutorum, erit &longs;umma, arcus & &longs;inus recti 1746. <lb/>differentia 4. igitur ratio <gap/> accipiamus 15. erit, &longs;umma 872. differentia <lb/>1. igitur ratio <gap/>. </s>

<s id="s.000619">Si vltra progredimur, &longs;ecantes ce&longs;&longs;ant in canone Pi<lb/>ti&longs;ci, et&longs;i veniamus ad <expan abbr="vn&utilde;">vnum</expan> <expan abbr="minut&utilde;">minutum</expan>, quid tandem erit? </s>

<s>TABELLE WAR HIER<lb/><arrow.to.target n="note57"/> <emph type="italics"/>&longs;enti examp<gap/>o e&longs;t<emph.end type="italics"/> 4638 51/<gap/>, <emph type="italics"/>is enim indicabit grauitatem auri <lb/>puri in ma&longs;&longs;a propo&longs;ita. </s>

<s id="s.000620">quid &longs;i ad vnum &longs;e<lb/>cundum, aut tertium &c. </s>

<s id="s.000621">immo quantumvis parvum arcum accipias, erit <lb/>maior proportio ex triplici capite. </s>

<s>Sed quoniam <gap/>c grauitas non est expre&longs;<lb/>&longs;a in partibus vige&longs;imis quartis totius grauitatis, id quod ad g<gap/>,<emph.end type="italics"/></s><pb pagenum="65"/>

<s id="s.000622">Primò, quia curva EQ e&longs;t maior rectâ <lb/>OQ, &longs;ed per EQ movetur punctum E, idem de aliis arcubus. </s>

<s id="s.000623">Secundò, <lb/>quia differentia &longs;ecantis & &longs;inus recti e&longs;t major RT, igitur, hic accipitur <lb/>maior, illic verò minor motus, quàm reverà &longs;it. </s>

<s><margin.target id="note57"/>19. <lb/><emph type="italics"/>huius.<emph.end type="italics"/></s>

<s id="s.000624">Tertiò quia E à puncto <lb/>oppo&longs;itionis versùs Q continuò retardat motum &longs;uum; igitur movetur <lb/>velociùs in primo gradu, quam in &longs;ecundo & in hoc citiùs, quàm in ter<lb/>tio, atque ita deinceps 5 cum tamen F à puncto oppo&longs;itionis ver&longs;us R mo<lb/>tum &longs;uum continuò acceleret; ac proinde moveatur citius in &longs;ecun<lb/>do gradu quàm in primo & in tertio quàm in &longs;ecundo, atque ita dein<lb/>ceps; con&longs;tat igitur: quod initio à me propo&longs;itum fuit, majorem <lb/>e&longs;&longs;e proportionem motus &longs;upremi puncti rotæ; quæ in plano volvi<lb/>tur, ad motum infimi, qualibet a&longs;&longs;ignabili; hinc paradoxum egre<lb/>gium, ita moveri duo extrema eju&longs;dem lineæ finitæ, vt vnum alio infi<lb/>nities velociùs moveatur, infinities, inquam, Syncategorematicè, <lb/>nec e&longs;t par ratio rotæ, quæ motu tantùm orbis movetur, quia centrum <lb/>illius &longs;upponitur immobile, nec vllum punctum a&longs;&longs;ignari pote&longs;t, in radio <lb/>mobili, circa alteram extremitatem, cujus motus ad motum alterius ex<lb/>tremitatis certam & finitam proportionem non habeat; denique huc etiam <lb/>plurimùm, immo totum facit angulus contingentiæ, quem prædictus circu<lb/>lus cum plano facit eo &longs;anè minorem, quo circulus major e&longs;t, cùm enim <lb/>quolibet angulo rectilineo, quamtumvis minimo, minor &longs;it, id que in infini<lb/>tum; motus puncti infimi rotæ, &longs;eu contactus, eo ip&longs;o incipit, quò tangere <lb/>planum de&longs;init, intercepto dumtaxat dicti anguli contingentiæ cu&longs;pide, <lb/>omni rectilineo minore. </s>

<s><emph type="italics"/>manam qualitatis auri pronunciationem requiritur, vt &longs;upra mul<lb/>tis o&longs;tendimus, reuocanda erit ad partes vige&longs;imas quartas hoc est <lb/>adpartes, qualium tota propo&longs;ita ma&longs;&longs;a est<emph.end type="italics"/> 24, <emph type="italics"/>quod factu non est <lb/>difficile. </s>

<s id="s.000625"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>Nam &longs;i fiat vt tota grauitas ma&longs;&longs;æ propo&longs;itæ<emph.end type="italics"/> 5301, <emph type="italics"/>al gra<lb/>uitatem auri puri<emph.end type="italics"/> 4638 45/116, <emph type="italics"/>velvt<emph.end type="italics"/> 272, <emph type="italics"/>ad<emph.end type="italics"/> 238, <emph type="italics"/>cum vtrobique <lb/>eadem &longs;it ratio ita<emph.end type="italics"/> 24, <emph type="italics"/>ad alium numerum. </s>

<s id="s.000626"> Quid &longs;i aliquis diceret, punctum illud aliquantulum quie&longs;cere, <lb/>ad in&longs;tar cuiu&longs;dam polygoni infinitorum laterum? </s>

<s id="s.000627">Sic enim polygonum in <lb/>plano volvitur, vt circa &longs;ingulos laterum angulos totum polygonum &longs;uc<lb/>ce&longs;&longs;ivè volvatur. </s>

<s>proculdubio quartus nu<lb/>merus proportionalis, erit ille qui quæritur. </s>

<s>Est autem hic quar<lb/>tus numerus<emph.end type="italics"/> 21. <emph type="italics"/>Quare aurum ma&longs;&longs;æ propo&longs;itæ appellabitur par<lb/>tium<emph.end type="italics"/> 21. </s>

<s id="s.000628"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000629"> Scio, à viro docti&longs;&longs;imo hæc iam olim fui&longs;&longs;e dicta, &longs;ed Geome-<pb pagenum="56" xlink:href="025/01/060.jpg"/>triæ repugnat, vt circulus polygonum dicatur, nam omnes radij circuli <lb/>æquales &longs;unt, &longs;ecus Polygoni; deinde Polygonum in plano moveri non <lb/>pote&longs;t, ni&longs;i eius centrum modò a&longs;cendat, modò de&longs;cendat, vt patet; at <lb/>centrum circuli ab eadem linea plano, in quo volvitur parallela; nunquam <lb/>de&longs;cendit; igitur circulus polygonum dici non pote&longs;t. </s>

<s><emph type="italics"/>Ex his igitur patet in inuenienda auri qualitate primum pro<lb/>portionis terminum<emph.end type="italics"/> 272, <emph type="italics"/>& &longs;ecundum<emph.end type="italics"/> 5301, <emph type="italics"/>perpetuo manere eo&longs;<lb/>dem, quia primus terminus est differentia inter grauitates primæ, <lb/>& tertiæ aquæ, quæ nunquam mutantur, nam illæ aquæ magnitu<lb/>dine &longs;unt æquales altera auro puro, reliqua mi&longs;to ex argento & ære, <lb/>quæ corpora aureum &longs;cilicet & mistum &longs;emper ponuntur eiu&longs;dem <lb/>grauitatis nempe<emph.end type="italics"/> 5301, <emph type="italics"/>Secundus vero terminus<emph.end type="italics"/> 5301, <emph type="italics"/>e&longs;t grauitas <lb/>ma&longs;&longs;æ propo&longs;itæ, quæ &longs;i maior fuerit, vel minor, ad eam facile reuo<lb/>cabitur. </s>

<s>Vnde inposterum &longs;olum opus erit inuenire tertium pro<lb/>portionis terminum, hoc est differentiam inter grauitates &longs;ecundæ <lb/>& tertiæ aquæ.<emph.end type="italics"/></s>

<s id="s.000630"><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/> Cùm illa inæqualitatis proportio ina&longs;&longs;ignabilis, ac &longs;uo modo <lb/>infinita, vt dicis, in minutis tantummodò primis, &longs;ecundis, tertiis lo<lb/>cum habeat, non verò in arcubus paulo majoribus, vt con&longs;tat ex iis quæ <lb/>dixi&longs;ti, nihil &longs;anè obe&longs;&longs;e pote&longs;t, ac proinde parum, aut nihil nobis curan<lb/>da, qui ad illa in&longs;en&longs;ibilia, in Phy&longs;ica præ&longs;ertim, minimè attendimus. </s>

<s><emph type="italics"/>Sed vt hoc etiam exemplo illustretur, proponatur aliqua ma&longs;&longs;a <lb/>auri, cuius <expan abbr="inue&longs;tigãda">inue&longs;tiganda</expan> &longs;it qualitas, & &longs;it ip&longs;ius ma&longs;&longs;æ grauitas qui<lb/>dem in aere<emph.end type="italics"/> 837, <emph type="italics"/>in aqua vero<emph.end type="italics"/> 784, <emph type="italics"/>ergo * grauitas aquæ magnitu-<emph.end type="italics"/><arrow.to.target n="note58"/><lb/><emph type="italics"/>dinem habentis æqualem propo&longs;itæ ma&longs;&longs;æ erit<emph.end type="italics"/> 53, <emph type="italics"/>differentia enim <lb/>inter primam, & &longs;ecundam grauitatem est<emph.end type="italics"/> 53. </s>

<s id="s.000631"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000632"> In digitalem rotam, &longs;i fortè trahatur à te&longs;tudine, i&longs;thæc opti<lb/>mè quadrant, &longs;ecus tamen in telluris globum, cujus &longs;ingula minuta 5000. <lb/>pedes continent; & motus adeò velox e&longs;t, vt habita tantùm ratione motus <lb/>orbis, quodlibet punctum circuli æquatoris, quolibet &longs;ecundo minuto, vt <lb/>iam dixi &longs;uprà conficiat pedes 1250.circiter. </s>

<s id="s.000633">Con&longs;tat igitur de illa incre<lb/>dibili motuum inæqualitate in partibus certè &longs;en&longs;ibilibus tum &longs;patij, tum <lb/>mobilis, etiam in &longs;ecundis & tertiis minutis, &longs;i terre&longs;tris globus moveatur; <lb/>con&longs;tat item maxima velocitas, quam ne quidem globi ex majoribus, vel <lb/>minoribus tormentis emi&longs;&longs;i adæquant. </s>

<s><emph type="italics"/>Ad inueniendum igitur tertium proportionis terminum manen<lb/>tibus primis duobus<emph.end type="italics"/> 272, 5301, <emph type="italics"/>hæc erit ratio. </s>

<s>Reuocetur primum <lb/>ptopo&longs;itæ ma&longs;&longs;æ grauitas<emph.end type="italics"/> 837, <emph type="italics"/>ad grauitatem<emph.end type="italics"/> 5301, <emph type="italics"/>hoc est intelli<lb/>gatur ip&longs;a ma&longs;&longs;a grauitatem babere<emph.end type="italics"/> 5301. <emph type="italics"/>deinde fiat vt<emph.end type="italics"/> 837, <emph type="italics"/>ad<emph.end type="italics"/> 53, <lb/><emph type="italics"/>grauitatem vidclicet aquæ ip&longs;i ma&longs;&longs;æ æqualis, ita<emph.end type="italics"/> 5301, <emph type="italics"/>ad<emph.end type="italics"/> 335 2/3, <lb/><emph type="italics"/>ergo<emph.end type="italics"/> 335 2/3, <emph type="italics"/>erit grauitas aquæ magnitudinem habentis æqualem <lb/>aureæ ma<32>æ, cuius grauitas<emph.end type="italics"/> 837, <emph type="italics"/>reuocata est ad grauitatem<emph.end type="italics"/> 5301; <lb/><emph type="italics"/>quare grauitas &longs;ecundæ aquæ erit<emph.end type="italics"/> 335 2/1, <emph type="italics"/>& con&longs;equenter differen-<emph.end type="italics"/></s>

<s id="s.000634"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000635"> Quantus apparatus, Deus bone, contra Copernicanam hypo<lb/>the&longs;im; vereor tamen vt &longs;ufficiat. </s>

<s>TABELLE WAR HIER<lb/><emph type="italics"/>tia inter ip&longs;am grauitatem &longs;ecundæ aquæ & grauitatem tertiæ<emph.end type="italics"/> 551, <lb/><emph type="italics"/>erit<emph.end type="italics"/> 215 1/1, <emph type="italics"/>&longs;ed ip&longs;a differentia ponitur pro tertio proportionis ter<lb/>mino; crgo<emph.end type="italics"/> 215 1/3, <emph type="italics"/>erit quæ&longs;itus terminus, nempe proportionis ter<emph.end type="italics"/></s><pb pagenum="66"/>

<s>TABELLE WAR HIER<lb/><emph type="italics"/>tius. </s>

<s id="s.000636"><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s>

<s id="s.000637"> Cave, Antime, ne tibi tritum illud occinamus, <emph type="italics"/>parturient mon<lb/>tes<emph.end type="italics"/>; tantò fortè apparatu terrere i&longs;tos volui&longs;ti, de me nihil dico, quia re<lb/>verà tecum &longs;entio; aut fortè tam multis & variis initio nos fatigare, &longs;eu <lb/>potiùs obruere volui&longs;ti, vt &longs;cilicet, ea quæ oppones minus alacriter retun<lb/>damus; age igitur, nam prælu&longs;um &longs;atis; illos Oratores imitari mihi vi&longs;us es, <lb/>qui toti &longs;unt in exordiis; ita vt finito orationis exordio, ad aliud tran&longs;eant <lb/>exordium, & ab hoc &longs;ecundo ad aliud, & nunquam ad punctum, quod <lb/>probandum &longs;u&longs;ceperant, de&longs;cendunt, proloqui duntaxat & magnifica ex<lb/>ordia fabricare contenti. </s>

<s>Quartus autem terminus<emph.end type="italics"/> 4196 25/116, <emph type="italics"/>indicabit grauitatcm <lb/>auri puri, quod est in ma&longs;&longs;a propo&longs;ita, eam tamen indicabit in par<lb/>tibus, qualibus tota ma&longs;&longs;a constat<emph.end type="italics"/> 5301, <emph type="italics"/>quæ quidem grauitas vt <lb/>auri qualitatem indicet, reuocanda erit ad partes qualium totæ <lb/>ma&longs;&longs;a propo&longs;ita est<emph.end type="italics"/> 24. <emph type="italics"/>&longs;ienim fiat vt<emph.end type="italics"/> 5301, <emph type="italics"/>ad<emph.end type="italics"/> 4196<gap/>, <emph type="italics"/>ita<emph.end type="italics"/> 24, <lb/><emph type="italics"/>ad<emph.end type="italics"/> 19, <emph type="italics"/>aurum propo&longs;itæ ma&longs;&longs;æ appellabitur partium<emph.end type="italics"/> 19. </s>

<s><emph type="italics"/>Denique &longs;i quis hunc modum conferat cum illo, quem &longs;upra tradi<lb/>dimus, cum argentum explorauimus, quod miftum in aurea corona <lb/>credebatur; is liquido intelliget hic nihil aliud acce&longs;&longs;i<32>e, ni&longs;i quod <lb/>loco argenti, a&longs;&longs;umptum &longs;it corpus ex argento & ære mistum, eo <lb/>quod hæc duo metalla tantum in alligationibus auri &longs;oleant adbibe<lb/>ri, vt diximus. </s>

<s id="s.000638"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000639"> Ludis, Chry&longs;ocome, &longs;ed profectò non impunè feres; nemo non <lb/>videt, ea quæ præmi&longs;i, non e&longs;&longs;e exordia, &longs;ed iacta principia, ex quibus de<lb/>inde meum ratiocinium deducam; ni&longs;i enim hoc facerem, ingenuè di<lb/>cam, ratiocinari non po&longs;&longs;em; Vt vt &longs;it, Galilæus ve&longs;ter, Augu&longs;tine, eo va<lb/>lebat ingenio, in hac præ&longs;ertim motuum doctrina, in qua, ne quid di&longs;&longs;i<lb/>mulem, parem non habuit, immo neque hoc di&longs;&longs;imulabo, quam primus <lb/>ip&longs;e invenit, vt tam audacter pronunciarit, ex dicta motuum terre&longs;tris <lb/>globi inæqualitate, Oceani huc illuc excur&longs;ionem &longs;equi; & &longs;i fortè hoc <lb/>cum principiis eju&longs;dem doctrinæ non con&longs;entit et, nunquam revera tanta <lb/>a&longs;&longs;everatione hoc dixi&longs;&longs;et. </s>

<s>Quod &longs;i con&longs;taret plura alia a&longs;&longs;umpta e&longs;&longs;e, etiam in <lb/>quauis alia ratione, facile erit cuiuis ad &longs;imilitudinem huius, for<lb/>mare alium modum, &longs;ed nos, ne longiores &longs;imus, ad v&longs;um &longs;equentis <lb/>tabulæ nos conferamus, qua illis con&longs;ultum volumus qui minus in <lb/>præceptis Aritbmeticis &longs;unt exercitati, velillis, qui alias ob cau&longs;as <lb/>tabulis vti malunt, quam calculis.<emph.end type="italics"/></s>

<s id="s.000640">Il<gap/>us ergo major propo&longs;itio vera e&longs;t, &longs;cilicet <lb/>aquarum motum &longs;equi ex prædicta motuum inæqualitate, nec illius inge<lb/>nium in hoc falli potuit, qui alios ferè omnes doctrinam motuum docuit; <lb/>erravit tamen in minore, in qua &longs;anè illius ingenium non de&longs;idero, &longs;ed <lb/>majorem diligentiam, nec non æ&longs;tus marini peritiam; itémque maiorem <lb/>fidem, periti&longs;&longs;imis Naucleris adhibendam; optimè docuit ex dicta inæ-<pb pagenum="57" xlink:href="025/01/061.jpg"/>qualitate aquarum motum &longs;equi in &longs;ua hypothe&longs;i ; &longs;ed malè intulit, mari<lb/>num æ&longs;tum qualis nunc e&longs;t, ex ea &longs;equi; de marino æ&longs;tu, quod &longs;it, & ta<lb/>lis &longs;it, res certa e&longs;t; oculi dumtaxat applicandi; de terræ motu, quod re<lb/>verà &longs;it, nequidem Galilæus ip&longs;e certum e&longs;&longs;e pronunciavit; dubium igitur <lb/>etiam apud vos; cùm igitur rectè componamus Telluris quietem cum eo <lb/>maris æ&longs;tu, qui modò e&longs;t, nec eum ob&longs;ervemus, qui reverà e&longs;&longs;et, &longs;uppo&longs;ito <lb/>terræ motu; quidni nece&longs;&longs;ariò, ni fallor, concludam; terram nor moveri, <lb/>cùm id nullo modo &longs;it, quod reverà e&longs;&longs;et, &longs;i terra moveretur? </s>

<s><emph type="italics"/>Hæc tabula accommodata e&longs;t primarie ad aurum vnius libræ, vt <lb/>apparet in <expan abbr="&longs;ec&utilde;da">&longs;ecunda</expan> ip&longs;ius columna in qua omnes numeri &longs;unt vnita<lb/>tes, re&longs;pondentes &longs;ingulis Denominatoribus qualitatum auri, a deno <lb/>minatore partium<emph.end type="italics"/> 24, <emph type="italics"/>v&longs;que ad denominatorem qualitatis partis ò, <lb/>quamuis proprie loquendo nulla &longs;it qualitas auri partis nullius, quia <lb/>tunc non e&longs;&longs;et aurum, &longs;ed mistum ex argento & ære. </s>

<s id="s.000641"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>Hos denomi<lb/>natores auri omnes inuenies in prima columna &longs;ub titulo qualitatis. </s>

<s id="s.000642"> Tecum &longs;entio, Antime, in hoc Galilæum, in re motuum ver<lb/>&longs;ati&longs;&longs;imum, falli non potui&longs;&longs;e, eiu&longs;que autoritatem longè pluris in hoc <lb/>faciendam e&longs;&longs;e, quàm multorum aliorum, qui tantum molo&longs;&longs;um, catelli <lb/>&longs;anè, allatrare non ce&longs;&longs;ant; ne tamen hoc tuum argumentum non tantùm <lb/>&longs;it ad hominem, &longs;ed pariter omnibus rem i&longs;tam per&longs;uadeat; &longs;epone, quæ<lb/>&longs;o, autoritatem Galilæi, & de&longs;cende ad illas conclu&longs;iones, quas ex iactis <lb/>&longs;upra principiis deducere, opinor, meditaris. </s>

<s><lb/>In columna vero &longs;ub titulo misti placuit etiam de&longs;cribere denomi<lb/>natores mi&longs;ti ex argento & ære, vt vnico intuitu appareat quot par<lb/>tes auri puri, & quot partes misti ex argento & ære contineantur <lb/>in &longs;ingulis qualitatibus.<emph.end type="italics"/></s>

<s id="s.000643"><emph type="italics"/>Antim<emph.end type="italics"/> Faciam, quod &longs;uggeris; Supponamus igitur globum D Terram <lb/>e&longs;&longs;e & ita moveri, vt &longs;upra dicebam, circuli, Æquatoris v.g. partes, inæ<lb/>qualiter, vt longè tardiùs punctum, quod &longs;pectat ad Solem, & velociùs <lb/>oppo&longs;itum moveatur, id e&longs;t F, quàm E, in hoc enim &longs;chemate &longs;i&longs;tere po&longs;<lb/>&longs;umus, nec declinatio æquatoris ab Eclyptica, nec perpetuus axis paralle<lb/>li&longs;mus, nec motus centri quinquies circiter major motu orbis, ad hanc <lb/>rem quidquam faciunt, puncta I & H ita moventur, vt motui centri ni<lb/>hil detrahant, nihil addant; ab H ad E ita additur vt crementum acce&longs;&longs;io<lb/>nis &longs;emper augeatur, donec tandem in E maximum &longs;it: hoc porrò cremen<lb/>tum acce&longs;&longs;ionis fit iuxta progre&longs;&longs;um &longs;inuum ver&longs;orum: ab E ad I; ita ad<lb/>ditur, vt crementa acce&longs;&longs;ionum &longs;emper minuantur, donec tandem in I <lb/>nullum &longs;it crementum; hoc verò crementum fit iuxta priorem progre&longs;&longs;io<lb/>nem, &longs;ed inver&longs;am ac proinde iuxta progre&longs;&longs;ionem &longs;inuum rectorum: Ab <lb/>I ad F ita detrahitur motui, centri, vt crementa detractionis &longs;emper ma<lb/>jora &longs;int, donec tandem in F &longs;it maximum, idque iuxta progre&longs;&longs;ionem &longs;i<lb/>nuum ver&longs;orum; denique ab Fin H ita etiam detrahitur, vt crementa de<lb/>tractionis &longs;emper minora &longs;int, idque iuxta progre&longs;&longs;ionem &longs;inuum recto<lb/>rum, donec tandem in H nullum &longs;it crementum: Accipe igitur punctum <lb/>circuli v.g.H, ab H movetur motu accelerato, per impetum &longs;cilicet, à <lb/>quocunque tandem producatur; igitur vbi pervenit ad E inten&longs;i&longs;&longs;imum <lb/>impetum habet, cur ergo tam cito de&longs;truitur, cùm fru&longs;trà non &longs;it, effe<lb/>ctumque &longs;uum in mobili præ&longs;tare queat? </s>

<s><emph type="italics"/>Porro in area tabulæ &longs;ub titulo grauitatis auri in aqua po&longs;ita est <lb/>grauitas auri cuiuslibet qualitatis quam obtinet in aqua, quæ qua <lb/>ratione inueniatur, dicetur inferius vbi agetur de compo&longs;itione <lb/>eiu&longs;dem tabulæ.<emph.end type="italics"/></s>

<s><emph type="italics"/>V&longs;us eius &longs;unt duo, quorum alterum titulus indicat, nimirum vt <lb/>tabulæ beneficio reperiatur ex grauitate auri quam babet in aere & <lb/>aqua, eius qualitas. </s>

<s id="s.000644"><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s>

<s id="s.000645"> Minimè verò, cùm enim punctum E &longs;it pars globi, eandem <lb/>cum aliis partibus di&longs;po&longs;itionem retinere debet, quod certè vt fiat, illius <lb/>motus retardari debet; &longs;i autem motus retardatur, pro rata de&longs;truitur <lb/>impetus. </s>

<s>Alter vero est vt cogno&longs;catur grauitas in aqua, <lb/>quando vnà cum grauitate quam aliquod aurum habet in aere da<lb/>tur ip&longs;ius qualitas. </s>

<s>& de hoc v&longs;u cum &longs;it &longs;implicior prius nobis erit <lb/>agendum.<emph.end type="italics"/></s><pb pagenum="67"/>

<s id="s.000646"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000647"> Nunquid in mea & tua hypothe&longs;i, hic vel ille Oceani tractus <lb/>æquè pars e&longs;t terre&longs;tris globi, atque in Copernicana? </s>

<s>TABELLE WAR HIER</s>

<s>TABELLE WAR HIER</s><pb pagenum="68"/>

<s id="s.000648"><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s>

<s id="s.000649"> Fru&longs;tra interrogas; nullum enim dubium e&longs;t. </s>

<s><emph type="italics"/>Quæratur exempli gratia quam habet grauitatem in aqua <expan abbr="aur&utilde;">aurum</expan> <lb/>purum &longs;eu aurum<emph.end type="italics"/> 24, <emph type="italics"/>partium cuius grauitas in aere est lib.<emph.end type="italics"/> 1. <emph type="italics"/>Hæc <lb/>in &longs;upremo ordine è regione denominatoris partium 24, &longs;ub titulo <lb/>grauitatis auri in aqua, datur vnc. </s>

<s>1<emph.end type="italics"/> 1. <emph type="italics"/>Scrup.<emph.end type="italics"/> 8, <emph type="italics"/>Gran.<emph.end type="italics"/> 20 172/1767, <lb/><emph type="italics"/>quæ fractio licet exprimi po&longs;&longs;it minoribus numeris <expan abbr="n&etilde;pe">nempe</expan><emph.end type="italics"/> 4/19, <emph type="italics"/>libuit <lb/>tamen illam maiorem in tabula ponere, vt omnes fractiones totius <lb/>tabulæ e&longs;&longs;ent eiu&longs;dem denominationis, & re&longs;ponderent denomina<lb/>toribus fractionum quæ habentur in tabella partis proportionalis.<emph.end type="italics"/></s>

<s id="s.000650"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000651"> Rectè; at po&longs;tquàm modica vis venti prædicto aquarum tractui <pb pagenum="58" xlink:href="025/01/062.jpg"/>motum & impetum impre&longs;&longs;it, nunquid etiam ce&longs;&longs;ante vento, adhuc per <lb/>aliquod tempus aquarum motus & agitatio non durat? </s>

<s><emph type="italics"/>Rur&longs;um quæratur quam habet grauitatem in aqua aurum ite<lb/>rum vnius libræ, qualitatis vero<emph.end type="italics"/> 20, <emph type="italics"/>partium. </s>

<s id="s.000652">quis hoc neget? <lb/></s>

<s id="s.000653">idem in latiore concha videbis; vbi enim aqua infu&longs;a plena fuerit, acce<lb/>dente minimo motu, a qua illa libratur ver&longs;us latera conchæ; ita vt huiu&longs;<lb/>modi librationes diutiùs durent, etiam po&longs;tquam omnis motus extrin&longs;e<lb/>cus ce&longs;&longs;avit; Vnde porrò hoc? </s>

<s>quam &longs;i in tabula <lb/>quæras, inuenies &longs;ub eodem titulo è regione denominatoris<emph.end type="italics"/> 20, <emph type="italics"/>par<lb/>tium. </s>

<s id="s.000654">rationem ex no&longs;tro primo principio facilè <lb/>deduces; durat enim aliquandiu impetus priùs impre&longs;&longs;us; quia non e&longs;t <lb/>fru&longs;tra, &longs;altem quoad aliquam portionem, cùm aliquid motus præ&longs;tare <lb/>po&longs;&longs;it; codem pror&longs;us modo, tractus Oceani circa punctum E, cum velo<lb/>ci&longs;&longs;imè moveatur, impetum impre&longs;&longs;um aliquandiu retinet, &longs;ecundùm ali<lb/>quem gradum, vi cujus excurrit ver&longs;us Ortum; nam perinde &longs;e habet, atque <lb/>&longs;i in va&longs;ti&longs;&longs;ima concha contineretur. </s>

<s id="s.000655"><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s>

<s>11, Scrup. 6, Gran.<emph.end type="italics"/> 9 177/1767. <emph type="italics"/>eademque est ratio de re<lb/>liquis.<emph.end type="italics"/></s>

<s id="s.000656"> Movetur igitur totus ille aquarum tractus, &longs;ecundùm totam <lb/>profunditatem. </s>

<s id="s.000657"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quando vero propo&longs;itum aurum non est vnius Libræ; tunc opus <lb/>erit ratiocinatione proportionis, in qua pro primo termino ponatur <lb/>vna libra auri propo&longs;itæ qualitatis, pro &longs;ecundo termino, grauitas <lb/>eidem re&longs;pondens in aqua quam tabula exhibet, pro tertio vero ter<lb/>mino collocetur vera grauitas auri propo&longs;iti. </s>

<s id="s.000658"> Non dico hoc, neque nece&longs;&longs;e e&longs;t, neque fieri pote&longs;t; quia vt <lb/>Conchæ &longs;upremus circulus longè major e&longs;t, quàm alij paralleli, versùs <lb/>imum conchæ, ita longè faciliùs libratur aqua, intra majorem circulum, <lb/>quàm intra minorem; quia &longs;cilicet in majore, habet liberiorem campum, <lb/>in quo excurtat, quod facilè demon&longs;trari à me po&longs;&longs;et, &longs;i hoc etiam paret<lb/>gum vobis arri&longs;erit. </s>

<s>Quartus enim ter<lb/>minus exhibebit grauilatem ip&longs;ius auri in aqua. </s>

<s id="s.000659"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>Vt &longs;i propo&longs;itum <lb/><expan abbr="aur&utilde;">aurum</expan> &longs;it trium lib.

<s id="s.000660"> Mihi opus non e&longs;t; quis enim hoc ne&longs;cit? </s>

<s id="s.000661">Sic videmus in con<lb/>chis angu&longs;tioribus, aquam difficiliùs librari, in majoribus verò faciliùs. </s>

qualitatis vero 18, partium. </s>

<s>fiat vt lib.

<s id="s.000662"><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s>

<s id="s.000663"> Ita e&longs;t, hoc videmus, quamobrem verò, non ita forte qui&longs;piam <lb/>dixerit. </s>

1. ad vnc <lb/>11, Scrup.<emph.end type="italics"/> 5, <emph type="italics"/>Gran.<emph.end type="italics"/> 3 963/1767, <emph type="italics"/>ita lib.<emph.end type="italics"/> 3. <emph type="italics"/>ad alium numerum, is erit <lb/>lib.<emph.end type="italics"/> 2, <emph type="italics"/>vnc. </s>

<s>9, Scrup. 15, Gran.<emph.end type="italics"/> 10 1122/1767. <emph type="italics"/>& tanta erit grauitas au<lb/>ri propo &longs;iti in aqua. </s>

<s id="s.000664"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000665"> Quid faciliùs dictu, Chry&longs;ocome; &longs;i vas angu&longs;tum e&longs;t, latera <lb/>minus di&longs;tant, hinc aqua nece&longs;&longs;ariò minùs excurrit, vtpote quæ à vicinis <lb/>lateribus continetur; &longs;i vas amplum &longs;it &longs;ecus accidit; quia &longs;cilicet illius la<lb/>tera à &longs;e&longs;e invicem magis di&longs;tant, nec vllo &longs;chemate opus e&longs;t ad exponen<lb/>dam vim hujus rationis. </s>

<s>Et &longs;ic de alys.<emph.end type="italics"/></s>

<s id="s.000666"><emph type="italics"/>Choy&longs;oc.<emph.end type="italics"/></s>

<s id="s.000667"> Non agitur hoc loco, vtrum librationes aquæ intra vas angu<lb/>&longs;tum contentæ citiùs perficiantur, quam illæ quæ fiunt in majore va&longs;e; <lb/>nempe huiu&longs;modi librationes, funependulorum librationes imitantum, <lb/>quæ citò fiunt in brevi funependulo, tardiùs verò in longiore; &longs;ed alia <lb/>pror&longs;us e&longs;t difficultas, cur &longs;cilicet illa vis motus, quæ &longs;ufficit ad huiu&longs;mo<lb/>di librationes in va&longs;ta concha excitandas, non &longs;ufficiat &longs;i vas angu&longs;tum &longs;it, <lb/>nec ad majores, quæ reverà in angu&longs;to va&longs;e fieri non po&longs;&longs;unt, nec ad mi<lb/>nores, quas alioqui major vis motus excitaret; hîc tuam opem, Antime, <lb/>&longs;ed breviter, quæ&longs;o. </s>

<s><emph type="italics"/>Quod vero ad priorem v&longs;um attinct, is per&longs;imilis est præcedenti, <lb/>& æquè facilis quando grauitas auri quam in aere & aqua habet, in <lb/>tabula reperitur precisè. </s>

<s>Nam &longs;i proponatur exemp. </s>

<s id="s.000668"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000669"> Brevi&longs;&longs;imè, neque hoc facerem, ni&longs;i ve&longs;tro ju&longs;&longs;u; Sit concha <lb/><figure id="id.025.01.062.1.jpg" xlink:href="025/01/062/1.jpg"/><lb/>DCG laxior, & alia ECF angu&longs;tior, vtraque <lb/>ferè plena; aqua longè faciliùs pote&longs;t librari in <lb/>arcu DCG, quàm in ECF; hic enim magis ar<lb/>duus e&longs;t, ille vetò longè mollior, &longs;eu mitior; mi<lb/>nùs enim recedit à plano horizontali ; hinc &longs;u<lb/>perficies aquæ DBG a&longs;cendere pote&longs;t per arcum GA, etiam cum modi<lb/>co impetu, &longs;ecus vetò per arcum FI, propter adductam rationem. </s>

<s>gratia aurum <lb/>vnius lib.

habens in aqua <expan abbr="grauitas&etilde;">grauitasem</expan> vnc.<emph.end type="italics"/> 11. <emph type="italics"/>Scr.<emph.end type="italics"/> 7, <emph type="italics"/>Gra.<emph.end type="italics"/> 14 1152/1767, <lb/><emph type="italics"/>quoniam hæc grauitas reperitur in tabula è regione qualitatis auri<emph.end type="italics"/><lb/>22, <emph type="italics"/>partium; manife&longs;tum e&longs;t totidem partium e&longs;&longs;e <expan abbr="aur&utilde;">aurum</expan> propo&longs;itum.<emph.end type="italics"/></s>

<s id="s.000670"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/> Hæc plu&longs;quàm &longs;ufficiunt, redeamus ad rem, pro qua circa ea, <lb/>quæ à te dicta &longs;unt, hoc præ&longs;ertim opponendum mihi occurrit. </s>

<s><emph type="italics"/>Quando vero grauitas auri in aere quiaem e&longs;t vnius lib.

in aqua <lb/>vero grauitatem habet, quæ in tabula non reperuur, indicium erit <lb/>aurum propo&longs;itum non e&longs;&longs;e aliquot partium præcisè, &longs;ed annexam <lb/>habere aliquam fractionem, quæ per partem proportionalem inue<lb/>nietur hoc modo.<emph.end type="italics"/></s>

<s id="s.000671">Quod &longs;cilicèt omnes partes terre&longs;tris globi, vel &longs;ingulæ &longs;e&longs;e moveant, <lb/>vel ab extrin&longs;eco moveantur; &longs;ed ita temperatè, vt omnes inter &longs;e primam, <lb/>di&longs;po&longs;itionem retineant; vnde non mirum e&longs;t, &longs;i tractus idem maris circa E <lb/>velociùs, circa I tardius moveatur. </s>

<s><emph type="italics"/>Proponatur aurum vnius libræ in aqua habens grauitatem vnc. </s>

<s><lb/>11. Scrup. 6, Gran.<emph.end type="italics"/> 16 264/1767, <emph type="italics"/>qualis in tabula non reperitur Gra<lb/>uitas enim proxime maior est vnc. </s>

<s id="s.000672"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000673"> Hoc ni fallor &longs;ummum caput e&longs;t hujus difficultatis, quod tamen <lb/>ex dictis facilè di&longs;&longs;olvi pote&longs;t; nempe &longs;ive tractus ille maris moveat &longs;e&longs;e, <lb/>&longs;ive ab alio, fieri non pote&longs;t, vt &longs;ine impetu moveatur; igitur impetum <lb/>illum acquirit proportionatum motui, quo movetur in E, vel circumcir<lb/>ca; &longs;ive illum in &longs;e producat, &longs;ive ab alio recipiat; &longs;ed impetus &longs;emel pro<lb/>ductus à <expan abbr="quacunq;">quacunque</expan> tandem cau&longs;a, tamdiu remanet, quamdiu fru&longs;tra non e&longs;t, <lb/>tandiu verò fru&longs;tra non e&longs;t, quamdiu <expan abbr="aliqu&etilde;">aliquem</expan> effectum præ&longs;tare pore&longs;t in mo<lb/>bili, non alium certè quàm motum; quantumvis <expan abbr="aut&etilde;">autem</expan> temperatè producatur <lb/>novus impetus, hoc certè non facit, vt is, qui jam productus e&longs;t de&longs;truatur; <lb/><expan abbr="quãdiu">quandiu</expan> &longs;cilicet fru&longs;tra non e&longs;t: & vt res illa novis exemplis magis per&longs;picua <lb/>fiat; &longs;i aqua in canali declivi motu accelerato de&longs;cendat, qui deinde per mol<lb/>liorem deflexionem &longs;ur&longs;um &longs;ub æquali, vel in æquali inclinationis angulo at<lb/>tollatur, vbi aqua ad imum canalis pervenerit, non &longs;i&longs;tet hauddubiè, &longs;ed <lb/>per aliud canalis planum inclinatum a&longs;cendet, de&longs;cendétque denuo, mul<lb/>tis qua&longs;i librationibus repetitis, hic tamen impetus productus e&longs;t ab in<lb/>trin&longs;eco, Quando animal currit per declivem collem, gradum profectò <pb pagenum="60" xlink:href="025/01/064.jpg"/>&longs;i&longs;tere nequit, quantumvis contranitatur, &longs;cilicet propter impre&longs;&longs;um ante <lb/>impetum; in vibratis librati&longs;que corporibus innumera ferè &longs;uppetunt <lb/>exempla. </s>

<s id="s.000674">Quid mirum igitur, &longs;i prædictus maris tractus impetum ante <lb/>impre&longs;&longs;um retineat & excurrat in Ortum; neque hoc impedit connexio <lb/>partium eju&longs;dem globi, ni&longs;i hæ &longs;clidæ &longs;int ac duræ, nec non ita inter &longs;e <lb/>connexæ, vt vna ab alia &longs;eparari non po&longs;&longs;it; tunc enim moventur iuxta <lb/>leges novi impetus de&longs;tructò priore; nec mirum, cùm fru&longs;tra &longs;it; fru&longs;tra au<lb/>tem e&longs;t, quia motum alium habere 1. on pote&longs;t, præter illum, quem novus <lb/>impetus exigit. </s>

<s>1<emph.end type="italics"/> 1. <emph type="italics"/>Scrup. 6, Gran.<emph.end type="italics"/> 23 1551/1767, <lb/><emph type="italics"/>re&longs;pondens auro 21, partium, & grauitas proxime minor e&longs;t vnc.<emph.end type="italics"/> 11, <lb/><emph type="italics"/>Scrup. 6, Gran.<emph.end type="italics"/> 9 177/1767, <emph type="italics"/><expan abbr="earumq;">earumque</expan> differentia e&longs;t Gran.<emph.end type="italics"/> 14 1374/1767, <lb/><emph type="italics"/>quem admodum & inter qua&longs;cunque duas alias grauitates proxi-<emph.end type="italics"/><pb pagenum="69"/><emph type="italics"/>mas eadem e&longs;t differentia, propterta quod omnes grauitates in tabu<lb/>la procedunt per æqualem exce&longs;&longs;um, vel defectum, vt inferius de<lb/>mon&longs;trabitur. </s>

<s id="s.000675"><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s>

<s id="s.000676"> Si ergo in puncto E e&longs;&longs;et corpus &longs;olidum & durum, totum <lb/>priorem impetum a mitteret accedente novo. </s>

<s id="s.000677"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>Inueniatur quoque differentia inter eandem gra<lb/>uitatem proxime minorem & inter grauitatem auri propo&longs;iti quam <lb/>habet in aqua, quæ <expan abbr="quid&etilde;">quidem</expan> e&longs;t Gran.<emph.end type="italics"/> 7 687/1767, <emph type="italics"/>& fiat vt<emph.end type="italics"/> 14 1374/1767, <lb/><emph type="italics"/>ad 1, ita<emph.end type="italics"/> 7 687/1767, <emph type="italics"/>ad alium numerum & inuenietur hæc fractio<emph.end type="italics"/><lb/>1/2, <emph type="italics"/>eademque adycienda erit ad denominatorem 20, partium, vt <lb/>componatur totus denominator auri propo&longs;iti partium<emph.end type="italics"/> 20 1/2, <emph type="italics"/>& eo<lb/>dem modo mueniendus erit denominator <expan abbr="cuiu&longs;cunq;">cuiu&longs;cunque</expan> alterius auri, <lb/>cuius grauitas in aqua, in tabula non reperitur.<emph.end type="italics"/></s>

<s id="s.000678"> Minimè verò, ni&longs;i arctè cum aliis corporibus duris connexum <lb/>e&longs;&longs;et, &longs;it enim v.g.globus lævigati&longs;&longs;imus in E, &longs;upra &longs;uperficiem &longs;olidam <lb/>etiam lævigati&longs;&longs;imam, vitream puta, haud dubiè curreret prædictus glo<lb/>bus versùs Ortum, præ&longs;ertim cùm ad hunc motum nullo a&longs;cen&longs;u opus &longs;it, <lb/>ac proinde nulla pror&longs;us inclinatio contraria ob&longs;tet. </s>

<s><emph type="italics"/>Ceterum qui volet contentus e&longs;&longs;e partibus vige&longs;imis quartis de<lb/>nominatorum auri, is multo breuius a&longs;&longs;equetur quod quæritur, per <lb/>tabellam partis proportionalis. </s>

<s id="s.000679"><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s>

<s>illic enim vnico ingre&longs;&longs;u offendet <lb/>partem proportionalem, quam quærit, vt in eodem exemplo apparet, <lb/>in quo differentia grauitatum auri erat Gran.<emph.end type="italics"/> 7 687/1767, <emph type="italics"/>quæ in <lb/>tabella partis proportionalis habetur præcisè è regione particularum<emph.end type="italics"/><lb/>12. <emph type="italics"/>Vnde concluditur, denominatorem auri propo&longs;iti e&longs;&longs;e partium<emph.end type="italics"/><lb/>20 12/24, <emph type="italics"/>vel quod idem est partium<emph.end type="italics"/> 20 1/2, <emph type="italics"/>vt prius. </s>

<s id="s.000680"> Igitur ille globus ita &longs;emper moveretur in &longs;uperficie tetræ; <lb/>nihil enim de&longs;trueretillum impetum; quod <gap/> modò ex tuis principiis <lb/>deduco, &longs;ed ex trito Mathematicorum dicto. </s>

<s>Quando vero <lb/>differentia grauitatum in tabella partis proportionalis non habetur <lb/>præcisè. </s>

<s id="s.000681"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>accipiatur alia ip&longs;i propinquior & particula illi in latere <lb/>re&longs;pondens addatur denominatori auri ex primaria tabula extra<lb/>cti. </s>

<s id="s.000682"> Hoc certè ex meis principiis non &longs;equitur, immo contrarium; <lb/>novus enim, qui præfato globo accederet, impetus ad motum oppo&longs;itum, <lb/>vel qua&longs;i oppo&longs;itum determinatus, priorem illum &longs;en&longs;im de&longs;trueret. </s>

<s id="s.000683">v. g. <lb/>impetus novus accedens in P, (<emph type="italics"/>in anteriori Schemate<emph.end type="italics"/>) partim per PQ, id <lb/>e&longs;t, versùs ortum, ratione motus centri, partim per tangentem punctum <lb/>P e&longs;t determinatus; mixta autem linea &longs;eu determinatio ex vtraque illa <lb/>&longs;equitur, vt con&longs;tat ex doctrina motuum. </s>

<s>&longs;ic enim &longs;altem non errabitur in vna particula vige&longs;imaquarta <lb/>vnius partis denominatoris auri.<emph.end type="italics"/></s>

<s id="s.000684">Quod verò &longs;pectat ad tritum <lb/>illud Mathematicorum dictum, etiam in terræ immobilis hypothe&longs;i locum <lb/>habet, &longs;ed pro&longs;ectò nullum planum ita lævigari pote&longs;t, quin aliquot Sa<lb/>lebris a&longs;peretur; quod reverà &longs;ufficeret, ad illum impetum de&longs;truendum; <lb/>qualis &longs;it terræ &longs;uperficies, vides; ille porrò aquæ excurrentis tractus &longs;en&longs;im <lb/>fine &longs;en&longs;u conceptum motum remittit, propter impetum <expan abbr="ari&umacr;">contrarium</expan> impre&longs;<lb/>&longs;um, vbi enim pervenit in R v.g.cum motus centri &longs;it contrarius motui <lb/>orbis, haud dubiè inde aqua aliquo modo regredi cogitur; hinc conflictus; <lb/>adde mutationem determinationis lineæ motus in &longs;ingulis punctis &longs;emi<lb/>circuli EIF; denique adde aquæ divi&longs;ionem, quæ non parum re&longs;i&longs;tit <lb/>motui, præ&longs;ertim alterius aquæ; quæ libet autem re&longs;i&longs;tentia impetum &longs;en&longs;im <lb/>de&longs;truit. </s>

<s><emph type="italics"/>Denique &longs;i proponatur aurum non vnius libræ &longs;ed vel plurium, <lb/>vel &longs;olum aliquot vnciarum. </s>

<s id="s.000685"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>Reducenda erit eius grauitas quam <lb/>babet maqua, ad grauitatem quam haberet &longs;i e<32>et vnius libræ, id <lb/>quod ab&longs;oluetur per proportionis ratiocinationem, &longs;i pro termino <lb/>primo ponatur vera grauitas auri propo&longs;iti, pro &longs;ecundo, e iu&longs;dem <lb/>grauitas in aqua, & pro tertio lib.

<s id="s.000686"> Iam mentem tuam intelligere mihi videor; vis enim quod<lb/>libet punctum terre&longs;tris globi, ratione duplicis motus, centri &longs;cilicet, <lb/>atque orbis, duas determinationes habere, quæ in tertiam mixtam de<lb/>inde abeunt, perinde atque &longs;i duplex impetus impre&longs;&longs;us e&longs;&longs;et ad motum <lb/>mixtum; finge globo, eodem tempore, duplicem impetum imprimi <lb/>alterum versùs Boream, <expan abbr="alter&utilde;">alterum</expan> versùs Occa&longs;um, hæc gemina determinatio <lb/>in eandem motus mixti lineam coale&longs;cit, vnde &longs;uppo&longs;ita vtriu&longs;que impe<gap/><lb/>tus æqualitate, globus ver&longs;us Corum ibit, id e&longs;t, Boream inter & Occa-<pb pagenum="61" xlink:href="025/01/065.jpg"/>&longs;um. </s>

<s id="s.000687">Ita que in puncto E vna eademque e&longs;t vtriu&longs;que motus determinatio, <lb/>&longs;cilicet per tangentem versùs Ortum; in F verò, altera determinatio alteri <lb/>ex diametro opponitur; nam determinatio motus centri e&longs;t tangens ducta <lb/>in <expan abbr="Ort&utilde;">Ortum</expan>; nempe hîc motus determinationem in vna &longs;altem revolutione non <lb/>murat; at verò determinatio motus orbis e&longs;t tangens ducta in Occa&longs;um; in <lb/>aliis punctis inter EI, & IF, in diver&longs;as partes tendunt; v.g.in puncto I de<lb/>terminatio centri e&longs;t DI producta versùs Ortum; determinatio orbis per<lb/>pendiculariter cadit versùs GF. pari modo habentur aliæ in tangentibus; <lb/>& provt vna magis aut minùs con&longs;entit cum alia, velocior aut tardior <lb/>e&longs;t motus; Sed dic mihi. </s>

1, quartus enim terminus indica<lb/>bit grauitatem in aqua re&longs;pondentem vni libræ auri propo&longs;iti. </s>

<s id="s.000688">&longs;odes Antime, po&longs;ito quod &longs;it globus in E, cur <lb/>per tangentem non projicitur ver&longs;us Ortum? </s>

<s>& <lb/>hac inuenta reliqua expedientur vt prius.<emph.end type="italics"/></s>

<s id="s.000689"><emph type="italics"/>Antimus.<emph.end type="italics"/></s>

<s><emph type="italics"/>Exemplum huius ca&longs;us hic non affero, quod per &longs;e res &longs;it clara. </s>

<s id="s.000690"> Cur me tentas, Augu&longs;tine, ne&longs;cire non potes, hoc jam à <lb/>Galilæo &longs;olutum fui&longs;&longs;e, in quo certè, more &longs;uo maximam ingenij vim <lb/>o&longs;tendit. </s>

<s id="s.000691">Nullum corpus grave per horizontalem projicitur, quod &longs;tatim <lb/>ip&longs;o initio de&longs;cendere non incipiat; &longs;emiparabolam à &longs;ummo vertice &longs;uo <lb/>motu de&longs;cribens; &longs;ed quælibet parabola ex E vertice ducitur infra Cycloi<lb/>dem EQV, vi Geometræ demon&longs;trant; itaque dictus globus projicitur <lb/>quidem, &longs;ed ita, vt cùm a&longs;&longs;urgere non po&longs;&longs;it, in &longs;uperficie terræ volvatur, vt <lb/>alij globi volvuntur. </s>

<s><lb/>Sed illud tantum obiter aduertere placet, quod videtur pertinere <lb/>ad commodiorem v&longs;um tabulæ, videlicet vt ys in ca&longs;ibus in quibus <lb/>nece<32>arius cst calculus, fractiones granorum ommittantur quando <lb/>minus valent quam<emph.end type="italics"/> 1/2, <emph type="italics"/>& quando valent plus, eorum loco, addatur <lb/>vnum granum reliquis granis, & &longs;i quando accidat binc procreari <lb/>grana<emph.end type="italics"/> 24. <emph type="italics"/>tunc etiam grana ommittantur addita prius vnitate ad <lb/>&longs;crupula in tabula inuenta. </s>

<s>hac enim ratione calculus erit expedi<lb/>tior & error qui hinc oborietur erit in&longs;en&longs;ibilis.<emph.end type="italics"/></s><pb pagenum="70"/>

<s id="s.000692"><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s>

<s id="s.000693"> Quid dicam ad hæc, ne&longs;cio, certa tamen e&longs;&longs;e non puto; <lb/>alioquin actum e&longs;&longs;et de hy pothe&longs;i Copernicana; aliunde illud principium <lb/>certum e&longs;&longs;e videtur, quòd &longs;cilicét impetus aliquamdiu duret modò fru&longs;tra <lb/>non &longs;it, & aliquem motum præ&longs;tare queat, videmus enim globum proje<lb/>ctum moveri, etiam à projicientis manu ab&longs;tractum; rotam item in quo<lb/>cunque &longs;itu collocatam, vbi tantulus impetus initio impre&longs;&longs;us &longs;uerit; in <lb/>funependulis, res e&longs;t plu&longs;quam per&longs;picua, itemque in motibus, qui per <lb/>repercu&longs;&longs;ionem fiunt; commune igitur principium e&longs;&longs;e videtur, ex quo, <lb/>ni fallor, rectè deducis tractum matis, qui e&longs;t circa E, versùs Ortum deinde <lb/>excurrere; quod enim de globo dixi&longs;ti in eodem puncto E &longs;ito, ex hypothe&longs;i <lb/>dumtaxataccipio, non verò ab&longs;olutè dictum. </s>

<s>Compo&longs;itio eiu&longs;dem tabulæ.</s>

<s><emph type="italics"/>Si ea quæ bactenus &longs;unt dicta rectè intelligantur liquido appare<lb/>bit compo&longs;itionem tabulæ in eo con&longs;istere, vt inuoniatur grauitas <lb/>quam aurum cuiu&longs;uis qualitatis habet in aqua, hoc e&longs;t &longs;i intelligan<lb/>tur propo&longs;itæ plures ma&longs;&longs;æ auri, &longs;ingulæ &longs;ingularum librarum, & <lb/>alia &longs;it qualitatis<emph.end type="italics"/> 24, <emph type="italics"/>partium alia<emph.end type="italics"/> 23, <emph type="italics"/>alia<emph.end type="italics"/> 22, <emph type="italics"/>&c. </s>

<s id="s.000694"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000695"> Immò ab&longs;olutè dictum e&longs;&longs;e velim; non ratò quippe accidit vt <lb/>globi lævigati&longs;&longs;imi in planis etiam lævigati&longs;&longs;imis collocentur, &longs;eu marmo<lb/>reis, &longs;eu vitreis; lævigata glacie nihil ferè lævius inuenio; & &longs;upra glaciem <lb/>glaciata fru&longs;tra citò & facilè currunt; itaque &longs;i aqua movetur, excurritque, <lb/>modò Ortum, modò Occa&longs;um, versùs, non video quare globus lævigati&longs;<lb/>&longs;imus in plano lævigati&longs;&longs;imo &longs;itus, vel &longs;upra lævigatam glaciem, propter <lb/>eandem motus inæqualitatem moveri non debeat; & hoc etiam ad homi<lb/>nem, contra tuam hypothe&longs;im militat; vnde ruitetiam illa re&longs;pon&longs;io iam <lb/>&longs;upra indicata; quod &longs;cilicet terræ motus æ&longs;tus quidem matini cau&longs;a &longs;it, <lb/>&longs;ed non adæquata, vt aiunt; nempe quidquid tandem motus in aquas <lb/>traducat, in globulum eo modo &longs;itum, quo dictum e&longs;t, etiam traducere <lb/>deberet, cùm æquè facile traduci queat; accipio enim globulos tam fa<lb/>cilè mobiles, vt nihil mobilius excogitari po&longs;&longs;it, tornatos &longs;cilicet ex Mer<lb/>curio. </s>

<s>quanta &longs;it gra<lb/>uitas vniu&longs;cuiu&longs;que in aqua, id quod hoc extremo loco inuestigare <lb/>docebimus.<emph.end type="italics"/></s>

<s><emph type="italics"/>Et primum &longs;it propo&longs;itum aurum purum, &longs;eu<emph.end type="italics"/> 24, <emph type="italics"/>partium. </s>

<s id="s.000696"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000697"> De puncto E fortè &longs;atis dictum, & plu&longs;quàm &longs;atis; de aliis <pb pagenum="62" xlink:href="025/01/066.jpg"/>quid cen&longs;es? </s>

<s>quo<lb/>niam igitur grauitas auri in aere, ad grauitatem eiu&longs;dem in aqua <lb/>&longs;e habet vt 19, ad<emph.end type="italics"/> 18, <emph type="italics"/>fiat vt<emph.end type="italics"/> 19, <emph type="italics"/>ad<emph.end type="italics"/> 18, <emph type="italics"/>ita lib.<emph.end type="italics"/> 1, <emph type="italics"/>auri puri ad aliam <lb/>grauitatem nempe lib.<emph.end type="italics"/> 1<gap/>/19, <emph type="italics"/>quæ grauitas ad vncias, &longs;crupula, & <lb/>grana reuocata valet vnc.<emph.end type="italics"/> 11, <emph type="italics"/>Scrup.8. Gran.<emph.end type="italics"/> 20 4/19, <emph type="italics"/>atque hæc est <lb/>grauitas auri puri in aqua, quam in tabula è regione denominaioris<emph.end type="italics"/><lb/>24, <emph type="italics"/>po&longs;uimus; fractione excepta cuius loco &longs;ub&longs;tituta est fractio<emph.end type="italics"/><lb/>372/1767, <emph type="italics"/>propter cau&longs;am &longs;uperius allatam.<emph.end type="italics"/></s>

<s id="s.000698">Non dubito enim, quin de iis aliquid dicturus &longs;is; ad quid <lb/>enim duo alia principia præmi&longs;i&longs;&longs;es? </s>

<s><emph type="italics"/>Sit deinde propo&longs;itum quod vis aliud corpus aureum vnius libræ, <lb/>&longs;itque exemp. </s>

<s id="s.000699"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>gratia illud aurum<emph.end type="italics"/> 20, <emph type="italics"/>partium, patet igitur ex defi<lb/>nitione qualitatis, ex<emph.end type="italics"/> 24, <emph type="italics"/>&longs;emiunciis totius grauitatis,<emph.end type="italics"/> 20, <emph type="italics"/>&longs;emiuncias <lb/>e&longs;&longs;e auri puri, duas argenti, & reliquas duas æris & quoniam gra<lb/>uitas misti in aere, ad grauitatem eiu&longs;dem in aqua rationem habet <lb/>vt<emph.end type="italics"/> 279, <emph type="italics"/>ad<emph.end type="italics"/> 250, <emph type="italics"/>vt exiam dictis patet, fiat vt<emph.end type="italics"/> 279, <emph type="italics"/>ad<emph.end type="italics"/> 250, <emph type="italics"/>ita qua<lb/>tuor &longs;emiunciæ, vel potius <gap/>, vnciæ misti quod componit qualitatem <lb/>auri<emph.end type="italics"/> 20, <emph type="italics"/>partium, paulo ante propo&longs;itam ad alias vncias. </s>

<s id="s.000700"> Etiam &longs;i nihil aliud dicerem, an fortè illa, quæ de puncto E <lb/>dixi non &longs;ufficiunt ad tuam &longs;ententiam impugnandam? </s>

<s id="s.000701">Sed agedum, <lb/>quandoquidem me &longs;timulas, etiam de aliis punctis nonnulla dicenda &longs;unt, <lb/>eaque ex duobus aliis principiis, quæ &longs;upra data opera præmi&longs;i eruenda. <lb/></s>

<s>inuenien<lb/>tur enim pro grauitate illius mi&longs;ti in aqua vnc.<emph.end type="italics"/> 1 221/274. <emph type="italics"/>Est autem <lb/>grauitas auri puri<emph.end type="italics"/> 20, <emph type="italics"/>&longs;emiunciarum vel<emph.end type="italics"/> 10, <emph type="italics"/>vnciarum in aqua vnc.<emph.end type="italics"/><lb/>9 9/19, <emph type="italics"/>eo quod ita &longs;e habeant<emph.end type="italics"/> 10, <emph type="italics"/>ad<emph.end type="italics"/> 9 9/29, <emph type="italics"/>vt 19, ad<emph.end type="italics"/> 18, <emph type="italics"/>Quare &longs;i hæ <lb/>duæ grauitates inuentæ colligantur in vnam &longs;ummam, inueniemus <lb/>totam ma&longs;&longs;am auri propo&longs;itam, cuius grauitas in aere ponebatur lib. <lb/>1, in aqua babere grauitatem vnc.<emph.end type="italics"/> 11 1409/5301. <emph type="italics"/>& facta reductione <lb/>fractionis ad &longs;crupula, & grana, vnc. </s>

<s id="s.000702">Si terræ globum quoquo versùm obtegeret aqua, ita vt v.g.ex 8. partibus <lb/>&longs;emidiametri, octava, &longs;uprema &longs;cilicet, aquea e&longs;&longs;et, extremaque &longs;uperfi<lb/>cies terræ convexa, cui &longs;uperficies aquæ incubat, lævis e&longs;&longs;et, nullis mon<lb/>tibus, nullis &longs;alebris a&longs;pera; Iam verò quàm celerrimè interior ille & in <lb/>aquis latens terræ globus circa &longs;uum centrum immobile volvatur; an for<lb/>tè putas, tunc motum in portionem aqueam traductum iri? </s>

<s id="s.000703"><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s>

<s>1<emph.end type="italics"/> 1, <emph type="italics"/>Scrup.<emph.end type="italics"/>6. <emph type="italics"/>Gran.<emph.end type="italics"/> 9 177/1767, <lb/><emph type="italics"/>vt videre e&longs;t in tabula è regione denominatoris<emph.end type="italics"/> 20, <emph type="italics"/>partium. </s>

<s id="s.000704"> Traducendum e&longs;&longs;e omnino crederem; terra enim illam etiam <lb/>aquam &longs;u&longs;tineret; igitur &longs;ecum vna deferret. </s>

<s>Atque <lb/>eodem modo deprehendentur grauitates auri in aqua <expan abbr="quarumcunq;">quarumcunque</expan> <lb/>aliarum qualitatum.<emph.end type="italics"/></s>

<s id="s.000705"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quia vero permolestum videri po&longs;&longs;et omnes grauitates totius <lb/>tabulæ hac via eruere; ob&longs;eruari quidem poterit prædicta Methodus <lb/>quando &longs;eor&longs;im inuestiganda fuerit alicuius auri grauitas in aqua, <lb/>in <expan abbr="cõpo&longs;itione">compo&longs;itione</expan> vero tabulæ &longs;ic forta&longs;&longs;is <expan abbr="cõpendio&longs;ius">compendio&longs;ius</expan> quis proce&longs;&longs;erit.<emph.end type="italics"/></s>

<s id="s.000706"> At ego &longs;ecus &longs;entio; hic enim ca&longs;us no&longs;tro &longs;imilis e&longs;t; &longs;i <lb/>enim vas probè tornatum aqua plenum in &longs;itu horizontali circa axem <lb/>verticalem accurati&longs;&longs;imè & citra vllam inclinationem erectum, etiam ce<lb/>lerrimè vertatur, immotam pror&longs;us aquam videbimus; Quid vis tibi di<lb/>cam, Chry&longs;ocome, oculos meos te&longs;tes appello, & &longs;i fidem detrectes, <lb/>vel in &longs;cutella &longs;tannea, quamvis imperfectè tornata, hoc ip&longs;um videbis. </s>

<s><emph type="italics"/>Equidem, cum huius tabulæ con&longs;tructionem diligentius mecum<emph.end type="italics"/><pb pagenum="71"/><emph type="italics"/>pertracto, video grauitates illas, quæ in eius area de&longs;criptæ &longs;unt ne<lb/>ce&longs;&longs;ario eadem differentia procedere, &longs;icut & denominatores quali<lb/>tatum eadem differentia procedunt; atque adco differentiam illam <lb/>e&longs;&longs;e eam, qua grauitas &longs;emiunciæ auri puri in aqua &longs;uperat in aqua <lb/><expan abbr="grauitat&etilde;">grauitatem</expan> &longs;emiunciæ mi&longs;ti, quæ <expan abbr="quid&etilde;">quidem</expan> differentia e&longs;t Gra.<emph.end type="italics"/> 14 1174/1767. <lb/><emph type="italics"/>Con&longs;iderentur enim quæcunque duæ grauitates proximæ in tabula <lb/>expre<32>æ, vt exemp. </s>

<s id="s.000707"><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s>

<s>gratia. </s>

<s id="s.000708"> Aqua igitur non &longs;u&longs;tinetur à va&longs;e, alioquin &longs;i vas illam &longs;u<lb/>&longs;tineret, &longs;ecum illam circumferret, &longs;ic librum hunc, quem manu teneo, <lb/>manus ip&longs;a, quocumque fertur, traducit. </s>

<s>grauitates auri<emph.end type="italics"/> 20, <emph type="italics"/>&<emph.end type="italics"/> 19, <emph type="italics"/>partium. </s>

<s id="s.000709"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>Quo<lb/>niam igitur in auro<emph.end type="italics"/> 20, <emph type="italics"/>partium &longs;unt auri puri<emph.end type="italics"/> 20. <emph type="italics"/>&longs;emiunciæ, misti <lb/>vero<emph.end type="italics"/> 4, <emph type="italics"/>& in auro<emph.end type="italics"/> 29, <emph type="italics"/>partium &longs;unt auri puri<emph.end type="italics"/> 19. <emph type="italics"/>&longs;emiunciæ, misti <lb/>vero<emph.end type="italics"/> 5, <emph type="italics"/>erit in auro<emph.end type="italics"/> 20. <emph type="italics"/><expan abbr="parti&utilde;">partium</expan> vna &longs;emiuncia auri puri plu&longs;quam in <lb/>auro<emph.end type="italics"/> 19, <emph type="italics"/>partium, in auro autem 19, partium erit vna &longs;emiuncia <lb/>misti plus quam in auro<emph.end type="italics"/> 20, <emph type="italics"/>partium; quare grauitas auri<emph.end type="italics"/> 20, <emph type="italics"/>par<lb/>tium in aqua &longs;uperabit in aqua grauitatem auri<emph.end type="italics"/> 19, <emph type="italics"/>partium gra<lb/>uitate, qua &longs;emiuncia auri puri &longs;uperat &longs;emiunciam mi&longs;li. </s>

<s id="s.000710"> Standum e&longs;t experimentis; tu fortè quid, Antime? </s>

<s id="s.000711">qui litem <lb/>movi&longs;ti, & cautè &longs;ubrides. </s>

<s>Quod <lb/>erat demon&longs;trandum. </s>

<s>Et eadem est ratio de alys grauitatibus, non <lb/>&longs;olum quæ in hac tabula de&longs;cribuntur, &longs;ed etiam de illis, quæ de&longs;cri<lb/>bentur in alys, copio&longs;ioribus, in quibus videlicet denominatores non <lb/>e&longs;&longs;ent partes integræ, &longs;ed partes partiam; dummodo etiam illæ partes <lb/>per vnam eandemque differentiam progrederentur.<emph.end type="italics"/></s>

<s id="s.000712"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000713"> Dicam quod &longs;entio, & quod verum e&longs;t; Aqua certè quie&longs;cit, <lb/>dum vas pernici&longs;&longs;imè volvitur; & &longs;i vas probè tornatum e&longs;&longs;et, & circa <lb/>axem minimè inclinatum volveretur, eaque demum e&longs;&longs;et cava &longs;uperficie, <lb/>quam nulla pror&longs;us ruga, nulla &longs;alebra, quantumvis in&longs;en&longs;ibilis a&longs;peraret, <lb/>dico nunquam fore, vt cum va&longs;e aqua moveretur; & hîc applico princi<lb/>pium &longs;upra iactum, &longs;cilicet nunquam motum, vel impetum ab aliquo mo<lb/>bili imprimi alteri, ni&longs;i hoc motum illius impediat, aut retardet: in hoc <lb/>autem ca&longs;u, aqua va&longs;e contenta motum va&longs;is nullo modo impedit, non <lb/>per &longs;uam molem, &longs;eu molis pondus; quia moles &longs;eu pondus re&longs;i&longs;tit tan<lb/>tummodo motui, &longs;ur&longs;um; &longs;ed nulla pars va&longs;is, in hoc motu a&longs;cendit; nulla <lb/>igitur aquæ pars attollenda e&longs;t; præterea nulla pars ob&longs;i&longs;tit motui va&longs;is, <lb/>quia id tantùm per contactum fieret; &longs;ed nulla pars tangens ob&longs;i&longs;tit, cùm <lb/>nulla pars cavæ va&longs;is &longs;uperficiei extare, & dam movetur, in aquam impin<lb/>gi &longs;upponamus; vt tamen dicam, quod res e&longs;t, cùm & axis ab&longs;que aliqua <lb/>inclinatione erigi, & &longs;ic &longs;tare vix po&longs;&longs;it, & quod caput e&longs;t, nullum &longs;it <lb/>corpus durum, quantumvis lævigatum, &longs;ine poris, rugis, & &longs;alebris, hinc <lb/>fit, aquam dicto va&longs;e contentam tantulùm ob&longs;i&longs;tere motui va&longs;is, ac proin<lb/>de non mirum videri, &longs;i initio quidem immota maneat, quia tamen &longs;en&longs;im <lb/>&longs;ine &longs;en&longs;u vires acquirit, circumferri tandem cum &longs;uo va&longs;e cernitur, & hoc <lb/>adjicere debueras, Augu&longs;tine, vt &longs;emper &longs;uus &longs;it veritati locus. </s>

<s><emph type="italics"/>Quibus in hunc modum præ osten&longs;is, &longs;i construenda fuerit tabula <lb/>per continuam additionem eiu&longs;dem numeri, &longs;ic erit progrediendum. </s>

<s><lb/>Primo inuenienda erit grauitas quam habet &longs;emiuncia auri puri in <lb/>aqua, quæ inuenietur &longs;i fiat vt<emph.end type="italics"/> 19, <emph type="italics"/>ad<emph.end type="italics"/> 18, <emph type="italics"/>ita &longs;emiuncia ad alium, <lb/>numenum qui &longs;it vnc.<emph.end type="italics"/> 9/19, <emph type="italics"/>is enim dabit grauitatem quæ&longs;itam, quæ <lb/>valet &longs;crup.<emph.end type="italics"/>1 1, <emph type="italics"/>Gran.<emph.end type="italics"/> 8 16/19. </s>

<s id="s.000714"><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s>

<s><emph type="italics"/>Secundo quærenda est grauitas &longs;emiuncie misti in aqua, quæ ha<lb/>bebitur &longs;i fiat vt<emph.end type="italics"/> 279, <emph type="italics"/>ad<emph.end type="italics"/> 250, <emph type="italics"/>ita &longs;emiuncia, ad alium numerum, qui <lb/>&longs;it vnc.<emph.end type="italics"/> 125/229, <emph type="italics"/>is enim dabit grauitatem quæ&longs;itam, quæ reducta ad <lb/>&longs;crupula, & grana valet &longs;crup.<emph.end type="italics"/> 10, <emph type="italics"/>Gran.<emph.end type="italics"/> 18 2/3. </s>

<s id="s.000715"> Quid verò fieret, &longs;i vas in circulo verticali verteretur? </s>

<s><emph type="italics"/>Tertio exploranda est differentia inter duas grauitates proximè <lb/>inuentas, quam per &longs;ubtractionem inuenies Gran.<emph.end type="italics"/> 14 452/589, <emph type="italics"/>cuius <lb/>tamen fractio reducta e&longs;t ad partes<emph.end type="italics"/> 1767, <emph type="italics"/>nempe ad<emph.end type="italics"/> 1374/1767, <emph type="italics"/>propter <lb/>tabellam partis proportionalis.<emph.end type="italics"/></s>

<s id="s.000716"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s><emph type="italics"/>Postremo inuestiganda erit grauitas in aqua vnius libræ misti, <lb/>quæ inuenietur &longs;i grauitas &longs;ecundo loco reperta per<emph.end type="italics"/> 24, <emph type="italics"/>multiplice<lb/>tur, productus enim numerus vnc.<emph.end type="italics"/> 10, <emph type="italics"/>&longs;crup. </s>

<s id="s.000717"> Eadam &longs;uppone; vas &longs;cilicet cylindricum, aut &longs;phæricum ca<lb/>vum, lævigata intus &longs;uperficie, circa axem plano horizontis planè paral<lb/>lelum; idemque &longs;ucce&longs;&longs;um iri puta; cùm eadem ratio vtrimque & æquè <lb/>militet. </s>

<s>18, Gran.<emph.end type="italics"/> 969/1767, <emph type="italics"/>da<lb/>bit quæ&longs;itam grauitatem. </s>

<s id="s.000718"><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s>

<s>Qua in calce tabulæ de&longs;cripta, compo<lb/>nentur reliquæ grauitates omnes per continuam additionem diffe<lb/>rentiæ tertio loco inuentæ. </s>

<s id="s.000719"> Immo ex alio tuo principio, quo dicis, eo motu moveri <lb/>mobile, quò faciliùs moveri pote&longs;t, colligo, ni fallor, longè potiori iure <lb/>pro i&longs;to vltimo ca&longs;u rationem militare; cùm enim faciliùs aqua illa à &longs;uo <lb/>va&longs;e, dum in plano horizontali volvitur, moveri po&longs;&longs;it, quàm ab eodem <lb/>in hoc &longs;ecundo ca&longs;u; quia vt imprimo illo moveatur aqua, ne latum quidem <lb/>vnguem attollenda e&longs;t, nullam igitur difficultatem, &longs;eu re&longs;i&longs;tentiam ex hoc <lb/>capite vas &longs;entit; cùm tamen in &longs;ecundo ca&longs;u, illa portio aquæ, quæ con<lb/>tinetur in inferiore parte dolij, &longs;eu cylindri, ad &longs;uperiorem partem cylin<lb/>dri locum attollenda &longs;it; vnde difficultas & re&longs;i&longs;tentia; igitur cùm mobi<lb/>le eo motu moveatur, quo facilius moveri pote&longs;t, longè facilius e&longs;t, vas <lb/>moveri &longs;ine aqua in &longs;ecundo ca&longs;u, quàm in primo </s>

<s>Si enim addatur ad grauitatem auri <lb/>partis o, idest ad grauitatem misti vnius libræ in aqua, componetur<emph.end type="italics"/><pb pagenum="72"/><emph type="italics"/>grauitai auri<emph.end type="italics"/> 1, <emph type="italics"/>partis. </s>

<s id="s.000720"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>addita veroad grauitatem 1, partis, procrea<lb/>bit grauitatem<emph.end type="italics"/> 2, <emph type="italics"/>partium, &c. </s>

<s id="s.000721"> Plurimùm &longs;anè me tibi ob&longs;trinxi&longs;ti, mi Chry&longs;ocome, cogita<lb/>bam &longs;tatim principium illud iam &longs;upra iactum, ac fusè non &longs;ine querela <lb/>expo&longs;itum, huc accer&longs;ere; &longs;ed ab hoc pen&longs;o me libera&longs;ti, ita e&longs;t; cùm vas <lb/>vtrumque faciliùs moveri po&longs;&longs;it, quie&longs;cente aqua, vt patet, etiam ab&longs;que <lb/>vlla penitus &longs;ui motus iactura; ita &longs;anè ex illo quoque principio probatur, <lb/>va&longs;a &longs;ine aqua contenta moveri; quod autem addis, longe facilius in <lb/>&longs;ecundo ca&longs;u quam in primo, pace tua dixerim; quia &longs;cilicet æquè facilè <lb/>vtrimque aqua cum &longs;uo va&longs;e movetur, nec ob&longs;tat inferiorem aquæ partem <lb/>in &longs;ecundo ca&longs;u ab imo ad &longs;upremum va&longs;is locum attolli, ac proinde illius <lb/>pondus ob&longs;tare ac re&longs;i&longs;tere; nam ita attollitur, vt eodem tempore, æqualis <lb/>portio deprimatur, e&longs;t enim perfectum æquilibrium, vt vides; &longs;ic vbi libra <lb/>in æquilibrio ver&longs;atur, &longs;i vel minimam vim alteri lancium &longs;ur&longs;um impre&longs;&longs;e<lb/>ris, illa &longs;tatim &longs;ur&longs;um attollitur; an fortè illa vis minima impre&longs;&longs;a ad hoc <lb/>&longs;ufficit? </s>

<s id="s.000722">Minimè vero; &longs;ed minima illa acce&longs;&longs;ione tollitur æquilibrium: <lb/>quid mirum ergo, fi portio præponderans, deor&longs;um eat, & oppo&longs;itam at<lb/>tollat? </s>

<s>propter rationem quam paulo ante <lb/>aperuimus.<emph.end type="italics"/></s>

<s id="s.000723">Sic æquè facilè rota volvitur in &longs;itu horizontali ac verticali. </s>

<s><emph type="italics"/>Hoc eodem artificio compo&longs;ita est quoque tabella partis propor<lb/>tionalis, primo enim inuenta e&longs;t vige&longs;ima quarta pars differentiæ <lb/>&longs;ecundum quam tabula progreditur quam &longs;upra inuenimus e&longs;&longs;e <lb/>Gran.<emph.end type="italics"/> 14 1374/1707, <emph type="italics"/>cuius pars vige&longs;ima quarta est<emph.end type="italics"/> 1072/1707, <emph type="italics"/>deinde <lb/>banc particulam addidimus primum &longs;ibi ip&longs;i, & produximus diffe<lb/>rentiam<emph.end type="italics"/> 2, <emph type="italics"/>particularum Gran.<emph.end type="italics"/> 1 409/1707 <emph type="italics"/>& buic differentiæ <expan abbr="iter&utilde;">iterum</expan> <lb/>adiecimus eandem particulam, & inuenimus pro tribus particulis <lb/>gran.<emph.end type="italics"/> 1 1497/1767. <emph type="italics"/>& ita deinceps progre&longs;&longs;i &longs;umus v&longs;que ad differen<lb/>tiam Gran.<emph.end type="italics"/> 14 1374/1767, <emph type="italics"/>quæ re&longs;pondet<emph.end type="italics"/> 24, <emph type="italics"/>particulis, &longs;eu differentiæ, <lb/>&longs;ecundum quam tabula progreditur.<emph.end type="italics"/><lb/><emph type="italics"/>FINIS.<emph.end type="italics"/></s>

<s id="s.000724"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/> Hæc veri&longs;&longs;ima e&longs;&longs;e, non diffiteor, ita enim à natura compa<lb/>ratus &longs;um, vt compertæ veritati numquam non me &longs;ubjiciam; movetur <lb/>autem aqua cum &longs;uo va&longs;e, vt dicis, per accidens<gap/> non per &longs;e, nimirum, <lb/>propter a&longs;peritatem & inæqualitatem interioris &longs;uperficiei; at numquid <lb/>non po&longs;&longs;et ab hoc vitio liberari, obducto &longs;cilicet oleo, vel alio quopiam <lb/>vliginis genere? </s>

<s>ERRATA SIC CORRIGE.</s>

<s>TABELLE WAR HIER</s>

<s id="s.000725"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000726"> An fortè putas, oleum &longs;uis rugis & &longs;triis, nec non filaminibus <lb/>carere? </s>

<s><emph type="italics"/><expan abbr="Contractior&etilde;">Contractiorem</expan> <expan abbr="quoq.">quoque</expan> ad inuenies dimidij pedis <expan abbr="men&longs;urã">men&longs;uram</expan> in margine pag. </s>

<s id="s.000727">Vidi&longs;ti, ni fallor, aliquando, majores illas guttas &longs;ive butyro, &longs;eu <lb/>va&longs;ibus vnctis oleo adhære&longs;cere, an fortè in plani&longs;&longs;ima &longs;uperficie adhæ<lb/>rete po&longs;&longs;ent? </s>

<s>34. <expan abbr="appo&longs;itã">appo&longs;itam</expan>, <lb/>quia mad facta papyrus, <expan abbr="d&utilde;">dum</expan> imprimeretur recipiebat <expan abbr="verã">veram</expan> <expan abbr="men&longs;urã">men&longs;uram</expan>, ex&longs;iccata <lb/>breuiorem reddidit. </s>

<s id="s.000728"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s>Ita que &longs;i quartadecima pars vnius vncia addatur ip&longs;i men <lb/>&longs;ura componetur dimidij pedis men&longs;ura; vel &longs;i ip&longs;a men&longs;ura duplicetur, & ei ad<lb/>datur &longs;eptima pars vnius vncia fiet men&longs;ura vnius pedis, ad cuius rationem em <lb/>nes calculi in tabulas optime re&longs;pond ebunt.<emph.end type="italics"/></s>

<s id="s.000729"> Sed vnde quæ&longs;o, i&longs;tæ guttulæ; rem illam &longs;æpè ob&longs;ervavi, cu<lb/>jus tamen rationem vix ac ne vix quidem mente a&longs;&longs;equor. </s>

<s><emph type="italics"/>Denique pagina<emph.end type="italics"/> 38. <emph type="italics"/>&<emph.end type="italics"/> 39. <emph type="italics"/>tabularum prapo&longs;terus e&longs;t ordo. </s>

<s id="s.000730"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s>ex quo tamen nihil sr<lb/>reris &longs;equitur &longs;i tituli recte accipiantur.<emph.end type="italics"/></s> </chap> </body> <back/> </text></archimedes>

<s id="s.000731"> Sunt quædam &longs;uperficies ita di&longs;po&longs;itæ inter &longs;e, vt in earum rimas <pb pagenum="64" xlink:href="025/01/068.jpg"/>&longs;eu rugas, aqua &longs;ubire non po&longs;&longs;it, aut &longs;i reverà &longs;ubeat, &longs;tatim effluar, in <lb/>pennis avium aquatilium v.g. An&longs;erum, Anatum, aliarumque &longs;imilium, <lb/>hoc ip&longs;um ob&longs;ervamus, immo in multis foliis, vt bra&longs;&longs;icæ, in quibus hu<lb/>ju&longs;modi aquæ guttulæ, qua&longs;i totidem liquatas gemmas, po&longs;t pluviæ vel <lb/>roris lap&longs;um &longs;æpè vidi&longs;ti; quia &longs;cilicet laxioribus rugis &longs;eu &longs;triis in longum <lb/>& rectam lineam ductis con&longs;tant, per quas aqua &longs;tatim de&longs;cendit, atque <lb/>effluit, ni&longs;i aliqua fo&longs;&longs;ula in&longs;it, in qua major gutta ex reliquis longè mi<lb/>noribus eò per rugam declivem confluentibus, componitur; in &longs;uperficie <lb/>butyri rectas huiu&longs;modi &longs;trias tantùm non videmus; nec fortè mirum; <expan abbr="n&etilde;pe">nempe</expan> <lb/>vligino&longs;a ex multis filaminibus con&longs;tant; fila autem in longum ducuntur; <lb/>iunge &longs;imul multas acus, & aliquid fortè &longs;imile a&longs;picies; cur verò guttæ <lb/>illæ majores in iis fo&longs;&longs;ulis tornatæ deinde non cadant, etiam &longs;i vas vnctum, <lb/>cui adhærent, ever&longs;o &longs;itu &longs;tatuatur, eadem ratio e&longs;t, propter quam na&longs;o, pa<lb/>leæ, ligno, alií&longs;que corporum extremitatibus gutta adhæret, ac de illis pen<lb/>det quam certè hoc loco explicare non po&longs;&longs;um, cùm inde va&longs;ti&longs;&longs;imus allis <lb/>experimentis ad &longs;uas veras cau&longs;as phy&longs;icas reducendis campus ape<lb/>riatur. </s>

<s id="s.000732"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000733"> Auguror rem grati&longs;&longs;imam fore, & fortè altero congre&longs;&longs;u <expan abbr="dignã">dignam</expan>, <lb/>quandoquidem tam latè patere dictitas; &longs;ed ad propo&longs;itum, qùæ&longs;o, redea<lb/>mus: Con&longs;tat igitur, illum terræ globum ver&longs;um iri, licèt aqua circum<lb/>po&longs;ita nullo modo moveretur; huc enim faciunt duo illa tua principia, <lb/>quæ libenter admitto, vtpote quæ cum experimentis mirabiliter con&longs;en<lb/>tiant; &longs;i verò terræ globum con&longs;ideremus, provt modò e&longs;t, & aquarum <lb/>congeries &longs;tagnat in va&longs;ti&longs;&longs;imis illis terrarum conchis; &longs;i terræ glo<lb/>bus volvatur, nunquid non &longs;uo motu aqueam illam molem &longs;ecum abri<lb/>piet? </s>

<s id="s.000734"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000735"> Abripiet &longs;anè majorem partem, eam &longs;cilicet, quàm arctiùs <lb/>&longs;uis brachiis &longs;tringit, & quæ à &longs;uperficie conchæ intror&longs;um &longs;atis &longs;uperque <lb/>di&longs;tat; huc facerent exempla concharum, quibus vulgò vtimur; &longs;ed ne <lb/>dicta repetam, libens omitto, <expan abbr="atq;">atque</expan> &longs;uppono. </s>

<s id="s.000736">Vt vt &longs;it, &longs;i <expan abbr="mot&utilde;">motum</expan> orbis con&longs;ide<lb/>remus haud dubiè facilior e&longs;t &longs;i aliqua portio aquæ retroagatur, ea &longs;cilicet, <lb/>quæ à &longs;uperficie parum di&longs;tat, cum tantula elevatione, ratione cujus in &longs;u<lb/>perficiem oppo&longs;itam excurrit, & in litora occidua deinde impingi, &longs;eu po<lb/>tiùs elevari, excurrere & in litus impingi videtur, eo quippe litus ip&longs;um fer<lb/>tur, & in aquam vel immobilem vel tardiorem impingitur, nempe quoad <lb/>effectum & <expan abbr="phænomer&utilde;">phænomerum</expan> perinde e&longs;t, &longs;ive caput in &longs;axum, five &longs;axum in ca<lb/>put incurrat: hoc autem potiori iure in terræ globo duplici illo motu, de <lb/>quo jam &longs;upra, locum habet, nempe à puncto H ad E cre&longs;cit motus per HE, <lb/>non tantùm ratione motus orbis, verùm etiam motus centri; idque per cre<lb/>menta majora & majora, vt iam o&longs;tendi; Igitur, aqua, iuxta &longs;uperficiem &longs;al<lb/>tem tantulùm ex currit in <expan abbr="part&etilde;">partem</expan> oppo&longs;itam, &longs;cilicet in occa&longs;um, &longs;i enim hoc <lb/>fiat, motu æquali &longs;uppo&longs;ito, potiori iure &longs;uppo&longs;ito inæquali, ac &longs;emper cre&longs;<lb/>cente: itaque ex iis. </s>

<s id="s.000737">quæ diximus huc <expan abbr="v&longs;q;">v&longs;que</expan>, nec <expan abbr="nõ">non</expan> meo judicio probavimus, <lb/>facilè defini: i po&longs;&longs;et æ&longs;tus marini ratio, in dicta hypothe&longs;i ; nempe aqua <lb/>à puncto E ad punctum I, id e&longs;t à media nocte ad Solis Ortum (&longs;up-<pb pagenum="65" xlink:href="025/01/069.jpg"/>pono enim circulum Æquatoris) excurreret aquæ &longs;uperficies versùs ortum; <lb/>ab I ad F, id e&longs;t ab ortu ad meridiem, nullo modo excurreret, &longs;altem <lb/>&longs;en&longs;ibiliter; &longs;i enim tantulùm, hoc motui centri prævalenti cedet; igitur <lb/>versùs Occa&longs;um, id e&longs;t, ab F, versùs R. quanquam determinatio mixta hoc <lb/>etiam compen&longs;at; pari modo ab F ad H nullo modo excurrit, &longs;altem &longs;en<lb/>&longs;ibiliter; &longs;i enim tantulùm, cedit motui centri, quanquam etiam determi<lb/>natio mixta hoc ip&longs;um compen&longs;at; igitur à Solis ortu v&longs;que ad occa&longs;um, <lb/>nulla fit &longs;en&longs;ibilis excur&longs;io; ab occa&longs;u ad mediam noctem, fit in occa<lb/>&longs;um, à media nocte ad ortum Solis, fit in ortum: mixtam illam determi<lb/>nationem facilè qui&longs;piam intelliget, &longs;i dividat æqualiter angulum, qui fit <lb/>à tangente datum aliquod punctum, & à linea motus centri, quæ &longs;emper <lb/>e&longs;t parallela HI, linea enim dictum angulum æqualiter dividens e&longs;t deter<lb/>minatio motus mixti. </s>

<s id="s.000738">Iam verò, &longs;i mihi non creditis, oculis ve&longs;tris credite, <lb/>& probate experimenta à me expo&longs;ita, in navi &longs;cilicet velorum dumtaxat <lb/>impul&longs;u acta, in aliquo tranquillo lacu, &longs;eu flumine; &longs;i enim &longs;tatuatur in <lb/>media navi, concha aquâ plena, pauio laxios in &longs;uperiore labro, &longs;ed mo<lb/>dicæ profunditatis, ad in&longs;tar illius, in qua cera liquari &longs;olet, ad cereos tor<lb/>nandos, videbitis haud dubiè, &longs;i navis motum acceleret, conchæ aquam <lb/>versùs puppim ire; <gap/> verò retardet, ire versùs proram; in hoc Ga&longs;&longs;endo <lb/>fides detrahi non debet, nec fortè mihi, nec aliis, qui hujus experimenti <lb/>oculati te&longs;tes fuerunt: & hæc de prima ratione contra tuam hypothe&longs;im, <lb/>Augu&longs;tine, jam ad alias de&longs;cendam. </s>

<s id="s.000739"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000740"> Sentio difficultatem, inficiari non po&longs;&longs;um; illud &longs;altem con<lb/>&longs;equi videor quod Galileus no&longs;ter à vero minime aberrarit, quando a&longs;&longs;e<lb/>ruit, prædictos motus ex hypothe&longs;i terræ mobilis, nece&longs;&longs;ariò &longs;equi. </s>

<s id="s.000741"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000742"> Ita e&longs;t; in eo tamen deceptus, quòd eo&longs;dem motus pro Marino <lb/>æ&longs;tu venditarit, licèt omnino di&longs;&longs;imiles &longs;int. </s>

<s id="s.000743">Iam verò vt ad alia tran&longs;eam ar<lb/>gumenta, è terra nobis migrandum e&longs;t, in qua profectò nihil aliud invenio <lb/>ex quo &longs;olidum argumentum ducere valeam &longs;altem, quod mihi faciat &longs;atis. </s>

<s id="s.000744"><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s>

<s id="s.000745"> Ludis, opinor, Antime; nunquid enim ex diver&longs;is motibus, <lb/>tum naturalibus, tum violentis docti&longs;&longs;imi viri ducunt in&longs;olubilia pror&longs;us <lb/>argumenta, contra præfatam hypothe&longs;im, in qua nequidem corpus grave <lb/>per lineam rectam de&longs;cenderet, nec accelerationis, nec retardationis, nec <lb/>percu&longs;&longs;ionis ratio explicari po&longs;&longs;et. </s>

<s id="s.000746"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000747"> Ridere &longs;oleo quorumdam hominum &longs;implicitatem, vt <lb/>&longs;ic loquar, qui cum Galileo no&longs;tro de motu contendunt, qui cerrè <lb/>doctrinæ motuum primus Autor & inventor fuit; nemo quippe <lb/>alius hanc laudem &longs;ibi arroget; Crede mihi, Chry&longs;ocome, &longs;uarum <lb/>rerum & inventionum vir ille amantior erat, quàm vt aliquem inter <lb/>eas conflictum pateretur, vidit, haud dubiè, vidit, motus accelera<lb/>ti progre&longs;&longs;ionem Geometricam, ita cum hypothe&longs;i Copernicana con<lb/>&longs;entive, vt in ea æquè facilè atque in tua explicari & ad &longs;ua princi<lb/>pia reduci po&longs;&longs;it; equidem in primis &longs;uis Dialogis de vtroque &longs;y&longs;tema<lb/>te, dubius aliquantulum hæ&longs;i&longs;&longs;e vi&longs;us. </s>

<s id="s.000748">e&longs;t, qua&longs;i motus gravium non <lb/>e&longs;&longs;et per &longs;e acceleratus, &longs;ed tantùm per accident; at in illo mirabili <pb pagenum="66" xlink:href="025/01/070.jpg"/>certè libro, quem de motu naturali accelerato edidit, ita de hoc argumen<lb/>to &longs;crip&longs;it, vt nullum po&longs;t &longs;e dubium reliquerit. </s>

<s id="s.000749"><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s>

<s id="s.000750"> Hic lapis te petit, Antime, vtpote qui, &longs;i rectè memini, <lb/>contra Galileum &longs;crip&longs;i&longs;ti, aliamque induxi&longs;ti motus naturaliter accele<lb/>rati progre&longs;&longs;ionem. </s>

<s id="s.000751"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000752"> Contra Galileum nihil me vnquam &longs;crip&longs;i&longs;&longs;e memini; è qui<lb/>dem Mon&longs;nerius meus tractatum de motu locali, ex meis prælectionibus <lb/>excerptum edidit, nihil tamen in eo contra Galileum. </s>

<s id="s.000753"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000754"> Immò ex profe&longs;&longs;o Galileum, &longs;ub Mon&longs;nerij nomine, im<lb/>pugnas, nec tibi, opinor, è memoria excidit? </s>

<s id="s.000755">nempe Galileus docet, &, <lb/>ni fallor, demon&longs;trat, motum gravium accelerari iuxta progre&longs;&longs;ionem geo<lb/>metricam, &longs;ecundùm quam decur&longs;a &longs;patia &longs;unt vt temporum quadrata, ac <lb/>proinde &longs;i primo tempore decurrat &longs;patium 1. &longs;ecundo æquali decurrit 3. <lb/>tertio 5. quarto 7. atque ita con&longs;equenter &longs;ecundum &longs;eriem numerorum <lb/>imparium, tu verò, Antime, vis, hanc &longs;eriem fieri &longs;ecundùm progre&longs;&longs;io<lb/>nem Arithmeticam &longs;impliorem numerorum 1.2.3.4.&c. </s>

<s id="s.000756"><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s>

<s id="s.000757"> Si rectè memini, Antime, omnibus experimentis hypothe&longs;is <lb/>tua repugnat; nam etiam &longs;umma quandoque altitudo &longs;umpta fuerit, Flo<lb/>rentiæ, Romæ, Bononiæ, & vt audio, in Gallia pa&longs;&longs;im, quantum tamen <lb/>periti&longs;&longs;imorum hominum oculis credendum e&longs;t, prima progre&longs;&longs;io illa Ga<lb/>lileana in decur&longs;is æquali tempore &longs;patiis &longs;emper apparuit. </s>

<s id="s.000758"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000759"> Summoperè lætor & gaudeo, quod &longs;ive ca&longs;u, &longs;ive &longs;tudio, hu<lb/>ju&longs;ce rei mentio à vobis facta fuerit; dico igitur, iterumque atte&longs;tor, ac <lb/>tertiò, nec meam hypothe&longs;im experimentis repugnate, nec à Galileana <lb/>di&longs;crepare in communi &longs;ententia quantitatis, tum continuæ, tum di&longs;cretæ; <lb/>nempe, vt probè &longs;citis, res quantitatis eas difficultates continet, quas huc <lb/>v&longs;que nemo ita &longs;olvit vt &longs;olutio vel omnibus arri&longs;erit, vel etiam illius a&longs;<lb/>&longs;ertoribus difficilis vi&longs;a non fuerit, in tempore præ&longs;ertim explicando; &longs;unt <lb/>enim qui capere nequeunt, vt quidquid temporis e&longs;t, ab eo, quod non <lb/>e&longs;t, &longs;ed fuit, vel erit, omnino di&longs;tinctum, in&longs;tans indivi&longs;ibile non &longs;it; &longs;ic <lb/>enim divi&longs;ibile e&longs;t in plura, ergo plura temporis &longs;imul exi&longs;tunt, quod di<lb/>ci nequit ; &longs;i autem ea in quæ e&longs;t divi&longs;ibile, non &longs;unt quidem, &longs;ed vel fue<lb/>runt, vel erunt; ergo id quod e&longs;t, quidquid &longs;it, ab iis omnino di&longs;tingui<lb/>tur; cùm repugnet, idem &longs;imul e&longs;&longs;e & non e&longs;&longs;e, igitur illud quod e&longs;t, ab <lb/>omni alio, quod non e&longs;t, di&longs;tinctum, in&longs;tans e&longs;t, indivi&longs;ibile e&longs;t: nec ju<lb/>vat à nonnullis dici, tempus e&longs;&longs;e fluenter; nempe fluenter e&longs;&longs;e; nihil e&longs;t <lb/>aliud, quàm vnum e&longs;&longs;e, &longs;eu fluere po&longs;t aliud, nec-plura &longs;imul e&longs;&longs;e po&longs;&longs;e; &longs;i <lb/>quid dicatur aliud, multorum captum & mentem &longs;uperat. </s>

<s id="s.000760"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000761"> Ad quid hæc: Galileus enim docet, componi tempus ex in<lb/>&longs;tantibus ii&longs;que Mathematicis. </s>

<s id="s.000762"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000763"> Sat &longs;cio; &longs;ed cùm alij huiu&longs;modi in&longs;tantia minimè admittant, <lb/>partibus dumtaxat in infinitum divi&longs;ibilibus, vel &longs;initis contenti in&longs;tan<lb/>tibus, &longs;cilicet phy&longs;icis, dico hypothe&longs;im Galilei circa progre&longs;&longs;ionem mo<lb/>tus accelerati, habere quidem locum in hypothe&longs;i in&longs;tantium infinitorum, <lb/>vel partium infinitarum, non ramen in hypothe&longs;i finitorum in&longs;tantium <pb pagenum="67" xlink:href="025/01/071.jpg"/>phy&longs;icorum; hîc non di&longs;cutio cau&longs;æ merita, ne &longs;altem extra chorum; id <lb/>vnum dumtaxat dico, illam progre&longs;&longs;ionem alteri præferendam e&longs;&longs;e, quæ & <lb/>vtrique quantitatis hypothe&longs;i &longs;atisfacit, & ip&longs;is experimentis non repu<lb/>gnat: quòd autem progre&longs;&longs;io Galileana in hypothe&longs;i finitorum in&longs;tan<lb/>tium non &longs;ub&longs;i&longs;tat, per&longs;picuè demon&longs;tro; Sit enim motus qui&longs;piam natu<lb/>ralis, qui duret per 4. in&longs;tantia, in quorum primo, mobile acquirat &longs;pa<lb/>tium 1. in &longs;ecundo 3. in tertio 5. in quarto 7. cùm velocitas cre&longs;cat, vt <lb/>tempus, in &longs;ecundo in&longs;tanti velocitas erit dupla, quomodo igitur acquiri<lb/>tur triplum &longs;patium? </s>

<s id="s.000764"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000765"> Nihil facilius triangulo Galileano, in quo res i&longs;ta clari&longs;&longs;i<lb/><figure id="id.025.01.071.1.jpg" xlink:href="025/01/071/1.jpg"/><lb/>mè demon&longs;tratur: Sit enim triangulum AEI, &longs;it <lb/>tempus divi&longs;um in 4.partes æquales, & primo tempo<lb/>re AB, &longs;patium acqui&longs;itum &longs;it triangulum ABF, & <lb/>velocitas acqui&longs;ita BF, &longs;ecundo tempore erit veloci<lb/>tas acqui&longs;ita CG, cre&longs;cit enim, vt tempus, & vt AB <lb/>ad BF, ita AC ad CG ; idem dico de quolibet alio <lb/>temporis puncto accepto inter BC ; igitur &longs;patium ac<lb/>qui&longs;itum erit trapezium BCGF, triplum trianguli <lb/>ABF, nempe cum velocitate BF æquabili motu, tem<lb/>pore BC, acquireret rectangulum BM, &longs;ed virtute ve<lb/>locitatis acqui&longs;itæ tempore BC æqualis velocitati BF, acquiritur triangu<lb/>lum FMG æquale ABF; igitur &longs;ecundo tempore triplum &longs;patium <lb/>prioris. </s>

<s id="s.000766"><emph type="italics"/>Antim.<emph.end type="italics"/> Hæc omittere poteras, quæ iam trita &longs;unt, nec à me negantur; <lb/>nempe velocitas BF acquiritur &longs;ucce&longs;tivè tempore AB, quod &longs;i &longs;uppona<lb/>tur e&longs;&longs;e in&longs;tans phy&longs;icum, accipienda e&longs;t velocitas. </s>

<s id="s.000767">BF tota &longs;imul, re<lb/>&longs;pondeo<gap/> enim toti in&longs;tanti, ac proinde tota &longs;imul e&longs;t, non verò &longs;ucce&longs;&longs;i<lb/>vè acqui&longs;ita, igitur &longs;patium debet accipi in rectangulo, non verò in trian<lb/><figure id="id.025.01.071.2.jpg" xlink:href="025/01/071/2.jpg"/><lb/>gulo; v.g. Sit tempus AE 4. in&longs;tantiam, &longs;it pri<lb/>mus gradus velocitatis AG, & &longs;patium acqui<lb/>&longs;itum rectangulum AV; &longs;ecundo in&longs;tanti ve<lb/>locitas acqui&longs;ita erit BH, dupla &longs;cilicet AG; <lb/>nempe tota prior remanet, & tantumdem ab ea<lb/>dem cau&longs;a, æquali tempore ponitur; igitur &longs;pa<lb/>tium e&longs;t duplum prioris, ac proinde erit rectan<lb/>gulum CH duplum prioris. </s>

<s id="s.000768"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000769"> Duo ab&longs;urda ex his mihi deducere videor; primò enim, pri<lb/>mo tempore AB, duplum &longs;patium trianguli Galileani a&longs;&longs;umis; nempe re<lb/>ctangulum AV duplum e&longs;t trianguli ABV, cùm tamen æquale primum <lb/>tempus a&longs;&longs;umi debeat, ad perfectam comparationem; &longs;ecundò longè majus <lb/>&longs;patium decurritur &longs;ecundùm tuam progre&longs;&longs;ionem, quàm &longs;ecundùm Ga<lb/>lileanam, in qua &longs;patium decur&longs;um tempore AE continet 16. triangula <lb/>æqualia triangulo ABV, in tua verò continet 10. rectangula æqualia <lb/>AV; igitur 20. triangula æqualia ABV, igitur &longs;patium Galileanum erit <lb/>ad tuum vt 16. ad 20. &longs;eu vt 4. ad 5. igitur majus vna quarta parte, quod <pb pagenum="68" xlink:href="025/01/072.jpg"/>&longs;anè omnibus experimentis repugnat, quæ cum &longs;patio Galileano pror&longs;us <lb/>con&longs;entiunt. </s>

<s id="s.000770"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000771"> Nemo vnquam hujus rei periculum fecit in 4. in&longs;tantibus, <lb/>&longs;ed tantùm in 4. temporibus &longs;en&longs;ibilibus, nempe in&longs;tantia &longs;ub &longs;en&longs;um non <lb/>cadunt; at &longs;upponuntur hoc loco 4.in&longs;tantia. </s>

<s id="s.000772">iuxta &longs;ingularem illam tem<lb/>poris hypothe&longs;im ; equidem &longs;i tempus AE ex quatuor partibus temporis <lb/>&longs;en&longs;ibilibus componas &longs;ecundùm communem, aut etiam Galileanam tem<lb/>poris hypothe&longs;im, & dividas AE in 8. tempora æqualia; in progre&longs;&longs;ione <lb/>Galilei, tempore AE, idem &longs;patium decurritur; at verò in mea decurritur <lb/>&longs;patium, quod complectitur 18.triangula æqualia ABV; igitur &longs;patium in <lb/>mea decur&longs;um majus erit Galileano, vna octava; & &longs;i adhuc tempora bi<lb/>fariam dividas, majus erit vna decima &longs;exta; atque ita deinceps decre<lb/>&longs;cent exce&longs;&longs;us iuxta hanc &longs;eriem 1/4. <gap/> &c. </s>

<s id="s.000773">igitur. </s>

<s id="s.000774">&longs;i vel in<lb/>&longs;tantia infinita &longs;unt, vel partes infinitæ, differentia &longs;patiorum in mea <lb/>progre&longs;&longs;ione & Galileana decre&longs;cit in infinitum; ac proinde Illa &longs;patia <lb/>æqualia cen&longs;enda &longs;unt, quorum vnum aliud &longs;uperat, exce&longs;&longs;u, minore quo<lb/>libet a&longs;&longs;ignabili: Hæc &longs;i non nemo paulò attentiùs con&longs;idera&longs;&longs;et, meam <lb/>progre&longs;&longs;ionem tam citò vt fal&longs;am & experimentis omnino repugnantem <lb/>minimè rejeci&longs;&longs;et, nec adeò dubita&longs;&longs;et de vera hujus accelerationis cau&longs;a, <lb/>quæ in eo po&longs;ita e&longs;t, quod prioribus gradibus impetus novi gradus conti<lb/>nuè accedant, idque &longs;i quodlibet tempus ex infinitis con&longs;ter, vel etiam ex <lb/>finitis, &longs;ed innumerabilibus, in triangulo; &longs;i verò ex paucis finitis, in <lb/>rectangulis, iuxta figuram AEF di&longs;po&longs;itis; nec alia &longs;uper hoc, meo judi<lb/>cio, difficultas re&longs;tat; vnde concludo, meam progre&longs;&longs;ionem alteri præfe<lb/>rendam e&longs;&longs;e, quia &longs;cilicet vtrique hypothe&longs;i facit &longs;atis; quanquam ad v&longs;um. <lb/></s>

<s id="s.000775">Galileana omnino adhibenda e&longs;t, cùm in eam mea re&longs;olvatur, vt verò ad <lb/>cau&longs;am phy&longs;icam accelerationis res reducatur pro vtraque hypothe&longs;i, mea <lb/>certè non modò præferenda e&longs;t, verùm etiam nece&longs;&longs;ariò tenenda; &longs;ed tam <lb/>multa de hac re &longs;crip&longs;imus, vt de his plura &longs;cribere operæ pretium non &longs;it. </s>

<s id="s.000776"><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s>

<s id="s.000777"> Ne&longs;cio, quomodo dicas, nullam &longs;upere&longs;&longs;e difficultatem, <lb/>cùm in&longs;uperabilis adhuc re&longs;tet; nempe &longs;i primo in&longs;tanti mobile acquirit <lb/>AV, & &longs;ecundo, &longs;patium CH, duplum, igitur, cùm mobile e&longs;&longs;et ih &longs;pa<lb/>tio AV tanquam in loco adæquato erit in CH duplo &longs;cilicet, tanquam <lb/>in loco adæquato majore. </s>

<s id="s.000778"><emph type="italics"/>Antim.<emph.end type="italics"/> Hæc maxima e&longs;t difficultas, fateor, & in communi temporis <lb/><figure id="id.025.01.072.1.jpg" xlink:href="025/01/072/1.jpg"/><lb/>hypothe&longs;i, &longs;i rèm ip&longs;am, non verba con&longs;ideremus, <lb/>ferè in&longs;uperabilis; immò & in Galilei opinione, qui <lb/>vult, tempus ex infinitis in&longs;tantibus Mathematicis <lb/>componi, in&longs;olubilis nodus e&longs;t; &longs;i enim in tempore <lb/>AE accipiantur duo in&longs;tantia, &longs;cilicet B & C, nem<lb/>pe vt linea AE repræ&longs;entat tempus, ita quodlibet illius <lb/>punctum repræ&longs;entat vnum in&longs;tans, porrò mobile, <lb/>quod movetur tempore AE, in&longs;tanti B e&longs;t in &longs;pa<lb/>tio BF, in&longs;tanti C in &longs;patio CG duplo prioris; <lb/>quia vt arca trianguli AEI repræ&longs;entat, totum <pb pagenum="69" xlink:href="025/01/073.jpg"/>&longs;patium, quod mobile acquirit, tempore AE, ita linea BF repræ&longs;entat <lb/>&longs;patium, in que fuit in&longs;tanti B; & CG, &longs;patium, in quo fuit in&longs;tanti <lb/>C &c. </s>

<s id="s.000779">In hypothe&longs;i in&longs;tantium phy&longs;icorum hæc difficultas omnino ce&longs;<lb/>&longs;at; &longs;ed ne huc accer&longs;am integram, & benè longam tractationem, in <lb/>qua natura temporis & motus explicanda e&longs;&longs;et, con&longs;ule, &longs;i vis, Chry<lb/>&longs;ocome, tractatum no&longs;trum, de motu locali; itemque Metaphy&longs;icam <lb/>non vno loco, ibi enim hoc munere perfuncti &longs;umus, quo certè in præ<lb/>&longs;enti congre&longs;&longs;u perfungi non vacat. </s>

<s id="s.000780">Addo tantùm, hypothe&longs;i Coperni<lb/>canæ nihil ob&longs;tare motum acceleratum, vt dicebas, &longs;icuti eidem mo<lb/>tui non ob&longs;tat navis motus, vt plu&longs;quam mille experimentis comproba<lb/>tum e&longs;t. </s>

<s id="s.000781"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000782"> Rectè omninò, nempe corpus grave de&longs;cenderet, motu <lb/>quodam mixto, ex æquabili, & accelerato; in navi exemplum luculen<lb/>tum e&longs;t, immò & in di&longs;co projecto per inclinatam &longs;ur&longs;um, qui non mo<lb/>dò per curvam &longs;ur&longs;um a&longs;cendit, verùm etiam per curvam deor&longs;um ruit <lb/>& licèt æqualia &longs;patia in dicta curva æqualibus temporibus omnino de<lb/>currat, &longs;altem ad &longs;en&longs;am, hoc tamen non ob&longs;tat, quin ratione perpen<lb/>dicularis, in quam vi motus naturalis inclinat, & in qua majora &longs;pa<lb/>tia decurrit. </s>

<s id="s.000783">eodem pror&longs;us modo quo fieret, &longs;i motus naturalis cum alio <lb/>horizontali conjunctus non e&longs;&longs;et; hoc inquam non ob&longs;tat, quin ratio<lb/>ne perpendicularis, dictum corpus grave motu accelerato moveatur; &longs;ed <lb/>&longs;i motus acceleratus e&longs;t, cre&longs;cit. </s>

<s id="s.000784">impetus; hinc major ictus &c. </s>

<s id="s.000785">Non <lb/>cre&longs;cunt &longs;patia, inquies; Re&longs;pondeo: non cre&longs;cunt in horizontali, con<lb/>cedo: vnde ratione horizontalis, e&longs;t motus æquabilis; non cre&longs;cunt in per<lb/>pendiculari, nego; &longs;ed profecto &longs;i non cre&longs;ceret impetus, in perpendicula<lb/>ri &longs;patia non cre&longs;cerent. </s>

<s id="s.000786"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000787"> Omitte quæ&longs;o hæc argumenta, à motu gravium, vel levium <lb/>petita, quæ &longs;anè multiplicem paralogi&longs;mis materiam nonnullis præ<lb/>buerunt, quos aliis, amabo di&longs;cutiendos <gap/>linquamus, præ&longs;ertim, cùm <lb/>mediocriter doctis, & i&longs;tarum rerum peritis cuncta hæc per&longs;pecta &longs;int; <lb/>vnum tantùm: in quo non nemo maximam vim facit, obiter indico; <lb/>&longs;i moveatur terra, inquit, explodaturque catapulta, vel quodlibet <lb/>aliud projectionis organum, versùs polum directè, globus projectus <lb/>incidet in planum oppo&longs;itum obliquè; igitur vis ictus longe minor erit, <lb/>quàm &longs;i explodatur versùs ortum, vel occa&longs;um; quod tamen expe<lb/>rimentis repugnat: Sed facilè re&longs;pondeo, dicti globi explo&longs;i motum <lb/>mixtum e&longs;&longs;e ex duobus, altero communi aliis partibus terræ, versùs <lb/>ortum, altero impre&longs;&longs;o à machina versùs polum; vterque totum effe<lb/>ctum habet, qui &longs;ibi competit; e&longs;t enim reverà duplex impetus, quo<lb/>rum vnus independenter ab alio id totum præ&longs;tat, quod præ&longs;tare po<lb/>te&longs;t; clari&longs;&longs;imum exemplum habemus in navi; vnde argumentum illud <lb/>facilè &longs;olvitur, nempe ictus per lineam obliquam minor e&longs;t, quando <lb/>vnus tantùm impetus ine&longs;t, ad talem lineam determinatus; at verò quan<lb/>do duplex impetus ine&longs;t, & alter per directam lineam determinatus e&longs;t, &longs;ive <lb/>alius in&longs;it, five non, æqualis ictus infligitur. </s>

<s id="s.000788"><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s>

<s id="s.000789"> Sed, quæ&longs;o te, Antime, quandoquidem alia non &longs;up<lb/>petunt argumenta in terre&longs;trl globo, ad confutandum illius motum pro<lb/>fer amabo, locos illos ex quibus alia erui po&longs;&longs;int. </s>

<s id="s.000790"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000791"> Nullus globus terre&longs;tri vicinior e&longs;t, quàm Luna; in Lunari <lb/>globo nonnihil habeo, quod fortè non minùs negotij tibi face&longs;&longs;et, Augu<lb/>&longs;tine, quàm Marinus æ&longs;tus. </s>

<s id="s.000792"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000793"> Immò in Iove mobili, circa quem moventur quatuor <lb/>Ioviales Lunæ, clari&longs;&longs;imam analogiam habemus terræ mobilis, circa <lb/>quam Luna volvitur; nonnihil &longs;imile in Saturno habemus, circa quem <lb/>etiam &longs;ua Stella, &longs;eu Luna Saturnia circumfertur; Luna igitur no&longs;træ <lb/>hypothe&longs;i non obe&longs;t, immò no&longs;tra hypothe&longs;is Lunari &longs;y&longs;temati favet, <lb/>quod &longs;cilicet, & à deformibus &longs;piris, & à motu raptus versùs Occa&longs;um <lb/>liberat. </s>

<s id="s.000794"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000795"> Negari non pote&longs;t, quin ex ip&longs;i&longs;&longs;imis, non illorum modò, <lb/>qui communem A&longs;tronomorum &longs;ententiam tenent, verùm etiam prin<lb/>cipium Copernicanæ &longs;ententiæ defen&longs;orum principiit, Planetarum mo<lb/>tus reales, vt vocant, æquales &longs;int, quamvis inæquales nobis appa<lb/>reant; hanc realium motuum inæqualitatem Antiqui omnes, ad vnum, <lb/>vt A&longs;tronomiæ pe&longs;tem ac mortem relegarunt; ex recentioribus verò <lb/>Copernicus ve&longs;ter, illam humano intellectui horrori e&longs;&longs;e dixit, Cla<lb/>vius &longs;ummæ dementiæ; Reinholdus imperitæ imaginationis; alij deni<lb/>que, vt Tycho, æqualem motum, in c&oelig;le&longs;tibus Sphæris, pro certo <lb/>& indubitato axiomate po&longs;uerunt: Scio, Keplerum, quem deinde pauci <lb/>alij &longs;ecuti &longs;unt, inæqualitatem motuum realium ad&longs;truxi&longs;&longs;e, in id dum<lb/>taxat ab ip&longs;a de&longs;peratione inductum extremi&longs;que angu&longs;tiis, in quas illum <lb/>multa phænomena redegerant, quæ &longs;cilicet &longs;uppo&longs;itis motibus realibus in <lb/>&longs;ua hypothe&longs;i explicare non poterat; hæc vnica huius con&longs;ilij cau&longs;a fuit, <lb/>quod certè penitus ruit, &longs;i po&longs;itis motibus æqualibus, cuncta phænomena <lb/>explicari po&longs;&longs;unt. </s>

<s id="s.000796"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000797"> In hac parte tecum facilè &longs;entio, & verò à Ptolemæo <lb/>alii&longs;que antiquis A&longs;tronomis, itemque à Tychone, Longomontano, <lb/>Copernico, Galileo, Lansbergio, Clavio, Magino, alii&longs;que rei A&longs;tro<lb/>nomicæ Principibus, in hoc di&longs;cedere, vix au&longs;im ; nec ratio dee&longs;t, quæ <lb/>meo &longs;altem iudicio, rem conficit; nempe omnis motus per &longs;e inæquabi<lb/>lis vel acceleratus, vel retardatus e&longs;t, neutrum de c&oelig;le&longs;tibus motibus <lb/>dici pote&longs;t; cùm enim eadem &longs;emper e&longs;&longs;et accelerationis vel retardatio<lb/>nis cau&longs;a, certè in infinitum acceleraretur, vel retardaretur; quod vel <lb/>ab&longs;urdum dictu e&longs;t; omitto certi&longs;&longs;imam totius A&longs;tronomiæ ruinam <lb/>ac de&longs;tructionem, cùm inæqualitas certis ac perpetuis regulis minimè <lb/>&longs;ubjaceat; incerta &longs;cilicet, varia, ignota; cùm enim vna dumtaxat <lb/>fit æqualitas, infinitæ &longs;unt ac variæ inæqualitates; cur hæc potiùs quam <lb/>illa? </s>

<s id="s.000798"><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s>

<s id="s.000799"> Multas tamen apud Autorem Neotericum de re A&longs;tro<lb/>nomica optimè meritum, rationes legi, quibus probare conatur, inæ<lb/>qualitatem realium motuum, quantum porrò conjicio, in &longs;ingula-<pb pagenum="71" xlink:href="025/01/075.jpg"/>rem hanc opinionem de&longs;cendit, eò quòd putarer, æqualitatem realium <lb/>motuum &longs;alvari non po&longs;&longs;e, ni&longs;i in hypothe&longs;i Copernicana, in qua <lb/>&longs;cilicet &longs;pectantis hominis oculus extra orbitarum c&oelig;le&longs;tium centrum <lb/>collocatur. </s>

<s id="s.000800"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000801"> Scio, quem intelligas, Chry&longs;ocome, rationes illæ de<lb/>bili&longs;&longs;imæ &longs;unt, & eadem facilitate de&longs;truuntur, qua ad&longs;truuntur; præ<lb/>&longs;ertim in hypothe&longs;i hujus no&longs;tri Antimi, in qua, motus realis vnicus <lb/>&longs;implex & æquabilis e&longs;t ab ortu in occa&longs;um; reliqui tantùm apparentes, <lb/>hos quidem inæquales e&longs;&longs;e do vltrò, &longs;ecus tamen realem & phy&longs;icum, <lb/>qui &longs;anè ita æqualis e&longs;t, vt æqualibus temporibus, æqualia &longs;patia in &longs;uis <lb/>&longs;piris &longs;eu revolutionibus Planeta decurrat. </s>

<s id="s.000802"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000803"> Non e&longs;t etiam, quod aliquis timeat, ne præ&longs;ata æqualitas hy<lb/>pothe&longs;i Copernicanæ &longs;uffragetur; ex illa enim poti&longs;&longs;imum contra i&longs;tam <lb/>argumentum duci pote&longs;t, vt paulò po&longs;t evincam. </s>

<s id="s.000804"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000805"> Vnum omi&longs;eram, quod &longs;cilicet in Luna maximè rea<lb/>lium motuum inæqualitas ponenda e&longs;&longs;et, quia &longs;cilicet Men&longs;es tum Sy<lb/>nodici, tum Periodici inter &longs;e inæquales &longs;unt; at etiam in mea hypothe<lb/>&longs;i, Luna &longs;pectatur ex eo centro, circa quod &longs;uos orbes agit; igitur ideò <lb/>æqualitas abigenda non e&longs;t, quod in hypothe&longs;i terræ mobilis, &longs;al<lb/>vari tantùm po&longs;&longs;it; cùm & in alia hypothe&longs;i fortè &longs;alvetur, & in illa, <lb/>Lunæ motus quamvis ex &longs;uo centro &longs;pectati, valde inæquales appa<lb/>reant. </s>

<s id="s.000806"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000807"> Ne dicas, <emph type="italics"/>fortè &longs;alvetur,<emph.end type="italics"/> dele illud <emph type="italics"/>fortè<emph.end type="italics"/>; quia profectò æqua<lb/>litatem illam optimè & facilè &longs;alvo; vt probè, ni fallor, intelligis ex iis, <lb/>quæ in proximo congre&longs;&longs;u de meo Solis &longs;y&longs;temate obiter expo&longs;ui. </s>

<s id="s.000808"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000809"> De Sole non abnuerim, &longs;ed de Luna quid? </s>

<s id="s.000810">In qua non<lb/>nulli ex tuis, etiam in tua hypothe&longs;i, motuum realium inæqualitatem <lb/>admittunt, propter vnam dumtaxat inæqualitatem men&longs;ium; nempe li<lb/>cèt motus inæqualitas in hoc, vel illo arcu orbitæ in meram apparen<lb/>tiam, &longs;alva &longs;emper æqualitate reali, refundi po&longs;&longs;it, &longs;i tamen brevior &longs;it <lb/>vna integra revolutio, quàm alia, realis profectò erit, non verò apparens <lb/>inæqualitas, &longs;ed hoc non vrgeo contra te, quia eadem vterque difficultate <lb/>laboramus. </s>

<s id="s.000811"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000812"> Nullo negotio præfatam men&longs;ium inæqualitatem in mea hy<lb/>pothe&longs;i explico; Cùm Lunæ æquè ac Soli motum &longs;implici&longs;&longs;imum attri<lb/>buam ab ortu ad occa&longs;um, cum gemina illa inclinatione, de qua &longs;upra, <lb/>& hac vna &longs;ingulari differentia, quòd terminus &longs;ecundæ inclinationis in <lb/>Sole &longs;it Æquator, in Luna verò &longs;it Ecliptica; longioris operæ res e&longs;&longs;et, i&longs;ta <lb/>fu&longs;iùs pro&longs;equi, præ&longs;ertim cùm appellata men&longs;ium inæqualitas alioquin <lb/>facilè in hac mea hypothe&longs;i intelligatur: fac enim, v. g. Solem e&longs;&longs;e cir<lb/>ca Apogæum, Lunæ conjunctum; Sol tardiùs &longs;uos orbes diurnos ab<lb/>&longs;olvit: igitur breviore intervallo Lunam po&longs;t &longs;e relinquit versùs or<lb/>tum; vnde nece&longs;&longs;ariò &longs;equitur, copulam deinde tardiùs fieri; vnde <lb/>men&longs;em illum periodicum longiorem e&longs;&longs;e, nece&longs;&longs;e e&longs;t; contra verò <lb/>breviorem illum, qui Sole in perigæo exi&longs;tente currit; quod verò <pb pagenum="72" xlink:href="025/01/076.jpg"/>&longs;pectat ad men&longs;em periodicum, eam &longs;cilicet temporis periodum, qua <lb/>Luna ab Occa&longs;u ad Ortum totum Zodiacum decurrere videtur; modò <lb/>longior, modò brevior e&longs;t, pro diver&longs;o Nodorum &longs;itu; &longs;i enim Nodi <lb/>exi&longs;tant, in punctis Eclipticæ Æquinoctialibus, haud dubiè Luna <lb/>&longs;uas &longs;piras agens longiùs versùs Polos excurrit, minùs verò longè <lb/>Nodis in punctis Sol&longs;titialibus exi&longs;tentibus; &longs;ed quò longiùs excur<lb/>rit, plus temporis ponit; Major igitur e&longs;t periodus; quid clarius <lb/>&longs;upet hoc dici, vel excogitari po&longs;&longs;it, vereor &longs;anè vt qui&longs;piam vi<gap/><lb/>deat. </s>

<s id="s.000813"><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s>

<s id="s.000814"> Mirum mihi accidit, Antime, cur adeò in motuum rea<lb/>lium inæqualitatem inveharis, cùm tamen motum vtriu&longs;que inclinatio<lb/>nis inæqualem in tuo &longs;y&longs;temate &longs;tatuas; acceleratum &longs;cilicet & retar<lb/>datum. </s>

<s id="s.000815"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000816"> Hanc in&longs;tantiam facilè &longs;olvere, vel; vt veriùs dicam, eludere <lb/>po&longs;&longs;em, &longs;i dicerem, e&longs;&longs;e motus rectos, qui ex natura &longs;ua accelerati &longs;unt, <lb/>vel retardati; nempe vel ad &longs;uum naturalem terminum tendunt, vel ab eo <lb/>recedunt; &longs;i primum, acceleratos; &longs;i alterum, retardatos e&longs;&longs;e, oportet; <lb/>&longs;ed hi re verà motus non &longs;unt, qui tantùm con&longs;iderantur in decur&longs;i &longs;patij <lb/>linea, in qua æqualibus temporibus æqualia &longs;emper &longs;patia à Planeta de<lb/>curruntur, licèt inæqualia nobis appareant: & verò æquabilem mo<lb/>rum e&longs;&longs;e, nece&longs;&longs;e e&longs;t, cuius æqualis eademque cau&longs;a &longs;emper manet, idem <lb/>&longs;cilicet impetus, vel initio impre&longs;&longs;us, vel eo, quo dixi modo, acqui<lb/>&longs;itus. </s>

<s id="s.000817"><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s>

<s id="s.000818"> Nunquid tantulùm &longs;altem retardat medij re&longs;i&longs;tentia, vt in <lb/>projectis, immò & deor&longs;um cadentibus fieri videmus? </s>

<s id="s.000819"><emph type="italics"/>Antim.<emph.end type="italics"/></s>

<s id="s.000820"> Certè non retardat, &longs;i medium &longs;imul & Planeta eodem <lb/>motu moveantur; Sed hoc ad&longs;truere non cogimur, cùm nulla ratio<lb/>ne nitatur; medium enim commune e&longs;t; Re&longs;pondeo igitur, cladem <lb/>illam à re&longs;i&longs;tentia medij acceptam à Planeta continuo re&longs;arciri, vel, <lb/>vt meliùs dicam, impediri; vt enim iuxta optimum Naturæ in&longs;titutum, <lb/>impetum non auget, ne &longs;cilicet obtinendo fini adver&longs;etur, ita nec eun<lb/>dem impetum minui &longs;init, quod non minùs eidem repugnaret in<lb/>&longs;tituto. </s>

<s id="s.000821"><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s>

<s id="s.000822"> Sed ne totus &longs;is in præludiis, ad tuum illud argumentum con<lb/>tra meam hypothe&longs;im à Luna petitum veniendum e&longs;&longs;et. </s>

<s id="s.000823"><emph type="italics"/>Antim.<emph.end type="italics"/></s>