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<?xml version="1.0"?> <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" ><archimedes> <info> <author>Fabri, Honoré</author> <title>Dialogi physici in quibus de motu terrae disputatur</title> <date>1665</date> <place>Lyon</place> <translator></translator> <lang>la</lang> <cvs_file>fabri_dialo_01_la_1665</cvs_file> <cvs_version></cvs_version> <locator>0000000025.xml</locator> </info> <text> <front> </front> <body> <chap> <pb/><p type="main"> <s><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></p><p type="main"> <s><emph type="center"/><emph type="italics"/>Necnon aquarum & Mercurij &longs;upra. </s> <s>libellam ele vatio examinatur.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/>AD EMINENTISSIMVM <lb/>CARDINALEM FACCHINETTVM.<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>Auctore<emph.end type="italics"/> R. P. HONORATO FABRI. <emph type="italics"/>Societatis<emph.end type="italics"/> IF<gap/>.<emph.end type="center"/></s></p><figure></figure><p type="main"> <s><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></p><p type="main"> <s><emph type="center"/><emph type="italics"/>M. DC. LXV.<emph.end type="italics"/><lb/>VM PERMISSV SVPERIORVM.<emph.end type="center"/></s></p><pb/><p type="main"> <s><emph type="center"/>IRREGULAR <lb/>PAGINATION<emph.end type="center"/></s></p><pb/><figure></figure><p type="main"> <s><emph type="center"/>LECTORI.<emph.end type="center"/></s></p><p type="main"> <s><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 <gap/><lb/>nio ab Eminenti&longs;&longs;ime<emph.end type="italics"/> CARDINALI FACCHI­<lb/>NFTTO, <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 boris, 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>Aliquid fortè de me inaudiera<gap/>, & vt <lb/>amici nunquam ferè de amico ni&longs;i hyperbolicè, illud, quod <lb/>in me &longs;entio, vel nullum, vel admodum tenue ingemum, <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 <gap/>micorum by­<lb/>perbolem, de me conceperat, apinione 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 audi vit. </s> <s>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>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/><emph type="italics"/>vt ea, qu<gap/> nuda voce prolata à me acceperat, &longs;eripto 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 fœdi errores in ex&longs;cripta irre­<lb/>pant. </s> <s>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>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>Vale.<emph.end type="italics"/></s></p><pb pagenum="1"/><figure></figure><p type="main"> <s><emph type="center"/>DIALOGVS PRIMVS.<emph.end type="center"/></s></p><p type="main"> <s><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></p><p type="main"> <s>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;<gap/>no voluptatis &longs;en­<lb/>&longs;u animum meum per&longs;undat: ita enim confabulando amœnus, promptus <lb/>arguendo, &longs;olvendo &longs;ubtilis, explicando elegans & limpidus omnibus no­<lb/>bis vi&longs;uses, vt conjuncta cloquentiæ &longs;apientia, ad fundenda oracula, tua <lb/>voce, tuis <gap/>rbis vti videretur. </s> <s>Vt autem petpetuum 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 amœnioribus literis plurimùm delectatum <lb/>fui&longs;&longs;e. </s> <s>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, cos tamen, in quos &longs;ingula <lb/>optimè quadrant, nullo negotio per&longs;picies Sed ad rem venio. </s></p><p type="main"> <s><emph type="italics"/>Antimui.<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>ngenium &longs;timulat, ad <gap/>a nonnunquam expromenda, quælon­<lb/>ga meditatione, & repetita cogitationum huc illuc ver&longs;atione, vix vnquam <lb/>elici potui&longs;&longs;ent. </s> <s>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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tinus.<emph.end type="italics"/></s><s> 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"/>nendum &longs;it, eo dumtaxat fine hoc à me fiet, ad vberiorem explicationis <lb/>lucem extorquendam. </s> <s>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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Dic, vt voles, illud &longs;altem con&longs;tat, quidquid vel ex tuis lu­<lb/>cubrationibus, vel ex tuo di&longs;&longs;erentis oreaccepi, 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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>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 negouum 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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 adæ quant, 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></p><pb pagenum="3"/><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Hebetiori, quæ&longs;o, ingenioigno&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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Legi haud dubiè; Vt enim Authorem illum maximi facio, ita <lb/>nihil ab co 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;teteles, &longs;ive Democritus; illa æquè grata & chara mihi &longs;emper accidit. <lb/></s> <s>Sed quæ&longs;o te, periculum faciamus, vt &longs;altem dum no&longs;trivenerint, hoc mo­<lb/>dicum tempus cum æ&longs;tu fallamus. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Per me licer; &longs;ed cur&longs;im, iis tamen prætermi&longs;&longs;is, quæ inter <lb/>Academieos quidem, non tamen inter Philo&longs;ophos locum obtinent, quas <lb/>potiùs rationum vmbras, quàm veras rationes appellare &longs;oleo. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Optimè judicas, quid enim juvat, tantirem momenti levi&longs;&longs;imis <lb/>fulcire adminiculis: Nonnulla obiter indico. </s> <s>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>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>Denique ex culina ip&longs;a nova depromunt argu­<lb/>menta; Videmus, inquiunt, veru 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>Hoc argumentum culinam olet, vnde profectum e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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 ponde: is 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"/>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>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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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 probèno&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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Su&longs;tine tanti&longs;per; ne&longs;cio quid intelligas per illum medium <lb/>motum. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Non capio, exi&longs;timo enim rem ita e&longs;iè, & æqualibus tempo­<lb/>ribus, æqualia &longs;patia decurri. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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 meridic 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 or<gap/>is pe­<lb/>des 1250. addevnum 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>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 globiin Æquatore, &longs;ingulis mi­<lb/>nutis &longs;ecundis, pedes circiter 1250.decurrit. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Quid tum? </s> <s>Non video, quid tibi velis, ad infirmandum <lb/>illud argumentum, quod ab incredibili velocitate motus raptus, &longs;eu <pb pagenum="5"/>primi mobilis contra ve&longs;tram hypothe&longs;im ducitur. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Jam iam videbis. </s> <s>Suppone terre&longs;tem globum in mundi centro, <lb/>co 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 totusradius, 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>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>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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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. </s> <s>g. </s> <s>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 altirudo a&longs;&longs;umi queat ad libitum, cx 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 cœlorum Conditori atque motori <lb/>Deo, gratis, vt aiunt, recu&longs;ent. </s></p><pb pagenum="6"/><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;lin.<emph.end type="italics"/></s><s> Duo motus, ni fallor, omnia &longs;alvant, orbis &longs;cilicet & centri, <lb/>terre&longs;tris globi, quie&longs;cente Sole in mundi centro. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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>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, qnæ 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>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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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>Ve&longs;trum enim, &longs;i rectè memini, in vno Solo 7. <lb/>vel 8. motus po&longs;tulat. </s> <s>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 priorisaxis 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"/>traducantur, &longs;ed vterque per &longs;e, vt aiunt, Soli competat, inde &longs;ortè <lb/>ture cuipiam impo&longs;&longs;ibiles videbuntur. </s></p><p type="main"> <s><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></p><p type="main"> <s><emph type="italics"/>Augu&longs;lin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Ne quæ&longs;o dubites, vbirem a me intellexetis, tibi fortè per­<lb/>&longs;uaderi &longs;ines; ea quippe dicam quæ, ni fallor, luce meridiana clatiora &longs;int. <lb/></s> <s>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;ursũ">&longs;ursum</expan>, <lb/>deor&longs;um, &longs;ini&longs;tro&longs;nm; & rotatione, &longs;eu turbinatione, circa axem æquè in­<lb/>clinatum ad planum Eclipticæ, ac &longs;ibi &longs;emper parallelum. </s> <s>En tibi mo­<lb/>tum &longs;implicidimum, quo &longs;uppo&longs;ito, cuncta facile ac planè explicantur. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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/>expliceutur. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Cuncta &longs;eor&longs;im explico, Cogita, &longs;i vis, Solem à puucto 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 cœlo ve&longs;tigia, atque ita deinceps moveri Solem <lb/>puta, &longs;ignatis &longs;ingnlorum 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, mulciplicatis 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Sed i&longs;ti &longs;unt duo motus, alter cuiu&longs;dam qua&longs;i librationis, al­<lb/>ter circularis. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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 lincam 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 reper cu&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"/>Solis motus &longs;implici&longs;&longs;imus &longs;it. </s> <s>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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tinus.<emph.end type="italics"/></s><s> Duo &longs;unt motus, ni fallor, orbis, &longs;cilicet, & centri &longs;implex <lb/>igitur motus non e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Antimus.<emph.end type="italics"/></s><s> Igitur motus naturalis, quo corpus grave, v.g. </s> <s>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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tinus.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antimus.<emph.end type="italics"/></s><s> Ita pror&longs;us. </s> <s>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;phærijad 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 phœnomenum 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>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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Igitur non tres, aut quatuor mot<gap/> in <expan abbr="nõ&longs;tra">non&longs;tra</expan> hypothe&longs;i &longs;ta­<lb/>tuendi &longs;unt, vt &longs;upra dicebas; cum vnus duntaxat, eo quo explicas modo <lb/>fufficiat: cur ergo quatuor nece&longs;&longs;arios e&longs;&longs;e fingis? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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>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"/>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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Omittis duos alios motus, quos adhibent, &longs;cilicet obli­<lb/>quitatis Zodiaci, præce&longs;&longs;ionis Æquinoctiorum, & fortè mutationem <lb/>excentricitatis. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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, tuillam 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="primũ">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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tinus.<emph.end type="italics"/></s><s> Vt vt &longs;it, Negarinon pote&longs;t, quin no&longs;tra hypothe&longs;is ad <lb/>calculos A&longs;tronomicos magis accommodata &longs;it. </s></p><p type="main"> <s><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>atque &longs;i ita e&longs;&longs;et. </s> <s>In quo, vt vides, nulla e&longs;t <lb/>difficultas. </s> <s>Sed de hoc argumento plura infra, &longs;i hoc tibi gratum accidat: <lb/>iam verò reliqua exprome, &longs;i quæ habes adversùm nos. </s></p><p type="main"> <s><emph type="italics"/>Augi&longs;tinus.<emph.end type="italics"/></s><s> 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>quá ne&longs;cio an major ex cogitari po&longs;&longs;it; <gap/>uta &longs;tationes, retrogre&longs;­<lb/>fiones, accelerationes &c. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><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></p><pb pagenum="10"/><figure></figure><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Schemate opus e&longs;&longs;e non putarem, quia tamen ita iubes, tibi <lb/>morem geram. </s> <s>Sit A. centrum vniver&longs;i, &longs;itque BCDE magnus Orbis, <lb/>vt vocant, in quo, primoloco, iuxta tuam hypothe&longs;im, terre&longs;trem globum <lb/>moveri&longs;uppono; &longs;it orbita Martis FRPS. </s> <s>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>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>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 mediocli 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></p><p type="main"> <s>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"/>ca proptium centrum, &longs;it ab Oin N, id e&longs;t, in con&longs;equentia, &longs;ecundùm <lb/>partem &longs;uperiotem, nec non eodem cum centro motu; Sitigitur centrum <lb/>Epicycli in S. planeta in D, id e&longs;t in Perigæo; <expan abbr="centrũ">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>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>Mars item in D. e&longs;t retrogradus, in I verò acceleratus. </s> <s>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;ionnm phænomena, <lb/>accelerationum; &longs;cilicet, &longs;tationum, repre&longs;&longs;ionum &c. </s> <s>Vter verò explican­<lb/>di modus magis aptus &longs;it, magi&longs;que naturæ ip&longs;i congtuat, demon&longs;trandum <lb/>re&longs;tat. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/> H<gap/>c 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>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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Magnus orbis etiama te ponendus e&longs;t, in quo Sol ip&longs;e mo­<lb/>veatur; orbes igitur multiplicas. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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>nece&longs;­<lb/>&longs;ariò con&longs;equentur. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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"/>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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antimus.<emph.end type="italics"/></s><s> Secus e&longs;&longs;e crediderim; nempe<gap/> ille modus veritati, rationi, & <lb/>naturz 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>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>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; Lic<gap/>t hic deinde ex aliis notionibus &longs;en­<lb/>&longs;um corrigat; & contra rerum naturam & rectæ rationis ordinem, plane­<lb/>ta &longs;emper in eoloco videtur, in quo non e&longs;t, & nunquam in eo, in quo e&longs;t, <lb/>citra puncta oppo&longs;itionum & conjunctionum. </s> <s>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 cœlo; 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>Quis homini cordato per&longs;uadeat? </s> <s>præ&longs;ertim vbi <lb/>nulla nece&longs;&longs;itas vrget, nulla ratio po&longs;tulat, nulla cogunt phænomena. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Illa facilitas Apogæi ac Perigæi, quæ in no&longs;tra hypothe&longs;i <lb/>mitabilis e&longs;t, negari profectò nequit. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Quæ major facilitas excogitari pote&longs;t, quàm illa, qua res Apo­<lb/>gæi ac Perigæi per Epicyclum explicatur? </s> <s>Quis &longs;tatim non capiat, Mar­<lb/>tem in O e&longs;&longs;e Apogæum, in C verò Perigæum<gap/> 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"/>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>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>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>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. </s> <s>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;picict 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; ide&longs;t, emergit ex radiis &longs;olaribus, Sole po&longs;t &longs;e <lb/>relicto versùs ortum; ac proinde incipit videri. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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 & Petigæum explicabis? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Per&longs;picuè omninò; &longs;uppo&longs;ito enim illo velocitatis gradu, <lb/>quem Mars motu recto acqui&longs;ivit, eo temporis <gap/>mmento, quo cœpit 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/>cœpit, 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 Apogæoad 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 cœpit 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>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"/>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></p><p type="main"> <s><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 hactua 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>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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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>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. </s> <s>g. </s> <s>&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>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>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/>nores, 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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 acceditad Apogæum, & <lb/>Sol ad Perigæum, Mars tardiùs, Sol citiùs &longs;uum orbem decurrit, hinc <pb pagenum="15"/>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>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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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, Marter <lb/>motu &longs;emper æquabili &longs;uos agere orbes, cum maiorem circulum de&longs;<gap/>r <lb/>bat in Apogæo, & minorem in Perigæo, hunc citiùs, tar liùs 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. </s> <s>g. </s> <s>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 b<gap/>euioti <lb/>tempore, & longiore directus; cur ab Apogæo ad Quadraturam plus <lb/>temporis ponat, quàm ab i&longs;ta ad Perigæum. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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>Si autem in mediocri di&longs;tantia &longs;uum orbem <lb/>æquè cirò ac &longs;tella conficeret, æque diu e&longs;&longs;et retrogradus, ac di. </s> <s>ectus; <lb/>ac proinde nunquam ad oppo&longs;itionem pervenire po&longs;&longs;et, & in Perigæo <lb/>e&longs;&longs;et etiam Soh 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Vis liberè dicam, quod &longs;entio; cum ex multis ob&longs;ervationi­<lb/>bu: &longs;y&longs;tema &longs;tatuatur, co &longs;emel &longs;tatuto, reliquas ad illud vt plurimùm <pb pagenum="16"/>accommodant v.g. </s> <s>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>omnes ob­<lb/>&longs;ervationes ad prædicta &longs;y&longs;temata, vt dixi, accommodant, licèt vt pluri­<lb/>mum, aliquæ parum congruant. </s> <s>Hinc non mirum, &longs;i fortè &longs;upponant, Mar­<lb/>tem pluribus gradibus retrogredi, quam reip&longs;a retrogrediatur. </s> <s>Sed iam ad <lb/>alia tua po&longs;tulata gradum fac<gap/></s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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>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>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 Ianuatij, 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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"/><figure id="fig1"></figure><lb/>Sit igitur contrum 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, atqueita 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>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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Quis amabo &longs;ciat, lineam illam curvam e&longs;&longs;e? </s> <s>quid &longs;i dixe­<lb/>rim e&longs;&longs;e rectam in latere cylindri, vel coni? </s> <s>Deinde &longs;i curva e&longs;t, quis de­<lb/>finiat, quæ & qualis &longs;it? </s> <s>vide, quàm ab&longs;tru&longs;a & ob&longs;cura nobis obtru­<lb/>das. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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"/>Apògæum, quod repugnat; nec etiam in latere coni. </s> <s>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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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="genitũ">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. </s> <s>erit. </s> <s>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;inuirecto <lb/>anguli grad 66.30 minut. </s> <s>qui e&longs;t ad <expan abbr="&longs;inũ">&longs;inum</expan> totum, vt 91706.ad 100000.Igi­<lb/>tur GF erit vt 8794.Igitur fere <gap/> totius AD. </s> <s>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></p><p type="main"> <s><emph type="italics"/>Angu&longs;tinus.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antimus.<emph.end type="italics"/></s><s> 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;qne 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Iam vtcumque tuam Soiarem hypothe&longs;im concipio, vis <lb/>enim Solem &longs;implici motu æquabili diu<gap/>no ferriab Ortu ad Occa&longs;um, <expan abbr="cũ">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 cl­<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 int<gap/>igo; &longs;ed non levis difficultas mihi e&longs;&longs;e videtur, <pb pagenum="19"/>tum in explicando Apogæi motu, tum in excogitanda aliqua ratione Ano­<lb/>maliæ Solis; Sol enim, vt nemo ne&longs;cit, ftatuto Apogæo in D, plures dies <lb/>ponit à Tropico Cancri ad Æquatorem, quàm ab Æquatore ad Tropicum <lb/>Capricorni. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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>Hoc autem ex duplici analogia facilè intelligitur; Prima e&longs;t; <lb/><figure id="fig2"></figure><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>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/></s> <s>tuum. </s> <s>Vtraque analogia facilè applicatur. </s> <s>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>v. </s> <s>g. </s> <s>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. </s> <s>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;ic<gap/> admitto; germa­<lb/>nam dabimus &longs;uo loco & Phy&longs;icam. </s> <s>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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tinus.<emph.end type="italics"/></s><s> 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"/>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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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>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>Hæc dixi ad reducendum ad calculos Ano­<lb/>maliæ motum; nam reip&longs;a AD habet minorem proportionem ad AH. <lb/>&longs;eu BD ad CH, quàm tempus, quo Sol Apogæus in Cancro decurrit <lb/>arcum E clipticæ 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>Ex his reliqua, ni fallor, quæ ad Solare <lb/>no&longs;trum &longs;y&longs;tema pertinent, facilè intelliges. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antimus.<emph.end type="italics"/></s><s> 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;cilicer <lb/>ab Apogæo ad Quadraturam, minus verò ab hac ad Perigæum. </s></p><p type="main"> <s><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; ones &longs;uperiorum Planetarum pertinent, pari facilitate ex <lb/>iactis à te principiis explic<gap/> po&longs;&longs;e. </s></p><p type="main"> <s><emph type="italics"/>Antimus.<emph.end type="italics"/></s><s> Ita e&longs;t pror&longs;us; nam res eodem modo explicatur in Iove & <lb/>Saturno; ni&longs;i quod cùm lupiter maioribus intervallis Solem po&longs;t &longs;e relin-<pb pagenum="21"/>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 tempotis intervallum, æquè dividatur à mediocris di&longs;tantiæ momen­<lb/>to, ad eundem finem obtin endum, Iovis &longs;cilicet Apogæi, in Coniunctio­<lb/>ne, & Perigæi in Oppo&longs;i<gap/>; brevior e&longs;t <expan abbr="acce&longs;&longs;uũ">acce&longs;&longs;uum</expan> & <expan abbr="rece&longs;&longs;uũ">rece&longs;&longs;uum</expan> periodus in <lb/>Iove quàm in Marte; vnde frequentiùs recurrunt Coniunctiones in Iove, <lb/><expan abbr="quā">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>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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antimus.<emph.end type="italics"/></s><s> Recti&longs;&longs;<gap/> Nam&longs;upponamus, Apogæum Marris coniuncti <lb/>e&longs;&longs;e in primo Arietis gradn; cùm illius revolntio ab Apogæo ad Apogæum, <lb/>duret die bus 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>Igitur &longs;ingulis annis & diebus 25. Apogæum Martis 25. circiter gradi­<lb/>bus in con&longs;equentia moveri videtur. </s> <s>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>Igitur &longs;ingulis annis <lb/>& diebus 34. Apogæum Iovis moveri videtur in con&longs;equentia 34. grad. <lb/></s> <s>In Satu<gap/>no denique, cùm eius revolutiofiat 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/>Sunr 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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. </s> <s>g. </s> <s>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></p><pb pagenum="22"/><p type="main"> <s><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></p><figure></figure><p type="main"> <s>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>circiter, <lb/>dum &longs;cilicet directus e&longs;t, & Saturnus. </s> <s>2. Sit arcus FM, grad. </s> <s>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. </s> <s>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>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;tario­<lb/>nem at<gap/>ingit, & paucis po&longs;t dicbus, fit retrogradus: eadem ratio facit <lb/>pro Iove, vt &longs;cilicet nunquam Saturno directo, retrogradus jungatur. <lb/></s> <s>Sed vt hæc paulò accuratiùs di&longs;cutiamus; cùm Saturni & Solis conjun-<pb pagenum="23"/>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/>contro 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. </s> <s>g. </s> <s>&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>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, & Sacurnus <lb/>retrogradus, nempe Martis &longs;tatio e&longs;t infrà trigonum a&longs; pectum, Saturni <lb/>verò paulò infrà quadratum; hinc motus Saturni retrogradus diuturniot <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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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, Satu. </s> <s>num eo <lb/>velocitatis gradu moveri, vt panlò infrà mediocrem di&longs;tantiam, æquè <lb/>citò &longs;uum circulum diurnum decurrat, ac Stellæ &longs;uum. </s> <s>Iupiter verò <lb/>adhuc infrà, qua&longs;i in trigono; Mars demùm infrà trigonum; idem aut<gap/>m <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 hucu&longs;que di&longs;&longs;eruimus, nece&longs;&longs;ariò con&longs;equuntur; nam <lb/>Saturnus altior motum retrogradum diuturoiorem 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 eriam, quàm Martis brevior; hinc frequentiores <lb/>recurrunt &longs;tationes in Saturno, quàm in Iove, & in hoc, quàin 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"/>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, quaie <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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Imò longè faciliùs & cum multiplici præ: ogativa: Nam p<gap/>i­<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>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>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>Quartò; <lb/>denique hab<gap/>o 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>Tu verò meras fallacias, & oculorum illu&longs;iones <lb/>e&longs;&longs;e contendis. </s> <s>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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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;itũ">&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="fig3"></figure><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>Sit Terra in B, Planeta in limite Bo­<lb/>reali F; apparebit prædictus atcus <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"/>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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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/>nequideminter &longs;e conveniunt, &longs;i rectè inemini, 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>In mea <lb/>hypothe&longs;ires &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/>decutrat, 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>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;c<gap/>nden<gap/>bus verò, versùs Au&longs;trum; variatur eriam Latitudo ex <lb/>varia di&longs;tantia Martis. </s> <s>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 comòinationes Apogæorum Solis & Martis; <expan abbr="Nodorũ">Nodorum</expan> item, <lb/>qui versùs Ortum in con&longs;equentia promoveri videntur; nempè ex diver­<lb/>&longs;o Nodorum & Apogæor<gap/>m loco ac &longs;itu, diver&longs;a Latitudinis mutatio ne­<lb/>ce&longs;&longs;ariò &longs;equitur. </s> <s>Hæc in Saturno & Iove etiam locum habent; atque <lb/>adeò, ni fallor, ex dictis habes, in mea hypothe&longs;i, trium &longs;uperiorum <lb/>Planetatum 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Veneris & Mercurij Conjunctiones in Copernicana hypo­<lb/>the&longs;i, ea clarimdine explicantur, qua ne&longs;cio, an major excogitari po&longs;&longs;it, <lb/>itémque Apogæa & Perigæa, tum etiam alioium Planetarum &longs;uperiorum, <lb/>&longs;ed jam prævideo, quid pro tua hypothe&longs;i de hoc atgumento dicturus &longs;is. </s></p><pb pagenum="26"/><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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></p><figure></figure><p type="main"> <s>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>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. </s> <s>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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Multa ob&longs;tant, quo minùs Epicyclum adhibeam. </s> <s>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. </s> <s>ducatur BV, tum perpendicularis <pb pagenum="27"/>DR, hæc erit &longs;emidiameter Epicycli, quanquam a&longs;&longs;umpto angulo maxi­<lb/>mæ digre&longs;&longs;ionis grad. </s> <s>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. Igitue. <lb/></s> <s>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>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></p><p type="main"> <s><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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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>Secundò Venus vbi ad mediocrem di&longs;tantiam pervenit, <lb/>puta in L, adhuc vltra digreditur, quia tardiùs Sole movetur. </s> <s>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>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>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;cilicetad occa&longs;um. </s> <s>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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Multa haud dubiè con&longs;ideranda &longs;unt, vt ritè de&longs;iniatur, 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"/>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>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>Atverò 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>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. </s> <s>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>Igitur figura SLD e&longs;t ad dictum &longs;ectorem, vt <lb/><gap/> SD ad <gap/> DB. </s> <s>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>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></p><p type="main"> <s><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. </s> <s>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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Parum negotij cuncta hæc mihi face&longs;&longs;unt, &longs;ecus fortè vobis <lb/>ac proinde tot epicyclos, excentricos, circellos, librationes arcus, Ellipi <lb/>&longs;es, Epicyclorum Epicyclos multiplicatis; quibus etiam admi&longs;&longs;is, vix &longs;i­<lb/>nem vobis propo&longs;itum obtin etis; 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"/>&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>lgitur 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>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>Quod verò &longs;pectat ad alterum po&longs;tulatum, æquè facil<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>Sole v. </s> <s>g. </s> <s>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>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. </s> <s>g. </s> <s>&longs;upponamus ma­<lb/>ximam digre&longs;&longs;ionem ve&longs;pertinam in. </s> <s>1. gradu Acietis ab&longs;que vlla latitu­<lb/>dine, erit Sol v.g. </s> <s>in grad. </s> <s>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>Si autem &longs;upponamus ibi­<lb/>dem Planetam, &longs;cilicet in 1. grad. </s> <s>Arietis ab&longs;que latitudine, in digre&longs;­<lb/>&longs;ione maxima matutina, Sol erit v. </s> <s>g. </s> <s>in gr. </s> <s>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 forteregula 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 crc&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 eòadegerit, <lb/>vt fateantur vltro, certum Sy&longs;tema Veneris, in quo omnia Phænomena <pb pagenum="30"/>explicentur nondum &longs;tatui po&longs;&longs;e, ri&longs;i plures & magis accuratæ Ob&longs;erva­<lb/>tiones fiant. </s> <s>Porrò cum Venus proximè ad terram accedat, & circa hor<gap/><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;aitem 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>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>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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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>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 Clobo Terræ delatam & circumactam, &longs;ed dict<gap/>otu <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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Negare non po&longs;&longs;um, quin hoc fuerit ingenio&longs;um inventum, <lb/>fictum tamen & commentitium. </s> <s>Primo enim ita æ&longs;tus diurnus &longs;uas pe­<lb/>riodos metitur, vtad 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/>clevationis 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: lgitur 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 di<gap/>ementum in<gap/>ipiat eadem hora <lb/>Lunari, ac proinde 48. minutis tardiùs, quàm pridie. </s> <s>Quid autem ad <lb/>hæc, Augu&longs;tine mi, Terræ motus conferat, nemo capiat; cùm enim ea­<lb/>dem motus inæqualitas, cadem &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 cadem hora &longs;emper e&longs;&longs;et &longs;ummum cre-<pb pagenum="31"/>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 Merid<gap/>e &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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Ita fortè di&longs;poni po&longs;&longs;unt prædicti duo motus, orbis &longs;cilic<gap/><lb/>& centri, vt motus mixtus inde re&longs;ultans tales in æ&longs;tu mutationes pro­<lb/>ducat. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Nullo&longs;ané modo id&longs;ieri po&longs;&longs;e, omni a&longs;&longs;everatione affirmo; quod <lb/>vt clariùs exponam. </s></p><figure></figure><p type="main"> <s>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 Htendat. </s> <s>Vnde re&longs;ulrat ex vtroque mo­<lb/>tu æquabili motus mixtus omnino inæqualis; nempe ab H in I, per E; <lb/>additur motus orbis, motuicentri; 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/>det<gap/>ahitur &longs;patio decur&longs;o mot<gap/> centri, hinc ab H in E, accierationis 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 paritcr <lb/>ab I in F, &longs;unt in ratione &longs;inuum ver&longs;orum; ab F verò in H, in ratione <pb pagenum="32"/>&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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Cuique &longs;uæ artis periro 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>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 re&longs;utatur; <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>Nihil pror&longs;us. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> In Novilunio Luna prop<gap/>s ad Solem accedit, & minores <lb/>arcus decurrit, contraverò in Plenilunio. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Quid in de? </s> <s>An fortè Luna &longs;uos motus in Terram derivat? </s> <s>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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Saltem negari non pote&longs;t, quin terræ aut Solis motus ali­<lb/>quid conferat ad mutationem illam æ&longs;tuum, quam omnes hucu&longs;que cir­<lb/>ca Æquinoctia Ob&longs;ervarunt; nihil enim ad hæc Luna. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Sed quid quæ&longs;o ad hæc terræ motus? </s> <s>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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Quid autem ad hæc Luna, quis hominum aliquando dicat? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Ego fortè minimus hominum; illam enim æ&longs;tus marini cau­<lb/>fam 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 cœpta di&longs;ceptatio intermittatur: itaque omi&longs;&longs;o maris <lb/>æ&longs;tu, quid tandem de Magnete dicis? </s></p><pb pagenum="33"/><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Facilè opinor conjicies; terram enim maiorem Magnetem <lb/>e&longs;&longs;e dicimus cum Gilberto; vnde ma<gap/>fe&longs;tam cau&longs;am ducimus perpetui <lb/>Axis paralleh&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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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 cœli puncta &longs;emper &longs;pectant; <lb/>rectè, quis hoc negat? </s> <s>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>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 cœli puncta &longs;pectat: ergo ex hoc neutra hypothe&longs;is probari pote&longs;t; <lb/>immò potiori iure mea, quàm tua inde probatur. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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>Fru&longs;trà licet: cùm illam <lb/>Ga&longs;&longs;endus vir toto orbe literario notus illam in Docti&longs;&longs;imorum honu­<lb/>num congre&longs;&longs;u, cui &longs;ummus quidam Princeps præerat, egregiè refutavit. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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 cœli puncta, exceptis polis, re&longs;pectum haberet, volebat enim vit <lb/>ille de re Magnetica optimè metitus, Magnetem in &longs;phæram tornatum, <lb/>in eo &longs;emper &longs;itu manerc, 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 com<gap/>uni omnium ni&longs;u. <lb/></s> <s>vn<gap/> 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 ra­<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 admiztæ &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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Hanc igitur Grandamici demon&longs;trationem tuo calculo do­<lb/>nas, quam tamen viri Docti&longs;&longs;imi & Sapienti&longs;&longs;imi rejecerunt. </s></p><pb pagenum="34"/><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Non habeo, vt iam dixi, pro demon&longs;tratione; quia nemo <lb/>hucu&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;u&longs;ficienti virtute magnetica <lb/>in&longs;tructam, qua tanta moles agi queat. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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 cœli puncta, neutrum in tua <lb/>habetur, quare vt fateor vlero, 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Egregiè &longs;anè; &longs;ic æquis armis pugnamus. </s> <s>Hucu&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></p><p type="main"> <s><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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Obiter, inquis, non pauciora certè, in<gap/>no 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 excquen­<lb/>dam, iu<gap/>meo po&longs;tulo. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;t.<emph.end type="italics"/></s><s> Crede mihi, Antime, certamen non detrecto, nec vinci metuo, <lb/>timeo tamen ne prolixior di&longs;ceptatio nonnihil tædij <expan abbr="circũ&longs;tantibus">circun&longs;tantibus</expan> afferat </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Rectè mones remittamus in <expan abbr="proximũ">proximum</expan> congre&longs;&longs;um, per me licet. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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 amœ­<lb/>niùs hæc di&longs;ceptatio terminetur; tenes enim, ni &longs;allor, ex lis aliquam, quæ <lb/>iam ab aliis excogitatæ fuerunt. </s></p><pb pagenum="35"/><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Toto cœlo erras; illam &longs;ententiam minimè approbo, quæ & <lb/>phænomenis & veritati non con&longs;entit; ex illa enim &longs;equitur. </s> <s>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>Secundò Præ­<lb/>dictam aëris pre&longs;&longs;ionem omnino &longs;entiremus. </s> <s>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>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></p><p type="main"> <s><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>Interea antequam hunc congre&longs;&longs;um terminemus nonnulla ex te per­<lb/>cunctabor, quælicèt 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>Dixi&longs;ti Solem inclinati <lb/>&longs;ur&longs;um ac deor&longs;um motu acceleiato, ac retardato in reciproco acce&longs;&longs;u <lb/>& rece&longs;&longs;u; quæro ex te, vtrùm Sol novum producat impetum. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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 acceierati & 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></p><p type="main"> <s><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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Non de&longs;unt, eáque plurima, duo in mentem veniunt, omnino <lb/>&longs;imilia; primum tale e&longs;t. </s> <s>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"/>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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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 impedime<gap/>o, 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/>rempore motu accelerato confectæ, &longs;ed applica quæ&longs;o ad &longs;pitas Solares. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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></p><figure></figure><p type="main"> <s>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>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;phæric<gap/>, <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>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>Iam verò <expan abbr="cõponaturvtraque">componaturvtraque</expan> <lb/>inclinatio, ita vt D partim versùs F, <pb pagenum="37"/>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<gap/> 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. </s> <s>igitur tempus, quo circulus diurnus decurritur in H, e&longs;t brevius <lb/>tempore, quo decurritur in D 48. minutis horæ. </s> <s>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;">Dque</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;">Dque</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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Pru&longs;tr à laboras, Antime, vt dierum æqualitatem retineas. </s></p><p type="main"> <s><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>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"/>di&longs;tantiam tendit motu recto, qui e&longs;t ad in&longs;taraccelerati; 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>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 cœle&longs;tium revolutiones fiant, <lb/>cuius extremitates &longs;unt Poli, vi huius inclinationis Sol à D, v.g. </s> <s>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 earn re­<lb/>tinendaminclinat; &longs;ed &longs;i in arcu DF feratur, eadem &longs;emper manebit di­<lb/>&longs;tantiz 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>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 mæquales, vt patet ad ocu­<lb/>lum, cui figura &longs;ubjacet. </s> <s>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 Qad H, ponendum <lb/>e&longs;&longs;et, quantum à D ad Q<gap/>&longs;unt enim &longs;egr<gap/>enta 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;upponur tur 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.">Dque</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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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>Minimè verò; Quomodo igitur tam &longs;ollicitè <pb pagenum="39"/>& accuratè inæqualitatis peticulum avertit? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Quæro à te, Augu&longs;tine, An fortè aqua illa tubi vitcei &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>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 &longs;unependulo, <lb/>aut per parabolam, vel aliam lineam in projectione; item corpus refle­<lb/>xum, quod per eandem lineam motum pto&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 ves 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<gap/>i 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>Sed vt ad rem no­<lb/>&longs;tram redeam, cùm Sol à Q ad H totum &longs;uum motum, in &longs;pitis 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 ptoptereà &longs;pirarnm motus re­<lb/>mittitur &longs;ed æqualis &longs;emper remanct; nempe cum Sol in Q non tendat <lb/>ad Tropicum, per curuam QH, &longs;ed per arcum inter ceptum 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 mitum &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> <s>Hinc &longs;emoto motu circulari, & relicta gemina illa inclinatione, adhuc <lb/>&longs;ecunda inclinatio decurreret citiùs QH, q<gap/>àm <expan abbr="Dq.">Dque</expan> Ex his ni fallor <lb/>&longs;equi vides, tum di&longs;tractionem maiorem &longs;pirarum, tum imminutum &longs;pi­<lb/>rarnm numerum, tum compen&longs;ationem talem motuum, ex qua perfecta <lb/>ferè &longs;pitarum diurnarum æqualitas nece&longs;&longs;ariò con&longs;equitur. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Si Apogæum &longs;it in Æquatore, quid tandem fieret? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Planum Troprci DI tantulùm accederet ad Æquatorem FK, <pb pagenum="40"/>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>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;oilicet 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 Capticorno ad Arietem, & ab hoc ad <lb/>Cancrum. </s></p><p type="main"> <s><emph type="italics"/>Angu&longs;tin.<emph.end type="italics"/></s><s> Ille tuus calamus volatilis, vt vocas, mihi &longs;ummopere ar­<lb/>ridet, itemque de&longs;cen&longs;t 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;pitas agitur, propter illam ta­<lb/>tionem, quam attuli&longs;ti. </s> <s>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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Certè no&longs;tri Philo&longs;ophi communiter docent, hunc effe­<lb/>ctum à varia reflexione procedere, quæ in circuma&longs;&longs;ur gentibus monti­<lb/>bus fiat. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Sat &longs;cio. </s> <s>Sed quænam reflexio in va&longs;ta terrarum & Oceani <lb/>planitic fieri pote&longs;t? </s> <s>in qua nulli montes a&longs;&longs;urguat. </s> <s>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 cumigne Typhon, aiiàs cum aqua conjunctus e&longs;t; igne qui­<lb/>dem quo inferiotis aëris tractus &longs;tatim rare&longs;cat, ac proinde maximo im­<lb/>petu aër Superioris tractus &longs;piratim ruat; aqua verò &longs;imagna 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 & pr<gap/>eps deor&longs;um ruat. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/> A vero abetras, 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 f<gap/>vente æ&longs;tu, altiùs vapores a&longs;&longs;urgunt, & perexiguæ <lb/>guttæ lenti&longs;&longs;imè de&longs;<gap/>ndent, vt &longs;æpè vidi&longs;li in nebula, dum re&longs;olvitur: <pb pagenum="41"/>tantulum porrò vapotis 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/>notes 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Circa tuam hypothe&longs;im multa e&longs;&longs;ent in accutatius 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;inet Planetis per motum acceleratum prævium. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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 hucu&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>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;let, definite altitudinem illam, ex qua Sol ad hunc velocitatis <lb/>gradum acquirendum de&longs;cenderit, cognita &longs;cilicet Solis Apogæi vel <lb/>Perigæi di<gap/>antia; 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>temporum, <lb/>&longs;cio, v.g. </s> <s>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/>&longs;icere circiter 1250. pedes. </s> <s>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 hoia; 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/>daco 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;eip&longs;um, pro­<lb/>ductus e<gap/>it 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"/>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 vetum 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>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>Immo, vt iam fortè <lb/>mecum ob&longs;ervas, &longs;i præcisè habeamus, quot pedes cotpus grave in de&longs;­<lb/>cen&longs;u decurrat vno &longs;ecundo minuto, habebimus haud dubiè quantum <lb/>decurrere debeat vno die integto, 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;uis <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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><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;eip&longs;o moveatur, <lb/>quod certè tanti non e&longs;&longs;et, cùm id cuipiam corporigravi 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 cœpit, versùs Occa&longs;um: cur, inquis, potiùs quàm versùs Ortum? <lb/></s> <s>Quia cum creatus fuerit in Tropico Cancri circa 180. grad. </s> <s>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>& 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>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 cœpit, cui prædicta turbinatio <lb/>non ob&longs;tat, Vides, cuncta hæc ex communibus illis principiis deduci, <lb/>per quæ aliorum corporum motus explicantur. </s></p><pb pagenum="43"/><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Rectè, illud &longs;altem commodi ex hac tua hypothe&longs;i acci­<lb/>dit, quod primi orbis incolæ diem primum integrum habuetunt, 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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></p><figure></figure><p type="main"> <s><emph type="center"/>DIALOGVS SECVNDVS.<emph.end type="center"/></s></p><p type="main"> <s><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></p><p type="main"> <s>DVBIVM mihi non e&longs;t, hanc di&longs;putationem ineunti, quin <lb/>pleri&longs;que fortè ia<gap/> actum agere videar, CARDINALIS <lb/>EMINENTISSIMS, quotus enim qui&longs;que invenitur, vel Philo­<lb/>&longs;ophorum in tractatione de Corpore Cœle&longs;ti; vel Theologo­<lb/>rum in Opere&longs;ex dierum enucleando;; vel &longs;acri Textus Interpretum, in <lb/>corum 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 mirtat, ac de mi&longs;ero Copernico novos triumphos agere nolit. <lb/></s> <s>Scribimus indocti, doctique poëmata: quanquam, vt ingenuè dicam, <lb/>maxima illorum argumentotum pars, quibus nonnulli præfatam Coper­<lb/>nici opinionem petierunt, non patum 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;<gap/>ovæ demon&longs;trationis novum &longs;plendo­<lb/>rein 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 habe<gap/>rui; 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 effegiat, &longs;i non de integra victoria, de potioribus &longs;altem partibus à <lb/>nobis in haccau&longs;a, vt benè &longs;pero, referendis, judicare, necnon æqui&longs;&longs;i­<lb/>mam ferre &longs;ententiam. </s> <s>Sed initium di&longs;&longs;ertationi demus. </s></p><pb pagenum="44"/><p type="main"> <s><emph type="italics"/>Antimus.<emph.end type="italics"/></s><s> Omittam, vt prudenter feci&longs;ti, argumentorum qui&longs;quilias, <lb/>quæ nonnulli, præ&longs;ertim ex antiquioribus terum Mathematicarum & <lb/>Phy&longs;icarum minù<gap/> 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tinus.<emph.end type="italics"/></s><s> 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 terum 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 ad<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 cor&longs;en&longs;ione convenire; itaque licèt ex &longs;ola ter­<lb/>re&longs;tris globi circuitione æ&longs;tus matini 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></p><p type="main"> <s><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, varinm &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 cert<gap/> ac fixo temporis puncte huiu&longs;modi aqua­<lb/>rum excurfiones fiunt, quod nemo neger, &longs;i c<gap/>cus & &longs;urdus; nullus e&longs;t <lb/>igitnr Terræ motus, ex quo alioqui prædicti effectus nece&longs;&longs;ariò &longs;eque­<lb/>rentur. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Facilis re&longs;pon&longs;ic 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 Cœle­<lb/>&longs;tium &longs;phærarum motus nobis è Terra ob&longs;ervantibus inæquales apparent; <lb/>cùm tamen re ip&longs;a æquabiles fint, igitur po&longs;ita reali motus æqualitate, <pb pagenum="45"/>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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Merum effugium e&longs;t; cùm &longs;it vera & realis, vt aiunt, motus <lb/>inæqualitas; & vt ad tuam figuram veniam. </s></p><figure></figure><p type="main"> <s>Punctum E longè velociùs movetur, quàm F; nam E in Ortum fertur, <lb/>vtroque motu, centri &longs;cilicetatque 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>Prætereà non tantùm aquarum excur&longs;io ex dicta motus inæqualitate &longs;eque­<lb/>retur, verùm etiam alia, quæfacilè 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></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocomus.<emph.end type="italics"/></s><s> 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"/>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 proiude 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, quæva&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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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 peraliam, 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. </s> <s>di&longs;cus æneus, Axevtrim­<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>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>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 partiab alia <lb/>parte, nam perinde e&longs;t, quoad hoc principium. </s></p><pb pagenum="47"/><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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>Sicanima, 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 tationalis. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ec.<emph.end type="italics"/></s><s> Hoc idem principium ad alias qualitates etiam extendi pote&longs;t; <lb/>caloris v.g. </s> <s>frigoris, &c. </s> <s>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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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>Sit igitur <lb/>&longs;ecundum principium ex eadem doctrina motuum huc derivatum, cor­<lb/>pus co 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> <s>&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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Licèt fortè in parergum incidamus, tantulum &longs;chematis de­<lb/>&longs;idero, vt rem à te &longs;olo auditam meliùs intelligam. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Non opus e&longs;t alio &longs;chemate: Supponamus enim cylindrum <lb/>BC (<emph type="italics"/>in Fig. </s> <s>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, reduxirem 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/>hete, & aliam addere, vt re&longs;idua &longs;it ad detractam, vt detracta ad addi-<pb pagenum="48"/>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 cœteris <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>Primò vno dumtaxat motu centri, quo &longs;ingulæ partes per lineas <lb/>plano inclinato parallelas eant. </s> <s>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></p><p type="main"> <s><emph type="italics"/>Augn&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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Nonnihil tamen figuræ adhibeo, vt maximam difficultatem, <lb/>quam ego quidem &longs;entio, in eo, quod dicis, mihi excutias. </s></p><figure></figure><p type="main"> <s>Sit planum inclinatum DH, & in eo <lb/>globusg ravis, 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>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 intelligi<gap/><lb/>an de BD ducto à puncto contactus, an verò de AF. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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, viteriùs 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>Sit enim planum horizontale CN, & in eo <lb/><figure id="fig4"></figure><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 rendit, & to­<lb/>tum rectangulum ruit. </s> <s>Idem prorsùs de globo <lb/>dicendum e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Crede mihi, Augu&longs;tine, multi&longs;æpè <lb/>ac &longs;æpiùs paralogi&longs;mis, & fal&longs;is præoccupatio-<pb pagenum="49"/>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 penultim<gap/><emph.end type="italics"/>) propiùs ad planumin cli­<lb/>natum DH accedere non pote&longs;t, à quo æquali &longs;empet di&longs;tantiæ men&longs;uta <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></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> Proptereà globus de&longs;cendit, quia cius 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Rectè, Proptereà globus de&longs;cendit; &longs;ed profectò non pro­<lb/>pterea globus velvitur, &longs;ive enim volvatur deor&longs;um, &longs;ive de&longs;cendatiux­<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>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>Sed hoc alio exemplo fortè luculentiore clariilimè <lb/>o&longs;tendo. </s></p><figure></figure><p type="main"> <s>Sit planum inclinatum AB, &longs;it rectan­<lb/>gulum C in eo collocatum; certè &longs;i &longs;ap­<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 a<gap/>it<gap/>r per &longs;e <lb/>de&longs;cendere pote&longs;t, nec volvi circa angu­<lb/>lum D, quod fieri deberet, vt <gap/>ueret; <lb/>alioquin centrum C in revolutione a&longs;cen­<lb/>deret, quod dici non pot &longs;t; <gap/>t 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;c<gap/>butie impedi<gap/>i polilt, latus AD, &longs;u­<lb/>perior p<gap/>o quæ libera e&longs;t, impetus vi acqui&longs;ui, prævalens, deor­<lb/>&longs;um circum volvitur circa angulum D; &longs;ed hoc per accidens fit. </s> <s>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 citca M radio MF volvatur, ibit infra FO, igitur non a<gap/>­<lb/>det &longs;ed de&longs;cender. </s> <s>itaque vt ad no&longs;t<gap/> globum redeat o<gap/>atio cùn. </s> <s>nec <lb/>citca punctum D volvi po&longs;&longs;it centrum A, (<emph type="italics"/>in Figura antipen<gap/>inia<emph.end type="italics"/>) ni&longs;i in-<pb pagenum="50"/>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 di&longs;&longs;iciliùs 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Audivi hactenus, in rotis vaiere 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Quis negat, in rotis haberi rationem vectis<gap/>in vecte tamen &longs;up­<lb/>ponitur aliquod punctum qua&longs;i immobile, quod in ip&longs;o Hypomoclio col­<lb/><gap/>catur; quod vt meliùs intelligatur. </s></p><figure></figure><p type="main"> <s>Supponatur plannum DH e&longs;&longs;e horizon­<lb/>tale, in quo &longs;itrota, eaque trahatur fune <lb/>AG, in&longs;erto &longs;cilicet axe per <expan abbr="centrũ">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="cũ">cum</expan> propter <expan abbr="af-frictũ">af­<lb/>frictum</expan> planireta; detur D, ac proinde difficiliùs acceda<gap/><expan abbr="punctũ">punctum</expan> Clongè faci­<lb/>liùs accedit; item A. &c. </s> <s>ac proinde citiùs <expan abbr="accedũt">accedunt</expan>, ex quo inæquali acce&longs;&longs;u, <lb/>propter partium nexum, motus orbis nece&longs;&longs;ariò &longs;equitur: Iam verb &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>maneat igitur illud <lb/>principium, quòd &longs;cilicet corpora eo motu moveantur, cæteris paribus, quo <lb/>faciliùs moveri po&longs;&longs;unt. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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>Illico probavi, vbi di&longs;ce&longs;&longs;i&longs;ti, palcherrimum 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.illem 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;phæ<gap/> infima verò ba&longs;is, omnino plana, &longs;aliem <lb/>provt oculo &longs;ubjicitur. </s></p><pb pagenum="51"/><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> Memini me legi&longs;&longs;e vel audii&longs;&longs;e præclari&longs;&longs;imam huiu; 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 cuneatam figu­<lb/>ram induit. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> An fortè pro demon&longs;tratione hoc venditares? </s> <s>Sed vndc, quæ&longs;o, <lb/>& qua vi, &longs;eu virtute aër in hanc formam &longs;e&longs;e fa&longs;tigiat? </s> <s>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, cunel enim <lb/>eò validiores &longs;unt, quò acutiores. </s> <s>Deinde æquè facilè aqua &longs;uper&longs;i<gap/>iem <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>Nempe vt corpus <lb/>grave majus gra<gap/>itatem &longs;uam potentiùs exerit, ita & leve majus &longs;uam le­<lb/>vitatem; &longs;ed cur aqua &longs;imiliter cuncum cuneo minimè opponit? </s> <s>an fortè <lb/>in ratione gravis corporis aëri cedit, quatenus hic corpus leve e&longs;t? </s> <s>itaque <lb/>alia omnino rati<gap/>; cùm enim aqua tendat vt: sùs latera tubi, per quæ <lb/>deinde &longs;uas &longs;p<gap/>gens, vt dixi, de&longs;cendit, eo certè ex medio tubo, <lb/>&longs;en&longs;im ruere non pore&longs;t, ni&longs;i quoquoversùm 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 cuneuslatior 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Si oleum loco aquæ, idem fiet; quanquam paulò lentiùs aëris <lb/>pottio &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 vteidem, vtpote leviori, <lb/>tran&longs;itum cedat. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Oleum, vt probè tenetis, &longs;ua vligine particulam aëris intra <lb/>buliam continere potuit, nempe bullæ ex materia vliginc&longs;a tornamtur; <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>Sed ad alia principia ex doctrina motuum accer&longs;enda pergen-<pb pagenum="52"/>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 vegetiot e&longs;t, obliquus verò debi­<lb/>bilior; in globulis, qui adhiberi &longs;olent in ludo minoris tudiculæ, res e&longs;t om­<lb/>nino per&longs;picua. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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;<gap/> e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Ita e&longs;t, paradoxum e&longs;&longs;e videtur; &longs;i quis tamen rectè perpendat, <lb/>impetum eum dumtaxat &longs;inem, vel effectum habere, ac præ&longs;tare immo­<lb/>bili, cui ine&longs;t, vt hoc movtatur, tali &longs;cilicet motu & modo, qui offectus <lb/>&longs;i non impeditur ab alio. </s> <s>&longs;iu&longs;tra certè contraillud vim &longs;uam exe<gap/>, &longs;i v. <lb/></s> <s>g. </s> <s>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 co &longs;cilicet, quod proprij mobilis motum impedit: Hinc &longs;i Phi­<lb/>lo&longs;opho in verbis ludere liceret, dicià me po&longs;&longs;et <emph type="italics"/>impeius,<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>His præ­<lb/>ini&longs;&longs;is, ad rem venio, Augu&longs;line; Repetamus figuram Sextam, & primo <lb/>quidem loco vnum dicam, quod vix apud vos fidem inveniat, licèt cer­<lb/>ti&longs;&longs;iinum &longs;it, geometrica &longs;cilicet demon&longs;tratione con&longs;irmatum; illud <lb/>autem ad incredibilem proportionem inæqualitatis motus rotæ, in <lb/>diver&longs;is illius punctis con&longs;iderati pertinet; dico irerum incredi­<lb/>bilem. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/> locaris, Antime: quis Auriga, Rhedarins, Carpentarius hoc <lb/>ne&longs;cit? </s> <s>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 in&longs;imuru, <lb/>in quo &longs;cilicet rota planum tangit. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Serioloquor, 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;t.<emph.end type="italics"/></s><s> Quanta pertò illa erit? </s> <s>fac &longs;upremum illud punctum moveri <lb/>duplo citiùs infimo, aut etiam triplo, quadruplo, decuplo, vt voles; quid <lb/>tandem erit? </s></p><p type="main"> <s><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 tigore geometrico, &longs;it incredibilis. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Si centuplam e&longs;&longs;e dixero, vera haud dubiè longè maior erit, & <pb pagenum="53"/>vix vllus tantam e&longs;&longs;e crediderit. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> At &longs;i maiorem centupla, immo & millecupla, & centena mille­<lb/>cupla e&longs;&longs;e dicerem, omnem fidem omnino detrectares? </s> <s>&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></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> Sed quæ&longs;o te, noli nos vltra in geometrica retia & Labyrinthos <lb/>deducere, hæc enim totam congre&longs;&longs;ui gratiam & amœnitatem &longs;enticeta eri­<lb/>piunt. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Si quando illis retibus aliquam veritatem nos fœliciter expi­<lb/>&longs;cari contingat, crede mihi Chry&longs;ocome, illa retia non &longs;unt adeò inamœna, <lb/>&longs;ed vt tibi morem geram, nihil ferè dicam quod etiam ab Ageometris facilè <lb/>intelliginon po&longs;&longs;it. </s></p><figure></figure><p type="main"> <s>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. </s> <s>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 fubduplam 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></p><pb pagenum="54"/><p type="main"> <s><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/>Farbij. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Non agno&longs;cerem pro inea lucubratiuncolam illam, ni­<lb/>&longs;i me <expan abbr="gratī">gratim</expan> animi ratio &longs;timulatet; 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>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. </s> <s>punctum E, dum prædictum ar cum decurrit, deferturque à cen­<lb/>tro D &longs;ini&longs;tror&longs;um, &longs;cilicer versùs V, acquirit &longs;ini&longs;tror&longs;um ratione vtriu&longs;­<lb/>que motus, totum &longs;patium OQ<gap/> &longs;cilicetratione motus orbis, rectam OP, <lb/>id e&longs;t &longs;inum rectum EP, quem &longs;uppono e&longs;&longs;e 30. grad. </s> <s>& tatione motus <lb/>centri, rectam PQ æqualem ip&longs;i arcui ER, tantumdem enim Spatij cen­<lb/>trum decurrit, ergo ratione vtrin&longs;que totu<gap/> &longs;patium <expan abbr="Oq.">Oque</expan> Iam verò &longs;it <lb/>FR arcus æqualis 30. &longs;cilicet grad. </s> <s>punctum R eodem tempore motu or­<lb/>bis acquirit dextror&longs;um <expan abbr="&longs;patiũ">&longs;patium</expan> RS, & motu centri&longs;ini&longs;tr or <expan abbr="&longs;ũ">&longs;um</expan> &longs;patium FT <lb/>æquale arcui FR. exi&longs;tis antem duobus motibus re&longs;ultat R<gap/>an. </s> <s>compa­<lb/>remus hæc duo &longs;patia, &longs;cilicct. </s> <s>EQ, & RT, ve<gap/> 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 terri<gap/> ars &longs;cilicet 52381. <lb/>erit æqualis arcui EP, vel rectæ <expan abbr="Pq;">Pque</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></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Sed vbinam illa tua millecupla inæqualitatis proportio? <lb/></s> <s>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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Parciùs<gap/>&longs;ta viris, Chry&longs;ocome, nam fortè aliquando incides in <lb/>manus cuiu&longs;piam ex iis, quos puros Geometras vocam, à quo immi&longs;ericor­<lb/>diter vapulabis, iis arma profectò non de&longs;unt, &longs;agittæ &longs;cilicet, &longs;ecantes, <lb/>&longs;ecures, cunci, ro&longs;tra & vngues; expecta igitur parumper, nam pedeten­<lb/>tim cum i&longs;ta rota progredimur, accipe arcum 15. grad. </s> <s>id e&longs;t &longs;ubduplam <pb pagenum="55"/>PQ, erit æqualis 26190. cui &longs;i addas &longs;inum rectum ein&longs;dem arcus, &longs;cili­<lb/>cet.25038. erit compo&longs;ita ex vtraque 51228. rejecta minutia, hic erit mo­<lb/>tus pun <gap/>E, eo tempore, quo decurrit <gap/> cum 15.grad.iam verò accipe <lb/>&longs;ecantem ein&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. </s> <s>&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. </s> <s>&longs;it ad motum F per arcum æqualemvt 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>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>Si vltra progredimur, &longs;ecantes ce&longs;&longs;ant in canone Pi­<lb/>ti&longs;ci, et&longs;i veniamus ad <expan abbr="vnũ">vnum</expan> <expan abbr="minutũ">minutum</expan>, quid tandem erit? </s> <s>quid &longs;i ad vnum &longs;e­<lb/>cundum, aut tertium &c. </s> <s>immo quantumvis parvum arcum accipias, erit <lb/>maior proportio ex triplici capite. </s> <s>Primò, quia curva EQ e&longs;t maior rectâ <lb/>OQ, &longs;ed per EQ movetur punctum E, idem de aliis arcubus. </s> <s>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>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, Syncategotematicè, <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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Quid &longs;i aliquis diceret, punctum illud aliquantulum quie&longs;cere, <lb/>ad in&longs;tar cuiu&longs;dam polygoni infinitorum laterum? </s> <s>Sic enim polygonum in <lb/>plano volvitur, vt circa &longs;ingulos laterum angulos totum polygonum &longs;uc­<lb/>ce&longs;&longs;ivè volvatur. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Scio, à viro docti&longs;&longs;imo hæc iam olim fui&longs;&longs;e dicta, &longs;ed Geome-<pb pagenum="56"/>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, v<gap/>atet; 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></p><p type="main"> <s><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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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>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/>eon&longs;tat item maxima velocitas, quam ne quidem globi ex majoribus, vel <lb/>minoribus tormentis emi&longs;&longs;i adæquant. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Quantus apparatus, Deus bone, contra Copernicanam hypo­<lb/>the&longs;im; vereor tamen vt &longs;ufficiat. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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>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"/>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 Galilæusip&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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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 platis 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 tanrùm <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 ptincipiis deducere, opinor, meditaris. </s></p><p type="main"> <s><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. </s> <s>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 potròcremen­<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></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> Fru&longs;tra interrogas; nullum enim dubium e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Rectè; at po&longs;tquàm modica vis venti prædicto aquarum tractui <pb pagenum="58"/>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>quis hoc neget? <lb/></s> <s>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>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 con cha contineretur. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> Movetur igitur totus ille aquarum tractus, &longs;ecundùm totam <lb/>profunditatem. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Non dico hoc, neque nece&longs;&longs;e e&longs;t, neque fieri pote&longs;t; quia vt <lb/>Conchæ &longs;uptemus cir culus 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Mihi opus non e&longs;t; quis enim hoc ne&longs;cit? </s> <s>Sic videmus in con­<lb/>chis angu&longs;tioribus, aquam difficiliùs librari, in majoribus verò faciliùs. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> Ita e&longs;t, hoc videmus, quamobrem verò, non ita forte qui&longs;piam <lb/>dixerit. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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 op<gap/> ad exponen­<lb/>dam vim hujus rationis. </s></p><p type="main"> <s><emph type="italics"/>Choy&longs;oc.<emph.end type="italics"/></s><s> 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 imitantu<gap/>, <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 optm, Antime, <lb/>&longs;ed breviter, quæ&longs;o. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Brevi&longs;&longs;imè, neque hoc facerem, ni&longs;i veftro ju&longs;&longs;u; Sit concha <lb/><figure id="fig5"></figure><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></p><pb pagenum="59"/><p type="main"> <s><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></p><figure></figure><p type="main"> <s>Quod &longs;cilicèt omnes partes terre&longs;tris globi, vel &longs;ingulæ &longs;e&longs;e moveant, <lb/>velab extrin&longs;eco moveantur; &longs;ed ita temperatè, vt omnes inter &longs;e primam, <lb/>di&longs;po&longs;itionem cetineant; vnde non mirum e&longs;t, &longs;i tractus idem maris circa E <lb/>velociùs, circa I tardius moveatur. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Hoc nifallor &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/>liotem deflexionem &longs;ur&longs;um &longs;ub æquali, vel in æquali inclinationis angulo at­<lb/>rollatur, vbi aqua ad imum canalis pervenerit, non &longs;i&longs;tet hauddubiè, &longs;ed <lb/>per alind 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"/>&longs;i&longs;tere nequit, quantumvis contranitatur, &longs;cilicet pro pter impre&longs;&longs;um ante <lb/>impetum; in vibratis librati&longs;que corporibus innumera ferè &longs;uppetuot <lb/>exempla. </s> <s>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 priorc; 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></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> Si ergoin puncto E e&longs;&longs;et corpus &longs;olidum & durum, totum <lb/>priorem impetum a mitteret accedente novo. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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 curteret 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></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Igitur ille globusita &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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Hoc certè ex meis principiis non &longs;equitur, immo contrarium; <lb/>novus enim, qui præfato globo accederet, impems 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>v. </s> <s>g. <lb/>impetus novus accedens in P, (<emph type="italics"/>in ant<gap/>riori 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 vt<gap/>aque illa <lb/>&longs;equitur, vt con&longs;tat ex doctrina motuum. </s> <s>Quod verò &longs;pectat ad tritum <lb/>illud Mathematicorum dictum, etiam in terræimmobilis 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 potrò aquæ excurrentis tractus &longs;en&longs;im <lb/>fine &longs;en&longs;u conceptum motum remittit, propter impetum contr <expan abbr="ariū">arium</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 aliquomodo 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 parnm re&longs;i&longs;tit <lb/>motui, præ&longs;ertim alterius aquæ; quæ libetautem re&longs;i&longs;tentia impetum &longs;en&longs;im <lb/>de&longs;truit. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Iam mentem tuam intelligere mihi videor; vis enim quod­<lb/>lihet 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; fing<gap/>e globo, eodem tempore, duplicem impetum imprimi <lb/>alterum versùs Boream, <expan abbr="alterũ">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 imp<gap/>­<lb/>tusæqualitate, globus ver&longs;us Corum ibit, id e&longs;t, Boream inter & Occa-<pb pagenum="61"/>&longs;um. </s> <s>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 centrie&longs;t tangens ducta <lb/>in <expan abbr="Ortũ">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 ant minùs con&longs;entit cum alia, velocior aut tardior <lb/>e&longs;t motus; Sed dic mihi. </s> <s>&longs;odes Antime, po&longs;ito quod &longs;it globus in E, cur <lb/>per tangentem non projicitur ver&longs;us Ortum? </s></p><p type="main"> <s><emph type="italics"/>Antimus.<emph.end type="italics"/></s><s> Cur me tentas, Augu&longs;tine, ne&longs;cire non potes, hoc jam à <lb/>Galilæo &longs;olutum fni&longs;&longs;e, in quo certè, more &longs;uo maximam ingenij vim <lb/>o&longs;tendit. </s> <s>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 quæliber 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></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> 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/>reper<gap/>&longs;&longs;ionem fiunt; commune igitur principium e&longs;&longs;e videtur, ex quo, <lb/>ni fallor, rectè deduci<gap/>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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Immò ab&longs;olutè dictum e&longs;&longs;e vehm; 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 curtunt; 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;ponfio 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 facil<gap/> traduei qneat; accipio enim globulos tam fa­<lb/>cilè mobiles, vt nihil mobilius excogitari po&longs;&longs;it, tornatos &longs;cilicet ex Mer­<lb/>curio. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> De puncto E fortè &longs;atis dictum, & plu&longs;quàm &longs;atis; de aliis <pb pagenum="62"/>quid cen&longs;es? </s> <s>Non dubito enim, quin de iis aliquid dicturus &longs;is; ad quid <lb/>enim duo alia principia præmi&longs;i&longs;&longs;es? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Etiam &longs;i nihil aliud dicerem, an fottè illa, quæ de puncto E <lb/>dixi non &longs;ufficiunt ad tuam &longs;ententiam impugnandam? </s> <s>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>Si terræ globum quoquoversùm 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, iævis 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></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> Traducendum e&longs;&longs;e omnino crederem; terra enim illam etiam <lb/>aquam &longs;u&longs;tineret; igitur &longs;ecum vna deferret. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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 inciinationem 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></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> 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;ie librum hunc, quem manu teneo, <lb/>manus in&longs;a, quocumque fertur, traducit. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Standum e&longs;t experimentis; tu fortè quid, Antime? </s> <s>quilitem <lb/>movi&longs;ti, & cautè &longs;ubrides. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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;upraiactum, &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, inhoc 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/>adjucere debueras, Augu&longs;tine, vt &longs;emper &longs;uus &longs;it veritati locus. </s></p><pb pagenum="63"/><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> Quid verò fieret, &longs;i vas in circulo verticali verteretur? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Ead: m &longs;uppone; vas &longs;cilicet cylindricum, aut &longs;phæricum ca­<lb/>vum, lævigara intus &longs;uperficie, circa axem plano horizontis planè paral­<lb/>lelum; idemque &longs;ucee&longs;&longs;um iri puta; cùm eadem ratio vtrimque & æquè <lb/>militet. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> 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 vitimo ca&longs;u rationem militare; cùm enim faciliùs aquailla 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 iuferiore 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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 facilins 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 infericrem aquæ partem <lb/>in &longs;ecundo ca&longs;u ab imo ad &longs;upremum va&longs;is locumattolli, ac proinde illius <lb/>pondus o<gap/>&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 vbilibra <lb/>in æquilibrio ver&longs;atur, &longs;i vel minimam vim alterilancium &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>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>Sic æquè facilè rota volvitur in &longs;itu horizontali ac verticali. </s></p><p type="main"> <s><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 compettæ 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, nimitum, <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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> An fortè putas, oleum &longs;uis rugis & &longs;triis, nec non filaminibus <lb/>carere? </s> <s>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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Sunt quædam &longs;uperficies ita di&longs;po&longs;itæ inter &longs;e, vt in earum rimas <pb pagenum="64"/>&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. </s> <s>An&longs;erum, Anatum, aliarumque &longs;imilium, <lb/>hoc ip&longs;um ob&longs;ervamus, immo in multis foliis, vt bra fficæ, 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;cilicetlaxioribus rugis &longs;eu &longs;triis in longum <lb/>& rectam lineam ductis con&longs;tant, per quas aqua ftatim de&longs;cendit, atque <lb/>effluit, ni&longs;i aliqua fo&longs;&longs;ula in&longs;it, in qua major guzta ex reliquis longè mi­<lb/>noribus cò 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 adhætent, ever&longs;o &longs;itu &longs;tatuatur, eadem ratio e&longs;t, propterquam 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 vafti&longs;&longs;imus allis <lb/>experimentis ad &longs;uas veras cau&longs;as phy&longs;icas reducendis campus ape­<lb/>riatur. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Augurorrem 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 aqna 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></p><p type="main"> <s><emph type="italics"/>Ahtim.<emph.end type="italics"/></s><s> 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>Vt vt &longs;it, &longs;i <expan abbr="motũ">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 impingividetur, eo quippe litus ip&longs;om &longs;tr­<lb/>tur, & in aquam vel immobilem vel tar diorem impingitur, nempe quoad <lb/>effectum & <expan abbr="phænomerũ">phænomerum</expan> perinde e&longs;t, &longs;ive caput in &longs;axum, five faxum 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 crof­<lb/>cente: itaque ex iis. </s> <s>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 mariniratio, 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"/>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 hocip&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 occaiu 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;empet <lb/>e&longs;t parallela HI, linea enim dictum angulum æqualiter dividens e&longs;t deter­<lb/>minatio motus mixti. </s> <s>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 pcofunditatis, 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Sentio difficultatem, inficiarinon 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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>Iam verò vt ad alia tran&longs;eam ar­<lb/>gumenta, è terra nobis migrandum e&longs;t, in qua profectò nihil aliud inveni<gap/><lb/>ex quo &longs;olidum argumentum ducere valeam &longs;altem, quod mihi &longs;aciat &longs;atis. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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; nermo quippe <lb/>alius hanc laudem <gap/>bi arroget; Crede mihi, Chry&longs;ocome, &longs;uarum <lb/>rerum & inventionum vit 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>e&longs;t, qua&longs;i motus gr<gap/>ium non <lb/>e&longs;&longs;et per &longs;e acceleratus, &longs;ed tantùm per accident; at in illo mirabili <pb pagenum="66"/>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 dubinm reliquerit. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Contra Galileum nihil me vnquam &longs;erip&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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Immò ex profe&longs;&longs;o Galileum, &longs;ub Mon&longs;nerij nomine, im­<lb/>pugnas, nec tibi, opinor, è memoria excidit? </s> <s>nempe Galileus docet, &, <lb/>ni faller, 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;implioem numerorum 1.2.3.4.&c. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> Si rectè memini, Antime, omnibus experimentis hypothe&longs;is <lb/>tua repugnat; nam etiam &longs;umma quandoque altitudo &longs;umpta fuerit, Flo­<lb/>Tentiæ, 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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 floenter; 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Ad quid hæc: Galileus enim docet, componi tempus ex in­<lb/>&longs;tantibus ii&longs;que Mathematicis. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Sat &longs;cio; &longs;ed cùm alij huiu&longs;modi in&longs;tantia minimè admirtant, <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 finitotum in&longs;tantium <pb pagenum="67"/>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 fatisfacit, & 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, pe&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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Nihil facilius triangulo Galileano, in quo res i&longs;ta clari&longs;&longs;i­<lb/><figure id="fig6"></figure><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></p><p type="main"> <s><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;livè 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>BF tota &longs;imul, te­<lb/>&longs;pond<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 tectangulo, non verò in trian­<lb/><figure id="fig7"></figure><lb/>gulo; v.g. </s> <s>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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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 iongè majus <lb/>&longs;patium decurritur &longs;ecundùm tuam progre&longs;&longs;ionem, quàm &longs;ecundùm Ga­<lb/>lileanam, in qua &longs;patium decui&longs;um rempore 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"/>&longs;anè omnibus experimentis repugnat, quæ cum &longs;patio Galileano pror&longs;us <lb/>con&longs;entiunt. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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>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; igirur &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>igitur. </s> <s>&longs;i wel 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 præfc­<lb/>rendam e&longs;&longs;e, quia &longs;cilicet vtrique hypothe&longs;i facit &longs;atis; quanquam ad v&longs;um. <lb/></s> <s>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></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Ne&longs;cio, quomo<gap/> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/> Hæc maxima e&longs;t difficultas, fateor, & in communi temporis <lb/><figure id="fig8"></figure><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;tanubus Mathematicis <lb/>componi, in&longs;olubilis nodus e&longs;t; &longs;i enim in tempcic <lb/>AE accipiantur duo in&longs;tantia, &longs;cilicet B & C, nem­<lb/>pe vt linea AE tepræ&longs;entat tempus, ita quodlibet illius <lb/>punctum repræ&longs;entat vnum in&longs;tans, poirò 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"/>&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>In hypothe&longs;i in&longs;tantium phy&longs;icorum hæc difficultas omnino cef­<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 vacar. </s> <s>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 expetimentis comproba­<lb/>tum e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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 æquahbus temporibus omnino de­<lb/>currat, &longs;altem ad &longs;en&longs;am, hoctamen non ob&longs;tat, quin tationc perpen­<lb/>dicularis, in quam vi motus naturalis inclinat, & in qua majora &longs;pa­<lb/>tia decurrit. </s> <s>eodem pror&longs;us modo quo &longs;ieret, &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>impetus; hinc major ictus &c. </s> <s>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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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/>timentis 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></p><pb pagenum="70"/><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> 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/>&longs;er amabo, locos illos ex quibur alia erui po&longs;&longs;int. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Immò in Iove mobili, circa quem moventut 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 circum&longs;ertur; 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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 cœle&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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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 cœle&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></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> 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"/>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 cœle&longs;tium centrum <lb/>collocatur. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antum.<emph.end type="italics"/></s><s> 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 evineam. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> De Sole non abnuerim, &longs;ed de Luna quid? </s> <s>In qua non­<lb/>nulli ex tuis, etiam in tua hypothe&longs;i, motuum tealium 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 revolutic, quàm alia, realis profectò erit, non verò apparens <lb/>inæqualitas, &longs;ed hoc non vrgeo contra te, quia eadem vterque difficultate <lb/>laboramus. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Nullo negotio præfatam men&longs;ium inæqualitatem in mea hy­<lb/>pothe&longs;i explico; Cùm Lunæ æquè ac Soli motum limplici&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. </s> <s>g. </s> <s>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"/>&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 btovior 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, vereot &longs;anè vt qui&longs;piam vi<gap/><lb/>deat. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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, oporter; <lb/>&longs;ed hireverà 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></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Nunquid tantulùm &longs;altem retardat medij re&longs;i&longs;tentia, vt in <lb/>projectis, immò & deor&longs;um cadentibus fieri videmus? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> 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 nitatnr; 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 luxta 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></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> 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></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> His præmi&longs;&longs;is, ad illud venio, ac dico, in tua hypothe&longs;i, realem <lb/>Lunæ motum, eum &longs;cilicet, qui nobis æqualis ferè apparet, adeò inæqualem <lb/>fore, vt aliquando infinities tardior aut vclocior e&longs;&longs;et. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Somnia narras, Antime, quis vnquam hoc dixit, vel cogita­<lb/>vit? </s> <s>Luna circa terram iret, quamvis mobilem, inæquali certè motu, quoad <lb/>apparentiam, reip&longs;a tamen ferè æquali; cùm arcus vno die decur&longs;us paucis <lb/>minutis arcum alio die decur&longs;um &longs;uperet; hæc e&longs;t trita illa anomalia, eaque <lb/>mul<gap/>iplex in Luna, quam no&longs;tri per excentricos, vel epicy clos, vel circellos <lb/>explicant; &longs;ed hæc inæqualitas præterquàm quòd apparens, non verò rea­<lb/>lis e&longs;t tanta, non &longs;tatuitur, ne dum infinita. </s></p><pb pagenum="73"/><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Non &longs;omnio, Augu&longs;tine; nihil dixi, quod demon&longs;trare non <lb/>poffim. </s></p><figure></figure><p type="main"> <s>Sit enim <expan abbr="centrũ">centrum</expan> vniver&longs;i A, in quo <lb/>Solem &longs;tatuitis; &longs;it arcus magni orbis <lb/>DB, 29. circiter grad. </s> <s>quem &longs;cilicet <lb/>terra decurrit, toto illo tempore; quo <lb/>Luna ab vna copula, ad aliam ve­<lb/>nit; Sit AD. 2000.Semidiam. </s> <s>terræ <lb/>DH 60. DB 508.circiter; vnde HD <lb/>in DB octies fere continetur. </s> <s>Sit au­<lb/>tem primùm Lunain copula H, vt <lb/>deinde tran&longs;eat per oppo&longs;itionem G <lb/>ad &longs;equentem copulam I eo tempore, <lb/>quo terra decurrit arcum DCB: divi­<lb/>datur arcus DC in 4.partes æquales <lb/>DELMC: ita progreditur terra cum <lb/>Luna, vt terra &longs;itin D, Luna in H; <lb/>terra in E, Luna in O; terra in L, <lb/>Luna in E; terra in M, Luna in P; <lb/>terra in C, Luna in G; codem pro­<lb/>gre&longs;&longs;ionis ordine terra à C tendit in B, & Luna à G tendit in I. </s> <s>En tibi <lb/>veram ac germanam lineam Lunaris motus in tua hypothe&longs;i; eodem por­<lb/>rò tempore Luna &longs;egmenta HE & EG conficit; vnde vides, quàm &longs;it inæ­<lb/>qualis motus; & multò majorem inæqualitatis proportionem iuvenies, &longs;i <lb/>compares &longs;egmentum HO cum &longs;egmento EP, vel PG; & vt &longs;egmentum <lb/>HO decurrit Luna, eo tempore, quo primum octantem &longs;uæ periodi, ap­<lb/>parenti motu decurrere videtur, id e&longs;t 45. grad. </s> <s>&longs;i accipiamus minorem <lb/>arcum v. </s> <s>g. </s> <s>12. grad. </s> <s>paulò plùs, qui e&longs;t arcus illius ferè diurnus, et&longs;i com­<lb/>paremus &longs;patium, quod acquirit intereà, reali motu, tum circa Novilu­<lb/>nium H, tum circa Plenilunium G, longè maior erit inæqualitatis propor­<lb/>tio inter illa duo &longs;patia, æqualibus temporibus decur&longs;a, licèt quoad appa­<lb/>rentiam æqualia &longs;patia videantur. </s> <s>Vnde nece&longs;&longs;ariò &longs;equitur, Lunam inæ­<lb/>quali motu moveri, reali &longs;cilicet & phy&longs;ico, atque in tanta inæqualitatis pro­<lb/>portione, vt qualibet a&longs;&longs;ignabili major &longs;it. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Si nihil aliud habes, hæc minimè nos vrgent; nam &longs;uppo­<lb/>nimus Lunam moveri in epicyclo, cujus terra centrum e&longs;t, ac proinde <lb/>Luna movetur motu mixto ex motu orbis & motu centri, vtroque certè <lb/>æquabili; &longs;ed ex duobus motibus æquabilibus, motum mixtum minimè <lb/>æquabilem re&longs;ultare mirum dictu non e&longs;t; immo ne&longs;cire non potes, cuili­<lb/>bet hypothe&longs;i, quæ epicyclos ad&longs;truit, hoc e&longs;&longs;e commune. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Non dubitabam, quin hæc dicturus e&longs;&longs;es, &longs;ed antequàm vlteriùs <lb/>progrcdiar, non adinittis, opinor, in Luna realem epicyclum; &longs;i enim realis <lb/>Epicyclus e&longs;&longs;er, haud dubiè cum &longs;uperficie terræ intra 24.horas &longs;uum orbem <lb/>ab&longs;olveret, quod certè ab&longs;ur dum dictu e&longs;t; cùm decurrat tantùm co tempo­<lb/>re 12.gradus paulò plus. </s></p><pb pagenum="74"/><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Accipe quæ&longs;o, totum Sy&longs;tema telluris globi, quod non modò <lb/>&longs;ublunarem omnem tractum, verùm etiam Lunarem complectitur; finge <lb/>totum illud ad modum vnius Epicycli, ita tamen, vt globus terræ, & por­<lb/>tio vicinior circumfu&longs;i ætheris volvatur ab occa&longs;u ad <expan abbr="ortũ">ortum</expan> &longs;patio 24.hora­<lb/>rum, &longs;uperior verò multò tardiùs, & Lunaris <gap/>tanrum gradus co tempore <lb/>acquirat, in tanta enim di&longs;tantia, vis rapic<gap/>is terræ, &longs;i non pror&longs;us evane&longs;­<lb/>cit, &longs;altem plurimùm remittitur. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Ingeniosè pror&longs;us; vis enim vim illam inotricem à terre&longs;tri glo­<lb/>bo, ad Lunarem traduci, eamque valde remi&longs;&longs;am, propter di&longs;t antiam, cujus <lb/>rei analogiam petes in mea quoque hypothe&longs;i, a Iove, qui quatuor Lunas <lb/>&longs;ecum ita volvit, immò & à Sole qui Venerem & Mercurium &longs;ecum in or­<lb/>bem agit; &longs;ed vt duo &longs;unt motus in terre&longs;tri globo, centri &longs;cilicet, atque or­<lb/>bis, cur debilitatur vis motrix in Lunam traducta à motu orbis, intacta re­<lb/>manente traducta à motu centri, vtramque enim, vel neutram di&longs;tantia <lb/>æquè debilitat. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Si fingas totum illud Sy&longs;tema vtroque motu moveri, fieri non <lb/>pote&longs;t, quin motus centri toti&longs;y&longs;temati cominunis &longs;it, atque adeò omnes <lb/>&longs;y&longs;tematis partes per &longs;e illo motu æquè moveantur, licèt aliquæ plus, aliæ <lb/>minùs propter motum orbis. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Fingo facilè totum illud &longs;y&longs;tema ad in&longs;tar &longs;phæræ, cujus majo­<lb/>rem tantùm circulum accipio, qui &longs;it ad in&longs;tar cpicych; &longs;ed cùm retardetor <lb/>motus orbis propter di&longs;tantiam, non video, cur propter eandem non re­<lb/>tardetur etiam motus centri; & verò, &longs;i &longs;olida quæpiam e&longs;&longs;et partium hu­<lb/>jus &longs;y&longs;tematisinter &longs;e connexio, optimè intelligerem, quomodo vterque <lb/>motus omnibus communicetur; &longs;ed hoc po&longs;ito, æquè citò omnes motum <lb/>orbis ab&longs;olverent; &longs;ed cùm hæc &longs;olida connexio non &longs;it, quid mirum. </s> <s>&longs;i vter­<lb/>que motus tum orbis, tum centri communicetur. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> Vnum tibi facilè &longs;uggererem, quod ad rem præ&longs;entem pluri­<lb/>mùm facir; nempe &longs;i motus orbis à globo terre&longs;tri in Lunarem traducitur; <lb/>igitur hic motus Lunæ versùs ortum icet per arcus parallelos circulis diur­<lb/>nis, &longs;imilis enim terræ motus &longs;imilem produceret; cùm tamen orbita Lu­<lb/>næ non modò Æquatori parallela non &longs;it, &longs;ed nequidem Eclipticæ; ac­<lb/>cedit quod totum illud &longs;y&longs;tema modò ad Au&longs;trum, modò ad Boream cum <lb/>terre&longs;tri globo librari deberet, hoc enim &longs;it in terre&longs;tri globo ad retinen­<lb/>dum axis paralleli&longs;mum; quare cùm non videatur quomodo Lunæ motus <lb/>à telluris motu profici&longs;ci, vel traduci queat dicerem potiùs, (<emph type="italics"/>in ænte­<lb/>riori Schemate<emph.end type="italics"/>) Lunam ab Angelo ita moveri ab&longs;que epicyclo; quia <lb/>revera nullum videmus cpicyclum, idque per lineam curvam HE <lb/>PGFI. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Ab Angelo igitur inæquali motu reali movetur; & hoc ip&longs;um <lb/>e&longs;t, quod ip&longs;e Antimus intendit, & opponit contra meam hypothe&longs;im; hoc <lb/>autem argumentum eju&longs;dem pror&longs;us e&longs;t energiæ, &longs;ive dicatur Luna moveri <lb/>ab Angelo per lineam HPG, &longs;ivc à &longs;eip&longs;a. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/> Cùm ergo ita reverà moveatur per lineam HPG, motus illius, <lb/>realis &longs;cilicet, omnino inæqualis e&longs;t, vt iamidixi. </s></p><pb pagenum="75"/><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Ille motus, qui fit per lineam HPG mixtus e&longs;t ac proinde <lb/>inæqualis, &longs;ed ex duobus æquabilibus, vt iam dixi. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Vnde porrò &longs;unt illi duo motus æquabiles' à quo principio? </s> <s>& <lb/>quo tandem organo traducuntur? </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Affulget novæ lux re&longs;pon&longs;ionis; &longs;upetficies terræ inæquali­<lb/>ter movetur, etiam in eodem circulo majore; nempe ille arcus, qui ad <lb/>Solem convertitur, tardi&longs;&longs;imus e&longs;t, oppo&longs;itus verò veloci&longs;&longs;imus, quid mi­<lb/>rum igitur, &longs;i hic Lunam longiùs promovet, &longs;cilicet circa Plenilunium, <lb/>ille verò longè minùs, &longs;cilicet circa Novilunium. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Non negarim, acutam, & non nemini fortè inexpectatam re­<lb/>&longs;pon&longs;ionem; &longs;ed præterquam quod &longs;ub&longs;i&longs;tunt alia &longs;upra oppo&longs;ita; quia nec <lb/>in arcubus, diurnis circulis parallelis Luna movetur, non videtur, cur mo­<lb/>tus centri in Lunam traductus debilior non exi&longs;tar. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Miror, hæc à te dici, cùm vterque debilior exi&longs;tat, vt mani­<lb/>fe&longs;tum e&longs;t; &longs;ic enim ab Had O parum progreditur, tum motu centri, tum <lb/>motu orbis; igitur à puncto terræ oppo&longs;ito &longs;uam vim accipit, majorem <lb/>&longs;cilicet, cùm velociùs illud movetur, quamvis alioquin motu mixto; mi­<lb/>norem verò cùm tardiùs, quid ad aliud de arcubus parallelis re&longs;pondeam, <lb/>non habeo, ni&longs;i fortè dicam, Lunam à &longs;eip&longs;a, vei ab Angelo per illam or­<lb/>bitam moveri: Sed cur per illam movetur inæqualiter? </s> <s>deinde hæc orbita <lb/>re&longs;pectum habet ad terram, quæ in &longs;ua libratione diver&longs;am periodum ha­<lb/>bet, malim ergo ingenuè fateri, me ne&longs;cire, quid ad hoc re&longs;pondeam. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Re&longs;umo quod &longs;upra dicere cœperam; præter illa argumenta, <lb/>inquam, quibus allata re&longs;pon&longs;io non congruit, dico aliam eamque in&longs;o­<lb/>lubilem re&longs;tare difficultatem; admi&longs;&longs;a enim prædicta re&longs;pon&longs;ione, fateris <lb/>in puncto G majorem vim impetus à puncto terræ oppo&longs;ito Lunam ac­<lb/>cipere, minorem verò à puncto H, cur ergo Luna impre&longs;&longs;um impetum <lb/>deinde non retinet? </s> <s>cum nihil &longs;it à quo de&longs;truatur; nec enim ob&longs;tat, à <lb/>novo puncto terræ oppo&longs;ito ad aliam tangentem determinari, quia cùm <lb/>hoc fiat per novi impetus acce&longs;&longs;ionem, hic aditus priori majorem vim <lb/>facit; igitur nulla e&longs;&longs;et ratio, cur deinde motus retar daretur versùs Qua­<lb/>draturas. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> Vereor, vt inde qui&longs;piam cau&longs;am deducat, reimi&longs;&longs;ionis marini <lb/>æ&longs;tus in Quadratoris; nempe, vt in Oppo&longs;itione vegetior e&longs;t, ita in Quadra­<lb/>turis minor e&longs;t & flaccidior; quia, inquiet, cùm à Luna procedat, Lunæ <lb/>motus in plenilunio maior e&longs;t, minor in Quadraturis; minorem igitur in <lb/>his, majorem in illo motus effectum producit. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Sed in Novilunio Lunaris motus adhuc minor e&longs;t, quam in <lb/>Qiadraturis, & tamen nemo ne&longs;cit, æ&longs;tum in Novilunio majorem e&longs;&longs;e; alia <lb/>igitur ratio prædictæ differentiæ inve&longs;tiganda e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Aliud in mentem venit, quod expromendum e&longs;&longs;e puto; <lb/>nempe &longs;i &longs;upponam Lunam 24. horarum &longs;patio orbem &longs;uum circa terram <lb/>ab&longs;olvere, illius velocitas ad velocitatem puncti æquatoris in &longs;uperficie <lb/>terræ erit vt 60.ad 1.&longs;unt enim motus vt circuli, hi vtrò, vt &longs;emidiametri; <lb/>igitur non mirum e&longs;t, cùm motus tardus velocem producere nequeat, &longs;i <pb pagenum="76"/>Luna longè tardiùs à terre&longs;tri globo circumagitur. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Neque hoc &longs;ufficit; quia cùm vnus motus alium æqualem ad <lb/>fummum producere po&longs;&longs;rt, e&longs;to terræ motus æqualem Lunæ imprimat, <lb/>hic erit <gap/> illius quo Luna 24.horarum tempore ab&longs;olveret circulum con­<lb/>&longs;ectis 360. grad. </s> <s>igitur erit tantùm 6. graduum; &longs;ed e&longs;t 12.grad. </s> <s>diurnus <lb/>&longs;cilicet; alinnde igitur cau&longs;a hujus motus petenda e&longs;t: &longs;ed nulla e&longs;&longs;e po­<lb/>te&longs;t, ni&longs;i hic motus inæqualis &longs;upponatur; igitur ex hoc etiam capite i&longs;ta <lb/>hypothe&longs;is terræ mobilis non &longs;ub&longs;i&longs;tit, quia &longs;cilicet in ea motus realis in­<lb/>æqualis per &longs;o e&longs;&longs;et. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Eadem difficultate tua laborat hypothe&longs;is, in qua Lunaris <lb/>motus &longs;ine vno &longs;altem epicyclo explicari nequit. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Nullum Epicyclum pono <foreign lang="greek">n</foreign> pro reali motu explicando; pro ap­<lb/>parenti verò vtcumque, fimplicem dumtaxat motum admitto, ab ortu ad <lb/>occa&longs;um, longè tamen tardiorem motu Solis, ita vt &longs;ingulis men&longs;ibus Sy­<lb/>nodicis Sol Lunam a&longs;&longs;equatur, atque adeò <foreign lang="greek">h</foreign> num integrum circulum &longs;u­<lb/>pra illam acquirat; adde vtramque inclinarionem, quâ &longs;cilicet tum ab <lb/>Apogæo ad Perigæum & vici&longs;&longs;im, tum à Borea ad Au&longs;trum, & vici&longs;&longs;im <lb/>Planeta librari videtur; vtriu&longs;que tamen periodus in Luna diver&longs;a e&longs;t à <lb/>Solari; vnde Lunæ Apogæum recurrit frequentiùs; præterea Lunæ &longs;ecun­<lb/>da inclinatio habet pro termino Eclipticam, vt jam dixi; anomaliæ primæ, <lb/>&longs;eu periodicæ ratio eadem e&longs;t, quæ anomaliæ Solaris; neque hîc repeto, <lb/>quæ jam dixi in alio congre&longs;&longs;u; quod verò pertinet ad aliam inæqualita­<lb/>tem, vel anomaliam &longs;ynodicam, vt vocant. </s> <s>in mea hypothe&longs;i, facilè ratio <lb/>redditur multiplicis inæqualitatis, quam huc v&longs;que, vt verum fatear, non­<lb/>dum accuratè indagatunt A&longs;tronomi, nedum &longs;tatuerunt; hinc vnus negat, <lb/>quod alius ad&longs;truit; &longs;cilicet eò qui&longs;que dumtaxat &longs;pectat, vt ob&longs;ervatio­<lb/>nes ad Sy&longs;tematis excogitati formam accommodet; &longs;ed hæc fu&longs;iùs di&longs;cu­<lb/>cutere huius loci non e&longs;t; hoc tantùm indica&longs;&longs;e contentus, ex diver&longs;o Lu­<lb/>næ &longs;itu, multiplicem inæqualitatem, apparentem &longs;cilicet, eamque variam <lb/>&longs;equi po&longs;&longs;e: vtrùm verò Lunæ apogeæ di&longs;tantia maior &longs;it in quadraturis, <lb/>quàm in copulis, & perigeæ minor, non de&longs;unt, etiam inter principes <lb/>A&longs;tromos, qui negent: & verò punctum ac momentum veræ ac germa­<lb/>næ quadraturæ vix di&longs;cerni pore&longs;t, maximè intra &longs;patium duorum vel qua­<lb/>tuor graduum; de Latitudine Lunæ nihil dico; cùm eam nullo negotio <lb/>explicemus; itemque Nodorum motum in antecedenria; quia citiùs &longs;ecun­<lb/>dæ inclinationis motus perficitur, quàm motus in Zodiaco; vnde nece&longs;­<lb/>&longs;ariò &longs;equitur motus Nodorum apparens contra &longs;eriem Signorum; motus <lb/>apogæi etiam apparens eodem modo explicatur, quo jam in Sole illum <lb/>explicuimus; itemque eorundem motuum inæqualitas, &longs;uppo&longs;ito motu <lb/>reali æquabili&longs;&longs;imo; & vbi certæ omnino & in omnibus con&longs;entientes <lb/>ob&longs;ervationes aliquando definientur, nullus dubito, quin ex jactis princi­<lb/>piis facilè in hac no&longs;tra hypothe&longs;i explicentur, quod tamen modò &longs;ieri ne­<lb/>quit, cùm multa etiamnum incerta maneant, & vix de Apogæo con&longs;tet, <lb/>vbi &longs;it, & qualis &longs;it excentricitas, an hæc &longs;emper eadem &longs;it; di&longs;tantia verò <lb/>Lunæ maxima, etiam incerta e&longs;t. </s></p><pb pagenum="77"/><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Probè intelligo tuum &longs;y&longs;tema Lunare; vis enim Lunam &longs;im­<lb/>plici motu moveri ab Ortu ad Occa&longs;um, &longs;ed longè tardiùs, quàm &longs;tellas; <lb/>ita vt intra tempos vnius men&longs;is periodici Luna à Stellis retro relicta ver­<lb/>sùs Ortum, videatur totum Zodiacum percurrere, & ad idem punctum <lb/>redire; & quia Sol toto eo tempore versùs Ortum relictus e&longs;t, qua&longs;i 27. <lb/>grad. </s> <s>antequam ad copulam Luna redeat, duobus diebus & aliquot horis <lb/>opus e&longs;t: hunc men&longs;is Synodicus longior periodico; addis vtriu&longs;que incli­<lb/>nationis motum, ita vt &longs;ecundæ terminus &longs;it Eclyptica; & quia motus &longs;e­<lb/>cundæ ab&longs;olvitur paulò ante finem periodici, hinc motus Nodorum ver­<lb/>sùs Occa&longs;um, itemque Apogæi versùs Ortum; quia periodus intra quam <lb/>Luna redit ad Apogæum, paulò longior e&longs;t men&longs;e periodico: inæqualitas <lb/>&longs;implex eodem modo à te explicatur in Luna, & in Sole; aliæ ex diver&longs;a <lb/>combinatione vtriu&longs;que inclinationis na&longs;cuntur: Latitudinem per motum <lb/>&longs;ecundæ inclinationis facilè omninò explicas, Vtrùm verò major &longs;it Lati­<lb/>tudo in Quadraturis, quàm in Copulis, incertum putas, itemque multa alia <lb/>incerta, quæ &longs;upra obiter recen&longs;ui&longs;ti; optimè demum explicas, quomodo <lb/>men&longs;es Periodici modò majores &longs;int, modò minores, itèmque Synodici, <lb/>men&longs;es enim Periodici majores &longs;unt, quando Nodi &longs;unt circa Æquato­<lb/>rem, minores verò, quando &longs;unt circa Iropicos; Synodici autem majores <lb/>&longs;unt, dum Sol e&longs;t circa Apogæum, dum verò circa Perigæum minores; <lb/>neque in his vlla re&longs;tat difficultas; vnum tantùm ex te re&longs;cire velim, Anti­<lb/>me, quid cen&longs;eas de libratione illa Lunari, qua &longs;it, vt quædam interdum <lb/>maculæ ad margines di&longs;ci Lunaris propiùs accedant, aliàs, ab iis longiùs <lb/>recedant. </s></p><p type="main"> <s><emph type="italics"/>Antim<emph.end type="italics"/> Hevelio fideli&longs;&longs;imo & accurati&longs;&longs;imo Lunarium Phænomenon <lb/>ob&longs;ervatori, in his detrectart fidem, non au&longs;im; hic autem vult, Lunam <lb/>ita librari, vt cùm maximè ab Æquatore dec.inat, versùs Boream, macu­<lb/>læ Boreales in ejus di&longs;co recedant à margine, Au&longs;trales contra ad margi­<lb/>nes accedant; & vici&longs;&longs;im cùm maximè declinat versùs Au&longs;trum, au&longs;tra­<lb/>les recedant, accedant verò Boreales. </s> <s>Nonnulli ex ve&longs;tris, Augu&longs;tine, &longs;ta­<lb/>munt ad hunc finem, Lunarem axem &longs;ibiip&longs;i parallelum, & Axi mundi; &longs;ed <lb/>meo judicio perperam &longs;atis, dum enim versùs Tropicum Cancri acce­<lb/>dit Luna, extremitas Borealis axis attolleretur, vt patet, igitur & Semicir­<lb/>culus di&longs;ci Borealis, & Au&longs;tralis de primeretur; ex quo contraria Phænome­<lb/>na &longs;equerentur; Malim dicere Lunarem Globum magnetica for&longs;an virtute <lb/>pellere, ac proinde habere duos polos magneticos; igitur codem pror&longs;us <lb/>modo &longs;e&longs;e componit ad terre&longs;trem Globum, quo terrella quæpiam, vel <lb/>acus magnetica; igitur quando Luna versùs Boream tendit ab Æquatore, <lb/>extremitas borealis axis deprimitur, Au&longs;tralis verò attollitur, & vici&longs;&longs;im; <lb/>cùm Luna ab Æquatore versùs Au&longs;trum excurrit; Au&longs;tralis deprimitur, <lb/>Borealis attollitur, ex quo prædicti effectus nece&longs;&longs;ariò con&longs;equuntur. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Parum admodùm abe&longs;t, quin hoc apprimè capiam; nonni­<lb/>hil &longs;chematis de&longs;iderarem, vt hoc meliùs inculcetur </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Id mihi præ&longs;tandum &longs;u&longs;cipio: &longs;it meridianus Lunaris SBTK, <lb/>Axis magneticus BK, &longs;emicirculus ad terram conver&longs;us BSK, qui in <pb pagenum="78"/>di&longs;co Lunari apparet projectus in BK; lineæ vi&longs;uales BO, SP, KR, <lb/>quas exhibeo parallelas, propter anguli tenuitatem; &longs;it A in Æquatore, <lb/><figure id="fig9"></figure><lb/>Axis BK &longs;ecat Æquatorem ad an­<lb/>gulos rectos; &longs;i verò A &longs;it in Tro­<lb/>pico Cancri, punctum B dep<gap/>imitur <lb/>in G, & K attollitur in H; Hinc ante <lb/>depre&longs;&longs;ionem macula E videbatur <lb/>in C, igitur vicina margini, N verò <lb/>in L. remota igitur à margine; at <lb/>verò po&longs;t depre&longs;&longs;ionem dicti Axis <lb/>Macula E erit in F, ac proinde vide­<lb/>bitur in D: igitur recedit à margi­<lb/>ne; at verò N erit in M; igitur vi­<lb/>debitur in I; accedit igitur ad mar­<lb/>ginem; hæc adeò per&longs;picua &longs;unt, vt <lb/>nihil clariùs dici, vel excogitaripo&longs;&longs;e <lb/>videatur. </s> <s>Vnum tamen dubium re­<lb/>&longs;tat de fide &longs;cilicet Hevelij, cùm non <lb/>defuerit, qui dictam fidem pror&longs;us elevarit, adductis ob&longs;ervationibus <lb/>omnino contrariis. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Scio, non defui&longs;&longs;e; Hevelio tamen adhærendum, eique fi­<lb/>dem habendam e&longs;&longs;e, putarem, præ&longs;ertim cum nonnulla ex iis, quæ con­<lb/>tra illum adducuntur, minimè &longs;ub&longs;i&longs;tant; Sed hæc di&longs;cutere non vacat; <lb/>Vt vt &longs;it, &longs;uppo&longs;ita veritate dictorum Hevelij. </s> <s>con&longs;tat rationem huius <lb/>librationis à me allatam per&longs;picuam e&longs;&longs;e; &longs;i res &longs;ecus &longs;e habeat, vt mihi, <lb/>Augu&longs;tine, non nocet, ita tibi nullo modo prode&longs;t. </s> <s>Sed iam ad alias ratio­<lb/>nes veniamus. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> Re&longs;tat, Antime, vtad alios cœle&longs;tes globos gradum facias, in <lb/>quo lepidi&longs;&longs;imum itineris extatici autorem imitari cuipiam fortè videberis; <lb/>quod ne&longs;cio an Copornicanis metuendum &longs;it. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Ne timeas, Chry&longs;ocome, &longs;i&longs;temus gradum in terra, nec de Ve­<lb/>nere quidquam a&longs;truam, ni&longs;i quod omnes facilè probare po&longs;&longs;int; Dico <lb/>igitur iuxta Copernicanam hypothe&longs;im, Venerem tam propè ad nos acce­<lb/>dere, circa conjunctionem &longs;cilicet ve&longs;pertinam, & tam procul abe&longs;&longs;e, <lb/>circa matutinam, vt cius diameter vna vice &longs;eptuplo ferè major, quàm <lb/>alia videnda &longs;it; quod vt in facili Schemate o&longs;tendam. </s></p><p type="main"> <s>Sit (<emph type="italics"/>in &longs;eq.Fig.<emph.end type="italics"/>) Sol in A immobilis; &longs;it magnus orbis, in quo movetur terrá <lb/>BCDE, &longs;int diametri BD, CE, &longs;itque angulus ABC grad 47. & &longs;uppo­<lb/>natur maxima digre&longs;&longs;io Veneris à Sole; ducatur AF perpendicularis in <lb/>BC, & &longs;ub radio AF de&longs;cribatur circulus FGHIK, hic erit orbis Veneris; <lb/>igitur Perigæum Veneris erit in K, po&longs;ito quod terra &longs;it in B; Apogæum <lb/>verò in H cuncta hæc pro conce&longs;&longs;is habeo; licèt Perigæum aliquando <lb/>propiùs accedat ad B, tum quia interdum major e&longs;t Veneris digre&longs;&longs;io; tum <lb/>etiam quia moveri cen&longs;etur in excentrico,; igitur cum &longs;imul e&longs;t in aphelio <lb/>& Perigæo, propiùs ad B haud dubiè accedit. </s> <s>Sit ergo in K, citra acura-<pb pagenum="79"/>tiores calculos, dico, KB e&longs;&longs;e <gap/> totius BH, paulo plus; igitur propter <lb/>parvitatem anguli, cùm linea recta pro arcu accipi po&longs;&longs;it, Veneris diame­<lb/>ter in K videtur Sextupla illius, quæ videtur in H&longs;unt <gap/>im anguli vt <lb/>di&longs;tantiæ permutando, acuti&longs;&longs;imi &longs;cilicet, qualem hoc loco con&longs;idera­<lb/>mus: &longs;ed profectò nemo vnquam vidit Venerem perigæam quadragecu­<lb/>plam apogææ. </s></p><figure></figure><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Miror, hæc à te dici, qui per&longs;picillorum majorum &longs;atis, opi­<lb/>nor, peritus es; illius &longs;altem amicus & familiaris, qu<gap/> præ cæteris optima <lb/>& longi&longs;&longs;ima fabricat; Galileus &longs;uo tubo&longs;picillo in&longs;tructus, argumentum <lb/>à te propo&longs;itum jam olim diluit, vt pote qui omnino comperit, Venerem <lb/>perigæam quadragecuplam apogææ, etiam mediocris tele&longs;copijoperâ vi­<lb/>deri, vt non &longs;emel ip&longs;e typis mandavit. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Sciò, hoc a&longs;&longs;ertum ab eo fui&longs;&longs;e; &longs;ed miror, à nemine, &longs;altem <lb/>quod &longs;ciam, in dubium vocatum. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Quis amabò hac de re dubitaret, & fidem huic homini detre­<lb/>ctaret, qui tam multa in cæle&longs;ti regione à &longs;e primùm explorata &longs;ub a&longs;pe­<lb/>ctum mortalium adduxit, quique &longs;uo tempore, optima ommum vitra tor­<lb/>nari & componi curavit. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> De his non di&longs;puto, nec quidquam de cuiu&longs;piam laude velim <lb/>detractum, dico tamen, me optimis alioquin tele&longs;cop<gap/>s v&longs;um, nunquam <lb/>Venprem perigæam quadtagecuplam apogææ vidi&longs;&longs;e; Non nego per&longs;pi­<lb/>cilla Galilei eximia fui&longs;&longs;e, &longs;ed longèiis breviora, quibus v&longs;us &longs;um; negari <pb pagenum="80"/>prof<gap/>ctò non pote&longs;t, quin vir præ&longs;tanti&longs;&longs;imus Eu&longs;tachius Divinus prædi­<lb/>ctam fabricand<gap/>rum tele&longs;copiotum artem cò adduxerit, quò illam nemo <lb/>hactenus ad<gap/>k; icaquo optimo vto<gap/> tele&longs;copio, quò Venerem perigæam <lb/>majotem quidem ap<gap/>gæa video, non tamen quadragecuplam; ad omnium <lb/>oculo<gap/>pcovoco. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> In qua proportione majotem diametrum perigææ vides? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Plu&longs;quam &longs;extuplam videre deberem; at non dicam &longs;extuplam, <lb/>aut quintuplam triplá non video; & hinc nece&longs;&longs;aria <expan abbr="cõ&longs;equutione">con&longs;equutione</expan> deduco, <lb/>Copernicanam hypothe&longs;im corruere, in qua nece&longs;&longs;e e&longs;t, diamet<gap/>m Vene­<lb/>ris perigeæ plu&longs;quam &longs;extuplam videri diametri eiu&longs;dem apogeæ. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ec.<emph.end type="italics"/></s><s> Tantulum &longs;chematis de&longs;iderarem; licèt enim multam fidem tibi <lb/>habeam, mens tamen maximè recreatur, &longs;i eadem quæ aure accepimus <lb/>oculorum etiam te&longs;timonio confirmentur. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;timus.<emph.end type="italics"/></s><s> Antimum ab hoc onere levabo; Sit AF radius partium <lb/>100000. & angulus ABF 47. graduum, tanta enim e&longs;t plerumque <lb/>maxima Veneris digre&longs;&longs;io; erit &longs;ecans AB 136733. igitur tota BH <lb/>236733. & KB 36733. igitur KB e&longs;t ad BH vt vnum ad 6. <gap/> paulò <lb/>plus. </s></p><figure></figure><p type="main"> <s>Sit antem quælib<gap/> linea P. ad MQ, <gap/>m ad <gap/> aff<gap/>ma<gap/> quæli­<lb/>bet diam<gap/>t PN quæ videatur <gap/> M &longs;ub angulo NMP, <gap/>m cadem &longs;ta-<pb pagenum="81"/>tuatur in QL ducaturque ML &longs;ecans PN i<gap/> D, haud dubiè etit PO, ad <lb/>QL, vel PN, vt MP ad MQ, id e&longs;t vt 1.ad 6.<gap/> &longs;ed angulus LML, vel <lb/>OMP e&longs;t ad angulum NMP, vt PO, ad PN, nempe in acuti&longs;&longs;imis angu­<lb/>lis, qualis &longs;upponitur is, &longs;ub quo videtur Veneris diameter, arcus &longs;unt <lb/>ad &longs;en&longs;um vt tangentes; igitur angulus OMP e&longs;t ad angulum NMP vt <lb/>1. ad 6.<gap/> cùm igitur Veneris di&longs;tantia minima &longs;it ad maximam, vt vnum ad <lb/>6<gap/> ejus diaineter apparens in ininima e&longs;t ad appate<gap/>m in mazima vt <lb/>NP ad PO, id e&longs;t vt 6<gap/> paulò pi<gap/>s ad <gap/>igitur di&longs;cus Veneris petigeæ <lb/>appatens e&longs;t ad di&longs;cum apogeæ vt 40.<gap/>ad 1.& rcip&longs;a talem e&longs;&longs;e Coperni­<lb/>canæ &longs;ententiæ defen&longs;ores pronunciant. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> Cur appellas Copernicanæ &longs;ententiæ defen&longs;ores? </s> <s>alios etiam <lb/>appellare debueras, cùm etiam ex Tychonico &longs;y&longs;temate eadem pror&longs;us <lb/>diamettorum apparentium ratio, &longs;eu proportio con&longs;equatur. </s></p><figure></figure><p type="main"> <s>Fac enim terram e&longs;&longs;e immobilem in B, Solemque per orbem ANML <lb/><gap/>, ac&longs;ecum deferte centrum epicycli Ven<gap/>s; hauddubi<gap/> enus <gap/>t <lb/>perigæa in K, apogæa in H. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Hoc ip&longs;um in primo no&longs;tro congre&longs;&longs;<gap/> à quo aberas, Chry&longs;oco­<lb/>me, indicatum à me &longs;u<gap/>rat, vt videte e&longs;t, in V.hgura, & ideò non circularem <lb/>epicyclum de&longs;ctip&longs;i nec etiam eliipticum, &longs;ed &longs;pital: quadam, &longs;eu qua&longs;i pa­<lb/>rabolica linea terminatum ab apogæo ad maximam digte&longs;&longs;ionem, & hinc <lb/>ad petigæum alia cutva ad rectam proxime accedente: po<gap/>ò no&longs;tro <pb pagenum="82"/>&longs;y&longs;tem<gap/>i quælibe<gap/> diam<gap/>um app<gap/>tium proportio convenire <lb/>pote&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Habe bis omnes Aftr <gap/>os tibi refragantes, non &longs;olùm <lb/>illos, qui Copetnieo adh<gap/>t, verùm etiam omnes propemodùm alios, <lb/>immo ex tuis non de&longs;unt v<gap/>i docti&longs;&longs;imi, & cœle&longs;tium ob&longs;ervationum <lb/>periti&longs;&longs;imi, qui non modò Veneris perigææ d<gap/>cum quadragecuplo, <lb/>&longs;ed etiam quinquagecuplo & vltra majotem e&longs;&longs;e, quàm apogææ liberè pro­<lb/>nuneiant. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Quid faceres? </s> <s>me<gap/> oculis fidem detracta<gap/> non po&longs;&longs;um, <lb/>optimum tele&longs;copium adhibui; longè tamen minorem proportionem <lb/><gap/>qualitatis e&longs;&longs;e comperi, quanquam &longs;ententiatum diver&longs;itas etiam inter <lb/>Principes A&longs;tronomiæ multam mihi hac de re &longs;u&longs;picionem injicit, quorum <lb/>aliqui Veneria perigææ diametrum 7.minut.e&longs;&longs;e volunt, alij 4. alij 3.2.alij <lb/>demum 1. eadem diver&longs;itas diametrorum apparentium Metcurij, Martis <lb/>& Iovisapud eo&longs;dem Autores ob&longs;ervatur. </s> <s>Sed, inquiet aliquis, ob&longs;er­<lb/>vationes meæ accuratiores &longs;unt, idem alius de &longs;uis &longs;entiet; Vt vt &longs;it ad om­<lb/>nium oculos provoco, nam &longs;æpè ac &longs;æpiùs Venerem a&longs;pexi, non procul <lb/>à perigæo, &longs;cilicet paulo ante, vel paulò po&longs;t conjunctionem ve&longs;per tinam, <lb/>diver&longs;is etiam modis adhibitis, nunquam tamen illius di&longs;cum quadrage­<lb/>cuplum comperi, illius quem in eadem non procul ab apogæo &longs;ita ob&longs;er­<lb/>varam, &longs;ed longè minorem; idem de Mercurio perigæo, quem nunquam <lb/>octuplum apogæi, idem de Marte, quem nunquam &longs;exagecuplum, multò <lb/>minùs octoge cuplum aut <expan abbr="noagecuplũ">noagecuplum</expan> ob&longs;ervare potui, Nihil &longs;anè docti&longs;&longs;i. <lb/></s> <s>morum hominum ob&longs;eruationibus & fidei <expan abbr="detractũ">detractum</expan> velim; &longs;ed igno&longs;cant, <lb/>&longs;i oculis meis plus triboam; vereor autem vt aliqui, vt &longs;y&longs;temati á &longs;e fabri­<lb/>cato, aut reformato meliùs <expan abbr="con&longs;ulãt">con&longs;ulant</expan>, ex paucis ob&longs;ervationibus, il&longs;que præ­<lb/>&longs;ertim, quoad minuta &longs;altem &longs;ecunda, &longs;allaciæ haud parum obnox<gap/>s, ea <lb/>nonnunquam ad&longs;truant, quæ dubito, an reliquis deinde ob&longs;ervationibus <lb/>&longs;ubjaceant. </s> <s>Vnum deinde in Venere notatu dignum e&longs;&longs;e puto, eam &longs;cilicet, <lb/>cùm circa perigæum vel apogæum ob&longs;ervatur, non procul abe&longs;&longs;e ab ho­<lb/>rizonte, ac proinde non modicam radios vi&longs;uales refractionem pati. </s> <s>quæ <lb/>hauddubie apparentem illius diametrum vatiabit; de&longs;iderandum, vt Ve­<lb/>nus &longs;ub Solis di&longs;cum aliquando veniret, tunc enim exceptis trajecti&longs;que <lb/>radiis &longs;olaribus tele&longs;copio, nec non projectis in planum directè <lb/>oppo&longs;itum, velip&longs;is oculis ratio diametr<gap/> Veneris ad diametrum Solis &longs;ub­<lb/>jiceretur. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Libenter exte re&longs;cirem vtrùm &longs;it aliquod Veneris phœnome­<lb/>non; quod in tua hypothe&longs;i explicari non po&longs;&longs;e putes. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Vix crediderim vllum e&longs;&longs;e; de certis enim loquor & indubi­<lb/>tatis; nempe: modò&longs;upponam. </s> <s>Venerem &longs;implici motu moveri ab ortu <lb/>ad occa&longs;um, eoque æquabili&longs;&longs;imo, cum illa duplici inelina<gap/>onc, itus ac re­<lb/>ditus reciptoci, ad in&longs;tar motusaccelerati & retardati; ptima quidem ab <lb/>Apogæo ad di&longs;tantiam mediam, eandem curn di&longs;tantia media Solis, & hinc <lb/>ad Perigæum, ita vi Venus in&longs;s a mediam di&longs;tantiam orbem &longs;uum i&longs;ochro­<lb/>non cum Sole perfici<gap/>; Secunda verò ab co latitudinis puncto, in quo <pb pagenum="83"/>fuit, antequam motu circulari <gap/>overet<gap/> ad Eclipticam, co modo, quo <gap/><lb/>&longs;upra dictum e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Qua quæ&longs;o linea, curva an rocta? </s> <s>deinde an perpen­<lb/>dicular<gap/>ter cadente in planum Eclipticæ? </s> <s>an verò in planum Æqu<gap/>­<lb/>totis? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Ad vtrumque re&longs;pondeo; ad primum quidem, per curvam fieri; <lb/><figure id="fig10"></figure><lb/>vt dixi de Sole v.g. </s> <s>pet arcum D. <lb/>F, vt eandem retineat à centro <lb/>mundi di&longs;tantiam, vi &longs;cilicet hujus <lb/>motus, &longs;eu inclinationis; quænam <lb/>verò &longs;it accelerationis ratio à D ver­<lb/>sùs F, iam &longs;upra indicavi. </s> <s>Suppone <lb/>horizontale planum AF & &longs;uperfi­<lb/>ciem &longs;phæræ inclinatam DF, in <lb/>qua de&longs;cendat corpus grave motu <lb/>accelerato, hæc e&longs;t accelerationis <lb/>progre&longs;&longs;io; quæ in &longs;ecundam incli­<lb/>nationem apprimè quadrat; <expan abbr="quænã">quænam</expan> <lb/>porrò & qualis &longs;it hæc progre&longs;&longs;io <lb/>motusaccelerati, altioris e&longs;t indagi­<lb/>nis; Licèt enim <expan abbr="ead&etilde;">eadem</expan> <expan abbr="nõ">non</expan> &longs;it cum illa, <lb/>quam &longs;ervant funependula in de­<lb/>&longs;cen&longs;u, ab ea tamen petenda e&longs;t; <lb/>Vt vt &longs;it, hæc di&longs;cu&longs;&longs;io hujus no&longs;tri <lb/>in&longs;tituti non e&longs;t, ad &longs;ecundum re­<lb/>&longs;pondeo, Lineam illam eadere per­<lb/>pendicularitet in planum Æquato­<lb/>ris, <expan abbr="n&etilde;pe">nempe</expan> determinatur à Plano cir­<lb/>culi parallelo Plano Æquatotis, cius <lb/>tamen terminus e&longs;t Ecliptica, vt di­<lb/>xi; nempe Plánetæ hinc terram a&longs;pi­<lb/>ciunt, cui &longs;erviunt, lumenque refun­<lb/>dunt; inde verò Solem, &longs;ub primo re&longs;pectu, &longs;uos orbes agunt circa­<lb/>terram, tanquam circa &longs;uum centrum; &longs;ub alio verò, Solis &longs;equun­<lb/>tur ve&longs;tigia, qui cùm ab Ecliptica punquam di&longs;cedat, hic &longs;olus circulus <lb/>&longs;ecundam inclinationem Planetarum tanquam terminus determinat. </s> <s>Ex <lb/>his autem per&longs;picuas rationes reddo, in mea hypothe&longs;i, acceleratio­<lb/>nis, retardationis, retrogre&longs;&longs;ionis, &longs;tationis, Nodorum motus, itemque <lb/>Apogæi & Perigæi, variæ digre&longs;&longs;ionis & latitudinis, vt jam &longs;upra indicavi­<lb/>mus. </s></p><p type="main"> <s><emph type="italics"/>Ch<gap/>y&longs;oc.<emph.end type="italics"/></s><s> Antequam alia argumenta expromas, per te mihi liceat, <lb/>Antime, vnum quidpiam, quod jam in mentem venit, breviter expo­<lb/>nore; &longs;cilicet in Copernicana hy pothe&longs;i, cuncta fetè gratis, vt aiunt, <lb/>& ad nutum con&longs;tr<gap/>entis ad&longs;trui, id e&longs;t &longs;ine vlla cau&longs;a, vel ratione, quæ <lb/>hoc, vel illud fieri p<gap/>&longs;tulet; v.g. </s> <s>terram moveri volunt in excentrico; cut <pb pagenum="84"/>amabò circa illud centrum potiùs quàm circa aliud? </s> <s>Cur non circa Solem, <lb/>qui e&longs;t in Mundi centro? </s> <s>aut &longs;i vis, moveri in Eclip&longs;i, cur hanc adhibes po­<lb/>tiùs quàm <expan abbr="aliã">aliam</expan>? </s> <s>cur Sol in hoc. </s> <s>vmbilico, <expan abbr="nõ">non</expan> verò in alio, vel in ip&longs;o ellip&longs;eos <lb/>centro? </s> <s>deinde cur & vnde movetur Apogæum? </s> <s>cur in con&longs;equentia potiùs <lb/>quàm in antecedentia? </s> <s>cur terra ab occa&longs;u ad ortum, tum motu centri, tum <lb/>ctiam orbis &longs;ecundùm he mi&longs;phærium à Sole aver&longs;um? </s> <s>cur per Eclipticam <lb/>cum tanta declinatione ab Æquatore? </s> <s>vnde etiam motus orbis annuus <lb/>diurno contrarius? </s> <s>denique vnde ip&longs;a vertigo Solis? </s> <s>cur tanta, non major <lb/>aut minor? </s> <s>Cuncta hæc, alia<gap/>; fortè &longs;imilia &longs;ine vlla ratione vel cau&longs;a exi­<lb/>gente Copernicana hypothe&longs;is habet, eo tantùm nomine, quod ad &longs;alvan­<lb/>da phænomena, nece&longs;&longs;aria e&longs;&longs;e credautur, quæ tamen alio modo &longs;alvari <lb/>po&longs;&longs;unt. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Par pari haud dubiè referre po&longs;&longs;um: nunquid enim hæc ead&ecedil;m <lb/>in ve&longs;tra hypothe&longs;i ad &longs;alvanda phænomena gratis & ab&longs;que alia cau&longs;a non <lb/>a&longs;truuntur? </s> <s>nunquid non ponitisex centricos, epicyclos, Apogæi Nodorum­<lb/>que motum? </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ec.<emph.end type="italics"/></s><s> Scio, à multis in no&longs;tra hypothe&longs;i, hæc gratis ad&longs;trui; Anti­<lb/>mus tamen no&longs;ter, vt jam non &longs;emel audii&longs;ti, vno &longs;implici motu æqua­<lb/>bili, & gemina inclinatione illa omnia explicat, & ad &longs;uas cau&longs;as re­<lb/>ducit. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Tuo illo argumento, Chry&longs;ocome, contra Copernicum non &longs;e­<lb/>mel v&longs;us &longs;um, re tamen paulò accuratiùs <expan abbr="cõ&longs;iderata">con&longs;iderata</expan>, illæ rationes, quæ mco <lb/>&longs;y&longs;temati favent, pro explicatione illorum capitum, quæ &longs;upra recen&longs;ui&longs;ti, <lb/>ad Copernicanum facilè traduci po&longs;&longs;unt, & pro illo æquè militant. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Magno certè beneficio me tibi ob&longs;tringes, &longs;i rem hanc me do­<lb/>cueris, quæ certè quanti momenti futura &longs;it, vix dici à me pote&longs;t; &longs;i enim <lb/>Keplerus pro metis nugis & fabulis, in quibus cau&longs;as phy&longs;icas cæle&longs;tium <lb/>phænomenon collocabat, tantom gloriam apud omnes obtinuit; quid de <lb/><gap/>lo faturum putas, qui veras corundem cau&longs;as in hac hypothe&longs;i Copernici <lb/>ad duxerit? </s> <s>inde &longs;altem maxima tua ingenuitas con&longs;picua & palam fiet<gap/>cùm <lb/>vel <gap/>o&longs;ti arma porrigas, quious &longs;e defendat. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Libenter faciam; nec enim in <gap/>&longs;ce di&longs;&longs;ertationibus literariis, ali­<lb/>quorum dolus mihi probatur, qui ca celant adver&longs;arium, quæ illius cau&longs;æ <lb/>&longs;uf&longs;ragantur; mihi &longs;anè &longs;ecus agendum e&longs;&longs;e puto. </s> <s>Itaque &longs;upponamus So­<lb/>lemin centro mundi A &longs;tabulari, terram in apogæo C.circulum CHFP in <lb/>plano Eclipticæ, per quem terræ <expan abbr="centrũmoveretur">centrummoveretur</expan> à C in N, quod vocamus <lb/>in con&longs;equentia Signorum, &longs;i e&longs;&longs;et in mediocri, vellconnaturali di&longs;tantia; &longs;ed <lb/>quia ab Apogæo ad mediocrem di&longs;tantiam tendit, &longs;en&longs;im motu accelerato <lb/>accedit versùs A, &longs;imulq, tendit motu circulari ver&longs;us H, vnde <expan abbr="nõ">non</expan> movetnr <lb/>per atcum CH, &longs;ed per al<gap/> CG; &longs;upponamus autem AG e&longs;&longs;e mediocr<gap/><lb/>di&longs;tantiam; in ea non &longs;i&longs;tit; &longs;ed motu retardato progreditur vltrà versus Peri­<lb/>gæum; & quia rece&longs;&longs;us à mediocri' di&longs;tantia æqualis e&longs;t acce&longs;&longs;ui, æquali tem­<lb/>pore decurret arcum GE, atque ita erit Perigæum in E, ex quo pari modo <lb/>pervenit in I, nam AI e&longs;t mediocris di&longs;tantia, reditque per i&longs;ochronum <lb/>rece&longs;&longs;um, ad Apogæum C; &longs;ive autem arcus CGE &longs;it &longs;emicirculus, vel <pb pagenum="85"/>&longs;piralis, &longs;ive etiam ellip&longs;is, cogita punctum C accedere ad R motu acce­<lb/>lerato per radium AC eo tempore quo radius AC circa centrum A in <lb/>eodem plano ductus pervenit in AG, ferens &longs;ecum punctum illud mobi­<lb/>le, quod tunc erit in G; deinde idem punctum moveatur motu retaidato <lb/><figure id="fig11"></figure><lb/>ab R in D, dum prædictus codem motu pervenit in AE, tunc certè præ­<lb/>dictum punctum crit in E &longs;cilicet in Perigæo; quare hæc linea erit vna ex <lb/>&longs;piralibus Archimedis, quæ ad &longs;emicirculum proximc accedit; quia veio <lb/>differentia &longs;en&longs;ibilis nen e&longs;t, &longs;emicirculus &longs;upponi pote&longs;t, in quo cen­<lb/>trum terræ motu æquabili movetur; pari modo punctum illud redit à D <lb/>in R, & ab R ad A, dum idem radius ab AE redit in AC. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/> Hæc mihi &longs;ummo perè placent, cùm ex &longs;implici&longs;&longs;imis princi­<lb/>piis deducantur; vna tamen difficultas &longs;e&longs;e oculis meis objicit; nam <lb/>æquali tempore, vt dicis, radius AC circumducitur in AG, vel AN, & <lb/>ab AN ad AF, igitur inæqualiter movetur, cùm arcus CN minor &longs;it <lb/>arcu NF. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Equidem extremitas radij AC movetur inæqualiter in cir­<lb/>culo CHFP; punctum tamen C, &longs;ou centrum terræ ita movetur pet <lb/>CGE motu mixto ex circulari, & recto, vt hic pror&longs;us æquabilis re&longs;ul­<lb/>tet: Hinc circulus CGEI e&longs;t quidem excentricus, non tamen verus, in <lb/>quo &longs;cilicet terra motu &longs;implici moveatur, &longs;ed apparens; & con&longs;equen­<lb/>ter centrum B, tantùm apparens; item excentricitas AB; quæ omnia ex <lb/>prædicto motu mixto con&longs;equi, nece&longs;&longs;e e&longs;t; itemque anomaliam, id e&longs;t, <pb pagenum="86"/>appatentem nob<gap/> eju&longs;<gap/>s inæqualitatem; licet enim raotus à C <lb/>in G; & à G in <gap/> r<gap/>vor<gap/> æqu<gap/> &longs;int, inæquales tamon nobis appa­<lb/>re<gap/>; nempe dum ter<gap/> deturrit a<gap/>cum CG, quadrar<gap/>m &longs;cilicer &longs;ul <lb/>Orbis, videtur nobis detumi&longs;&longs;o al c<gap/>m CN minorom quadrante; & dum <lb/>decurrit GE æqualem CH, videtur nobis decurrere arcum NF majo­<lb/>rem, perinde quippe e&longs;t, &longs;ive terram in G a&longs;picias ex A, &longs;ive ex G Solem <lb/>in A &longs;pectes; vt &longs;cilicet illum videas in puncto Eclypticæ, oppo&longs;ito, <lb/>puncto G. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Sed vndo <gap/>pogæi motus, i&longs;que in con&longs;equentia. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Fac terran ex C, peract<gap/> &longs;emicirculo nondum ad Perigæum <lb/>perveni&longs;&longs;e, nec peracto orbe integro ad Apogæum; inde nece&longs;&longs;ariò &longs;e­<lb/>quitur, Apogæum promoveri in con&longs;equen tia, &longs;cilice<gap/>à Gversùs H; in <lb/>antecedentia autem moveretur, &longs;iterra ad Apogæum reditet nondum <lb/>peracto orbe integro. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Omit<gap/>e, quæ&longs;o hæc enim faciliora &longs;unt, quàm vt longio­<lb/>rem explicationem po&longs;tulent; &longs;ed vnde quæ&longs;o orbis annuus centri; vnde <lb/>diurnus orbis, i<gap/>mquo annuus illi oppo&longs;itus? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Nequo in hoc multùm laboto; &longs;i enim &longs;upponas terræ globum <lb/>ita demi&longs;&longs;um fui&longs;&longs;e ex &longs;ublimi, ad acquiren dum illum velocitatis gradum, <lb/>qui nece&longs;&longs;arius &longs;it, vt vna pats globi fortè præponderans, ante aliàs de­<lb/>&longs;cenderit, vnde motus quidam mixtus &longs;equatur, ex motu orbis & cen­<lb/>tri; &longs;i hoc &longs;upponas, inquam, vbi dictus globus ad di&longs;tantiam mediam <lb/>pervenit, illico motu circulari movericœpit in eam partem, in quam <lb/>motus Orbis prævius illum determinat; analogiam habes in globo vel <lb/>di&longs;co, qui deor&longs;um præfato modo dimi&longs;&longs;us de&longs;cendit; vbi enim planum <lb/>horizontale attingit, in eo movetur, &longs;eu rotatur, priore determinatione <lb/>durante. </s> <s>v. </s> <s>g. </s> <s>&longs;it globus BCDE, (<emph type="italics"/>in Figura <expan abbr="&longs;eq.">&longs;eque</expan><emph.end type="italics"/>) centro A ita demi&longs;&longs;us <lb/>per lineam perpendicularem AH, vt centrum quidem A rectam de&longs;cri­<lb/>bat; aliæ verò partes etiam moveantur circa A, v.g. </s> <s>B in C, D, E, vbi <lb/>globus attinget planum horizontale KL, in H, vi prioris determina­<lb/>tionis, &longs;eu motus Orbis, F tendet in GH, I, vnde rotabitur globus in <lb/>dicto plano versùs K. </s> <s>Idem dicendtun de globo terræ tali modo de­<lb/>mi&longs;&longs;o, cujus centrum movetur motu æquabili in Plano Eclipticæ cum <lb/>eo velocitatis gradu, quem in primo illo de&longs;cen&longs;u acqui&longs;ivit, qui <lb/>deinde &longs;emper intactus manet; pari modo motus Orbis etiam durat, <lb/>cùm eadem &longs;it pro vtroque motu ratio, vt videre e&longs;t in prædicto <lb/>globo. </s></p><p type="main"> <s><emph type="italics"/>Choy&longs;oc.<emph.end type="italics"/></s><s> Sed cur circa talem axem potiùs quàm circa alium? </s> <s>deinde <lb/>cur libratur prædictus axis? </s> <s>denique cur omnes circuli diurni Æquatori <lb/>&longs;unt paralleli? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Ni&longs;i orationem meam interrupi&longs;&longs;es, hæc continuò æquè facilè <lb/>explicabam; Suppono terræ globum vel magnum Magnetem e&longs;&longs;e, vel &longs;al­<lb/>tem magnetica virtute in&longs;tructum, vnde nece&longs;&longs;e &longs;it, duos polos magneticos <lb/>ine&longs;&longs;e, & axem ad vtremque polum terminatum, quem etiam &longs;ibi ipfi &longs;em-<pb pagenum="87"/>per e&longs;&longs;e parallelum oportet; igitur circa hunc, domtaxat <expan abbr="ax&etilde;">axem</expan> terte&longs;tris glo­<lb/>bus volvitur; dioquin &longs;i circa <expan abbr="aliũ">alium</expan> ille &longs;ibi ip&longs;i pamllelus non &longs;emper e&longs;&longs;et. <lb/><figure id="fig12"></figure><lb/>Ex hoc codem axis paralleli&longs;mo, &longs;equia<gap/> præfata eju&longs;dem globi inclina­<lb/>tio, qua fit, vt idem globi punctum modò &longs;upra Eclipticæ planum attolla­<lb/>tur, modò infra deprimatur; vnde Æquinoctia, Sol&longs;titia & quatuor anni <lb/>tempe&longs;tates nece&longs;&longs;ario con&longs;equuntur; nempe, vt jam monui, &longs;upra, ille mo­<lb/>tus annuus orbis e&longs;t tantùm apparens, & ex præfatoaxis, circa quem fit mo­<lb/>tus diurnus, paralleli&longs;mo re&longs;ultut. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Omnia probè intelligo; re&longs;tat, vt cau&longs;am afferas Solaris re­<lb/>volutionis. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Pro hac nihil occurrit in hac hypothe&longs;i, quod &longs;olidum &longs;it, ni&longs;i <lb/>fortè dicamus. </s> <s>Solarem globum vi motrice pollere; non &longs;anè quòd vivat, <lb/>hoc enim ab&longs;urdum puto; &longs;ed quòd ea vi pollere po&longs;&longs;it, qua etiam vilia no­<lb/>&longs;tra elementa pollent; ac proinde cùm <gap/>jus finis &longs;it &longs;uo calore & luce alia <lb/>corpora perfundere, mirum non e&longs;le, fi qua&longs;i ab aliis globis inuitatus &longs;eu <lb/>deter minatus, circa &longs;uum centrum immobil<gap/> volxatur, vt &longs;altem illam po­<lb/>t<gap/>nt<gap/>m quæ ine&longs;t, exerceat; alioquin por <gap/>m æternitatem hæc fru&longs;tra <lb/>e&longs;&longs;et, quod dixerit. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Bea&longs;ti me, Antime; jam facil<gap/> ad alios Planetas adductas à <lb/>te rationes tradu cam. </s> <s>hoc vnum præ cæteris mihi mole&longs;tum erat, quòd <lb/>in no&longs;tra hypothe&longs;i, omnia ferè aratis dici atque adduci crederem; <lb/>huic &longs;anè incommodo abundè occurri&longs;ti, cùm omnia, ni fallor attigeris, <pb pagenum="88"/>necenim m<gap/>tationem obliquitatis Eclipticæ admittendam e&longs;&longs;e putarem, <lb/>præce&longs;&longs;ion<gap/>m <gap/> lenti&longs;&longs;imus ille &longs;tellarum mo<gap/>us &longs;atis ex­<lb/>plicat. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Ingenuitati meæ, <gap/>inor, tribues, quòd tibi ea &longs;ugge&longs;&longs;erim, <lb/>quibus mole&longs;tum illud, vt ais, argumentum refellere valeas. </s> <s>Vnum tibi <lb/>per&longs;uadeas velim, cuncta hæc non obe&longs;&longs;e quidem ve&longs;træ hypothe&longs;i, &longs;ed non <lb/>prode&longs;&longs;e; &longs;icuti no&longs;træ nec ob&longs;unt, nec pro&longs;unt; de obliquitatis Eclipticæ <lb/>mutatione, idem tecum &longs;entio; præce&longs;&longs;iont<gap/> Æquinoctiorum rectè omni­<lb/>no explicas per lenti&longs;&longs;i<gap/>um illum fixarum motum; nec in tua hypothe&longs;i <lb/>alius modus e&longs;&longs;evidetur; Li<gap/>t enim Copernicus, Keplerus, aliíque ex ve&longs;tris <lb/>velint fixarum motum non e&longs;&longs;e realem, &longs;ed apparentem, co quòd, inquiunt, <lb/>Æquinoctialia puncta tantulùm adducantut versùs occa&longs;um, &longs;cilicet in an­<lb/>tecedentia, quia libratio terre&longs;tri globi citiùs ab&longs;olvitur, quàm motus in <lb/>Zodiaco, hoc tamen, m<gap/>o &longs;altem iudicio, non &longs;ub&longs;i&longs;tit, nempe prædicta li­<lb/>bratio, vt &longs;ic loquar, orltur ex motu orbis integro, cir ca axem axi Eclipticæ <lb/>parallelum, &longs;eu ex paralleli&longs;mo axis terræ, circa quem orbes diurni cunt; <lb/>hoc autem in i<gap/>&longs;dem punctis Eclipticæ Æquinoctialia puncta e&longs;&longs;e &longs;uppo­<lb/>nit, &longs;ed hæc ad rem no&longs;tram mihil faciunt. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Expecta tantulùm, Antinre, hic enim &longs;tellarum motus <lb/>in tua hypothe&longs;i difficilè, &longs;altem, vt audio, explicatur; vnde for­<lb/>tè meam vel hoc nomine, tuæ qui&longs;piam præferendam e&longs;&longs;e putaret. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Longè faciliùs, Augu&longs;tine, &longs;tellarum motus, quàm Planeta­<lb/>rum, in qualibet hypoth e&longs;i evplicat<gap/> pro quo &longs;uppono 1. fixum æter­<lb/>numque e&longs;&longs;e Natu<gap/>e inititutum, vt &longs;tcllæ omnes eundem inter &longs;e ordin<gap/>m <lb/>& &longs;itum &longs;ervent. </s> <s>2. Nunquam mutari illarum latitu linem: His po&longs;itis, <lb/>cogita &longs;tellam quampiam in ip&longs;a Ecliptica, cogita etiam circulum quem­<lb/>liber immobilem, puta meridiànum, in quo &longs;tella, primùm &longs;ita &longs;it, co­<lb/>grta denique ip&longs;am Eclipticam, circa Axem mundi, &longs;uum <expan abbr="motũ">motum</expan> ab&longs;olvere, <lb/>ita vt ide<gap/> punctum, quod erat in dicto meridiano ad illum redeat, orbe <lb/>peracto ab ortu, in occa&longs;um 24.horis. </s> <s>Iam cogita &longs;tellam illam &longs;imul cum <lb/>Ecliptica ab ortu in occa&longs;um ferri, & circumduci, & paulo tardiùs, vteo <lb/>momento, quo dictum punctú Eclipticæ, in quo erat, attingit meridianum, <lb/>ip&longs;a tantulùm versùs ortum remaneat, non quidem extra Eclipticam, <lb/>&longs;ed in ip&longs;amet Eclip<gap/> nec enim perfectum orbem de&longs;cribit, &longs;ed <lb/>talem &longs;piram, vt&longs;emper Eclipticç re&longs;pondeat; aliæ verò, quæ &longs;unt extra Ecli­<lb/>pricam, <gap/>andem &longs;emper ab illa di&longs;tantiam retineant, vnde prætet circularé <lb/>motum, altera &longs;altem inclinatioue opus e&longs;t, cujus terminus &longs;it æquator, <expan abbr="nõ">non</expan> <lb/>Ecliptica; ita tamen moven<gap/>ur, vt &longs;emper eandem ab Ecliptica di&longs;tantiam <lb/>retineant: inde præc e&longs;&longs;io Æq<gap/> aoctiorum fec<gap/>è explicatur, quæ tamen <lb/>ex eo explicari non pote&longs;t, quod Sol in diver&longs;is punctis Æquarorem &longs;ecet; <lb/>quia cum Sol &longs;emper Eclipticæ in&longs;i&longs;tat, licèt versùs occa&longs;um &longs;ectio Ecli­<lb/>pticæ cum Æquatoro, ip&longs;o Æquinoctij momento fingulis, annis promo­<lb/>veatur, non tamen ex hoc &longs;equitur Æquinoctiorum præce&longs;&longs;ro, ne­<lb/>que propterea &longs;tulla quæpiam ab Æquinoctij puncto versùs Ortum remove-<pb pagenum="89"/>cur vt non nemo perperam exi&longs;ti<gap/>et, &longs;ed ideò fit Æquinoctiorum præ­<lb/>ce&longs;&longs;io, quod Stellæ &longs;ingulis diebus & annis, tantulùm versùs Ortum qua­<lb/>&longs;i retroagantur, id e&longs;t, non omnino diurnum orbem conficiant plenis 24. <lb/>horis. </s> <s>Illum autem inclinationis motum lenti&longs;&longs;imum e&longs;&longs;e oportet; quod <lb/>fortè propter maximam di&longs;tantiam accidit; &longs;eu veriùs propter veloci&longs;&longs;i­<lb/>mum circularen motum, qui nihil ferè. </s> <s>prædictæ inclinationi relictum <lb/>&longs;init. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Sed quæ&longs;o te, Antime, ad alias rationes, &longs;i quæ tibi re&longs;tant, <lb/>orationem converte, ne huc totam A&longs;tronomiam accer&longs;ere videaris. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> In Venere, Mercurio, & Marte, illud præ&longs;ertim Copernicanæ <lb/>hypothe&longs;i repugnare &longs;upra dictum e&longs;t, quòd Venus in Perigæo quinqua­<lb/>gecuplo, Mercurius no vecuplo, Mars octogecuplo, majores videri debe­<lb/>rent; quod tamen: vt dixi, meis ob&longs;ervationibus repugnat in Iove, qui &longs;e­<lb/>quitur, aliquid etiam invenio; vnde tua hypothe&longs;is, Augu&longs;tine, impugne­<lb/>tur: Iovem igitur, vt fortè putabas, ita propitium non habes. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Immò nobis præ cæteris favet, cum &longs;uis a&longs;tris medicæis quæ <lb/>totidem Lunæ circa Iovem cunt, vt Luna circa terram, Venus & Mercu­<lb/>rius circa Solem, & circa Saturnum Satellites. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Non ita profectò res &longs;e habet, vt jam intelligere debui&longs;&longs;es ex <lb/>opu&longs;culo Diviniano, adver&longs;us Chri&longs;tiani Hugenij viri &longs;ane docti&longs;&longs;imi a&longs;­<lb/>&longs;ertionem; primò enim accipiamus vnam ex præfatis Iovialibus Lunis; <lb/>codem pror&longs;us rno do circa Iovem &longs;uum circulum agit, quo Luna circa <lb/>terram mobilem, in tua &longs;cilicet hypothe&longs;i; ac proinde &longs;i accipia arcum <lb/><figure id="fig13"></figure><lb/>HI, &longs;imilem illi, quem Iupiter de­<lb/>currit, eo tempote, quo quæpiam <lb/>ex Lunis Iovialibus &longs;uum circulum <lb/>ab&longs;olvit, hæc haud dubiè de&longs;criber <lb/>reali motu, ab vno Perigæo ad aliud, <lb/>lineam &longs;imilem HGI, eodemque <lb/>motus genere; igitur longè; tardiùs <lb/>in H, quàm in G, reali &longs;cilicet mo­<lb/>tu, idque in ea inæqualitatis pro­<lb/>portione, quæ a&longs;<gap/>gnabili qualibet <lb/>minor erit, quod videtur ab&longs;urdi&longs;&longs;i­<lb/>mum, & jam &longs;upra demon&longs;tratum <lb/>e&longs;t; neque hic repeto, cùm &longs;it ea­<lb/>deni vtrimque ratio; & ne hoc ip&longs;um <lb/>paulò po&longs;t repetere cogar, hæc ca­<lb/>dem ratio Lunæ Saturniæ à Chri­<lb/>&longs;tiano Hugenio primùm detectæ, eo­<lb/>demque modo contra tuam hypo­<lb/>the&longs;im applicatur. </s> <s>Igitur contra <lb/>illam ab a&longs;tris Medicæis & Iove, immò & Luna Saturnia eadem ratio pe­<lb/>titur, quam &longs;upra ex Lunæ motu deduximus. </s></p><p type="main"> <s>Secundò, vt in præfato opu&longs;culo <expan abbr="ob&longs;ervatũ">ob&longs;ervatum</expan> e&longs;t, Stellæ Medicææ &longs;ub Iove <pb pagenum="90"/>omnino &longs;ingulis fetè diebus viderentur, præ&longs;ertim cùm per zonas &longs;ub­<lb/>ob&longs;curas irent; &longs;unt enim lucidi&longs;&longs;imæ, illarumque candidi&longs;&longs;imus color à <lb/>&longs;ubob&longs;curo zonatum colore adhibito præ&longs;ertim optimo t<gap/>le&longs;copio, quo re­<lb/>verà vti po&longs;&longs;umus, facilè di&longs;tingueretur; nempe &longs;i Stellulæ à love teguntur <lb/>versùs Apogæum, intercepto &longs;cilicet Iovis di&longs;co, inter oculum & Stellam, <lb/>certè in Perigæo Iovem ex aliqua parte tegent; nec qui&longs;piam celeriorem <lb/>Stellæ tran&longs;itum cau&longs;ati debet, cùm &longs;ub lovis di&longs;eo, per horam ferè integram <lb/>manere debeat, vt in dicto opu&longs;culo demon&longs;tratum fuit; cùm autem &longs;ub <lb/>lovis di&longs;co nunquam dictas Stellas videre potucrimus, nanquam haud du­<lb/>biè &longs;ub illum defcendunt, quod certè tuæ hypothe&longs;i repugnat, vt nemo <lb/>negat; nec &longs;alli potuimus in ob&longs;ervando, qua&longs;i Conjunctionem Stellæ in <lb/>Apogæo, à <expan abbr="Cõjunctione">Conjunctione</expan> eju&longs;dem in Perigæo, non rectè di&longs;tinxerimus, nam <lb/>di&longs;tinctu facilè fuit; illa enim Conjunctio fit in Perigæo, quæ maximam di­<lb/>gre&longs;&longs;ionem Ortivam &longs;equitur, vt in Venere & Mercutio. </s></p><p type="main"> <s>Tertiò cùm lupiter lumen &longs;uum à Sole habeat, vt Mars, Venus, aliique <lb/>Planetæ, Stella Medicæa &longs;altem vicinior vmbram in Iovis di&longs;cum projice­<lb/>ret, quod negati non pote&longs;t ab vllo, qui rem hanc intelligat; nunquam au­<lb/>tem vmbram illam videre potuimus, quamvis Stella circa Perigæum e&longs;&longs;et; <lb/>Igitur Stellæ illæ &longs;ub Iovem minimè de&longs;cendunt; quod certè tuæ hypo­<lb/>the&longs;i non favet. </s></p><p type="main"> <s>Quartò adhibito etiam longi&longs;&longs;imo tele&longs;copio Stellas Medicæas &longs;plen­<lb/>dentes &longs;emper micante&longs;que fixatum ad in&longs;tar, non verò tornatas in di&longs;cum, <lb/>vt reliquos Planetas a&longs;picimus; vnde, ni fallor, deduco, ip&longs;o Iove longè al­<lb/>tiores e&longs;&longs;e, quod periti Optices, opinor, minimè negabunt: Adde his, ob&longs;er­<lb/>vationes non re&longs;pondere calculis factis in orbe, vel Epicyclo. </s> <s>Ex his, ni fal­<lb/>lor, non leve contra tuam hypothe&longs;im ducitur argumentum; ac proinde, <lb/>vt ante dicebas, lupiter non adeò vobis propitius e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> In tua verò hvpothe&longs;i quonam pacto Stellarum Medicæarum <lb/>motum explices, non in<gap/>liigo, vt de&longs;cen&longs;um illarum &longs;ub Iovem &longs;alves; quid <lb/>enim aliud de iis dicere potes, ni&longs;i illud ip&longs;um quod de Venere & Mercurio <lb/>&longs;upra dixi&longs;t? </s> <s>Atqui Venus & Mercurius &longs;ub Solis di&longs;cum de&longs;cendunt. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Si ex ob&longs;ervationibus haberemus, Stellas ilias &longs;ub Iovis di&longs;cum <lb/><gap/>e&longs;cendere, æquè facilè illarum motum <expan abbr="explicar&etilde;">explicarem</expan>, ac &longs;upra Veneris & Mer­<lb/>curij motum explicui; &longs;ed quandoquidem infra Iovem non de&longs;cendunt, non <lb/>minùs facilè illarum motum explicamus, a&longs;&longs;umpta illarum mediocri di­<lb/>&longs;tantia &longs;upra Iovem, ita vt in mediocri di&longs;tantia æquè citò ac Inpiter orbem <lb/>&longs;uum diurnum, infra verò illam citiùs, &longs;upra demum tardiùs ab&longs;o<gap/>vant, & <lb/>periodus acce&longs;&longs;uum & rece&longs;&longs;uum, quibus Stella redit ad Apogæum, intra <lb/>idem tempus perficiatur, quo &longs;uum orbem quælibet Stella decurrere com­<lb/>muniter dicitur; &longs;ed quia in dicto opu&longs;culo hæc &longs;atis in&longs;inuata fuctunt, ne <lb/>huc eadem traducam, eò vos remitto. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Nihil, opinor, amplius re&longs;tat, quod contra meam hypothe&longs;im <lb/>afferre po&longs;&longs;is; jam enim Saturnus &longs;uam Lunam tibi &longs;uppeditavit, cujus <lb/>&longs;alcem intentares. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Aliud quidpiam e&longs;t, quod tibi fortè novum videbitur: Annulus <pb pagenum="91"/>ille Saturnius à Chri&longs;tiano Hugenio viro clari&longs;&longs;imo & omnigena literatura <lb/>probè in&longs;tructo, ingeniosè profectò excogitatus, & quem ve&longs;tris mirum in <lb/>modum placui&longs;&longs;e intelligo; &longs;i fortè verus e&longs;&longs;et, quod &longs;anè maximè percu­<lb/>pio, ve&longs;træ hypothe&longs;i vltimam fetè ruinam afferret; cùm enim præfatus an­<lb/>nulus plano Æquatoris &longs;emper parallelus &longs;it, haud dubiè non movetur per <lb/>Eclipticam, alioquin &longs;itum acciperet, in quo Eclipticæ plano patallelus e&longs;­<lb/>&longs;et; eo quippe motu movetur, quo faciliùs moveri pote&longs;t, iuxta regulam ex <lb/>doctrina motuum a&longs;&longs;umptam, de qua jam &longs;upra. </s> <s>Et verò nemo non videt, <lb/><gap/>nnulum planum longè faciliùs moveri, & cum minore medij re&longs;i&longs;tentia, &longs;i <lb/>in plano annuli, &longs;it ip&longs;a linea motus; igitur cùmillud planum annuli Æqua­<lb/>toris plano parallelum &longs;emper &longs;it, haud dubiè in eo circulo movetur, cujus <lb/>planum Æquatoris plano parallelum e&longs;t; igitur in parallelo diurno, iuxta <lb/>no&longs;tram hypothe&longs;im, licèt enim &longs;piræ planum tantulùm ab Æquatoris pla­<lb/>no declinet, hoc tamen &longs;ub &longs;en&longs;um non cadit: Hæc ratio &longs;ingularis e&longs;t; quia <lb/>præfatus annulus e&longs;t etiam valdè &longs;ingularis, & ante Hugenium incompertus <lb/>orbi, faxit Deus, vt ex futuris ob&longs;ervationibus Saturno præ&longs;ertim circa <lb/>Æquatorem exi&longs;tente, ita luce nova confirmetur, vt de illo nullus vltra du­<lb/>bitare po&longs;&longs;it; quod maximoperè, vt dixi, percupio, cùm in no&longs;tram hypo­<lb/>the&longs;im mirificè Q iadret; & hæc &longs;unt, quæ contra tuam hypothe&longs;im, Augu­<lb/>&longs;tine dicenda mihi occurrunt. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Addere poteras per&longs;picua Scripturæ loca, ex quibus con&longs;tat <lb/>terram &longs;tare & Solem moveri iuxta literalem illorum &longs;en&longs;um, qui profecto <lb/>retinendus e&longs;t, &longs;i ab&longs;que ab&longs;urdo retineri queat; adde Sanctorum Patrum <lb/>auctoritatem, quæ certe maximi momenti e&longs;t, pro definiendo legitimo San­<lb/>ctæ Scripturæ &longs;en&longs;u; ex his enim &longs;equitur pre&longs;picua mens Eccle&longs;iæ, quæ <lb/>S.Scripturæ &longs;en&longs;um ex Sanctis Patribus &longs;emper eruit; denique cùm divina <lb/>potentia in &longs;acro textu laudati velit, & magnifieri, ex celerrimo illo motu, <lb/>quo a&longs;tra cientur, quis hanc illi laudem jure detraliat? </s> <s>nemo certe, illorum <lb/>præ&longs;ertim, qui &longs;acram Scripturam admittunt. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Licèt manus omnino dare nequeam, negati tamen à me non <lb/>pote&longs;t, quin aliquid &longs;altem plau&longs;us no&longs;træ hypothe&longs;i &longs;ubduxeris, & in tuam <lb/>traduxeris; &longs;ed de hac re &longs;atis. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Optimè mones; quate hic &longs;u&longs;tinendum e&longs;&longs;: iudico, ne nimia <lb/>fortè huius congre&longs;&longs;us prolixitas nobili&longs;&longs;imæ coronæ tædium affetat. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Prudenti&longs;&longs;imè judica&longs;ti; quare hoc vnum re&longs;tat, vt primo <lb/>congre&longs;&longs;ui diem indicamus. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;t.<emph.end type="italics"/></s><s> Po&longs;t triduum, ni&longs;i vobis &longs;it incommodum; Sed quodnam erit <lb/>di&longs;put at ionis atgumentum? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Meam &longs;ententiam, &longs;eu veriùs hypothe&longs;im de Marinoæ&longs;tu, vobis <lb/>exponam; interim con&longs;ulite tabulas Nauticas, vt inde vobis &longs;uppetat, quod <lb/>mihi opponatis. </s></p><pb pagenum="92"/><figure></figure><p type="main"> <s><emph type="center"/>DIALOGVS TERTIVS.<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>In quo, nova & vera cau&longs;a Marini æ&longs;tus declaratur <lb/>& demonstratur.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> <s>REM magnam aggredior, Princeps Eminenti&longs;&longs;ime, adeó­<lb/>que difficilem, vt Philo&longs;ophorum maximi, Stagiritæ &longs;ui <lb/>principis mi&longs;erando ca&longs;u & naufragio territi, in&longs;uperabilé <lb/>illam & Mortalium ingenio inacce&longs;&longs;am publicis monu­<lb/>mentis in lucem editis declararint. </s> <s>Vnde factum e&longs;&longs;e, <lb/>reor, vt quique illorum prudenti&longs;&longs;imi hunc &longs;copulum <lb/>cautè prætergre&longs;&longs;i, vix extremo indice illum indicarint; cùm tamen alij <lb/>certè incauti ad illum propiùs acce&longs;&longs;erint, ibique tanquam in tidicula &longs;ce­<lb/>na, the&longs;es &longs;uas communi &longs;apientum ludibrio expo&longs;uerint. </s> <s>Et verò vix ea <lb/>in &longs;ommiantis animum caderent, quæ ip&longs;i excogitarunt, ad cau&longs;am Ma­<lb/>rini æ&longs;tus explicandam; &longs;unt qui Soli, alij Terræ, neutri quidam præfa­<lb/>tam cau&longs;am attribuunt: in Luna multiplicem virtutem, &longs;eu vim alij agno­<lb/>&longs;cunt; magneticam, qua &longs;cilicet a quas adducit atque attollit; humefacti­<lb/>vam, cùm &longs;it humoris vehiculum, quo humida corpora variè afficiuntur, <lb/>pro diver&longs;o Lunæ a&longs;pectu; compre&longs;&longs;ivam, rarefactivam &c. </s> <s>Sed in Ple­<lb/>nilunio, de Meridie, Luna in puncto oppo&longs;ito exi&longs;tens, qua vi, amabo, <lb/>ciet æ&longs;tum? </s> <s>Qui ad Solem confugiunt, dicere nequeunt, quid Sol præ&longs;tet, <lb/>cem bis &longs;ingulis men&longs;ibus in Novilunio &longs;cilicer & Plenilunio æ&longs;tum <lb/>in media nocte, ab&longs;ente Sole habeamus. </s> <s>Vapores tepidos accer&longs;unt aliqui; <lb/>&longs;ed vnde, à quo excitati? </s> <s>Quid iis cum Luna, cuius motum Marinus æ&longs;tus <lb/>æmulatur? </s> <s>Vapores demum aquam in bullas attollunt, non verò in tu­<lb/>morem; & quid nitrum ad hoc conferat, divinare, ni&longs;i fingam, profectò <lb/>non po&longs;&longs;um; Terræ motum inæqualem, cui aliqui tribuunt æ&longs;tum, iam <lb/>&longs;upra rejecimus; item aëris compre&longs;&longs;ionem à præterlabente Luna æquè <lb/>facilè explodimus; quia Luna in Meridiano exi&longs;tente, ibi compre&longs;&longs;ionis <lb/>maxima vis e&longs;&longs;et; nullus igitur æ&longs;tus. </s> <s>Omitto alia figmenta potiùs quàm <lb/>argumenta, & ex communibus principiis rem i&longs;t am ita de&longs;inio, vt ex iis, <lb/>etiam ab ignaro æ&longs;tus Marini, immò qui nequidem Oceanum e&longs;&longs;e &longs;ciat, <lb/>illi omnes effectus, qui &longs;en&longs;ibus no&longs;tris & ob&longs;ervationibus &longs;ubjiciuntus, <lb/>deduci po&longs;&longs;int: id &longs;altem erit operæ pretium, quod hanc hypothe&longs;im <lb/>meam cen&longs;uræ tuæ &longs;ubjectam, vel inde nobili&longs;&longs;imo & docti&longs;&longs;imo calculo <lb/>probatam, vel ju&longs;to, à quo ab&longs;que temeritatis nota, nemo appellarit, <lb/>judicio reprobatam e&longs;&longs;e, non &longs;ine volaptate intelligam: &longs;ed ad rem ve­<lb/>niamus. </s></p><pb pagenum="93"/><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Multa &longs;anè, ac ferè omnia in memoriam tevocavi, vt facilè <lb/>mihi per&longs;uadeo, quæ pro ad&longs;truenda Marini æ&longs;tus cau&longs;a, dicturus e&longs;tes; <lb/>&longs;ed nihil occurrit profectò, quod iam ab aliis dictum, &longs;eu fictum non fuerit: <lb/>nempe, vt vel inde initium di&longs;&longs;ertationis ducamus, negari non pote&longs;t, quin <lb/>Lunaris globus in hac &longs;cena &longs;uas, ea&longs;que præcipuas partes agat; quid por­<lb/>rò Luna præ&longs;tare queat, quod jam excogitatum, &longs;eu fictum non &longs;it, immò <lb/>& rejectum? </s> <s>intume&longs;cit aqua in æ&longs;tu, quod nemo peritus negare au&longs;it; <lb/>cùm tantus &longs;it in quibu&longs;dam oris aquarum tumor, vt ad quinquaginta pe­<lb/>dum altitudinem facilè a&longs;cendat; quibus porrò organis, &longs;eu trochleis, <lb/>& qua vi Luna hunc aquis motum imptimat, præ&longs;ertim, cùm ab&longs;ente <lb/>Luna aqua etiam per æ&longs;tum intume&longs;cat, conjicere non po&longs;&longs;um. </s> <s>Video, <lb/>Lunam Marini æ&longs;tus cau&longs;am e&longs;&longs;e, cùm ex diver&longs;a Lunæ applicatione, im­<lb/>mò & a&longs;pectu, diver&longs;is æ&longs;tus con&longs;equatur; quonam verò pacto, id Luna <lb/>præ&longs;tet, nec video, nec alij profectò vident. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/> Hæc vna poti&longs;&longs;imùm ex iis rebus cen&longs;enda e&longs;t, quas Deus <lb/>occultas & ignotas Mortalibus e&longs;&longs;e voluit; ita vt ingeniosè iuxta atque <lb/>&longs;apienter ille recentior dixerit, Marinum æ&longs;tum humanæ curio&longs;itatis nau­<lb/>fragium e&longs;&longs;e; &longs;ed quid tandem tu, Antime? </s> <s>Modicam Augu&longs;tinus de te <lb/>&longs;pem habere videtur, qua&longs;i &longs;uper hac re nihil novi afferre valeas; ego ve­<lb/>ro te adeò imprudentem e&longs;&longs;e, non puto, vt fidem tuam fru&longs;tra & in ca&longs;&longs;um <lb/>oppigneratis, vt antiquum, de quo jam &longs;upra, adagium in &longs;cenam revoces; <lb/><emph type="italics"/>parturient montes, n<gap/>&longs;cetur ridiculus mus.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Parum quidem admodùm mihi arrogo; &longs;pero tamen, aliquid <lb/>me adducturum, idque ex communibus principiis, quod &longs;i fortè non mul­<lb/>tis, nonnullis tamen arrideat: Concedo igitur. </s> <s>Augu&longs;tine, id quod paulò <lb/>ante dic<gap/>bas, Lunam &longs;cilicet in hoc negotio &longs;uas agere partes, nempe &longs;unt <lb/>qua&longs;i tres Marini æ&longs;tus periodi, diurna &longs;cilicet, men&longs;trua, annua; &longs;ingulis <lb/>ferè diebus bis accedit, & af<gap/>luit æ&longs;tus, bis recurtit; dico feiè, quia hic ge­<lb/>minus cut&longs;us & recur&longs;usnon 24. &longs;ed 25. horis, paulò minùs per ficitur, &longs;ci­<lb/>licet ad Lunæ motum; nen pe Luna, vt redeat ad idem Me<gap/>diani pun­<lb/>ctum, qua&longs;i 25. horas ponit; igitur &longs;ingulis diebus vna ferè hora tardior <lb/>æ&longs;tus tumet, v.g. </s> <s>&longs;i hodie hora Meridiana fuit &longs;ummum æ&longs;tus, cra&longs;tina die <lb/>erit ferè prima po&longs;t Meridiem hora: die verò &longs;equenti, hora po&longs;t Meri­<lb/>diem &longs;ecunda; atque ita con&longs;equenter. </s> <s>Hic porrò Lunæ motus e&longs;t; altera <lb/>periodus e&longs;t men&longs;trua; nempt pro diver&longs;o Lunæ a&longs;pectu, æ&longs;tus major, vel <lb/>minor e&longs;t; v. </s> <s>g. </s> <s>in Plenilunio major e&longs;t, quàm in Novilunio, & in hoc <lb/>major quàm in Quadraturis, cùm igitur ex Lunæ motu & a&longs;pectu tota il­<lb/>la æ&longs;tuum varictas procedat, negari non pote&longs;t, quin à Luna pendeat. <lb/></s> <s>Tertia demum periodus e&longs;t annua, nam ob&longs;ervatum fuit in Æquinoctiis <lb/>& Sol&longs;titiis, non modicam fieri mutationem æ&longs;tuum præ&longs;ertim in Æqui­<lb/>noctiis, ita vt in Æquinoctio, v.g. </s> <s>Autumnali cum Plenilunio conjuncto, <lb/>&longs;emper &longs;it maximus æ&longs;tus, in quo etiam Luna &longs;uo munere defungitur; &longs;i <lb/>enim fiat Æquinoctium in Quadratura, modicus æ&longs;tus e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Lunam, cau&longs;am e&longs;&longs;e fateor vltrò; &longs;i autem cau&longs;a e&longs;t, aliquid <lb/>agit & confert; quid porrò illud e&longs;t? </s> <s>fac age, me doceas, & eris mihi magnus <lb/>Apollo. </s></p><pb pagenum="94"/><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Dare non po&longs;&longs;um, Lunam Marini æ&longs;tus cau&longs;am e&longs;&longs;e; &longs;i enim <lb/>cau&longs;a e&longs;t, cau&longs;at, & aliquid præ&longs;tat: &longs;ed nihil penitus præ&longs;tat. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Ludis nos, Antime, Lunæ totum hunc effectum paulò ante <lb/>tribuebas; cur igitur modò cau&longs;am e&longs;&longs;e negas? </s> <s>Si cau&longs;a non e&longs;t, ad æ&longs;tum <lb/>nullo modo pertinet; Solve i&longs;tum nodum. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Communi di&longs;tinctione vtor, ad &longs;olvendum hunc nodum; <lb/>Luna ita pertinet ad Marinum æ&longs;tum, vt &longs;ine illa hic non &longs;it, licèt revera <lb/>Luna cuu&longs;a non &longs;it, id e&longs;t, tumorem illum aquæ minimè attollat, vel aquas <lb/>cieat; nullum enim motum aquis imprimit, nullum humorem affundit, <lb/>qui &longs;cilicet ad cel&longs;um illum tumorem &longs;ufficiat; quomodo igitur ab illa <lb/>æ&longs;tus pendet? </s> <s>Verbo dico; Luna Marini æ&longs;tus cau&longs;a non e&longs;t, &longs;ed mera Oc­<lb/>ca&longs;io, qua reverà &longs;ublata, æ&longs;tus non e&longs;&longs;et. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Ne quæ&longs;o ludas in verbis; &longs;olus enim verborum ludus ad <lb/>res phy&longs;icas explicandas non &longs;ufficit; quid igitur illud e&longs;t, quod dicis, nam <lb/>profectò non intelligo. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Faciam intelligas, Chry&longs;ocome, &longs;ed priùs illa principia jacien­<lb/>da&longs;unt, ex quibus res i&longs;ta deducitur. </s> <s>Suppono igitur primò, illum e&longs;&longs;e fi­<lb/>nem gravitatis, quæ gravibus ine&longs;t, vt &longs;ingulæ partes globi totalis versùs <lb/>illiùs centrum, ni&longs;u quodam communis con&longs;pirationis tendant; quod re­<lb/>verà nece&longs;&longs;arium fuit, tum ad conflandum totalem globum, tum ad eun­<lb/>dem &longs;ervandum; fac enim omnes partes alicujus globi totalis à &longs;eip&longs;is di&longs;­<lb/>&longs;itas e&longs;&longs;e, illico communi dictæ con&longs;pirationis vel inclinationis, versùs <lb/>idem centrum, vi, &longs;eu ni&longs;u, &longs;eu impetu &longs;e&longs;e iterum in orbem component; <lb/>deinde fac partes globi totalis non contraniti vlla re&longs;i&longs;tentia; &longs;tatim mi­<lb/>nima ferè ventorum, vel alterius impul&longs;us vi di&longs;&longs;ipabuntur; igitur non <lb/>potuit facilior modus excogitari, tum ad conflandum, tum ad &longs;ervandum <lb/>globum totalem; id e&longs;t, tum ad colligendas omnes partes, in vnum glo­<lb/>bum; tum ad impediendum, ne à globo facilè avellantur, non potuit, in­<lb/>quam facilior modus excogitari, quàm &longs;i partes &longs;ingulæ nativa quadam vi <lb/>& inclinatione, versùs idem & commune centrum eant, &longs;eu tendant, atque <lb/>nitantur. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Illud commune e&longs;t principium, vt gravia deor&longs;um, levia <lb/>&longs;ur&longs;um &longs;ua &longs;ponte ferantur, necenim opinor eorum &longs;ententiam defenditis, <lb/>quos tacito nomine Stagirita no&longs;ter refutavit, qui&longs;uperum, atque in&longs;erum <lb/>negabant: mundi ac terræ centrum deor&longs;um e&longs;t; cælum verò &longs;ur&longs;um; hoc <lb/>igitur &longs;uperum, illud inferum. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> De iis ferè omnibus, quæ paucis complexus es, dubitarem, <lb/>de eo præ&longs;ertim, quod dicis, gravia deor&longs;um, levia &longs;ur&longs;um &longs;ua &longs;ponte ferri; <lb/>de gravibus vltrò concederem; nec enim illorum commentum approba­<lb/>re po&longs;&longs;um, qui volunt, corpus grave à terra deor&longs;um trahi, &longs;pi&longs;&longs;i cuju&longs;dam <lb/>capillitij opera; aut certè trudi à ficta ne&longs;cio qua &longs;ubtili materia, quæ &longs;en­<lb/>&longs;um omnem fugit; nempe, &longs;i trudit illa materia, motum in &longs;e habet, & à <lb/>&longs;e; &longs;i enim ab alio, de hoc idem dicam; Satius igitur e&longs;t dicere, corpus <lb/>grave à &longs;e moveri, ac deor&longs;umire, quod &longs;cilicet videmus atque palpamus, <lb/>quàm trudi ab illa &longs;ubtili materia, mota à &longs;eip&longs;a, quàm nullo tactu, nullo <pb pagenum="95"/>&longs;en&longs;u percipimus; is profectò, magis tidiculus non e&longs;&longs;et, qui diceret, <lb/>corpus grave deor&longs;um trudi ab Angelo, quod tamen nulla ratione, nullo­<lb/>que experimento probari pote&longs;t, quàm ij, qui dieunt, ab ea &longs;ubtili materia <lb/>trudi, cùm nulla ratione, & nullo experimento id probare po&longs;&longs;int. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Rectè omnino; neque id ab vllo cordato viro negari pote&longs;t, <lb/>gravia &longs;cilicet &longs;ponte &longs;ua deor&longs;um ire. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Sed non item levia, quæ ideò &longs;ur&longs;um eunt, quia &longs;ur&longs;um à <lb/>graviore medio extruduntur; Supponamus enim corpus aliquod levius <lb/>graviori &longs;ube&longs;&longs;e; vel gravius <expan abbr="tãtùm">tantùm</expan> &longs;ua &longs;ponte deor&longs;um ibit & &longs;ur&longs;um levius <lb/>extrudet; vel tantùm hoc &longs;ua &longs;ponte &longs;ur&longs;um a&longs;cendet, ac deor&longs;um ex­<lb/>trudet gravius; vel &longs;imul vtrumque &longs;ua &longs;ponte ibit; quod levius tantùm <lb/>nemo dixeiit, & manife&longs;tæ convinci po&longs;&longs;et fal&longs;itatis. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Scio neminem e&longs;&longs;e, qui hoc dicat; &longs;ed quæ&longs;o te, fac, aliquem <lb/>e&longs;&longs;e; quomodò illum convinceres; dic mihi &longs;odes. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> In hunc modum; eo modo, quo &longs;ur&longs;um extruditur corpus <lb/>leve à gravi, aër v.g. </s> <s>ab aqua, cui &longs;ube&longs;t, corpus grave deor&longs;um detrude­<lb/>retur à levi, aqua, v. </s> <s>g. </s> <s>ab aëre, qui aquæ &longs;ube&longs;&longs;et: &longs;it ergo globus plum­<lb/>beus in aëre, ideò de&longs;cendit, quia aër, qui &longs;ube&longs;t, &longs;ua &longs;ponte a&longs;cendens, <lb/>illum deor&longs;um extrudit; ille autem Cylindrus aëris in globum levitat; ita <lb/>mihi loqui fas &longs;it, qui à globo ad terram v&longs;que extenditur, vt patet; nec <lb/>enim is, qui e&longs;t &longs;upra globum in illum levitat, &longs;ed potiùs gravitaret; corpus <lb/><gap/>nim gravitat deor&longs;um, &longs;nr&longs;um verò levitar; igitur &longs;i prædictus Cylin­<lb/>drus aëris primò &longs;it pedalis, ac deinde bipedalis, cùm tota vis gravitatio­<lb/>nis, &longs;eu detru&longs;ionis deor&longs;um &longs;it ab aëre, qui e&longs;t infra globum, & in eum le­<lb/>vitat; erit dupla vis detru&longs;ionis, &longs;eu gravitationis, quando aëris Cylin­<lb/>drus plumbeo globo &longs;ubjectus erit duplus; dupla enim cau&longs;a duplum effe­<lb/>ctum producir. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Id quod dicis ex hoc experimento probari pote&longs;t. </s> <s>Sit v. </s> <s>g. <lb/></s> <s>Scyphus vacuus &longs;ecundum perpendiculum in aquam immer&longs;us, ore præ­<lb/>vio, ita vt nihil pror&longs;us aëris ante in Scypho contenti avolare po&longs;&longs;it; <lb/>haud dubiè, quo profundiùs immergitur, major vis &longs;ur &longs;um illum extru­<lb/><gap/>s ip&longs;o tactu &longs;entitur; nempe totus aquæ &longs;uperpo&longs;itæ, Cylindrus cuju<gap/><lb/>baus ori va&longs;is, &longs;eu Scyphi circiter æqualis e&longs;t, in aëra Scypho conten­<lb/>tam gravitat, magis autem, Cylindrus altior. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Igitur &longs;i prædictus Scyphus ita immergatur, vt primum <lb/>vno palmo à &longs;uprema &longs;uperficie aqua di&longs;tet, ac deinde profundiùs im­<lb/>mergatur, ita vt di&longs;tet ab eadem &longs;uperficie duobus palmis, dupla tunc erit <lb/>vis gravitationis; quia duplæ cau&longs;æ duplus effectus e&longs;t: igitur cùm &longs;it eadem <lb/>ratio, duplus Cylindrus aëris &longs;ubjecti globo duplam vim motus in illum <lb/>exeret, &longs;cilicet levitationis, quod tamen fal&longs;um e&longs;&longs;e con&longs;tar. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Non dico duplam vim motus, &longs;ed tantùm dico majorem vim, <lb/>quod certè ad tuum propo&longs;itum &longs;atis e&longs;&longs;e puto; cùm prædicti globi pon­<lb/>dus idem &longs;it, eademque vis illa, qua deor&longs;um &longs;ertur, &longs;ive vnum, &longs;ive duos <lb/>palmos altus à terra pendatur. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Non dicis duplam vim motus? </s> <s>dupla cau&longs;a duplum effe-<pb pagenum="96"/>ctum producit, cùm cadem &longs;it cau&longs;arum & effectuum proportio. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Nonnego, duplum e&longs;&longs;e effectum, &longs;ed nego, duplam e&longs;&longs;e vim <lb/>morus, id e&longs;t motum duplum, &longs;eu duplo velociorem, & ne diutiùs te &longs;u­<lb/>&longs;pen&longs;um habeam, &longs;imili ferè experimento rem i&longs;tam explico: Sit vas quod­<lb/><figure id="fig14"></figure><lb/>libet AB; &longs;itque in&longs;erta fi&longs;tula in B, per quam, <lb/>&longs;i aperiatur, effluat aqua priùs infu&longs;a; & primò <lb/>quidem aqua occupet totam altitudinem AB, <lb/>Tum deinde &longs;ubduplum BE, non e&longs;t dubium, <lb/>quin Cylindrus BA extrudat aquam per fi&longs;tulam <lb/>BC, majore vi, quàm Cylindrus EB; non ta­<lb/>men duplo majore, licèt Cylindrus BA fit du­<lb/>plus Cylindri BE; &longs;i enim dupla e&longs;&longs;et vis motus, <lb/>id e&longs;t motus ille, quo per fi&longs;tulam aqua erumpit, <lb/>duplo velocior, duplæ cau&longs;æ, quadruplus e&longs;&longs;et ef­<lb/>fectus; nam &longs;i motus e&longs;t duplo velocior, eo tem­<lb/>pore, quo data quantitas aquæ v.g. </s> <s>vncia effluit, <lb/>extru&longs;a à Cylindro BE, effluent duæ vnciæ ex­<lb/>tru&longs;æ à Cylindro BA; &longs;ed extrudere duas vncias, <lb/>duplo motu, e&longs;t quadruplus effectus: nempe extrudere vnam duplo motu <lb/>e&longs;t effectus duplus, ergo extrudere duas, duplo motu, e&longs;t quadruplus. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Rem capio, igitur ad effectum quadruplum, opus e&longs;t cau&longs;a qua­<lb/>drupla; igitur Cylindrus BA producet duplam vim motus, comparatus <lb/>cum Cylindro AF &longs;ub quadruplo. </s> <s>Et verò licèt in majore &longs;axo aliqua cau­<lb/>&longs;a motrix eundem morum producat, quem in minore, non propterea æqua­<lb/>lis effectus dicendus e&longs;t; vt patet: Vnde minùs cautè duplum illum dixe­<lb/>ram motum. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Effectus igitur &longs;unt vt cau&longs;æ, cau&longs;æ vt altitudines, motus in &longs;ub­<lb/>duplicata altitudinum, effectus demum in compo&longs;ita motuum & quanti­<lb/>tatum; & quia motus &longs;unt vt quantitates, effectus &longs;unt in duplicata mo­<lb/>tuum, vel quantitatum. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;t.<emph.end type="italics"/></s><s> Mihi tamen gravis &longs;uboritur difficultas; nam in &longs;cypho illo im­<lb/>mer&longs;o, vna tantùm e&longs;t quantitas aëris; igitur non cre&longs;cit effectus ex quan­<lb/>titate, quæ non cre&longs;cit; igitur tantùm ex motu; igitur &longs;i cau&longs;a dupla e&longs;t, <lb/>motus erit duplus. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Acutè pror&longs;us: facilis tamen e&longs;t re&longs;pon&longs;io, cùm perinde gravitet <lb/>Cylindrus aquæ in &longs;ubjectum aëra, atque &longs;i hic &longs;tatim extruderetur, & alius <lb/>&longs;uccederet; &longs;icut Cylindrus AB primum gravitat in primam vnciam, quam <lb/>extrudit, &longs;ive deinde <expan abbr="&longs;ecundã">&longs;ecundam</expan> extrudat, &longs;ive non extrudat; quia &longs;tatim clau­<lb/>ditur fi&longs;tula; indeigitur vis motus extru&longs;ionis petenda e&longs;t, quod produca­<lb/>tur vis motus dupla, ac proinde prima vncia duplo velociore motu extru­<lb/>datur; igitur &longs;ubduplo tempore; igitur reliquo &longs;ubduplo &longs;ecunda vncia, <lb/>vel extrudatur eodem motu, vel extrudi po&longs;&longs;it, licèt non extrudatur; idem <lb/>dicendum de aëre immer&longs;o &longs;cy pho contento, in quem Cylindrus ea vi gra­<lb/>vitat, qua illum extruderet, &longs;i extrudi po&longs;&longs;et; eadem igitur e&longs;t vtrinque <lb/>ratio. </s></p><pb pagenum="97"/><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Quem porrò effectum ptædictailla gravitatio producat, non <lb/>video; cùm nec moveri, nec extrudi po&longs;&longs;it. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Manu ip&longs;a, &longs;cy phum illum ne fur&longs;um extrudatur immer&longs;um reti­<lb/>nente, vim illam, impul&longs;um illum, vel impetum, vel impre&longs;&longs;ionem &longs;entimus; <lb/>præterquam quod vis illa gravitantis aquæ comprimit aëra &longs;chypho con­<lb/>tentum. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Rectè; inde petitur ratio quorumdam fontium artefacto­<lb/>rum in quibus aër ab aqua compre&longs;&longs;us aliam aquam, cujus &longs;uperficiem <lb/>premit, &longs;ur&longs;um extrudit; &longs;i quis verò non aquam, &longs;ed Mercurium ad <lb/>comprimendum aëra adhibeat, longè major vis pre&longs;&longs;ionis &longs;equetur, & <lb/>longè altiùs aqua extrudetur; &longs;ed jam hæc trita &longs;unt; vnum tantùm ob&longs;er­<lb/>vo; hallucinari &longs;cilicet illum, qui in magno va&longs;e in aquas, iuxta prædi­<lb/>ctum modum immer&longs;o, vivere &longs;e po&longs;&longs;e credidit, & profundum maris &longs;cru­<lb/>tari; nempe aër in illo va&longs;e altè immer&longs;o vi&longs;upra gravitantis aquæ ita com­<lb/>primetur, vt ducendo halitui minimè aptus e&longs;&longs;et: immo ip&longs;e aër thorace <lb/>contentus & abdomine, ita comprimeretur, vt mu&longs;culi ducendo aëri &longs;er­<lb/>vientes, vix ad &longs;uam functionem habiles re&longs;tarent; &longs;ed quæ&longs;o re&longs;ume alia <lb/>capita, hoc enim tibi damus vltrò; &longs;cilicet corpus grave à levi deor&longs;um non <lb/>detrudi, &longs;ed &longs;ua &longs;ponte de&longs;cendere. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Hocip&longs;um e&longs;t, quod volo, nimirum, corpus grave tantùm &longs;ua <lb/>&longs;ponte deor&longs;um ire, & ab eo leve &longs;ubjectum extrudi. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> Licèt fatear corpus grave à levi deor&longs;um non detrudi, &longs;ed <lb/>&longs;ponte &longs;ua de&longs;cendere, non tamen propterea dare cogor, à gravibus de&longs;­<lb/>cendentibus, levia &longs;ur&longs;um extrudi, nam & gravia deor&longs;um, ac levia &longs;ur&longs;um <lb/>ire&longs;ua &longs;ponte cum Ari&longs;totele cen&longs;eo. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Fingamus &longs;altem, Chry&longs;ocome, corpus grave tantùm &longs;ua <lb/>&longs;ponte de&longs;cendere, præci&longs;a qualibet alia virtute, &longs;eu potentia, quæ <lb/>corpori levi in&longs;it; quæro ex te, vtrùm aliquid diver&longs;um ab eo, quod <lb/>modò apparet, in de&longs;cen&longs;u gravium, hoc po&longs;ito, futurum &longs;it, nihil pror­<lb/>&longs;us, lapis enim v.g.per medium aëra de&longs;cenderet, & &longs;ur&longs;um aëra extrude­<lb/>ret, cùm aliter de&longs;cendere non po&longs;&longs;it, idemque pror&longs;usfieret, quod modò <lb/>fieri videmus. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> Eadem ratio probat, corpus leue ea vi pollere, qua &longs;ur&longs;um fe­<lb/>ratur, quæ id probat, de corpore gravi; vt enim corpus grave ea pollet, vt <lb/>feratur in locum &longs;uum, versùs centrum Mundi, ita & leue, vt tendat in &longs;uum <lb/>ab eodem centro remotum, in hanc rem multos Ari&longs;totelis textus adducete <lb/>po&longs;&longs;em; &longs;ed fru&longs;tra, cùm Philo&longs;ophi mentem tibi per&longs;pectam e&longs;&longs;e non du­<lb/>bitem. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Quid quæ&longs;o corpori gravi cum Mundi centro? </s> <s>quid ab eo <lb/>loco commodi refert? </s> <s>cur igitur illud adeò appetit? </s> <s>corpus verò leve, <lb/>quid rixæ aut di&longs;&longs;idij habet cum illo centro? </s> <s>quid ab eo &longs;ibi timet? </s> <s>curillud <lb/>fugit, vt infe&longs;tum ho&longs;tem? </s> <s>Præterea &longs;i rectè memini, Stagirita ve&longs;ter lib. <lb/></s> <s>4. de Cœlo textu 39. expre&longs;sè dicit aëra deor&longs;um ferri, &longs;i aqua vel terra <lb/>&longs;ubtrahatur, non verò &longs;ur&longs;um, &longs;ubtracto illo corpore, cui &longs;ube&longs;t; & tamen <lb/>non minùs levis e&longs;t, quàm gravis, nec minor, vt dicis, illi virtus intrin-<pb pagenum="98"/>&longs;eca ine&longs;t, vt recedat à centro Mundi, quàm aquæ, vt ad illud accedat, <lb/>Denique, vt hoc vel obiter dicam, ad quem amabò finem huju&longs;modi cor­<lb/>porum lationes Natura de&longs;tinavit, ni&longs;i ad rectam Vniver&longs;i di&longs;po&longs;itionem? <lb/></s> <s>quod nec ip&longs;e Ari&longs;toteles vnquam negavit; atqui finis ille certò obtinetur, <lb/>modò graviora, quibus levia &longs;ub&longs;unt, deor&longs;um eant, & partes omnes <lb/>versùs idem centrum, cùm fieri non po&longs;&longs;it, vt graviora de&longs;cendant, ni&longs;i le­<lb/>viora &longs;ur&longs;um trudantur; Quod &longs;pectat ad <expan abbr="Ari&longs;totel&etilde;">Ari&longs;totelem</expan>, in lib.de Cœlo, multa <lb/>profectò habet, quæ cum veritate minùs con&longs;entiun; in iis præ&longs;ertim, quæ <lb/>&longs;crip&longs;it de motu locali; quòd enim Cœli &longs;int &longs;olidi; quòd &longs;tellæ nullum ha­<lb/>beant motum, præter motum primi Mobilis, quòd Mundus &longs;it ab æterno, <lb/>quòd Cœlum ortum non habuerit, nec corrumpi po&longs;&longs;it; quòd cuncta, quæ <lb/>ortumhabuerunt, &longs;int interitura, quòd duplo gravius duplo velociore <lb/>motu de&longs;cendat, quod Deus &longs;it Agens nece&longs;&longs;arium, aliaque huju&longs;modi, non <lb/>modò in iis Ari&longs;totelem non debemus &longs;equi, &longs;ed eidem apertè à nobis re­<lb/>pugnari, par e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Addo vnum, quod in re præ&longs;enti ponderandum e&longs;t, &longs;cilicet, non <lb/>agi hoc loco, vtrùm terra &longs;it ab&longs;olutè ac &longs;impliciter gravis, ignis verò ab&longs;o­<lb/>lutè & &longs;impliciter levis; de aqua & aëre tantùm &longs;ermo e&longs;t; vtrumque au­<lb/>tem ab&longs;olutè leve e&longs;&longs;e Philo&longs;ophus negat lib. </s> <s>4. de Cœlo text. </s> <s>27.ni fallor, <lb/>additque text. </s> <s>39. in &longs;uoloco pondus habere non levitatem; id pa&longs;&longs;im re­<lb/>petit aliis locis, & expre&longs;sè fatetur, præ&longs;ertim text. </s> <s>30.aëra gravem e&longs;&longs;e; <lb/>adde &longs;is, quod habet lib. </s> <s>3. text. </s> <s>10. grave nihil aliud e&longs;&longs;e, quàm den&longs;um, <lb/>& leve nihil aliud quàm rarum; Idem habet lib. </s> <s>4. Phy&longs;ic. </s> <s>cap. 9. item <lb/>lib. </s> <s>8. c. </s> <s>7. & alibi pa&longs;&longs;im. </s> <s>Non de&longs;unt etiam Autores cla&longs;&longs;ici præter At­<lb/>chimedem, & quotquot de Statica & innatantibus humido &longs;crip&longs;erunt, <lb/>quorum hac in re autoritas maximi &longs;anè momenti e&longs;t, vt Iavellus tract. </s> <s>1. <lb/>in 4. de Cœlo, cap. 3. concl. </s> <s>3. Cabeus Tom. </s> <s>4. Meteor. </s> <s>Tract. </s> <s>14. Ru­<lb/>vius lib.4.de Cœlo cap.6.quæ&longs;t. </s> <s>1.Bovius lib.3.Philo&longs;oph. </s> <s>p. </s> <s>221. & multi <lb/>alij, quosfacilè adducerem; &longs;ed vt jam dixi, ad rem præ&longs;entem hæc contro­<lb/>ver&longs;ia non &longs;pectat, &longs;atis enim mihi e&longs;t, &longs;i aër & aqua gravia &longs;int, &longs;altem &longs;e­<lb/>cundum quid; quid quid tandem &longs;it de levitate po&longs;itiva, qua levia &longs;ua &longs;ponte <lb/>fur&longs;um ferantur, quam vobis quæ&longs;tionem animi gratia di&longs;putandam relin­<lb/>quo; quantum enim ex iis, quæ hucu&longs;que à vobis dicta &longs;unt, alter eam ad­<lb/>ftruit, alter verò de&longs;truit. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocomus.<emph.end type="italics"/></s><s> Ita e&longs;t, illam ad&longs;truo, non &longs;anè quòd ratio à priori <lb/>me moveat; nullam enim e&longs;&longs;e, quæ hoc mihi certò per&longs;uadeat, vl­<lb/>tro fateor; &longs;ed qnia nonnulla &longs;unt experimenta, quæ id pror&longs;us <lb/>evincunt. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Huc volo te; refer quæ&longs;o illa experimenta, iis enim, &longs;i ta­<lb/>lia &longs;unt, & hoc &longs;anctè iuro, illico cedam & dabo manus. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/> primo quidem loco, &longs;it tubus vitreus, cuius altera extre­<lb/>mitas probè ob&longs;tructa &longs;it, altera verò aperta, infundatur aqua, non <lb/>tamen v&longs;que ad &longs;ummum, tum admoto pre&longs;sè digito, ne aqua effluat, <lb/>in<gap/>&longs;oque tubo, illa portio aëris, quæ in tubo reman&longs;it, &longs;ur-<pb pagenum="99"/>&longs;um fertur, non tamen &longs;ervata cylindri forma; licet enim ima portio cy­<lb/>lyndrica &longs;it, &longs;uperior tamen habet &longs;uperficiem qua&longs;i &longs;phæricam<gap/><lb/>&longs;eu &longs;phæroidalem, hanc porrò induit aër, vt qua&longs;i cuneatim aqua <lb/>perrumpat; propria igitur &longs;pontè; vi &longs;cilicet levitatis, qua <lb/>pollet. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Si primo no&longs;tro congre&longs;&longs;ui interfui&longs;&longs;es, Chry&longs;ocome, hoc <lb/>experimentum, dubio procul omni, minimè adduxi&longs;&longs;es, ob&longs;erva&longs;&longs;es <lb/>enim aquam &longs;ecundùm latera tubi &longs;piratim de&longs;cendere, & ab ea &longs;ur&longs;um <lb/>aëra extrudi, longè tardioremotu; quia &longs;ur&longs;um aër motu recto fertur, <lb/>aqua verò deor&longs;um, non recto, &longs;ed &longs;pirali, quo rectum acceleratum im­<lb/>peditum compen&longs;at; illud porro aëris fa&longs;tigium qua&longs;i cuneatum, non ab <lb/>aëre vi propria induitur, &longs;ed inducitur ab aquæ pondere versùs tubi late­<lb/>ra deflectente ad de&longs;cen&longs;um; alioquin &longs;i aër propria vi hanc figuram in­<lb/>duit, cur non conicam, quæ ad a&longs;cen&longs;um & aquam perrumpendam lon­<lb/>gè aptior e&longs;&longs;et; nec enim difficiliùs vnam quàm aliam indueret; immo <lb/>fortè conicam, quæ ad cylindricam propriùs accedit. </s> <s>Vtinam æquè <lb/>facile mihi e&longs;&longs;et, definire, quænam figura illa &longs;it, illiu&longs;que cau&longs;am <lb/>afferre, quam nemo, &longs;altem quod &longs;ciam, hucu&longs;que adinvenit; hîc <lb/>tuam operam, Antime; nec enim eum me reputo<gap/>, qui hunc nodum <lb/>&longs;olvam. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Non e&longs;t mihi dubium, quin hæc &longs;uperficies curva ab aqua ver­<lb/>sùs latera va&longs;isinclinante formetur; cùm enim aqua de&longs;cendere non po&longs;&longs;it, <lb/>ni&longs;i aër loco cedat, extru&longs;us &longs;cilicet ab aqua, & hic &longs;ur&longs;um extrudi non <lb/>po&longs;&longs;it, ni&longs;i humor illi &longs;e&longs;e &longs;upponat, vt hoc faciat, eundem aëra qua&longs;i <lb/>complexa per tubi latera &longs;piratim de&longs;cendit. </s> <s>An verò dicta &longs;uperficies pa­<lb/>rabolica &longs;it, dubium e&longs;t; cum enim aqua versùs latera va&longs;is tendat, &longs;imul <lb/>& deor&longs;um motu accelerato, inde re&longs;ultas motus mixtus, qui lineam pa­<lb/>rabolicam po&longs;t &longs;e relinquit, vt jam alij demon&longs;trarunt; &longs;ed vnde erit mo­<lb/>tus ille horizontalis cum perpendiculari conjunctus? </s> <s>an fortè dicendum <lb/>e&longs;t, aquam &longs;piratim de&longs;cendere, cœpta qua&longs;i à centro &longs;pira; donec ad <lb/>latera va&longs;is perveniat; ab illa autem &longs;pira deor&longs;um producta &longs;upremum <lb/>illud aëris fa&longs;tigium tornari, cùm aliter &longs;piræ deor&longs;um produci non po&longs;­<lb/>&longs;int: &longs;ed his omi&longs;&longs;is, cùm cylindrus aëris ab aqua &longs;tringatur, per latera <lb/>delabente, tantulùm a&longs;&longs;urgat, nece&longs;&longs;e e&longs;t; vnde aqua, cui &longs;uprema illius <lb/>ba&longs;is &longs;ube&longs;t, cedit locum; & cùm hæc attolli non po&longs;&longs;it, versùs latera <lb/>cat oportet, vbi dumtaxat ei locus patet; &longs;cilicet inter aëra & late­<lb/>ra va&longs;is, vnde linea parabolica re&longs;ultat; hinc &longs;i tubus &longs;it angu&longs;tior, vix <lb/>aqua cylindrum inter aëris & latera tubi intercipi pote&longs;t; vnde prædicta <lb/>&longs;upremi fa&longs;tigijforma non &longs;equitur, quæ certè minùs convexa e&longs;t, &longs;eu <lb/>acuta, quò rima inter aëra & latera va&longs;is, qua perrumpitaqua, e&longs;t angu­<lb/>&longs;tior: immo &longs;i tubus inclinetur, convexitas prædicti fa&longs;tigij deor&longs;um ver­<lb/>sùs in&longs;eriùs tubi inclinati latus producitur; quia eò major ponderis aquæ <lb/>vis fertur, ex quo etiam manife&longs;tè colligitur, hanc convexi fa­<lb/>&longs;tigij figuram ab aqua versùs latera va&longs;is labente tornari. </s> <s>Porrò ne&longs;cio an <pb pagenum="100"/>vllus ob&longs;ervarit, quando minor e&longs;t aëris portio, tornari etiam & <lb/>turbinari inferiorem aëris ba&longs;im, qua&longs;i ad in&longs;tar lentis, i<gap/>no &longs;i adhuc <lb/>m<gap/>or &longs;it, ad in&longs;tar rotundæ gemmæ apparet; an fortè quia hæc figu­<lb/>ra ab aqua ambiente inducitur, cùm inter omnes &longs;implici&longs;&longs; ma &longs;it, & <lb/>inter æquales minimam &longs;uperficiem habeat; &longs;ed hæc tantulum figuræ de­<lb/>&longs;iderant. </s></p><figure></figure><p type="main"> <s>Sit tubus AD vitreus, plenus aqua, excepta por­<lb/>tone aëris, quæ &longs;i innataret occuparet cylindrum <lb/>FG; primùm ita re&longs;tringitur, vt ba&longs;is diameter &longs;it <lb/>TV, occupante aqua Spatia HTGV, ex cujus <lb/>lap&longs;u, cùm duo corpora &longs;e&longs;e penetrare non po&longs;lint, <lb/>cylindrum aëris re&longs;tringi ac turbinari versùs K, vbi <lb/>labens aqua versùs & &longs;ecus latera, locum illi cedit <lb/>pror&longs;us nece&longs;&longs;e e&longs;t: cùm <expan abbr="aut&etilde;">autem</expan> aqua per &longs;patia HTGV <lb/>de&longs;cendens &longs;piratim, præ impetu, in aquam conten­<lb/>tam cylindri portione CE altè &longs;ubeat, &longs;uperficies <lb/>aquæ FE nece&longs;&longs;ariò attollitur; vnde portionem aë­<lb/>ris I &longs;ur&longs;um extrudi, nece&longs;&longs;e e&longs;t; idque &longs;en&longs;im, in <lb/>proportione a&longs;&longs;ignabili; detracto enim cylindro &longs;ub <lb/>ba&longs;i TV, ex cylindro FG, vt re&longs;iduum ad cylin­<lb/>drum FG, ita motus ba&longs;is TV ad motum aquæ la­<lb/>bentis per &longs;patia HTGV, præ&longs;cindendo à &longs;pira. <lb/></s> <s>Iam verò &longs;it cylindrus aëris OM minor priore; at­<lb/>tollitur quidem in X, & cum aqua lap&longs;a versùs N refle ctatur à lateribus <lb/>tubi, &longs;tatimque cum aqua inferiore mi&longs;ceatur, ita vt per &longs;piram integram <lb/>minimè de&longs;cendat, qua&longs;i tondet marginem inferioris ba&longs;is cylindruli aë­<lb/>ris, eamque in &longs;uperficiem <expan abbr="convexã">convexam</expan> NPM facilè tornat; Porrò ab illa &longs;pira <lb/>non integra labentis aquæ, lens aëris extru&longs;a &longs;ur&longs;um, huc illuc libratur <lb/>cundo, quia cùm modò hinc, modò illinc labens aqua &longs;e&longs;e &longs;ubjiciat aëri, <lb/>quid mirum, &longs;i prædicta libratio, &longs;eu tremor quidam con&longs;equatur: <lb/>quod etiam accidit in cylindrulis aëris minoribus, propter eandem <lb/>rationem; in majoribus enim de&longs;cendens aqua cum majore impetu <lb/>aliam aquam &longs;ubit, vnde hæc &longs;ecundùm Planum horizontale &longs;en&longs;im at­<lb/>tollitur. </s></p><figure></figure><p type="main"> <s>Sit demum tubus AC in &longs;itu inclinato, cylindrus <lb/>aëris EH ita conformatur, vt convexitas MFN multo <lb/>longiùs producatur, quàm connexitas ME; nempe <lb/>aqua gravior in latus inferius CB inclinat & versùs <lb/>punctum Hlateris inferioris CB de&longs;inunt &longs;piræ, quod ad <lb/>oculum patet. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Ex iis omnibus manife&longs;tum fit, aëra <lb/>&longs;ur&longs;um ab aqua extrudi, non verò &longs;ua &longs;ponte ire; <lb/>alioquin cur illæ &longs;piræ? </s> <s>aut illa parabola? </s> <s>cur ini­<lb/>tio a&longs;cen&longs;us, cylindri aërei fa&longs;tigium à Plano pa-<pb pagenum="101"/>rum di&longs;tat? </s> <s>cur &longs;i aëris portio modica &longs;it, etiam ima ba&longs;is convexa e&longs;t? <lb/></s> <s>c<gap/>r major aëris portio tardiùs, minor citiùs a&longs;cendit? </s> <s>imò &longs;i <expan abbr="id&etilde;">idem</expan> tubus inæ­<lb/>qualis &longs;it, per &longs;egmentum angu&longs;tius tardiùs aër incedit, citiùs per laxius; <lb/>quia in angu&longs;tiore aër in longiorem cylindrum producitur; cur ille tre­<lb/>mulus motus Lentium aëris? </s> <s>Cur figura Lentis, non Sphæræ? </s> <s>cur in tubo in­<lb/>clinato longior e&longs;t convexitas aëris versùs latus interius, versùs &longs;uperius, <lb/>brevior. </s> <s>Cuncta hæc explicari non po&longs;&longs;unt, &longs;i aër &longs;ur&longs;um &longs;ua &longs;ponte a&longs;cen­<lb/>dit; &longs;cire tamen velim, cur eadem aëris portio in tubo angu&longs;tiore tardiùs, <lb/>in laxiore citiùs a&longs;cendat. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Miror à te rationem non videri; in angu&longs;tiore tubo aëris por­<lb/>tio in cylindrum longiorem formatur; igitur aqua per latera de&longs;cen­<lb/>dens longius &longs;patium decurrere debet, antequam cum aqua inferiore <lb/>conjungatur, & aëra fur&longs;um extrudat; igitur in eo plus temporis <lb/>ponit. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Satis e&longs;t, rem intelligo, vnde etiam per&longs;picua ratio ducitur, <lb/>cur modica portio aëris in eodem tubo citiùs a&longs;cendat, quàm major, quia <lb/>hæc in longiorem cylindrum extenditur; quid mitum ergo, &longs;i tardiùs a&longs;­<lb/>cendat? </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Infunde, quæ&longs;o te, in tubum aliquid olei; multa enim vi­<lb/>debis, quæ tibi fortè oppo&longs;itum per&longs;uadeant: primo enim oleum tar­<lb/>diùs a&longs;&longs;urgit, quia longè gravius e&longs;t aëre. </s> <s>Secundo eandem figuram induit <lb/>quam Aër, tertio Aëris cylindrus per medium oleum citi&longs;&longs;imè &longs;ur&longs;um per­<lb/>rumpit: quartò Aër nonnunquam oleum &longs;ecum longè citiùs rapit, quàm <lb/>Oleum per &longs;eip&longs;um a&longs;&longs;urgeret; nihil horum explicari pote&longs;t, ni&longs;i dicamus, <lb/>aëra &longs;ur&longs;um &longs;ua &longs;ponte ferri. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Immo nihil horum explicari pote&longs;t, &longs;i hoc dicamus; primò <lb/>igitur Aër citiùs fertur, tardiùs Oleum, cæteris paribus quia aliquando <lb/>accidit, vt modica olei portio &longs;ur&longs;um citiùs avolet; tar diùs aurem æqua­<lb/>lis portio; quia minus e&longs;t aquæ momentum adversùs gravitatem, &longs;eu pon­<lb/>dus olei, & majus adversùs pondus aëris. </s> <s>Secundo de figura nihil adden­<lb/>dum e&longs;&longs;e puto; ni&longs;i quòd inferior ba&longs;is ni&longs;i longior &longs;it olei cylindras, con­<lb/>vexa e&longs;t. </s> <s>Tertio vbi aëris cylindrus ad cylindrum aëris pervenit, &longs;tatim <lb/>de&longs;cendit Oleum, in libero &longs;cilicet aëre, & ab aquæ lap&longs;u circumagitur <lb/>in mille orbes & &longs;piras; & verò Oleum in aëre po&longs;itum &longs;ua &longs;ponte citò <lb/>de&longs;cendere, mirum non e&longs;t. </s> <s>Qiarto Aëris bulla aliquando &longs;upremo cylin­<lb/>dro olei adhæret, & tunc citiùs a&longs;&longs;urgit; quia &longs;cilicet totum illud per <lb/>modum vnius attollitur; neque in hoc e&longs;t difficultas; Supponamus enim, <lb/>e&longs;&longs;e vnciam aëris, & vnciam olei; certè major e&longs;t proportio momenti <lb/>duarum vnciarum aquæ adversùs pondus aggregati, ex vna vncia <lb/>olei, & vna aëris, quàm vnius vnciæ aquæ, adver&longs;us vnam <lb/>Olei; nec ob&longs;tar aggregatum illud e&longs;&longs;e gravius alterutro; quia in <lb/>comparatione duorum gravium, æqualis &longs;emper vtriu&longs;que exten&longs;io, <lb/>&longs;eu moles accipitur. </s> <s>Sed hæc &longs;unt facilia, nec in his explicandis tua <lb/>opera indigeo, Antime; in his tamen non dubito, quin alia multa à <pb pagenum="102"/>te ob&longs;ervata fuerint, quæ quia præ&longs;entis in&longs;tituti non &longs;unt, à te non po­<lb/>&longs;tulo. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Negare non po&longs;&longs;um, quin multa mihi &longs;uppetant in hac ma­<lb/>teria, quæ tamen quia à propo&longs;ito argumento aliena &longs;unt, in alium lo­<lb/>cum tractanda & exponenda remitto. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Vnde igitur motus levium &longs;ur&longs;um acceleratus? </s> <s>quòd certè <lb/>in diver&longs;is globulis aqua levioribus probatum e&longs;t; immo in aëris cylindro <lb/>per tubum a&longs;&longs;urgente, per&longs;picuè videtur; itemque in cylindro ligneo, per <lb/>vim ad fundum latioris va&longs;is vel putei detento, qui &longs;ur&longs;um ita erumpit, <lb/>vt longè altiùs a&longs;cendat; etiam &longs;i in imo va&longs;is fundo foramen &longs;it. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Ita e&longs;t; ii globuli motu accelerato a&longs;cendunt, diver&longs;o tamen <lb/>à gravium motu; Supponimus enim liberum &longs;patium in ampli&longs;&longs;imo va&longs;e <lb/>aqua pleno, ex quo leviora corpora, per mediam aquam a&longs;cendunt; v.g. <lb/></s> <s>cylindrus ligneus motu accelerato non quidem &longs;ponte, &longs;ed impre&longs;&longs;o ab <lb/>aqua extrudente; nempe impetus initio productus durat deinde; quid <lb/>mitum ergo, &longs;i motus inde acceleratus evadat? </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Igitur ad in&longs;tar gravium e&longs;&longs;et acceleratus, quod tamen <lb/>omnibus experimentis repugnat; </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/> Æqualibus temporibus, æqualia velocitatis momenta non <lb/>accedunt, vt fit in motu gravium, &longs;ed minora &longs;emper & minora, priùs ta­<lb/>men acqui&longs;itis &longs;emper remanentibus; an fortè vt in de&longs;cen&longs;u fune­<lb/>penduli? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Minimè verò; cùmenim velocitates &longs;int vt motus, & hi in <lb/>&longs;ubduplicata altitudinum vt &longs;upra demon&longs;tratum e&longs;t. </s></p><p type="main"> <s>Sit &longs;emiparabola ABC, &longs;patium <lb/>acqui&longs;itum motu naturaliter acce­<lb/><figure id="fig15"></figure><lb/>lerato erir AB, velocitas verò ac­<lb/>qui&longs;ita &ecedil;rit BC; &longs;it etiam AB altitu­<lb/>do aquæ, intra quam corpus leve <lb/>per vim intruditur & ex qua, præ­<lb/>valente eju&longs;dem aquæ pondere &longs;ur­<lb/>&longs;um deinde extruditur; &longs;it ergo BH <lb/>æqualis BA item IN æqualis IH <lb/>&longs;itque alia &longs;emiparabola NKC ita <lb/>vt CI &longs;it Axi parallela; erit motus <lb/>corporis levis initio extru&longs;ionis vt <lb/>BC emen&longs;a verò tota aquæ altitu­<lb/>dine erit vt HN: nempe vt ab A <lb/>ad B acquiritur velocitas BC, & in <lb/>patio DB &longs;upra DE jam acqui&longs;i­<lb/>tam in &longs;patio AD, acquiritur EG; ita in BH acquiritur IN &longs;upra jam <lb/>acqui&longs;itam BC, & vt in DB acquiritur EG ita in BL acquiritur MK <lb/>æqualis EG; denique vt in AD acquiritur DE ita in LH acquiritur ON. <lb/></s> <s>Sed quid de foramine in fundo va&longs;is aperto, cujus &longs;upra Chry&longs;ocomus <lb/>meminit? </s></p><pb pagenum="103"/><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> De re mihi non con&longs;tat, nunquam enim hoc à me ob&longs;erva­<lb/>tum e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Omninò di&longs;tinguendum e&longs;t; &longs;i enim tale e&longs;t, vt tantumdem <lb/>aquæ per illud effluat, quantum infra cylindrum de&longs;cendit; cylindrus <lb/>erit immobilis; &longs;i minùs de&longs;cendat, quàm effluat, cylindrus ip&longs;e, &longs;i de­<lb/>&longs;cendere pote&longs;t, de&longs;cendet; &longs;i verò plus aquæ de&longs;cendat, quàm ex fora­<lb/>mine effluat, tantulùm cylindrus a&longs;&longs;urgit. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Hoc ip&longs;um per&longs;picuè probat, corpus leve non attolli &longs;ua <lb/>&longs;ponte; quod enim gravius deor&longs;um de&longs;cendat, non impedit, quò minùs <lb/>leve &longs;ua &longs;ponte a&longs;cendat: &longs;ed accipe luculentum experimentum, iis ta­<lb/>men &longs;imile, quæ jam expo&longs;ita fuere. </s> <s>Sit pixis quælibet, in cujus fundo he­<lb/>mi&longs;phærium, vel minor Sphæræ portio accuratè & affabrè ita excavetur, <lb/>vt Sphæram ligneam omninò capiat, nulla relicta intercapedine; tum <lb/>pixis impleatur aqua; Sphærula lignea, quamvis levior, nullo modo a&longs;­<lb/>cendit; quia &longs;cilicet cum aqua in cavitatem illam &longs;ubire non po&longs;&longs;it, ab ea <lb/>Sphæra &longs;ursùm extrudi non pote&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Dicerem non a&longs;&longs;urgere Sphæram, ne detur vacuum; idem <lb/>enim fieri videmus, &longs;i duo plana probè congruant. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Hoc dictum iri &longs;ciebam; &longs;ed fiat foramen in medio cavita­<lb/>tis, quò &longs;cilicet aër ambiens facile &longs;ubeat, non propterea Sphærula a&longs;cen­<lb/>dit, licèt nullum re&longs;tet vacui periculum: per vos etiam mihi liceat, hic <lb/>obiter, ea &longs;altem indicare, quæ tuam illam &longs;ententiam, Chry&longs;ocome, om­<lb/>ninò expugnare videntur. </s> <s>1. Quandoquidem per vnum principium <lb/>motus cuncta explicari po&longs;&longs;unt, quo &longs;cilicet corpus grave &longs;ua &longs;ponte <lb/>deor&longs;um fertur, quod inficiatur nemo, & leve &longs;ur&longs;um extrudi pote&longs;t, <lb/>fru&longs;tra ponitur aliud principium: Hæc ratio, licèt commnnis &longs;it, maximi <lb/>&longs;anè momenti e&longs;t. </s> <s>Secundò, cùm ab eodem centro multæ lineæ ducantur, <lb/>fi corpus levi&longs;&longs;imum ef&longs;et, in centro, non po&longs;&longs;et vllo modo a&longs;&longs;urgere; cur <lb/>enim potiùs per vnam lineam quam per aliam? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Facilè retorqueo argumentum, nec enim pariter &longs;ur&longs;um ex­<lb/>trudi po&longs;&longs;et; cur enim potiùs per vnam lineam quàm per aliam? </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Hoc quidem verum e&longs;t, modò ambiens gravius æqualis e&longs;&longs;e<gap/><lb/>momenti; per omnes lineas; &longs;ed hoc per accidens; illud autem per &longs;e <gap/><lb/>præterea, linea motus recti à termino, ad quem determinatur; cùm au­<lb/>tem vnum centrum &longs;it, a&longs;&longs;umpto quolibet quncto extra centrum, ab illo <lb/>ad centrum vnica tantùm linea ducitur, cùm tamen ab eodem, plures ad <lb/>periphætiam duci po&longs;&longs;int; vna quidem producta ad centrum; &longs;ed quomo­<lb/>do à centro determinatur hæc linea, quod neque &longs;it terminus ad quem, <lb/>nec terminus à quo illius motus? </s> <s>Tertiò non pote&longs;t idem corpus in par­<lb/>tes oppo&longs;itas &longs;imul move<gap/>i; igitur nec &longs;imul conniti, &longs;cilicet ab intrin&longs;e­<lb/>co; quod vt meliùs in telligatur, &longs;it vas aqua plenum, &longs;itque pondus aquæ <lb/>40. libr. </s> <s>Sit fru&longs;tum ligni in fundo va&longs;is retentum pendens 5.libr. </s> <s>appen­<lb/>datur &longs;imul vtrumque, &longs;u&longs;tinebitur à 45. libris po&longs;itis in altera lance li­<lb/>bræ, eritque æquilibrium, &longs;tatimque impedimento &longs;ublato, lignum emer­<lb/>git, &longs;ur&longs;umque attollitur eodem pror&longs;us æquilibrio manente; igitur hic <pb pagenum="104"/>motus &longs;ur&longs;um non e&longs;t ab intrin&longs;eco; vt patet, &longs;u&longs;tinetur ab aqua, inquies; <lb/>rectè, ergo &longs;eip&longs;um lignum non &longs;u&longs;tinet; igitur multò minùs &longs;e movet. <lb/></s> <s>Omitto innumera ferè experimenta, quæ rem hanc penitùs evincunt; &longs;ed <lb/>ne in Parergum prolixius abeamus, cœptam di&longs;putationem à te re&longs;umi <lb/>velim, Antime, præ&longs;ertim cùm hæc ad rem præ&longs;entem parùm faciant, <lb/>modò enim aër gravis &longs;it, hoc tibi &longs;atis e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Vt igitur partes omnes terre&longs;tris globi versùs commune cen­<lb/>trum nituntur, ita etiam partes aëris ambientis: Sed cùm aër &longs;ive purior, <lb/>&longs;ive impurior, nam perinde e&longs;t, ambiat etiam alios totales globos, putà <lb/>Lunam, globum enim totalem appello illum, qui alterius pars non e&longs;t, & <lb/>&longs;eor&longs;im po&longs;itus manet, medium quoddam commune dici pote&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Et cùm &longs;inguli globi totales &longs;uo centro gaudeant, versùs <lb/>quod omnes illorum partes connituntur; hæc enim veri&longs;&longs;ima e&longs;t ratio, <lb/>qua totales globi tornari, & figuram obtentam &longs;ervare po&longs;&longs;unt, aëris <lb/>etiam, &longs;eu communis medij ambientis portio, versùs illos globos gravitat, <lb/>&longs;eu nititur. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Rectè omninò; cùm enim medium commune tot v&longs;ibus nece&longs;­<lb/>&longs;arium &longs;it, non minùs pertinet ad vnum globum, quàm ad alium; vnde <lb/>rationiac rerum naturæ con&longs;entaneum e&longs;&longs;e videtur, vt versùs vtrumque <lb/>gravitet; quota verò pars versùs vnum, & quota versùs alium, non diffi­<lb/>cilè definiri pote&longs;t. </s></p><figure></figure><p type="main"> <s>Sit enim centrum A terre&longs;tris globi CBED, &longs;it centrum Lunæ I, du­<lb/>catur recta AI, connectens <expan abbr="vtrumq;">vtrumque</expan> <expan abbr="centrũ">centrum</expan>; con&longs;ideretur BK vt cylindrus <pb pagenum="105"/>aëris, cujus pars versùs A, & pars versùs I gravitet, tribus modis definiri <lb/>pote&longs;t hujus cylindri portio, quæ versùs A, & ea; quæ versùs I gravitar; <lb/>Primo divi&longs;a AI bifariam in F; & &longs;ic FK gravitat versùs I & FB versùs A. <lb/></s> <s>Secundo divi&longs;a bifariam BK in M, & &longs;ic BM versùs A, & MK <lb/>versùs I. gravitat. </s> <s>Tertiò ita divi&longs;a AI vt &longs;egmentum gravitans ver­<lb/>sùs A, &longs;it ad aliud gravitans versùs I, vt globus A ad globum I. <lb/></s> <s>Quartus modus addi pote&longs;t, vt &longs;cilicet BK &longs;ecetur juxta dictam propor­<lb/>tio nem globorum. </s> <s>Quidquid autem ex his dicatur, ad rem no&longs;tram perinde <lb/>e&longs;t; quare majoris facilitatis gratia, primum modum accipio, & per punctum <lb/>F duco GFH per pendiculariter, quæ vocetur dirimens connectentem <lb/>centra, &longs;eulinea confinium. </s> <s>Quod dixi de AF, IF, de AN, IN dictum e&longs;to, <lb/>item dereliquis lineis, &longs;eu cylindris. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Multis &longs;anè, præ&longs;ertim Peripateticis, hæc tua doctrina mi­<lb/>nimè probabitur, qui juxta mentem Philo&longs;ophi docent, centrum terræ <lb/>idem e&longs;&longs;e cum centro Vniver&longs;i, versùs quod omnia gravia tendunt; nega­<lb/>bunt igitur portionem aëris &longs;upra dirimentem GH, versùs Lunæ cen­<lb/>trum gravitare. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Videtur quidem Stagirita hoc ip&longs;um, quod dicis ad &longs;truere; præ­<lb/>&longs;ertim lib.2. de cœlo text. </s> <s>100. <emph type="italics"/>Accidit autem,<emph.end type="italics"/> inquit, <emph type="italics"/>idem terræ medium <lb/>e&longs;&longs;e, ac Vniver&longs;i,<emph.end type="italics"/> &longs;ed vt terræ centrum e&longs;t, in id ferri per accidens; per &longs;e <lb/>verò ad centrum Vniver&longs;i; de hoc tamen lib. </s> <s>3. text.33. dubitare videtur; <lb/>vbi enim dixi&longs;&longs;et, quidquid pondus habet, ferri ad medium, &longs;eu versùs <lb/>centrum, &longs;tatim &longs;ubdit hæc: <emph type="italics"/>vtrùm autem ad terræ medium, an Vniver&longs;i <lb/>feratur, cùm idem medium &longs;it ip&longs;orum, alia ratio e&longs;t.<emph.end type="italics"/> Cùm autem Ari&longs;toteles <lb/>cœlos &longs;olidos po&longs;uerit, & Sphæiam ignis aëre &longs;uperiorem, & quintam <lb/>e&longs;&longs;entiam, quam animatam e&longs;&longs;e indicare videtur, quid mirum, cùm ele­<lb/>menta no&longs;tra, juxta illum, vltra concavum Lunæ non extendantur, & &longs;uis <lb/>orbibus &longs;olidis &longs;olidi Planetæ affixi &longs;int, nihil vltra prorsùs gravitare aut <lb/>levitare, ac proinde gravium & levium commune centrum in Mundi & <lb/>Terræ centro collocavit. </s> <s>Si tamen cœlum e&longs;&longs;e fluidum puta&longs;&longs;et, & cœ­<lb/>le&longs;tes Sphæras in illo communi medio moveri, & &longs;uos agere orbes; &longs;i <lb/>Cometas de novo gigni & mori in ætherea regione, nec non faculas & <lb/>maculas in Solis di&longs;co. </s> <s>Martem propiùs ad terras nonnunquam accedere <lb/>quàm Solem; novas Stellas in Cœlo na&longs;ci; &longs;i demùm alia multa, quæ <lb/>jam ex ob&longs;ervationibus comperta &longs;unt, &longs;civi&longs;&longs;et, non e&longs;t dubium, quin alia <lb/>de Cœlo & Vniver&longs;i con&longs;tructione &longs;crip&longs;i&longs;&longs;et; quanquam cum Ari&longs;totele <lb/>Dico centrum terræ Vniver&longs;i centrum e&longs;&longs;e, circa quod cœle&longs;tes Sphæræ <lb/>&longs;uos orbes agunt, versùs quod illa omnia gravia tendunt, &longs;ublunaria &longs;ci­<lb/>licet, quæ Ari&longs;toteles agnovit; &longs;ed cùm hoc commune medium vltra <lb/>extendatur, & eadem ratione pro formatione & con&longs;ervatione militet <lb/>in aliis globis; tot pono centra, in quæ partes circumpo&longs;itæ nituntur, <lb/>quot &longs;unt globi totales; gravitas enim non totius, &longs;ed partium proprieta<gap/><lb/>e&longs;t, cujus vi quælibet pars versùs &longs;uum centrum nititur, & contranititur, <lb/>ne ab eo &longs;eparetut, & &longs;i vnquam ab eo &longs;eparetur, in illud denuò &longs;e reci­<lb/>pit. <gap/> ad conmmne medium &longs;pectat, illius po<gap/>tio <gap/><pb pagenum="106"/>globum tendit, quæ &longs;cilicet propior e&longs;t, &longs;i quis autem ab&longs;olutè hoc neget, <lb/>(quanquam non video cur ab&longs;olutè non po&longs;&longs;it ad&longs;trui) permittat &longs;altem <lb/>hoc à me &longs;upponi, & ex illa hypothe&longs;i, ratiocinando, di&longs;cutere, quid ex <lb/>illa &longs;equatur, & hæc qua&longs;i dicta ex hypothe&longs;i accipiat. </s></p><p type="main"> <s><emph type="italics"/>Auguftin.<emph.end type="italics"/></s><s> Quintam illam e&longs;&longs;entiam in cœlis nunquam probavi; cùm <lb/>cœle&longs;tia corpora ex no&longs;tris elementis conflata e&longs;&longs;e communis &longs;it apud <lb/>Sanctos Patres &longs;ententia, quos vide&longs;is apud Scheinerum, Ricciolum, Ce­<lb/>ladam &c. </s> <s>immo Beda expre&longs;&longs;is verbis a&longs;&longs;erit, <emph type="italics"/>a<gap/>hera e&longs;&longs;e &longs;uperius aëris <lb/>&longs;patium in quo &longs;idera ferri perhibentur.<emph.end type="italics"/></s><s> In his autem, &longs;acræ Scripturæ &longs;an­<lb/>cti&longs;que Interpretibus &longs;tandum potiùs e&longs;&longs;e duxerim; quam Petipateticis. <lb/></s> <s>Porrò ex &longs;uppo&longs;itione, quod cœle&longs;tia corpora ex no&longs;tris elementis con­<lb/>&longs;tent, de quo po&longs;t novas ob&longs;ervationes dubitari nequit; non video, quo­<lb/>modo &longs;alvariomnia po&longs;&longs;int, ni&longs;i <expan abbr="prædictã">prædictam</expan> hypothe&longs;im ab&longs;olutè &longs;tatuamus; <lb/>itavt &longs;inguli globi totales &longs;uum &longs;ingulate centrum habeant, versùs quod <lb/>partes omnes eju&longs;dem globi connituntur, cum illa communis medij, <lb/>aëris &longs;cilicet portione, quæ ad illud propiùs accedit, quàm ad <lb/>aliud; centrum verò terræ, præter illam centri rationem, quæ illi <lb/>cum aliis globis communis e&longs;t, habet aliam rationem, quæ illi <lb/>dumtaxat competit, centri &longs;cilicet Vniver&longs;i, quod certè terre­<lb/>&longs;tri globo &longs;ingulare e&longs;t cui reliqui globi &longs;erviunt; nam propter ho­<lb/>mines terre&longs;tris globi incolas totum corporeum mundum Deus condidit, <lb/>nec aliis globis res viventes in&longs;unt, etiam, vt vocant, vegetantium vita, <lb/>nihil enim hæc ad terræincolas conferre po&longs;&longs;ent, vt patet; & quidquid <lb/>&longs;uper his ad&longs;truitur, fictitium e&longs;t, & merum commentum; hinc circa ter­<lb/>ram immobilem eunt cœle&longs;tes &longs;phæræ, eidem famulantes; vel diffu&longs;a luce, <lb/>vt <gap/>ol, vel eadem repercu&longs;&longs;a, vt reliqui Planetæ, & &longs;tellæ veri&longs;imiliùs; adde <lb/>quod diver&longs;is variorum motuum periodis tempora &longs;ignant, vt &longs;tellæ <lb/>fixæ loca, propter invariabilem, quem inter &longs;e habent ordinem; &longs;ed quæ­<lb/>&longs;o, perge, hæc à te &longs;uppo&longs;ita libenter admitto, etiam citra maris <lb/>æ&longs;tum. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Secundo loco &longs;uppono, corpus liquidum, humidum, voca <lb/>vt voles, &longs;i ab omni parte æqualini&longs;u prematur, figuram &longs;phæricam in­<lb/>duere; cùm enim corpori humido v. </s> <s>g aquæ figura va&longs;is facilè inducatur, <lb/>nempe humidum terminis alienis facilè continetur, certè &longs;i æqualiter ab <lb/>omni parte prematur, nulla e&longs;t ratio, cur potiùs hinc cedat, quàm illinc; inde <lb/>igitur nece&longs;&longs;ariò figura &longs;phærica &longs;equitur: &longs;i verò minùs ab vna parte, quàm <lb/>ab aliis, reliquæ haud dubiè prævalent, ac proinde hæc tantulum cedat & <lb/>attollatur, nece&longs;&longs;e e&longs;t; In his, quæ per&longs;picua &longs;unt, diutiùs non hæreo. </s></p><p type="main"> <s>Tertiò &longs;uppono corpus liquidum, cui corpus grave admixtum e&longs;t, inde <lb/>graviùs effici; &longs;ic aqua, cui&longs;al admixtum e&longs;t, gravior evadit, item aër <lb/>gravior, &longs;i multæ humoris particulæ, vt fit in nebula, admi&longs;ceantur; in <lb/>hoc etiam nulla e&longs;t difficultas. </s> <s>His &longs;uppo&longs;itis, ad marinum æ&longs;tum explican­<lb/>dum venio; & varias a&longs;&longs;ertiones ad&longs;truo ex iactis principiis deductas. </s> <s>Sit <lb/>terra in A, vt dixi, & Luna in I, cum reliquo apparatu, vt &longs;upra, totus <pb pagenum="107"/><gap/>èr infra lineam GFH, &longs;uppo&longs;ito v<gap/>que globo immobili, gravitat ver­<lb/>sùs centrum A; totus aër &longs;upra GH, gravitat v<gap/>sùs I; hic enim propriùs <lb/>accedit ad I, quàm ad A; ille verò propiùs ad A, quàm ad I. </s> <s>Prætereà <lb/>linea FB e&longs;t minor NV: itemque illæ minores, quæ propiùs accedunt <lb/>ad FB; &longs;upponantur infinitæ, hinc inde, quarum maxima erit ES paral­<lb/>lela dirimenti GH cum oppo&longs;ita æquali ZC: cùm autem prædictæ lineæ <lb/>&longs;int totidem cylindri aëris gravitantis, haud dubiè gravitatio inæqualis e&longs;t, <lb/>& con&longs;equenter pre&longs;&longs;io; igitur &longs;i &longs;upponatur globus totus aqueus, &longs;altem <lb/>quo ad&longs;uperficiem, &longs;eu corticem exteriorem ex dicta pre&longs;&longs;ione inæquali, <lb/>&longs;equitur figuræ &longs;pæricæ mutatio; & cùm ES, CZ &longs;int omnium maximæ <lb/>in punctis E & C, maximum e&longs;t pre&longs;&longs;ionis momentum; igitur deprimun­<lb/>tur C & E in Q & I v. </s> <s>g. </s> <s>igitur attollitur B in P, punctum enim B, in quo <lb/>e&longs;t minimum pre&longs;&longs;ionis momentum, prævalentibus aliis, tantulùm attolli <lb/>nece&longs;&longs;e e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Quàm magnum mihi campum aperis; pudet me, hæc priùs <lb/>non cogita&longs;&longs;e; tam facilia, tam obvia, tam trita & communia: fac quæ&longs;o <lb/>circulum DCBE volvi circa axem BD, punctum X de&longs;cribit circulum, <lb/>cujus radius e&longs;t XB, in cujus tota peripheria fit æqualis pre&longs;&longs;io, &longs;cilicet <lb/>vt XO, quæ e&longs;t major BF; item C de&longs;cribet peripheriam circuli radio <lb/>CA, in qua tota e&longs;t æqualis pre&longs;&longs;io, &longs;ed longè major, quàm in priore; <lb/>tum quia circulus major premitur, tum quia in &longs;ingulis punctis major e&longs;t <lb/>pre&longs;&longs;io; in &longs;ingulis verò punctis inter CD, circuli pre&longs;&longs;ionum minores <lb/>&longs;unt; quilibet &longs;cilicet &longs;ub &longs;inu recto; cùm autem pre&longs;&longs;iones &longs;int, vt præ­<lb/>dicticirculi, ac proinde major &longs;it pre&longs;&longs;io in CE, &longs;equitur nece&longs;&longs;ariò de­<lb/>pre&longs;&longs;io punctorum C & E & elevatio B & D, in oppo&longs;itis &longs;cilicet punctis, <lb/>per quæ ducitur linea connectens centra, &longs;cilicet ID; vna tamen mihi <lb/>re&longs;tat difficultas, cui&longs;olvendæ imparem profectò me &longs;entio, nempe in <lb/>&longs;ingulis punctis quadrantis CD, æqualis e&longs;t vis pre&longs;&longs;ionis; cur igitur <lb/>a&longs;&longs;urgit in R? cur vnum prævalet &longs;upra aliud<gap/></s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Hic nodus indi&longs;&longs;olubilis e&longs;&longs;et, &longs;i tantùm pre&longs;&longs;io fieret in pun­<lb/>ctis C & D, alií&longs;que eiu&longs;dem arcus CD; &longs;ed quia æqualis radiorum, &longs;eu <lb/>linearum pre&longs;&longs;io fit in circulo, v. </s> <s>g. </s> <s>in circulo radio CA, in circulo ra­<lb/>dio ba, alií&longs;que parallelis, certè pre&longs;&longs;iones &longs;unt vt peripheriæ prædi­<lb/>ctorum circulorum, & hæ vt radij CA, ba &c. </s> <s>vnde &longs;equitur, majorem <lb/>e&longs;&longs;e vim pre&longs;&longs;ionis circuli, cujus radius e&longs;t CA, quàm circuli, cujus ra­<lb/>dius e&longs;t Ba, deprimitur ergo aqúa in prædicto circulo CE, quem dein­<lb/>ceps circulum maximæ pre<gap/>onis, &longs;eu depre&longs;&longs;ionis vocabo; & attollitur <lb/>versùs P & R, qui &longs;unt poli prædicti circuli, &longs;eu puncta maximæ eleva­<lb/>tionis: hinc ex &longs;phæra fit &longs;phærois, licèt autem pre&longs;&longs;io in b &longs;it major quam <lb/>in X; hoc tamen pro nihilo habendum e&longs;t; cùm primaria cau&longs;a elevatio­<lb/>nis aquæ &longs;it à circulis pre&longs;&longs;ionis, non procul à circulo maximæ pre&longs;&longs;ionis <lb/>di&longs;tantibus; accedit quod cùm non ob&longs;tante circulo pre&longs;&longs;ionia, radio ba, in­<lb/>tume&longs;cat aqua in R, ac proinde in <expan abbr="arcũ">arcum</expan> Qb, oblique cylindrus incidat, pel­<lb/>lit potiùs punctum b per ba <expan abbr="quã">quam</expan> per b A; vnde fit qu&ecedil;dam compen&longs;atio; nam <pb pagenum="108"/>X minùs re&longs;i&longs;tit directa pre&longs;&longs;ione per XA; quid mirum igitur, &longs;i à circulis <lb/>majoris pre&longs;&longs;ionis altiùs attollatur ver&longs;us AP; itemque minùs premit per <lb/>XB; b verò magis re&longs;i&longs;tit directa pre&longs;&longs;ione per bA, vnde ab aliis circulis <lb/>majoris pre&longs;&longs;ionis minùs a tollitur; plus tamen per ba, quam vocare <lb/>po&longs;&longs;umus obliquam pre&longs;&longs;ionem; vnde vides vnam compen&longs;ari per aliam; <lb/>nempe X habet minorem pre&longs;&longs;ionem tum directam, tum obliquam; hinc <lb/>ratione directæ plus attollitur, ratione obliquæ minùs, b verò habet majo­<lb/>rem vtramque, ac proinde ratione directæ minùs attollitur, & plus ra­<lb/>tione obliquæ; en vobis per&longs;picuam compen&longs;ationem. </s> <s>Denique licèt <lb/>aliqua e&longs;&longs;et differentia elevationis, parum admodùm referret; de quo <lb/>infra. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> Hucu&longs;que qua&longs;i meditabundus conticui; negari tamen non <lb/>pote&longs;t, quin peregrinum inventum &longs;it; modò omnia probè con&longs;entiant, <lb/>ac phænomenis non repugnent; vnum tamen occurrit, quod mihi diffici­<lb/>le videtur; cur &longs;cilicet pre&longs;&longs;io per vnum dumtaxat majorem circulum fiat, <lb/>cujus radius e&longs;t CA; cur enim per alios non fit, quotum radij &longs;int XA, VA, <lb/>BA. &c. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Rectè mones, hoc enim mihi explicandum incumbit, equi­<lb/>dem fit pre&longs;&longs;io per omnes circulos majores, vt fit in circulo ma­<lb/>jore, BCDE, &longs;ed quia propter pre&longs;&longs;ionem inæqualem, huju&longs;modi <lb/>circuli in Ellip&longs;es, vel qua&longs;i Ellip&longs;es mutantur, con&longs;idero tantùm <lb/>pre&longs;&longs;ionem in iis circulis, in quibus æqualis, vel vniformis e&longs;t pre&longs;&longs;io, <lb/>inter quos vnus dumtaxat major e&longs;t, quem maximæ pre&longs;&longs;ionis &longs;upra voca­<lb/>vi, in quem axis ab&longs;idum, &longs;eu maximæ elevationis, perpendiculariter <lb/>cadit; aliíque minores eidem paralleli. </s> <s>Nempe &longs;i pre&longs;&longs;io vniformis e&longs;t, <lb/>ni&longs;u quodam communi exeritur, nec vnum eju&longs;dem circuli punctum ab <lb/>alio attollitur; &longs;i verò difformis & inæqualis, ni&longs;us communis non e&longs;t, vt <lb/>patet. </s> <s>Po&longs;ita igitur Luna in I, eaque immobili, terra in A, ita vt tota il­<lb/>lius &longs;uperficies aquea &longs;it, terra non jam &longs;phæra, &longs;ed &longs;phærois eritad in&longs;tar <lb/>pruni, cujus major diameter e&longs;t axis ab&longs;idum, vel in linea connectente <lb/>centra, minor verò e&longs;t diameter circuli maximæ pre&longs;&longs;ionis. </s> <s>Et &longs;i Luna &longs;it <lb/>in Æquatore, prædictum Planum BCDE erit in plano Æquatoris, CE <lb/>erit Meridianus, polus in C erecta CA perpendiculari ad planum Æqua­<lb/>toris. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Quæ &longs;equuntur facilia reputo; demns enim moveri Lunam <lb/>per IHS, eodem motu moveri videbitur punctum P; & vbi Luna per­<lb/>veneritin S, punctum maximæ elevationis erit in E, erítque EC linea ab­<lb/>&longs;idum, & BD diameter maximæ pre&longs;&longs;ionis; atque ita prædictus aquæ tu­<lb/>mor motum Lunæ omninò æmulatur, & orbe peracto, Luna redeunte <lb/>ad punctum I, tumor rediret ad punctum P. </s> <s>Pro quo etiam fingendum <lb/>e&longs;t, &longs;imul cum Luna, eodemque motu, cit ca centrum A, moveri lineam <lb/>connectentem centra A, I, cum ip&longs;a linea dirimente GFH, &longs;ed profe­<lb/>ctò hic æ&longs;tus ab eo diver&longs;us e&longs;t, quem modò habemus, vel ob&longs;ervamus in <lb/>mari. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Ita e&longs;t, fateor vltro; quia totam terre&longs;tris globi &longs;uperficiem aqua <pb pagenum="109"/>non tegit; fac autem v. </s> <s>g. </s> <s>alti&longs;&longs;imum terræ tractum attolli &longs;upra aquas in <lb/>V, hauddubiè eo tempore, quo tumor aquæ re&longs;ponderet radio AV, &longs;ecun­<lb/>dùm eundem radium a&longs;&longs;urgit aqua per clivum montis, donec <expan abbr="tand&etilde;">tandem</expan> Luna <lb/><expan abbr="reced&etilde;te">recedente</expan> versùs S, aqua &longs;ub&longs;idit, & refluit proprio pondere; quia pre&longs;&longs;ionis <lb/>vi non &longs;u&longs;tinetur amplius; hinc fiet æ&longs;tus reciprocus, <expan abbr="qual&etilde;">qualem</expan> modò habemus, <lb/>&longs;ive, vt <expan abbr="vocãt">vocant</expan>, fluxus, & refluxus. </s> <s>Siverò ad <expan abbr="occasũid&etilde;">occasunidem</expan> terræ tractus versùs <lb/>mare inclinet; hinc inde maximus erit aquætumor ad <expan abbr="vtrũq;">vtrunque</expan> montis <expan abbr="clivũ">clivum</expan>, <lb/>occiduum &longs;cilicet, atque ortivum; & Luna tendente versùs S, &longs;en&longs;im &longs;ub&longs;i­<lb/>det aqua, excurrétque, hinc versùs ortum, inde occa&longs;um versùs; vt autem <lb/>refluit aqua in partes oppo&longs;itas, abeunte Luna, ita Luna accedente à parti­<lb/>bus oppo&longs;itis, <expan abbr="nimirũab">nimirunab</expan> occa&longs;u & ortu accurrit, vel affluit, a&longs;&longs;urg ítque aqua <lb/>versùs terræ tractum V, & vtrimque ad vtrumque clivum &longs;en&longs;im attolli­<lb/>tur. </s> <s>Hinc &longs;i per medium terræ trectum, angu&longs;tum fretum perrumperet, aqua <lb/>hinc inde &longs;imul a&longs;&longs;urgente, in medio freto gemini æ&longs;tus concurrerent. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/> Hæc mihi&longs;ummoperè placent; &longs;ed non intelligo, quid fiat Lu­<lb/>na extra Æquatorem &longs;ita. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Faciam intelligas: finge tibi terram ad in&longs;tar &longs;phæroidis, id e&longs;t, <lb/>Solidi Elliptici; cogita prunum PQRT, quod obtinebis, &longs;i ellip&longs;im hanc <lb/>circa axem RP volvi iubeas. </s> <s>Finge autem prædictum prunum cujus &longs;ectio <lb/>PQRT e&longs;t in plano Æquatoris, librari circa <expan abbr="ax&etilde;">axem</expan> CE modò versùs <expan abbr="Poreã">Poream</expan>, <lb/>modò versùs Au&longs;trum, per <expan abbr="arcũ">arcum</expan> 18. circiter graduum, hinc inde; ac &longs;imul <expan abbr="li-neã">li­<lb/>neam</expan> <expan abbr="ab&longs;idũ">ab&longs;idum</expan> RP volvi circa <expan abbr="ax&etilde;">axem</expan> Mundi, in plano &longs;cilicet Æquatoris perpen­<lb/>diculariter erectum, eodem pror&longs;us <expan abbr="cũ">cum</expan> Luna motu, <expan abbr="tũ">tum</expan> integræ revolutionis, <lb/>tum etiam prædictæ librationis, en tibi germanum marini æ&longs;tus &longs;y&longs;tema. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Maxima difficultas &longs;e&longs;e mihi objicit; nempe po&longs;ita linea ab&longs;i­<lb/>dum extra Planum Æquatoris, Luna v.g.in Tropico Capricorni exi&longs;tente, &longs;i <lb/>accipiamus quodlibet punctum extra Æquatorem, elevatio aquæ in eo <lb/>puncto inæqualis e&longs;&longs;et, licèt Luna in Meridiano &longs;ita &longs;upponatur; & vt cla­<lb/>riùs hanc difficultatem exponam. </s></p><figure></figure><p type="main"> <s>Sit circulus verticalis & meri­<lb/>dianus in globo terre&longs;tri ADCF, <lb/><expan abbr="Horizõ">Horizom</expan> AC, Æquator FK; Tropi­<lb/>cus Cancri HI, Capricorni GL, <lb/>Axis mundi PM; &longs;upponatur Lu­<lb/>nain G, &longs;cilicet in Tropico Capri­<lb/>corni, & in meridiano &longs;upra hori­<lb/>zontem; circulus maximæ depre&longs; <lb/>&longs;ionis e&longs;t <expan abbr="Bq;">Bque</expan> & à terræ <expan abbr="pũcto">puncto</expan> D, <lb/>quod a&longs;&longs;umptum e&longs;t extra Æqua­<lb/>torem; <expan abbr="punctũ">punctum</expan> maximæ elevatio <lb/>nis, quod e&longs;t in G, e&longs;t enim line <lb/><expan abbr="ab&longs;idũ">ab&longs;idum</expan> GI, di&longs;tat toto areu GD, a <lb/>quo tamen circulus maximæ de <lb/>pre&longs;&longs;ionis di&longs;tat tantùm arcu BM, po&longs;ita verò Luna in <expan abbr="pũcto">puncto</expan> mediæ noctis <lb/>L, circulus maximæ depre&longs;&longs;ionis erit NO, Linea ab&longs;idum LH, arcus di&longs;tan-<pb pagenum="110"/>tiæ à puncto maximæ clevationis HD, maximæ depre&longs;&longs;ionis DN; igitur <lb/>æ&longs;tus nocturnus longè major e&longs;t in loco D, quàm diurnus; immo &longs;i accipia­<lb/>tur punctum B, in eo erit maxima depre&longs;&longs;io aquæ, Luna po&longs;ita in G; &longs;cilicet <lb/>de meridie, po&longs;ita verò in L, de media nocte, di&longs;tabit B à puncto maximæ <lb/>depre&longs;&longs;ionis arcu BN; cuncta hæc repugnare videntur ob&longs;ervationibus, cùm <lb/>æ&longs;tus diurnus & nocturnus æquales &longs;int. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Fateor vnum e&longs;&longs;e ex præcipuis Nodis, qui mihi &longs;olvendi &longs;unt, <lb/>qui tamen facilè a me&longs;olvitur, in hypothe&longs;i facta. </s> <s>Nempe dato quod tota <lb/>&longs;uperficies terre&longs;tris globi &longs;itaquea, cuncta hæc, vt dicis, &longs;uccederent; duo <lb/>tamen ob&longs;erves, velim; primum e&longs;t, di&longs;tinguendam e&longs;&longs;e aquarum elevatio­<lb/>nem, &longs;eu tumorem, ab carundem rapido cur&longs;u; vnum enim ab alio di&longs;tin­<lb/>guitur, licèt vnum ex alio con&longs;equatur; vnde fieri pote&longs;t, vt cum minore ele­<lb/>vatione &longs;eu tumore, rapidior cur&longs;us conjunctus &longs;it; & vici&longs;&longs;im minùs rapi­<lb/>dus cur&longs;us, cum majore elevatione propter loci &longs;itum: Secundum e&longs;t, versùs <lb/>Polos æ&longs;tus ferè &longs;ine legibus ire, quia cum punctum elevationis, quod non <lb/>procul à Po<gap/>o di&longs;tat brevem circulum, <expan abbr="diurnũ">diurnum</expan> &longs;cilicet de&longs;cribat, circa axem <lb/>Mundi, quid mirum, &longs;i maxima inde aquarum perturbatio na&longs;catur; & verò <lb/>præ&longs;cindendo à vario terrarum &longs;itu, qui multa variat, versùs Polos, qua&longs;i <lb/>vortex quidam tumentis aquæ, &longs;patio 24. horarum min 48. circa polum iret, <lb/>ex quo reverà non modica aquarum perturbatio &longs;ine certa lege &longs;equere­<lb/>tur. </s> <s>Sed de hoc infra. </s> <s>Porrò fateor vltro, <expan abbr="præ&longs;cind&etilde;do">præ&longs;cindendo</expan> à diver&longs;o partium &longs;itu <lb/>& po&longs;ito quod tota &longs;uperficies terre&longs;tris globi aquea e&longs;&longs;et, in puncto D, tu­<lb/>morem aquæ altiorem fore de meridie quàm de media nocte, Luna exi&longs;ten­<lb/>te in Tropico Cancri, contra verò in Tropico Capricorni; immo Luna exi­<lb/>&longs;tente in Cancro de meridie, vel in Capricorno, de media nocte, altiorem <lb/>fore tumorem in D, quàm &longs;i Luna exi&longs;teret in Æquatore. </s> <s>Cur verò hoc <lb/>modo <expan abbr="nõ">non</expan> fiat, ex diver&longs;o terræ ac maris &longs;itu & à vario affluentis & refluen­<lb/>tis aquæ cur&longs;u, variaque illius deflexione, reflexione, inclinatione, contra­<lb/>ctione &c. </s> <s>de quibus infrà, omninò &longs;equitur. </s> <s>Itaque jam mihi &longs;ufficit, hanc <lb/>veram cau&longs;am e&longs;&longs;e prædicti aquarum tumoris & motus, eju&longs;demque revo­<lb/>lutionis, ad Lunæ motum diurnum ita compo&longs;it&ecedil; vt Luna in Meridiano exi­<lb/>&longs;tente, &longs;ive &longs;upra, &longs;ive infra horizontem, præfatus tumor maximus &longs;it in lo­<lb/>cis, &longs;ub eodem Meridiano &longs;itis: maxima verò ibidem depre&longs;&longs;io, Luna 90. <lb/>gradibus à dicto Meridiano di&longs;tante; &longs;ic enim &longs;ingulis diebus tumor vna <lb/>ferè hora tardiùs accedit; quia talis e&longs;t Lunæ motus, & jam vides, ni fallor, <lb/>Chry&longs;ocome, quid ad mitabilem i&longs;tum effectum Luna conferat, & quàm <lb/>providè antè dixerim, Lunam marini æ&longs;tus cau&longs;am non e&longs;&longs;e, nec enim re­<lb/>verà cau&longs;a e&longs;t, &longs;ed mera occa&longs;io; cau&longs;a verò, inæqualis aëris gravitatio, eo <lb/>modo, quo dixi. </s> <s>Ex qua po&longs;ita Luna, eju&longs;que motu ab ortu in occa&longs;um, ne­<lb/>ce&longs;&longs;ariò &longs;equitur æ&longs;tus, id e&longs;t, aquarum elevatio & tumor, in dato quolibet <lb/>Oceani puncto; &longs;uppo&longs;ita &longs;cilicet tota &longs;uperficie globi aquea, idque bis &longs;in­<lb/>gulis diebus, &longs;cilicet de meridie, & media nocte Lunari; meridiem autem, <lb/>&longs;eu mediam noctem Lunarem voco, illud temporis punctum, quo Luna e&longs;t <lb/>in Meridiano, cui prædictus locus &longs;ube&longs;t; vtrùm verò tumor de meridie Lu­<lb/>nari, &longs;it æqualis tumori de media nocte, jam dictum e&longs;t &longs;upra; nimirum <pb pagenum="111"/>æqualis e&longs;t, dum Luna non procul ab Æquatore exi&longs;tit; inæqualis verò, <lb/>dum Luna versùs Tropicos excurrit; quid autem accidat, in hoc rerum <lb/>&longs;tatu, nimirum ex diver&longs;o marium ac terrurum &longs;itu, paulò po&longs;t dicam, <lb/>nec me opinor, ab onere illo eximetis. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Germanam ac facilem cau&longs;am habemus marini æ&longs;tus, qui <lb/>&longs;ingulis diebus bis a&longs;&longs;urgeret in illa hypothe&longs;i totius &longs;uperficiei aqueæ, de <lb/>qua vltra di&longs;putandum e&longs;&longs;e, non puto; quare ad aliam marini æ&longs;tus pro­<lb/>prietatem venio; prima enim diurna e&longs;t, de qua huc v&longs;que; juxta illam <lb/>hypothe&longs;im; &longs;ecunda men&longs;trua, tertia denique annua. </s> <s>Quod &longs;pectat ad <lb/>men&longs;truam, nemo ferè ne&longs;cit, æ&longs;tum maximum e&longs;&longs;e in Plenihinio, medio­<lb/>crem in Novilunio, minimum in Quadraturis; Quæro igitur ex te, vtrùm <lb/>in hac eadem hypothe&longs;i, ratio & cau&longs;a reddi po&longs;lit huju&longs;modi varietatum. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Non e&longs;t dubium, quin po&longs;ita majore vi pre&longs;&longs;ionis, major ex <lb/>illa tumoris, vel elevationis effectus con&longs;equatur, nimitum cre&longs;cente cau­<lb/>&longs;a, cre&longs;cit effectus; atqui in Plenilunio major pre&longs;&longs;ionis vis e&longs;t, quàm in <lb/>Novilunio; & in vtroque, quàm in Quadraturis; quia &longs;cilicet major vis <lb/>e&longs;t gravitationis; hæc verò major, quia tunc aër longè gravior. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/> Hæc probè inter &longs;e con&longs;entiunt, modò illud, quod vltimo loco <lb/>a&longs;&longs;eris, &longs;ub&longs;i&longs;tat; at, vt ingenuè dicam, non video, our aër &longs;it gravior in <lb/>Plenilunio. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Aliquid fortè novi afferam; quod tamen cum reliquis experi­<lb/>mentis, immo & principiis con&longs;entit; nempe certum e&longs;t circa Plenilu­<lb/>nium omnibus corporibus &longs;pongio&longs;is & humidis, plus huinoris & &longs;ucci <lb/>ine&longs;&longs;e; vt videre e&longs;t in ovis, cancris, medulla, cerebro, alii&longs;que corpori­<lb/>bus, quibus humor facilè affunditur; Hæc profectò negari non po&longs;&longs;unt <lb/>ab iis, qui vel oculis in&longs;tructi &longs;unt; accedit, quod in corporibus appel­<lb/>latis, non modò cre&longs;cit moles, &longs;ed etiam pondus, vt quivis probare pote­<lb/>rit; quidni ergo longè plus humoris aëri circa Plenilunium in&longs;it, cùm aër <lb/>facilè humorem excipiat, divi&longs;um &longs;cilicet in perexiguas, quæque omnem <lb/>fugiant &longs;en&longs;um particulas. </s> <s>Humor autem aëri admixtus majus pondus <lb/>conciliat, vt &longs;uppono ex jactis &longs;upra principiis. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> In mo etiam fortè major e&longs;t aquæ vis circa Plenilunium; hu­<lb/>mor enim humori facilè admi&longs;cetur; quod licèt nunquam expertus &longs;im, <lb/>judico tamen probabile; licèt in parvis aquarum receptaculis &longs;en&longs;um <lb/>omné facilè fugiat; &longs;ecus in majoribus, vt in Mari; &longs;ed cùm <expan abbr="periculũ">periculum</expan> <expan abbr="nõ">non</expan> fe­<lb/>cerim, vix affirmare au&longs;im, licèt inaudierim in <expan abbr="quibu&longs;dã">quibu&longs;dam</expan> &longs;epulchris marmo­<lb/>reis &longs;ubterraneis, <expan abbr="aquã">aquam</expan> cre&longs;cere ac decre&longs;cere, pro diver&longs;o Lunæ ad&longs;pectu. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Ita e&longs;t, apud Arelaten&longs;es aliquid &longs;imile e&longs;&longs;e dicunt, &longs;ub templo <lb/>Patrum S Franci&longs;ci de Paula; nempe illorum cœnobium &longs;itum e&longs;t extra <lb/>vrbem, in eo loco, quem Campum Eli&longs;ium vocant, in quo innumeri vi­<lb/>dentur tumuli lapidei, &longs;eu potiùs cap&longs;æ, in crypta verò &longs;ub templo, &longs;unt <lb/>aliquot huju&longs;modi &longs;epulchra, in quorum vno paulo elatiore, aqua cre&longs;ce­<lb/>re, ac decre&longs;cere dicitur, pro diver&longs;o Lunæ ad&longs;pectu; hoc non a&longs;&longs;ero, qui<gap/><lb/>periculum non feci; mihi tamen vrna illa o&longs;ten&longs;a e&longs;t, & hoc mihi ab illis <lb/>Patribus <expan abbr="a&longs;&longs;ertũ">a&longs;&longs;ertum</expan>, penes quos &longs;it fides. </s> <s>Vt vt &longs;it, cùm circa Plenilunium plus <pb pagenum="112"/>humoris in&longs;it aliis corporibus, quæ facile humorem, &longs;ubtilem &longs;cili­<lb/>cet exugunt, aëri quoque plus humoris ine&longs;&longs;e, nece&longs;&longs;e e&longs;t, cùm facillimè <lb/>tenuis humor ab illo exugatur. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Sed vnde amabò ille humor; an fortè Luna ex corporibus <lb/>illum educit, circa Plenilunium, tunc enim major illius vis e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Si Luna humorem illum educeret, inde certè corpora humi­<lb/>da &longs;icciora manerent, vt patet ex terminis, & vt mole ita & pondere im­<lb/>minuta; cùm tamen &longs;ecùs accidat. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Vnde procedat hic humor, cujus major vis ine&longs;t aëri, &longs;icuti aliis <lb/>corporibus, circa Plenilunium, ad præ&longs;entem effectum nihil facit, pro <lb/>quo &longs;atis e&longs;t, rem ita e&longs;&longs;e, à quacumque tandem cau&longs;a &longs;it; certum e&longs;t, ta­<lb/>men, Lunam cau&longs;am e&longs;&longs;e, vel occa&longs;ionem, pro cujus &longs;cilicet diver&longs;o ad­<lb/>&longs;pectu, humoris affu&longs;i diver&longs;a ratio e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Rem mihi grati&longs;&longs;imam feceris, &longs;i vel obiter &longs;altem indicâ­<lb/>ris, quid &longs;entias de cau&longs;a illa; ni&longs;i enim fallor, fieri non pote&longs;t, quin aliquid <lb/>apud te &longs;tatueris. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Dicam, &longs;ed ex hypothe&longs;i; &longs;upponamus, Lunam ex no&longs;tris ele­<lb/>mentis con&longs;tare, ac præ&longs;ertim ex multo humore, longè no&longs;tro &longs;ubtiliore, <lb/>& puriore; nempe lympha no&longs;tra non e&longs;t pura, &longs;ed mixta ex aliis elemen­<lb/>tis; quis &longs;cit, an aquæ illæ ibi &longs;int, quæ &longs;uper cœlos in &longs;acro textu e&longs;&longs;e <lb/>dicuntur; nullos tamen in iis pi&longs;ces e&longs;&longs;e putes, nulla animantium, aut <lb/>vegetantium &longs;emina; ibienim ftu&longs;tra e&longs;&longs;ent, cùm hæc propter hominem <lb/>&longs;int terre&longs;tris orbis incolam; Sol autem, vt agit in terram, ita & in Lu­<lb/>nam, & caloris vi, multum humoris rarefacti educit; cùm enim &longs;ubtilior <lb/>&longs;it, longè faciliùs calore &longs;olvitur, educitúrque; hic porrò humor aëri ad­<lb/>mixtus, caloris vi etiam vltra rare&longs;cit; donec tandem à Lnna recedens, <lb/>in conum vmbræ terræ immergatur, vbi præ frigore, den&longs;atur, & pri&longs;ti­<lb/>næ gravitati re&longs;tituitur; quia verò Luna versùs occa&longs;um interim non pa­<lb/>rum deflectit, ille tractus aëris, cui prædictus humor admixtus e&longs;t, pro­<lb/>pior terræ fit, quàm Lunæ, atque adeò, infra lineam dirimentem, versùs <lb/>ip&longs;am terram gravitat. </s> <s>Sed vt hoc clariùs explicetur, nonnihil &longs;chematis <lb/>adhibeo: Sit <expan abbr="centrũ">centrum</expan> terræ A, (<emph type="italics"/>Po&longs;terioris Fig.<emph.end type="italics"/>) &longs;it Luna L, & Sol è regione op­<lb/>po&longs;itus, &longs;ecundùm lineam LAK, erit Plenilunium; ac proinde <expan abbr="hemi&longs;phætiũ">hemi&longs;phætium</expan> <lb/>Lunaris globi BED &longs;olaribus radiis illu&longs;tratur, quorum vi, humor ex illo <lb/>educitur, &longs;ecundùm lineas eductas ex centro L, vt fit in globo terræ; <lb/>cùm pariter Luna globus totalis &longs;it: Cùm autem vmbram &longs;uam terra proji­<lb/>ciat &longs;ecundum lineam AL, hauddubiè &longs;i Luna &longs;it in Nodis, &longs;eu in plano <lb/>Eclipticæ, in dictam vmbram immer&longs;a e&longs;t, &longs;ecus verò, &longs;i à dicto plano <lb/>ab&longs;it, & quia interea Luna ab L tran&longs;it in M, K, R, aëris tractus, cuiprædictus <lb/>humor admixtus e&longs;t, paulò inde gravior redditus, <expan abbr="cũ">cum</expan> iam &longs;it vicinior terræ, <lb/>quam Lunæ, versùs terram tendit; vnde fit, vt redeunte Luna in L, <expan abbr="invmbrã">invmbram</expan> <lb/>immer&longs;us, <expan abbr="cõden&longs;ato">conden&longs;ato</expan> humore, multo gravior evadat, & <expan abbr="cũ">cum</expan> &longs;it infra <expan abbr="dirim&etilde;-t&etilde;">dirimen­<lb/>tem</expan>, in terram magis gravitet: <expan abbr="id&etilde;">idem</expan> dico de reliquo aëris tractu, in <expan abbr="orb&etilde;">orbem</expan> circa <lb/>A<gap/>proinde major &longs;equitur pre&longs;&longs;ionis vffectus, igitur major æ&longs;tus In No <lb/><gap/><pb pagenum="113"/>erit in K, & illius Hemi&longs;phærium QP Oillu&longs;tratur, educiturque vapor per <lb/>lineam KP, alia&longs;que à centro K ductas; vnde prædictus vapor longiùs <lb/><figure id="fig16"></figure><lb/>recedit à terra, ac proinde vbi Luna, orbe peracto, redit in K, licèt non <lb/>modica illius portio infra dirimentem de&longs;cenderit, minor tamen quàm an­<lb/>te; quia versùs terram longè majus &longs;patium decurrendum fuit: hæc au­<lb/>tem in terram circumquaque gravitat quidem, &longs;ed minùs; vnde minor <lb/>pre&longs;&longs;io; igitur minor æ&longs;tus. </s> <s>At verò po&longs;ita Luna in Quadraturis M & R, <lb/>&longs;uppono enim Solem in eodem loco; illu&longs;trantur Hemi&longs;phæria GIF, <lb/>STV; vnde po&longs;tquam Luna, peracto orbe, redit in M, aëris <lb/>tractus, cui admixtus e&longs;t eductus humor, per MI, alia&longs;que ductas à centro <lb/>M, propior e&longs;t Lunæ, quàm terræ; vnde in Lunam gravitat, & cùm Lu­<lb/>na tendat ab M in K, ad illum aëris tractum ip&longs;a accedit; ac proinde ma­<lb/>ximam educti humoris partem colligit; immò Luna exi&longs;tente in K, Sol fe­<lb/>rè lineæ AS re&longs;pondet, vnde ille aëris tractus inter MK, cui eductus hu­<lb/>mor admixtus e&longs;t, majori ex parte intra vmbram à Luna projectam jacet, <lb/>vnde &longs;tatim adden&longs;atur humor, & in ip&longs;am Lunam de&longs;cendit: Idem dico <lb/>de Luna po&longs;ita in altera Quadratura R; humor enim educitur per RT, <lb/>alia&longs;que rectas excentro R directas; cùm autem Lunæ motus &longs;it ab R in <lb/>L, humor per RT eductus recedit ab vmbra projecta ab vtroque globo; <lb/>vnde parum omninò den&longs;atur; igitur etiam &longs;i terræ propior &longs;it, quàm Lu­<lb/>næ, non tamen inde gravitatio cre&longs;cit; igitur neque pre&longs;&longs;io; igitur nec <lb/>æ&longs;tus: igitur inde conveniens; ni fallor, ratio redditur, cur plus humoris <pb pagenum="114"/>Luna communicet corporibus &longs;ublunaribus, in Plenilunio; longè minùs <lb/>in Quadraturis; in Novilunio demum minùs quidem quam in Plenilunio, <lb/>plus verò quam in Quadratutis. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/> Hæc &longs;anè mihi &longs;ummopere placent; volvo tamen in mente <lb/>nonnihil difficilè. </s> <s>Fingamus enim Lunam in L, vaporemque eductum <lb/>attolli &longs;ecundùm altitudinem LE, quem vocemus radium Atmo&longs;phæræ <lb/>Lunaris; erit prædictæ Atmo&longs;phæræ Hemi&longs;phærium BED; & in toto <lb/>illo orbe LMKR, æquale Hemi&longs;phærium, vt HGI, QNO, TVX fin­<lb/>gendum e&longs;t. </s> <s>In Novilumio verò, Hemi&longs;phærium Atmo&longs;phæræ Lunaris <lb/>erit QPO, & in orbe illo diurno, TSX, BCD, HFI, in Quadratura <lb/>verò M, erit GIF, PQN, SXV, CDE, denique in Quadratura R, erit <lb/>STV, CBE, GHF, PON. </s> <s>Vnde &longs;equitur meo judicio, æqualem <lb/>&longs;empet e&longs;&longs;e humoris educti copiam circumfu&longs;am, ac proinde æqualem <lb/>gravitationem & pre&longs;&longs;ionem; igitur æqualem æ&longs;tum. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Fateor vltro æqualem ferè &longs;emper e&longs;&longs;e portionem humoris Lu­<lb/>naris educti, admixtique aëris tractui intra Atmo&longs;phæram orbitæ Lunaris <lb/>contenti, &longs;ed hic parum den&longs;atur, ac proinde vix gravior evadit, ni&longs;i intra <lb/>vn. </s> <s>bras ab alterutro globo projectas immergatur; neque hoc &longs;ufficit, ni&longs;i <lb/>gravior factus propior terræ &longs;it, quàm Lunæ; hoc autem circa Plenilunium <lb/>fieri con&longs;tat, in quo &longs;cilicet vmbra terræ projicitur qua&longs;i directè versùs Lu­<lb/>nam; vnde magna humoris educti copia in dictam vmbram immergitur, <lb/>ac proinde den&longs;atur, & gravior evadit; Lunâ autem recedente ab L, ver­<lb/>sùs M, & K, humor ille tandem propior terræ fit: quid mirum igitur, &longs;i <lb/>aër, cui admixtus e&longs;t magis in terram gravitet? </s> <s>Idem dico de Novilunio. <lb/></s> <s>Vbi enim Luna ex K Novilunij puncto pervenit per R in L, Sol ferè li­<lb/>neæ EC re&longs;pondet, vnde vtraque vmbra tum Lunæ, tum terræ projicitur <lb/>in illum aëris tractum, qui e&longs;t circa P, & cui eductus humor admixtus e&longs;t; <lb/>hinc valdè den&longs;atur & gravior fit, & cùm &longs;it propior terræ, ver&longs;us illam <lb/>tendit, de&longs;cenditque infra dirimentem: Si autem Luna ponatur in Quadra­<lb/>tura M, vmbræ Lunæ ille aëris tractus, qui e&longs;t inter IO, & cui humor <lb/>eductus admixtus e&longs;t, &longs;tatim diuque immergitur, vt patet; &longs;ive vmbra pro­<lb/>jecta &longs;it à Luna, Sole po&longs;ito inter QT, & Luna inter OI, &longs;ive ab ip&longs;a <lb/>terra, Sole &longs;ito paulò vltra R & Luna in K; hinc den&longs;atur & gravior fit, & <lb/>cùm Luna tunc fit propior, in eam gravitat & tendit. </s> <s>Denique &longs;i Luna <lb/>ponatur in Quadratura R, ille aëris tractus, cui humor eductus admixtus <lb/>e&longs;t, vmbræ terræ immergitur, quando Sol pervenit ferè in M; Sed tunc Lu­<lb/>na e&longs;t circa K, igitur vicinior, igitur in Lunam gravitat; pari modo, So­<lb/>le po&longs;ito inter IO, Luna verò inter QT, immergitur in vmbram Lu­<lb/>næ; &longs;ed tunc etiam gravitat in Lunam, cui propior e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Rem hanc probè intelligo, & nihil clarius e&longs;&longs;e videtur; duo <lb/>tantùm ex te &longs;cire velim, immò tria; primum e&longs;t, vtrùm Sol æquali­<lb/>ter agat in illud Hemi&longs;phærium Lunæ, quod illu&longs;trat, v.g.in BED, quan­<lb/>do e&longs;t Plenilunium; Secundum e&longs;t, quid tandem fiat de humore illo ex <lb/>Luna educto, terri&longs;que illap&longs;o. </s> <s>Tertium vtrùm ip&longs;o Plenilunij die &longs;it ma­<lb/>ximus æ&longs;tus, an paulò ante, &longs;eu po<gap/> Oppo&longs;itionis momentum. </s></p><pb pagenum="115"/><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Ab hoc vltimo incipiam, in quo licèt varij &longs;int ij Autores, qui <lb/>de hoc argumento &longs;crip&longs;erunt, quorum aliqui maximam vim æ&longs;tus die 17. <lb/>Lunæ fieri volunt, quos arguit manife&longs;ta experientia; dico tamen etiam <lb/>iuxta præmi&longs;&longs;am hypothe&longs;im, in qua totam &longs;uperficiem globi aqueam e&longs;&longs;e <lb/>&longs;upponimus, maximam vim æ&longs;tus, &longs;eu quod idem e&longs;t, aquarum elevatio­<lb/>nem, non fieri vbique in ip&longs;o Oppo&longs;itionis, &longs;eu Plenilunij puncto; &longs;ed tan­<lb/>tùm in illo Meridiano, &longs;ub quo fit oppo&longs;itio, vel Plenilunium, idque per &longs;e, <lb/>& in præfata hypothe&longs;i; nam ratione &longs;itus, accidere pote&longs;t, vt iis omnibus, <lb/>qui &longs;ub eodem Meridiano &longs;unt, eodem momento maximus æ&longs;tus non fiat, <lb/>de quo infra; dixi etiam per &longs;e; nam per accidens &longs;ecus erit, vt &longs;i ex ortiva <lb/>di&longs;ci Lunaris parte, plus humoris educatur, quàm ex occidua: & verò &longs;i <lb/>maculæ Lunares aquæ &longs;unt, quanquam diver&longs;æ à no&longs;tris, & &longs;ine pi&longs;cibus, <lb/>& virtute aliqua &longs;eminali, in parte ortiva longè plures & majores &longs;unt; <lb/>Vnde &longs;equitur plus humoris educi paulò po&longs;t Plenilunium, quàm ante; <lb/>quia Sol magis directè in eam partem Lunaris di&longs;ci agit, cui plus humoris <lb/>educendi ine&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Ni fallor, apud aliquos Autores legi maximam vim <lb/>æ&longs;tus vno vel altero die, po&longs;t Plenilunium e&longs;&longs;e; quod rectè in hanc rem <lb/>Quadraret. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Legi&longs;ti haud dubiè; nam ad Diepam & alibi, vt Furnerius ob&longs;er­<lb/>vat, &longs;ummum incrementum e&longs;t Die 17. Lunæ, biduo &longs;cilicet po&longs;t Plenilu­<lb/>nij punctum; idem te&longs;tatur Cre&longs;centius lib. </s> <s>3. Nautic. </s> <s>cap.2. idem Plin. <lb/></s> <s>lib.2. cap.97. vbi habet, maximè fervere æ&longs;tum, non in plena, aut novi&longs;&longs;i­<lb/>ma, &longs;ed po&longs;tea: alibi tamen, vt in ora Gallica, te&longs;te Scaligero, exercit.52. <lb/>cui &longs;ub&longs;crip&longs;it Furnerius lib.9.cap.21.in ip&longs;o Plenilunio maximè attollitur. <lb/></s> <s>Itaque ex diver&longs;o &longs;itu, hæc diver&longs;itas procedit; in præmi&longs;&longs;a tamen hypo­<lb/>the&longs;i, eductoque vniformiter & æqualiter humore ex globo Lunari, ma­<lb/>ximus æ&longs;tus &longs;ieret &longs;ub illo Meridiano, in quo fit Oppo&longs;itio; in aliis verò <lb/>punctis citiùs vel tardiùs; ortiva &longs;cilicet intra Quadrantem citiùs, occidua <lb/>verò tardiùs: ex illa verò hypothe&longs;i macularum Lunæ, quam tamen non <lb/>ad&longs;truo, haud dubiè maximus æ&longs;tus fieret po&longs;t Plenilunium, ob rationem <lb/>allatam. </s> <s>Sed jam ad &longs;ecundum tuum po&longs;tulatum re&longs;pondeo, mi Augu&longs;ti­<lb/>ne, &longs;cilicet humorem illum, & facilè admi&longs;ceri no&longs;tris elementis, & facilè <lb/>ex iis educi; nec enim cum iis mixtum quodpiam componit: ac proinde non <lb/>mitum, &longs;i vt facilè educitur, atque avolat, ita facilè in Lunam redeat, <lb/>cùm &longs;cilicet immergitur in vmbram, &longs;ive à terre&longs;tri, &longs;ive à Lunari globo <lb/>projectam, & e&longs;t propior Lunæ, quàm terræ; in quo, meo judicio, nulla <lb/>e&longs;t difficultas, nec e&longs;t quod aliquis timeat, ne hic vapor in nubes concre­<lb/>&longs;cat quia nubes contexi non po&longs;&longs;unt ni&longs;i ex halitu heterogeneo; hic autem <lb/>Lunatis vapor totus e&longs;t Homogeneus. </s> <s>Quod verò pertinet ad primum quæ­<lb/>&longs;itum, dico Solem in eam globi Lunaris &longs;ectionem, &longs;eu portionem in quam <lb/>radij magis directi incidunt, fortiùs agere; v. </s> <s>g. </s> <s>plus agit in arcum EY, <lb/>quàm in YD, ita vt actio Solis in EY, &longs;it ad actionem in YD, vt Sinus re­<lb/>ctus EY id e&longs;t LB, ad BD Sinum ver&longs;um arcus YD; & hoc in ip&longs;a &longs;e­<lb/>ctione Lunæ; &longs;i enim accipiatur &longs;uperficies, actio in EY e&longs;t ad actionem <pb pagenum="116"/>in YD, in ratione compo&longs;ita, ex ratione Quadrati ab ad differentiam <lb/>Quadrati BD & ex permutata Quadrati &longs;ub chorda arcus EY ad differen­<lb/>tiam Quadrati &longs;ub chorda arcus ED, vel ex ratione Quadrati LB, ad Qua­<lb/>dratum bD, plus bis rectangulum &longs;ub LbD, &longs;eu ad rectangulum &longs;ub bD, <lb/>& aD, & Lc. </s> <s>ad cE &c. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Non intelligo hæc Geometrica, tam enim jejunè illa pro­<lb/>ponis; cùm tamèn ab&longs;tru&longs;as demon&longs;trationes contineant; vix ea curtim & <lb/>raptim indicata potiùs quàm expo&longs;ita qui&longs;quam mente capiat. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Suppono ea, quæ jam aliàs demon&longs;travi, &longs;cilicet circulum &longs;ub <lb/>radio, æquali chordæ, æqualem e&longs;&longs;e portioni &longs;uperficiei Sphæræ, quam <lb/>metitur, vel gignit arcus, cujus e&longs;t chorda, v. </s> <s>g. </s> <s>&longs;i accipiatur circulus &longs;ub <lb/>radio æquali chordæ &longs;ubten&longs;æ arcui EY, erit æqualis portioni &longs;uperficiei <lb/>Sphæræ, <expan abbr="quã">quam</expan> metitur, vel gignit arcus EY revolutus &longs;cilicet circa axem EC, <lb/>hinc chorda &longs;ubten&longs;a arcui ED e&longs;t æqualis radio circuli æqualis &longs;uperficiei <lb/>Hemi&longs;phærij; demon&longs;tratum e&longs;t item, portionem &longs;uperficiei genitæ ab arcu <lb/>YE e&longs;&longs;e ad genitam ab arcu YD, vt Ec, ad cL; præterea lumina inci­<lb/>dentia, per parallelas, &longs;unt vt ba&longs;es, &longs;i con&longs;iderentur in &longs;e; &longs;i verò con&longs;i­<lb/>derentut in &longs;ubjecto, id e&longs;t in diver&longs;a &longs;uperficie, cui incidunt, &longs;i &longs;int <lb/>æqualia lumina, erunt in &longs;ubjecto, vt &longs;uperficies illu&longs;tratæ permutando; v. <lb/></s> <s>g. </s> <s>&longs;i eadem vis, &longs;eu quantitas luminis, (&longs;ic enim vocare liceat) incidat in <lb/>&longs;uperficiem duplam alterius, erit lumen, vel luminis inten&longs;io &longs;uperficiei <lb/>duplæ ad aliam, vt 1.ad 2. Si verò &longs;uperficies &longs;unt æquales, &longs;ed lumina inæ­<lb/>qualia, erunt inten&longs;iones, vt ip&longs;a lumina; &longs;i demum & &longs;uperficies inæqua­<lb/>les &longs;unt, erunt inten&longs;iones in ratione compo&longs;ita luminum & &longs;uperficierum <lb/>permutando; jam applica. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Satis e&longs;t, probe intelligo; inde autem con&longs;tat, quod jam <lb/>&longs;ubindicare vi&longs;us es, vim Solis poti&longs;&longs;unum effectum habere circa Polum <lb/>Hemi&longs;phærij Lunaris ab eo illu&longs;trati, v. </s> <s>g. </s> <s>circa E, intra arcum Zy, vltra <lb/>verò versùs B & D parum valet; hinc etiam &longs;imilis ratio ducitur, cur Sol <lb/>Oriens vel Occidens, terræ &longs;uperficiem parum afficiat, plus verò de meri­<lb/>die, plus demum, quò Sol propiùs ad punctum verticale accedit; hinc vis <lb/>debilior radij obliqui, non tantùm à radij reflexi carentia petenda e&longs;t; vt <lb/>aliqui faciunt. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Ex iis, quæ dicis, Antime, &longs;equeretur Lunaris di&longs;ci, vel <lb/>Hemi&longs;phærij extremitates, minùs &longs;plendidas & illu&longs;tratas videri; nul­<lb/>lum tamen ego di&longs;crimen ob&longs;ervo; oculis autem meis magis credo, quàm <lb/>ve&longs;tris demon&longs;trationibus. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Demon&longs;tratio, Chry&longs;ocome, nunquam fallit, nec fallere pote&longs;t <lb/>&longs;tatue igitur oculum in A; Lunam, licèt Sphærica &longs;it, vt planum di&longs;cum <lb/>a&longs;picis, cujus diameter e&longs;t BD, paulò minor; & Ba, &longs;egmentum &longs;cilicet <lb/>apparentis Semidiametri, vides &longs;ub angulo BAa; aL verò &longs;ub angulo <lb/>aAL; &longs;ed ob parvitatem anguli BAL, qui vix e&longs;t 16.minutorum, anguli <lb/>&longs;ub quibus videntur &longs;egmenta aB, aL, &longs;unt vt ip&longs;a &longs;egmenta; igitur tanta <lb/>lux videtur in aB quanta in aL; quia in eadem ratione videtur contra­<lb/>ctior, in qua primùm incidit di&longs;tractior; vt enim rem in plano tantùm, <pb pagenum="117"/>&longs;eu &longs;ectione lucis con&longs;ideremus, & &longs;upponamus lineam Aa, pro­<lb/>pter di&longs;tantiam &longs;ecare arcum EB in Z, cùm lux incidens in &longs;e­<lb/>gmentum aB, & incidens in &longs;egmentum aL, &longs;it æquè inten&longs;a; inci­<lb/>dentis verò in BZ inten&longs;io; &longs;it ad inten&longs;ionem incidentis in ZE, vt <lb/>aB, ad al, & cùm tota incidens in ZB, videatur contracta in aB; <lb/>haud dubiè æquè inten&longs;a videbitur; & perinde atque &longs;i reverà incideret in <lb/>rectam Bl: &longs;ecus autem accideret, &longs;i in arcum BZ directè radij vi&longs;uales <lb/>inciderent. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/> Hæc fusiùs, quàm par &longs;it exponis; fingo ego radios ab arcu <lb/>BZ profectos, à recta Ba profici&longs;ci; vnde opticè transfertur totum, id <lb/>quod ine&longs;t BZ, in rectam Ba; &longs;ed in BZ tota illa luminis quantitas vi­<lb/>detur, quæ, &longs;i radij liberum tran&longs;itum nacti e&longs;&longs;ent, ip&longs;i Ba incidi&longs;&longs;et; &longs;cio, <lb/>ex his multa optica, eaque præclara deduci, v.g. </s> <s>cur flamma procul &longs;pe­<lb/>ctata minùs candida appareat; cur Mars, dum minor apparet, candidior <lb/>&longs;it; aliaque huju&longs;modi, quæ ad Opticam ac præ&longs;ertim rem colorum perti­<lb/>nent; &longs;ed his omi&longs;&longs;is, vt ad rem no&longs;tram veniam, quæto à te, vtrùm reverà <lb/>in Novilunio major æ&longs;tus &longs;it, quàm in Plenilunio. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Quibu&longs;dam in locis major e&longs;&longs;e dicitur in Novilunio; &longs;ecus ve­<lb/>rò in aliis, idque vt plurimùm in Plenilunio; quod vel ex majore humoris <lb/>affu&longs;i copia rectè deducitur: & verò iuxta præmi&longs;&longs;am hypothe&longs;im, nihil &longs;u­<lb/>per hoc definiri pote&longs;t, ni&longs;i fortè ex &longs;uperiore aver&longs;oque Lunæ Hemi&longs;phæ­<lb/>rio, plùs vel minùs humoris educatur; minùs autem educi videtur, tum <lb/>quia minùs terris affunditur, tum quia ex libratione Lunæ apparet, gran­<lb/>diores maculas in aver&longs;o Hemi&longs;phærio non e&longs;&longs;e; cùm demum ex fideli&longs;&longs;imâ <lb/>omnium peritorum artis nauticæ relatione, maxima vis æ&longs;tus in Plenilu­<lb/>nio e&longs;&longs;e dicatur, his, meo &longs;altem judicio &longs;tandum e&longs;t, quod reverà &longs;i &longs;uppo­<lb/>natur, ad præmi&longs;&longs;a principia facilè reducitur: &longs;ed expectabam, Augu&longs;tine, <lb/>vt quædam fortè &longs;ingulatia ex iis, quæ diximus, pro ea qua vales ingenij <lb/>&longs;agacitate deduceres. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Multa quidem animo volvi atque revolvi, &longs;ed vix temerè me <lb/>committere au&longs;us &longs;um, ne the&longs;es meas ludibrio exponerem; non dubito ta­<lb/>men, cùm hæc dicas, quin aliquid occurrat tibi &longs;citu dignum, quapropter <lb/>te etiam atque etiam rogo, vt nobis illud participare digneris. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Illud &longs;anè te minimè effugi&longs;&longs;et; &longs;ed ad meas nugas non <lb/>adeò &longs;edulò mentem applicas, quin circa alia longè fortè graviora <lb/>ver&longs;eris. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Non ita res profectò &longs;e habet, &longs;ed cùm res i&longs;tæ tuæ novæ mi­<lb/>hi accidant, vix eas primò intuitu meute complector; quomodò igitur, <lb/>quid ex iis nece&longs;&longs;aria con&longs;ecutione &longs;equatur, videre po&longs;&longs;em? </s> <s>Mon&longs;tra quæ&longs;o <lb/>viam; <gap/> præ illico &longs;equar. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Illud inprimis &longs;equi videtur, aëra &longs;cilicet infimæ hujus regionis <lb/>e&longs;&longs;e compre&longs;&longs;um vi ponderis innitentis. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Quodnam pondus intelligis? </s> <s>An fortè Carte&longs;ij &longs;ententiam <lb/>ad&longs;truis, qúi volebat à præter labente Luna aëra terram inter & Lunam in­<lb/>terjectum comprimi? </s></p><pb pagenum="118"/><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Ab&longs;it, vt hoc dicam; licet enim fortè tantula compre&longs;&longs;io in Lunari <lb/>Atmo&longs;phæra &longs;iat, non tamen ad nos v&longs;que <expan abbr="ext&etilde;ditur">extenditur</expan>, vt videre e&longs;t in explo­<lb/>&longs;ione majoris bombardæ, ex qua circumfu&longs;i aëris compre&longs;&longs;io &longs;equitur, quæ <lb/>tamen ad modicam di&longs;tantiam producitur; intelligo igitur de ip&longs;ius aëris <lb/>pondere; vt enim aquæ pondus aëra in fontibus illis artefactis, quos &longs;æpè <lb/>videritis, contentum, comprimit, quidni pondus &longs;uperioris aëris alium <lb/>comprimat? </s> <s>cogita Cylindrum plumbeum rantæ altitudinis, quanta opus <lb/>e&longs;t, vt tanti ponderis vi, versùs ba&longs;im &longs;ub&longs;idat, ac dilatetur; multò magis <lb/>&longs;i columnam ceream, vel ex butyro, aut charta crectam, maximæ &longs;cilicet <lb/>altitudinis tibi ante oculos ponas; &longs;ub&longs;idet enim pars inferior, quanquam <lb/>inæqualiter, erunt enim pre&longs;&longs;iones, vt altitudines, nimirum vt pondera; <lb/>quidni ergo aër, qui certè dilatari nequit, vt butyrum, nec enim locus e&longs;t, <lb/>&longs;ed tantùm comprimi, innitentis ponderis vi comprimatur? </s> <s>cùm perinde <lb/>&longs;it, ex quacumque tandem materia pondus con&longs;tet, & mille aëris libræ eun­<lb/>dem effectum gravitando habeant, quem totidem aquæ, vel alterius mate­<lb/>riæ libræ haberent. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Sentiremus haud dubiè ingens illud pondus, nec ferendo pa­<lb/>res e&longs;&longs;emus. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> An fortè &longs;entiunt vrinatores immer&longs;i ingens aquæ pondus <lb/>illorum capiti &longs;uper&longs;u&longs;um? </s> <s>Minimè verò; immò &longs;entire non debent, cùm <lb/>præcipuus corporis gravitantis, liquidi &longs;cilicet, effectus &longs;it corpus <lb/>&longs;ubjectum levius non deor&longs;um, at &longs;ur&longs;um extrudere; &longs;ic aqua in li­<lb/>gnum immer&longs;um gravitat; equidem aqua in fundum va&longs;is lignei gravitat, <lb/>deor&longs;umque pellit, &longs;i aër &longs;ubtus e&longs;t, vt patet, & &longs;imile pondus aquæ, ma­<lb/>nus foramini in fundo dicti va&longs;is appo&longs;ita &longs;entiret, modò manus foramen <lb/>adæquaret: at &longs;i lignum vel corpus levius aquæ immergatur, in id aqua <lb/>ita gravitat, vt illud &longs;ut&longs;um extrudat, non verò deprimat deor&longs;um; &longs;i ve­<lb/>rò &longs;it gravius aqua, ex parte &longs;altem illud &longs;u&longs;tentat, vnde appen&longs;um in <lb/>aqua, minùs illius pondus &longs;entitur: ab illo igitur periculo immunes &longs;umus, <lb/>nec timendum nobis e&longs;t, ne ab aëre obruamur: at ni fallor, ex præmi&longs;&longs;a <lb/>gravitatione longè latéque aëris &longs;uperfu&longs;i, &longs;equitur egregium illud experi­<lb/>mentum Mercurij in tubo vitreo contenti, & immer&longs;a alterius illius ex­<lb/>tremitate, in &longs;ubjectum Mercurium, &longs;cutella contentum; &longs;u&longs;tinetur enim ad <lb/>duos pedes altitudinis paulò plus reliquo tubo vacuo pror&longs;us manente, ab <lb/>aëris gravitantis Cylindro. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> De hoc argumento in hoc congre&longs;&longs;u agere non po&longs;&longs;umus, cùm <lb/>&longs;ufficiens alterius materia e&longs;&longs;e queat; in quo præclariffima & &longs;anè mirifica <lb/>phænomena explicabimus & demon&longs;trabimus, quæ tum ab aliis, tum <lb/>à nobis explorata fuerunt; illud vnum vel obiter indica&longs;&longs;e &longs;ufficiat, &longs;cilicet <lb/>experimentum illud nullo modo cum à te præmi&longs;&longs;a hypothe&longs;i con&longs;entire; <lb/>quod ni fallor per&longs;picuè demon&longs;tro. </s> <s>Sit enim di&longs;tantia Lunæ à terra 50. <lb/>Semidiametrorum terræ & Semidiameter terræ iuxta vulgarem calculum <lb/>&longs;it pa&longs;&longs;uum Geometricorum 3436363. quem numerum &longs;i ducas in 25. <lb/>quæ e&longs;t &longs;emidi&longs;tantia à terra &longs;cilicet ad lineam dirimentem, de qua &longs;upra <lb/>venient 86909075. pa&longs;&longs;us, hæc e&longs;t altitudo aëris gravitantis; &longs;i autem <pb pagenum="119"/>hunc numerum ducas in 5. venient 434544375 pedes; iam demus, aquæ <lb/>gravitatem e&longs;&longs;e ad gravitatem aëris non vt 400.ad 1.vt non nemo voluit, <lb/>led vt 1000. ad 1. dividatur vltimus numerus per 1000. quotiens veniet <lb/>rejecta minutia, 434544. igitur Cylindrus aëris prædictæ altitudinis adæ­<lb/>quabit pondere Cylindrum aquæ altum pedes 434544. Sit autem aqua ad <lb/>Mercurium, ad &longs;ummum, vt 1.ad 15. prædictus Cylindtus aëris adæquabit <lb/>pondere Cylindrum Mercurij altum pedes 28969. quomodo igitur, duos <lb/>tantum pedes altum adæquat & &longs;u&longs;tinet? </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Rectè omnino; hoc enim confirmat illorum &longs;ententiam, <lb/>qui volunt Mercurium &longs;u&longs;tineri ab aëre compre&longs;&longs;o, cuius vis tanta e&longs;t, vt <lb/>Mercurij Cylindrum 2.pedes altum adæquet. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Hoc etiam dici non pote&longs;t, cùm enim aëris compre&longs;&longs;i vis per <lb/>Cylindres æqualibus ba&longs;ibus non exeratur, &longs;icuti exeritur vis aëris gravi­<lb/>tantis, certè quo major e&longs;&longs;et ba&longs;is tubi vitrei, eo minor e&longs;&longs;e deberet altitudo <lb/>Mercutij ab aëre compre&longs;&longs;o &longs;u&longs;tentati; alia igitur ratio e&longs;t & cau&longs;a, quæ di­<lb/>ctum Mercurium &longs;u&longs;tinet. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Maxima igitur aëris no&longs;tri compre&longs;&longs;io e&longs;&longs;et ab illa imma­<lb/>nis ponderis vi proveniens, ac proinde vix nobis toleranda; & vereor, vt <lb/>per illam re&longs;pirare, vt aiunt, aut ducere anhelitum liceret. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Modica pror&longs;us illa vis e&longs;t; & jam olim Galileus, pro &longs;ummo, <lb/>quo pollebat, ingenio, ob&longs;ervavit vim percu&longs;&longs;ionis infinitam propemo­<lb/>dùm rationem habere ad vim gravitationis; quod facilè probabis, vel vni­<lb/>co ictu mallei, in glandem plumbeam impacti; illa enim ictus vi depre&longs;&longs;a <lb/>ita dilatatur, vt &longs;imilis effectus vix ab immani ponderis gravitantis mole <lb/>obtineri po&longs;&longs;it; omitto rationes phy&longs;icas, alioquin pulchertimas, ne à pro­<lb/>po&longs;ito fine longiùs declinem; admitto igitur infetiorem aëris tractum pau­<lb/>lò compre&longs;&longs;iorem e&longs;&longs;e, ac proinde parùm admodùm aut certè nihil ducen­<lb/>do anhelitui obe&longs;&longs;e: licèt enim Thorax inde paulò difficiliùs explicetur, <lb/>nonnihil tamen compen&longs;ationis ex eo fieri videtur, quod intra pulmones <lb/>explicatos faciliùs adducatur, cùm jam &longs;ponte &longs;ua eò tendat, tum ratione <lb/>gravitationis, tum ratione compre&longs;&longs;ionis, pari modo licèt aëris expul&longs;io­<lb/>ni præfara compre&longs;&longs;io tantulum ob&longs;it, re&longs;i&longs;tit enim aër compre&longs;&longs;us; aliun­<lb/>de tamen aër compre&longs;&longs;us ambiens thoracem, eju&longs;dem contractionem ju­<lb/>vat; hinc etiam aliqua fit compen&longs;atio: prætereà e&longs;to, aër compre&longs;&longs;us tan­<lb/>tulum impediat præfatam naturæ functionem; alia pariter alias impediunt; <lb/>hinc motu ip&longs;o defatigamur. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/> I am mihi venit in mentem illud Plinij dictum, lib.2.cap.98. <lb/>ex Ari&longs;totele, nullum &longs;cilicet animal, ni&longs;i æ&longs;tu recedente expirare; quod <lb/>inter fabulas referebam; nunc verò hujus dicti aliqua ratio affulget; nem­<lb/>pe cùm accedente æ&longs;tu &longs;it minor aëris gravitatio, ac proinde minor illius <lb/>pre&longs;&longs;io; contrà verò recedente; inde fit, re&longs;pirationem faciliorem e&longs;&longs;e, ac­<lb/>ce&longs;&longs;us, quàm rece&longs;&longs;us tempore; cùm autem moribundi tantùm non vi­<lb/>vant, & re&longs;pirandi pote&longs;tas in iis tantùm non extincta &longs;it; accedente mi­<lb/>nimo illo impedimento, quod à compre&longs;&longs;ione aëris provenit, eo tempore, <lb/>&longs;altem vt plurimùm, vitæ &longs;imul & anhelitus filum rumpitur. </s></p><pb pagenum="120"/><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Nihil potuit meliùs applicari, & facilè crediderim ex hac do­<lb/>ctrina, non pauca Medicos in rem &longs;uam derivare po&longs;&longs;e in prædicendo ægro­<lb/>rum animam agentium tran&longs;itu. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Vnum e&longs;t, ne quid di&longs;&longs;imulem, à me lectum, apud celeberri­<lb/>mum illum Hydrographiæ &longs;criptorem Furnerium lib.9.cap.1.plus humo­<lb/>ris &longs;cilicet ine&longs;&longs;e corporibus eo tempore, quo mare per æ&longs;tum intume&longs;cit; <lb/>minùs verò tempore refluxus, vt vocant; illud autem, ita mihi difficilè vi­<lb/>detur, vt huic nodo &longs;olvendo impar &longs;im. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Ex præmi&longs;&longs;is principiis non adeò difficilè mihi videtur; <lb/>cùm enim maximus æ&longs;tus &longs;it in Plenilunio, & tunc multus humor Lunari <lb/>effluvio terris affundatur; quid mitum, &longs;i quo tempore maximus æ&longs;tus e&longs;t, <lb/>corpora multo humore abundent. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Propo&longs;itæ à me difficultatis vim non capis; nec enim agi­<lb/>tur de ip&longs;o æ&longs;tu Plenilunij, &longs;ed de quolibet alio. </s> <s>Et verò in Plenilunio fit <lb/>refluxus, quo tempore minùs humotis corporibus ine&longs;t, & in Quadratu­<lb/>ris etiam fit æ&longs;tus; & tunc corporibus multus humot ine&longs;t: &longs;i nobis non <lb/>&longs;uccurras, Antime, animum de&longs;pondeo; ni&longs;i fortè rem ip&longs;am in dubium <lb/>voces. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> In dubium revocanda non e&longs;t; is enim non e&longs;t Furnerius, qui <lb/>aliis imponat; & verò miror à vobis non videri, ex præmi&longs;&longs;is principiis <lb/>hoc ip&longs;um &longs;equi: nempe in eo loco, in quo fit æ&longs;tus, aër minùs compre&longs;­<lb/>&longs;us e&longs;t, quia minùs gravitat, vt jam diximus, nec repetendum e&longs;&longs;e du­<lb/>xerim, &longs;i autem e&longs;t minùs compre&longs;&longs;us, minùs gravis e&longs;t, vt patet ex <lb/>terminis; corpus enim den&longs;um &longs;eu compre&longs;&longs;um gravius evadit; igi­<lb/>tur Lunatis ille humor admixtus difficiliùs, aut tardius a&longs;cendit; <lb/>quo enim medium gravius e&longs;t, corpus leve eò faciliùs &longs;ur&longs;um ex­<lb/>truditur; at verò tempore refluxus aër magis gravitat, in eum &longs;ci­<lb/>licet tractum, in quo refluxus e&longs;t, igitur aër compre&longs;&longs;ior gravior <lb/>evadit; quid mirum igitur, &longs;i Lunaris humor fur&longs;um faciliùs extrudatur? <lb/></s> <s>igitur tempore æ&longs;tus &longs;eu fluxus plus humoris ine&longs;t, minùs verò, tempore <lb/>refluxus. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Libenter mihi &longs;uccen&longs;erem, qui rem ob oculos po&longs;itam non <lb/>viderim; illud &longs;altem video ex dictis con&longs;tare, quæ & quanta &longs;it Lunæ <lb/>vis in corpora &longs;ublunaria; multi enim effectus, in ægris præ&longs;ertim corpo­<lb/>ribus ob&longs;ervantut, qui à celeberrimis Medicis Galenum &longs;ecutis Lunæ tri­<lb/>buuntur; quid porrò Luna conferat, non vt cau&longs;a, &longs;ed vt &longs;ubjectum & oc­<lb/>ca&longs;io, patet ex dictis hucu&longs;que; &longs;c licet majorem vel minorem humoris <lb/>vim, majorem item vel minorem aëris compre&longs;&longs;ionem, gravitatem, levita­<lb/>tem, gravitationem; quid etiam in malè affectis corporibus cuncta hæc <lb/>præ&longs;tare po&longs;&longs;int nemo non videt; quid ad hæc diver&longs;i Lunæ a&longs;pectus, im­<lb/>mò & fortè diver&longs;us Lunarium macularum &longs;itus, &longs;i fortè vt nonnullis vi­<lb/>&longs;um e&longs;t, aqua &longs;it, à no&longs;tra tamen diver&longs;a; quid denique deliquium Solis <lb/>vel Lunæ conferat ad diver&longs;as in &longs;ublunaribus corporibus mutationes; im­<lb/>mò quid conus vmbræ ab vtroque globo projectæ, pro vario &longs;itu; nempe <lb/>vapor Lunatis immer&longs;us vmbræ, den&longs;atur & gravior evadit, ferturque <pb pagenum="121"/>versùs illud ecutrum, cui ptopior e&longs;t; accedit, quòd ex Luna vmbræ im­<lb/>mer&longs;a vapor non educitur, vnde nova in &longs;iccitatis aut humotis vi muta­<lb/>tio &longs;equitur, immò & minor æ&longs;tus dicbus, qui deinde &longs;equuntur; quia &longs;ci­<lb/>licet totus ille humor de&longs;ideratur, qui toto Lunaris deliquij tempore So­<lb/>lis vi eductus fui&longs;&longs;et. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Vnum omittis, quod certè diguum &longs;citu e&longs;t; &longs;it enim lagennla <lb/><figure id="fig17"></figure><lb/>quæpiam A, ex cuius ventre a&longs;&longs;urgat &longs;ur&longs;um <lb/>canaliculus GF ad in&longs;tar ro&longs;tri; impleatur aqua <lb/>&longs;it què &longs;uprema &longs;uperficies aquæ BC, per cana­<lb/>liculum a&longs;turgit &longs;upra libellam CD; an fortè eo <lb/>tempore, quo tumet æ&longs;tus, id e&longs;t, quo Luna e&longs;t <lb/>in Meridiano; minùs a&longs;&longs;urgit <gap/> puta in E; plus <lb/>verò, puta in F, eo tempore quo à Meridlano 90. <lb/>gradibus di&longs;tat. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Rem magnam narras, Antime; &longs;ed f<gap/>tè fabulam nartas, <lb/>cuipiam haud ab&longs;imilis, qui aquam Marinam in canaliculo contentam flu­<lb/>xum & refluxum pati a&longs;&longs;erebat. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Seriò loquor, in his enim religioni ducerem, tibi alii&longs;que tui <lb/>&longs;imilibus imponere: &longs;ed miror à te non videri; totum hoc ex præmi&longs;&longs;a do­<lb/>ctrina &longs;equi; nempe aër in hoc infimo tractu compre&longs;&longs;us, vt dixi, premit <lb/>&longs;uperficiem aquæ BC; &longs;ed cùm &longs;uperficiem D minùs premat, quid mirum, <lb/>&longs;i pre&longs;&longs;io in BC prævaleat? </s> <s>Minùs autem premitur &longs;uperficies D, quàm <lb/>CF; quia compre&longs;&longs;um corpus exerit &longs;uam vim quoquo versùm per om­<lb/>nes lineas, v.g. </s> <s>centrum ba&longs;is BC, aër &longs;uperfu&longs;us per omnes lineas premit, <lb/>contentas intra conum maximè obtu&longs;um, & ba&longs;im D, per lineas contentas <lb/>intra conum valdè acutum; quid mirum igitur, &longs;i pre&longs;&longs;io in BC &longs;uperet <lb/>pre&longs;&longs;ionem in D, ac proinde aqua a&longs;&longs;urgat. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Nunquid hoc tribui non po&longs;&longs;et Cylindro aëris gravitanti <lb/>in ba&longs;im BC, qui longè gravior e&longs;t Cylindro gravitante in ba&longs;im D; &longs;unt <lb/>enim Cylindri; vt ba&longs;es. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Nullo modo, nempe &longs;i habeatur ratio gravitatior. </s> <s>is, non <lb/>a&longs;cendit aqua &longs;upra D; quia gravitatio in perpendicularibus parallelis <lb/>accipienda e&longs;t; neque in hoc vlla e&longs;t difficultas; cum &longs;it primum qua&longs;i <lb/>principium Hydraulicæ, aquarum <expan abbr="cõ&longs;i&longs;tentium">con&longs;i&longs;tentium</expan> &longs;uperficies e&longs;&longs;e ad libellam; <lb/>attenta &longs;cilicet dumtaxat aquæ gravitate, &longs;ecus tamen res &longs;<gap/> habet, &longs;i am­<lb/>bientis pre&longs;&longs;io accedat; in hoc quippe gravitatio à pre&longs;&longs;ione di&longs;fert, quod <lb/>hæc in Sphæram agat; ac proinde in idem punctum pre&longs;&longs;æ &longs;uperficiei per <lb/>lineas infinitas ad illud idem punctum terminatas, illa verò per lineas <lb/>parallelas deor&longs;um; ac proinde in idem punctum &longs;uperficiei vna tantùm <lb/>linea gravitationis cadat; vnde ratio petitur propter quam Cylindrus <lb/>major aquæ BG attollere minorem GD &longs;upra D non poffit. </s> <s>Porrò ex te <lb/>&longs;cire velim, Antimo, vtrùm in refluxu aqua altiùs a&longs;&longs;urgat quam in fluxu <lb/>per canaliculum GF. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Omnia ferè complecti vi&longs;us es, & &longs;ingularem aëris compre&longs;&longs;i <lb/>effectum per&longs;picuè di&longs;tinxi&longs;ti ab ip&longs;o ni&longs;u gravitationis; &longs;i vel vnum ver-<pb pagenum="122"/>bulum addidi&longs;&longs;es, perfecta & ab&longs;oluta explicatio fui&longs;&longs;et; verbo igitur di­<lb/>co; aër in æ&longs;tu &longs;eu fluxu e&longs;t minùs compre&longs;&longs;us; in refluxu verò compre&longs;­<lb/>&longs;ior; quid mirum ergo fi compre&longs;&longs;ior majorem vim & ni&longs;um exerat, & <lb/>fortè attollat aquam in F; minùs verò compre&longs;&longs;us in E; dixi fortè; quia <lb/>nondum periculum feci; faciam tamen brevi; quanquam &longs;i res non &longs;uc­<lb/>cedat, non propterea phy&longs;ica ratio deerit. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Igitur pariter in Plenilunio altiùs a&longs;&longs;urget aqua; quia tunc <lb/>aër gravior e&longs;t; igitur compre&longs;&longs;ior. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Gravior e&longs;t, vltrò concedo, quia multus humor admixtus; igi­<lb/>tur compre&longs;&longs;ior, nego con&longs;equentiam; quia illud non comprimitus, ra­<lb/>tione cujus gravior e&longs;t; cùm tamen &longs;ecus accidat, quàndo gravior e&longs;t, ra­<lb/>tione altioris Cylindri: Vt vt &longs;it, in Plenilunio differentiá altitudinis aquæ <lb/>ob&longs;ervare non potui, &longs;altem quæ &longs;ub &longs;en&longs;um cadat; &longs;i fortç ab aliquo dein­<lb/>ceps ob&longs;ervetur, ex jactis principiis ratio in promptu e&longs;t. </s> <s>Hîc autem aliud <lb/>experimentum omittere non po&longs;&longs;um, quod dictam hypothe&longs;im æquè con­<lb/>firmat; Sit vas ABG, cui tantulùm Mercurij in&longs;it, cujus &longs;uperficies EF; <lb/><figure id="fig18"></figure><lb/>fit tubus vitreus Mercurio plenus, admotoque ori digito, inver&longs;us im­<lb/>mergatur in Mercurium va&longs;e contentum; &longs;ubducto digito, ruit cum impe­<lb/>tu magna pars Metcurij tubo contenti, cujus tamen portio CI &longs;u&longs;pen&longs;a <lb/>manet; fui&longs;&longs;e autem ob&longs;ervatum aiunt, Luna exi&longs;tente in Meridiano, <lb/>Mercurij &longs;uperficiem infra C deprimi: di&longs;tante verò à Meridiano 90. grad. <lb/></s> <s>&longs;upra C attolli; modica fortè vtrimque differentia; hoc experimentum, &longs;i <lb/>verum e&longs;&longs;et, omnino evinceret æ&longs;tus cau&longs;am ab aliqua aëris pre&longs;&longs;ione, cui <lb/>Luna occa&longs;ionem præbeat, petendam effe. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Immò evinceret Cylindrum Mercurij ab aëre extrin&longs;eco <lb/>in &longs;uperficiem Mercurij EI gravitante &longs;u&longs;tineri, quod tamen ante negare <lb/>vi&longs;us es. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Ctede mihi, Augu&longs;tine, primò a&longs;pectu ita e&longs;&longs;e videtur; rem <lb/>tamen penitiùs & accuratiùs in&longs;picienti &longs;ecus e&longs;&longs;e videbitur; hîc tantùm <lb/>obiter indico; plus humoris ine&longs;&longs;e &longs;ublunaribus corporibus tempore flu-<pb pagenum="123"/>xus, quàm refluxus, vt jam dixi &longs;upra, ex hoc autem hujus effectus ra­<lb/>tio petitur, &longs;i tamen verus e&longs;t, de quo aliàs. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Huc potiùs accer&longs;erem diver&longs;am pre&longs;&longs;ionem; hæc enim mi­<lb/>nor e&longs;t in fluxu, in refluxu major; quid mirum igitur &longs;i in fluxu Mercurij <lb/>&longs;uperficies minùs, in refluxu altiùs &longs;upra C attollatur, premit enim aër <lb/>compre&longs;&longs;us &longs;uperficiem Mercurij EF. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Vel ex hoc conjicere poteris, quàm fallax &longs;it vnum experimen­<lb/>tum, & quàm facilè in errorem inducat, ni&longs;i ab aliis experimentis corri­<lb/>gatur; con&longs;ulenda e&longs;t igitur tota experimentorum collectio, vt error vi­<lb/>tetur, quod maximè in hoc ca&longs;u locum habet; Si enim vas A impleas <lb/><figure id="fig19"></figure><lb/>Mercutio, non jam vt ante aqua, a&longs;&longs;urgit in E <lb/>vel F, per canaliculum, &longs;ed infra D &longs;ub&longs;idit: plu­<lb/>ra de hoc argumento non dicam, quod reverà <lb/>adeò &longs;ingulare e&longs;t & amplum, vt &longs;ingulatem con­<lb/>gre&longs;&longs;um po&longs;tulet; eò igitur vos remitto, præ&longs;er­<lb/>tim cùm vix tempus &longs;uppetat ad reliqua pro&longs;e­<lb/>quenda, quæ ad &longs;u&longs;ceptum de Marino æ&longs;tu argu­<lb/>mentum pertinent. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Optimè mones, in proximum congre&longs;&longs;um remittamus, <lb/>vt ea quæ re&longs;tant de maris æ&longs;tu pro&longs;equamur; de quo, ni fallor, illa <lb/>omnia diligenter expo&longs;ui&longs;ti; quæ in præmi&longs;&longs;a hypothe&longs;i fierent, &longs;uppo&longs;ita <lb/>&longs;cilicet tota &longs;up erficie aquea, quæ ad diurnam & men&longs;truam mutationem <lb/>pertinent: duo re&longs;tant, opinor, primum ad mutationem annuam &longs;pectat, <lb/>quæ fit in punctis anni cardinalibus, vt vocant, nimirum in Æquinoctiis <lb/>& Sol&longs;titiis; alterum verò vt ex jactis principiis explices, varias æ&longs;t<gap/>um <lb/>mutationes, quæ in diver&longs;is globi terraquei locis ob&longs;ervantur; &longs;uppo&longs;ita <lb/>&longs;cilicet, ea globi &longs;uperficie, quæ modò e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/> Hæc duo explicanda re&longs;tant, fateor; primùm facilè expedio. </s> <s>Pri­<lb/>mò, Luna exi&longs;tente in Æquatore, maxima e&longs;&longs;et elevatio aquarum iis, qui <lb/>&longs;unt &longs;ub Æquatore, minima &longs;ub Polis; major autem vel minorpro majore <lb/>vel minore loci a&longs;&longs;umpti di&longs;tantia ab Æquatore; e&longs;&longs;et autem diurnus æ&longs;tus <lb/>æqualis nocturno. </s> <s>Secundò, Luna exi&longs;tente in Tropico Cancri, minor <lb/>e&longs;&longs;et æ&longs;tus, quàm ante, iis, qui &longs;unt &longs;ub Æquatore; <expan abbr="quãquam">quanquam</expan> diurnus æqua­<lb/>lis nocturno; iis verò, qui &longs;unt in Latitudine Boreali vltra Tropicum Can­<lb/>cri, diurnum majorem haberent, quàm ante, minorem verò nocturnum; <lb/>& vici&longs;&longs;im ij, qui &longs;unt in Latitudine Au&longs;trali, majorem nocturnum, <expan abbr="minor&etilde;">minorem</expan> <lb/>diurnum; & permutatis vicibus, exi&longs;tente Luna in Tropico Capricorni, i&longs;ti <lb/>majorem diurnum, minorem nocturnum, illi verò nocturnum majorem, <lb/>diurnum minorem: Porrò ad vitandam appellationum confu&longs;ionem, il­<lb/>lum æ&longs;tum diurnum appello, qui fit die Lunari, id e&longs;t Luna in Meridiano <lb/>&longs;upra horizontem exi&longs;tente. </s> <s>Tertiò, Quod pertinot ad alia loca inter Æqua­<lb/>torem & Tropicos &longs;ita, &longs;ervata proportione, æ&longs;tus major aut minor definiri <lb/>pote&longs;t, vt major &longs;it iis diurnus æ&longs;tus, ad quorum verticem Luna propiùs <lb/>accedit. </s> <s>Quartò, Linea ab&longs;idum per centrum terræ &longs;emper ducitur, & cùm <pb pagenum="124"/>circa axèm Mundi moveri cen&longs;eatur, Luna exi&longs;tente in Æquatore, de&longs;cri­<lb/>bit planum circuli; at verò extra Æquatorem de&longs;cribit &longs;uperficiem coni <lb/>acutioris, vel obtu&longs;ioris, pro majore vel minore Lunæ di&longs;tantia ab Æqua­<lb/>tore. </s> <s>Quintò, Maxima depre&longs;&longs;io in eo circulo &longs;em per e&longs;t, in cujus planum, <lb/>& centrum, linea ab&longs;idum perpendieulariter cadit. </s> <s>Sextò, Diver&longs;am quoque <lb/>mutationem inducere pote&longs;t diver&longs;us gradus caloris in aëre; nempe aër ca­<lb/>lidior, tarior e&longs;t & levior, frigidior verò; den&longs;ior & gravior, unde varij ef­<lb/>fectus gravitationis, pre&longs;&longs;ionis, Lunatis humoris, motus, &c. </s> <s>Hinc fortè il­<lb/>lud, quod à nonnullis ad&longs;truitur, cum veritate con&longs;entit; &longs;cilicet majores <lb/>cieri æ&longs;tus Luna in Aquarij Signo &longs;ita; quia Luna in Plenilunio, in quo ma­<lb/>jor æ&longs;tus con&longs;ideratur, &longs;i e&longs;t in Aquario, Sol, cui opponitur, e&longs;t in Leone, <lb/>tuncigitur maximè ardet æ&longs;tns; aër igitur valdè calidus e&longs;t; igitur rarus & <lb/>levis, vnde majore cum impre&longs;&longs;ione, aër Superior, humorque Lunaris gra­<lb/>vitant in inferiorem tractum; &longs;ed hoc parum profectò, aut nihil ju­<lb/>vat; nec cum obfervationibus con&longs;entit; & quam vis dici po&longs;&longs;it, va­<lb/>rietatem, quæ ex diver&longs;is ob&longs;ervationibus habetur, ad diver&longs;um ter­<lb/>ratum tractum reduci po&longs;&longs;e; quia tamen non tantùm aër calidus, qui <lb/>ad terras proximè accedit con&longs;ideratur, nec is, qui prædicto climati re­<lb/>&longs;pondet, &longs;ed is totus quantus quantus e&longs;t, qui versùs terræ centrum gravi­<lb/>tat, nulla fortè inde mutatio induci videtur. </s> <s>Hæc &longs;unt, ni fallor, quæ <lb/>&longs;tando in præmi&longs;&longs;a hypothe&longs;i, de mutationibus, quæ per annum fiunt in <lb/>Marino æ&longs;tu, dici po&longs;&longs;unt. </s> <s>Alterum re&longs;tat, quod fortè paulò difficilioris <lb/>e&longs;t operæ. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Duo &longs;uggero, quæ mihi veniunt in mentem; primum <lb/>e&longs;t, inter effectus diver&longs;æ & inæqualis gravitationis aëris, recen&longs;eri <lb/>po&longs;&longs;e ventum illum, qui cum æ&longs;tu conjunctus e&longs;t, levis quidem, &longs;en&longs;ibi­<lb/>lis tamen, vbi &longs;cilicet montium obices non ob&longs;tant, nec aliæ cau­<lb/>&longs;æ ob&longs;unt, ab ortu versùs occa&longs;um, de quo dubium e&longs;&longs;e nequit, <lb/>cùm longè faciliùs navigetur versùs occa&longs;um, quàm ver&longs;us ortum; cùm <lb/>enim aër, Luna in Meridiano po&longs;ita, &longs;it minùs pre&longs;&longs;us, haud dubiè le­<lb/>vior e&longs;t; igitur ab alio, qui versùs ortum e&longs;t, vtpote graviore extru ditur; <lb/>accedit, quòd altior e&longs;t aër in O, quàm in F; (<emph type="italics"/><expan abbr="&longs;eq.">&longs;eque</expan> Schem.<emph.end type="italics"/>) igitur versùs f <lb/>de&longs;cendere pote&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Sed cur potiùs aër, qui e&longs;t in O, de&longs;cendet in F, ab ortu &longs;cili­<lb/>cet ad occa&longs;um, quà is, qui e&longs;t in N, versùs ortum; cùm eadem vtriu&longs;que <lb/>&longs;it pre&longs;&longs;io, gravitas, altitudo. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Rem haud dubiè hoc argumento conficeres, &longs;i Luna <lb/>immota in I &longs;emper e&longs;&longs;et, &longs;ed admi&longs;&longs;o illius motu versùs S aër N le­<lb/>vius redditur, & aër O gravius; quid mirum ergo, &longs;i O prævaleat? <lb/></s> <s>Alterum fortè altioris indaginis e&longs;&longs;et; obiter tamen indicabo: nem­<lb/>pe varij Autores referunt, vatias inundationes accidi&longs;&longs;e eo tempore, <lb/>quo varij Planetæ Conjuncti erant; cujus ratio ex præmi&longs;&longs;is facilè, <lb/>meo judicio, deducitur; Sit enim Luna I in principio Arietis, So­<lb/>li conjuncta; Sint etiam Mercurius, Venus, Mars ibi conjuncti; ad-<pb pagenum="125"/><figure id="fig20"></figure><lb/>de &longs;is Iovem; haud dubiè linea AS ad maximam di&longs;tantiam producendæ <lb/>erit, antequam incidat in aliam lineam dirimentem re&longs;pectu alterius cu­<lb/>ju&longs;libet globi totalis; vnde major erit circulus maximæ pre&longs;&longs;ionis, vt &longs;u­<lb/>pra vocabas, Antime; igitur major illius vis atque pre&longs;&longs;io, igitur major <lb/>aquæ tumor; major igitur inundatio; vt tamen de &longs;ingulis &longs;eor&longs;im aliquid <lb/>definiatur; varius terrarum &longs;itus con&longs;iderandus e&longs;t; & hoc e&longs;t alterum ca­<lb/>put, Antime, quod tibi explicandum re&longs;tat. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Egregia pror&longs;us ob&longs;ervatio; inde enim per&longs;picua & qua&longs;i pal­<lb/>pabilis cau&longs;a & ratio multorum effectuum &longs;tatuitur, qui vulgò virtutibus <lb/>occultis tribuuntur; &longs;ed vt pen&longs;um impo&longs;itum per&longs;olvam, terre&longs;tris globi <lb/>Plani&longs;phærium ve&longs;tris oculis &longs;ubjicio, & antequam oculos in globum <lb/>conjiciatis, nonnulla &longs;uppono ex præmi&longs;&longs;is. </s> <s>Primò, Vim pre&longs;&longs;ionis, quæ <lb/>tum à circulo maximæ pre&longs;&longs;ionis, vt &longs;upra appellavi, tum ab aliis paral­<lb/>lelis procedit, ita vatiari, ac perturbari po&longs;&longs;e, vt diver&longs;um æ&longs;tus effectum <lb/>producat, etiam &longs;ub eodem Parallelo; vatiatur autem &longs;eu pertutbatur ex <lb/>eo quod terre&longs;tris globi &longs;uperficies tota aquea non &longs;it, &longs;ed partim aquea <lb/>partim continens; nempe arcus ille circuli pre&longs;&longs;ionis, cui continens &longs;ub­<lb/>e&longs;t, nullum pre&longs;&longs;ionis effectum con&longs;equitur, reliquo tamen eju&longs;dem circuli <lb/>arcu, cui aqua &longs;ube&longs;t, effectum præ&longs;tante; brevitatis ergo, hunc arcum <lb/>vtilem vocemus; illum verò inutilem. </s> <s>Secundò, Non tantùm vim pre&longs;­<lb/>&longs;ionis con&longs;iderandam e&longs;&longs;e, quatenus e&longs;t ab vno arcu, &longs;ed quatenus e&longs;t etiam <lb/>abaliis; ita vt ab illo commuai qua&longs;i ni&longs;u aqua elevari cen&longs;eatur, quæ re-<pb pagenum="126"/>vera elevatio licèt aliq<gap/>em aquarum motum dicat, non tamen ita acci­<lb/>pienda e&longs;t, vt aqua à circulo maximæ pre&longs;&longs;ionis ad punctum maximæ ele­<lb/>vationis excurrat, totumque illud &longs;patium conficiat, &longs;ed vt pars aquæ aliam <lb/>partem pellat, & hæc aliam; cogita ve&longs;icam aqua plenam, quam vel ma­<lb/>nu, vel fune in &longs;piras acto &longs;tringis, ac proinde temporis ferè momento tu­<lb/>mor attollitur, quod certè per motum obtineri non po&longs;&longs;et. </s> <s>Tertiò, per <lb/>motum aquam elevatam versùs litus excurrere, & aver&longs;is ire fluminibus, <lb/>ad in&longs;tar majoris cuju&longs;dam dolij; vbi enim litore altior e&longs;t, in litus exun­<lb/>dat; idem dico de &longs;uprema fluminum &longs;uperficie: & hæc e&longs;t ratio cur <lb/>aqua, per æ&longs;tum exundet, quia cum prædictæ pre&longs;&longs;ionis vi, etiam ver­<lb/>sùs oram & litus extollatur, in litus ip&longs;um, quod inferius e&longs;t, & in &longs;ub­<lb/>jacentis fluminis alveum excurrit, &longs;ublata verò pre&longs;&longs;ione, aqua illa, <lb/>quæ priùs exundarat in litus, cum &longs;it altius ip&longs;a maris, po&longs;tquam detu­<lb/>muit, &longs;uperficie, versùs ip&longs;um mare refluit. </s> <s>Quartò, Majorem arcum <lb/>vtilem plùs, minorem verò minùs præ&longs;tare; præ&longs;ertim cùm &longs;uo modo <lb/>accedat ratio vectis, &longs;icuti brevior baculus difficiliùs curvatur, quàm <lb/>longio<gap/>; hinc major arcus minorem &longs;uperat, & major &longs;uperficies aquæ <lb/>ex præ&longs;atis arcubus con&longs;tans vincit minorem ex arcubus etiam con&longs;tan­<lb/>tem; &longs;unt autem huju&longs;modi arcus paralleli circulo maximæ pre&longs;&longs;ionis; <lb/>& cum in &longs;ingulis punctis circuli vtilis, æqualis pre&longs;&longs;io cen&longs;eatur, inæ­<lb/>qualitas pre&longs;&longs;ionis directæ accipienda e&longs;t in arcubus ad angulos rectos <lb/>&longs;ecantibus prædictos pre&longs;&longs;ionum arcus. </s> <s>Quintò, Suppono ad aquam extru­<lb/>dendam, per angu&longs;tiorem alveum, &longs;eu canalem, minorem pre&longs;&longs;ionis vim de­<lb/>&longs;iderari, vt con&longs;tat ex doctrina motuum; nempe major mobilis, &longs;eu moven­<lb/>di corporis moles motui magis re&longs;i&longs;tit. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Cuncta hæc &longs;atis intelligo; &longs;tatuo enim globum i&longs;tum in <lb/>&longs;itu Sphæræ rectæ; ita vt axis & poli &longs;int in plano horizontis; a&longs;lum­<lb/>ptoque &longs;upremo globi puncto, &longs;eu vertice, illius horizon, qui per Po­<lb/>los de&longs;cribitur, e&longs;tque vnus ex Meridianis & di&longs;tat à puncto a&longs;&longs;umpto <lb/>90. grad. </s> <s>circulus maximæ pre&longs;&longs;ionis erit, cui &longs;i omnes parallelos acci­<lb/>piam, omnes circulos pre&longs;&longs;ionum habeo, & probè di&longs;tinguo arcus <lb/>vtiles ab inutilibus, & portionem &longs;uperficiei ab vtilibus rectam, &longs;eu <lb/>occupatam, ab alia; quæ profectò quantum varia &longs;it, cùm hinc expli­<lb/>cetur, illinc contrahatur, inde versùs Ortum, hinc versùs Boream ex­<lb/>currat &longs;atis patet. </s> <s>Vt autem majoris, vel minoris vim definiam, ratio­<lb/>ne &longs;cilicet puncti a&longs;&longs;umpti, initio ducto ab horizonte, &longs;eu circulo ma­<lb/>ximæ pre&longs;&longs;ionis, con&longs;idero ac metior &longs;uperficiem vtilem <gap/> &longs;ic eam vo­<lb/>co, quam arcus vtiles occupant) pro cujus diver&longs;o &longs;itu, & diver­<lb/>&longs;a exten&longs;ione, diver&longs;a &longs;equitur pre&longs;&longs;io & elevatio in puncto a&longs;&longs;um­<lb/>pto Æquatoris; Hoc &longs;at benè intelligo; vellem tantùm, vt illud quod <lb/>vltimo loco ad&longs;truxi&longs;ti, de aqua in angu&longs;tias redacta paulò fu&longs;iùs ex­<lb/>plicares. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Per me licet; &longs;upponamus ita extrudi per canalem ADH. <lb/>vt altitudo alvei pleni &longs;it AC, latitudo verò initio &longs;it AB, &longs;ed qui <lb/>retenta eadem altitudine, contrahatur &longs;ecundùm latitudinem, ac proin-<pb pagenum="127"/>de lineæ AH, BK, non &longs;int parallelæ, &longs;ed vna ad aliam accedat; jam <lb/>alij demon&longs;tratunt velocitatem aquæ in AB ad velocitatem aquæ in HK <lb/><figure id="fig21"></figure><lb/>&longs;uppo&longs;ita eadem vi motrice, e&longs;&longs;e vt HE ad AD, id e&longs;t vt HK ad AB, id <lb/>e&longs;t in ratione latitudinum permutando, &longs;i verò decre&longs;cat etiam altitu­<lb/>do, ita vt altitudo in HK, &longs;it HI, velocitas in AB e&longs;t ad velocita­<lb/>tem in HK, vt HF, ad AD vel in compo&longs;ita latitudinum & altitu­<lb/>dinum permutando; hoc inquam jam alij demon&longs;trarunt; cùm enim <lb/>tota aqua fluat per planum AD, & per planum HE, quæ ad in&longs;tar duo­<lb/>rum foraminum con&longs;iderare po&longs;&longs;umus, &longs;uppo&longs;ita &longs;emper eadem vi motri­<lb/>ce, haud dubiè velociùs fluere debet per HE, quàm per AD, idque in ea <lb/>proportione, in qua AD major e&longs;t quàm HE; in hoc nulla e&longs;t difficultas, <lb/>& omnibus congruit experimentis; hinc aqua quæ &longs;ur&longs;um extruditur, di­<lb/>latatur, quæ verò &longs;ua &longs;ponte de&longs;cendit, contrahitur; quia hæc motu acce­<lb/>lerato, illa retardato fertur. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;t.<emph.end type="italics"/></s><s> Hoc &longs;æpè miratus &longs;um in filo labentis olei, quod certè ad hunc <lb/>effectum aptius e&longs;t, quàm aqua, propter vliginem; contrahitur enim & ex­<lb/>tenuatur filum illud; &longs;ed rem grati&longs;&longs;imam faceres, &longs;i demon&longs;trares in qua <lb/>proportione contrahatur. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Hoc jam alij demon&longs;trarunt; quia tamen nihil e&longs;t, quod tibi <lb/><figure id="fig22"></figure><lb/>negare au&longs;im; &longs;upponamus e&longs;&longs;e vas CB, in cujus <lb/>fundo &longs;it foramen CD, accipiatur quæcunque <lb/>altitudo puta CF, &longs;it quælibet Semiparabola <lb/>AFH, &longs;ub axe FA, ducanturque applicatæ CE, <lb/>FH; in Parabola &longs;i accipiatur motus accelera­<lb/>tus, axis erit &longs;patium, applicatæ verò tem­<lb/>pus & velocitas; igitur &longs;patium acqui&longs;itum <lb/>tempore CE erit ad acqui&longs;itum tempore FH, <lb/>vt AC ad AF, &longs;unt enim &longs;patia, vt tempo­<lb/>rum Quadrata; igitur velocitas aquæ in CD <lb/>erit ad velocitatem in FG vt CE ad FH, <lb/>&longs;ed tran&longs;itus aquæ &longs;unt vt velocitates, per­<lb/>mutando, vt jam dixi &longs;upra; igitur vt FH <lb/>ad CE, ita circulus CD ad circulum FH; igitur &longs;i vt Diameter CD <lb/>ad FG, ita hæc, ad K, erit vt FH, ad CE, ita CD ad K. &longs;it vt <pb pagenum="128"/>FH ad CE, ita hæc ad L, & vt CD ad K, ita hæc ad M, &longs;itque inter KM <lb/>media proportionalis N, erit vt FH ad CE, vel CD ad M, ita AF ad <lb/>AC; igitur AF e&longs;t ad AC in ratione quadruplicata CD ad FG, id e&longs;t, <lb/>vt CD ad M, facilè autem invenitur FG, quia vt FH ad CE, ita CD, <lb/>quam habeo ad K; inter K & D invenio mediam proportionalem FG; <lb/>item inter K & M &longs;cilicet N. </s> <s>Sed hæc &longs;ufficiant, jam ad &longs;u&longs;ceptum pro­<lb/>po&longs;itum redeo, & quia omnia &longs;ingularia explicari non po&longs;&longs;unt; fru&longs;tra <lb/>enim id fieret, mihi &longs;atis e&longs;&longs;e videtur, &longs;i vnum vel alterum &longs;ingulare ex­<lb/>ponam. </s> <s>Accipio igitur punctum in Æquatore 345. longitudinis, vt vi­<lb/>des in globo; cum circa illum tractum, celeberrimus ille fluvius, quem <lb/>Amazonum vocant, ex Orientali Americæ ora in mare influat, & maxi­<lb/>mum &longs;tatis horis patiatur æ&longs;tum, qui ad 300. milliaria per alveum flu­<lb/>minis a&longs;cendit; huic tractui Luna oritur in Meridiano longitudinis 75. & <lb/>tunc maxima e&longs;t pre&longs;&longs;io circa tractum longitudinis 545. quæ &longs;en&longs;im ver­<lb/>sùs Ortum decre&longs;cit; quid mirum ergo, &longs;i versùs oram Guineæ ad Afri­<lb/>cam, mare intume&longs;cat? </s> <s>Vbi præ&longs;ertim Luna per 30. gradus versùs occa&longs;um <lb/>progre&longs;&longs;a e&longs;t, vbi verò tandem pervenit ad grad. </s> <s>345. tunc ibi maxima <lb/>e&longs;t aquarum elevatio; & quia longè ante aqua a&longs;&longs;urgere cœpit, ab eo <lb/>&longs;cilicet momento, quo à grad.75. Luna occa&longs;um versùs progre&longs;&longs;a e&longs;t, quid <lb/>mirum &longs;i a&longs;&longs;urgens aqua in apertum & &longs;atis directum fluminis alveum ex­<lb/>currat? </s> <s>In quem tamdiu excurrit; quamdiu a&longs;&longs;urgit aqua ad illam oram; <lb/>hæc autem tamdiu a&longs;&longs;urgit, quamdin pre&longs;&longs;io decre&longs;cit; hæc demum tam­<lb/>diu decre&longs;cit, quamdiu Luna ad Meridianum longit.745. accedit; vbi <lb/>enim Metidianum illum attingit, maxima e&longs;t aquarum elevatio, nec vltra <lb/>pre&longs;&longs;io decre&longs;cit; &longs;ed deinde cre&longs;cit pre&longs;&longs;io, progrediente ad occa&longs;um Lu­<lb/>na, idque continuè donec perveniat ad nonage&longs;imum inde gradum, id <lb/>e&longs;t, ad longitud. </s> <s>grad. </s> <s>255. hinc refluit aqua, non modò proprio acta <lb/>pondere, &longs;ed accedente majore vi pre&longs;&longs;ionis &longs;ollicitata, idque, quam­<lb/>diu pre&longs;&longs;io cre&longs;cit, vnde per &longs;e tamdiu fluxus durat, quamdiu refluxus, <lb/>& hoc vt plurimum fieri &longs;olet, licet per accidens alter altero diuturnior &longs;it, <lb/>de quo infra præterea progrediente Luna à gradu 255. ad 165. in hoc <lb/>puncto erit maxima elevatio; igitur circulus maximæ pre&longs;&longs;ionis &longs;ecabit <lb/>Æquaterem in punctis 255. & 75. vt patet, at in ii&longs;dem punctis circulus <lb/>maximæ pre&longs;&longs;ionis Æquatorem &longs;ecabat, quando Luna erat in gradu 345. <lb/>igitur in eodem tractu maxima e&longs;t aquarum elevatio; &longs;en&longs;im enim ibi a&longs;­<lb/>&longs;urgit aqua, vbi &longs;en&longs;im pre&longs;&longs;io decre&longs;cit; igitur dum Luna à puncto 255.ad <lb/>punctum 165. progreditur, cre&longs;cit æ&longs;tus ad prædictam oram, & in fluminis <lb/>alveum intrat. </s> <s>Denique peracto circulo Luna redit ad grad.75. & tunc e&longs;t <lb/>maxima pre&longs;&longs;io in dicto tractu 345. Vides quàm facilè cuncta hæc ex præ­<lb/>mi&longs;&longs;is deducta præfato tractui applicentur. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;t.<emph.end type="italics"/></s><s> Duo mihi occurrunt difficilia; primùm e&longs;t, &longs;ita Luna ingradu <lb/>longit. </s> <s>345. circulum maximæ pre&longs;&longs;ionis Meridianum illum e&longs;&longs;e, qui <lb/>Æquatorem &longs;ecat in grad. </s> <s>255. ac proinde per medium qua&longs;i mare paci­<lb/>ficum ducitur; licèt autem hujus maris pre&longs;&longs;io aliquem effectum habere <lb/>po&longs;&longs;it, non tamen vllam vim derivare pote&longs;t in oram maritimam, <pb pagenum="129"/>inquam prædictum flumen influit, cùm interjectus va&longs;ti&longs;&longs;imus Americæ <lb/>tractus ob&longs;tet; &longs;ecat etiam Æquatorem in grad. </s> <s>Longit.75. Sed hic locus <lb/>non mari &longs;ed terris incubat, ducitur enim per mediam ferè Æthiopiam <lb/>& Africam ab Au&longs;tro in Boream; igitur cùm mare non premat, nullus in­<lb/>de pre&longs;&longs;ionis effe ctus &longs;equitur. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Antequam ad &longs;ecundam difficultatem orationem convertas, <lb/>hæc quam expo&longs;ui&longs;ti, mihi priùs &longs;olvenda e&longs;t; & fateor, vel nullam, vel <lb/>minimam pre&longs;&longs;ionis vim à &longs;emicirculo maximæ pre&longs;&longs;ionis per mare pa­<lb/>cificum ducto, ad grad Longit.255.ad o&longs;tia præfati fluminis traduci, pro­<lb/>pter interjectum continentis Americæ impedimentum; dixi vel mini­<lb/>mam, quia negari non pote&longs;t, traduci aliquam tum versùs Au&longs;trum pet <lb/>&longs;reta Magellanicum, Marium &c. </s> <s>tum versùs Septenttionem per freta <lb/>Davi&longs;ium, Hud&longs;onium &c. </s> <s>Fateor etiam minimam vim traduci ad præfa­<lb/>ta o&longs;tia à &longs;emicirculo ortivo maximæ pre&longs;&longs;ionis Æquatorem &longs;ecante ad <lb/>grad Longit.75. cùm major illius pars &longs;it inutilis, arcus verò vtiles hinc <lb/>versùs Septentrionem, indèversùs Au&longs;trum, à promontorio, quod bo­<lb/>næ Spei vocant, excurrant, cùm tamen vis pre&longs;&longs;ionis non tantùm &longs;it <lb/>à prædicto circulo maximo, &longs;ed etiam ab aliis minoribus parallelis, <lb/>prædictæ elevationis ad illa o&longs;tia plu&longs;quam &longs;ufficientem cau&longs;am ha­<lb/>bemus. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Cur verò ad 300. milliaria per alveum fluminis æ&longs;tus a&longs;­<lb/>cendit? </s> <s>cùm tamen ad oram Guineæ oppo&longs;itam longè minus a&longs;cendat: <lb/>& hæc e&longs;t altera difficultas. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Ex illo communi pre&longs;&longs;ionis ni&longs;u, motus quidam mixtus vel <lb/>eju&longs;dem motus linea re&longs;ultat, &longs;ecundùm quam æ&longs;tus in oram excurrit; cùm <lb/>igitur circuli pre&longs;&longs;ionum, qui mari A tlantico incumbunt, aquam attol­<lb/>lant extrudantque qua&longs;i versùs Au&longs;trum, ac proinde versùs Borealem <lb/>Americæ oram; circuli verò qui Æthiopicum premunt, extrudant aquam <lb/>per fauces illas inter Bra&longs;iliam & Africam interceptas, versùs Caurum; <lb/>ex vtroque ni&longs;u, mixtus quidam re&longs;ultat ver&longs;us Libycum, ac proinde in <lb/>o&longs;tia præfati fluminis, qua&longs;i directè in cidit æ&longs;tus; Quid mirum igitur, &longs;i <lb/>longiùs excurrat? </s> <s>accedit quod fluminis alveus per 10. integros gradus <lb/>id e&longs;t 600.milliaria, qua&longs;i &longs;ecundùm rectam lineam versùs Libycum fer­<lb/>tur; quod reverà plutimùm confert ad hoc, vt æ&longs;tus per dictum alveum <lb/>longius excurrat: At verò ad oram Guineæ licèt rapidi&longs;&longs;imus æ&longs;tus a&longs;­<lb/>&longs;urgat torrentis ad in&longs;tar, quia in prædictam oram ad Au&longs;trum conver­<lb/>&longs;am, versùs Boream extru&longs;us qua&longs;i directè fertur; non tamen per alveum <lb/>fluminum longè excurrit, cùm nec &longs;int capaces alvei, nec &longs;ecundùm di­<lb/>rectam lineam eant, neque, vt vides in hoc globo, Guinea magnos flu­<lb/>vios habeat; equidem ad 7. grad. </s> <s>Latit. </s> <s>Au&longs;tralis magnus fluvius Zaire in <lb/>Oceanum influit, &longs;ed à 6. gradu ad promontorium bonæ Spei perexiguus <lb/>æ&longs;tus e&longs;t; prærerquam quòd linea æ&longs;tus in eo tractu; (&longs;ic deinceps appel­<lb/>labo) tendit ad Vulturnum, vel Euronotum; vnde valdè obliquè in oram <lb/>illabitur; non mirum igitur &longs;i potiùs præterfluat, quàm irrumpat. </s> <s>Vnum <lb/>omi&longs;eram, &longs;cilicet, Oceanum Æthiopicum in iis faucibus, quas in <pb pagenum="130"/>globo vides, inter Gibbum Africæ, extremumque Bra&longs;iliæ promontorium <lb/>coërceri, vnde intume&longs;cat a&longs;&longs;urgatque cum impetu, nece&longs;&longs;e e&longs;t, adver­<lb/>sùs oppo&longs;itam &longs;ibi, qua&longs;i aggerem, Guineæ oram. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Non e&longs;t dubium, quin æ&longs;tus linea ad tem hanc multùm, ne <lb/>dicam totum conferat; nondum tamen &longs;atis capio, vnde & quomodò <lb/>hæc linea &longs;tatuatur potiùs quàm alia; hac enim &longs;emel &longs;uppo&longs;ita, inde <lb/>facilè deducam, vtrùm magnus, an parvus æ&longs;tus &longs;it, in data quali­<lb/>bet ora. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Rem acu tetigi&longs;ti; hæc enim linea æ&longs;tus, &longs;eu cur&longs;us <expan abbr="aquarũm">aquarumm</expan>, <lb/>quem &longs;i paulò vehementior &longs;it & contractior, Eurippum vocant, ab ea­<lb/>dem cau&longs;a procedit, à qua æ&longs;tus ip&longs;e, vel aquarum elevatio; &longs;cilicet ab in­<lb/>æquali aëris pre&longs;&longs;ione, & inæquali ni&longs;u; itaque ex pluribus capitibus hæc <lb/>linea æ&longs;tus determinari pote&longs;t. </s> <s>Primò, in præmi&longs;&longs;a hypothe&longs;i &longs;olus e&longs;&longs;et <lb/>aquarum motus ab ortu in occa&longs;um, vt jam &longs;upra dictum e&longs;t; nempe ille <lb/>idem pre&longs;&longs;ionis ni&longs;us &longs;emper duraret, & tantus e&longs;&longs;et aquarum tumor, <lb/>&longs;ub vno Meridiano, quantus &longs;ub alio, &longs;ub eodem &longs;cilicet Parallelo; at <lb/>po&longs;ita tali &longs;uperficie terræ qualis modò e&longs;t, in &longs;ingulis ferè punctis eju&longs;­<lb/>dem Paralleli, mutatur ni&longs;us; quia mutatur illius cau&longs;a; diver&longs;a e&longs;t enim <lb/>arcuum vtilium ratio; hinc diver&longs;a linea &longs;equitur; &longs;i enim æqualis &longs;it <lb/>ni&longs;us ab Au&longs;tro; Aquilone & Ortu, & minor, aut nullus ab occa&longs;u, in <lb/>occa&longs;um linea motus ibit; &longs;i æqualis ab Au&longs;tro, Occa&longs;u & Ortu, & mi­<lb/>nor in Aquilone, ad Aquilonem ibit; atque ita de aliis; & cùm infinitæ <lb/>&longs;int combinationes ni&longs;uum, vt &longs;unt infinitæ diver&longs;arum pre&longs;&longs;ionum, <lb/>etiam &longs;ub eodem Parallelo, quia infinitæ-mutationes &longs;uperficierum <lb/>ex arcubus vtilibus con&longs;tantium, tum in magnitudine, tum in &longs;itu, <lb/>inde &longs;equitur infinitas e&longs;&longs;e po&longs;&longs;e, ac reverà e&longs;&longs;e lineas æ&longs;tus, quæ ex <lb/>diver&longs;o ni&longs;u na&longs;cuntur: Primum igitur caput, ex quo talis linea &longs;tatui­<lb/>tur, e&longs;t talis ratio ni&longs;us, &longs;eu pre&longs;&longs;ionis. </s> <s>Secundò à quibu&longs;dam locorum <lb/>angu&longs;tiis petitur, &longs;eu maris &longs;eu freti, quod &longs;ecundùm talem vel talem <lb/>lineam excurrit; cùm enim aqua pre&longs;&longs;ionis vi extrudatur, & continen­<lb/>tis vtrimque aggeres aquam contineant, quid mirum, &longs;i per freta <lb/>eurrat, atque adeò ab alveo freti linea æ&longs;tus determinetur. </s> <s>Tertiò, Si <lb/>vtrimque vis pre&longs;&longs;ionis in vtrumque freti o&longs;tium aquam intrudat, in­<lb/>tra fretum æ&longs;tus concurrent. </s> <s>Quartò, quando æ&longs;tus valdè obliquè in­<lb/>cidit in aliquam oram, non reflectitur, &longs;ed ip&longs;am oram præterlabitur; <lb/>immò &longs;i ip&longs;a hora ad modum &longs;inus cavi e&longs;t, æ&longs;tus &longs;emiorbe peracto, ver­<lb/>sùs eam partem, vnde venerat, declinat; hinc mutatio lineæ: ad hoc ca­<lb/>put revoca reflexionem. </s> <s>Quintò, Æ&longs;tus alterius maris ex angu&longs;tis fauci­<lb/>bus erumpens, & in alium incidens, lineam mutat; nempe ex vtroque qui­<lb/>dam motus mixtus re&longs;ultat, ac proinde nova linea. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Cuncta hæc in rem hanc optimè quadrant: quare nihil aliud <lb/>re&longs;tat, ni&longs;i vt fidelis & accurata Marini æ&longs;tus hi&longs;toria de&longs;cribatur, vt &longs;cia­<lb/>mus quænam &longs;it linea æ&longs;tus in qualibet ora; Tu verò me tibi &longs;ummopere <lb/>ob&longs;tringeres, &longs;i aliqu ot exempla breviter afferres, quibus ea, quæ dixifti, <lb/>meliùs con&longs;tarent. </s></p><pb pagenum="131"/><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Prædicta hi&longs;toria ad rem hanc maximè opportuna, immò & <lb/>nece&longs;&longs;aria e&longs;&longs;et, in qua tamen à rei Nauticæ Scriptoribus nonnulli de&longs;i­<lb/>dera&longs;&longs;ent, vt &longs;altem in præcipuis Oceani oris fideliter retuli&longs;&longs;ent de ma­<lb/>ris æ&longs;tu; Primo quàm altus. </s> <s>Secundo quantum excurrat; Tertio quamdiu <lb/>a&longs;&longs;urgat; Quarto quamdiu refluat; Quinto quâ horâ &longs;ummus æ&longs;tus &longs;it. <lb/></s> <s>Sexto quo die &longs;ynodalis periodi, maxima in æ&longs;tu aquarum elevatio, & quo <lb/>die minima; Septimo, quo anni Plenilunio aut Novilunio &longs;it maximus <lb/>æ&longs;tus. </s> <s>Octavo, quænam &longs;it æ&longs;tus linea, quæ fortè &longs;ingulis diebus tantulum <lb/>mutatur; mutatur enim pre&longs;&longs;ionis ratio, quia mutantur &longs;uperficies ex ar­<lb/>cubus vtilibus con&longs;tantes; hi porrò mutantur; quia mutatur ab&longs;idum linea, <lb/>cuncta hæc in qualibet ora ob&longs;ervanda e&longs;&longs;ent. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Tuæ &longs;ententiæ omnino &longs;ub&longs;cribo, & hæc eadem in præfatis <lb/>Hi&longs;toricis de&longs;iderarem; &longs;ed quæ&longs;o te, &longs;i me amas, profer aliquot exempla, <lb/>quæ tibi haud dubiè memoria &longs;uggeret. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Hujus globi a&longs;pectus nonnulla fortè in memoriam mihi revo­<lb/>cabit. </s> <s>Primo loco circa polum vnum occurrit; ad &longs;ummum enim pro­<lb/>montorium Finnomarchiæ currit Eurippus à Cauro &longs;cilicet versùs Eu­<lb/>ronotum &longs;eu Vulturnum; &longs;unt enim angu&longs;tiæ maris inter Nieulandiam & <lb/>Groelandiam, per quas mare facilè extruditur vi pre&longs;&longs;ionis, tum Oceani <lb/>Tartarici, tum illius qui Americam Septentrionalein alluit, nec non ver­<lb/>sùs dictam oram per dictam lineam pellitur. </s> <s>Secundo, A pulchra In&longs;ula, <lb/>quæ novæ Franciæ Borealis e&longs;t, ad fretum Davi&longs;ium, à medio Iulio ad fi­<lb/>nem Augu&longs;ti; linea æ&longs;tustendit ad Au&longs;trum, reliquo tempore ad Occa&longs;um, <lb/>quo æ&longs;tus in &longs;inum S. </s> <s>Laurentij irrumpit; ratio e&longs;t, quia men&longs;e Augu&longs;to <lb/>glacies maris congelati liquatæ &longs;unt, ac proinde liberè fluunt, aquæ ex <lb/>freti Davi&longs;ij & Hud&longs;onij angu&longs;tiis versùs Vulturnum; itémque ex iis quæ <lb/>&longs;unt Fri&longs;landiam inter & continentem Groelandiæ in Libycum; item ex <lb/>iis quæ &longs;unt inter Fri&longs;landiam & I&longs;landriam in Vulturnum; ex iis demum, <lb/>quæ &longs;unt inter I&longs;landiam & Britannicas in&longs;ulas in occa&longs;um, &longs;eu Zephyro <lb/>Libycum; igitur motu quodam mixto in Au&longs;trum æ&longs;tus currit, cùm tamen <lb/>reliquis men&longs;ibus, concreto mari glaciali ex prioribus angu&longs;tiis æ&longs;tus vix <lb/>currat, &longs;ed liberè tantùm in occa&longs;um feratur; ob&longs;tant enim in&longs;ulæ Britan­<lb/>nicæ, ne in Au&longs;trum eat, ac proinde in &longs;inum S. </s> <s>Laurentijinde apertum &longs;u­<lb/>beat; cùm tamen ex prædictorum fretorum aqua erumpens æ&longs;tum à <lb/>prædicto &longs;inu S. </s> <s>Laurentij facilè amoveret. </s> <s>Tertiò, Inter promontorium <lb/>floridæ & Havanam Cubæ Eurippus versùs ortum veloci&longs;&longs;imè currit, <lb/>non tantùm propter multa flumina, quæ in &longs;inum Mexicanum intrant; &longs;ed <lb/>quia aqua pre&longs;&longs;a circa Antillas, qua&longs;i circuitu facto, vi pre&longs;&longs;ionis, per <expan abbr="dictũ">dictum</expan> <lb/>fretum versùs ortum extruditur. </s> <s>Et verò versùs Antillas & Mexicanum <lb/>&longs;inum æ&longs;tus obliquè incidit, per lineam quæ ad Libycum <expan abbr="t&etilde;ndit">tenndit</expan>; hinc <lb/>parum attollitur, & frangitur illius vis ab innumeris ferè in&longs;ulis; quæ <lb/>circa o&longs;tia prædicti &longs;inus qua&longs;i totidem aggeres &longs;itæ &longs;unt; addo etiam <lb/>præfatum &longs;inum innumeris in&longs;ulis &longs;eminatum e&longs;&longs;e, quæ tum pre&longs;&longs;io­<lb/>nem, tum æ&longs;tum impediunt. </s> <s>Velociter autem prædictus Eurippus <lb/>fluit, quia per angu&longs;tum alveum magnum aquæ pondus aquam velo <gap/><pb pagenum="132"/>&longs;imo motu extrudit; preme vas quod piam aqua plenum, di&longs;co ligneo, vi­<lb/>debi&longs;que quam cito per canalem applicatum aqua erumpat. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Hoc&longs;æpè probavi, & hæc veri&longs;lima cau&longs;a e&longs;t pernici&longs;&longs;imi <lb/>Euripporum motus, &longs;eu cur&longs;us; immo lu&longs;i aliquando hoc experimento, <lb/>plenum aqua tubum cylindricum, di&longs;co æreo apprimè tubi o&longs;tio appo&longs;ito, <lb/>ex cujus centro angu&longs;tus canaliculus a&longs;&longs;urgebat, tantulùm premebam, <lb/>& aqua per dictum canaliculum pernici&longs;&longs;imè a&longs;&longs;urgebat erumpebatque; <lb/>vellem autem &longs;cire proportionem velocitatis, de&longs;cen&longs;um inter operculi, <lb/>& erumpentis aquæ a&longs;cen&longs;um. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Velocitates &longs;unt vt ba&longs;es permutando; cùm enim illa tota por­<lb/>tio extru&longs;æ aquæ per canaliculum tran&longs;eat, &longs;ub&longs;idente interim operculo, <lb/>motus operculi in tubo e&longs;t ad motum aquæ in canaliculo, vt ba&longs;is canali­<lb/>culi ad ba&longs;im cubi, neque in hoc e&longs;t difficultas. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Satis e&longs;t; optimè capio: alia difficultas occurrit; &longs;upra di­<lb/>xeras, ni fallor, geminos æ&longs;tus concurrere in fretis &longs;upra appellatis; quo­<lb/>modò igitur fieri pote&longs;t, vt ex angu&longs;tiis, quæ ex dictis fretis &longs;ubjiciuntu<gap/><lb/>æ&longs;tus in Vulturnum eat. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Bellè; Linea fluxus versùs Caurum in dictis angu&longs;tiis, & fre­<lb/>to Hud&longs;on, in freto Davi&longs;io versùs Septentrionem tendit; at verò linea <lb/>refluxus, in freto Davi&longs;io versùs Au&longs;trum, in Hud&longs;onio & dictis faucibus <lb/>in. </s> <s>Vulturnum; &longs;ed ad propo&longs;itum redeo. </s> <s>Quartò, igitur à maris tractu in­<lb/>ter Fortunatas & He&longs;peridum in&longs;ulas interjecto, æ&longs;tus currit versùs Oc­<lb/>ca&longs;um, nempe in eam partem mare curvatur ad in&longs;tar &longs;inus immen&longs;i; &longs;ed <lb/>versùs &longs;inuum extremitates vt plurimùm mare currit: ratio ex præmi&longs;&longs;is <lb/>principiis nece&longs;&longs;ariò &longs;equitur; cùm enim &longs;inus versùs extremitates con­<lb/>trahantur, aut &longs;altem contractiores &longs;int eo maris tractu, ex quo &longs;uo modo <lb/>na&longs;cuntur &longs;inus, arcus pre&longs;&longs;ionum &longs;inui minores, reliquo tractui majores <lb/>incumbunt; quid mirum ergo, &longs;i prævaleant i&longs;ti, & aqua illuc versùs ex­<lb/>tremum &longs;inum extrudatur? </s> <s>Finge &longs;inum e&longs;&longs;e fretum, &longs;ed ob&longs;tructum; <lb/>inde quoque &longs;equitur, motu velociore extrudi, quando &longs;inus e&longs;t longè <lb/>contractior; hinc magnus æ&longs;tus in &longs;inu Gangetico, Per&longs;ico, Arabico, in <lb/>quo longè major e&longs;&longs;et, cùm maxima vi mare ab ortu eò feratur, ni&longs;i ab <lb/>In&longs;ulis circa illius o&longs;tia &longs;itis, itemque ab angufti&longs;&longs;imo aditu, vis æftus fran­<lb/>geretur; ad de &longs;is &longs;inum Adriaticum, in quo versùs extremitatem æ&longs;tus non <lb/>minimus e&longs;t, extra Quadraturas, propter rationem expo&longs;itam, quæ maxi­<lb/>mè hîc locum habet. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Sed quæ&longs;o te, cur etiam in mari Mediterraneo, quod maxi­<lb/>mi &longs;inus ad in&longs;tar e&longs;t, æ&longs;tus non attollitur. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Equidem Oceani æ&longs;tus per Gaditanum fretum influit, remi&longs;­<lb/><gap/>or tamen; quia cùm versùs Cæciam linea æ&longs;tus huic oræ illap&longs;i eat, <lb/>valdè obliquè in o&longs;tra freti incidit; vnde valdè remittitur, atque adeò in <lb/>oram Syriæ oppo&longs;itam vix traducitur; traducitur tamen, & &longs;en&longs;u perci­<lb/>pitur in Novilunio & Plenilunio; licèt verò mare mediterrancum longi&longs;­<lb/>&longs;imum &longs;it, quia tamen multis in&longs;ulis interrum pitur, & ab occa&longs;u in ortum <lb/>recta excurrit, & æqualis ferè e&longs;t illius latitudo, arcus pre&longs;&longs;ionum in eo <pb pagenum="133"/>&longs;ecundùm totam illius longitudinem æquales &longs;unt; vna pars igitur non <lb/>prævalet &longs;upra aliam, igitur nullus æ&longs;tus; is enim; qui e&longs;t ad oram Syriæ <lb/>minimus quidem, &longs;ed jam olim à Phænicibus ob&longs;ervatus; item ad oram <lb/>Provinciæ, vt Scaliger ip&longs;e ob&longs;ervavit, ab Oceano per fretum Gaditanum <lb/>traducitur, non certè motu &longs;ed pre&longs;&longs;ionis vi, at verò cùm in &longs;inu Adriati­<lb/>co arcus pre&longs;&longs;ionum longè minores &longs;int, quàm in reliquo mari, quid mi­<lb/>rum &longs;i æ&longs;tus in eo fiat, effectus &longs;cilicet nece&longs;&longs;arius inæqualis pre&longs;&longs;ionis? </s> <s>mi­<lb/>nor tamen propter angu&longs;tias o&longs;tij, & Corcyram ad prædictum o&longs;tium &longs;i­<lb/>tam, in qua vis æ&longs;tus frangitur; item in Africæ ora prædicto maris Adtia­<lb/>tici o&longs;tio, &longs;ecundum eundem Meridianum, è regione oppo&longs;ita; ibi enim <lb/>mediocris &longs;altem æ&longs;tus attollitur; nempe ibi mare &longs;e&longs;e explicat, & versùs <lb/>Africam qua&longs;i in &longs;inum lunatur; item in reliqua ora Africæ versùs Tune­<lb/>tum, in quam vis æ&longs;tus perfretum traducta à Balearibus & Sardinia ad Bo­<lb/>ream &longs;itis coërcita, impingitur; æ&longs;tus porrò ad dictam oram Africæ a&longs;&longs;ur­<lb/>gentis jam olim meminit S. Augu&longs;tinus. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Sed vnde quæ&longs;o Eurippus ille mirabilis in freto Siculo, de quo <lb/>multi multa? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Certum e&longs;t, rapidum illum motum e&longs;&longs;e ab æ&longs;tu; quia cum <lb/>motu Lunæ omnino con&longs;entit; & verò vis æ&longs;tus per Gaditanum traducta, <lb/>à Balearibus & Sardinia coërcita, & ab angu&longs;tiis illius tractus maris qui <lb/>inter Africam & occiduum promontorium Siciliæ interjacet impedita, <lb/>immo abip&longs;a Sicilia repre&longs;&longs;a, declinat tantulùm versùs fauces freti Siculi, <lb/>in cujus angu&longs;tiis aqua velociùs currit, proptèr rationem &longs;upra explicatam; <lb/>fimiliter in &longs;inum Tarentinum æ&longs;tus a&longs;cendit propter eandem rationem; <lb/>ad Ravennam item & Aquileiam; quia &longs;itæ &longs;unt versùs extremum &longs;inum; ad <lb/>oram Dalmatiæ, ab&longs;que tumore, aqua &longs;ur&longs;um versùs extremum &longs;inum ire vi­<lb/>detur; ad oppo&longs;itam verò Italiæ oram ver&longs;us o&longs;tium & fauces de&longs;cendere; <lb/>fed hic motus, fi tamen vertitati con&longs;entit, vel ab æ&longs;tu diver&longs;us e&longs;t, vel ex eo <lb/>procedit, quod æ&longs;tus in fauc&ecedil;s &longs;inûs irrumpat per <expan abbr="lineã">lineam</expan>, quæ ad <expan abbr="Boreã">Boream</expan> ten­<lb/>dit; & cùm &longs;inus ab extremo faucium collo, declinet &longs;ini&longs;tror&longs;um versùs <lb/>Caurum, motus etiam aquæ versùs eandem partem declinat, &longs;ecundum <lb/>oram Dalmaticam; in refluxu verò, qua&longs;i circuitu facto, per oram Italiæ <lb/>oppo&longs;itam priori de&longs;cendit; æ&longs;tus etiam minimus ob&longs;ervatur ad Melitam, <lb/>Sardiniam, Cor&longs;icam, Iluam, Cretam, &longs;ed vix ad &longs;emipedem attollitur; <lb/>Ma&longs;&longs;iliæ & Tolone ad pedem integrum; quia &longs;cilicet cùm prædictæ in&longs;u­<lb/>læ, tum pre&longs;&longs;ionis inæqualitatem induca <gap/>t, tum etiam vim pre&longs;&longs;ionis tra­<lb/>ductam &longs;i&longs;tant, quid mirum, &longs;i aliquam vim æ&longs;tus &longs;entiant; & verò ad <lb/>oram occiduam Sardiniæ & Cor&longs;icæ vis pre&longs;&longs;ionis ab Oceano traducta <lb/>impingitur; & magna e&longs;t maris latitudo; &longs;ub Meridiano Ma&longs;&longs;iliæ, quod <lb/>&longs;anè ad pre&longs;&longs;ionis inæqualitatem multùm confert; accedit, quòd &longs;i ad <lb/>oram Africæ, in qua e&longs;t Hippona &longs;entitur æ&longs;tus, quidni ad oram Provin­<lb/>ciæ oppo&longs;itam? </s> <s>Æ&longs;tus porrò ad oram ortivam Sardiniæ & Cor&longs;icæ, item­<lb/>que ad Iluam procedit à pre&longs;&longs;ionis vi traducta ab extremo meditertaneo <lb/>ortivo; ad Melitam, Cretam, Siciliam, à vi pre&longs;&longs;ionis ab vtraque parte pro­<lb/>veniente. </s> <s>In reliquo mediterraneo nullus æ&longs;tu<gap/>entitur; in quibu&longs;dam oris. <pb pagenum="134"/>propter in&longs;ulas, in aliis verò, quia iis non favet pre&longs;&longs;io<gap/>is inæqualitas <lb/>&longs;en&longs;ibilis, propter&longs;itum: & verò qui&longs;quis rem in hanc longo illo Medi­<lb/>terranei tractu attentè con&longs;iderabit, &longs;tatim comperiet, ex præmi&longs;&longs;is princi­<lb/>piis optimè explicari. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/> Hæc, quæ dicis, mirificè placent; difficilius tamen re&longs;tat; nem­<lb/>pe in freto illo Siculo, diver&longs;us e&longs;t vtrimque æ&longs;tus, cùm &longs;imul & &longs;emel ab <lb/>vna parte deor&longs;um, ab alia &longs;ur&longs;um ire videatur, quod nonnulli in cavitates <lb/>&longs;ubterraneas rejiciunt, quas etiam volunt cum iis quæ Monti Æthnæ &longs;ub­<lb/>jiciuntur, & incendio materiam &longs;uppeditant, per cuniculos e&longs;&longs;e conjun­<lb/>ctas: Vnde Abbas Maurolycus, aiunt, vnum ex alio conjiciebat; &longs;cili­<lb/>cet ex diver&longs;a incendij ratione, diver&longs;am rationem æ&longs;tus, & vi­<lb/>ci&longs;&longs;im. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Hoc etiam &longs;pero exii&longs;dem principiis deductum iri; con&longs;ide­<lb/>ra enim fretum Siculum qua&longs;i in meditullio Mediterranei &longs;itum, & recta <lb/>directum ab Au&longs;tro ad Septentrionem, atque inde ad extremam Medi­<lb/>terranei oram, ortivam &longs;cilicet, ferè numerati triginta gradus longitudi­<lb/>nis; vnde certè &longs;ufficiens pre&longs;&longs;ionis vis e&longs;&longs;e videtur; accedente præ&longs;ertim <lb/>maxima latitudine eju&longs;dem maris, à faucibus Adriatici ad oram Africæ <lb/>oppo&longs;itam exporrecta, vt aqua per fretum ab Au&longs;tro ad Septentrionem <lb/>extrudatur &longs;imiliter vis pre&longs;&longs;ionis traducta ab Oceano per Gaditanum, re­<lb/>pre&longs;&longs;aque, vt jam dictum e&longs;t, à faucibus Africam inter & Sardiniam in­<lb/>terjectis, ac proinde tantulùm declinans &longs;ini&longs;tror&longs;um, plu&longs;quam &longs;uffici­<lb/>ens e&longs;t ad extrudendam aquam per idem fretum, à Septentrione ad Meri­<lb/>diem; quamvis enim paulò obliquiùs incidat, cùm tamen priore major <lb/>&longs;it, licèt frangatur ab obliquo appul&longs;u, vel potiùs &longs;uo modo reflectatur, <lb/>&longs;ufficiens e&longs;t, vt dixi, ad <expan abbr="extrudendã">extrudendam</expan> aquam per fretum à Septentrione ad <lb/>Au&longs;trum; quid mirum igitur &longs;i agatur æ&longs;tus in contrarias pactes, & gemini <lb/>&longs;ibi invicem occurrant, vt jam de aliis fretis diximus? </s> <s>cùm autem vtrim­<lb/>que aqua obliquè incidat, quid mirum &longs;i ex illius reflexione à cavo & di­<lb/>ver&longs;imodè &longs;ito litore, ad Scyllam &longs;cilicet & Charybdim; diver&longs;i aquarum <lb/>vortices & gyri con&longs;equantur? </s> <s>neque in hoc, &longs;altem meo judicio, re&longs;tat <lb/>vlla difficultas; cùm enim con&longs;tet, prædictum motum ab æ&longs;tu e&longs;&longs;e, <lb/>nempe accedunt & concurrunt aquæ &longs;enis quibu&longs;que horis, & cùm in <lb/>aliis fretis, æ&longs;tus etiam concurrant, negari non pote&longs;t, quin primaria <lb/>huju&longs;inodi motuum cau&longs;a &longs;it æ&longs;tus; nempe ex tali illap&longs;u, concur&longs;u, collu­<lb/>ctatione, reflexione, mirabilis motuum varietas na&longs;citur, vnde non tantum <lb/>24. vt nonnemo dicebat, &longs;ed longè plures ob&longs;ervari po&longs;&longs;unt; &longs;ed jam ad <lb/>Oceanum redeamus. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Benè e&longs;t; vnum tamen præ cæteris ex te&longs;cire velim, vtrùm <lb/>prædictus æ&longs;tuum concur&longs;us in medio freto fiat. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/> fortè in quibu&longs;dam hoc eveniet; &longs;i tamen vis æ&longs;tus eodem tem­<lb/>poris momento vtrimque ad o&longs;tia freti perveniat; quod in Siculo facilè con­<lb/>ce&longs;&longs;erim, quod &longs;cilicet, &longs;ub ea linea porrigatur, quæ eidem Meridiano &longs;ub­<lb/><gap/>acet, at verò de illo æ&longs;tu, qui fit in freto Magellanico, &longs;ecus dicendum e&longs;t, <pb pagenum="135"/>quia cùm elevatio aquarum Lunæ motum æmuletur, & cùm Luna priùs ar­<lb/>cum ortivum, quàm occiduum decurrat, inde fit, &longs;ummam elevationem <lb/>ad o&longs;tium ortivum primùm fieri, ac deinde ad occiduum; vnde &longs;equitur <lb/>concur&longs;um æ&longs;tuum, longiùs di&longs;tare ab o&longs;tio Orientali, quàm Occidentali, <lb/>quod certè cum ob&longs;ervationibus omnino con&longs;entit; Nam Arnaldus Nau­<lb/>clerus non ignobilis ob&longs;ervavit, concur&longs;um æ&longs;tuum fieri &longs;eptuage&longs;ima ab <lb/>Orientali o&longs;tio leuca, & trige&longs;ima <expan abbr="tantũ">tantum</expan> ab Occidentali, longitudo quippe <lb/>freti 100 circiter <expan abbr="leucarũ">leucarum</expan> e&longs;t, accedit, quòd versùs o&longs;tium Ortivum in &longs;inum <lb/>longi&longs;&longs;imum Oceanus de&longs;init; ac proinde aquam vel æ&longs;tum, qua&longs;i admo­<lb/>to infundibnlo in fretum pellit de freto Hud&longs;onio eadem ratio militat, <lb/>cùm ab ortu in occa&longs;um eat; &longs;ecus de Davi&longs;io, qui ab Au&longs;tro ad Septen­<lb/>trionem. </s> <s>Sed ad Eurippos redeo & lineas æ&longs;tuum; jam dixi &longs;upra, cur æ&longs;tus <lb/>in oram Guineæ incidentis linea ad Cæciam tendat; in Africum verò, inci­<lb/>dentis in o&longs;tium fluminis Amazonum: frequentes &longs;unt Eurippi inter Cycla­<lb/>das, Maldivas, Moiuccas, Iaponicasin&longs;ulas &c hoc enim &longs;olemne e&longs;t, &longs;i vis <lb/>pre&longs;&longs;ionis ad&longs;it omnibus Marium angu&longs;tiis, augu&longs;tias autem in&longs;ulæ pa<gap/>m <lb/>&longs;eminatæ <expan abbr="inducũt">inducunt</expan>; igitur & determinationem ad talem lineam motus. </s> <s>Hinc <lb/>per <expan abbr="totã">totam</expan> <expan abbr="orã">oram</expan> Oceani Germanici & Britannici <expan abbr="tã">tam</expan> diver&longs;is & <expan abbr="cõtrariis">contrariis</expan> lineis æ­<lb/>&longs;tus <expan abbr="illabũtur">illabuntur</expan>, propter <expan abbr="in&longs;ularũ">in&longs;ularum</expan> obicem, <expan abbr="locorũ">locorum</expan> angu&longs;tias &c. </s> <s>Igitur inter <expan abbr="Bra-&longs;iliã">Bra­<lb/>&longs;iliam</expan> & <expan abbr="Angolã">Angolam</expan> &longs;ub Parallelo 10. grad. </s> <s>Latit. </s> <s>Au&longs;tralis à 20. die Aprilis ad 26. <lb/>Iulij, æ&longs;tus currit versùs <expan abbr="Cautũ">Cautum</expan>, <expan abbr="it&etilde;">item</expan> à 26. Iulij, ad 20. Ianuarij versùs <expan abbr="part&etilde;">partem</expan> <expan abbr="op-po&longs;itã">op­<lb/>po&longs;itam</expan> &longs;cillcet versùs <expan abbr="Notapeliot&etilde;">Notapeliotem</expan>; à 20. Ianuarij ad 20. Aprilis in <expan abbr="neutrã">neutram</expan> <expan abbr="par-t&etilde;">par­<lb/>tem</expan>; ratio primi e&longs;t, quia <expan abbr="cũ">cum</expan> prædictæ angu&longs;tiæ &longs;int ferè &longs;ub Æquatore, & <expan abbr="cũ">cum</expan> <lb/>Solà 20. Martij ad 22. Iunij ab Æquatoreversùs <expan abbr="Boreã">Boream</expan> declinet, &longs;en&longs;im lique­<lb/>&longs;cit Mare glaciale, quo certè glaciato, vis pre&longs;&longs;ionis minor e&longs;t; quia arcus gla­<lb/>ciei incubates inutiles <expan abbr="&longs;ũt">&longs;unt</expan>; quid <expan abbr="mirũ">mirum</expan> ergo, &longs;ivis pre&longs;&longs;ionis Æthiopici præva­<lb/>leat, & aquas per fauces trudat versùs <expan abbr="Cautũ">Cautum</expan>; eò enim fauces illæ <expan abbr="&longs;pectãt">&longs;pectant</expan>: at <lb/>circa 26. Iulij glaciato mari <expan abbr="&longs;alt&etilde;">&longs;altem</expan> ex parte liquato, cre&longs;cit vis pre&longs;&longs;ionis At­<lb/>lantici, prævalet igitur, & aquas per ea&longs;dem angu&longs;tias versùs <expan abbr="Notapeliot&etilde;">Notapeliotem</expan> <lb/>retrudit; reliquo verò tempore, cùm iterum Mare versùs Boream concre&longs;­<lb/>cat, ac proinde vis pre&longs;&longs;ionis Atlantici minuatur, aër verò temperatæ Au­<lb/>&longs;tralis rare&longs;cat, Sole præ&longs;ertim perigæo, inde vis pre&longs;&longs;ionis Æthiopici mi­<lb/>nuitur, vnde per&longs;picua e&longs;t compen&longs;atio, & mare in neutram partem currit; <lb/>adde &longs;is mare Au&longs;trale incognitum etiam gelu concre&longs;cere; vnde quoque <lb/>mutatur pre&longs;&longs;ionis ratio. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Vix crediderim in alia hypothe&longs;i cuncta hæc phænomena <lb/>&longs;alvari po&longs;&longs;e; &longs;ed perge quæ&longs;o. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Sexto. </s> <s>Inter In&longs;ulam Madaga&longs;car & Africam à 10. grad. </s> <s>Latit. <lb/></s> <s>Au&longs;tralis ad promontiorum Bonæ &longs;pei versùs Au&longs;trum it mare; habes <lb/>enim angu&longs;tias, intra quas Eurippi currunt; cùm autem ab ortu in di­<lb/>ctam oram æ&longs;tus veniat, obliquè omnino incidit; vnde ad Au&longs;trum li­<lb/>neam motus determinari, nece&longs;&longs;e e&longs;t; &longs;ic enim ex tali aquarum illap&longs;u li­<lb/>nea motus pa&longs;&longs;im determinatur, & æ&longs;tus in Eurippum, &longs;i angu&longs;tiæ ad­<lb/>&longs;int, degenerat. </s> <s>Septimo, Ad Parallelum grad. </s> <s>30. Latit. </s> <s>Borcal. </s> <s>inter Phi-<pb pagenum="136"/>lippinas & Iaponicas, <gap/>re ita in ortum movetur, vt hinc paucis diebus in <lb/>Californiam navigetur; quia cùm &longs;ub Zona torrida in toto mari Pacifico <lb/>æ&longs;tus & aqua in occa&longs;um liberè feratur, modico circuitu facto refluit per <lb/>Septemtrionalem oram Americæ, quam relegit: cujus &longs;anè mirabilis effe­<lb/>ctus alia ratio e&longs;&longs;e non pote&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Hauddubièrem citiùs expedies, &longs;icut Oceanus, ita & oratio <lb/>tua terrarum oras breviter & raptim ip&longs;um æ&longs;tum æmulata, præterlegat, <lb/>initio ducto v.g. </s> <s>à Gaditano freto. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Libenter faciam & ne prolixior evadam, rem &longs;anè in pauca con­<lb/>traham, præ&longs;ertim cum & Mediterraneum & maximam Oceani partem jam <lb/>lu&longs;traverimus; & primo loco à prædicto freto Gaditano versùs Boream a&longs;­<lb/>cendam, majorí&longs;que di&longs;tinctionis gtatia numeros adhibebo. </s></p><p type="main"> <s>Primò, Occurrit Ora Bæticæ in quam &longs;atis magnus æ&longs;tus incidit Cæciam <lb/>versùs cùm vis maxima pre&longs;&longs;ionis ab Africo veniat; hinc quia directè in <lb/>Bætim &longs;ubit, ad 30. milliaria fluvius regreditur; &longs;ecus verò Anas non pro­<lb/>cul hincdi&longs;tans; quia in ejus o&longs;tia æ&longs;tus obliquè incidit; hujus enim flumi­<lb/>nis cur&longs;us in Au&longs;trum recta linea tendit. </s></p><p type="main"> <s>Secundo. </s> <s>Succedit ora Hi&longs;paniæ occidua, quæ recta ferè ad Septentrio­<lb/>nem ducitur, in qua æ&longs;tus modicus e&longs;t, quia incidit per eandem lineam ver­<lb/>&longs;us Cæciam; igitur obliquè; paulò tamen major e&longs;t, ad o&longs;tia Tagi, quia <lb/>ille tractus qua&longs;i quoddam æ&longs;tui illabenti receptaculum & &longs;inum <lb/>aperit. </s></p><p type="main"> <s>Tertiò. </s> <s>In ora boreali Hi&longs;paniæ nullus, vel modicus e&longs;t, nempe hic quo­<lb/>que fertur in Cæciam, propter rationem adductam; nempe à Septemtrio­<lb/>ne In&longs;ulæ Britannicæ, & minor Britannia magnum obicem ponunt; cùm <lb/>igitur æ&longs;tus in Cæciam eat, vix in prædictum litus incidit; id que ferè v&longs;que <lb/>ad o&longs;tia Garumnæ, ibi enim, & ad rotam oram Aquitanicam, immo ad <lb/>extremum v&longs;que minoris Britanniæ promontorium magnus æ&longs;tus e&longs;t; nem­<lb/>peibi mare ad in&longs;tar &longs;inus in terras excurrit, & propter adductam ratio­<lb/>nem in Cæciam æ&longs;tus currit: vnde &longs;atis directè illabitur, præ&longs;ertim in oram <lb/>Meridionalem minoris Britanniæ. </s></p><p type="main"> <s>Quartò Ad extremam oram, occiduam &longs;cilicet, minoris Britanni&ecedil; à fonte­<lb/>navia ad promontorium Clarium, currit æ&longs;tus ab Hypotra&longs;cia, ac proinde <lb/>obliquè incidit, & minùs a&longs;&longs;urgit licèt rapidi&longs;&longs;imus &longs;it in freto fontenaviæ, <lb/>propter angu&longs;tias; &longs;ic autem incidit, quia ab ea parte liberiùs excurrit; con­<lb/>trahitur enim Oceanus in hoc tractu versùs occa&longs;um; hinc eò currit æ&longs;tus, <lb/>vt fit in reliquis &longs;inubus, ac proinde obliquè incidit, & minor e&longs;t; haud <lb/>procul verò, quia lunatur mare vulturnum versùs in minorem & acu­<lb/>tiorem &longs;inum, eò directè fertur æ&longs;tus, & hic maximè a&longs;&longs;urgit ad fanum &longs;cili­<lb/>cet S. Maclovij, & ad Sanctum Michaelem, non procul hinc &longs;itum; inde <lb/>porrò Cadomum v&longs;que currit versùs Libycum, ac proinde obliquiùs; per <lb/>aliam autem lineam vix in hanc oram Neu&longs;triæ incidere pote&longs;t, vt patet ex <lb/>ip&longs;a in&longs;pectione; cùm vis pre&longs;&longs;ionis à mari Germanico per fretum Gallicum <lb/>cò traducatur; ad o&longs;tia Sequanæ altiùs a&longs;&longs;urgit æ&longs;tus, quia illic mare luna­<lb/>tur in &longs;inum. </s></p><pb pagenum="137"/><p type="main"> <s>Quintò, Inde Gravelingam v&longs;que, per eandem ferè lineam incidit <lb/>propter eandem rationem; &longs;en&longs;im tamen declinat ad Au&longs;trum, cùm à <lb/>longto Maris Germanici tractu, versùs Boream ad Polum v&longs;que porre­<lb/>cto, vis pre&longs;&longs;ionis Au&longs;trum versùs incumbat; ac proindo obliquè incidit <lb/>in oram illam Belgicam, hinc flante Cauro, quo fit, vt æ&longs;tus directè incidat, <lb/>longè major æ&longs;tus cietur, vt & in fretis, æ&longs;tuariis, finubus &c. </s> <s>Pro quibus <lb/>nihil e&longs;t, quod addam, cùm jam &longs;upra rationem attulerim, porrò concur­<lb/>runt æ&longs;tus haud procul à Freto Gallico; vis enim pre&longs;&longs;ionis ab vtro­<lb/>que mari, Britannico &longs;cilicet & Germanico procedit; concurrunt autem <lb/>æ&longs;tus, vt dixi extra fretum, versùs occa&longs;um; rationem jam &longs;upra adduxi, <lb/>cum de Freto Magellanico. </s></p><p type="main"> <s>Sextò, Ad ortivam oram Angliæ innumeris ferè &longs;inubus, fretis, æ&longs;tua­<lb/>riis a&longs;peratam, tendit æ&longs;tus versùs Au&longs;trum; vnde parvus e&longs;&longs;et æ&longs;tus, <lb/>propter illap&longs;um valdè obliquum, &longs;ed propter illam oræ a&longs;peritatem <lb/>& inæqualitatem, nec non locorum angu&longs;tias, illap&longs;us directus e&longs;t, <lb/>& altior æ&longs;tus, & multi Eurippi: ad oram verò Meridionalem, æ&longs;tus <lb/>qua&longs;i ad Cæciam tendit, versùs Ortum tantulùm deflectens; cùm enim <lb/>Mate Britannicum &longs;it ad in&longs;tar magni &longs;inus, na&longs;centis ex Oceano Oc­<lb/>cidentali, in quo, vt &longs;upra dictum e&longs;t, fluit æ&longs;tus in Cæciam; nihil mi­<lb/>rum, &longs;i in Britannico versùs eandem partem eat; ab extremo verò An­<lb/>gliæ termino Occidentali, quem Lezardum vocant, deflectit æ&longs;tus ma­<lb/>gis ad Ortum; hinc maximus e&longs;t ad Bri&longs;toliam, vbi Mare a&longs;&longs;urgit ad <lb/>pedes 66. quia in extremis &longs;inubus, modò æ&longs;tus in eandem cum &longs;inu <lb/>plagam excurrat, mare plurimùm a&longs;&longs;urgit; deflectit autem tantulum <lb/>ad Ortum, propter obicem Hiberniæ versùs Septemtrionem &longs;itæ. <lb/></s> <s>Denique inter Angliam & Hiberniam non parum &longs;ævit æ&longs;tus <lb/>propter fretorum locorumque angu&longs;tias; vnde multi na&longs;cuntur Eu­<lb/>rippi. </s></p><p type="main"> <s>Septimò, Suprà Scotiam liberiùs æ&longs;tus excurrit, ac ferè &longs;ine lege; item <lb/>ad oram Norvegiæ inter Bergam & Stadem, propter Eurippos valde in­<lb/>&longs;ignes, ob in&longs;ulas è regione &longs;itas: ad oram Finnomarchiæ & Lappiæ <lb/>æ&longs;tus à Cauro fluunt, vnde vis major pre&longs;&longs;ionis e&longs;t; hinc ad extremum <lb/>Lappiæ &longs;inum, Ortum versùs, in quem æ&longs;tus directè incidit, in&longs;ignis <lb/>æ&longs;tus e&longs;t: Ad Fretum Na&longs;&longs;ovium concurrunt æ&longs;tus, traducta ab <lb/>vtroque mari vi pre&longs;&longs;ionis, Tartarico &longs;cilicet & Septemtrionali: De <lb/>Niculandia jam &longs;upra dictum e&longs;t; quanquam facilè crediderim, illo Ma­<lb/>ri per Brumam glaciato, diver&longs;am in vicinis oris æ&longs;tuum rationem & li­<lb/>neam &longs;equi. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Iam ferè dixi&longs;ti de reliquis oris, quas Oceanus alluit, præter­<lb/>lectis &longs;upra litoribus Americæ & Africæ; re&longs;tat vt ad alia tran&longs;eamus, non­<lb/>dum enim hoc argumentum probè exhau&longs;tum e&longs;t, Ante omnia &longs;cire velim, <lb/>cur æ&longs;tus alicubi major, alicubi minor a&longs;&longs;urgat. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Hoc facilè deducere poteras ex iis, quæ dicta &longs;unt; multis au­<lb/>tem nominibus cre&longs;cit; Primò, ex majori vi pre&longs;&longs;ionis quæ ex duplici ca­<lb/>pite cre&longs;cit: primum petitur à majore &longs;uperficie, quam occupant vtiles <pb pagenum="138"/>arcus pre&longs;&longs;ionis, re&longs;pectu alicujus loci, qui prædictorum arcuum qua&longs;i Po­<lb/>lus e&longs;t; ex hoc capite maximus æ&longs;tus fit ad Indi O&longs;tia, ad Guineam, ad <lb/>O&longs;tia fluminis Amazonum, ad oram Peruviæ. </s> <s>Secundum caput e&longs;t majot <lb/>aëris gravitas, quæ oritur ab humore admixto, vel aëre den&longs;o, & compre&longs;&longs;o. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Tertium caput omittis, nempe quando Luna altior e&longs;t, altior <lb/>quoque e&longs;t aëris gravitantis tractus, & linea dirimens à centro terræ lon­<lb/>giùs di&longs;tat. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Hocmihi reverà exciderat, quod exqui&longs;ita ob&longs;ervatione con­<lb/>firmare po&longs;&longs;um; quando enim Luna in Apogæo exi&longs;tit, tunc æ&longs;tus minor <lb/>e&longs;t: itaque vis pre&longs;&longs;ionis alia major e&longs;t exten&longs;ivè, alia inten&longs;ivè; exten &longs;ivè <lb/>à majore &longs;uperficie, cui arcus pre&longs;&longs;ionis incumbunt, idque cæteris pari­<lb/>bus; modò &longs;cilicet inæqualem pre&longs;&longs;ionem inducant; inten&longs;ivè autem à <lb/>majore aëris gravitatione, quæ vel e&longs;t à majore altitudine aëris, vel à ma­<lb/>jore humoris copia admixta; hinc major æ&longs;tus in Plenilunio, minorverò <lb/>Luna Apogæa. </s> <s>Secundò, Cre&longs;cit æ&longs;tus ex illap&longs;u magis directo; &longs;ic enim <lb/>excurrit in illam oram, præ&longs;ertim per fluminum alveos: nempe a&longs;&longs;urgit <lb/>æ&longs;tus per majores vndas, doliorum in&longs;tar, quarum vna aliam &longs;equitur; vn­<lb/>de fit, vt &longs;i obliquè incidat, non in oram, &longs;ed in ip&longs;um mare excurrat; &longs;i au­<lb/>tem in litus impingeret, altera &longs;uperveniente, a&longs;&longs;urgeret aqua, & plus ad­<lb/>huc tertiæ vndæ appul&longs;u. </s> <s>Tertiò, Cre&longs;cit æ&longs;tus ratione &longs;inuum, nempe, vt <lb/>jam dixi, &longs;i æ&longs;tus directè in &longs;inum paulò acutiorem & breviorem incidat, <lb/>mirum quantum attollatur aqua, non tantùm propter angu&longs;tias va&longs;is, &longs;ed <lb/>propter directum appul&longs;um; &longs;ic ad Bri&longs;toliam, vt dixi, & ad fanum Sancti <lb/>Michaëlis alti&longs;&longs;imus æ&longs;tus e&longs;t, hic 70. illic 66. pedes; ad O&longs;tia fluminis Ama­<lb/>zonum, ni&longs;i per alveum fluvij excur&longs;us pateret, altior for&longs;itan e&longs;&longs;et: dixi &longs;u­<lb/>pra breviorem & acutiorem &longs;inum; vt enim expre&longs;&longs;ione &longs;uperficiei aquæ <lb/>quolibet va&longs;e contentæ per canaliculum altiùs a&longs;cendit, quàm per majorem <lb/>canalem; ita pror&longs;us æ&longs;tus in breviore & Pyramidem de&longs;inente &longs;inu; <lb/>cùm enim minùs capax &longs;it, intru&longs;a per vim pre&longs;&longs;ionis aqua altiùs a&longs;cendat, <lb/>nece&longs;&longs;e e&longs;t. </s> <s>Inter in&longs;ulas, vt plurimùm minùs a&longs;&longs;urgit aqua, tum quia vis <lb/>pre&longs;&longs;ionis interrumpitur, tum quia cùm aqua per freta & angu&longs;tias di&longs;cur­<lb/>rat, ac proinde effluat, tam altè a&longs;cendere non pote&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Sed cur alicubi velociùs & rapidiùs, alibi &longs;en&longs;im æ&longs;tus <lb/>currit? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Velocior motus, qui ab æ&longs;tu e&longs;t, à multis cau&longs;is procedit. </s> <s>Primò <lb/>à majore vi pre&longs;&longs;ionis<gap/> &longs;ic majus pondus tubi erecti & aqua pleni, eam ve­<lb/>lociùs perforamen iuxta ba&longs;im apertum extrudit; major autem vis pre&longs;­<lb/>&longs;ionis e&longs;t à majore &longs;uperficie ex arcubus vtilibus con&longs;tante. </s> <s>Secundò, ab an­<lb/>gu&longs;tiis per quas aqua extrudenda e&longs;t, vi pre&longs;&longs;ionis; &longs;icut dixi &longs;upra, in Fre­<lb/>tis, rapidus æ&longs;tus e&longs;t, v.g. </s> <s>in angu&longs;tiis ad Havanam, & alibi pa&longs;&longs;im; &longs;ic <lb/>in fluminis alveo contracta aqua velociùs currit. </s> <s>Tertiò à breviore angu­<lb/>&longs;tiarum alveo; &longs;ie per breviorem fi&longs;tulam foramini admotam, aqua velo­<lb/>ciùs extruditur </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Ne quid di&longs;&longs;imulem, hoc non capio, quanquam anguror ali­<lb/>quid &longs;citu digni&longs;&longs;imum, ex hoc ip&longs;o argumento affulgere. </s></p><pb pagenum="139"/><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Faciam capias. </s> <s>Sit tubus AB &longs;empet aquâ plenus, &longs;it fi&longs;tula <lb/><figure id="fig23"></figure><lb/>primum GH, per quam aqua extruditur, vi <lb/>ponderis AB. haud dubiè &longs;i&longs;it fi&longs;tula GI duplo <lb/>longior, extrudetur aqua per GH, velociore <lb/>motu, & tardiore per GI. experientia hujus rei <lb/>per&longs;pecta e&longs;t; quia &longs;æpè probata; ratio verò <lb/>non itafortè cuipiam in promptu e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Iam mihi venit in mentem; nem­<lb/>pe vis eadem motrix minus mobile velociùs, <lb/>majus verò tardiùs movet; quid mirum igitur, <lb/>&longs;i minorem aquæ molem fi&longs;tula GH contentam, <lb/>vis ponderis GH faciliùs & velociùs extrudat, <lb/>quàm duplò majorem contentam fi&longs;tula GI. im­<lb/>mò facilè crediderim, motus e&longs;&longs;e, vt longitudines <lb/>permutando. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Ab hoc vltimo incipio, quod manife&longs;tè fal&longs;um e&longs;&longs;e, demon­<lb/>&longs;tro, nempeinde &longs;equeretur infinitè velociùs extrudi aquam per nudum & <lb/>nulla fi&longs;tula in&longs;tructum foramen B, quàm per fi&longs;tulam quamlibet etiam bre­<lb/>vi&longs;&longs;imam; prætereà cùm per fi&longs;tulam GH, aut GI aqua extru&longs;a motu <lb/>æquabili moveri cen&longs;eatur, acqui&longs;ito &longs;cilicet in ip&longs;a extru&longs;ione, id e&longs;t, in <lb/>ip&longs;o foramine: &longs;i in præci&longs;a vi motrice &longs;i&longs;tamus, cùm hæc æqualem mo­<lb/>tum omnibus partibus extru&longs;is imprimat, quem deinde retinent pertotam <lb/>fi&longs;tulæ longitudinem, non videtur, cur velociùs per breviorem, tardiùs per <lb/>longiotem moveatur; aliunde igitur illa motuum inæqualitas petenda <lb/>e&longs;t; nimitum ab impedimento & re&longs;i&longs;tentia fi&longs;tulæ; nempe cavailla &longs;uper­<lb/>&longs;icies, non ita e&longs;t lævigata, quin aliquid &longs;cabrum, aliquæ &longs;alebræ, &longs;triæ, aut <lb/>rugæ in&longs;int; cum enim aqua nullum &longs;patium liberum habeat intra fi&longs;tu­<lb/>lam, vix credi pote&longs;t, quantum inde illius cur&longs;us retardetur; & verò aquæ <lb/>currentis &longs;uperficies adeò plana e&longs;&longs;e non &longs;olet, præ&longs;ertim &longs;i velociore motu <lb/>fluat; vt igitur &longs;uperficies aquæ convexa probè congruat &longs;uperficiei cavæ <lb/>fi&longs;tulæ, id certè non &longs;ponte, &longs;ed vi quadam fieri dumtaxat pote&longs;t; vnde illius <lb/>cur&longs;um retardari nece&longs;&longs;e &longs;it: cùm igitur in longiore fi&longs;tula longior &longs;it &longs;u­<lb/>perficies, longius &longs;eu majus erit impedimentum; igitur per longiorem fi­<lb/>&longs;tulam plus remoræ nacta, tardius aqua extruditur. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> In qua porro proportione vnus motus alium &longs;uperat? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/> Hæc proportio ita inveniri pote&longs;t; comparetur aquæ quantitas <lb/>extru&longs;a per nudum foramen B, factum in lamina qua&longs;i indivi&longs;ibili, cùm ea <lb/>quæ per fi&longs;tulam GH extruditur, æquali tempote, motus erunt vt quanti­<lb/>tates permutando; fiatque vt differentia quantitatum &longs;it ad aliam vt GH, <lb/>ad GI, id e&longs;t, in ratione dupla, erit aqua extru&longs;a per GH ad extru&longs;am per <lb/>GI, vt aqua extru&longs;a per nudum foramen, minus prima differentia ad ean­<lb/>dem, minùs &longs;ecunda differentia; erunt autem motus vt quantitates aquæ <lb/>extru&longs;æ: hic non con&longs;idero modicam illam & in&longs;en&longs;ibilem re&longs;i&longs;tentiam, <lb/>quæ procedit à peripheria foraminis laminæ; quia hæc &longs;upponitur indivi­<lb/>&longs;ibilis &longs;uperficies, ac proinde quælibet &longs;uperficies cava ad illam peripheriam <pb pagenum="140"/>infinitam habet rationem; igitur & re&longs;i&longs;tentia illius ad re&longs;i&longs;tentiam hujus. </s></p><p type="main"> <s><emph type="italics"/>Angu&longs;tin.<emph.end type="italics"/></s><s> Hoc certè callent ij, qui aquæ ex publicis fontibus di&longs;tri­<lb/>buendæ præ&longs;unt, nempe æquales longitudine fi&longs;tulas omnibus aquædu­<lb/>ctibus apponunt, &longs;ive tubi majores &longs;int, &longs;ive minores; vt &longs;cilicet æqualis &longs;it <lb/>ratio impedimenti quod ex longitudine fi&longs;tulæ ducitur, ac proinde extru&longs;æ <lb/>aquæ quantitates &longs;int vt tubi, &longs;eu tuborum ba&longs;es. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> In hoc etiam errant, Augu&longs;tine, quod vt liquidò demon&longs;trem, <lb/>&longs;upponantur duæ fi&longs;tulæ æqualis longitudinis GH, &longs;ed ba&longs;is inæqualis, <lb/>&longs;itque exempli gratia Diameter ba&longs;is minoris vnius digiti, & Diameter <lb/>majoris, duorum digitorum, cùm æquali longitudine fi&longs;tularum & al­<lb/>titudine fontis BA, haud dubiè vires erunt, vt ba&longs;es, ac proinde &longs;i <lb/>præcisè vis ponderis gravitantis, & aquam extrudentis con&longs;ideretur, <lb/>eadem e&longs;t vtrimque ratio; nempe mobilia &longs;unt vt ba&longs;es, ba&longs;es vt vires; <lb/>igitur æquales vtrimque motus; quia vires vt 4. æquè facilè movebunt <lb/>pondus vt 4. ac vires vt vnum pondus vt vnum. </s> <s>Igitur &longs;tando præci­<lb/>sè in ip&longs;a vi ponderis extrudentis, quo tempore, per majorem fi&longs;tu­<lb/>lam ex appellatis, fluunt 4. libræ aquæ, vna tantùm libra per minorem <lb/>effluet; &longs;ed hoc per&longs;picuis experimentis repugnat; nec demon&longs;tratio dee&longs;t; <lb/>nempe vt eadem proportio maneret, impedimenta ex cava &longs;uperficie fi&longs;tu­<lb/>læ petita deberent e&longs;&longs;e proportionalia; igitur cùm hæc impedimenta &longs;int, <lb/>vt &longs;uperficies cavæ, &longs;uperficies cava majoris fi&longs;tulæ deberet e&longs;&longs;e quadrupla <lb/>&longs;uperficiei cavæ minoris, cùm tamen &longs;it tantùm dupla; &longs;unt enim illæ vt Pe­<lb/>pheriæ circulorum, & hæ vt Diametri: igitur cùm major &longs;it ratio impe­<lb/>dimenti in minore fi&longs;tula, quàm in majore, quid mirum, &longs;i aquæ quantitas <lb/>extru&longs;æ per majorem, &longs;it plu&longs;quam quadrupla extru&longs;æ per minorem? </s> <s>e&longs;&longs;et <lb/>autem pror&longs;us & accuratè quadrupla, &longs;i major fi&longs;tula longitudine dupla <lb/>minoris &longs;it. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Bellè omninò, vt hæc mihi nova, ita gravi&longs;&longs;ima pror&longs;us acci­<lb/>dunt. </s> <s>Sed quid &longs;i aliquis æqualem in fi&longs;tulis longitudinem &longs;ervare velit, <lb/>cupiat tamen apponere fi&longs;tulam majorem, per quam extrudatur, a&longs;&longs;umpta <lb/>eadem fontis altitudine, quadrupla quantitas aquæ, quanta ba&longs;is fi&longs;tulæ a&longs;&longs;i­<lb/>gnanda erit? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Hoc etiam facilè haberi pote&longs;t: &longs;i enim major fi&longs;tula longi­<lb/>tudine dupla & ba&longs;i quadrupla extrudit præcisè quantitatem aquæ qua­<lb/>druplam, &longs;it ba&longs;is majoris 16. minoris 4. ac proinde Diameter minoris 2. <lb/>majoris 4. erit ba&longs;is 16. ad &longs;uperficiem cavam majoris fi&longs;tulæ, vt ba­<lb/>&longs;is 4. ad cavam minoris; igitur vires majoris ad impedimentum fi&longs;tulæ <lb/>majoris, vt vires minoris ad impedimentum eju&longs;dem; &longs;it minoris impe­<lb/>dimentum vt vnum, erit majoris impedimentum vt 4. & &longs;i impedimen­<lb/>tum vt 1. &longs;ubducit vnam partem aquæ, vel motus ex 4. impedimen­<lb/>tum vt 4. &longs;ubducit partes 4. ex 16. vnde re&longs;idua erunt in eadem pro­<lb/>portione, &longs;cilicet vt 3. ad 12. jam verò &longs;i longitudo dupla ma­<lb/>joris fi&longs;tulæ &longs;ubducit 4. partes, longitudo &longs;ubdupla &longs;ubducet tantùm <lb/>2. igitur &longs;i major fi&longs;tula æqualis longitudine a&longs;&longs;umatur extrudet 14. <lb/>partes &longs;eu libras aquæ. </s> <s>Vt autem inveniatur bafis fi&longs;tulæ, eju&longs;dem cum <pb pagenum="141"/>minore longitudinis, per quam quadrupla quantitas eodem tempote ef­<lb/>fluat, ad i&longs;tud problema præparatorium res reducitur; dato Quadrato, cui <lb/>&longs;ubtractum &longs;it &longs;ubquadruplum, ide&longs;t Quadrato &longs;emilateris, invenire Qua­<lb/>dcatum cui &longs;ubtracto rectangulo, &longs;ub eius latere, & quarta parte laceris <lb/>prioris, re&longs;iduum &longs;it quadruplum, primi re&longs;idui, &longs;en triplum primi Qua­<lb/><figure id="fig24"></figure><lb/>drati. </s> <s>Supponamus CB e&longs;&longs;e latus, &longs;eu Diame­<lb/>trum ba&longs;is minoris fi&longs;tulæ, & LA e&longs;&longs;e Quadra­<lb/>tum quæ&longs;itum, ita vt&longs;ubtracto HE &longs;ub latere LH, <lb/>& LE æquali MB, quæ e&longs;t &longs;ub quadrupla BA, <lb/>re&longs;iduum EA &longs;it triplum Quadrati CA: &longs;it au­<lb/>tem latus Quadrati 12 KN, quod mihi notum <lb/>e&longs;t, hoc enim e&longs;t triplum Quadrati CA; &longs;it etiam <lb/>KR, æqualis MB, mihi notæ, e&longs;t enim &longs;ubqua­<lb/>drupla BA; his præmi&longs;&longs;is, &longs;ic formo problema <lb/>decretorium: Data media proportionali, &longs;cilicet <lb/>KN, & differentia extremarum, &longs;cilicet KR, invenire <lb/><figure id="fig25"></figure><lb/>extremas; dividatur RK bifariam in S & &longs;ub radio SN <lb/>de&longs;cribatur &longs;emicirculus ONB, erunt KO, KP, extre­<lb/>mæ quæ&longs;itæ, vt patet; igitur KO e&longs;t latus quæ&longs;itum, <lb/>æquale &longs;cilicet LH. </s> <s>Pari modo procedam &longs;i velim ha­<lb/>bere fi&longs;tulam eju&longs;dem longitudinis, ex qua eodem tem­<lb/>pore tripla, vel dupla quantitas effluat. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Non paucæ mihi &longs;uboriuntur difficultates circa hæc, quæ à <lb/><figure id="fig26"></figure><lb/>te dicta &longs;unt; primò enim, &longs;i longitudo fi&longs;tulæ GH <lb/>tale impedimentum affert, vt vnam quartam <lb/>partem motus auferat; igitur dupla longitudo <lb/>GI, duplum auferet; igitur quadrupla totum <lb/>motum; nihil aquæ igitur ex illa efflueret, quod <lb/>ab&longs;urdum e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Si&longs;te quæ&longs;o, neque enim huc Hydrau­<lb/>lica traducenda e&longs;t, cùm &longs;it res longioris operæ; <lb/>dicam igitur breviter, motum retardari po&longs;&longs;e in <lb/>infinitum, v<gap/> nemo. </s> <s>ne&longs;cit; vnde &longs;i longitudo fi­<lb/>&longs;tulæ GH. Subtrahit<gap/>. </s> <s>velocitatis, longitudo <lb/>GI &longs;ubtraher 1/4. & dupla GI <gap/> & dupla ejus <lb/>totam; &longs;ed huc v&longs;que &longs;upponitur fi&longs;tula &longs;emper <lb/>plena, eaque in &longs;itu horizontali; vbi autem <lb/>aqua ea tarditate, movetur, vt pars aquæ &longs;uprema proprio pondere qua&longs;i <lb/>per planum inclinatum ire po&longs;&longs;it, de&longs;cendit haud dubiè, & tunc &longs;uperior <lb/>fi&longs;tulæ cavitas, vacua re&longs;tat: &longs;ed quæ&longs;o te ad rem no&longs;tram redeamus, cùm <lb/>hæc hujus in&longs;tituti non &longs;int. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Inde rantùm colligo, quantum detrimentum ij patiantur in <lb/>di&longs;tributione aquarum, qui parvas fi&longs;tulas habent, & quantum vici&longs;&longs;im <lb/>commodi ij, qui magnas habent; nempe illi, cui<gap/>aquæ vncia competit, da­<lb/>tur fi&longs;tula, cujus ba&longs;is Diameter v. </s> <s>g. </s> <s>vncia e&longs;t; alteri verò cui competunt <pb pagenum="142"/>quatuor, datur &longs;i&longs;tula eju&longs;dem longitudinis, cujus ba&longs;is quadrupla e&longs;t <lb/>prioris, &longs;ed e<gap/> tempote, q<gap/>oper illam minotem fi&longs;tulam tanta aquæ quan­<lb/>titas ext<gap/>, major quadrupla peti&longs;tam majorem effluit, vt patet ex di­<lb/>ctis; igitur vt legitimæ aquarum men&longs;uræ e&longs;&longs;ent, vel modus &longs;upra expo &longs;i­<lb/>tus adhibend<gap/> e&longs;&longs;et, v<gap/>; fi&longs;tularum longitudines, vt Diametri e&longs;&longs;e deberent, <lb/>&longs;ed his mi&longs;&longs;is ad <gap/>&longs;tum <gap/>di. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Iraque ex dictarum fi&longs;tularum analogia, explicabam &longs;upra, <lb/>cur per breviorem freti, vel angu&longs;tiarum tractum, aqua vi pre&longs;&longs;ionis ve­<lb/>lociùs extrudatur, ad proinde rapidiore motu; illud tamen di&longs;crimiais <lb/>intercedir, quòd in fi&longs;tulis, cre&longs;cente ba&longs;i fi&longs;tulæ, ponderis gravitantis <lb/>viros cre&longs;cant <gap/>vt paterex dictis: at verò idem pondus gravitans, & <lb/>cadem vis pre&longs;&longs;ionis effe &longs;upponitur, in eodem tractu, quando &longs;eilicet <lb/>maxima pre&longs;&longs;io e&longs;t, re&longs;pectu illius, &longs;ive contractiores &longs;int angu&longs;tiæ freti, &longs;ive <lb/>laxiotes; &longs;ive longior illius tractus, &longs;ive brevior &longs;it: Vnde duplici nomine, <lb/>quando brevior, e&longs;t, rapidiùs extruditur; nimirum quia arctus e&longs;t, & quia <lb/>brevis; ex vtroquo enim capite aquæ extrudendæ moles minuitur. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Sod quæ&longs;o te, cur alicubilongè breviore tempore æ&longs;tus a&longs;­<lb/>&longs;urgis, ex<gap/>tque; alicubi verò plus temporis ponit? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Ita e&longs;t; nempe ad Guineam, non procul ab o&longs;tio Nigri flumi­<lb/>nis 4. horis æ&longs;tus a&longs;&longs;urgit; item ad otam Cambaiæ, iuxta Indi fauces, dua­<lb/>bus horis æ&longs;tus ad 30. leucas excurrit, ad o&longs;tia Garumnæ, &longs;eptem horis <lb/>a&longs;&longs;urgit, quinque refluit, vt ait Scaliger exerc. </s> <s>52. Sed accuratior Ob&longs;er­<lb/>vator, idemque nobili&longs;&longs;imus Geometra D. Candala, expre&longs;&longs;is verbis te&longs;ta­<lb/>tur, Gaoumnam attolli &longs;ex integris horis, deprimi verò &longs;ex horis & 24. <lb/>min<gap/> cui plus fidei habendum e&longs;&longs;e nemini dubium erit; vtpote qui ad <lb/>accuratiùs ob&longs;e<gap/>vanda acce&longs;&longs;us rece&longs;&longs;u&longs;que tempora, circa Garumnæ <lb/>o&longs;tium, magnum horologium con&longs;trui curaverit, quod etiam minuta &longs;i­<lb/>gnabat, vt ip&longs;emet te&longs;tatur in libello à &longs;e in lucem edito Ann. </s> <s>1575. Quem <lb/>etiam citat Furnerius. </s> <s>Quod ad me attinet, exi&longs;timo, æqualia vtrimque e&longs;&longs;e <lb/>tempora; cùm enim æ&longs;tus initio & &longs;ub finem parum cre&longs;cat, vt dicam pau­<lb/>lò po&longs;t, id o&longs;t, iuxta minimam ferè proportionem, facilè fieri potuit, vt <lb/>minimum coementum primis 16. minutis & 16. vltimis &longs;ub &longs;en&longs;um & ob­<lb/>&longs;ervationem vonim non potuetit; ac proinde æquè diu acce&longs;&longs;us atque re­<lb/>ce&longs;&longs;us duraverit. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Metiri <gap/>rgo æ&longs;tum debemus horis Lunatibus, divi&longs;a &longs;cilicet <lb/>integra revolutione Lunæ, &longs;eu die Lunari in 24. partes, &longs;eu horas æqua­<lb/>les, ita vt quælibet hora Lunatis &longs;it major hora Æquinoctiali 2. minutis; <lb/>ac proinde &longs;enis &longs;omper horis Lunaribus æ&longs;tus reciproci fiunt per &longs;e, aut <lb/>certè &longs;enis horis Æquinocti alibus & 12. minutis; non verò &longs;ex horis tem­<lb/>poralibus, inæqualibus &longs;cilicet, inxta formam horologij antiqui, vt vocant; <lb/>& ita intelligendum e&longs;&longs;e Plinij locum <emph type="italics"/>lib.<emph.end type="italics"/> 2. <emph type="italics"/>cap.<emph.end type="italics"/> 97. per&longs;picuum e&longs;t; Vnde <lb/>miror illoru<gap/> etro<gap/>em, qui volunt incipere æ&longs;tum vbi Luna &longs;upra Ho­<lb/>rizontem vno Signo elevata fuerit, & continuo cre&longs;cere donec Luna Me­<lb/>ridianum illius loci atligerit; decre&longs;cere verò ab hoc puncto, donec Luna <lb/>æqualem po&longs;t Meridiem arcum decurrit terminatum &longs;cilicet ad 30. gra-<pb pagenum="143"/>dum &longs;upra Horizontem; errorem e&longs;&longs;e dico; quia Luna exi&longs;tente in maxi­<lb/>mâ declinatione Au&longs;trali, arcus illius diuinus ab Ortivo puncto Hoti<gap/>on­<lb/>tis ad Meridianum, vix e&longs;t 60. graduum; igitur &longs;oder <gap/>antur 50. &longs;uper­<lb/>&longs;unt 30. quos dum Luna decurrit, duabus &longs;cilicet horis Æquinoctialibus <lb/>& 4. minutis, durat æ&longs;tus; quod ape<gap/>è fal&longs;um e&longs;&longs;e con&longs;tat; tamdiu re­<lb/>fluxus duraret. </s> <s>Prætereà, æ&longs;tus, qui fieret po&longs;t Occa&longs;um Lunæ, longè <lb/>major e&longs;&longs;et priore; nempè arcus illius paralleli &longs;ub Horizonte, longè ma­<lb/>jor e&longs;t alio; quem Luna &longs;upta Horizontem excurrit, <gap/> cuncta hæc experi­<lb/>mentis repugnant. </s> <s>Dixi&longs;uprà, per &longs;e, cùm per accidens fieri po&longs;&longs;it, vt tem­<lb/>pora fluxus & refluxus inæqualia &longs;int. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Ex præmi&longs;&longs;is principiis hoc manife&longs;tè deducitur<gap/> nempè &longs;in­<lb/>gulis pænè momentis, mutatur in globo punctum, &longs;eu Polus maximæ ele­<lb/>vationis, ac proinde centrum circulorum & arcuum pre&longs;&longs;ionis, quorum <lb/>cum diver&longs;a &longs;it ratio & proportio, propter varios continentis & Maris <lb/>tractus, in &longs;uperficie globi, &longs;ine certâ lege di&longs;tinctos, inde nece&longs;&longs;ariò &longs;e­<lb/>quitur diver&longs;a vis pre&longs;&longs;ionis, diver&longs;a impre&longs;&longs;io, diver&longs;a appul&longs;us, vel illa­<lb/>p&longs;us linea: quod vt meliùs intelligas fige pedem circini ad Occiduum <lb/>Guineæ Promontorium, non procul ab O&longs;tio Nigri, ductí&longs;que innumeris <lb/>circulis ex illo centro, concentricis & paralleli<gap/>, di&longs;tingne arcus vtiles ab <lb/>inutilibus, &longs;en&longs;imque promoto versùs Ortum illo centro, v&longs;que ad 60. <lb/>gradus, &longs;i vlteriùs illud promoveas, v&longs;que ad 90. circuli pre&longs;&longs;ionis <lb/>maxima ex parte, vel continenti Africæ, Europæ, A&longs;iæ vel Indico Ocea­<lb/>no incumbent, ac proinde inutiles erunt re&longs;pectu prædicti loci: quid mi­<lb/>rum igitur, &longs;i 4. dumtax at horis in eo æ&longs;tus a&longs;&longs;urgat, deprimatur verò plu­<lb/>ribus? </s> <s>Nam promoto versùs Oceanum centro, diver&longs;a e&longs;t circulorum pre&longs;­<lb/>&longs;ionis ratio. </s> <s>Aliquid &longs;imile ob&longs;ervabis, fixo circini pede ad litus Cam­<lb/>baiæ; tanquam in centro: accedit, quòd ex multis capitibus prædicta <lb/>æ&longs;tuum inæqualitas inducitur; Primò, per planum magis inclinatum, lon­<lb/>giùs excurrit & velociùs, licèt plus temporis ponat in decurrendo magis <lb/>inclinato, cuncta hæc ex doctrina motuum per&longs;picua &longs;unt; tantumdem <lb/>temporis aqua ponit in de&longs;cen&longs;u per planum inclinatum., quantum in <lb/>a&longs;cen&longs;u. </s> <s>Secundò, Si po&longs;t quàm aqua regredi cœpit, nova quædam fiat <lb/>æ&longs;tus reflexio, versùs fluminis fauces, vel &longs;i aqua libero quidem aditu &longs;u­<lb/>beat, &longs;ed exitu difficiliore, tunc acce&longs;&longs;us breviore tempore fiet quàm re­<lb/>ce&longs;&longs;us. </s> <s>Tertiò, Si nova reflexio accedat, antequam aqua regredi incipiat, <lb/>vel agger quidam appo&longs;itus ad fauces &longs;inus, aut fluminis primam vim ac­<lb/>ce&longs;&longs;us retundat, vt videre e&longs;t ad fauces Sequanæ & Garumnæ, rece&longs;&longs;us bre­<lb/>viore tempore fiet quàm acce&longs;&longs;us. </s> <s>Quartò, Pro diver&longs;o æ&longs;tus ad oram ap­<lb/>pul&longs;u, vel illap&longs;u, longiùs per alveum fluviorum vel minùs longè aqua ex­<lb/>currit; item pro diver&longs;a alvei inclinatione; hinc facilè crediderim, alveum <lb/>illorum fluminum, in quibus ad aliquot centena milliaria æ&longs;tus excurrit, <lb/>e&longs;&longs;e valde inclinatum Quintò, Dicam ampliùs, ratione eju&longs;dem loci, non <lb/>modò æ&longs;tum altiùs aut minùs altè attolli, verùm e&longs;&longs;e aliquando acce&longs;&longs;um <lb/>majorem, aliàs minorem e&longs;&longs;e po&longs;&longs;e; quia mutatur &longs;ingulis diebus centrum <lb/>circulorum pre&longs;&longs;ionis, clium reipectu eju&longs;dem loci; item aliquando ac-<pb pagenum="144"/>ce&longs;&longs;um æqualem e&longs;&longs;e <gap/>&longs;&longs;ui, aliquando diururniorem, aliàs breviotem <lb/>cu<gap/>cta hæc ex diver&longs;a pro<gap/> ratione pendent: e&longs;t autem diver&longs;a ratio <lb/>pro div<gap/> tractu & <gap/></s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Sed <gap/> ex <gap/> vtrùm eadem &longs;emper hora Meridiana <lb/>Lunari, id e&longs;t, eo momento, quo Luna Meridianum loci attigit, &longs;ummus <lb/>æ&longs;tus &longs;it? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Per &longs;e quidem &longs;ummns æ&longs;tus &longs;emper e&longs;t, exi&longs;tente Luna in Me­<lb/>ridiano loci, &longs;ive &longs;upra, &longs;ive infra Horizontem; per accidens tamen &longs;ecus <lb/>accidit; & Primò quidem ex diver&longs;a pre&longs;&longs;ionis ratione; Nempe fieri po­<lb/>te&longs;t, vt hora decima Lunari re&longs;pectu alicujus l<gap/>, &longs;it maximus pre&longs;&longs;ionis <lb/>effectus, ac proinde &longs;ummus æ&longs;tus. </s> <s>Secundò, Ob concur&longs;um æ&longs;tuum Ge­<lb/>mini Matis tractus, vt fit in Germanico & Britannico, nempe longè ante <lb/>Meridiem Lunatem, re&longs;pectu Dieppæ & O&longs;tij Sequanæ Oceanus Septem­<lb/>trionalis intume&longs;cit, àquo in Germanicum vis pre&longs;&longs;ionistraducitur, & hinc <lb/>per Fretum Gallicum, Dieppam, & ad O&longs;tium Sequanæ; quò etiam cùm ex <lb/>Britannico, qua&longs;i ex aver&longs;o vis pre&longs;&longs;ionis incumbat, licèt paulò tardiùs <lb/>quàm ex Germanico, quod ad Ortum &longs;itum e&longs;t, vtriu&longs;que concur&longs;u &longs;um­<lb/>mus æ&longs;tus Dieppæ a&longs;&longs;urgit, i<gap/> émque ad O&longs;tium Sequanæ; hîc quidem priùs <lb/>vna ferè hora propter reflexionem magis directam. </s> <s>Hinc fieri pote&longs;t; vt a&longs;­<lb/>&longs;urgat &longs;ummus æ&longs;tus in duobus locis &longs;ub diver&longs;o Meridiano &longs;itis, eodem <lb/>tempore, v.g. </s> <s>&longs;i accipiatur alter locus di&longs;tans Dieppa 7. grad.1/2. ver&longs;us Or­<lb/>tum, in quo &longs;ummus æ&longs;tus &longs;it hora vnde cima Lunari; illic enim & Dieppæ <lb/>eodem tempore &longs;ummus erit æ&longs;tus. </s> <s>Pari modo facilè dici pote&longs;t, cur mul­<lb/>tis in locis &longs;ummus æ&longs;tus &longs;it po&longs;t Meridiem v, g. </s> <s>Burdigalæ, ad Garumnam, <lb/>Antuerpiæ ad Sealdim, Hamburgi ad Albim, &longs;ummus æ&longs;tus e&longs;t hora &longs;exta <lb/>Lunari po&longs;t eju&longs;dem Meridiem, quia per motum æ&longs;tus a&longs;cendit in alveo <lb/>fluminum; igitur tardiùs pervenit ad localongè di&longs;&longs;ita à fluminis &longs;aucibus: <lb/>Am&longs;terodami 3. hora Lunari po&longs;t Meridiem; in ip&longs;o verò Meridie Lu­<lb/>nari, Encu&longs;æ, haud procul po&longs;itæ; quia per diver&longs;os mæandros in <lb/>eo maris &longs;inu, Am&longs;terodamum æ&longs;tus appellit, liberiùs Encu&longs;am; in <lb/>oram Fri&longs;iæ adhuc liberiùs; hinc tertia hora Lunati ante Meridiem Luna­<lb/>rem, ibi fit &longs;ummus æ&longs;tus; nempe ab Oceano Septemtrionali tantulùm <lb/>versùs Ortum declinante vis pre&longs;&longs;ionis traducitur in Germanicum, & qua­<lb/>&longs;i directè in oram Fri&longs;iæ; Oceanus autem Septemtrionalis propter mo­<lb/>dicam Meridianorum di&longs;tantiam in eo Boreali tractu, in Germanicum <lb/>incumbit, antequam Luna ad illum Meridianum perveniat; cui Ma­<lb/>re Germanicum &longs;ube&longs;t, vnde prior ratio indicata plurimùm confirmatur. <lb/></s> <s>Itaque ex dictis con&longs;tat, &longs;ummum æ&longs;tum e&longs;&longs;e po&longs;&longs;e &longs;ub diver&longs;is Meridia­<lb/>nis, eodem tempore, & &longs;ub eodem, in diver&longs;is locis, diver&longs;o, & &longs;in­<lb/>gulares quo&longs;libet ca&longs;us ad præmi&longs;&longs;a & communia principia reduci, mo­<lb/>do &longs;ingu&longs;ares circum&longs;tantiæ habeantur, ratione quarum, vel &longs;ummus æ&longs;tus <lb/>cum Lunæ motu convenit, vel tardiùs aut citiùs accidit; mihi &longs;atis &longs;it ali­<lb/>quas obiter indicate. </s></p><p type="main"> <s>Primò, Si nihil appul&longs;um æ&longs;tus impediat, nihil promoveat, &longs;ed mare <lb/>ab incubante aëre pre&longs;&longs;um inæqualiter, liberè intume&longs;car, &longs;ummus æ&longs;tus <pb pagenum="145"/>erit &longs;emper hora meridiana Lunari, id e&longs;t, eo temporis puncto, <lb/>quo Luna Meridianum illius loci attingit, &longs;ive &longs;upra, &longs;ive infra Hori­<lb/>zontem, </s></p><p type="main"> <s>Secundo. </s> <s>Siresita compo&longs;itæ, &longs;eu di&longs;po&longs;itæ &longs;int, vt concurrant æ&longs;tus, vel <lb/>in freto, vel vltra freti fauces, in quibu&longs;dam tractibus &longs;ummus æ&longs;tus erit <lb/>ante metidiem, vt Dieppæ; quia &longs;cilicetaqua citiùs per freti angu&longs;tias extru­<lb/>ditur; adde reflexionem quamdam, quæ &longs;equitur ex vttoque ni&longs;u maris ver­<lb/>sùs fretum connitentis. </s></p><p type="main"> <s>Tertio. </s> <s>Si mare vetsùs Au&longs;trum eat, &longs;en&longs;imque declinet ora versùs <lb/>Boream, ad oram illam, &longs;ummus æ&longs;tus erit ante meridiem Lunarem vt in <lb/>Fri&longs;iæ ora. </s></p><p type="main"> <s>Quarto. </s> <s>Si per varios &longs;inus & mæandros mare in terras &longs;e&longs;e in&longs;inuat, &longs;um­<lb/>mus æ&longs;tus erit po&longs;t meridiem Lunarem, vt Am&longs;terodami, & in iis locis, quæ <lb/>&longs;ita &longs;unt ver&longs;us extremum &longs;inum. </s></p><p type="main"> <s>Quinto. </s> <s>Si æ&longs;tus per alueos fluviorum a&longs;cendat, quò longiùs di&longs;tat ab <lb/>o&longs;tio fluvij locus aliquis, eò tardiùs &longs;ummum æ&longs;tum habet, &longs;ci′icet <lb/>po&longs;t meridiem Lunarem, vt Burdigala, Hamburgum, Rotomagus, An­<lb/>tuerpia. </s></p><p type="main"> <s>Sexto. </s> <s>Si aliquis terræ tractus longiùs im mare porrigatur, citiùs habet <lb/>&longs;ummum æ&longs;tum, & tardiùs, vt dixi, extremitas &longs;inuum. </s></p><p type="main"> <s>Septimo. </s> <s>Diver&longs;us litorum &longs;itus ad talem vel talem reflexionem di&longs;po­<lb/>&longs;itus non parum confert; reflexionem, inquam, ni&longs;us, &longs;eu pre&longs;&longs;io­<lb/>nis aquæ cuju&longs;vis ab oppo&longs;ito latere &longs;eu littore versù; aliud qua&longs;i refle­<lb/>ctitur. </s></p><p type="main"> <s>Octavo. </s> <s>Adde lineam cur&longs;us aquæ, prout &longs;cilicetvel obliquiùs, vel minus <lb/>obliquè incidit. </s></p><p type="main"> <s>Nono. </s> <s>Adde etiam diver&longs;am pre&longs;&longs;ionis rarionem, qua fieri pote&longs;t, vt <lb/>&longs;umma vis pre&longs;&longs;ionis non &longs;it te&longs;pectu alicujus loci con&longs;tituto centro ar­<lb/>cuum pre&longs;&longs;ionis in dicto loco, &longs;ed in alio, &longs;eu versùs ortum, quo po&longs;ito, <lb/>&longs;ummus æ&longs;tus erit ante meridiem Lunarem; &longs;eu versùs occa&longs;um, quo &longs;up­<lb/>po&longs;ito, po&longs;t meridiem Lunarem in dicto loco erit. </s> <s>Ex his reliqua, ni fallor, <lb/>facilè intelligetis, aut &longs;altem &longs;i quid difficile, re&longs;tet &longs;ignificare dignabi­<lb/>mini. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Pauca hauddubiè re&longs;tant, quæ vel abundè non fuerint ex­<lb/>po&longs;ita, vel ex iis, quæ à te dicta &longs;unt, facilè non intelligantur, & mihi <lb/>videor rationem afferre po&longs;&longs;e illorum omnium, quæ in hac materia maxi­<lb/>mam admirationem conciliare &longs;olent v.g. </s> <s>cur multalitora, vel nullum vel <lb/>modicum æ&longs;tum patiantur, alia verò maximum; quid Lunaad æ&longs;tum con­<lb/>erat, ita vt in Plenilunio & Novilunio maximus æ&longs;tus &longs;it, eiu&longs;que &longs;ummum, <lb/>Luna in Meridiano exi&longs;tente, ni&longs;i per accidens &longs;ecus fiat; cur in duobus <lb/>locis, &longs;ub eodem Meridiano &longs;itis diver&longs;o tempore, eodem verò, &longs;ub di­<lb/>ver&longs;o Meridiano; cur in fretis gemini æ&longs;tus concurrant; cut is, qui fer­<lb/>tur ab ortu intra fretum longiùs accedat, minus verò, qui venit <lb/>ab occa&longs;u; cur alibi rapidi&longs;&longs;imus &longs;it, mitior alibi, cur alicubi ante <lb/>meridiem Lunarem, alibi po&longs;t; pa&longs;&longs;im tamen in ip&longs;o meridie; <pb pagenum="146"/>cur in quibu&longs;dam tractibus acce&longs;&longs;us plus duret, quàm rece&longs;&longs;us; in aliis ve­<lb/>rò plus rece&longs;&longs;us; quàm acce&longs;&longs;us, licèt vnus per &longs;e alteri &longs;it aquè diutur­<lb/>nus; cur per &longs;e mare &longs;ex horis 12. minutis a&longs;cendat, & totidem depri­<lb/>matur, cur &longs;ingulis diebus vna ferè hora, hoc e&longs;t 48.minutis æ&longs;tus tardiùs <lb/>a&longs;&longs;urgere incipiat, quàm pridie, idque &longs;emper & per &longs;e, Luna in Meridia­<lb/>no horæ &longs;extæ exi&longs;tente; cur in quibu&longs;dam oris ad 70. & 80. pedum alti­<lb/>tudinem mare per æ&longs;tum in Plenilunio attollatur, in aliis vix ad vnum pe­<lb/>dem, in multis verò nihil pror&longs;us; cuncta hæc & alia multa ex principiis <lb/>à te jactis nullo negotio deducuntur; alia quædam occurrunt, quæ mihi <lb/>vel dubia &longs;unt, vel eorum ratio incomperta; à dubiis initium duco. </s> <s>Pri­<lb/>mum e&longs;t quod aliqui dicunt, in Plenilunio &longs;cilicet majorem e&longs;&longs;e vim æ&longs;tus, <lb/>quàm in Novilunio ad Calecutium; cùm tamen ad indi o&longs;tia in Novilunio <lb/>majotes &longs;int æ&longs;tus; alterum verò quod alij referunt, quibu&longs;dam in <gap/>cis <lb/>per totos quindecim dies, à Novilunio &longs;cilicet, ad Plenilunium continuò <lb/>æ&longs;tum crefcere; ita vt &longs;ummum crementum &longs;it in Novilunio & Plenilunio, <lb/>ac totidem diebus aquam &longs;ub&longs;idere, vt ob&longs;erva tum e&longs;t, inquiunt, cirea <lb/>Cubam & Hi&longs;paniolam; item in fluvio Vanna vel Van&longs;one ad Pachinum <lb/>Sinarum </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Ab hoc vltimo incipio, quia involvit repugnantia; nempe cùm <lb/>in prædictis, vt & in multis aliis Mediterranei locis, æ&longs;tus&longs;it tantùm &longs;en&longs;i­<lb/>bilis in Plenilunio & Novilunio, quia cùm tunc Majores &longs;int, vt &longs;upra di­<lb/>ximus, con&longs;tatque experientia; quid mirum, &longs;i tunc &longs;en&longs;ibiles &longs;int? </s> <s>vnde <lb/>nonnemo occa&longs;ionem arripuit, dicendi, cre&longs;cere continuo in iis locis <lb/>per totos 15. dies, à Novilunio &longs;cilicet ad Plenilunium; quod fal&longs;i&longs;&longs;imum <lb/>e&longs;t; quia &longs;ingulis diebus-bis cre&longs;cit, & bis refluit. </s> <s>Sed in&longs;en&longs;ibiliter, ni&longs;i <lb/>paucis diebus ante & po&longs;t Novilunium ac Plenilunium; hæc autem &longs;une <lb/>inter &longs;e repugnantia, decre&longs;cere continuo à Plenilunio ad Novilunium ac <lb/>proinde in Novilunio mare e&longs;&longs;e maximè depre&longs;&longs;um, cùm in eo &longs;it terminus <lb/>decrementi, & toto reliquo menfe nullum &longs;en&longs;ibilem æ&longs;tum apparere; <lb/>fieri tamen aquarum tumorem &longs;en&longs;ibilem in Novilunio & Plenilunio. </s> <s>Ve­<lb/>nio ad primum, & dico, de eo mihi maximum dubium e&longs;&longs;e, quanquam <lb/>pro diver&longs;o Lunæ &longs;itu, non negarim fieri po&longs;&longs;e, vt major æ&longs;tus &longs;it in Novi­<lb/>lunio, quàm in Plenilunio; cum enim fauces Indi &longs;int ferè &longs;ub Tropico <lb/>Caneri, &longs;i fupponamus Novilunium fieri in Tropico Cancri, de Meridie <lb/>maximus erit ibi aquæ tumor, cùm linea ab&longs;idum eo terminetur, minor <lb/>tamen erit de media nocte; quia extremitas lineæ ab&longs;idum inde di&longs;tat 47. <lb/>gradibus; &longs;i verò Plenilunium fiat in Tropico Capricorni, de Meridie ma­<lb/>ximus æ&longs;tus ibidem erit, quia vt linea ab&longs;idum à Tropico ad Tropicum <lb/>per centrum globi tunc eat, de Meridie extremitas prædictæ lineæ, quæ <lb/>ad Tropicum Cancri terminatur, re&longs;pondet lineæ Meridianæ; itaque &longs;i <lb/>compatetur diutnus Plenilunij cum nocturno Novilunij, in Novilunio mi­<lb/>nor æ&longs;tus erit, quàm in Plenilunio, &longs;ive diurnus <expan abbr="Novilunijcũ">Novilunijcum</expan> nocturno Ple­<lb/>nilunij, major erit in Novilunio, &longs;ed profectò de&longs;unt ob&longs;ervationes, & Au­<lb/>tores &longs;uper hoc in &longs;en&longs;us contrarios eunt, vtpote qui non tam ex ob&longs;erva­<lb/>tionibus, quàm ex propriis conjecturis multa deducant & &longs;cribant, quæ <pb pagenum="147"/>omitto, vobi&longs;que refutanda relinquo; accedit, quòd diver&longs;a pre&longs;&longs;ionis ra­<lb/>tio rem hanc plurimùm variat; immo Autores &longs;uper hoc &longs;ibi non con&longs;tant, <lb/>& vnus illorum, &longs;i rectè memini, cùm docui&longs;&longs;et, incrementa matis majora <lb/>fieri in Pleniluniis ad Calecutium, in Noviluniis verò ad Indi o&longs;tia, &longs;equen­<lb/>ti &longs;tatim pagina dicit, alicubi majora e&longs;&longs;e in Noviluniis, vt ad Calecu­<lb/>tium, alibi verò majora in Pleniluniis, vt ad Indi O&longs;tia; idem re­<lb/>petit po&longs;t quintam paginam; vnde vides, cuncta hæc patum certa <lb/>e&longs;&longs;e. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> In hac re nihil aliud de&longs;idero, ni&longs;i novas & accuratas ob&longs;er­<lb/>vationes, circa diurnum & nocturnum æ&longs;tum, dum Luna &longs;ita e&longs;t <lb/>extra Æquatotem, ac præ&longs;ertim circa Tropicos; alia quædam de <lb/>quibus certò con&longs;tat, quorum cau&longs;æ mihi compertæ non &longs;unt, ex <lb/>te quærenda re&longs;tant: primum e&longs;t, cur dum æ&longs;tus a&longs;&longs;urgit &longs;ub initium <lb/>& finem minoribus, crementis a&longs;&longs;urgat, majoribus verò &longs;ub me­<lb/>dium. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> In Sinu Tarentino dum æ&longs;tus &longs;ex horis a&longs;&longs;urgit, & fortè duo­<lb/>decim minutis, quæ &longs;ub &longs;en&longs;um non cadunt, vt dixi &longs;upra, & toti­<lb/>dem refluit, hæc accuratè ob&longs;ervata &longs;unt, in Novilunio v. </s> <s>g. </s> <s>prima <lb/>hora lentè accedit, &longs;ecunda tantulùm intenditur motus, tertia & <lb/>quarta, longè velocior evadit, quinta remittit, vt in &longs;ecunda: in &longs;ex­<lb/>ta denique vt in prima: idem fit in Plenilunio: vegetior autem æ&longs;tus e&longs;t <lb/>quatriduo ante & quatriduo po&longs;t Novilunium & Plenilunium, reliquo <lb/><figure id="fig27"></figure><lb/>tempore longè remi&longs;&longs;ior. </s> <s>Hæc literis ad me datis à <lb/>viro &longs;apienti&longs;&longs;imo qui præ&longs;ens illa in&longs;piciebat, acce­<lb/>pi ac fideliter retuli: Vt autem rationem, quam <lb/>petis exponam, &longs;uppono ex Geometria, &longs;inus com­<lb/>plementi, quo magis accedunt ad &longs;inum totum, <lb/>habere minorem proportionem inæqualitatis. </s> <s>Sit <lb/>enim quadrans MLN in quo accipiantur arcus <lb/>æquales L, P, E, R, Z, & ducantur &longs;inus com­<lb/>plementi XP, TE, SR, VZ, dico ML ad XP, habere minorem <lb/>proportionem inæqualitatis, quàm XP ad TE, & XP, ad TE, <lb/>quàm TE ad SR, atque ita deinceps quod vel ex ip&longs;is &longs;inuum Ta­<lb/>bulis con&longs;tat; hoc &longs;uppo&longs;ito, cùm aqua intume&longs;cat magis vel minùs <lb/>iuxta proportionem inæqualis pre&longs;&longs;ionis, & pre&longs;&longs;io inæqualis &longs;it iuxta <lb/>rationem circulorum pre&longs;&longs;ionis inæqualium, hi porrò inæquales &longs;int <lb/><figure id="fig28"></figure><lb/>iuxta rationem prædictorum &longs;inuum com­<lb/>plementi, mare per æ&longs;tum intume&longs;cit ad <lb/>in&longs;tar pruni, vel &longs;phæroidos, vt jam &longs;upra <lb/>dictum e&longs;t. </s> <s>Sit autem quadrans ellip&longs;eos <lb/>ABD, & quadrans circuli ABY di­<lb/>vi&longs;us in quotcunque arcus æquales; item <lb/>quadrans circuli AGD; &longs;int anguli <lb/>GAF, DAE æquales, quadrans <lb/>ABY e&longs;t ad quadrantem ellipticum <pb pagenum="148"/>cum ABD, vt AY ad AD, &longs;unt enim figuræanalogævel homoge­<lb/>neæ, vt vocare &longs;oleo; item quadrans ABD e&longs;t ad quadrantem AGD, vt <lb/>AY ad AD; igitur figura YDB e&longs;t ad figuram BGD, vt AY ad AD, &longs;unt­<lb/>que duæ i&longs;tæ figuræ homogeneæ; igitur vt YD ad GB, ita EO ad CI, <lb/>ita HO ad CF, ita K a ad ab; &longs;ed YD, BG &longs;unt æquales, igitur OE <lb/>& IC æquales, item OH & CF, item a K & ab, igitur tantum cre&longs;­<lb/>cit aqua vi pre&longs;&longs;ionis à B in I, quantum ab H ad Y, vel ab E in D; igitur <lb/>&longs;ub initium & finem cre&longs;cit aqua modicis incrementis, ii&longs;que reciprocè <lb/>æqualibus hinc inde, a&longs;&longs;umptis &longs;cilicet angulis æqualibus; majori­<lb/>bus verò &longs;ub medium; en tibi germanam & facilem tui quæ&longs;iti ra­<lb/>tionem, quæ dubito, an æquè facilè in qualibet alia hypothe&longs;i afferri <lb/>po&longs;&longs;it. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Quid dici queat, quod in rem hanc meliùs quadret, certè non­<lb/>video; &longs;ed cur in Æquinoctiis æ&longs;tus major e&longs;t? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Iam &longs;upra ea &longs;uper hoc expo&longs;ui, quæ tibi facerent &longs;atis, &longs;i for­<lb/>tè in memoriam revocares; nempe, vt jam indicavi, &longs;i Autores illos­<lb/>con&longs;ulamus, qui de hoc argumento &longs;crip&longs;erunt, nihil ferè ni&longs;i repugnan­<lb/>tia inter &longs;e inveniemus; nimirum aliqui &longs;crip&longs;erunt, æ&longs;tum maximum e&longs;&longs;e <lb/>in Sol&longs;titiis, minimum verò in Æquinoctiis, alij contra maximum in <lb/>Æquinoctiis, minimum in Sol&longs;titiis; alij majorem in Æquinoctio ver­<lb/>no; alij majorem in autumnali; alij majorem in Sol&longs;titio Brumali, mi­<lb/>norem in Æ&longs;tivo; alij majorem in æ&longs;tivo, minorem in Brumali nihil af­<lb/>fingo; Augu&longs;tine, hæc adeò repugnantia apud Autores invenies. </s> <s>De Sol­<lb/>&longs;titiis nihil certi, cùm etiam in hoc Autores varient, non dubito tamen, <lb/>quin, id quod e&longs;t, in no&longs;tram notitiam venire po&longs;&longs;it, fidelis ob&longs;ervatio­<lb/>nis opera, in eodem &longs;cilicet loco; nempe pro diver&longs;is locis, diver&longs;a ra­<lb/>rio e&longs;t, cùm diver&longs;a &longs;it pre&longs;&longs;io; &longs;ed pro eodem loco facilè ob&longs;ervari po­<lb/>te&longs;t in vtroque Sol&longs;titio æ&longs;tus a&longs;&longs;urgentis men&longs;ura, tum diurni, tum no­<lb/>cturni; cùm multum inter vtrumque di&longs;crimen e&longs;&longs;e po&longs;&longs;it; nulla autem re­<lb/>gula certa &longs;tatui pote&longs;t, propter diver&longs;am pre&longs;&longs;ionis rationem, ob &longs;uperfi­<lb/>ciem globi variis, &longs;ine lege & ordine, maris & continentis tractibus di­<lb/>&longs;tinctam. </s> <s>Quod pertinet ad Æquinoctia; hoc vnum certò con&longs;tat, maxi­<lb/>mum in iis cieri æ&longs;tum, Luna &longs;cilicet plena aut nova, &longs;altem in no&longs;tro <lb/>Oceano, intra Europam; rationem hic globus tibi &longs;uggeret, in quo <lb/>vides, Luna exi&longs;tente in Æquatore arcus pre&longs;&longs;ionum e&longs;&longs;e majores; vbi <lb/>verò Luna declinat versùs Boream, in quo tractu, Europa no&longs;tra &longs;ita e&longs;t, <lb/>vides, ni fallor, quantam prædictorum arcuum aream circulus maximæ <lb/>pre&longs;&longs;ionis re&longs;cindat, traducátque ad oppo&longs;itum hemi&longs;phærium, exi&longs;ten­<lb/>te Luna infra horizontem ad Meridianum; qua &longs;ita &longs;upra horizontem, de <lb/>meridie &longs;cilicet Luna nova, de media nocte, in Plenilunio vides quan­<lb/>tam maxima pars Americæ inutilem reddat: vbi porro Lu<gap/>a declinat in <lb/>Au&longs;trum, eadem pror&longs;us ratio militat; po&longs;ita enim Luna in Tropico <lb/>Gapricorni, in Novilunio de meridie idem e&longs;t circulus maximæ pre&longs;&longs;io­<lb/>nis, qui erat de media nocte dum Luna nova e&longs;&longs;et in Tropico Can­<lb/>cri; in Plenilunio verò, de meridie, idem e&longs;t circulus maximæ <pb pagenum="149"/>pre&longs;&longs;ionis, qui erat de media nocte, dum Luna e&longs;&longs;et in dicto Tropico <lb/>Cancri; vnde vt vides, eadem pro vtroque Sol&longs;titio ratio militat. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/> Hæc tua ratio probat, in vtroque Æquinoctio, æ&longs;tum æqualem <lb/>e&longs;&longs;e; at gravi&longs;&longs;imi Autores dicunt majorem e&longs;&longs;e in Æquinoctio autumnali <lb/>v.g.ad o&longs;tia Garumnæ. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Ita e&longs;t æquè pro vtroque probat hæc ratio, & ita e&longs;&longs;e nemo <lb/>inficiatur. </s> <s>Scilicet per &longs;e; nam per accidens &longs;ecus accidere pote&longs;t; v.g.eo <lb/>quod major vis humpris aëri admixta &longs;it &longs;ub Æquinoctium Autumnale, <lb/>quàm &longs;ub Vernum; & verò cum &longs;it terminus æ&longs;tatis, dubium non e&longs;t, <lb/>quin longè major humoris &longs;eu vaporis, in quem humor abit copia aëri ad­<lb/>mixta &longs;it; vnde major evadit gravitatio, major pre&longs;&longs;io, & major æ&longs;tus: in <lb/>Zona torrida & Au&longs;trali &longs;ecus dicendum e&longs;t; accedit, quod in Æquino­<lb/>ctio, rarò fit Novilunium aut Plenilunium; &longs;ed tantùm aliquot ante, vel <lb/>po&longs;t diebus; adde diver&longs;am venti vim, quæ ad majorem æ&longs;tum non parum <lb/>confert; &longs;i hæc tibi non faciant &longs;atis, nihil habeo vltra quod tibi ex­<lb/>ponam. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Faciunt hauddubiè; nec dubito, quin paucis aliis po&longs;tu­<lb/>latis, quæ mihi re&longs;tant etiam facturus &longs;is &longs;atis; quæro igitur ex, <lb/>te, vtrum vrinatores, qui profundiùs immerguntur, vim & motum æ&longs;tus &longs;en­<lb/>tiant. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Ga&longs;&longs;endus hoc ip&longs;um probari curavit, invenítque non &longs;entiri <lb/>æ&longs;tum pluribus pa&longs;&longs;ibus infra &longs;uperficiem maris, quod certè ex præmi&longs;&longs;is <lb/>omnino &longs;equitur; nempè infra arcum BY ne minima quidem impre&longs;&longs;io <lb/>aquæ accidit; in quo meo judicio, nulla e&longs;t difficultas; vnde fabulam reputo, <lb/>ab ebulliente mari per æ&longs;tum, marinas bellnas &longs;nr&longs;um ad &longs;uperficiem pelli, <lb/>illud fortè verius, &longs;eu veri&longs;&longs;imilius, ad litus Per&longs;ieum allidi pi&longs;ces <lb/>ad &longs;copulos, quod aliquando vi &longs;ævi&longs;&longs;imæ tempe&longs;tatis actum e&longs;&longs;e <lb/>ferunt; hinc pi&longs;ces &longs;æviente procella in maris profundum &longs;e reci­<lb/>piunt. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Illud etiam fabulo&longs;um crediderim; quod à quibu&longs;dam Auto­<lb/>ribus refertur, &longs;cilicet ad Norvegiam, e&longs;&longs;e quemdam maris tractum, in quo <lb/>&longs;enis horis Naves & grandia cete &longs;orbentur à mari, & aliis Senis extrudun­<lb/>tur; itémque inter Angliam & Nortmanniam e&longs;&longs;e voraginem, versùs quam <lb/>naves veloci&longs;&longs;imo cur&longs;u actæ etiam vicinæ gurgiti repelluntur. </s> <s>Hæc meta <lb/>&longs;unt Nautarum garrientium figmenta. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Idem quoque &longs;entio; quanquam prædictus gurges Angliaur <lb/>inter & Nortmanniam, ip&longs;e fortè e&longs;t gemini æ&longs;tus concur&longs;us, qui non <lb/>di&longs;&longs;imilem effectum præ&longs;taret, vt confideranti patebit; Ille verò tractus <lb/>ad Norvegiam, qui naves votat, ac deinde evomit, dubito an &longs;it circel­<lb/>lns maximæ depre&longs;&longs;ionis, quem circa Polum mundi de&longs;cribit punctum di­<lb/>&longs;tans à Parallelo Lunari 90. gradibus nempe ad in&longs;tar cuju&longs;dam <gap/>oraginis <lb/>e&longs;t, &longs;ub&longs;idente aqua &longs;enis horis, ae totidem a&longs;&longs;urgente; &longs;ed dum res certò <lb/>non con&longs;tet, quod &longs;it, fru&longs;tra quæritur, propter quid &longs;it: Non negarim <expan abbr="tam&etilde;">tamen</expan>, <lb/>versùs Norvegiam, in quo reveràtractu mare profundi&longs;&longs;imum e&longs;t, qua&longs;dam <pb pagenum="150"/>votagines e&longs;&longs;e po&longs;&longs;e, in quibus ratione &longs;itus, æ&longs;tus ip&longs;e mirificos præ&longs;tet ef­<lb/>fectus. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Proba&longs;ine quod aliqui&longs;cribunt, in cingulis ex Lupi marini co­<lb/>tio factis, pet æ&longs;tum pilos erigi & &longs;tare, in refluxu verò deprimi, hoc etiam <lb/>fabulam olet, ni fallor. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Vt vt &longs;it, quædam humore rige&longs;cunt, ac proinde eriguntur, <lb/>vt funes ex canabe, præterea per æ&longs;tum, aër minus compre&longs;&longs;us e&longs;t, magis <lb/>in refluxu; quid mi<gap/>um ergo, &longs;i refluxu<gap/> tempore pilos illos de­<lb/>primat. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Sed quid cen&longs;es de iis fontibus & puteis, quorum aliqui at­<lb/>tolluntur <gap/>um Oceano per æ&longs;tum, alij contra &longs;ub&longs;idunt. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Multa etiam fabulo&longs;a de his Scriptoribus promulgata fue­<lb/>runt; difficile tamen non e&longs;t; rationem horum adducere; nempè altior <lb/>aqua per æ&longs;tum, plus aquæ extrudit per exiguos areno&longs;æ terræ meatus; <lb/>minus verò aqua &longs;ub&longs;idens; quòd &longs;i per longiores mæandros aqua tradu­<lb/>cenda e&longs;t, ad putei, &longs;eu fontis recepta culum non tam citò pervenit, &longs;ed fortè <lb/>&longs;ex horis tardiùs. </s> <s>Sic <expan abbr="nõ">non</expan> &longs;tillant fornices, eo die, quo pluit, &longs;ed altero, immo <lb/>tertio po&longs;t die, pro diver&longs;a for nicis cra&longs;&longs;itudine; nec obe&longs;t, aquam dul­<lb/>cem e&longs;&longs;e; quia marina per arenam percolata du ce&longs;&longs;it: nihil dico de aliis <lb/>multis fontibus, qui aliquoties per diem intume&longs;cunt, ac deinde &longs;ub&longs;i­<lb/>dunt, nulla tamen temporum &longs;ervata lege, quia ad hoc argumentum non <lb/>pertinent: quanquam in diver&longs;is fontibus artefactis facilè videmus, quid <lb/><gap/>tiam indu&longs;trio&longs;a natura in hac materia præ&longs;tare valeat. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Alia Exciderant; quid enim de Mari Ca&longs;pio, de Ponto Euxino, <lb/>de Mari Baltico, de Eurippo ad Eubeam, de quibu&longs;dam lacubus in Ameri­<lb/>ca, in quibus æ&longs;tus fieri dicitur? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> In Ca&longs;pio, Euxinio, Baltico, vel nullus, vel modicus æ&longs;tus e&longs;t <lb/>cùm ab Oceano traduci non po&longs;&longs;it, & tractus aquarum breviores &longs;int, & <lb/>ita &longs;iti, vt &longs;en&longs;ibilem pre&longs;&longs;ionis inæqualitatem non inducant. </s> <s>De lacubus <lb/>Americæ memoratis, dicendum e&longs;t, vele&longs;&longs;etantæ longitudinis vt 700. <lb/>etiam milliatia adæquent, quod &longs;ufficit, vt aliqua pre&longs;&longs;ionis inæqualitas <lb/>inducatur, vel per majorem fluminis alveum ab Oceano vim æ&longs;tus eò tra­<lb/>duci, quod &longs;altem meo judicio, difficultate caret. </s> <s>Iam de celeberrimo <lb/>illo Græciæ Eurippo nunc dicam, de quo fabulo&longs;a multa narrantur; nem­<lb/>pe aliàs &longs;epties &longs;ingulis diebus æ&longs;tua&longs;&longs;e dicitur, nunc verò quater in die: <lb/>quod ad me &longs;pectat, fateor vltro, me nunquam vidi&longs;&longs;e; quantum tamen <lb/>ex incolarum relationibus audire potui, bis &longs;ingulis diebus in præfato Eu­<lb/>rippo recurrit æ&longs;tus; &longs;ed quia it reditque duodecim horis, alii&longs;que duo­<lb/>decim pariter fluit, ac reflnit æquè rapido cur&longs;u, quater in die æ&longs;tuare vi­<lb/>detur; hujus autem Eurippi eadem ratio e&longs;t, quæ aliorum, de qua jam <lb/>&longs;upra; fieri ta<gap/>en pote&longs;t, vt quemadmodum de Siculo diximus, concur­<lb/>rant in i&longs;to gemini æ&longs;tus, abvtraque &longs;cilicet extremitate, nempe ad orti­<lb/>vam vis æ&longs;tus traducitur per fauces illas, quæ &longs;untinter Cretam & Orien­<lb/>tale Peloponen&longs;i cornu, non procul ab In&longs;ula Cythere, vulgò <emph type="italics"/>Cerigo,<emph.end type="italics"/><pb pagenum="151"/>præter fluente aqua Orientalem Pelopone&longs;i & Atticæ oram; ad occiduam <lb/>verò per medium qua&longs;i Ægeum vis æ&longs;tus appellitur; ex præfato verò con­<lb/>cur&longs;u varij vortices na&longs;ci videntur, qui vulgo ventorumvi, vel ali&longs;s cau&longs;is <lb/>tribui &longs;olent; vnum dumtaxat libenter addo, anilem fabulam jam olim de <lb/>Ari&longs;totele &longs;par&longs;am fui&longs;&longs;e, cum &longs;cil<gap/>et, præ de&longs;peratione, Eurippi cau&longs;am <lb/>non capientem &longs;e&longs;e in medium Euripum præcipitem dedi&longs;&longs;e; quis hoc <lb/>amabò credat? </s> <s>ni&longs;i qui nimiæ laboret vitio credulitatis? </s> <s>Sed quid tamdiu <lb/>taciturnus fui&longs;ti, &longs;uavi&longs;&longs;ime Chry&longs;ocome? </s> <s>curhuc v&longs;que de argumento <lb/>adeò difficili di&longs;&longs;erentem non interpella&longs;ti? </s> <s>An fortè res i&longs;ta tibi non pla­<lb/>cuit? </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Placuit haud dubiè, neque hoc inficiari po&longs;&longs;um; &longs;ilui tamen, <lb/>nec inter pellavi vnquam, quia multa &longs;anè volvebam animo, quæ contra ea, <lb/>quæ dicebas, mihiopponenda e&longs;&longs;e videbantur, quæ mihi haud parum diffi­<lb/>cultatis præferre videbantur. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Su&longs;tine tanti&longs;per Antime, & per te mihi liceat nodos <lb/>i&longs;tos à Chry&longs;ocomo contextos di&longs;&longs;olvere mentem tuam callere ap­<lb/>prime mihi videor; &longs;i quidin &longs;olutione mea de&longs;ideretur facilè &longs;upplere po­<lb/>teris. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Legem accepto; profer igitur, Chry&longs;ocome, illa omnia, <lb/>quæ volvi&longs;ti animo adversùm nos: vtrumque di&longs;&longs;erentem libenter au­<lb/>diam. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocomus.<emph.end type="italics"/></s><s> Primo quidem loco incredibile e&longs;&longs;e videtur, tantam <lb/>vim ine&longs;&longs;e aëri, qua immen&longs;um propemodum aquarum pondus attolle<gap/>e <lb/>po&longs;&longs;it. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> An fortè putas, totam aquarum molem ab aëre gravitante <lb/>attolli, aut &longs;u&longs;tineri? </s> <s>falleris; cùm illa tan tùm aquæ portio &longs;u&longs;tineatur, <lb/>quæ &longs;upra libellam maximæ depre&longs;&longs;ionis attollitur, & quæ mihi videtur <lb/>per exigua, & ferè nulla, &longs;i cum tota aëris móle comparetur; & verò &longs;i <lb/>tota vis prementis aëris libera e&longs;&longs;et; id e&longs;t, &longs;i omnes circuli & arcus pre&longs;­<lb/>&longs;ionis vtiles e&longs;&longs;ent; id e&longs;t, &longs;i totam globi &longs;uperficiem aqua tegeret, æ&longs;tus <lb/>profectò longè alciùs a&longs;&longs;urgeret: &longs;ed dic mihi, &longs;odes, quanta &longs;it altitudo <lb/>aëris gravitantis in circulum maximæ pre&longs;&longs;ionis, &longs;eu depre&longs;&longs;ionis; ne ti­<lb/>bi nimius videar, la&longs;&longs;umo tantùm 1000. &longs;emidiametros terræ; igitur <lb/>859000.leucas, quarum quælibet continet 4. millaria, vt quodlibet mil­<lb/>liare 1000. pa&longs;&longs;us geometricos, quilibet pa&longs;&longs;us 5. pedes; &longs;upponamus au­<lb/>tem aquam e&longs;&longs;e graviorem aëre millie<gap/>; igitur &longs;i cylindrus prædictæ alti­<lb/>titudinis iuxta communem innatantium legem, aquæ innataret, vna &longs;ui <lb/>mille&longs;ima parte immergeretur, atque adeò &longs;egmentum immer&longs;nm <lb/>859. Leucarum e&longs;&longs;et; tantumdem igitur aquæ attolleret; miror <lb/>igitur, illum, de quo dubitare videris, aëris gravitantis ni­<lb/>&longs;um majorem non e&longs;&longs;e: immo inde facilè colligo, longè majo­<lb/>rem e&longs;&longs;e gravitatis aquæ proportionem ad gravitatem aëris, & in­<lb/><gap/>eriorem aëra fortè graviorem &longs;uperiore, tum propter humorem ad­<lb/>mixtum, tum fortè, quia compre&longs;&longs;ior e&longs;t: ca&longs;tiga igitur præoccupatum <pb pagenum="152"/>animum, & ratiocinare ex certis principiis, & dubitationi locus non <lb/>erit. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/> Hæc &longs;ententia nimiam novitatem præ&longs;efert; ac proinde vel <lb/>hoc nomine &longs;u&longs;pécta multis e&longs;&longs;<gap/> videbitur. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Fateor vltro, hanc &longs;ententiam novam e&longs;&longs;e, &longs;ed ex antiquis <lb/>& certis principiis deducta; quòd &longs;i minimè liceat, nullus vnquam ref <lb/>literariæ progre&longs;&longs;us &longs;perandus e&longs;t: & verò quid damni ex hac novitate ti­<lb/>meri po&longs;&longs;it, nonvideo; &longs;upponit enim hæc&longs;ententia marinum <expan abbr="æ&longs;tũ">æ&longs;tum</expan> cum iis <lb/>omnibus phænomenis, quæ à terum i&longs;tarum periti<gap/>mis ob&longs;ervata fuere; <lb/>docet, prædictum æ&longs;tum e&longs;&longs;e à Luna, eiu&longs;que incrementum in Novilunio <lb/>& Plenilunio; decrementum in Quadraturis; maximam vimcirca Æqui­<lb/>noctia; agno&longs;cit aëta gravem e&longs;&longs;e; quis hoc neget? </s> <s>atque adeò &longs;uo ni&longs;u, <lb/>&longs;ua vi pro&longs;&longs;iva pollere, quæ toties in actum exeritur, quoties major e&longs;t, <lb/>quàm re&longs;i&longs;tentia; docet præterea Lunam ex no&longs;tris elementis compactam <lb/>e&longs;&longs;e; & hæc communis e&longs;t Sanctorum Patrum &longs;ententia; ac proinde So­<lb/>lis & caloris vi humorem educi ex Luna; denique docet commune me­<lb/>dium versùs illum globum gravitare, cui p<gap/>opiùs e&longs;t, vnde gravitationis, <lb/>ac proinde pre&longs;&longs;ionis inæqualitatem &longs;equi, nece&longs;&longs;e &longs;it, & ex hac, aqua­<lb/>rum tumbrem & æ&longs;tum. </s> <s>Cuncta hæc, etiam præ&longs;cindendo ab æ&longs;tu, ita à <lb/>natura con&longs;tituta e&longs;&longs;e putarem; &longs;i vltra dubitas, ponamus ex hypothe&longs;i, <lb/>nec enim, opinor, negabis ita e&longs;&longs;e po&longs;&longs;e; fingamus igitur, ita <lb/>e&longs;&longs;e; & vide, vtrùm cuncta æ&longs;tus marini phænomena rectè expli­<lb/>centur. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> Si aër gravitat, cur eius pondus non &longs;entimus? </s> <s>deinde quomo­<lb/>dò fieri pote&longs;t, vt idem aëris tractus modò versùs vnum, modò ver&longs;us aliud <lb/>centrum gravitet? </s> <s>An fortè novit, cui proprior e&longs;t? </s> <s>denique, humor ille <lb/>Lunaris, vbi &longs;emel terræ illap&longs;us e&longs;t, cùm hæc immobilis con&longs;i&longs;tat, non <lb/>videtur, quomodò in maternum patriumque &longs;inum & globum denuò redi­<lb/>re valeat. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/> Hæc facilè &longs;olvo; primum quidem, quia non &longs;entimus <lb/>aëris pondus &longs;icuti nec vrinatores pondus aquæ; nempe ideò me­<lb/>dium gravitat, vt corpus &longs;ubjectum levius &longs;ur&longs;um extrudat; nihil <lb/>ergo ab eius pondere nobis timendum e&longs;t, qui aëre graviores &longs;u­<lb/>mus; immo id vnum dumtaxat aëris, vel alterius medij gravita­<lb/>tio in nobis præ&longs;tat, vt minùs graves &longs;imus, dettacta nobis ea <lb/>gravitatis, &longs;eu gravitationis parte, quæ pondus tantæ molis aëris, quan­<lb/>tæ nos &longs;umus, adæquat. </s> <s>Secundum verò &longs;ic diluo; terminus extrin&longs;ecus <lb/>determinat lineam motus gravium, ex naturæ in&longs;ti<gap/>to, &longs;eù præ&longs;cripto <lb/>fine; nec opus e&longs;t, vt mobile cognitione, aut &longs;en&longs;u polleat; &longs;ed cum &longs;uum <lb/>finem obtinere debeat, &longs;uam vim exerit ad illum obtinendum; cùmigitur <lb/>corpus grave debeat con&longs;tituere vnum totum, &longs;eu <expan abbr="vnũ">vnum</expan> <expan abbr="globũ">globum</expan> totalem, cum <lb/>aliis corporibus, &longs;eu partibus <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> globi, vt <expan abbr="hũc">hunc</expan> finem obtineat, ferri debet <lb/>versùs commune centrum, in quo natura con&longs;tituit terminum illius latio­<lb/>nis; vnde &longs;i fortè centrum illud locum mutaret, etiam corpus grave lineam <lb/>motus mutaret. </s> <s>Res e&longs;t per&longs;picua interræ mobilis hypothe&longs;i, quæ licèt vera <pb pagenum="153"/>non &longs;it, nemo tamen huc v&longs;que negavit, po&longs;&longs;ibilem e&longs;&longs;e. </s> <s>Quemadmodùm <lb/>verò corpus grave determinatur à termino extrin&longs;eco, id e&longs;t, à centro, ad <lb/>talem lineam gravitationis, licèt centrum illud non videat, nec cogno&longs;cat, <lb/>ita determinatur ab eodem termino vel centro, cui propius e&longs;t, licèt ne&longs;ciat, <lb/>cuinam propius &longs;it. </s> <s>Tertium denique jam &longs;upra &longs;olutum e&longs;t; nempe caloris <lb/>vi, Lunaris humor longè no&longs;tro liberior ac proinde &longs;ubtilior, facilè rare&longs;cit, <lb/>atque avolat, is præ&longs;ertim, qui extra vmbram terræ po&longs;itus &longs;olares radios <lb/>diu excipit; in quo, meo judicio, nulla e&longs;t difficultas. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> In quadraturis eadem ratio pre&longs;&longs;ionis e&longs;&longs;et; quia eadem <lb/>gravitationis inæqualitas, quæ e&longs;t in copulis & oppo&longs;itione; æqualis igitur <lb/>æ&longs;tus, quod tamen ob&longs;ervationibus repugnat, deinde in lacubus Lunari <lb/>globo &longs;ubjectis, æ&longs;tus attolli deberet; denique in Oceano Septenttionali mo­<lb/>dicus æ&longs;tus e&longs;&longs;et, quia &longs;cilicet à punctis maximæ elevationis multum di&longs;tat. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;t.<emph.end type="italics"/> Hæc etiam facilè &longs;olvuntur; primum quidem, quia licèt in Qua­<lb/>draturis eadem &longs;it ratio pre&longs;&longs;ionis, ratione altitudinis Cylindrorum aëris <lb/>gravitantis, diver&longs;a tamen e&longs;t ratione medij; nempe in Quadraturis aëri <lb/>versùs terram gravitanti, minus humoris ine&longs;t igitur; inde &longs;equitur, e&longs;&longs;e <lb/>minùs gravem, ac proinde minorem exeri gravitationis effectum, æ&longs;tum <lb/>videlicet. </s> <s>Secundùm jam &longs;upra dilutum e&longs;t; cùm enim lacuum &longs;uperficies <lb/>paucos admodùm gradus complectatur, inæqualitas pre&longs;&longs;ionis in ea &longs;en&longs;i­<lb/>bilis non e&longs;t; quid mirum ergo, &longs;i effectus illius, nimirum æ&longs;tus, &longs;en&longs;ibilis <lb/>non &longs;it; hinc vbi &longs;unt majores lacus vt Americani illi, de quibus &longs;uptà, vel <lb/>vbi lacus per aliquod Fretum Oceano conjuncti &longs;unt, &longs;en&longs;ibilis in iis æ&longs;tus <lb/>ob&longs;ervatur. </s> <s>Tertium denique fic rejicio; in prima illa hypothe&longs;i, qua &longs;up­<lb/>poniturtota globi &longs;uperficies aquea; ita res &longs;e haberet; at &longs;ecundùm præ­<lb/>&longs;entem rerum &longs;tatum, eáque globi terraquei &longs;uperficie &longs;uppo&longs;ita, quæ modò <lb/>e&longs;t pro pter diver&longs;as reflexiones, pre&longs;&longs;iones, angu&longs;tias, eò currit æ&longs;tus, quo <lb/>major vis, vel alia quæpiam lineæ determinatio inclinat; hinc ad eandem <lb/>&longs;æpè oram etiam in locis parum di&longs;&longs;itis, adeò diver&longs;us æ&longs;tus e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;oe.<emph.end type="italics"/></s><s> Per aver&longs;a igitur flumina non a&longs;cenderet æ&longs;tus, in quorum &longs;u­<lb/>perficie inæqualitatis pre&longs;&longs;ionis &longs;en&longs;ibilis non e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Non ideò a&longs;cendit per alveum fluminis, quòd fluminis &longs;uper­<lb/>ficies prematur, &longs;ed quòd &longs;uperficies maris, cùm per æ&longs;tum intume&longs;cat, & <lb/>&longs;it &longs;upra &longs;uperficiem fluminis, more gravium, versùs eam partem excurrat; <lb/>neque in hoc vlla difficultas re&longs;tat. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> Circuli pre&longs;&longs;ionum ad libitum à vobis accipiuntur; cur enim pe<gap/><lb/>tiùs hi, quàm illi? </s> <s>vnde, ni fallor, ruit præcipua hujus ve&longs;træ &longs;ententiæ &longs;ub­<lb/>&longs;tructio. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Nego, fingi ad libitum; nempenon fingitur linea Ab&longs;idum, <lb/>vel connectens centra; neque linea confinium, &longs;eu dirimens, neque circuli <lb/>paralleli, per quotum centra, Ab&longs;idum linea ducitur, cadit que perpendicu­<lb/>lariter in eorum plana; nec æqualis gravitatio, &longs;eu pre&longs;&longs;io in quolibet pun­<lb/>cto circuli paralleli; nec communis ni&longs;us ab omnibus punctis eju&longs;dem cir­<lb/>culi; quia &longs;cilicet æqualis; &longs;i enim e&longs;&longs;et inæqualis, vna aliam &longs;uperaret; igi­<lb/>tur adversùs illam ageret; igitur actio communis non e&longs;&longs;et. </s> <s>Hinc mani-<pb pagenum="154"/>fefta ratio, cur ij circuli pre&longs;&longs;ionum minimè ponantur, in quorum &longs;ingulis <lb/>punctis ni&longs;us inæqualis e&longs;t; cuncta hæc igitur non ad libitum &longs;tatuuntur, <lb/>&longs;ed ex linea connectente centra, quæ ex globorum &longs;itu &longs;emper re&longs;ult<gap/>t, ne­<lb/>ce&longs;&longs;ariò con&longs;equuntur: non ruitigitur hujus &longs;ententiæ fundamentum, &longs;ed <lb/>maximoperè inde confirmatur. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Verbulum addo, & con&longs;idero lineam connectentem centra; ad <lb/>in&longs;tar axis coni, cu&longs;us vertex ad centrum terræ de&longs;init; Diameter verò ba­<lb/>&longs;is, in quam prædictus axis perpendiculariter cadit, e&longs;t ip&longs;a linea confinium; <lb/>con&longs;idero item infinitos conos, &longs;eu &longs;uperficies conicas, quarum ba&longs;es &longs;int <lb/>circuli concentrici in plano prædictæ ba&longs;is, & quarum maxima e&longs;t planum <lb/>circuli majoris, parallelum prædictæ ba&longs;i; minima verò præfata Ab&longs;idum <lb/>linea; quælibet &longs;uperficies conica, &longs;ecat &longs;uperficiem globi terraquei in cir­<lb/>culo, & omnes huju&longs;modi &longs;ectiones &longs;unt circuli paralleli, per quorum cen­<lb/>tra linea Ab&longs;idum rectâ ducitur; hi &longs;unt circuli pre&longs;&longs;ionum, inæquales qui­<lb/>dem inter &longs;e, ita tamen, vt in quolibet eju&longs;dem circuli puncto, æqualis pre&longs;­<lb/>&longs;io fiat; vereor, vt alius modus e&longs;&longs;e po&longs;&longs;it pre&longs;&longs;ionis inæqualis, re&longs;pectu eju&longs;­<lb/>dem centri. </s> <s>Reliqua omitto; perge Chry&longs;ocome. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Si æ&longs;tus à Lunæ motu e&longs;&longs;et, ad Lunæ motum &longs;e&longs;e compone­<lb/>ret; ac proinde nunquam æ&longs;tus ab occa&longs;u ad ortum excurreret, quod certè <lb/>omnibus expetimentis refragatur. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Si aqua totam globi terraquei &longs;uperficiem tegeret, tumor il­<lb/>le, &longs;eu maximæ elevationis punctum, quod nunquam Lunæ non re&longs;pondet <lb/>&longs;em per ab ortu in occa&longs;um ire videretur; at in hoc rerum &longs;tatu versùs litus <lb/>humilius a&longs;&longs;urgens peræ&longs;tum aqua excurrit, quoquover&longs;um tandem &longs;pectet, <lb/>idque maximè &longs;i linea cur&longs;us in oram illam directè incidat. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Ventus impediret vim æ&longs;tus, cùm tamen illam augeat, aëre <lb/>&longs;cilicet acto, per lineam Horizontalem, ac proinde impedito illius gravi­<lb/>tationis ni&longs;u. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/> Aër, quamvis alioquin per lineam Hotizontalem actus, re­<lb/><gap/>inet tamen totam vim &longs;uæ gravitationis; exemplum luculentum habes in <lb/>ligno humido innatante, quod licèt ad in&longs;tar naviculæ per Horizontalem <lb/>impellatur; totum tamen illius pondus &longs;uam vim exerit gravitando; v. </s> <s>g. <lb/></s> <s>fit vas aqua plenum 20.libr.&longs;it lignum aquæ innatans.5.libr. </s> <s>quod per Ho­<lb/>rizontalem moveatur, haud dubiè, &longs;i vas ip&longs;um tunc appendas, 25.librarum <lb/>pondus &longs;enties: &longs;ic aqua, quæ &longs;upra fundum alvei currit; in hoc &longs;uæ gravi­<lb/>tatis vim totam exerit; idem dico de globo in plano Horizontali rotato: <lb/>aër igitur quantumvis agitatus totius gravitationis effectum præ&longs;tat. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Vix crediderim, lapidem per Horizontalem projectum, to­<lb/>tius gravitationis &longs;uæ vim exerere; alio quin recta deor&longs;um iret; igitur nec <lb/>aër per lineam Horizontalem à Vento actus. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Ex eo quod lapis totam vim &longs;uæ gravitationis exerat, non <lb/>&longs;equitur, quod recta deor&longs;um ire debeat, cùm motu quodam mixto movea­<lb/>tur, idque per Parabolam, vt jam multi demon&longs;tra&longs;&longs;e dicuntur: Deinde non <lb/>e&longs;t par ratio lapidis & aëris; lapis enim non gravitat cum aëre gravitatio­<lb/><gap/>e communi, ni&longs;i &longs;ecundùm modicam illam ponderis portionem, quæ aëri <pb pagenum="155"/>eju&longs;dem cum lapide molis competit; at verò pars aëris, quæ in medio aëre <lb/>per Horizontalem movetur, cum aliis&longs;ibi &longs;ubjectis, & impo&longs;itis, gravitatio­<lb/>ne communi gravitat. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Per vos mihi liceat, breve Parergon inter&longs;erete, vt hæc meliùs <lb/>intelligantur. </s> <s>Corpus, quod e&longs;t in medio, vel eju&longs;dem e&longs;t cum medio gra­<lb/>vitatis, vel majoris, vel minoris; &longs;i minoris, innatat medio; &longs;i majoris, im­<lb/>mergitur; &longs;i æqualis, in quocunque loco illud colloces, ibi manet: porrò <lb/>corpus humido innatans, gravitatione communi cum ip&longs;o medio gravitat; <lb/>cujus rei luculentum exéplum, vel experimentum attuli&longs;ti, Augu&longs;tine; nem­<lb/>pe totum illud vas appen&longs;um 25.libr.pendit, &longs;ive lignum quie&longs;cat, &longs;ive flu­<lb/>ctuet; &longs;ive in fundo va&longs;is atte retineatur; &longs;ive &longs;ur&longs;um emergat; &longs;ive pet <lb/>Horizontalem feratur: Et verò vbi nihil propriæ & &longs;ingularis gravitatio­<lb/>nis retinet, in communem gravitationem totam &longs;uam vim refundit; hinc <lb/>manus ligno innatanti &longs;uppo&longs;ita nullum pondus &longs;entit, ni&longs;i fortè illud tan­<lb/>tulum attollas, vel filo ex parte immer&longs;um &longs;u&longs;tineas; tunc enim vas ip&longs;um <lb/>minùs pendit; v.g. </s> <s>&longs;i dum lignum ex parte immer&longs;um &longs;uftines, &longs;entis trium <lb/>libr.pondus, vas 22.libr. </s> <s>tunc erit; hinc &longs;i vas dextrâ, lignum verò filo ap­<lb/>pen&longs;um &longs;ini&longs;trâ &longs;u&longs;tineas, vtraque &longs;imul totum pondus, &longs;ed qua propor­<lb/>tione plus ligni &longs;ini&longs;tra &longs;u&longs;tinet, eadem in va&longs;e dextera minus pondus &longs;u­<lb/>&longs;tinet: porrò &longs;i corpus aqua gravius &longs;it, v.g.plumbum, haud dubiè immer­<lb/>gitur, &longs;it v.g, idem vas 20.libr.&longs;it pila plumbea 10. libr. </s> <s>vbi hæc fundum <lb/>va&longs;is attigit, totum va&longs;is pondus erit 30.libr.at &longs;i vas pendatur eo dumtaxat <lb/>tempore, quo pila plumbea per aquam de&longs;cendit, &longs;upra 20.libr. </s> <s>illam tan­<lb/>tum ponderis acce&longs;&longs;ionem &longs;enties, quam aqua, vt &longs;ic loquar, plumbo detra­<lb/>hit, æqualem &longs;cilicet ponderi portionis aquæ, eju&longs;dem molis; &longs;upponamus <lb/>autem gravitatem plumbi e&longs;&longs;e decuplam gravitatis aquæ, vas erit 21. libr. <lb/></s> <s>idem &longs;iet, &longs;i pila omnino immer&longs;a filo &longs;u&longs;tineatur. </s> <s>Hinc duo Paradoxa facilè <lb/>deducetis; primum &longs;it, corpus leve, quod &longs;ur&longs;um per mediam aquam va&longs;e <lb/>contentam emergit, magis gravitat in eum, qui vas ip&longs;um &longs;u&longs;tinet, quàm <lb/>corpus grave, quod per mediam aquam deor&longs;um fertur: ac proinde corpus <lb/>levius majorem vim gravitationis exerit, quàm gravius; hinc quò plus &longs;in­<lb/>gularis gravitationis corpus retinet intra medium va&longs;e contentum, mino­<lb/>rem vim facit adversùs illum, qui vas &longs;u&longs;tinet; & quoad vim ponderis, perin­<lb/>de e&longs;t, &longs;ive prædicta pila plumbea liberè per aquam deor&longs;um eat, &longs;ive aquæ <lb/>immer&longs;a & filo appen&longs;a &longs;u&longs;tineatur; contra verò quò minus &longs;ingularis gra­<lb/>vitationis corpus retinet, eò magis gravitat in eum, qui præfatum vas &longs;u­<lb/>&longs;tinet. </s> <s>Alterum Paradoxum e&longs;t: Qui&longs;quis prædictum vas portat, præter 20. <lb/>libr.aquæ 1.libram plumbi &longs;u&longs;tentat, quamvis alioquin plumbum immer­<lb/>&longs;um & filo appen&longs;um ab infinita potentia &longs;u&longs;tineatur; quia &longs;cilic<gap/>t me­<lb/>dium <gap/> gravitationis plumbo detrahit, &longs;cilicet 1.libram: cùm igitur ille <lb/>aëris tractus, qui à vento igitur, nihil propriæ gravitationis retineat, &longs;ed to­<lb/>tam in communem conferat, quamvis per diver&longs;as lineas &longs;ur&longs;um deor&longs;um­<lb/>ve, dextror&longs;um aut &longs;ini&longs;tror&longs;um à vento agatur, nullam tamen proprij pon­<lb/>deris jacturam facit, &longs;ed totam illius vim ac ni&longs;um exerit gravitatione com­<lb/>muniquare hoc nodo &longs;oluto, vide, an quidpiam aliud ocourrat, quod nobis <lb/>oppo<gap/>as. </s></p><pb pagenum="156"/><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Nihil prorsùs: vnicum tantùm dubium re&longs;tat; vtrùm &longs;ci­<lb/>licet diver&longs;a vmbræ projectæ ratio in Novilunio ac Plenilunio aliquod <lb/>di&longs;crimen in æ&longs;tu faciat. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Fat<gap/>or, diver&longs;am e&longs;&longs;e in vtroque, vmbræ projectæ rationem; <lb/>nempe in Novilunio vmbra à globo Lunari projicitur in Hemi&longs;phærium <lb/>fupra Horizontem, & à terre&longs;tri in Hemi&longs;phærium infra Horizontem; in <lb/>Plenilunio verò ab vtroque globo projicitur in Hemi&longs;phærium, noctu &longs;u­<lb/>pra, diu infra Horizontem; &longs;ed hoc magnum di&longs;crimen in æ&longs;tu non facit; <lb/>præ&longs;ertim cùm humot ille dumtaxat Lunatis ad æ&longs;tum aliquid conferat, <lb/>qui terre&longs;tri globo propior e&longs;t, &longs;ive den&longs;ior &longs;it, &longs;ive rarior, ju&longs;ta enim fit com­<lb/>pen&longs;atio; quippe &longs;i rarior e&longs;t, plus loci occupat, igitur illius gravitatio in <lb/>plura di&longs;trahitur, ac proinde &longs;inguli Cylindri minorem vim habent; &longs;i au­<lb/>tem den&longs;ior e&longs;t, deor&longs;um tendit, hinc minùs confert in gravitationem com­<lb/>munem: vnde vides vnum ab alio compen&longs;ari: &longs;ed jam &longs;atis de hoc argu­<lb/>mento, quod certè majorem di&longs;cu&longs;&longs;ionem po&longs;tularet, quam vobis ve&longs;tro <lb/>commodo faciendam relinquo. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Su&longs;tine parumper, Antime, maximum dubium mihi injeci&longs;ti; <lb/>&longs;i enim humor Lunaris den&longs;ior minùs confert in gravitationem commu­<lb/>nem, nulla igitur ratio e&longs;t, cur in Novilunio & Plenilunio major æ&longs;tus <lb/>&longs;iat. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Multa, crede mihi, adhuc ratio re&longs;tat; nam præter eam, quæ à <lb/>projectis vmbris, vt &longs;upra dictum e&longs;t, peti po&longs;&longs;et, non ignoras corpu&longs;cula <lb/>etiam gravi&longs;&longs;ima tum aquæ, tum aëri innatare, ac proinde vtrumque ele­<lb/>mentum inde gravius reddi; &longs;ic fœtæ nubes, & multus vapor affu&longs;us ab au­<lb/>ftro, aëra graviorem reddunt, vt Sal vel Sabulum aquæ admixtum; idem de <lb/>præfato humore Lunari dictum puta: cur verò corpu&longs;cula illa gravi&longs;&longs;ima <lb/>leviori medio innatent, non e&longs;t hujus loci di&longs;cutere, &longs;ed quæ&longs;o vos, huic <lb/>congre&longs;&longs;ui finem imponamus, ne docti&longs;&longs;imorum hominum auribus & pa­<lb/>tientia, immodica garrulitate abutamur. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Rectè mones; &longs;ed quando nobis commodum erit ad pro­<lb/>ximum congre&longs;&longs;um redire? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Quando voles, diem indicendum tibi relinquo. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;t.<emph.end type="italics"/></s><s> Po&longs;t tridum igitur vos expecto, vt pulcherrimum illud argu­<lb/>mentum de a&longs;&longs;urgente per fi&longs;tulam humido & Mercurio in eadem ab ex­<lb/>teriori aëris Cylindro, vt multi volunt, ad certam altitudinem &longs;u&longs;tentato, <lb/>di&longs;cutiamus. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Hoc ip&longs;um e&longs;t, quod nobis di&longs;cutiendum re&longs;tat; quare con&longs;ulite <lb/>illos Autores, qui de hac materia &longs;crip&longs;erunt, vt ex variis probati&longs;que expe­<lb/>rimentis, veritas tandem eluce&longs;cat; nonnihil addemus, delibando &longs;altem, <lb/>de vi eloctrica, quam aliqui ad rem hanc nonnihil conferre putarunt. </s></p><pb pagenum="157"/><figure></figure><p type="main"> <s><emph type="center"/>DIALOGVS QVARTVS.<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>In quo, de libratis &longs;uspen&longs;i&longs;que liquoribus <lb/>& Mercurio di&longs;putatur.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> <s>AMOENISSIMVM argumentum, quod tibi fortè <lb/>arrideat, Princeps Eminenti&longs;&longs;ime hodierna die di&longs;cutien­<lb/>dum &longs;u&longs;cepi, vtinam feliciter, quod tuis au&longs;piciis futurum <lb/>&longs;pero, demon&longs;trandum. </s> <s>Antiquis omnino intactum fuit, <lb/>& paucis ex recentioribus compertum experimentum; <lb/>primùm ca&longs;u innotuit; at demde &longs;tudio & arte, vltra <lb/>promotu<gap/> perfectum; in varias porrò partes itum e&longs;t, ad illius cau&longs;am <lb/>explorandam, quod vrrùm cuipiam pro votis &longs;ucce&longs;&longs;e<gap/>ir, vix definine au­<lb/>&longs;im; &longs;ed vt meliùs di&longs;&longs;ertatione pareat, huic demus in<gap/>um rejectis <gap/>utili­<lb/>bus præludiis, quæ & ad rem de qua agitur, parum aut nihil conferunt, & <lb/>tibi Cardinalis Eminenti&longs;&longs;ime alioquin occupati&longs;&longs;imo, nihil aliud ni&longs;i me­<lb/>rum tædium afferrent. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Para&longs;ti, vt video, dulci&longs;&longs;ime Augu&longs;tine, totam illam &longs;upelle­<lb/>ctilem, quæ ad ea, de quibus di&longs;putare in&longs;tituimus, experimenta pertinent; <lb/>video limpidi&longs;&longs;imam in va&longs;e aquam admoto&longs;que canaliculos vitreos vtrim­<lb/>que pervios; video Mercurium in va&longs;e & longiorem fi&longs;tulam vitream al­<lb/>tera parte clau&longs;am; accipio vnum ex i&longs;tis canaliculis, in &longs;uperficiem aquæ <lb/>immergo, humor &longs;tatim per canaliculum a&longs;&longs;urgit, ad digitalem ferè altitu­<lb/>dinem, vt vides. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Video quidem, &longs;ed miror magis; canaliculum in clino, altiùs <lb/>humor a&longs;cendit; & quod fortè mirabilius e&longs;t, breviorem canaliculum aquæ <lb/>admoveo, ad tantam altitudinem minimè a&longs;cendit; longiorem adhibeo <lb/>eju&longs;dem onmino ba&longs;is, altiùs humor a&longs;cendit; alterum orificium admo­<lb/>to pre&longs;sè digito, claudo, non a&longs;&longs;urgit humor; digitum amoveo, illicò <lb/>a&longs;&longs;urgit. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Dicerem, ab illo impetu aquam attolli, quo canaliculus <lb/>aquæ admovetur; &longs;ed admoto canaliculo, cujus &longs;upremum orifi­<lb/>cium digito clauditur, & jam eo quie&longs;cente, cùm nullus impetus <lb/>re&longs;tet, amoto digito, humor illico a&longs;&longs;urgit; vnde nece&longs;&longs;ario &longs;equi­<lb/>tur, minimè a&longs;&longs;urgere, propter impetum appul&longs;us canaliculi: aliquis <lb/>fortè diceret, nonnihil tarefactionis accedere; &longs;ed hoc totum inutile e&longs;t; <lb/>cur enim aqua intra canaliculum potiùs rare&longs;ceret, quàm intra vas ip&longs;um? <lb/></s> <s>deinde æquè frigida ac calida a&longs;&longs;urgit; item æquè vinum ac oleum, &longs;altem. <lb/></s> <s>vt audio. </s></p><pb pagenum="158"/><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Ita e&longs;t; in his omnibus &longs;æpè probavi; item in &longs;piritu vini, & <lb/>variis aquis di&longs;t<gap/>; immò &longs;i canaliculum olco immergas, paulò altiùs <lb/>a&longs;&longs;urgit, qúod non <gap/> ovidentiam expertus &longs;um; &longs;ed cuncta hæc ex­<lb/>perimenta luculentiora &longs;unt in &longs;cypho, vel ampulla, cujus imaginem ha­<lb/>bes pag. </s> <s>&longs;equenti, in qua &longs;cilicet humor per canaliculum GF a&longs;&longs;urgit &longs;upra <lb/>&longs;uperficiem BC, eo profectò altiùs, quo canaliculus angu&longs;tior erit. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> An fortè dici po&longs;&longs;et, pondus aquæ contentæ in majore am­<lb/>pulla, longè majus e&longs;&longs;e pondere aquæ contentæ intra minorem canalicu­<lb/>lum GF, ac proinde prævalere, & inde aquam altiùs extrudi, &longs;eu <lb/>attolli. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Scio, non neminem e&longs;&longs;e, cui hæc cogitatio in mentem venit, <lb/>quæ tamen, meo &longs;altem judicio, legitima non e&longs;t, cùm aqua ratione pon­<lb/>deris, &longs;eu gravitatis ad perfectam libellam &longs;e&longs;e componat; nempe gravi­<lb/>tat per Cylindros parallelos, &longs;eu lineas parallelas, in quocunque &longs;itu cana­<lb/><figure id="fig29"></figure><lb/>les &longs;tatuantur; &longs;int enlm canales ABC, IDE; <lb/>infundatur aqua per Orificium AB, &longs;it libella <lb/>Horizontalls ABFG; &longs;i canales æqualis &longs;int <lb/>cra&longs;&longs;itudinis &longs;uperficies aquæ vtrimque &longs;i&longs;tet in <lb/>ABFG, vt patet; tunc enim perfectum erit <lb/>æquilibrium; &longs;i verò canalis IDE &longs;it angu&longs;tior, <lb/>a&longs;&longs;urget aqua v. </s> <s>g. </s> <s>in DE, &longs;upra libellam AG, <lb/>ratione tamen gravitationis, Cylindrus aquæ <lb/>cujus ba&longs;is æqualis &longs;it FG, facit perfectum æqui­<lb/>librium cum Cylindro aquæ æquali IG, vt patet; <lb/>&longs;i enim tota moles aquæ contentæ in ABC, &longs;u­<lb/>&longs;tineret contentam intra IDE, cùm illa hujus po&longs;&longs;it e&longs;&longs;e decupla, centu­<lb/>pla, & in quavis data proportione majoris inæqualitatis, aqua per cana­<lb/>liculum IDE ad quamcunque po&longs;tulatam altitudinem a&longs;cenderet, quod <lb/>manife&longs;tè fal&longs;um e&longs;t; igitur totus Cylindrus aquæ ABC non facit æqui­<lb/>librium cum Cylindro aqueo IDE, &longs;ed tantùm Cylindrus eju&longs;dem ba&longs;is <lb/>DE; &longs;ed hic facit æquilibrium cum Cylindro IFG, vt patet; igitur inde <lb/>pet&longs;picuum fit, aquam per canaliculum IDE non a&longs;&longs;urgere in DE &longs;upra <lb/>libellam, propter majorem vim ponderis ABC. </s> <s>Accedit quod &longs;i ba&longs;is <lb/>AB Diameter &longs;it bipedalis, & ba&longs;is DE &longs;it pedalis, non a&longs;&longs;urget aqua in <lb/>DE, immò ad &longs;en&longs;um &longs;i&longs;tet in FG, cùm tamen pondus aquæ ABC &longs;it <lb/>quadruplum aquæ IFG; igitur in majoribus canalibus aqua non a&longs;&longs;urgit, <lb/>vt in minoribus; vnde manife&longs;tè con&longs;tat, hunc effectum e&longs;&longs;e ab alia cau&longs;a. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/> Cùm hæc nudius tertius viro cuidam ingenio&longs;i&longs;&longs;imo pro­<lb/>po&longs;u<gap/>&longs;&longs;em, illico re&longs;pondit vim quandam adhæ &longs;ivam in corporibus præ&longs;er­<lb/>tim liquidis, &longs;ibi compertam e&longs;&longs;e, ratione cujus, vnum alteri accedit, &longs;e&longs;e <lb/>arctiùs conjungit; &longs;ic inquiebat ille, &longs;i aquæ gutta tangat aliam guttam, <lb/>in vnam majorem guttam &longs;tatim mutuo qua&longs;i amplexu coale&longs;cunt; &longs;ic duo <lb/>&longs;tammæ con<gap/> in vnam abeunt; vnde fieri putabat, vt aquà per canalicu­<lb/>lum min<gap/>è a&longs;&longs;urgeret, ni&longs;i priùs cava illius &longs;uperficies maduerit, quod vbi <lb/>à me probatum e&longs;t, dicto re&longs;pondit eventus: ne&longs;cio vtrùm hæc ratio vobis <lb/>atrideat. </s></p><pb pagenum="159"/><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Minimè verò, & alia ratio e&longs;t congre&longs;&longs;us guttarum & cono­<lb/>rum flammæ, de qua infra. </s> <s>Primò, enim gratis affingitur prædicta vis <lb/>adhæ&longs;iva liquidis corporibus, ex iis &longs;cilicet effectibus, qui aliis cau&longs;is tri­<lb/>buendi &longs;unt. </s> <s>Secundò, etiam&longs;i canaliculus ante non maduerit, aqua <lb/>tamen a&longs;&longs;urgit, &longs;i paulò laxior e&longs;t; centics probavi infu&longs;o in ampullam <lb/><figure id="fig30"></figure><lb/>A oleo; & ne qui&longs;piam diceret, oleum a&longs;&longs;urgere <lb/>per GF, propter impetum infu&longs;ionis, infudi <lb/>oleum, inclinata versùs B ampulla; ita vt &longs;uper­<lb/>ficies olei per canaliculum vix a&longs;&longs;urgeretin H; <lb/>tum deinde erecta ampulla, oleuin a&longs;cendit in F, <lb/>licèt inferior canaliculi &longs;uperficies &longs;icca omnino <lb/>e&longs;&longs;et; idem fiet admoto canaliculo &longs;uperfieiei <lb/>olei, &longs;i paulo major &longs;it. </s> <s>Tertiò, Non video cur <lb/>major aquæ portio minorem potiùs ad &longs;e non adducat, quàm minor ma­<lb/>jorem; &longs;i enim prædicta vi vtraque pollet, major certè majore, &longs;cilicet <lb/>exten&longs;ivè, vt major flamma magis calefacit, quàm minor; accedit, quod <lb/>in hoc ca&longs;u, minor longè faciliùs ad majorem accederet, &longs;cilicet de&longs;cen­<lb/>dendo, quàm major ad minorem a&longs;cendendo. </s> <s>Quartò, in majore tubo <lb/>madefacto eadem ratio militaret; nec dicas ob&longs;tare majorem vim pon­<lb/>deris; quia cùm vis illa adhæ&longs;iva omnibus partibus aquæ in&longs;it, eadem e&longs;t <lb/>illius proportio ad re&longs;i&longs;tentiam ponderis in majore, quæ in minore; & <lb/>vt duæ partes in minore &longs;uperant duas partes ponderis; ita mille partes in <lb/>majore &longs;uperabunt mille partes ponderis. </s> <s>Quintò, Cur oleum altiùs a&longs;­<lb/>&longs;urgit, quàm aqua? </s> <s>Cur Mercurius ferè nihil? </s> <s>dico ferè, quia infra evin­<lb/>cam tantulùm a&longs;&longs;urgere; Cur aliquando ip&longs;a aqua altiùs, aliàs minùs <lb/>altè a&longs;cendit? </s> <s>Nihil horum cum illa vi adhæ&longs;iva &longs;tare pote&longs;t. </s> <s>Sextò, <lb/>Cur aqua per canaliculum inclinatum longiùs excurrit? </s> <s>Cur per bre­<lb/>viorem, quamvis madefactum interiùs, minùs altè, & &longs;i adhuc breviorem <lb/>accipias, ferè nihil a&longs;&longs;urgit? </s> <s>Cur per tubulos alioquin &longs;icci&longs;&longs;imæ materiæ, <lb/>vt panis bis cocti, panni, telæ &c. </s> <s>Ex his vides, ni fallor, Chry&longs;ocome, aliam <lb/>omnino hujus effectus cau&longs;am quærendam e&longs;&longs;e. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Sed cur per canaliculum &longs;iccum non a&longs;&longs;urgit, atque adeò ca­<lb/>va illius &longs;uperficies humectanda e&longs;t? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Si canaliculus paulò laxior &longs;it, & majoris ba&longs;is etiam per &longs;ic­<lb/>cum a&longs;cendit; non a&longs;cendit, tamen &longs;i angu&longs;ti&longs;&longs;imus &longs;it, ni&longs;i &longs;en &longs;im ac <lb/>lentè; quia licèt &longs;uperficies vitri lævigata e&longs;&longs;e viddatur, mille tamen <lb/>&longs;alebris & rugis, &longs;eu &longs;triis a&longs;peratur, quæ ni&longs;i affuio humore com­<lb/>planentur, a&longs;perum iter faciunt, & modicam aquæ portionem faci­<lb/>lè &longs;i&longs;tunt; cùm tamen in majore canaliculo non ob&longs;tent; quin major <lb/>aquæ copia a&longs;&longs;urgat; accedit, quod &longs;i juxta Figuras præcedentes va&longs;a <lb/>conformentur, aqua etiam per canaliculum &longs;iecum a&longs;cendit; cur au­<lb/>tem aquæ gutta intra aliam &longs;ubeat, vel flamma intra flammam, dicemus <lb/>po&longs;tea. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Ex his ergo con&longs;tat, totam rem i&longs;tam ab aëris com­<lb/>pre&longs;&longs;ione petendam e&longs;&longs;e, vt jam indica&longs;ti in &longs;uperiore congre&longs;&longs;n, <pb pagenum="160"/>&longs;ed quia paulò fu&longs;iùs explicandum re&longs;tat, hoc tibi certè onus in­<lb/>cumbit. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Rectè mones, tem hanc paulò fu&longs;iùs explicandam e&longs;&longs;e; quod <lb/>yt meliùs fiat; nonnulla &longs;uppono expetimenta, partim commu­<lb/>nia & trita, partim &longs;ingularia. </s> <s>Primùm &longs;it hoc. </s> <s>Ampulla vitrea <lb/><figure id="fig31"></figure><lb/>DACB, cui per os D canaliculus vitreus vtrim­<lb/>que pervius in&longs;eratur, & probè ob&longs;tructo ori­<lb/>ficio D, exugatur ducto anhelitu per E, aër <lb/>intra ampullam contentus; tum &longs;tatim, vbi <lb/>removetur ab ore, immergatur in aquàm ex­<lb/>tremitas E; &longs;ugitur enim aqua, dum aër intra <lb/>dilatatus &longs;e&longs;e contrahit; &longs;ic demum AB &longs;uper­<lb/>ficies aquæ per &longs;uctum adductæ; tum extremo <lb/>E ore admoto, pul&longs;us anhelitus magna vi in­<lb/>trudatur; inde &longs;it, vt aër ABD appul&longs;u novi <lb/>aëris comprimatur, & compre&longs;&longs;us &longs;uperficiem <lb/>aquæ AB premat, ac proinde &longs;upra &longs;uperficiem AB aqua per canalicu­<lb/>lum CE a&longs;&longs;urgat; immò &longs;i &longs;it magna vis pre&longs;&longs;ionis, ad in&longs;tar jaculi erum­<lb/>pat. </s> <s>Idem fiet opera di&longs;ci, &longs;uperficiem aquæ prementis, vt jam dixi in &longs;u­<lb/>periore congre&longs;&longs;u. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Certum & per&longs;picuum e&longs;t, illum aquæ jactum e&longs;&longs;e ab vna <lb/>pre&longs;&longs;ione aëris va&longs;e contenti & compre&longs;&longs;i; quia &longs;cilicet aquæ &longs;uperficiem, <lb/>cui incumbit, premit; & cùm nihil ob&longs;i&longs;tat pre&longs;&longs;ioni intra canaliculum, <lb/>prædicta vi aqua facilè extruditur; hæc vt dixi, adeò certa &longs;unt, vt nul­<lb/>lum po&longs;t &longs;e dubium relinquant. </s> <s>Sed quid hoc ad aquam, per canaliculum <lb/>in aëre libero a&longs;&longs;urgentem? </s> <s>Licèt enim concedam, aëra e&longs;&longs;e compre&longs;&longs;um, <lb/>cùm non minùs premat &longs;uperficiem aquæ intra canaliculum contentæ; <lb/><figure id="fig32"></figure><lb/>quàm intra majus vas, v.g. </s> <s>&longs;uperficiem DE, quàm <lb/>AB, neque hinc, neque illine vis illa pre&longs;&longs;ionis <lb/>prævalere pote&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Fateor, maximum di&longs;crimen e&longs;&longs;e in­<lb/>ter experimentum Figuræ 31. & 32. quia in hac, <lb/>aër ADB novam compre&longs;&longs;ionem patitur, qua <lb/>tamen aër exterior caret; vnde non modò tan­<lb/>tulùm a&longs;&longs;urgit aqua per canaliculum CE, vt <lb/>fit, etiam &longs;i nova compre&longs;&longs;io minimè accedat, <lb/>& os ampullæ D pateat; &longs;ed magna vi, ad in&longs;tar <lb/>jaculi extruditur; quem reverà effectum il­<lb/>la modica vis pre&longs;&longs;ionis, quæ ine&longs;t aëri, præ&longs;tare non po&longs;&longs;et; por­<lb/>rò licèt aër exterior incumbat vtrique &longs;uperficiei aquæ &longs;cilicet AB <lb/>& GF, major tamen vis premit AB, quam FG, quia corpus <lb/>pre&longs;&longs;um quoquo ver&longs;um pellit in orbem; igitur eò major vis e&longs;t, <lb/>quo &longs;ub majori angulo incidit; v. </s> <s>g. </s> <s>a&longs;&longs;umatur centrum &longs;uperficiei <lb/>AB, premitur per infinitos radios, vndequaque illap&longs;os; cogita co­<lb/>num, cujus vertex prædicto centro incumbat; igitur quò prædictus <pb pagenum="161"/>angulus, &longs;eu conus obtu&longs;ior e&longs;t, vis pre&longs;&longs;ionis major e&longs;t, & hæc eò minor, <lb/>quò ille acutior; Sit autom centrum &longs;uperficiei FG canaliculo contentæ, <lb/>in quod aëris prementis conus incumbat, vides, <gap/>ni fallor, quàm acu­<lb/>tus angulus futurus &longs;it; ac proinde vis pre&longs;&longs;io<gap/> minor; quid mi­<lb/>rum ergo, &longs;i pre&longs;&longs;io in AB prævaleat, ac proinde aqua &longs;upra FG a&longs;­<lb/>&longs;urgat? </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Quid verò fict, &longs;i canaliculi &longs;egmentum &longs;upta FG, &longs;it minus <lb/>FE? an fortè aqua vi prædictæ pre&longs;&longs;ionis effluet per canaliculum? </s> <s>&longs;i hoc <lb/>fieret, perpetuum motum haberemus. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Prævideram, te in hunc &longs;copulum impacturum; nempe, in­<lb/>quis, &longs;i aqua per canaliculum majore vi pre&longs;&longs;ionis vigente in AB, a&longs;&longs;ur­<lb/><figure id="fig33"></figure><lb/>git in DE, haud dubiè &longs;i re&longs;cindatur &longs;egmen­<lb/>tum canaliculi ME, effluet per os ML, cum <lb/>eadem vis pre&longs;&longs;ionis aplicata &longs;it in in AB; &longs;ed <lb/>reverà non effluit ex ML; & hoc e&longs;t alterum <lb/>experimentum; cùmtamen alioquin iuxta com­<lb/>munes Hy draulicæ regulas faciliùs &longs;it effluere <lb/>ex ML, quàm in DE attolli; ratio e&longs;t, quia vt <lb/>in centrum ba&longs;is AB aëris pre&longs;&longs;io incumbit, <lb/>&longs;ecundùm angulum, &longs;eu conum maximè obtu­<lb/>&longs;um, ita in ba&longs;im DE, vel in ba&longs;im ML, re&longs;ecto <lb/>&longs;egmento canaliculi ME, &longs;ecundùm æqualem <lb/>angulum incumbit; quid mirum ergo, &longs;i neurra pre&longs;&longs;io prævaleat? </s> <s>At <lb/>verò &longs;i non re&longs;cindatur &longs;egmentum ME, incumbit in <gap/>um ba&longs;is <lb/>ML, &longs;ecundùm angulum acutum, cujus ba&longs;is e&longs;t DE, & latus recta ducta <lb/>à D, ad centrum ML. </s> <s>Vnde pre&longs;&longs;io in AB omnino prævalet. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> Sed infta, pre&longs;&longs;io in AB &longs;emper major e&longs;t pre&longs;&longs;ione in ML; <lb/>etiam re&longs;ecto &longs;egmento ME; nempe vt aëris pre&longs;&longs;io incumbit centro <lb/>ba&longs;is AB, idque in reliquis punctis &longs;ecundùm æqualem pre&longs;&longs;ionis angu­<lb/>lum, &longs;eu conum, item in &longs;ingula puncta ba&longs;is ML, &longs;ecundùm æqualem <lb/>priori angulum, refecto &longs;cilicet &longs;egmento ME; igitur pre&longs;&longs;iones &longs;unt, <lb/>vt bafes; initur ba&longs;is AB, quæ longè major e&longs;t prævalet; igitur &longs;i tua <lb/>pre&longs;&longs;ionis ratio &longs;ub&longs;i&longs;teret, aqua ex ML omnino efflueret; non effluit ta­<lb/>men, vt fateris vltrò. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Acutè omnino paralogizas; vt enim gravitatio aquæ con­<lb/>tentæ in canali AC, exerit tantùm &longs;uamvim, attollendo cylindrum IG, <lb/>ad libellam v&longs;que, &longs;ecundùm cylindrum æqualem IG, vt &longs;upra o&longs;ten­<lb/>&longs;um e&longs;t; ita vis pre&longs;&longs;ionis ba&longs;is AB exeritur, attollendo aquam per ca­<lb/>naliculum &longs;ecundùm ba&longs;im æqualem ML, vbi autem aqua elevata e&longs;t in <lb/>ML, æqualis incumbit pre&longs;&longs;io vtrimque, &longs;cilicet in ba&longs;i ML, & ip&longs;i æqua­<lb/>li a&longs;&longs;umptæ in AB; &longs;i verò aquæ fuperficies &longs;upponatur in FG, haud <lb/>dubiè minor e&longs;t pre&longs;&longs;io in FG, quàm in ML; igitur quàm im æquali <lb/>ML a&longs;&longs;umptæ in AB; igitur hæc prævalet; vnde a&longs;&longs;urgit aqua ex FG <lb/>in ML: cogita quæ&longs;o duci totidem cylindros parallelos deor&longs;um præ­<lb/>&longs;ci&longs;a gravitatione, ex &longs;ingulis punctis ba&longs;is AB, quibus totidem pre&longs;-<pb pagenum="162"/>&longs;ionis coni incumbunt; itemque ex ba&longs;i ML; pares certè cum paribus <lb/>contranituntur, &longs;inguli &longs;cilitet cylindri cum &longs;ingulis; igitur neutra pars <lb/>prævalet, &longs;i verò non re&longs;eindatut &longs;egmentum ME, equidem &longs;inguli <lb/>cylindri ducti ex &longs;ingulis punctis ba&longs;is ML pugnant cum &longs;ingulis ductis <lb/>ex ba&longs;i AB, hi tamen victores &longs;unt; quia fortiores; cùm &longs;ingulis vis <lb/>pre&longs;&longs;ionis &longs;ecundùm majorem conum, vel angulum incumbat; igitur <lb/>quamvis alioquin angu&longs;ti&longs;&longs;imus &longs;it canaliculus, &longs;i tamen &longs;upra libellam <lb/>AG non producatur, par vtrimque e&longs;t vis pre&longs;&longs;ionis; ac proinde <lb/>neutra pars prævalet; vnde, ni fallor, tuus ille paralogi&longs;mus &longs;olutus <lb/>manet. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Ex dictis rectè deduco, aquam attolli altiùs in longiore, ca­<lb/>naliculo; nempe in longiore, angulus pre&longs;&longs;ionis acutior & minor e&longs;t, <lb/>quàm in breviore v. </s> <s>g. </s> <s>angnlus DFE, minor e&longs;t angulo DME, vt <lb/>patet. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Hoc erat tertium experimentum; aqua enim in canaliculis <lb/>longioribus tantulùm immer&longs;is altiùs a&longs;&longs;urgit: & ni&longs;i nimiæ ob&longs;tarent <lb/>angu&longs;tiæ, per quas &longs;ine aliqua vi aqua traduci nequit, ad quamcumque <lb/>certè altitudinem aqua a&longs;&longs;urgeret. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Prudenter occurri&longs;ti in&longs;tantiæ, quam tibifacere meditabar; <lb/>alia tamen longè difficilior &longs;e&longs;e mihi objicit; cùm enim finguli pre&longs;&longs;ionis <lb/>cylindri &longs;ingulis contranituntur; perinde e&longs;t, five laxior &longs;it canaliculus, <lb/>&longs;ive angu&longs;tior, quod tamen experimentis repugnat, cùm per canalicu­<lb/>lum angu&longs;tiorem longè altiùs humor a&longs;&longs;urgat. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Hand inficior, difficultatem à<gap/>e propo&longs;itam eam e&longs;&longs;e, quæ in­<lb/>genio tuo digna e&longs;&longs;e videatur; quam tamen, ni fallor, &longs;atis facilè folvo: <lb/>nempe aër pre&longs;&longs;us majorem vim non imprimit &longs;uperficiei majori AB <lb/>quàm minori DE; Cogita di&longs;oum ligneum, quo premitur &longs;uperficies A <lb/>B, motu vt vnum, itemque alium minorem, quo premitur &longs;uperficies DE, <lb/>motu vt vnum; certè vterque æqualem vim imprimit &longs;uperficie, DE & <lb/>AB; licèt enim alter major &longs;it, & majorem &longs;uperficiem premat; quia <lb/>tamen idem aër compre&longs;&longs;us circumfu&longs;us vtramque æquè premit, æqua­<lb/>lis &longs;emper pre&longs;&longs;ionis effectus &longs;equitur, id e&longs;t, eju&longs;dem quantitatis aquæ <lb/>elevatio; cæteris tamen paribus: vbi enim hæc elevata e&longs;t, & ab eadem <lb/>vi premente &longs;u&longs;tinetur, nullus alius effectus illi competit, cùm tota in <lb/>co exeratur; dixi cæteris paribus, id e&longs;t, &longs;uppo&longs;ita eadem proportione <lb/>pre&longs;&longs;ionis aëris incumbentis &longs;uperficiei canaliculi, &longs;i enim propter bre­<lb/>vitatem canaliculi prædicta proportio cre&longs;cat, vel &longs;it major canaliculus, <lb/>ac proinde angulus pre&longs;&longs;ionis major, itemque major pre&longs;&longs;io, haud dubiè <lb/>aqua minùs altè per canaliculum a&longs;cendit: Suppo&longs;ita autem eadem pro­<lb/>portione pre&longs;&longs;ionum, altitudines aquæ elevatæ in diver&longs;is canaliculis, <lb/>&longs;unt vt ba&longs;es permutando, vt pater, v.g. </s> <s>&longs;i ba&longs;is vnius &longs;it dupla ba&longs;is alte­<lb/>riùs, altitudo ejus erit dupla altitudinis illius, vt &longs;cilicet cylindri æqua­<lb/>les &longs;int. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Iam optimè intelligo id, quod paulò ante capere non po­<lb/><gap/>am; quod &longs;cilicet, vt aiebas, ad quamcumque altitudinem aqua po&longs;-<pb pagenum="163"/>&longs;it attolli; modò per qua&longs;libet angu&longs;tias immitti & traduci queat; qua <lb/>enim proportione decre&longs;cit ba&longs;is, cre&longs;eit, altitudo; &longs;ed quæ&longs;o te, quid fiet, <lb/>&longs;i aquæ &longs;uperficies non &longs;it in AB, &longs;ed in HK. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Certum e&longs;t, minotem inde fore aquæ elevationem; quia pre&longs;­<lb/>&longs;io in ba&longs;im HK minor e&longs;t quam in ba&longs;im AB; quia fit &longs;ub minore an­<lb/>gulo, v.g. </s> <s>&longs;tante ba&longs;i in AB, a&longs;&longs;urgetaqua in DE &longs;upra libellam FG, de­<lb/>pre&longs;&longs;a verò ba&longs;i in HK &longs;upra libellam HP, a&longs;&longs;urget aqua in R, eritque <lb/>PR minor quàm GE. </s> <s>Hîc autem ob&longs;ervo aliud experimentum, reverà <lb/>pulcherrimum, nempe &longs;uperficies aquæ in HK, non e&longs;t plana, nedum <lb/>convexa, &longs;ed omnino concava; cùm tamen AB modo humor extet, &longs;it <lb/>convexa. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Hoc etiam &longs;æpiùs ob&longs;ervavi, & cau&longs;am huju&longs;ce peregrini <lb/>effectus curiosè per&longs;crutatus &longs;um; nec crediderim ab vllo v&longs;piam prodi­<lb/>tam fui&longs;&longs;e. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Ex præmi&longs;&longs;is facilè deducitur, modò tantulum Geometriæ ac­<lb/>cedat. </s> <s>Suppono enim AB qua&longs;i ba&longs;im trianguli, cujus vertex terminetur <lb/>ad HK, cujus trianguli angulus verticis major e&longs;t, qui cadit in centrum <lb/>D prædictæ ba&longs;is, quàm is, qui cadit in extremitates ba&longs;is H vel K; vt pa­<lb/>tet ex Geometria; igitur major vis pre&longs;&longs;ionis incumbit in centrum O, <lb/>quàm in H vel K, & con&longs;equenter in ea puncta major, quæ accedunt <lb/>propiùs ad centrum O; quid mirum igitur, &longs;i punctum O &longs;ub&longs;idat, & <lb/>tota &longs;uperficies HOK cava &longs;it, propter inæqualem illam pre&longs;&longs;ionis vim. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> Sed quæ&longs;o te, Antime, cur aquæ &longs;uperficies AB convexa e&longs;t? <lb/></s> <s>video enim, cur cava non &longs;it, cùm inæqualis illa pre&longs;&longs;io de&longs;ideretur; cur <lb/>tamen convexa &longs;it, non plana, haud &longs;atis video. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Res &longs;atis trita e&longs;t; nempe illa humoris &longs;uperficies à centro <lb/>mundi æqualiter di&longs;tat &longs;ecundùm omnes partes; &longs;i enim aliqua longiùs <lb/>à præfato centro di&longs;taret, quàm aliæ, de&longs;cenderet illico; hæc certè vt ve­<lb/>ritati con&longs;ona, negari ab vllo non po&longs;&longs;unt; &longs;ed profectò hæc convexitas <lb/>in&longs;en&longs;ibilis e&longs;t, nempe arcus vnius minuti continet 1000. pa&longs;&longs;us geome­<lb/>tricos, vnius &longs;ecundi arous 16. pa&longs;&longs;us & <gap/> id e&longs;t 83. pedes circiter arcus <lb/>vnius tertij vnum pedem tubos vix habemus majoris diametri; quis <lb/>porrò arcum vnius tertij minuti à linea recta &longs;en&longs;u di&longs;tinguat? </s> <s>Cùm igi­<lb/>tur convexam &longs;uperficiem aquæ probè di&longs;cernamus, aliam omnino e&longs;&longs;e <lb/>nece&longs;&longs;e e&longs;t (& hoc &longs;it aliud experimentum) nempe vbi humor extremita­<lb/>tes A & B ba&longs;is attigit, non effluit aqua, &longs;ed intume&longs;cit in centro &longs;uper­<lb/>ficiei; centro enim minor vis pre&longs;&longs;ionis incumbit, quàm partibus extre­<lb/>mis, v.g. </s> <s>in centrum V vis pre&longs;&longs;ionis incumbens infra horizontalem AB <lb/>non cadit, cum tamen incumbens in A & in B infra prædictam horizon­<lb/>talem de&longs;cendat, vt pat<gap/>, quò fit, ne aqua ex A vel B <gap/>at & hæc vera <lb/>e&longs;t & legitima triti hujus experimenti ratio. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom<gap/>.<emph.end type="italics"/></s><s> Non bene capio quid tibi velis; nonnihil, quæ&longs;o te, <lb/>&longs;chematis adhibe, tunc enim oculis potiùs quàm auribus fidem ha­<lb/>bebo. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Sit vas quodpiam aqua plenum AEDB, &longs;it aquæ &longs;uprema <pb pagenum="164"/>&longs;uperficies AB, & centrum illius G, premitur punctum G, non tantùm <lb/>per HG perpendic<gap/>em, verùm enam per inf<gap/>tas inter <lb/><figure id="fig34"></figure><lb/>HG. AG, item inter GH, GB; nulla autem <lb/>e&longs;t <gap/> AB horizontàlem per quam punctum <lb/>G prematur, vt per&longs;picuum e&longs;t, at verò punctum <lb/>A, versùs quod aqua effluere nititur, proptia <lb/>gravitatione, <gap/>on tantum premitur à perpendi­<lb/><gap/> IA & ab aliis contentis <gap/>ter IA, MA, <lb/>item inter IA, AB, &longs;ed etiam ab aliis in&longs;ia MA <lb/>ductis, vt à PA. idem dico de puncto B, item­<lb/>que de aliis in totius marginis orbe di&longs;pofitis, <lb/>in quibus haud dubiè pre&longs;&longs;io prævalet, v<gap/>de aquam in &longs;uperficiem con­<lb/>vexam intume&longs;cere nece&longs;&longs;e &longs;it. </s> <s>Hinc quò major e&longs;t va&longs;is &longs;uperficies mi­<lb/>nùs intume&longs;cit; quia ad tumorem æquè altum; plus aquæ, vi pre&longs;&longs;ionis <lb/>attollendum e&longs;&longs;et; &longs;ic vt jam dixi, per canaliculum angu&longs;tiorem altiùs a&longs;­<lb/>&longs;urgit aqua, per majorem &longs;eu laxiorem, minùs altè, e&longs;t enim ea<gap/>em pror­<lb/>sùs ratio. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Vnum mihi venit in mentem; ne&longs;cio vtrùm tuo calculo <lb/>probaturus &longs;is, Antime; redeo ad primum &longs;chema & &longs;uperficiem AB, <lb/>(<emph type="italics"/>vid. </s> <s>Figuram in pag.<emph.end type="italics"/>161.) &longs;upremam &longs;cilicet, quam convexam e&longs;&longs;e &longs;uppo­<lb/>no; &longs;uperficiem verò ML, excurrente canaliculo v&longs;que ad DE, conca­<lb/>vam; quo po&longs;ito, numquid dici po&longs;&longs;et, partes extremas A & B, quibus ma­<lb/>jor vis pre&longs;&longs;ionis imprimitur, quam centro V efficere vt partes extremæ <lb/>alterius ba&longs;is ML, altiùs affurgant; <expan abbr="centrũ">centrum</expan> verò minùs. </s> <s>Vnde vt ex hac in­<lb/>æquali pre&longs;&longs;ionis vi ba&longs;is AB convexa evadit, ita & bafis ML concava. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Quàm acute patalog<gap/>zas, Augu&longs;tine, &longs;upponamus enim ba&longs;im <lb/>in HK majoris canalis, & in R minotis, vtraque cava per&longs;picitur; vnde, <lb/>ni fallor, ruit tua ratio; quare vis illa pre&longs;&longs;ionis inæqualis, quæ incum­<lb/>bit in &longs;uperficiem &longs;upremam AB, alium effectum præ&longs;tat, nimirum illum <lb/>quem dixi; atto<gap/>it enim &longs;uperficiem AB &longs;upra libellam, eamque totnat <lb/>in convexam; ideò verò cava e&longs;t &longs;uperficies HK; quia vis pre&longs;&longs;ionis in <lb/>O major e&longs;t, quàm in H vel in K, quia &longs;ub majore angulo incumbit. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Hoc jam &longs;uprà dixeras, &longs;ed ne quid di<gap/>imulem, non mihi <lb/>&longs;tatim oc<gap/> demon&longs;tratio illa geomertica, quam appella&longs;ti quidem, <lb/>non tamen expo&longs;ui&longs;ti. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Ad prima elementa me reducis, Chry&longs;ocome, &longs;int latera va­<lb/><figure id="fig35"></figure><lb/>&longs;is AE, BF; os verò AB; &longs;uper<gap/>ies aquæ EF, cen­<lb/><gap/>m C, &longs;int anguli ACB, AEB, dico ACB e&longs;&longs;e <lb/>majorem, ducatur enim circulus per 3. puncta ABC, <lb/>fecæ<gap/> BE in D; ducatur AD, anguli ADB, ACB &longs;unt <lb/>æquales quia &longs;u&longs;tinent eundem arcum AB, &longs;ed ADB <lb/>e&longs;t major prædicto AEB, cùm &longs;it exterior; igitur an­<lb/>gulus AEB e&longs;t minor ACB; idem de quolibet alio <lb/>demon&longs;tratur: &longs;ed jam ad alia experimenta venia­<lb/>mus, Sit ampulla A, de quà &longs;upra; aquæ fuperfi-<pb pagenum="165"/><figure id="fig36"></figure><lb/>cies KI in canaliculo verò &longs;it D; volam manus admove <lb/>ori BC cum modica pre&longs;&longs;ione; &longs;tatim aqua per canalicu­<lb/>lum altiùs a&longs;&longs;urgit versùs F; vbi verò repenti<gap/> motu ma­<lb/>nus ab ore AB, amove<gap/>, de&longs;cendit aqua præ<gap/>ps in G. <lb/>&longs;ed &longs;tatim denuo a&longs;&longs;urgit versùs F. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Ex præmiffis huius experimenti facilè ratio­<lb/>nem afferam, nempe aër vola pre&longs;&longs;us aquæ &longs;uperficiem KI premit, ex cujus <lb/>proffione, per canaliculum nece&longs;&longs;ariò altiùs ar&longs;&longs;urgit<gap/>aniota a<gap/>rem repente <lb/>vola, aquæ &longs;uperficiem AB &longs;ecum tantulum adducit, attollítque; vnde <lb/>aquam per canaliculum &longs;ub&longs;idere nece&longs;&longs;e e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Inde omnium huiu&longs;modi experimeatorum communem ratio­<lb/>nem reddo: &longs;i enim aër magis compre&longs;&longs;us aquam per canaliculum attol­<lb/>lit; certè minùs altè attollit; nullo modo pre&longs;&longs;us non attollit; adductus <lb/>verò, &longs;ecum versùs G aquam m canaliculo contentam adducit. </s> <s>Et verò, <lb/>vt tandem ad rem propiùs accedam, cùm hic motus, quo aqua a&longs;&longs;urgit, <lb/>non &longs;it ab intrin&longs;eco, vt con&longs;tat ex dictis, nec enim aqua &longs;pontè &longs;ua a&longs;­<lb/>cendit, ab alia cau&longs;a extrin&longs;e ca illum e&longs;&longs;e, nece&longs;&longs;e e&longs;t; eaque profectò <lb/>applicata quænam porrò illa e&longs;t, ni&longs;i aër? </s> <s>quidquid tandem aër &longs;it, &longs;ive <lb/>p<gap/>us, &longs;ive imputus, id e&longs;t aliis corporibus admixtus; aër porrò applica­<lb/>tus motum illum imprimere nequit, ni&longs;i vel gravitando, vel illo ni&longs;u, qui <lb/>ex compre&longs;&longs;ione corporum &longs;equitur; primum dici non pote&longs;t, cùm enim <lb/>gravitet per cylindros parallelos, æquè gravitat in minorem aquæ &longs;uper­<lb/>ficiem, ac in majorem; ac proinde vtraque, &longs;i gravitationis dumtaxat ra­<lb/>tio habeatur, in eadem libella &longs;ita e&longs;t, nec vna a&longs;&longs;urgit &longs;upra aliam, re­<lb/>&longs;tat igitur, vt dicamus, aëra tantulum compre&longs;&longs;um cum ni&longs;um exerere in <lb/>&longs;uperficiem BC, non quidem per cylindros parallelos; &longs;ed per conos, <lb/>quorum &longs;inguli vertices &longs;ingulis &longs;uperficiei punctis incumbunt; ac proin­<lb/>de minorem ni&longs;um exeri adversùs &longs;uperficiem aquæ CD canaliculo con­<lb/>tentæ, quia &longs;ub minoribus angulis exeritur, vt &longs;upra luculenter o&longs;ten&longs;um <lb/>e&longs;t; prævalet igitur pre&longs;&longs;io incidens in &longs;uperficiem BC; ac proinde aliam <lb/>CD attollit versùs F. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> Iam ob&longs;ervo inde germanam duci rationem, illius addu­<lb/>ctionis atramenti; vbi enim atramenti guttam calami ro&longs;trum extre­<lb/>mum attingit, (quod pueri facere &longs;olebamus) attramentum illico <lb/>a&longs;&longs;urgit, & cavum calami ro&longs;trum implet; in alio liquore idem &longs;ac­<lb/>ce&longs;&longs;um iri, certi&longs;&longs;imum e&longs;t; calamum tamen priùs humectatum fui&longs;&longs;e <lb/>oportet. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Luculentam rationem jam attulit Antimus; &longs;ic enim com­<lb/>planatur &longs;uperficies calami, alioquin multis rugis & &longs;alebris &longs;triata & a&longs;­<lb/>perata, huic autem experimento communis illa ratio Antimi facilè ap­<lb/>plicatur, ab inæqualis pre&longs;&longs;ionis ni&longs;u petita; nam reverà in totam guttæ <lb/>&longs;uperficiem, excepto &longs;cilicet puncto illo contactus, in quo extre­<lb/>mum ro&longs;trum guttæ immergitur, major e&longs;t pre&longs;&longs;ionis ni&longs;us, quàm in ca­<lb/>vam ro&longs;tri &longs;uperficiem; quid mirum ergo &longs;i prævaleat illa, & humor per <lb/>cavum ro&longs;trum a&longs;cendat? </s> <s>aliquid &longs;imile in omnibus guttis ob&longs;ervo, ad-<pb pagenum="166"/>mota &longs;cilicet tenui lamella, vel bacillo; nempe eò &longs;tatim liquor ex­<lb/>currit. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Guttarum res nonnihil fortè &longs;citu dignum nobis exhiber; &longs;ed <lb/>ne hoc excidar, antequam illam aggrediar; &longs;i ro&longs;trum calami longiùs &longs;it, <lb/>& valde te<gap/>e, & in mucronem extenuatus, quamvis extremum ro&longs;trum <lb/>guttæ immergas, nihil aut parum attramenti a&longs;&longs;urgit: ratio e&longs;t<gap/> quia par­<lb/>vum, aut nullum ferè obicem ponit ad pre&longs;&longs;ionis inæqualiratem inducen. <lb/></s> <s>dam; nempe tenuis illa ro&longs;tri linea pauci&longs;&longs;imos pre&longs;&longs;ionis radios intercipit; <lb/>nulla igitur vel modica inæqualitatis pre&longs;&longs;ionis proportio; ex hoc etiam <lb/>experimento efficax, meo judicio, argumentum ducitur, quò per&longs;picuè <lb/>concluditur, huju&longs;modi aquarum elevationem ab inæquali ambientis aëris <lb/>pre&longs;&longs;ione procedere. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Quid &longs;i cylindrus &longs;olidus immergatur, an fortè ali­<lb/>quid aquæ attollitur; cùm hic obex inæqualem pre&longs;&longs;ionem in­<lb/>ducat? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Aliquid omnino, quod tamen longè melius ad oculum <lb/>patet, &longs;i prædictus tantulum &longs;triatus &longs;it, pro quo eadem, vt vides, ratio <lb/>militat. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Quid verò fieret, &longs;i canaliculus in alium paulo am­<lb/>pliorem immergatur? </s> <s>vel duo &longs;imul quorum minor majori inclu­<lb/>&longs;us &longs;it? </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Pro diver&longs;a canalium & immer&longs;ionum ration<gap/>, diver&longs;a &longs;ucce­<lb/>dunt à me ob&longs;ervata experimenta & ad idem principium &longs;atis feliciter re­<lb/>ducta. </s></p><figure></figure><p type="main"> <s>Primò enim &longs;it canalis major HB aqua plenus; ad. <lb/></s> <s>moveatur, vt priùs dictum e&longs;t, minor canaliculus MN, <lb/>humori illico a&longs;&longs;urgit in K, perinde atque &longs;i in quam­<lb/>libet aliam aquæ, etiam majore va&longs;e contentæ &longs;uperfi­<lb/>ciem immergatur; propter eandem rationem, de qua <lb/>huc v&longs;que. </s></p><p type="main"> <s>Secundò. </s> <s>Si aquæ &longs;uperficies &longs;it tantùm in C & de­<lb/>mittatur canaliculus MN in C, a&longs;&longs;urget aqua v.g. </s> <s>in G <lb/>ita <expan abbr="tam&etilde;">tamen</expan> vt CG, &longs;it minor NK; ratio e&longs;t, quia minor e&longs;t <lb/>inæqualitatis proportio in pre&longs;&longs;ionibus, <expan abbr="quã">quam</expan> antè, vt pa­<lb/>tet; minor igitur illius effectus, minus igitur attollitur <lb/>aqua: &longs;uppono enim <expan abbr="major&etilde;vim">majorenvim</expan> exeri per <expan abbr="vacuitat&etilde;in-terceptam">vacuitatenin­<lb/>terceptam</expan> inter <expan abbr="cavã">cavam</expan> majoris & convexam minoris ca­<lb/>nalis &longs;uperficiem, quàm per minorem canaliculum. </s></p><p type="main"> <s>Tertiò. </s> <s>Si &longs;ecus accidat, id e&longs;t, &longs;i cavitas canaliculi <lb/>major e&longs;t prædicta vacuitate intercepta, humor per <lb/>vacuitatem illam a&longs;cendet v.g. </s> <s>in FE, &longs;ed nullo modo <lb/>per canaliculum NC a&longs;&longs;urget; quia major e&longs;t aëris pre&longs;&longs;io per canalicu­<lb/>lum, quàm per vacuitatem interceptam. </s></p><p type="main"> <s>Quartò. </s> <s>Si æqualis &longs;it vtriu&longs;que &longs;patij, id e&longs;t, cavitatis & vacuitatis ca­<lb/>pacitas, & canaliculus demittatur in C, neque hinc, neque illinc <pb pagenum="167"/>humor a&longs;&longs;urgit; quia æqualis vtrimque pre&longs;&longs;io: neutra igitur præ­<lb/>valet. </s></p><p type="main"> <s>Quintò. </s> <s>Iam verò ad aliud quæ&longs;itum venio, & &longs;uppono vtrum­<lb/>que canaliculum pervium, ita vt minor intra majorem, qua&longs;i intra vagi­<lb/>nam conditus &longs;it, & tunc etiam pro diver&longs;a di&longs;po&longs;itione varia &longs;uccedunt; <lb/><figure id="fig37"></figure><lb/>Primò, &longs;it &longs;uperficies Aquæ AB, &longs;it carnalis major FE, <lb/>& minor inclu&longs;us HD, vterque eju&longs;dem altitudinis, <lb/>& &longs;imili modo immer&longs;us; &longs;i vacuitas majoris (&longs;ic de­<lb/>inceps appellabo inter ceptum illud &longs;patium) æqualis <lb/>&longs;it minori canaliculo, &longs;cilicet eiu&longs;dem cavitati, per <lb/>vtramque æquè altè humor a&longs;&longs;urgit; v.g. </s> <s>in LK, quia <lb/>vis æqualis pre&longs;&longs;ionis exeritur; quod vt fiat ba&longs;is ma­<lb/>joris FG debet e&longs;&longs;e dupla minoris IH; dico ba&longs;im, <lb/>non diametrum ba&longs;is, ne fortè &longs;chema vos deci­<lb/>piat. </s></p><p type="main"> <s>Secundo. </s> <s>Si ba&longs;is majoris &longs;it major dupla, altiùs a&longs;­<lb/>&longs;urgit aqua per minorem, quàm per majorem, v.g. <lb/></s> <s>per minorem in LK, per majorem in MN; quia ma­<lb/>jor e&longs;t proportio inæqualitatis pre&longs;&longs;ionum ad mino­<lb/>rem; quàm ad vacuitatem interceptam; igitur & ef­<lb/>fectum. </s></p><p type="main"> <s>Tertio. </s> <s>Si verò ba&longs;is majoris &longs;it minor dupla, &longs;ecus <lb/>accidet; & a&longs;&longs;urget humor altiùs per vacuitatem, quàm per canaliculum, ra­<lb/>tio patet ex dictis. </s></p><p type="main"> <s>Quartò. </s> <s>Simajor altiùs immergatur, quàm minor, cæteris paribus, humor <lb/>altiùs a&longs;cendet per minorem, &longs;uppo&longs;ita tamen ba&longs;i majoris &longs;altem dupla <lb/>ba&longs;is minoris. </s></p><p type="main"> <s>Quinto. </s> <s>Si verò canaliculus minor profundiùs demittatur, certè ex <lb/>hoc capite altiùs deberet a&longs;cendere per majorem, quàm per minorem; <lb/>quia tamen major e&longs;t portio renitentis aëris, ne aqua per majorem a&longs;­<lb/>cendat, quæ priùs non erat, compen&longs;atio fieri videtur, & pro diver&longs;a <lb/>ba&longs;ium ratione, modò altiùs, modò æquè altè, modò minùs altè a&longs;­<lb/>&longs;urgit. </s></p><p type="main"> <s>Sexto. </s> <s>Si &longs;olus major immergatur, ac proinde tantulum a&longs;cendat aqua, &longs;i <lb/>deinde minor canaliculus in cum, vt priùs, immittatur, altiùs per vtrumque <lb/>aqua a&longs;&longs;urget, tum quia minus &longs;patij occupandum e&longs;t, tum quia vis reni­<lb/>tentis aëris minor e&longs;t. </s></p><p type="main"> <s>Septimo. </s> <s>Si minor &longs;olus profundiùs immergatur, v.g. </s> <s>v&longs;que in O, minùs <lb/>altè a&longs;cendet, quàm ante; per minorem quidem, quia brevius, &longs;upra &longs;uperfi­<lb/>ciem aquæ &longs;egmentum extat; per majorem verò, quia cum angulus pre&longs;&longs;io­<lb/>nis renitentis cre&longs;cat, minùs altè humor a&longs;&longs;urgit. </s></p><p type="main"> <s>Octavo. </s> <s>Si verò major &longs;olus profundiùs deprimatur, retento minore in <lb/>codem &longs;itu, paulò altiùs a&longs;cendit per minorem; quia vis pre&longs;&longs;ionis circa illius <lb/>infimam ba&longs;im cre&longs;cit; hæc autem ratio facit, ne per majorem æquè altèa&longs;­<lb/>&longs;urgat. </s></p><pb pagenum="168"/><p type="main"> <s>Nonò. </s> <s>Pro diver&longs;<gap/> ba&longs;ium ratione, altiùs aut minùs altè a&longs;cendit per <lb/>cavit<gap/>em minoris, aut per vacuitatem interceptam inter vtrumque de­<lb/><gap/>oque vno vel altero, diver&longs;a erit altitudinum ratio, &longs;ecundum regu­<lb/>las &longs;upra traditas; nunquam tamen quantu<gap/>vis minor deprimatur aqua <lb/>per illum a&longs;&longs;urgens ex illo effluet. </s></p><p type="main"> <s>Decimò, Vbi minoris convexa &longs;uperficies cum majoris cava conjungi­<lb/>tur, aqua intercepta illico a&longs;&longs;urgit, & qua&longs;i quodam glutinevna cum alia <lb/>conjungitur: idem ferè fiet, &longs;i duæ &longs;uperficies convexæ conjungantur. <lb/></s> <s>Ex his, quæ huc v&longs;que dixi, de duobus canaliculis, quorum vnus alteri <lb/>immittitur, reliqua facilè conjicies. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Nunquam per&longs;uadere mihi potui&longs;&longs;em, in re hac minima <lb/>tantam ob&longs;ervationum &longs;ylvam recondi; ex qua ego, &longs;olo ratiocinio mul­<lb/>tas alias deducere po&longs;&longs;em. </s> <s>Sed quæro ex te, quot fint capita, ex quibus <lb/>humor altiùs per canaliculum immer&longs;um a&longs;cendat. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Sex aut &longs;eptem, ni fallor, recen&longs;eo. </s> <s>Primò, quo longior e&longs;t ca­<lb/>naliculus, altiùs humor a&longs;cendit, non tamen vbi valdè producitur in pro­<lb/>portione &longs;en&longs;ibili; Secundò, quo minor e&longs;t canaliculi ba&longs;is; vt patet. </s> <s>Ter­<lb/>tiò, quo minùs altè immergitur canaliculus, altiùs a&longs;&longs;urgit aqua. </s> <s>Quartò, <lb/>major aëris ambientis libertas, & major angulus pre&longs;&longs;ionis, vi cujus hu­<lb/>mor a&longs;&longs;urgit. </s> <s>Quintò major vel minor aëris ambientis compre&longs;&longs;io. </s> <s>Sextò <lb/>Minor gravitas liquoris attollendi. </s> <s>Septimò, major eju&longs;dem flu<gap/>itas, vel <lb/>humiditas, &longs;ic &longs;piritus vini altiùs a&longs;cendit quàm aqua, & metallum li­<lb/>quatum nihil aut parum admodùm. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Quid porrò de Mercurio? </s> <s>nonnulla enim de illo mihi veniunt <lb/>in mentem, quæ vix a&longs;&longs;erere au&longs;im; quia nunquam illa experimento <lb/>probavi. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Exprome tamen, vt &longs;altem videamus vtrum rectè ratioci­<lb/>neris; cùm fieri non po&longs;&longs;it, quin Antimus illa ob&longs;ervarit. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Primò Mercurius, aut nihil aut parum a&longs;&longs;urgere debet per <lb/>canaliculum propter cra&longs;&longs;itudinem & &longs;ummam vim ponderis. </s> <s>Secundò, <lb/>Suprema &longs;uperficies intra canalem depre&longs;&longs;a, non e&longs;t cava, &longs;altem &longs;en&longs;ibi­<lb/>liter, propter eandem rationem. </s> <s>Tertiò, Mercurij gu<gap/> per calami ro&longs;trum <lb/>non a&longs;&longs;urgit, vt reliqui humores. </s> <s>Quartò non a&longs;&longs;urgit, etiam &longs;i cylindrus <lb/>&longs;olidus immergatur, licèt tantulùm a&longs;cendat aqua, &longs;i in ejus &longs;uper&longs;iciem <lb/>immergatur. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Parum abes à &longs;copo, Augu&longs;tine, eaque tantùm non prævidi&longs;ti, <lb/>quæ nonnulli in Mercurio cum &longs;ummo &longs;tupore mirantur. </s> <s>Primò enim &longs;i <lb/>canaliculus Mercurio &longs;ecundum alteram extremitatem immergatur, non <lb/>modò non a&longs;&longs;urgit per canaliculum, &longs;upra libellam exterioris &longs;uperficiei, <lb/>&longs;ed tantulùm &longs;ub&longs;idit, quod hi&longs;ce oculis centies ob&longs;ervavi. </s> <s>Secundò, Non <lb/>modo &longs;uprema illius &longs;uperficies cava non e&longs;t, &longs;ed omnino convexa; & <lb/>vbi ad os tubi, in quo continetur pertingit, longè convexior, quàm &longs;uper­<lb/>ficies aquæ. </s> <s>Tertiò, Non modò non a&longs;&longs;urgit gutta Mercurij per ro&longs;trum <lb/>calami, &longs;ed ne quidem ro&longs;trum in eam &longs;ubit, &longs;ed vel cedit, non &longs;ine fo&longs;&longs;ula <lb/>in puncto contactus, vel repentino motu &longs;e&longs;e &longs;ubducit. </s> <s>Quartò, non <pb pagenum="169"/>modo non a&longs;&longs;urgit Cylindro &longs;olido immer&longs;o; &longs;ed qua&longs;i fo&longs;&longs;ula circa illius <lb/>&longs;uperficiem acta &longs;ub&longs;idit, & circa fo&longs;&longs;ulam Mercurij &longs;uperficies attollitur, <lb/>idque ad &longs;en&longs;um & evidentiam. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Non video, ne quid di&longs;&longs;imulem, quomodo hæc ex præmi&longs;&longs;is <lb/>con&longs;equi po&longs;&longs;int; ac proinde non mirum &longs;i ex iis à me non deducta. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Con&longs;equuntur tamen; nempe cùm Mercurius vitro non adhæ­<lb/>reat, vt per&longs;picuum e&longs;t, intantum enim corpus humidum aliorum corpo­<lb/>rum &longs;uperficiei adhæret, in quantum in cavitates, &longs;trias & pororum o&longs;tiola <lb/>&longs;ubit; certè Mercurius præ cra&longs;&longs;itudine in eas angu&longs;tias &longs;e&longs;e minimè inge­<lb/>rit; vnde aëri locus vitrum inter & Mercurium relinquitur; nec enim va­<lb/><figure id="fig38"></figure><lb/>cuum datur. </s> <s>Sit &longs;uperficies Mercurij AB, in quam <lb/>immergatur Cylindrus vitreus EC, &longs;ub&longs;idet M rcurius <lb/>in fo&longs;&longs;ulam GH, quæ optimè concipitur, &longs;i tota hæc <lb/>Figura circa Cylindri EC axem volvi &longs;upponatur; <lb/>cùm enim non adhæreat Mercurius lateri ED, aër <lb/>compre&longs;&longs;us qua&longs;i cuneatim penetrat v&longs;que ad G, & fa­<lb/>cilè à latere ED Mercurium removet; hinc tantulum <lb/>attolli Mercurium nece&longs;&longs;e e&longs;t; hinc circa &longs;uperficiem Cylindri EC fo&longs;&longs;ula, <lb/>& circa fo&longs;&longs;ulam modicus tumor; vt enim cuneus dum &longs;ubit vnum ab alio <lb/>removet, ita premens aër ad in&longs;tar cunei interceptus inter &longs;uperficiem Cy­<lb/>lindri & Mercurium, hunc ab illa tantulum removet; atque ita, v<gap/> vides, <lb/>quartum experimentum ad commune no&longs;trum principium reducitur. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Iam verò &longs;ecundum, eodem modo, te duce explicabo, nempe <lb/>aër etiam &longs;e&longs;e in&longs;inuat ad in&longs;tar cunei inter &longs;uperficiem cavam canalis & <lb/>Mercurium contentum, vn de <expan abbr="illũ">illum</expan> à dicta &longs;uperficie remover, idque in <expan abbr="orb&etilde;">orbem</expan>, <lb/>ac proinde circa <expan abbr="mediũ">medium</expan>, vel centrum tantulum attollitur, atque intume&longs;ci<gap/>; <lb/>&longs;ed quid de primo? </s> <s>vix enim video, quonam pacto ad idem principium re­<lb/>duci queat; idem de tertio dictum &longs;it; &longs;uggere quæ&longs;o mihi, quid &longs;entias. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Per admotum canaliculum Mercurius non a&longs;&longs;urgit; tum quia <lb/>cùm longè cra&longs;&longs;ior &longs;it reliquo humore in angu&longs;tias difficiliùs intruditur; <lb/>vnde per telam, &longs;eu pannum non colatur, vt aqua; quia per exigua coli fo­<lb/>ramina difficilè trajicitur; tum quia prædicta fo&longs;&longs;ula exterior circa canali­<lb/>culi immer&longs;i &longs;uperficiem convexam excavata vim pre&longs;&longs;ionis di&longs;trahit à &longs;u­<lb/>perficie Mercurij, quæ ba&longs;i canaliculi adhæret, eam que in contrariam par­<lb/>rem traducit; vnde non mirum, &longs;i vi pre&longs;&longs;ionis Mercurius per canaliculum <lb/>non a&longs;&longs;urgat. </s> <s>Sed potiùs ex vtroque capite Mercurius intra canaliculum <lb/>&longs;ub&longs;idat infra &longs;uperficiem exteriorem, cùm & vitrum &longs;uo appul&longs;u, & vis <lb/>pre&longs;&longs;ionis, quæ per canaliculum exeritur, &longs;upra aliam prævalens, ob ratio­<lb/>nem expo&longs;itam, Mercurium deprimant. </s> <s>Inde quoque ratio ducitur tertij <lb/>experimenti; nempe ro&longs;trum calami propter cra&longs;&longs;itudinem Mercurij in <lb/>eum non &longs;ubit, &longs;ed potiùs Mercurius ro&longs;tro cedens in fo&longs;&longs;am &longs;ub&longs;idit; cùm <lb/>difficiliùs quàm aqua dividatur; vnde mutatur pre&longs;&longs;ionis ratio, ac proinde <lb/>per ro&longs;trum admotum non a&longs;&longs;urgit, vt aqua. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Quid &longs;i in va&longs;e compo&longs;ito iuxta formam præ&longs;criptam & <lb/>delineatam in Figura &longs;equente. </s></p><pb pagenum="170"/><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Hoc ip&longs;um &longs;ubnectere meditabar; &longs;ed præveni&longs;ti; infundo igi­<lb/><figure id="fig39"></figure><lb/>tur Mercurium in AB, donec totum vas plenum <lb/>&longs;it, &longs;tatue libellam AG; ob&longs;erva quantumlibet, <lb/>vides Mercurium a&longs;&longs;urgere in FG; equidem cir­<lb/>ca centrum V altiùs attollitur, quàm &longs;i e&longs;&longs;et aqua, <lb/>propter rationem à me &longs;upra expo&longs;itam; tantu­<lb/>lum enim &longs;ubït cuneus aëris inter latera va&longs;is & <lb/>Mercurium, quod inaqua non fit; vnde altiùs <lb/>centrum V. attollitur; minus verò centrum &longs;u­<lb/>perficiei FG, quia minor e&longs;t &longs;uperficies: vides ta­<lb/>men, vix oculo di&longs;cerni po&longs;&longs;e, vtra &longs;uperficies al­<lb/>tiùs a&longs;&longs;urgat; equidem &longs;i eanaliculus IE angu­<lb/>&longs;tior e&longs;&longs;et, difficilius per illum cra&longs;&longs;ior Mercurius a&longs;&longs;urgeret; hinc minùs <lb/>altè, in plumbo, & melle idem probabis; &longs;i verò, vt hic, paulò laxiorad ean­<lb/>dem &longs;en&longs;ibiliter a&longs;cendit altitudinem, & licèt tantulum a&longs;&longs;urgat, per cana­<lb/>liculum id compen&longs;atur ab altiore tumore &longs;uperficiei AB. </s> <s>Illud porrò tan­<lb/>tulum, quo a&longs;&longs;urgit ab eadem ratione inæqualis pre&longs;&longs;ionis procedit; cùm <lb/>enim aquæ gravitas &longs;it ad <expan abbr="gravitat&etilde;">gravitatem</expan> Mercurij ferè vt 1.ad 15.fit &longs;egmentum <lb/>aquæ &longs;upra libellam AG a&longs;&longs;urgens, FL; dividatur linea FM in 15.partes <lb/>æquales, vna ex illis erit altitudo &longs;egmenti Mercurij a&longs;&longs;urgen tis in canali­<lb/>culo ID; &longs;i tamen paulò laxior &longs;it, vt dixi; &longs;i enim angu&longs;tior, præ cra&longs;&longs;itudi­<lb/>ne minùs a&longs;&longs;urgit: vides quàm facilè cuncta hæc ad commune illud princi­<lb/>pium reducantur, immò ad aliud reduci nequeant; ac proinde ex præmi&longs;&longs;is <lb/>omnibus experimentis idem principium etiá &longs;tatuitur & confirmatur. </s> <s>Sci­<lb/>licet humorem attolli in canaliculo propter inæqualem aëris pre&longs;&longs;ionem. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/> Hæc mihi &longs;upra modum arrident; quid porrò fiat &longs;i canàli­<lb/>culus intra alium in&longs;eratur, quando &longs;cilicet in Mercurium immergitur, ex <lb/>te re&longs;cire de&longs;idero, cùm mihi dubium non &longs;it, quin cuncta hæc probaveris. </s></p><figure></figure><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Rectè conjicis, à me probata e&longs;&longs;e: Sit ergo <lb/>Cylindrus vitreus AD, cavus, &longs;ed clau&longs;us in CD, <lb/>apertus in AB; in quem tantulum Mercurij in&longs;u&longs;us <lb/>occupet &longs;egmentum CO, & in&longs;eratur canaliculus <lb/>vt rimque pervius IE; non a&longs;&longs;urgit Mercurius &longs;upra <lb/>libellam NO, &longs;ed tantulum deprimitur in canaliculo; <lb/>a&longs;&longs;urgit verò in vacuitate intercepta, propter rationem <lb/>jam expo&longs;itam. </s> <s>Si verò in&longs;undatur aqua in prædictam <lb/>vacuiratem interceptam, tantulum Mercurius in præ­<lb/>dicta vacuitate contentus deprimitur infra libellam <lb/>NO, a&longs;&longs;urgit verò &longs;upra in canallculo, puta in G; quod <lb/>certè fieri debet, vt &longs;it perfectum æquilibrium; cùm <lb/>&longs;cilicet non modò pondus Mercutij NE attollat Mer­<lb/>curium, verùm etiam poudus &longs;imul aquæ in&longs;u&longs;æ; igitur <lb/>&longs;i pondus &longs;olius Mercurij &longs;u&longs;tinet &longs;egmentum Mercu­<lb/>tij EE, majus pondus, vtpote compo&longs;itum ex Mercu­<lb/>rio & aqua infu&longs;a, majus Mercurij &longs;egmentum &longs;u&longs;tinet, puta EG; &longs;i autem <pb pagenum="171"/>a&longs;cendat per canaliculum &longs;upra NO, infra NO de&longs;cendat, nece&longs;&longs;e e&longs;t, in­<lb/>tra vacuitatem. </s></p><p type="main"> <s>Præteteà &longs;i his &longs;tantibus, attollatur canaliculus IE, v&longs;que ad imam aquæ <lb/>&longs;uperficiem, puta v&longs;que ad NO, tunc de&longs;cendente Mercurio ex &longs;egmento <lb/>FG, &longs;ubit aqua canaliculum impletque, tum cananiculum, tum vacuitatem, <lb/>&longs;i&longs;titque vtraque aquæ &longs;uperficies, tum intra, tum extra canaliculum, in ea­<lb/>dem libella, puta HM nec a&longs;&longs;urgit aqua per canaliculum altiùs contra mo­<lb/>rem &longs;olitum; ratio ex eo petitur, quòd aëris pre&longs;&longs;io aquam per canaliculum <lb/>attollere nequeat, ni&longs;i &longs;imul attollat Mercurium; &longs;upponitur enim canali­<lb/>culus tantulum immer&longs;us in Mercurium; hunc autem, vt dixi, attollere non <lb/>pote&longs;t; hinc &longs;i canaliculus ita attollatur, vt ima illius extremitas &longs;it &longs;upra <lb/>&longs;uperficiem Mercurij, tunc aqua altiùs a&longs;&longs;urgit &longs;upra libellam HM, puta <lb/>in I, quia tunc inæqualis aëris pre&longs;&longs;io &longs;uum effectum habet; neque ad <lb/>hunc finem Mercurius, vt ante, attollendus e&longs;t, &longs;ed aqua &longs;ola; &longs;i demum <lb/>ex illo &longs;itu, quo ima ba&longs;is canaliculi &longs;upremæ Mercurij adhæret, & vtra­<lb/>que &longs;uperficies aquæ, tum in vacuitate, tum in canaliculo æquè a&longs;&longs;urgit in <lb/>HM, deprimas canaliculum v&longs;que ad E, aquæ &longs;uperficies in vacuitate <lb/>a&longs;cendit &longs;upra HM, infra quam de&longs;cendit in canaliculo; quia &longs;egmentum <lb/>canaliculi immer&longs;um Mercurio ex eo loco imi va&longs;is, quem occupat, extru­<lb/>dit Mercurium in vacuitatem interceptam faciliùs quàm in canaliculum, <lb/>propter angu&longs;tias; quid mirum ergo, &longs;i &longs;uperficies aquæ in vacuita­<lb/>te a&longs;&longs;urgat &longs;upra HM, hanc enim attollit extru&longs;us à &longs;egmento im­<lb/>mer&longs;o Mercurius, in canaliculo verò &longs;ub&longs;idente Mercurio, incu­<lb/>bans aqua etiam &longs;ub&longs;idit, ex his, ni fallor, reliqua facilè intelli­<lb/>getis. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Cuncta hæc illam aëris pre&longs;&longs;ionem omnino evincunt, ad <lb/>quam etiam multa alia, quæ vi cuidam tractrici vulgò tribuuntur, æquè <lb/>facilè reducere po&longs;&longs;um. </s> <s>Sic &longs;pongio&longs;a corpora humotem dicuntur exuge­<lb/>re, vt panis, præ&longs;ertim bis coctus, aut recens, &longs;pongia, pannus, terra <lb/>&longs;icca, pumex, aliaque huju&longs;modi; nam pori &longs;eu meatus, quantumvis <lb/>obliqui totidem canaliculos faciunt, per quos aqua facilè a&longs;&longs;urgit: Vn­<lb/>de vis illa tractrix, vt omnino fictitia, rejicitur; item illa Fromondi fa­<lb/>bula, qui ni&longs;i me fallit memoria lib. </s> <s>5. Meteor. </s> <s>cap.2. art.2. Vbi Conimbri­<lb/>cen&longs;ium aliorumque &longs;ententias rejeci&longs;&longs;et, recurrit ad qua&longs;dam partes aquæ <lb/>tenuiores, quæ &longs;ur&longs;um a&longs;cendunt; &longs;ed illa aqua, vbi deinde &longs;pongia expti­<lb/>mitur, æquè cra&longs;&longs;a e&longs;t atque alia, & aëre longè gravior; cur ergo a&longs;cen­<lb/>dit? </s> <s>Idem Fromondus aquam frigidi&longs;&longs;imam exugi negat; &longs;ed merum men­<lb/>daeium e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Sine quæ&longs;o i&longs;tum hominem; &longs;ufficiat à te optimè deduci, il­<lb/>los effectus, qui vulgò &longs;uctioni, &longs;eu vi tractrici tribuuntur, ad idem prin­<lb/>cipium no&longs;trum reduci; vt autem ad illud redeam, novum experimentum <lb/>adduco, per quod, meo judicio, mirificè confirmatur: Sit vas quodlibet <lb/>aqua plenum, admoveatur canaliculus, in &longs;itu perpendiculari, illico aqua <lb/>a&longs;&longs;urgit; appendatur in hoc eodem &longs;itu canaliculus, fideli bilance, aqua, quæ <lb/>&longs;ubit, nullum momentum addit ponderi canaliculi vitrei; quod vt accura-<pb pagenum="172"/>tè fiat, &longs;u&longs;pendatur canaliculus tenui filo pendulo ex brachio extremo bi­<lb/>lancis; ita vt deor&longs;um ire non po&longs;&longs;it, &longs;ed tantùm parum immergatur in <lb/>&longs;uperficiem aquæ &longs;ubjecto va&longs;e contentæ; occludaturque &longs;upremum os ca­<lb/>naliculi cera, aut &longs;uilla ve&longs;ica, antequam immergatur, ac deinde immer&longs;um <lb/>illius pondus accuratè appendatur, admoto &longs;cilicet iu&longs;to pondere oppo&longs;itæ <lb/>lanci; po&longs;teà verò aperiatur acu &longs;upremum os prius ob&longs;tructum; a&longs;&longs;urgit <lb/>illico aqua per canaliculum, licèt nihil ponderis pror&longs;us accedat: Illa igi­<lb/>tur aquæ portio, quæ per canaliculum a&longs;cendit, dicto filo pendulo non <lb/>&longs;u&longs;tinetur, &longs;ed ab alio principio, eoque applicato; &longs;cilicet ab aëre com­<lb/>pre&longs;&longs;o; hoc experimentum, &longs;i accuratè fiat, rem i&longs;tam evincit. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Sed vnde huju&longs;modi aëris compre&longs;&longs;ionem e&longs;&longs;e putares? </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Huic tuo quæ&longs;ito faciam &longs;atis; &longs;i dixero ex duplici capite pro­<lb/>venire, Primò, ex admixtione vaporis & halitus; cùm enim no&longs;ter aër purus <lb/>non &longs;it, multa huju&longs;modi habet admixta, vnde illius compre&longs;&longs;io &longs;oquitur. <lb/></s> <s>Secundò, ex pondere &longs;upremi aëris incubantis: fieri enim non pote&longs;t, quin <lb/>aër &longs;ubjectus inde compre&longs;&longs;us evadat. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/> E&longs;t quod multa opponam. </s> <s>Primò, totus aër gravitat gra­<lb/>vitatione communi; ne igitur pars inferior in &longs;e ip&longs;um gravitare dica­<lb/>tur, dicendum videtur. </s> <s>Superiorem aëris tractum in inferiorem non <lb/>gravitare. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Dare non po&longs;&longs;um totum aëra gravitatione communi gravi­<lb/>tare in quodlibet corporis &longs;ubjecti punctum; nec enim vllum centrum <lb/>gravitatis commune habet, quod iis dumtaxat gravibus competit (de <lb/>phy&longs;ico loquor) quorum tota vis gravitationis per vnicam lineam à præ­<lb/>dicto centro ductam exeritur; corpus liquidum, vt aqua, & &longs;pirabile, vt <lb/>aër, ni&longs;i contineantur in va&longs;e, per Cylindros deor&longs;um, parallelos, gra­<lb/>vitant; &longs;cilicet ad &longs;en&longs;um; cùm alioquin omnes Cylindri gravitationia <lb/>versùs idem centrum eant; vnde paralleli e&longs;&longs;e non po&longs;&longs;unt; equidem &longs;e­<lb/>cundùm eundem Cylindrum gravitatio omnium partium, quæ illum <lb/>componunt, ita communis e&longs;t, vt omnes &longs;imul in corpus &longs;ubjectum gra­<lb/>vitent, & &longs;ingulæ &longs;upra &longs;ingulas &longs;ubjectas immò &longs;upra eandem &longs;ubjectam <lb/>omnes &longs;uperiores, in eodem tamen Cylindro; cogita lapidem lapidi &longs;uppo­<lb/>&longs;itum, &longs;ubjectus enim omnes &longs;uperiores ferre cen&longs;etur. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Tota igitur illa gravitatio reducitur in lineas; &longs;inguli enim <lb/>Cylindri &longs;unt totidem lineæ; linea autem, aurnihil, aut parum ponde­<lb/>nis habet; nulla igitur inde compre&longs;&longs;io, aut certè modica; quid enim <lb/>tam parvi ponderis vis efficeret: ponamus enim Cylindrum aqueum da­<lb/>tæ ba&longs;is & altitudinis pendere vnam libram; &longs;upponamus item aquæ gra­<lb/>vitatem e&longs;&longs;e ad gravitatem aëris vt 1000. ad 1. haud dubiè Cylindrus aë­<lb/>ris æqualis pendit tantùm vnam mille&longs;imam partem vnius libræ; igitur <lb/>&longs;i 1000. huju&longs;modi Cylindros ita di&longs;ponas, vt vnus alteri imponatur, om­<lb/>nes fimul vnam libram pendent; cùm autem in infinitum contrahi ba&longs;is <lb/>po&longs;&longs;it, & in eadom proportione cre&longs;cere altitudo, certè habebis Cylindrum <lb/>petitæ cuju&longs;libet altitudinis, qui vnam libram pendat, licèt ad lineam non­<lb/>dum redactus, &longs;eu contractus &longs;it. </s></p><pb pagenum="173"/><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Nulla e&longs;t in hoc difficultas, & valde miror, te in hoc ar­<lb/>gumento diutiùs hætere; in qua enim proportione decre&longs;cit pondus, de­<lb/>cre&longs;cit re&longs;i&longs;tentia; id e&longs;t, in qua proportione contrahitur ba&longs;is Cylindri <lb/>comprimentis, contrahitur & Cylindri compre&longs;&longs;i: nempe, vt &longs;e habet <lb/>comprimens Cylindrus, cujus ba&longs;is e&longs;t vt quatuor, ad Cylindrum com­<lb/>pre&longs;&longs;um bafis vt quatuor, ita &longs;e habet Cylindrus ba&longs;is 2.ad Cylindrum ba­<lb/>&longs;is vt 2.eju&longs;dem &longs;cilicet altitudinis. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Quis, quæ&longs;o capiat, tantam pre&longs;&longs;ionis vim, quam haud du­<lb/>biè immane pondus incubantis aëris omninò efficeret, etiam &longs;i demus, <lb/>aëris gravitatem e&longs;&longs;e ad gravitatem aquæ vt 1. ad 1000. aut etiam &longs;i vis, <lb/>duplo, vel triplo minorem; porrò aëra parum admodum compre&longs;&longs;um e&longs;&longs;e, <lb/>vel ex eo probatur argumento, vt aiunt, ad hominem, quod tantulum aquæ <lb/>dumtaxat elevet. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> In hoc &longs;altem hallucinaris, quòd eandem aëris gravitantem <lb/>vbique e&longs;&longs;e &longs;upponas, quod tamen à veritate pror&longs;us alienum e&longs;t, nempe <lb/>aër inferior gravior e<gap/>, quia compre&longs;&longs;ior, in quacumque voles ratione; <lb/>cùm enim aëris altitudinem certam ne&longs;ciamus, &longs;uper hoc, ni&longs;i tantùm in <lb/>genere, aliquid definire nequimus; quòd autem modicam vim pre&longs;&longs;ionis, <lb/>&longs;eu potiùs compre&longs;&longs;ionis aëris ex eo probes, quòd modicus &longs;it illius effe­<lb/>ctus, aqua &longs;cilicet per canaliculum a&longs;&longs;urgens, rectè, meo judicio, non de­<lb/>ducis; cùm etiam aër exterior compre&longs;&longs;us, per &longs;upremum os canaliculi per­<lb/>vijeam vim retundat; minùs tamen; vnde alia pre&longs;&longs;io prævaleat nece&longs;­<lb/>&longs;e e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Immò tu potiùs hallucinaris, Augu&longs;tine, licèt enim retun­<lb/>dat, repellatque humotem per caniculum a&longs;&longs;urgentem aër compre&longs;&longs;us, per <lb/>eundem &longs;cilicet canaliculum &longs;uam vim exerens; quia tamen vires pre&longs;&longs;io­<lb/>nis &longs;unt vt anguli, &longs;eu coni pre&longs;&longs;ionum, de quibus ante, haud dubiè pre&longs;&longs;io <lb/>intra canaliculum vix e&longs;&longs;et millecupla alterius, ac proinde mille&longs;imam <lb/>tantùm effectus, &longs;cilicet elevationis partem impediret, quæ reverà &longs;ub &longs;en­<lb/>&longs;um non cadit. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Sentio vim hujus argumenti, cui &longs;olvendo vix parem me &longs;en­<lb/>tio; immò alia duo mihi veniunt in mentem, quæ non parum negotij mihi <lb/>face&longs;&longs;unt; fer opem, Antime, nempe de tua cau&longs;a & &longs;ententia hîc agitur. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Citiùs quàm par e&longs;&longs;et, animum de&longs;pondes; quid quæ&longs;o hîc diffi­<lb/><figure id="fig40"></figure><lb/>cile? </s> <s>Repete Figuram &longs;uperiorem. </s> <s>Sitque &longs;uperfi­<lb/>cies aquæ AB, in quam vis pre&longs;&longs;ionis exeritur; <lb/>itemque FG, in quam etiam vis pre&longs;&longs;ionis <lb/>cadit, minor certè, &longs;ed in minima proportione <lb/>inæqualitatis incumbit; nempe totus aër æqua­<lb/>liter premit AB & FG, v&longs;que ad terminum <lb/>DE, cùm æquè liber &longs;it, vt patet; illa &longs;olùm <lb/>aëris portio contenta in &longs;egmento canaliculi <lb/>FE inæqualitatem inducit; nimirum totus aër <lb/>liberè premit FG, &longs;ed excepta portione FE; <lb/>cujus angulus pre&longs;&longs;ionis contrahitur, de hoc <pb pagenum="174"/>enim angulo intelligi debent ea, quæ &longs;upra dicta &longs;unt; quo &longs;emel admi&longs;­<lb/>&longs;o, vides, quàm modica &longs;it pre&longs;&longs;ionis differentia, ac proinde minimus ferè <lb/>illius effectus. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Ea, quæ modò dixi&longs;ti, multam mihi lucem attulerunt; & <lb/>jam mihi &longs;olvere po&longs;&longs;e videor illa, quæ mihi paulò ante in mentem ve­<lb/>nerunt; primum erat, quod in imo aëris tractu, aqua per canalicu­<lb/>lum altiùs attolli deberet, quod tamen fieri non exi&longs;timo; &longs;ed hoc facilè <lb/>&longs;olvitur; quia modica illa differentia in vtroque &longs;itu &longs;ub &longs;en&longs;um non ca­<lb/>dit. </s> <s>Alterum erat paulò difficiliùs, quod &longs;cilicet in Plenilunio & Novi­<lb/>lunio longè altius attolli deberet, quia tunc aër graviot e&longs;t; &longs;ed profe­<lb/>ctò cùm illa gravitas aëris ab humore admixto procedat, qui reverà non <lb/>comprimitur, non &longs;equitur, aëra compre&longs;&longs;iorem e&longs;&longs;e, licèt gravior &longs;it, <lb/>non quidem per &longs;e, &longs;ed per accidens, vt aiunt. </s> <s>Te<gap/>ium denique, quod <lb/>jam &longs;upra indicaveras, cuipiam fortè difficillimum videbitur; nempe <lb/>tempore &longs;ummi æ&longs;tus, cùm minor incubet aëris gravitatio, aër minus <lb/>compre&longs;&longs;us e&longs;t; &longs;ub finem verò refluxus cùm major incubet gravitatio, ac <lb/>proinde aër compre&longs;&longs;ior fit; hac hora humor per canaliculum altiùs, il­<lb/>la verò minùs altè a&longs;&longs;urgeret, quod tamen, opinor, minimè &longs;uccedit; <lb/>facilè tamen re&longs;ponderi pote&longs;t, immò re&longs;pondeo, hoc non facere, vt hu­<lb/>mor al<gap/>iùs attollatur, cùm maneat &longs;en&longs;ibiliter eadem inæqualis pre&longs;&longs;ionis <lb/>proportio; &longs;ive aër compre&longs;&longs;ior, &longs;ive minùs compre&longs;&longs;us &longs;it; &longs;ed hoc jam <lb/>&longs;upra indica&longs;ti, Antime; Non negc tamen compre&longs;&longs;ioris aëris alios ef­<lb/>fectus e&longs;&longs;e po&longs;&longs;e; &longs;ed in hoc ca&longs;u novus effectus non e&longs;t; hæc porrò re­<lb/>&longs;pon&longs;io in primum illud, quod &longs;upra expo&longs;ui, optimè quadrat, vt patet: <lb/>antequam autem ad tuas guttulas & bullas otationem convertas, &longs;cire ve­<lb/>lim, cur humor aliquando a&longs;&longs;urgat per canaliculum veloci&longs;&longs;imo motu, ali­<lb/>quando verò tardiùs; præ&longs;ertim &longs;i canaliculus inclinetur, quod aliquando <lb/>memini, à me probatum fui&longs;&longs;e. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Citò a&longs;&longs;urgit, quando humefacta &longs;uperficie cava canali­<lb/>culi, nullas &longs;alebras, nulla impedimenta humor invenit; vbi tamen in <lb/>dictas a&longs;peritates a&longs;&longs;urgens humor incurrit, tardiùs haud dubiè progredi­<lb/>tur; cujus rei clari&longs;&longs;imam analogiam habes in aqua per &longs;iccum alveum <lb/>currente, cujus cur&longs;us ab inæquali alvei &longs;uperficie &longs;i&longs;titur & impedi­<lb/>tur, ac proinde lentiùs fluit; ideò porrò per inclinatum alveum prædi­<lb/>cta motus tarditas ob&longs;ervatur, quia &longs;cilicet ex parte, in dictam vitri <lb/>&longs;uperficiem incumbit, ac proinde in prædictas &longs;aleb<gap/> magis incut­<lb/>rit; &longs;ed jam ad guttas & bullas venio, & ante omnia, quæro ex te, <lb/>Augu&longs;tine, vnde illam Figuram Sphæricam habeat gutta, præ&longs;ertim &longs;i pau­<lb/>lò minor e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;t.<emph.end type="italics"/></s><s> Varij varia de hoc argumento, quæ quia merè commenti­<lb/>tia e&longs;&longs;e puto, & fictitia, ad &longs;alvandum hoc experimentum vltro præter­<lb/>mitto, præ&longs;ertim cùm ex iis, quæ hucv&longs;que à te dicta &longs;unt, veram hu­<lb/>jus rei cau&longs;am, germanamque rationem conjiciam; nempe cùm ab aë­<lb/>re compre&longs;&longs;o æquali ni&longs;u tota guttæ &longs;uperficies prematur, quid mi­<lb/>rum &longs;i inde Sphæriea Figura inducatur. </s> <s>Vix obnitente, &longs;eu reluctan-<pb pagenum="175"/>te humoris gravitate, qui cùm in puncto contactus qua&longs;i &longs;u&longs;tinea­<lb/>tur, & partes inter &longs;e aliquam tenacitatem habeant, & premens aër <lb/>vndequaque premat, ac proinde ab ima parte qua&longs;i &longs;u&longs;tineat latera­<lb/>les humoris partes, hæ minimè &longs;ub&longs;idunt; hinc vbi major e&longs;t humoris <lb/>quantitas, &longs;ub&longs;idit humor, & gutta deprimitur, prævalente &longs;cilicet humo­<lb/>ris pondere. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Rectè omninò mentem meam & &longs;en&longs;um a&longs;&longs;equeris; hinc <lb/>multa experimenta omnibus obvia ad idem principium reduco. </s> <s>Primò, <lb/>vbi vna gutta in aliam incidit, duæ in vnam eandemque abeunt; nem­<lb/>pe in eo contactus puncto, in quo vna tangit aliam, ab externo aëre non <lb/>premitur, &longs;ed in aliis omnibus; hinc cedit humor in eo puncto, atque <lb/>adeò vna intra aliam intruditur. </s> <s>Secundò, Gutta pendula hæret aliquan­<lb/>do vel in &longs;uperficie ligni, quæ deor&longs;um vergit, vel extremo na&longs;o; vnde <lb/>hoc? </s> <s>quia premit aër ab omni parte, ea dumtaxat excepta, quæ ligno <lb/>vel na&longs;o adhæret; ea autem vis e&longs;t pre&longs;&longs;ionis, quæ guttam hærentem &longs;u­<lb/>&longs;tineat; &longs;i autem &longs;cire velis, quanta &longs;it hæc gutta, illico reponam, æqua­<lb/>lem e&longs;&longs;e humoris portioni, quæ per canaliculum attollitur, vt &longs;æpè pro­<lb/>bavi. </s> <s>Tertiò, Si partem inferiorem guttæ pendulæ, vel minima &longs;e&longs;tu­<lb/>ca tangas, &longs;tatim effluit per admotam fe&longs;tucam; quia in eo puncto, in <lb/>quo fe&longs;tuca guttæ admovetur, aër non premit, quia non tangit; aliæ <lb/>igitur partes prementes prævalent; igitur accedente præ&longs;ertim gravita­<lb/>te, &longs;eu pondere gutræ pendulæ, gutta decidit. </s> <s>Quartò, Si verò tangas in <lb/>&longs;uperiore portione laterali, & lentè fe&longs;tucam adducas, gutta &longs;equitur, <lb/>non quòd vlla vis tractrix in&longs;it, quæ in hoc præ&longs;ertim ca&longs;u fictitia e&longs;t, <lb/>&longs;ed quia partem illam aër non premit, &longs;ed oppo&longs;itam, illa cedit huic præ­<lb/>valenti; vnde &longs;i fe&longs;tuca reducitur, vi pre&longs;&longs;ionis, in prædicta parte oppo&longs;i­<lb/>ta, guttam &longs;equi nece&longs;&longs;e e&longs;t. </s> <s>Quintò, Guttæ humoris, plano in &longs;itu ver­<lb/>ticali &longs;ito etiam adhærent, propter eandem rationem, quam non re­<lb/>peto. </s> <s>Sextò, In guttis Mercurij id di&longs;criminis e&longs;t, quod paulò majores <lb/>non adhæreant, propter majus pondus, &longs;ecus minores, pro quo e&longs;t eadem <lb/>ratio, i&longs;tæ autem perfectiùs tornantur; quia Mercurius tenacior e&longs;t & cra&longs;­<lb/>&longs;ior; accedit, quòd in planorum Strias & Salebras non &longs;ubit, vt aqua; igi­<lb/>tur faciliùs &longs;e&longs;e &longs;u&longs;tinet. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> De bullis vel ampullis, idem facilè dixero; quæ &longs;ic tornan­<lb/>tur ab aëre pre&longs;&longs;o tum interiore, tum exteriore: fe&longs;tucam etiam admotam <lb/>ac deinde reductam &longs;equitur bulla, propter eandem rationem: in hoc certè <lb/>nullam video difficultatem; &longs;ed perge quæ&longs;o, Antime, ac recen&longs;e alia expe­<lb/>rimenta, quæ haud dubiè ob&longs;erva&longs;ti. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Hoc facere meditantem interpella&longs;ti. </s> <s>Septimò, Igitur vbi pup­<lb/>pus vel extremam linguam papillæ mammæ affigit, lac &longs;tatim effluit; <lb/>quia &longs;cilicet aër vndequaque mammæ &longs;uper&longs;iciem premit, excepta illa par­<lb/>te extrema, cuilingua puppuli adhætet; quid mirum igitur &longs;i lac exprima­<lb/>tur? </s> <s>Octavò, Ni&longs;i extra chorum &longs;altare timerem, hucetiam adducerem co­<lb/>nicam flammæ Figuram, ad quam inducendam aëris pre&longs;&longs;io non parum <lb/>confert; cùm enim ab halitu igneo &longs;ur&longs;um extru&longs;o aër valde rare&longs;cat, <pb pagenum="176"/>& di&longs;pergatur, ab ea parte non premit, &longs;ed ab omnialia, vnde Figuram <lb/>conicam &longs;equi nece&longs;&longs;e e&longs;t; &longs;ed hoc argumentum alterius loci e&longs;t; in libro <lb/>&longs;ingulari de igne rem hanc fusè pro&longs;ecutus &longs;um. </s> <s>Nonò, Arborum trun­<lb/>ci & rami, immò & pili, o&longs;&longs;a, nervi, & multa alia Figuram Cylindricam <lb/>habent, cùm enim initio molliora e&longs;&longs;ent, ab aëre premente tornata <lb/>fuerunt. </s> <s>Decimò, Si linguam vulneri admoveas, dum recens e&longs;t, <lb/>illico &longs;anguis effluit, ob aëris &longs;cilicet pre&longs;&longs;ionem in circumpo&longs;itam car­<lb/>nem. </s> <s>Omitto alia ferè innumera, quæ ex dictis facilè & nullo negotio intel­<lb/>ligetis. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Vna difficultas re&longs;tat, eaque maxima: nempe intelligo, hu­<lb/>morem etiam per canaliculum a&longs;&longs;urgere intra vas, in quo aër maximè di­<lb/>latatus e&longs;t; vnde manife&longs;tè colligi videtur, non attolli proptor aëris com­<lb/>pre&longs;&longs;ionem. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Non nego, difficilè argumentum e&longs;&longs;e; &longs;ed quia connexum e&longs;t <lb/>cum illo celebri experimento &longs;u&longs;pen&longs;i in fi&longs;tula vitrea Mercurij, vel alio <lb/>recipientis vitrei, in quo aër vi emboli adducti dilatatur, quæ paulò po&longs;t <lb/>di&longs;cutiemus, rem illam eò remitto; antequam porrò de præfato experi­<lb/>mento agam, vnum profectò non omittam, quod viro ingenio&longs;i&longs;&longs;imo <lb/>meique amici&longs;&longs;imo aliquando in mentem venit, &longs;cilicet ab ea vi humo­<lb/>rem per canaliculum attolli, quàm vulgò electricam vocant, quod tamen, <lb/>meo judicio, dici non pote&longs;t; cùm diver&longs;i&longs;&longs;ima &longs;int vtriulque motio­<lb/>nis principia; nempe vis electrica in eo po&longs;ita e&longs;t, quod Vi&longs;cidorum &longs;i­<lb/>laminum ten&longs;orum priùs ac deinde reductorum vi, facilè mobilia &longs;imul <lb/>adducantur, affiganturque &longs;uccino, ex quo prædicta filamina effluvio quo­<lb/>dam perenni erumpunt; quid porrò hæc ad elevationem humoris per ca­<lb/>naliculum? </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Inaudij aliquid de hoc argumento à te fui&longs;&longs;e excogitatum, <lb/>&longs;ed majori &longs;altem ex parte mihi excidit; quare rem mihi grati&longs;&longs;imam facies, <lb/>&longs;i obiter &longs;altem explanes, neque hoc Parergum Chry&longs;ocomo di&longs;plicebit; im­<lb/>mò inde meliùs con&longs;tabit eorum veritas, quæ huc v&longs;que de humoris per ca­<lb/>naliculum elevatione nobis expo&longs;ui&longs;ti. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Per me licèt, Augu&longs;tine, &longs;ed obiter; &longs;uccinum igitur po&longs;t <lb/>modicum affrictum in modica di&longs;tantia, trahit, & ad &longs;e adducit corpo­<lb/>ra facilè mobilia, eaque omnis generis, excepta dumtaxat flamma, alii&longs;­<lb/>que accen&longs;is, vt prunis, ferro candente, idque in omni &longs;itu, &longs;ur&longs;um, deor­<lb/>&longs;um, dextror&longs;um, &longs;ini&longs;tror&longs;um, modò nihil pror&longs;us interponatur; &longs;i <lb/>enim vel tenui&longs;&longs;imum chartæ folium interponatur, nihil trahit, præ­<lb/>ter ip&longs;um folium; trahit autem corpora facilè mobilia omnis generis, <lb/>vt dixi, & in omni corporis &longs;tatu; duro &longs;cilicet, liquido, &longs;pirabili; &longs;ic <lb/>&longs;umum trahit agitque in diver&longs;os vortices &longs;eu turbines, pulverem, <lb/>aquam, oleum, &c. </s> <s>Videres enim guttam aquæ vel olei, cui &longs;uc­<lb/>cinum admovetur extendere &longs;e&longs;e atque attolli; Videtes innumera pul­<lb/>veris grana tripudio quodam &longs;alientia, Atomos intra Solis ra­<lb/>dium, conclavi probè clau&longs;o fluitantes, admoto &longs;uccino turmatim <lb/>accurrere, fumum in mille, ductum filamina hinc & illinc &longs;uccino <pb pagenum="177"/>advolvi, acum magneticam libratam in orbem agi pernici&longs;&longs;ime; libræ <lb/>lancem in perfecto æquilibrio &longs;latutam, vel attolli, &longs;i &longs;ur&longs;um &longs;uccinum <lb/>applicetur, vel deprimi, &longs;i deor&longs;um, dixi, po&longs;t affrictum &longs;uccini; quia ta­<lb/>men ad diver&longs;i corporis &longs;uperficiem prædictus affrictus fieri pote&longs;t, ob­<lb/>&longs;ervavi etiam, diver&longs;os inde effectus &longs;equi; nempe &longs;i affrictus fiat ad <lb/>pannum omnis generis, &longs;ed præ&longs;ertim ad coactilem, tunc &longs;uccinum ma­<lb/>ximè trahit; ad telam etiam, &longs;ed minus, item ad cutem, chirothecam, <lb/>corium, modo pinguius non &longs;it, chartam, olo&longs;ericum, barbam, capillos, <lb/>ad o&longs;&longs;a, metalla, cornu, ceram, ligna, te&longs;tam, vitrum, vel nihil, vel pa­<lb/>rum admodum: item &longs;i affrictus fiat ad cutem, humore, melle, bal&longs;a­<lb/>mo, atramento, adipe ferè omnis generis, therebinthina, &longs;ucco mali au­<lb/>rei, &longs;apone, aquis di&longs;tillatis ferè omnis generis, dilutam &longs;eu perfu&longs;am, <lb/>itemque &longs;i pulvere a&longs;per&longs;o affrictus fiat; &longs;ecus tamen &longs;i butyro, &longs;uillo <lb/>adipe, oleo fere omnis generis; tunc enim &longs;altem parum trahit, ni&longs;i &longs;al <lb/>oleo admixtum &longs;it, quod mihi ante aliquot annos indicavit vir acuti&longs;&longs;imi <lb/>ingenij meique amanti&longs;&longs;imus Laurentius Magalottus. </s> <s>Accedit, quod <lb/>non &longs;uccinum modò, vt vulgò dicitur, vi electrica pollet, &longs;ed alia multa <lb/>corpora, vt Lacca, quàm vulgò ceram Hi&longs;panicam vocant, gagates, <lb/>concretum &longs;cilicet bituminis genus, adamas, multique lapilli; non ta­<lb/>men vnio; cry&longs;tallus & multa alia, nullum tamen ligni genus, te&longs;tæ, me­<lb/>talli, carnis &c. </s> <s>Illud vnum ob&longs;ervo, corpus omne electrica virtute pol­<lb/>lens e&longs;&longs;e vitrificum, vt &longs;ic loquar, id e&longs;t, quod ad in&longs;tar vitri malleo frangi <lb/>&longs;eu teri, non verò duci, aut findi, aut friari po&longs;&longs;it. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Tam multa, tam varia in vnum conge&longs;&longs;i&longs;ti experimenta, re­<lb/>ticitis tamen rationibus, vt mentem potiùs obrueris, quàm refeceris, aut <lb/>recrearis; &longs;ingula quæ&longs;o te repetamus & reducamus ad certa principia, <lb/>vt inde veritas phy&longs;ica eluce&longs;cat, itaque ante omnia, edi&longs;cere nobis tuam <lb/>hypothe&longs;im. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> In vno tantùm corpore electrico hypothe&longs;im meam &longs;tatuo, <lb/>cùm &longs;cilicet pro aliis omnibus eadem ratio militet; accipio igitur Laccam <lb/>&longs;eu ceram hi&longs;panicam, tum quia magis obvia e&longs;t, tum quia vi electrica <lb/>maximè pollet; illamque adhibui ad omnia ferè experimenta, con&longs;tat <lb/>multo igne; quippe accenditur; & multa vligine, quia ducitur &longs;eu ne­<lb/>tur in filamina vi&longs;cofa; ignis autem qui ine&longs;t, perenni actione in partes <lb/>vicinas agit, quas haud dubiè rarefacit, ac proinde intra pororum an­<lb/>gu&longs;tias contractæ inde nituntur erumpere, qua data porta; pori enim ob­<lb/>&longs;tructi &longs;unt; &longs;ublata autem huju&longs;modi ob&longs;tructione per affrictum, ma­<lb/>teria intus compre&longs;&longs;a erumpit ad in&longs;tar &longs;ulphurei jaculi; & quia vi&longs;co&longs;a <lb/>e&longs;t, netur in filamen tenui&longs;&longs;imum, quod præ impetu, quo erumpit, cum <lb/>intus altera ejus extremitas, propter vi&longs;co&longs;itatem aliis partibus eju&longs;dem <lb/>materiæ adhæreat; maximè tenditur; at &longs;tatim ce&longs;&longs;ante impetu, redu­<lb/>citur vt chorda ten&longs;a, & &longs;ecum a&longs;portat corpu&longs;cula facilè mobilia, quæ <lb/>occurrunt. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> Hoc fortè gratis dicitur; quis enim filamina illa vnquam vi­<lb/>dit, aut &longs;en&longs;it? </s> <s>quis alia multa his &longs;imilia non fingat? </s></p><pb pagenum="178"/><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Perennia corporum effluvia agno&longs;cimus omnes, quod ex odo­<lb/>re, &longs;itu, &longs;iccitate ac re&longs;olutione corporum facilè probamus; accedit, <lb/>quod partes ignis, eá&longs;que multas ine&longs;&longs;e con&longs;tat, quæ vi activa eaque ne­<lb/>ce&longs;&longs;aria pollent; multùm item materiæ rectè di&longs;po&longs;itæ, in quam ignis <lb/>agat, vligino&longs;æ &longs;cilicet & pinguis; quidni ergo effectus nece&longs;&longs;arius ex <lb/>cau&longs;a nece&longs;&longs;aria? </s> <s>Calor &longs;cilicet & rarefactio eju&longs;dem materiæ; &longs;ed cum <lb/>intra pororum angu&longs;tias comptimatur, pori enim, majore &longs;cilicet ex par­<lb/>te ob&longs;tructi &longs;unt; vbi deinde affrictu, pori os ab&longs;tergitur, inde erumpit <lb/>cum impetu, & cùm materia vi&longs;co&longs;a &longs;it, ducitur in filum, cujus alcera ex­<lb/>tremitas intra porum hæret. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;oc.<emph.end type="italics"/></s><s> Sed quid tandem poros ob&longs;truit? </s> <s>deinde vnicus affrictus &longs;uf­<lb/>&longs;iceret, cùm tamen aliquo po&longs;t affrictum tempore fortè non trahat. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Ille halitus vligino&longs;us, &longs;ic enim vocare liceat, ductus in fila­<lb/>men, eo ferè modo, quo fumus; netur in fila; &longs;i enim candelam recèns <lb/>extinctam a&longs;picias, &longs;itam inter oculum & Solem, vel luculentam flam­<lb/>mam, incredibilem prorsùs tenui&longs;&longs;imorum filaminum vim miraberis; <lb/>quia verò &longs;tatim concte&longs;cit externo frigore, ad o&longs;tium pori omnino riget, <lb/>inde manife&longs;ta ob&longs;tructionis cau&longs;a, concretum &longs;cilicet ad pori os <lb/>filamen. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Inaudij &longs;emper, affrictum illum fieri, vt inde calor produ­<lb/>catur, quem nece&longs;&longs;arium e&longs;&longs;e, dicunt, ad virtutem illam electricam exci­<lb/>tandam. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Scio pro&longs;ectò, hæc vulgò dici ac doceri; non tamenres ita &longs;e­<lb/>habet; Lacca enim, &longs;i nimium incale&longs;cat, nihil trahit, deinde &longs;i po&longs;t af­<lb/>frictum; Laccam vel &longs;uccinum in aliqua di&longs;tantia flammæ admoveas, ac <lb/>deinde ad ea corpu&longs;cula, quæ alioquin facilè trahuntur, applices, nihii <lb/>prorsùs trahit, vt millies &longs;altem probavi; calor igitur vim electricam non <lb/>excitat, &longs;ed potiùs impedit; equidem &longs;i denuò Laccam panno affrices, <lb/>corpu&longs;cula, vt ante, illico trahit, ea potrò di&longs;tantia flammæ, vel primis <lb/>lacca admovetur, qua, vt modicum &longs;altem trahat, corpu&longs;culis admo­<lb/>vetur. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocom.<emph.end type="italics"/></s><s> Non video, quid flamma ad id conferat, vt tractionem im­<lb/>pediat. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Id tamen video; licèt tu ip&longs;e longè oculatior &longs;is; nempe fi­<lb/>lamina illa vligino&longs;a &longs;unt, ac proinde ignem &longs;tatim concipiunt, abeuntque <lb/>in auras; &longs;ublata igitur cau&longs;a tractionis, filaminum &longs;cilicet ten&longs;ione & <lb/>adductione ce&longs;&longs;at tractio; immo licèt jam corpu&longs;culum &longs;uccino adhæ­<lb/>reat, v. </s> <s>g. </s> <s>fru&longs;tum chartæ, &longs;i ju&longs;ta di&longs;tantia flammæ admovetur, eo ip&longs;o à <lb/>&longs;uccino avellitur, ac deor&longs;um proprio pondere cadit; quia &longs;cilicet funicu­<lb/>los illos con&longs;umit ignis, quibus affixum tenebatur. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Nihil addi pote&longs;t, adeòque i&longs;ta difficultas penitus exhau&longs;ta e&longs;t; <lb/>con&longs;tat igitur non ideò affrictu opus e&longs;&longs;e, ad excitandum calorem, &longs;ed ad <lb/>&longs;uperficiem ab&longs;tergendam, & purganda pororum o&longs;tiola, vt &longs;cilicet nova <lb/>filamina ex iis erumpant; non negarim tamen, affrictu ill<gap/>liquid etiam <lb/>caloris produci, & colligi ignis partes; calor enim congregat homoge-<pb pagenum="179"/>nea, calidi &longs;cilicet; &longs;ic affrictu manus incale&longs;cit; calor porrò auctus vbe­<lb/>rioris effluvij cau&longs;a e&longs;t; perfectam, ni fallor, hujus reianalogiam habe­<lb/>mus in corporibus odoratis, præ&longs;ertim durioribus; certum enim e&longs;t, <lb/>odorem diffundi in halitu odorifero; affrictu autem eorundem corpo­<lb/>rum major vis prædicti halitus educitur: primarius tamen affrictus finis <lb/>in electricis alio &longs;pectat, &longs;cilicet ad pororum o&longs;tia expurganda: hinc pan­<lb/>no potiùs, quàm tela, aut &longs;erico, prædictus finis obtinetur; quia pannus <lb/>laneus a&longs;perior e&longs;t: ad id porrò quod dicebas, à nemine vnquam præ­<lb/>dicta filamina vi&longs;a fui&longs;&longs;e, vt cum tua bona venia dicam, futile e&longs;t; quis enim <lb/>pariter halitum odoratum vidit? </s> <s>aut contagio&longs;um? </s> <s>eumque, in quem &longs;in­<lb/>gulis diebus aliqua no&longs;tri corporis pars avolat? </s> <s>proba &longs;is, in&longs;igni aliquo <lb/>micro&longs;copio; quod ad me &longs;pectat, nonnihil videre, auribu&longs;que percipere <lb/>mihi videor. </s> <s>Videre quidem, adhibitis divinianis micro&longs;copiis, quæ iure <lb/>omnibus huc v&longs;que fabricatis anteponenda e&longs;&longs;e duxerim; audire verò <lb/>admota auribus tenui&longs;&longs;ima lamina, quæ &longs;onora vi maximè polleat, cui <lb/>&longs;tatim po&longs;t affrictum &longs;uccinum applicatur; minimum enim & acuti&longs;&longs;imum <lb/>tinnitum audite mihi videor, qui edi non pote&longs;t, ni&longs;i à prædictorum fila­<lb/>minum appul&longs;u; neutrum tamen pro certo vendito: neque id nece&longs;&longs;e e&longs;t, <lb/>cùm aliundè con&longs;tet; nec enim prædicta corpu&longs;cula propria vi, &longs;eu vir­<lb/>tute a&longs;cendunt; v.g. </s> <s>pulvis gravi&longs;&longs;imus; aliunde igitur moventur; non ab <lb/>aëre; quid enim ad hoc affrictus iuvaret? </s> <s>quid noceret flamma? </s> <s>cur alia <lb/>corpora ad eundem finem æquè idonea non e&longs;&longs;ent, ac electrica? </s> <s>à &longs;uc­<lb/>cino igitur adducuntur; qua vi amabo? </s> <s>tractrice, inquies; cur ergo af­<lb/>frictu opus? </s> <s>cur obe&longs;t flamma? </s> <s>cur major Laccæ aut &longs;uccini fru&longs;tum <lb/>majus pondus non attollit? </s> <s>deinde &longs;uccinum vertibile accedit ad quod­<lb/>libet corpus, ni&longs;i ignitum &longs;it; &longs;i ad vnum tantùm, vt magnes ad ferrum, <lb/>& vici&longs;&longs;im, e&longs;&longs;et aliqua analogia, &longs;ed quod ad omnia; nativa vi ab intrin­<lb/>&longs;eco, non dictu modò, &longs;ed cogitatu ridiculum e&longs;t: Itaque, cùm jam <lb/>aliunde, & ex communibus principiis habeam, præ&longs;atum filaminum efflu­<lb/>vium; & cum iis adductis, illi omnes motus explicari facilè po&longs;&longs;int, ad­<lb/>duciverò nece&longs;&longs;e &longs;it, &longs;i priùs tendantur, tendi autem oporteat, &longs;i cum im­<lb/>petu ex poro erumpant; itemque cum impetu erumpere, &longs;i ptiùs materia <lb/>vligino&longs;a & vi&longs;co&longs;a vi partium ignis rarefacta; ob&longs;tructis porisavolare <lb/>prohibita, compre&longs;&longs;a intus retineatur, ac demum erumpant prædicta fila­<lb/>mina, &longs;i affrictu, obex tollatur: fru&longs;tra oculorum, quorum aciem fu­<lb/>giunt, te&longs;timonium quæritur; nec ea propter meritò dici pote&longs;t, hæc à <lb/>me gratis ad&longs;trui; accedit, quòd multæ ob&longs;ervationes hæc filamina pror­<lb/>&longs;us evincunt. </s> <s>Primò, &longs;i po&longs;t affrictum, &longs;uccinum pulveri admoveatur, quo­<lb/>quover&longs;um di&longs;pergitur pulvis, adducitur que. </s> <s>Secundò, fru&longs;tula chartæ, <lb/>quibus admovetur, eodem modo di&longs;perguntur. </s> <s>Tertiò, vbi ad ducuntur <lb/>illa in diver&longs;os gyros & &longs;piras eunt, &longs;itumque mutant, & modo hinc, mo­<lb/>dò illinc trahuntur. </s> <s>Quartò, Nonnunquam a&longs;&longs;urgunt ex plano, in quo ja­<lb/>cebant, & &longs;ic erecta manent, licèt &longs;uccinum non tangant. </s> <s>Quintò, Vnum <lb/>alteri catenatim adhæret, quod non fit alio corpore admoto. </s> <s>Sextò, vidi <lb/>aliquando, idque non &longs;emel, fru&longs;tum chartæ citra contactum, è &longs;uccino <pb pagenum="180"/>pendulum; dici tamen po&longs;&longs;et adhæ&longs;i&longs;&longs;e &longs;uccino per aliquod in&longs;en&longs;ibile <lb/>chartæ filamentum. </s> <s>Septimò. </s> <s>Vbi fru&longs;tra illa levi digito moveo, Sen&longs;io re­<lb/>&longs;i&longs;tentiam omnino illi &longs;imilem, quam &longs;entirem, &longs;i tenui&longs;&longs;imo reticulo impli­<lb/>cata e&longs;&longs;e<gap/>t; immo po&longs;tquam loco &longs;uo mota &longs;unt, in eandem non recipiunt <lb/>&longs;e&longs;e, &longs;ed huc illuc, ab aliis filaminibus abripiuntur. </s> <s>Octavo. </s> <s>Quando po&longs;t af­<lb/>frictum, fru&longs;tum adducitur, qua&longs;i tripudio quodam huc illuc agitur; vix hæc <lb/>aliaque multa &longs;imilia &longs;ine prædictis filaminibus explicari po&longs;&longs;unt, immo nec <lb/>intelligi. </s></p><p type="main"> <s><emph type="italics"/>Augu&longs;tin.<emph.end type="italics"/></s><s> Perge quæ&longs;o, & alia nobis expone, quæ ad rem hanc per­<lb/>tinent. </s></p><p type="main"> <s><emph type="italics"/>Antim.<emph.end type="italics"/></s><s> Per me licet; Nono, igitur &longs;i po&longs;t affrictum, &longs;uccinum &longs;uccu­<lb/>tias, eoque tundas aliud corpus, non trahit, vel longè minùs; quia prædicta <lb/>filamina &longs;uccu&longs;&longs;u illo di&longs;&longs;ipantur. </s> <s>Decimò. </s> <s>Item &longs;i valido anhelitu &longs;uccinum <lb/>perfles, etiam po&longs;t affrictum; quia &longs;ic eadem filamina difflantur. </s> <s>Vndecimò. <lb/></s> <s>Idem accidit, &longs;i Aquiloni. </s> <s>Vel Au&longs;tro vehementi, po&longs;t affrictum, exponas. <lb/></s> <s>Duodecimò. </s> <s>Item &longs;i po&longs;t affrictum &longs;uccinum, vel humido immergas, vel <lb/>humore perfundas; nempe illa filamina humor diluit; hinc ad ten&longs;ionem <lb/>inepta: Analogiam habes in membrana tympani. </s> <s>Decimo-tertiò. </s> <s>Po&longs;tquam <lb/>traxit, &longs;ibique affixit pulverem &longs;uccinum, licèt illud admoveas fru&longs;tulis <lb/>chartæ, illa vix trahit; ab&longs;ter&longs;o tamen pulvere, citra novum affrictum, char­<lb/>tulas trahit; quia filamina circa pulverem occupata, aliud quidqiam non <lb/>trahunt; ab&longs;ter&longs;o tamen pulvere, fractis &longs;cilicet vinculis, nova erumpunt, <lb/>quæ prædictum præ&longs;tant effectum, ad quem præ&longs;ertim præfata ab&longs;ter&longs;io <lb/>plurimum confert. </s> <s>Pari modo, po&longs;tquàm traxit aliquot fru&longs;ta chartæ, vix <lb/>pulverem trahit, propter eandem rationem. </s> <s>Decimo-quartò. </s> <s>Si po&longs;t aftri­<lb/>ctum, &longs;uccinum immergas Oleo, non ob&longs;tat, quo minùs trahat, quia Oleum <lb/>prædicta filamina vligino&longs;a non diluit. </s> <s>Decimo-quintò. </s> <s>Sicuti humorem <lb/>affundas, & in ea&longs;uccinum frices, po&longs;t affrictum nihil trahit, quia affu&longs;us <lb/>liumor filamina diluit, & ten&longs;ionem impedit; idem dico de aquis di&longs;tillatis, <lb/>vino, oxymo, aceto, &longs;ucco mali autei, propter eandem rationem; idem de <lb/>&longs;apone adipe, melle, bal&longs;amo, therebinthjna propter nimiam tenacitatem, <lb/>quæ filamina impedit. </s> <s>Decimo-&longs;extò. </s> <s>Si perfundatur cutis oleo, po&longs;t af­<lb/>frictum in ea &longs;uccini, &longs;equitur tractio; quia vt jam dixi &longs;upra, Oleum non <lb/>ob&longs;tat, ni&longs;i &longs;al Oleo adini&longs;ceatur, quia &longs;cilicet poros &longs;uccini ob&longs;truit; idem <lb/>de butyro, & &longs;uillo adipe recente, propter eandem rationem. </s> <s>Decimò-&longs;e­<lb/>ptimò. </s> <s>Si pulverem cuti a&longs;pergas, ac deinde frices, nihil trahit; quia pulve­<lb/>ris admoti mordacitas, vel a&longs;peritas filamina fecat. </s> <s>Decimo-octavò. </s> <s>Si affri­<lb/>ctus fiat in capillis, & tenera barba, tractioni non obe&longs;t; quia e&longs;t ad in&longs;tar la­<lb/>næ. </s> <s>Ex his, ni fallor, reliqua facilè intelligetis; quare illa omitto, ne prolixior <lb/>&longs;im. </s></p><p type="main"> <s><emph type="italics"/>Chry&longs;ocomus.<emph.end type="italics"/></s><s> Experimentorum, quæ Primò loco ad duxi&longs;ti, rationem & <lb/>cau&longs;am afferre omifi&longs;ti, &longs;upple illam quæ&longs;o. </s&